text:
\section{Introduction}\label{intro}
Over the last two decades the physics of hypernuclei has gained considerable attention in the strangeness nuclear physics community
through numerous studies of exotic hypernuclei (for recent reviews, see e.g.,
Refs.~\cite{Petschauer:2020urh,Hammer:2019poc,Hiyama:2018lgs,Gal:2016boi}), and in astrophysical studies of neutron stars where
hyperonic matter is expected to appear at their cores (e.g., see
Refs.~\cite{Tolos:2020aln,Watts:2016uzu,SchaffnerBielich:2000wj}). In particular, the strangeness $S=-2$ sector of late has elicited
great interests behind ideas, such as the existence of putative bound states like the {\it H-dibaryon} and light exotic
{\it $\Xi$-hypernuclei}, and to seek possible resolution of the well-known {\it hyperon puzzle}~\cite{Demorest:2010bx,Antoniadis:2013pzd}.
For example, with regard to the feasibility of the $H$-particle, as conjectured by Jaffe more that 40 years ago~\cite{Jaffe:1976yi},
no definite conclusion has been reached till date, despite the extensive
theoretical~\cite{Beane:2010hg,Inoue:2010es,Beane:2011iw,Shanahan:2011su,Haidenbauer:2011ah,Inoue:2011ai,Yamaguchi:2016kxa,Francis:2018qch}
and experimental investigations~\cite{Ahn:1998fj,Sasaki:2018mzh}. It is envisaged that a thorough understanding of the underlying
character of and role played by two-body hyperon-nucleon ($YN$) and hyperon-hyperon ($YY$) interactions, as well as
hyperon-nucleon-nucleon ($YNN$) and hyperon-hyperon-nucleon ($YYN$) three-body forces (3BF), may be vital towards arriving at definite
conclusions in regard to these contentious issues. Especially, in the context of the stability of neutron stars, it has been realized
that the sole inclusion of the two-body interactions becomes questionable since they lead to considerable {\it softening} of the
{\it equation-of-state} (EoS) to support stellar masses typically close to or larger than twice the solar mass ($2M_{\odot}$) against
gravitational collapse. The answer in this case probably lies in the inclusion of an admixture of $NNN$, $\Lambda NN$, $\Xi NN$ and
$\Lambda\Lambda N$ 3BFs that may potentially be the key in estimating the correct stiffness of the EoS of dense baryonic matter
governing the stability of the cores. Notably, the Quantum Monte Carlo calculations by Lonardini
{\it et al}~\cite{Lonardoni:2013gta,Lonardoni:2014bwa} have already shown encouraging indication that the inclusion of $\Lambda NN$ 3BF
compensates the excessive overbinding due to the $\Lambda N$ interactions, ostensibly resolving the ``$B_\Lambda$-overbinding" problem.
More of such work in this direction would be worthwhile toward a comprehensive understanding of the 2017 observation of gravitational
waves from two-neutron star mergers by the LIGO Scientific Collaboration~\cite{TheLIGOScientific:2017qsa}.

\vspace{0.1cm}

In 2001, the NAGARA event~\cite{Takahashi:2001nm} from the KEK E373 emulsion experiment undoubtedly provided the first evidence of
the light double-$\Lambda$ hypernuclei ${}^{\,\,\,\,6}_{\Lambda\Lambda}$He, demonstrating that the $S=-2$ $\Lambda\Lambda$
interactions are less attractive than $S=-1$ $\Lambda N$ interactions. On the other hand, the feasibility of a light
$\Xi$-hypernuclei based on the state-of-the-art experimental~\cite{Khaustov:1999bz,Aoki:2009pvs,Nakazawa:2015joa}, and
theoretical~\cite{Hiyama:2008fq,Carames:2012zz,Garcilazo:2015noa,Sun:2016tuf,Garcilazo:2016ylj,Garcilazo:2016ams,Filikhin:2017fog,Hiyama:2019kpw,Jin:2019sqc}
studies remains largely equivocal, since they were first claimed in the 1959 experimental work of Wilkinson
{\it et al.}~\cite{Wilkinson:1959zz}. This is primarily due to the current acute scarcity of $S=-2$ empirical information needed to
determine the underlying character of hypernuclear interactions, caused by the non-availability of any $\Xi$-hyperon scattering data,
either current or obtainable soon in near future. All that one finds in the literature are a few scattered upper bounds for $\Xi^- p$
elastic and inelastic cross sections from emulsion experiments~\cite{Aoki:1998sv,Ahn:2005jz}. Thus, it is no surprise that different
existing model analyses lead to substantially contrasting views regarding the nature of the $\Xi N$ potentials, ranging from moderately
or weakly attractive~\cite{Khaustov:1999bz,Hiyama:2019kpw,Aoki:1998sv,Ahn:2005jz,Yamaguchi:2001ip,Friedman:2007zza,Hiyama:2010zz,Haidenbauer:2015zqb,Li:2018tbt,Haidenbauer:2018gvg}, even vanishing~\cite{Kohno:2009ny}, to weakly repulsive~\cite{Krishichayan:2010zza}. In fact, the KISO
event~\cite{Nakazawa:2015joa} from the KEK E373 experiment in 2015, which undeniably confirmed the particle-stable $\Xi$-hypernucleus
$^{15}_\Xi$C (interpreted as the ground state of a deeply bound $\Xi^{-}\!\!-\!{}^{14}$N cluster system with binding energy
$4.38 \pm 0.25$~MeV), at the least corroborated that the constituent $\Xi N$ channels are attractive. Specifically, the updated
{\it Extended-soft-core} (ESC08c) Nijmegen potential model~\cite{Nagels:2015dia,Rijken:2016uon} has predicted that the $\Xi N$ two-body
system in the maximal spin-isospin $(i=1,j=1)$ channel is stable with ${}^3S_1$ scattering length
$a^{(j=1)}_{\Xi n}=4.911$ fm, while the $(i=1,j=0)$ channel is mainly repulsive with ${}^1S_0$ scattering length
$a^{(j=0)}_{\Xi n}=0.579$~fm.  With the former attractive $\Xi N$ channel having such a large scattering length, the two-body system
was found to be bound, the so-called $D^*$ state, with an estimated binding energy of $1.56$~MeV ($1.67$~MeV) with (without) taking
into consideration the latter repulsive $\Xi N$ channel~\cite{Garcilazo:2016ams,Filikhin:2017fog,Nagels:2015dia,Rijken:2016uon}. In
a contrasting scenario, the recent SU(3) chiral effective field theory (EFT) based predictions from the relativistic
calculations~\cite{Li:2018tbt}, as well as non-relativistic {\it in-medium G-matrix} analysis~\cite{Haidenbauer:2018gvg} have
practically ruled out the possibility of a stable $\Xi N$ bound state in the (1,1) channel, being constrained respectively by the
recent HAL QCD lattice results of Ref.~\cite{Sasaki:2019qnh}, and the aforementioned empirical upper bounds from $\Xi^- p$ cross
sections data~\cite{Aoki:1998sv,Ahn:2005jz,Haidenbauer:2015zqb}. Nevertheless, the Faddeev calculation
analyses~\cite{Garcilazo:2015noa,Garcilazo:2016ylj,Garcilazo:2016ams,Filikhin:2017fog} on the ($I=3/2, J^P={1/2}^+$) $\Xi NN$
three-body system, relying on the same updated $\Xi N$ Nijmegen ESC08c potential~\cite{Nagels:2015dia,Rijken:2016uon} as input,
have hinted at the feasibility of a deeply bound $\Xi NN$ state implying a strongly attractive nature of the $\Xi N$ interaction.
\section{Pionless EFT (${}^{{\pi}\!\!\!/}$EFT): A Brief Survey}
Prompted by this unresolved scenario, we present in this work an alternative qualitative assessment regarding the viability of a
putative $\Xi^{-} nn$ two-neutron {\it halo-bound} state in the $I=3/2, J^P={1/2}^+$ channel. In particular, the reasons motivating
our study of the $\Xi NN$ system in this maximal spin-isospin channel are as follows:
\begin{itemize}
\item first, the decoupling of this channel from strong decay into the open $\Lambda\Lambda N$ channel {\it via}
$\Xi N\rightarrow \Lambda\Lambda$ is forbidden by isospin conservation, while Pauli principle works favorably,
thereby supporting stable $\Xi NN$ bound states, and
\item second, the absence of Coulomb effects to a great extent simplifies the construction of the Faddeev-like
integral equations.
\end{itemize}
Our treatment is based on a low-energy {\it pionless EFT}
(${}^{{\pi}\!\!\!/}$EFT)~\cite{Kaplan:1996xu,Kaplan:1998tg,Kaplan:1998we,Kaplan:1998sz,vanKolck:1998bw,Bedaque:1998mb,Birse:1998dk,Braaten:2004rn}
where explicit pion exchanges are integrated out at scales much smaller than the pion mass. A speciality of such an approach
is that the results are obtained following a general perturbative scheme without underlying model assumptions by utilizing principles of
low-energy universality with controlled error estimates; observables are expressed as an expansion of a small low-energy parameter
$\epsilon=Q/\Lambda_H$, with $Q$ being the typical momentum scale of dynamics within the system in question, and $\Lambda_H\sim m_\pi$,
the {\it hard} or {\it breakdown} scale of the EFT which is identified with the pion mass $m_\pi$. Such a methodology is complementary to
{\it ab initio} approaches, where the universal couplings or {\it low-energy constants} (LECs) in the effective Lagrangian are fixed from
phenomenology (e.g., available scattering data and information on binding energies) could be used to make predictions on various few-body
observables. Such universal aspects of ${}^{{\pi}\!\!\!/}$EFT have been successfully exploited to investigate the dynamics of
{\it finely tuned} systems driven arbitrarily close to the unitary limit, either artificially, as in
{\it Feshbach resonances}~\cite{Braaten:2004rn} in ultra-cold atoms, or even naturally, as in nuclear systems with large two-body scattering
lengths leading to formation of threshold two-body bound states, such as the {\it deuteron} or the aforementioned putative $D^*$ state. More
interestingly, interacting three-body S-wave systems when driven to the unitary limit, lead to the well-known
{\it Efimov phenomenon}~\cite{Braaten:2004rn,Danilov:1961,Efimov:1970zz,Efimov:1971zz,Efimov:1973awb,Naidon:2016dpf}, associated with an
infinite tower of geometrically spaced three-body level states emerging from zero-energy (i.e., {\it three-particle} or
{\it particle-dimer} break-up) threshold (see, e.g., \cite{Hammer:2019poc,Braaten:2004rn,Naidon:2016dpf} and reference therein for a
detailed review of Efimov physics and its applications in atomic and nuclear physics). In that case a modified ${}^{{\pi}\!\!\!/}$EFT
{\it power counting} scheme was suggested by Bedaque {\it et al}~\cite{Bedaque:1998kg,Bedaque:1999ve}, in which a non-derivatively coupled
(naively subleading) three-body contact interactions was required to be promoted to leading order (LO) due to the appearance of a
renormalization group (RG) {\it limit cycle} behavior with the onset of a {\it discrete scaling symmetry} in its couplings.

\vspace{0.1cm}

An important variant based on the generalization of the standard ${}^{{\pi}\!\!\!/}$EFT, the so-called
{\it halo/cluster EFT}~\cite{Bertulani:2002sz}, was introduced to study light {\it halo} nuclei and their clustering phenomena,
characterized by multi-scale threshold dynamics at scales typically lower than in standard ${}^{{\pi}\!\!\!/}$EFT. Such modified
${}^{{\pi}\!\!\!/}$EFT  analyses have been successfully extended to study light hypernuclei, since the very first in 2002 by
Hammer~\cite{Hammer:2001ng} on the LO investigation of hypertriton (${}^3_\Lambda$H) as a ($I=0, J=1/2$) $\Lambda NN$ Efimov-like bound
system. Subsequently, a number of halo/cluster EFT works based on similar LO analysis appeared in the literature, both in the
$S=-1$~\cite{Ando:2015fsa,Hildenbrand:2019sgp} and $S=-2$~\cite{Ando:2013kba,Ando:2014mqa,Meher:2020rsd} strangeness sectors, in the search
for exotic single and double-$\Lambda$ hypernuclear states, e.g., $nn\Lambda$,\footnote{The ${}^{{\pi}\!\!\!/}$EFT analysis by Ando
{\it et al.}~\cite{Ando:2015fsa} attempted to investigate the feasibility of the putative $nn\Lambda$ bound state, as reported by the HypHI
Collaboration~\cite{Rappold:2013jta} in 2013. In that analysis a coupled system of integral equation was constructed in the physical basis
involving only the spin projected two-couplings but without considering isospin projections. This led to a slightly different estimation of
the asymptotic RG limit cycle scaling exponent $s^{nn\Lambda}_0=0.80339$, which is inconsistent with the expected universal scaling based on the
the relative three-particle mass ratios~\cite{Braaten:2004rn}. As recently elucidated by Hildenbrand and Hammer~\cite{Hildenbrand:2019sgp},
the correct scaling could be restored by a proper reformulation of the integral equations in the spin-isospin basis leading to value,
$s^{nn\Lambda}_0=1.0076$, which is identical to that obtained in the study of hypertriton, and also reproduces the well-known asymptotic
scaling, $s_0=1.00624$, for identical masses~\cite{Braaten:2004rn,Naidon:2016dpf}. Furthermore, with their revised $nn\Lambda$
analysis~\cite{Hildenbrand:2019sgp} a threshold ground state appeared at a momentum cut-off scale $\Lambda_c\sim 600$~MeV, whereby the
likelihood of a physically realizable Efimov-like bound/resonance state may not be excluded outright, unlike in Ref.~\cite{Ando:2015fsa}
where such a possibility was practically ruled out with $\Lambda_c \gtrsim 1.5$~GeV.}
${}^{\,\,\,\,\,4}_{\Lambda\Lambda}{\rm He}$,\, ${}^{\,\,\,\,\,5}_{\Lambda\Lambda}{\rm H}$,\,
${}^{\,\,\,\,\,5}_{\Lambda\Lambda}{\rm He}$ and ${}^{\,\,\,\,\,6}_{\Lambda\Lambda}{\rm He}$. It is worth mentioning here that a novel
{\it ab initio} LO ${}^{{\pi}\!\!\!/}$EFT technique using few-body {\it stochastic variational} method of calculation was initially suggested
in Refs.~\cite{Barnea:2013uqa,Kirscher:2015yda,Contessi:2017rww,Kirscher:2017fqc} for the study of lattice nuclei, complimentary to the halo
${}^{{\pi}\!\!\!/}$EFT approach. The same framework was later used by Contessi {\it et al.}~\cite{Contessi:2018qnz} in the $S=-1$ sector to
seek a solution to the $B_\Lambda$-overbinding problem, and more recently in the feasibility studies of several light $S=-2$
double-$\Lambda$ hypernuclei~\cite{Contessi:2019csf}.

\section{Halo ${}^{{\pi}\!\!\!/}$EFT of $\Xi^- nn$}\label{sec:1}
In this work, we use halo ${}^{{\pi}\!\!\!/}$EFT at LO to assess the feasibility of a ($S=1/2,I=3/2$) $\Xi^- nn$ bound state primarily on the
basis of Efimov universality as reflected through the sharp momentum cut-off scale ($\Lambda_c$) dependence of the RG limit cycle exhibited by
the three-body coupling $g_3(\Lambda_c)$ (see details in the following subsection). Despite the significant uncertainties regarding the exact
nature of the $\Xi N$ interactions in existing approaches, we preferably assume the following scenario for the purpose of an exploratory study.
Our approach is motivated by the results from a series of recent potential model
analyses~\cite{Garcilazo:2015noa,Garcilazo:2016ylj,Garcilazo:2016ams,Filikhin:2017fog} based on Faddeev calculations, which rely on the basic
assumption that the ${}^{3}S_1$ $\Xi^{-} n$ sub-system is dominantly attractive and bound with the aforementioned large and {\it positive} S-wave
scattering length $a^{(1)}_{\Xi n}$, as predicted by the Nijmegen ESC08c model~\cite{Nagels:2015dia,Rijken:2016uon}. It was especially noted in
some of these model studies that if one included the real bound ${}^{3}S_1$ channel as the only $\Xi^- n$ sub-system channel (other than the
virtual bound ${}^{1}S_0$ $nn$ sub-system with large and {\it negative} S-wave scattering length $a_{nn}=-18.63$~fm~\cite{Chen:2008zzj}), the
$\Xi^-nn$ system exhibited a three-body deeply bound state. On the other hand, no bound state was obtained with the ${}^{3}S_1$ $\Xi^- n$
channel replaced by the repulsive ${}^1S_0$ $\Xi^- n$ sub-system channel with the aforementioned small but {\it positive} S-wave scattering
length $a^{(0)}_{\Xi n}$~\cite{Nagels:2015dia,Rijken:2016uon}. A similar situation happens with our framework as well, which primarily motivated
the work in this paper. The Faddeev-type coupled system of integral equations in the momentum space~\cite{Braaten:2004rn} (also termed as the
{\it Skornyakov-Ter-Martirosyan} or STM equations~\cite{STM1,STM2}) does not exhibit an RG limit cycle with the repulsive ${}^1S_0$ $\Xi^- n$
channel included as the only $\Xi^- n$ sub-system channel. This implies an unbound $\Xi^- nn$ system. On the other hand, we have checked that
an {\it asymptotic} RG limit cycle in the (two-body) unitary limit is always found to manifest itself in the presence of the $\Xi^- n$ triplet
channel, irrespective of the inclusion of the $\Xi^- n$ singlet channel. However, a full-fledged numerical evaluation of the integral equations
in our context of the so-called {\it dibaryon} formalism~\cite{Birse:1998dk,Bedaque:1998kg,Bedaque:1999ve} becomes technically demanding,
especially when dealing with the repulsive $\Xi^- n$ sub-system with a small and positive scattering length. The problem is attributed to the
presence of a deep pole in the ${}^1S_0$ $\Xi^- n$ dibaryon propagator [cf. Eq.~\ref{eq:dimer_props}] corresponding to an unphysically large
binding momentum, $\gamma^{(0)}_{\Xi n}\approx 1/a^{(0)}_{\Xi n}\approx 340$~MeV (estimate based on the Nijmegen ESC08c
model~\cite{Nagels:2015dia,Rijken:2016uon}). Since there is no straightforward way of ``renormalizing" the effect of such a (two-body) pole,
evidently the EFT breaks down leading to erroneous estimation of the Efimov spectrum that turns out to be anomalously deep. Consequently, in this
work we take recourse to a simplistic study of the $\Xi^- nn$ system to look for possible emergence of physically realizable Efimov-like trimer
states by completely excluding the repulsive ${}^{1}S_0$ $\Xi^- n$ channel. Moreover, in our halo EFT formalism the same scale associated with
the triplet dibaryon pole defines the $n-(\Xi^- n)_t$ particle-triplet dimer break-up threshold, only beyond which the $\Xi^- nn$ trimer levels
are expected to appear with binding energies given by the eigensolutions to the integral equations~\cite{Braaten:2004rn}.

\vspace{0.1cm}

In the ensuing EFT analysis, we present a qualitative investigation of the regulator scale ($\Lambda_c$) dependence of the {\it a priori}
undetermined three-body coupling $g_3$ introduced in the integral equation for the purpose of renormalization. Through this study we hope to
establish a correspondence with existing potential model analyses on the same
system~\cite{Garcilazo:2015noa,Garcilazo:2016ylj,Garcilazo:2016ams,Filikhin:2017fog}, thereby serving as a consistency check between both the
approaches. In particular, based on existing model estimates for the three-body binding energy $B_3$, we naively predict a window of possible
values of the S-wave three-body scattering length $a_3$, associated with the elastic $n-(\Xi^-n)_t$ scattering process, leading to three-body
universal correlations such as the {\it Phillips line}~\cite{Phillips:1968zze}. Hence, the rationale behind our preliminary study is to bring
to light the inherent universal features, albeit approximately, which could yield valuable insights for facilitating more rigorous future
analyses to assess the fate of the realistic $\Xi^- nn$ system.

\subsection{Effective Lagrangian and Formalism}
In a simplified picture, the $\Xi^- nn$ system may be visualized as a two-neutron halo with the two loosely bound neutrons orbiting about the
$\Xi^-$-hyperon ``elementary" core forming a shallow bound state with a diffuse structure. Such universal class of systems exploits the distinct
separation of scale between the typical dynamical scale, $Q\sim\gamma^{(1)}_{\Xi n}\sim 40$~MeV, associated with the ``attractive pole" momentum of
the ${}^3S_1$ $\Xi^- n$ dibaryon propagator (ignoring possible artifact due to the deep pole at $\gamma^{(0)}_{\Xi n}\sim 340$~MeV associated with
the repulsive ${}^1S_0$ $\Xi^- n$ sub-system), and the breakdown scale, $\Lambda_H\sim m_\pi$ of standard ${}^{{\pi}\!\!\!/}$EFT. This implies that
$\epsilon \sim Q/m_\pi \sim 1/3$ defines a reasonable expansion parameter that is amenable to an halo EFT treatment. The effective Lagrangian is
constructed on the basis of available low-energy symmetries and degrees of freedom.  The interaction vertices are represented by local contact
interactions and the Lagrangian is expressed in a derivative expansion of the fundamental fields. For our system, the fundamental degrees of freedom
consist of the $\Xi^-$-hyperon and neutron ($n$) fields. The LO non-relativistic Lagrangian is free from derivative terms and expressed as a sum of
one-, two-, and three-body parts, namely,
\begin{equation}
\mathcal{L}_{{}^{{\pi}\!\!\!/}{\rm EFT}} = \mathcal{L}_{\rm 1-body} + \mathcal{L}_{\rm 2-body} + \mathcal{L}_{\rm 3-body}\,\,.
\label{eq:1}
\end{equation}
Below we consider each of the components of the effective Lagrangian separately. \\

\noindent{\it One-body part.\,\,}
The terms $\mathcal{L}_{\Xi}$ and $\mathcal{L}_n$ constitute the one-body Lagrangian $\mathcal{L}_{\rm 1-body}$ corresponding to the kinetic part of
the $\Xi^-$-hyperon and neutron fields respectively, and are expressed in the physical basis as
\begin{eqnarray}
\mathcal{L}_{\rm 1-body} &=& \mathcal{L}_{\Xi} + \mathcal{L}_{n}\,\,,
\nonumber \\
\mathcal{L}_{\Xi} &=& {\Xi}^{\dagger}\bigg[iv\cdot\partial+\frac{(v\cdot\partial)^2-\partial^2}{2M_{\Xi}}\bigg]{\Xi}\,\,,
\nonumber \\
\mathcal{L}_{n}  &=&  n^{\dagger}\bigg[iv\cdot\partial+\frac{(v\cdot\partial)^2-\partial^2}{2M_n}\bigg]n\,\,,
\end{eqnarray}
where, $M_{\Xi,\,n}$ are the physical masses of the $\Xi^-$-hyperon and neutron fields, as given in Table~\ref{tab:1}, and $v^{\mu}=(1,{\bf 0})$ is the
four-velocity vector which is used to express the Lagrangian in a manifestly covariant manner akin to the heavy-baryon formalism~\cite{Bernard:1995dp}.
It follows that the non-relativistic propagators associated with these fundamental fields are given by
\begin{eqnarray}
 iS_{\Xi}(p_0, {\bf p}) &=& \frac{i}{p_0-\frac{\bf p^2}{2 M_{\Xi}}-i\eta}\,\,,
 \nonumber \\
 iS_n (p_0, {\bf p}) &=& \frac{i}{p_0-\frac{\bf p^2}{2 M_n}-i\eta}\,; \quad \eta\to 0\,\,,
\end{eqnarray}
where, $p_0$ and ${\bf p}$ are temporal and spatial parts of the generic four-momentum $p^\mu$. \\
\begin{table}[tbp]
\begin{center}
\caption{PDG~\cite{Zyla:2020zbs} values of particle masses considered in the analysis.}

\vspace{0.2cm}

\label{tab:1}
\begin{tabular}{|c|c|c|}
\hline
Particle & Mass Symbol  & Numerical Value (MeV)\\
\hline\hline
$\Xi$-Hyperon & $M_{\Xi}$ & 1321.710  \\
Neutron (n) & $M_n$ & 939.565 \\
\hline\hline
\end{tabular}
\end{center}
\end{table}

\noindent{\it Two-body part.\,\,}
In ${}^{{\pi}\!\!\!/}$EFT, to deal with the formation of shallow S-wave bound states one needs to {\it unitarize} the two-body sector by
employing the so-called Kaplan-Savage-Wise (KSW) power counting rule~\cite{Kaplan:1996xu,Kaplan:1998tg,Kaplan:1998we,Kaplan:1998sz,vanKolck:1998bw}.
To efficiently capture such two-body physics in the vicinity of a  {\it non-trivial fixed-point} described by the RG of the two-body contact
interactions, it was suggested to introduce auxiliary {\it dimer} fields in the effective
Lagrangian~\cite{Bedaque:1998mb,Birse:1998dk,Braaten:2004rn,Bedaque:1998kg,Bedaque:1999ve}. Thus, in our case we introduce the dimer fields,
namely, the spin-isospin triplet ($i=1,j=1$) $\Xi^- n$ dibaryon field $u_1$, and the isospin-triplet spin-singlet ($i=1,j=0$) $nn$
dibaryon field $u_0$. Here we re-emphasize that the spin-singlet isospin-triplet ($i=1,j=0$) $\Xi^- n$ sub-system is considered decoupled
from the picture as it is not amenable to our EFT formalism. The corresponding two-body LO Lagrangian (physical basis) in terms of the dibaryon
fields is given as
\begin{eqnarray}
\mathcal{L}_{\rm 2-body} &=&\ \mathcal{L}_{u_0} + \mathcal{L}_{u_1}\,\,,
\nonumber \\
\mathcal{L}_{u_0} &=& -(u_0)^{a\dagger}\bigg[iv\cdot\partial+\frac{(v\cdot\partial)^2-\partial^2}{4M_n}\bigg](u_0)^a
-y_0\!\bigg[(u_0)^{a\dagger}\left(n^{T}\hat{\mathscr P}_{(nn)}^{(1,0)\,a}\,n\right)+ {\rm h.c.}\bigg]\,\,,
\nonumber\\
\mathcal{L}_{u_1} \!&=&\! -({\bf u}_1)_k^{a\dagger}\bigg[iv\cdot\partial+\frac{(v\cdot\partial)^2
-\partial^2}{2(M_{\Xi}+M_n)}\bigg]\!({\bf u}_1)^a_k-y_1\!\bigg[({\bf u}_1)_k^{a\dagger}
\left(n^{T}\hat{\mathscr P}_{({\Xi} n)\,k}^{(1,1)\,a}\,{\Xi}\right)+ \rm{h.c.}\bigg]\,\,,
\nonumber\\
\end{eqnarray}
noting that the ``wrong sign" in front the respective kinetic terms suggest the non-dynamical or quasi-particle nature of the dibaryon fields.
Here, $\hat{\mathscr P}_{({\Xi} n)\,k}^{(1,1)\,a} = \frac{1}{2} \tau^2\tau^a\sigma_2\sigma_k$, and
$\hat{\mathscr P}^{(1,0)\,a}_{(nn)}= \frac{1}{\sqrt{8}}\tau^2\tau^a\sigma_2$ are the spin-isospin projection operators, with $\sigma_k$ and
$\tau^a\,(k,a=1,2,3)$ being the Pauli matrices in the spin and isospin spaces respectively. The two-body non-derivatively coupled LO contact
interactions or LECs $y_{0,1}$ between the respective dibaryons and their constituent elementary fields encode all UV physics that remain
unresolved in the EFT. These LO couplings are easily fixed as~\cite{Griesshammer:2004pe}

\begin{equation}
 y_1=\sqrt{\frac{2\pi}{\mu}}\,, \quad{\rm and}\quad y_0=\sqrt{\frac{4\pi}{M_n}}\,,
\label{eq:y01}
\end{equation}
where $\mu=M_n M_\Xi/(M_n + M_\Xi)=549.174$~MeV is the reduced mass of $\Xi^- n$ two-body sub-system. Next, we spell out the ``dressed"
(unitarized) non-relativistic propagators for the $nn$ and $\Xi^- n$ dibaryon fields (cf. Fig.\ref{FIG-1}), consistent with the KSW power
counting scheme~\cite{Kaplan:1996xu,Kaplan:1998tg,Kaplan:1998we,Kaplan:1998sz,vanKolck:1998bw} after being renormalized using the
{\it power-divergence subtraction} (PDS)~\cite{Kaplan:1998tg}:
\begin{eqnarray}
 i{\mathscr D}_0(p_0,{\bf p}) &=&
\frac{4\pi}{y_0^2 M_n}\frac{i}{\gamma^{(0)}_{nn}-\sqrt{-M_n(p_0-\frac{ {\bf p}^2}{4M_n})-i\eta}-i\eta}\,\,,
\nonumber \\
 i{\mathscr D}_1(p_0,{\bf p}) &=&
\frac{2\pi}{y_1^2\mu}\frac{i}{\gamma^{(1)}_{\Xi n}-\sqrt{-2\mu (p_0-\frac{ {\bf p}^2}{2(M_n+M_{\Xi})})-i\eta}-i\eta}\,; \quad \eta\to 0\,\,,
\label{eq:dimer_props}
\end{eqnarray}
where at LO in ${}^{{\pi}\!\!\!/}$EFT, $\gamma^{(0)}_{nn} = 1/a_{nn}$ and $\gamma^{(1)}_{\Xi n} = 1/a^{(1)}_{\Xi n}$, are the (1,0) $nn$
and (1,1) $\Xi^-n$  binding momenta respectively. \\
\begin{figure}[tbp]
\centering
\includegraphics[width=13cm]{fig1.eps}
\caption{The renormalized  dressed  propagators for (A) ${}^1S_0$ $nn$, and  (B) ${}^3S_0$ $\Xi^- n$ dibaryon fields.
         The dashed lines represent the $\Xi^-$-hyperon field propagator and the solid lines represent the neutron field
         propagator.}
\label{FIG-1}
\end{figure}

\noindent{\it Three-body part.\,\,}
Formally the $\Xi^- nn$ three-body system with a possible fine-tuned two-body sector exhibits the well-known Efimov effect at the unitary
limit. This is reflected by the fact that the integral equations for the system with two-body interactions only become ill-defined in the
asymptotic UV limit. The inherent reason for this anomalous UV behavior is the partial breakdown of the expected {\it fixed-point} scaling
invariance of the system in the vicinity of bound states at the unitary limit into a discrete scaling invariance. A possible remedy to this
problem is obtained by introducing a sharp momentum UV cut-off regulator $\Lambda_c$ in the integral equations, which simultaneously
necessitates the introduction of LO 3BF contact terms with scale dependent couplings $g_3(\Lambda_c)$ to renormalize the artificial cut-off
dependence. The resulting atypical scaling behavior gets reflected through the emergence of a RG limit cycle behavior in the 3BF couplings
(for a pedagogical review on this topic, see Ref.~\cite{Braaten:2004rn}). Here we present a certain choice of the LO three-body contact
interaction (counterterm) Lagrangian in the $I=3/2, J=1/2$ channel, given by
\begin{eqnarray}
 \mathcal{L}_{\rm 3-body} &=&-\frac{g_3(\Lambda_c)}{\Lambda_c^2}\Bigg{[}\frac{M_{\Xi} y_1^2}{2}
 \Big{\{}{(\bf u}_1)_l^a \,\,\hat{\mathcal{P}}_l^{ab} \,\,n\Big{\}}^{\dagger}
 \Big{\{}({\bf u}_1)_k^c \,\,\hat{\mathcal{P}}_k^{cb}\,\,n\Big{\}}
 \nonumber\\
 &&\hspace{2cm}-\frac{\sqrt{3}M_{n} y_0y_1}{\sqrt{2}} \Big{\{}({\bf u}_1)_l^a\,\,\hat{\mathcal{P}}_l^{ab} \,\,n\Big{\}}^{\dagger}
 \Big{\{}u_0^c \,\,\hat{\mathcal{P}}^{cb} \,\,{\Xi}\Big{\}}+ {\rm h.c.}\Bigg{]},\,\quad\,
\label{eq:type_3body}
\end{eqnarray}
where the spin-isospin projection operators have the following forms:
\begin{eqnarray}
  \left[\hat{\mathcal{P}}_k^{cb}\right]_{\alpha\beta} &=&
  \frac{1}{3\sqrt{3}}\Big{[}(\tau^c\tau^b)_{\alpha\beta}+\delta_{cb}\delta_{\alpha\beta}\Big{]}\sigma_k\,\,,
  \nonumber\\
\left[\hat{\mathcal{P}}^{cb}\right]_{\alpha\beta} &=& \frac{1}{3}\Big{[}(\tau^c\tau^b)_{\alpha\beta}
+\delta_{cb}\delta_{\alpha\beta}\Big{]}\,\,,
\end{eqnarray}
with $\alpha,\beta=1,2$ being the isospin-1/2 SU(2) indices~\cite{Wilbring:2016bda}. As mentioned earlier, the cut-off dependence of
$g_3$ is {\it a priori} undetermined in the EFT and can be fixed only using a three-body datum, e.g., three-body binding energy $B_3$
or the corresponding scattering length $a_3$, none of which is currently available from experimental data. Thus, in the absence of such
empirical information, we rely on the $\Xi^- nn$ binding energy estimates from the Faddeev calculations provided by erstwhile
potential model analyses, as in Refs.~\cite{Carames:2012zz,Garcilazo:2015noa,Garcilazo:2016ylj,Garcilazo:2016ams,Filikhin:2017fog}.

\subsection{Coupled Integral Equations}
\label{sec:2}
For the sake of theoretical analysis, we study the $\Xi^- nn$ system in both the kinematical three-body bound and scattering domains
using a representative choice of $1+2\to 1+2$ elastic reaction channel, given by the following low-energy scattering process with dominant
S-wave contributing:
\begin{equation}
 n + (\Xi^- n)_t \longrightarrow  n+ (\Xi^- n)_t \,\,.
\label{eq12}
\end{equation}
In this regard, we must emphasize that above ``reference" scattering process is chosen solely for the sake of demonstrating our
theoretical methodology, irrespective of the impracticability of performing such experimental studies at current facilities. The chosen
reaction channel yields a set of coupled Faddeev-type (Fredholm) integral equations in the momentum space, whose eigenvalues yield all
possible values of binding energies $B_3$ of trimer level states and the corresponding eigenvectors yield the scattering amplitudes. In
Fig.~\ref{FIG-2}, we display the relevant Feynman diagrams for the scattering process in question, in term of the two
{\it half-off-shell\,} S-wave scattering amplitudes, namely, $t_A(k,p;E)$ representing the elastic process,
$n + u_1 \rightarrow n + u_1$, and $t_B(k,p)$ representing the open inelastic channel, $n + u_1 \rightarrow \Xi^- + u_0$. Here
$k=|{\bf k}|\,\, (p=|{\bf p}|)$ denotes the on-shell (off-shell) incoming (outgoing) relative three-momentum in the center-of-mass (CM)
system, and $E$ is the total CM energy of the three-body system given by
\begin{equation}
 E=\pm\frac{k^2}{2\mu_{n(n\Xi)}} - \mathcal{B}_2\quad;\quad \mathcal{B}_2= \frac{\left(\gamma^{(1)}_{\Xi n}\right)^2}{2 \mu}=1.47~{\rm MeV}\,,
\end{equation}
where, the ``$-$'' sign is to be used for the kinematical three-body bound state domain and the ``$+$'' sign for the corresponding
scattering domain. $\mathcal{B}_2$ is the CM binding energy of a possible threshold bound $(\Xi^- n)_t$ sub-system which also sets the
particle-triplet dimer ($n + u_1$) break-up threshold energy,\footnote{The value ${\mathcal B}_2$ which corresponds to the the pole
position of the $u_1$ dibaryon propagator in our halo EFT formalism may be compared to the binding energy of the putative (1,1)
$\Xi N$ bound state ($D^*$) predicted in the potential model analyses in
Refs.~\cite{Garcilazo:2016ams,Filikhin:2017fog,Nagels:2015dia,Rijken:2016uon}.} and
$\mu_{n(n\Xi)}= M_n(M_{\Xi}+M_n)/(2M_n+M_{\Xi})=663.768$~MeV is the corresponding reduced mass of three-body (particle-dimer) system.
The construction methodology of these integrals equation is similar to those employed in several earlier ${}^{{\pi}\!\!\!/}$EFT
works~\cite{Ando:2015fsa,Ando:2013kba,Ando:2014mqa,Meher:2020rsd,Raha:2017ahu}. The renormalized S-wave projected coupled channel
elastic and inelastic integral equations with the introduced UV sharp momentum cut-off $\Lambda_c$ are respectively given as
\begin{figure}[tbp]
\centering
\includegraphics[width=16cm]{fig2.eps}
\caption{ Feynman diagrams for the representative coupled channel elastic scattering process,
          $n+ (\Xi^- n)_t \rightarrow n + (\Xi^- n)_t$, where ``$t$" is used to denotes the ${}^3S_1$ $\Xi^- n$
          sub-system. The solid (dash) line represents neutron ($\Xi^-$-hyperon) propagator. The off-shell double
          lines with insertions of the small empty oval (square) blobs represent the renormalized dressed
          ${}^1S_0$ $nn$ ($u_0$) and ${}^3S_0$ $\Xi^- n$ ($u_1$) dibaryon field propagators. The large blob
          $t_A$ ($t_B$) denotes the elastic (inelastic) half-off-shell scattering amplitude corresponding to the
          $n + u_1 \rightarrow n+ u_1$ ($n+ u_1 \rightarrow \Xi^- + u_0$) scattering. The dark blobs represent
          three-body contact interaction.}
\label{FIG-2}
\end{figure}
\begin{eqnarray}
t^{(R)}_A(p,k;E) \!\!&=&\!\!  {\mathcal Z}_{\Xi n}\frac{\left(y_1^2M_{\Xi} \right)}{2}
\left[K_{(a)}(p,k;E)-\frac{g_3(\Lambda_c)}{\Lambda_c^2}\right]
\nonumber\\
&&\!\!\! -\, \frac{M_{\Xi}}{2\pi\mu}\!\int_0^{\Lambda_c}\!\! dq\,  q^2
\left[K_{(a)}(p,q;E)-\frac{g_3(\Lambda_c)}{\Lambda_c^2}\right]\!\!
{\mathscr D}_1\left(E-\frac{q^2}{2M_n},{\bf q}\right)t^{(R)}_A(q,k;E)
\nonumber\\
&&\!\!\! +\, \frac{\sqrt{6}y_1}{\pi y_0}\!\int_0^{\Lambda_c}\!\! dq\,  q^2
\left[K_{(b2)}(p,q;E)-\frac{g_3(\Lambda_c)}{\Lambda_c^2}\right] \!\!
{\mathscr D}_0\left(E-\frac{q^2}{2M_\Xi},{\bf q}\right)t^{(R)}_B(q,k;E)\,\,,
\nonumber\\
\label{eq:11}
\end{eqnarray}
and
\begin{eqnarray}
t^{(R)}_B(p,k;E) \!\!&=&\!\! -{\mathcal Z}_{\Xi n}\sqrt{\frac{3}{2}} \left(y_1 y_0 M_n\right)
\left[K_{(b1)}(p,k;E)-\frac{g_3(\Lambda_c)}{\Lambda_c^2}\right]
\nonumber\\
&&\!\!\! +\, \sqrt{\frac{3}{2}} \frac{M_n y_0}{\mu \pi y_1}\! \int_0^{\Lambda_c}\!\! dq\,  q^2
\left[K_{(b1)}(p,q;E)-\frac{g_3(\Lambda_c)}{\Lambda_c^2}\right]\!\!
{\mathscr D}_1\left(E-\frac{q^2}{2M_n},{\bf q}\right)t^{(R)}_A(q,k;E),
\nonumber \\
\label{eq:12}
\end{eqnarray}
where the renormalized amplitudes
\begin{equation}
t^{(R)}_{A,B}(p,k;E)= \sqrt{{\mathcal Z}_{\Xi n}}\, t_{A,B}(p,k;E)\, \sqrt{{\mathcal Z}_{\Xi n}}
\end{equation}
are obtained by multiplying the corresponding half-off-shell amplitudes $t_{A,B}(p,k;E)$ by the wavefunction renormalization
factor ${\mathcal Z}_{\Xi n}$ associated with the possible bound $(\Xi^- n)_t$ sub-system, given as
\begin{equation}
{\mathcal Z}^{-1}_{\Xi n}=\frac{y_1^2\mu^2}{2\pi \gamma^{(1)}_{\Xi n}}\,\,.
\end{equation}
Finally, the renormalized elastic amplitude could be used to calculate the S-wave $n-(\Xi^- n)_t$ three-body scattering length
by considering the threshold limit of the on-shell momentum, i.e., $k\to 0$, namely,
\begin{eqnarray}
\label{eq:a3}
  a_3=-\lim_{k\to 0}\frac{\mu_{n(n\Xi)}}{2\pi}\, t^{(R)}_A(k,k)\,.
\end{eqnarray}
In the above integral equations, the term $K_{(a)}$ denotes the S-wave projected one-$\Xi^-$-exchange interaction kernel, while
$K_{(b_1,b_2)}$ are the two possible variants of the one-neutron-exchange interaction kernel, namely,
\begin{eqnarray}
  K_{(a)}   (p,\kappa;E) &=& \frac{1}{2p\kappa} \ln\left(\frac{p^2+\kappa^2+ap\kappa -2\mu E}{p^2+\kappa^2-ap\kappa -2\mu E}\right) \,\,,\\
  K_{(b_1)} (p,\kappa;E) &=&  \frac{1}{2p\kappa} \ln\left(\frac{bp^2+\kappa^2+p\kappa -M_n E}{bp^2+\kappa^2-p\kappa -M_n E}\right)\,\,, \\
  K_{(b_2)} (p,\kappa;E) &=&  \frac{1}{2p\kappa} \ln\left(\frac{p^2+b\kappa^2+p\kappa -M_n E}{p^2+b\kappa^2-p\kappa -M_n E}\right)\,\,,
\end{eqnarray}
where, the generic momentum $\kappa$ denotes either the incoming on-shell relative momentum ($k$) or the loop momentum ($q$). Also,
$a=2\mu/M_{\Xi}$ and $b=M_n/(2\mu)$ are mass dependent parameters.

\subsection{Asymptotic Analysis}
In order to assess that the coupled system of integral equation indeed has the potentiality to yield three-body bound state solutions,
one needs to check for possible manifestation of Efimov effect at the asymptotic unitary limit as $\Lambda_c \rightarrow \infty$. In this
case, all other low-energy scales in the problem (e.g., $E,\gamma_{0,1},k \ll p,q\sim \Lambda_c$) become irrelevant, and the integral
equations can be well approximated by considering only the homogeneous parts, as well as dropping all the $k$ dependence and three-body
interactions terms with $g_3$. Thus, with no other relevant scales in the theory, the integral equations become {\it dilation} invariant
and symmetric under the inversion transformation $q \to 1/q$, such that the half-off-shell channel amplitudes exhibit a power-law scaling,
namely, $t_{A,B}(\kappa)\sim \kappa^{s-1}$, with $\kappa\sim\Lambda_c$ and exponent $s$ is an undetermined three-body parameter. By
performing a sequence of {\it Mellin} transformation the integral equations can be converted in to a single transcendental equation which
could be used to solve for the exponent $s$, namely,
\begin{eqnarray}
  1 &=& \frac{M_{\Xi}}{2\mu C_1} \Bigg[ \frac{\sin[s \sin^{-1}(a/2)]}{s\cos(\pi s/2)}\Bigg]
  + \frac{3M_n}{\mu C_1C_2} \Bigg[\frac{\sin[s \cot^{-1}\sqrt{4b-1}]}{s\cos(\pi s/2)}\Bigg]^2,
  \label{eq18}
\end{eqnarray}
where
\begin{eqnarray}
  C_1=\sqrt{\frac{\mu}{\mu_{n(n\Xi)}}}, \quad{\text{and}}\quad
  C_2=\sqrt{\frac{M_n}{2\mu_{\Xi(nn)}}}\,\,,
  \label{eq19}
  \end{eqnarray}
and $\mu_{\Xi(nn)} = 2 M_n M_{\Xi}/(2 M_n +M_{\Xi})=775.942$~MeV is the reduced mass of the $\Xi^- + u_0$ particle-dimer system. Solving
Eq.~\eqref{eq18} yield an imaginary solution, i.e., $s=\pm i s_0^{\infty}= \pm i 0.803391\cdots $. The solution immediately suggests the
existence of an asymptotic UV RG limit cycle with a discrete scaling symmetry associated with the scale factor,
$\lambda_\infty =e^{\pi/s^{\infty}_0}=49.919712\cdots$. Consequently, our LO EFT formally manifests Efimov effect in the unitary limit of
the $\Xi^- nn$ system. Thus, it becomes imperative to introduce scale dependent 3BF as counterterms in the effective Lagrangian to
renormalize the ill-defined asymptotic limit of the two-body sector. Such 3BF terms which are otherwise considered subleading in the naive
dimensional counting must be promoted to the LO for consistency of renormalization (see Ref.~\cite{Braaten:2004rn} for a detailed discussion
on asymptotic analysis of integral equations in the context of ${}^{{\pi}\!\!\!/}$EFT). Here we must, however, mention that the asymptotic
scaling exponent $s^\infty_0$ we obtain considerably differs from the expected value, $(s^\infty_0)_{\rm exp}\sim 1.01$, that follows from
the universal RG limit cycle scaling depending on the relative three-particle mass ratios~\cite{Braaten:2004rn}. This difference is
attributed to the effect of complete decoupling of the isospin-triplet spin-singlet (1,0) $\Xi^- n$ sub-system channel from the integral
equations, whose dynamics are not easily captured in our present low-energy EFT description.

\section{Results and Discussion}\label{sec:3}
In this section we present the results of our preliminary investigation of the cut-off regulator ($\Lambda_c$) dependence of the integral
equations, Eq.~\eqref{eq:12}, at non-asymptotic low-energy scales. For the sake of numerical evaluations, we use the particle masses as
presented in Table~\ref{tab:1}, while the S-wave scattering lengths $a_{nn}=-18.63$~fm~\cite{Chen:2008zzj} and
$a_{\Xi n}=4.911$~fm~\cite{Nagels:2015dia,Rijken:2016uon} constitute the principal input two-body parameters in our LO EFT framework. In
the last section, our asymptotic analysis demonstrated the evidence of Efimov states at the unitary limit of the $\Xi^- nn$ system with an
RG limit cycle discrete scaling symmetry determined by the multiplicative factor $e^{\pi/s^\infty_0}\sim 50$. With
$\kappa^{(1)}\equiv \gamma^{(1)}_{\Xi n}\sim 40$~MeV as the typical momentum scale of the problem, it is envisaged that the next higher
momentum scale appears at $\kappa^{(2)}\equiv \lambda_\infty \gamma^{(1)}_{\Xi n}\sim 2~{\rm GeV}\,\gg \Lambda_H\sim m_\pi$, which is
well beyond the accessibility of our low-energy EFT description. Hence, it is likely that only one Efimov-like state emerges as a plausible
bound $\Xi^- nn$ hypernucleus, if at all. Figure~\ref{FIG-3} shows the cut-off dependence of the three-body contact interaction coupling
$g_3(\Lambda_c)$. In the absence of a three-body datum to constrain this {\it a priori} unknown coupling, we at the very outset of our
analysis assume that the $\Xi^- nn$ system already exhibits at the least one three-body bound state whose eigenenergy $E=-B_3$, corresponds
to the one of possible binding energy predictions from the erstwhile Faddeev analysis based potential models, as in
Refs.~\cite{Garcilazo:2015noa,Garcilazo:2016ylj,Garcilazo:2016ams,Filikhin:2017fog}. Hence, we choose our benchmark range of the input
three-body binding energy, namely, between $B_3= 2.886$~MeV taken from Ref.~\cite{Filikhin:2017fog}, and $B_3= 4.06$~MeV taken from
Ref.~\cite{Garcilazo:2015noa}, both relying on the same two-body inputs, e.g., S-wave scattering length $a^{(1)}_{\Xi n}=4.911$~fm,
provided by the updated ESC08c Nijmegen potential model analysis~\cite{Nagels:2015dia,Rijken:2016uon}.\footnote{It is notable that the value
$B_3= 2.886$~MeV, as obtained in model analysis of Ref.~\cite{Filikhin:2017fog}, resulted from considering both the repulsive (1,0) and
attractive (1,1) $\Xi N$ channels in the Feddeev calculations, whereas the value $B_3= 4.06$~MeV in model analysis of
Ref.~\cite{Garcilazo:2015noa} resulted from considering only the attractive channel. However, irrespective of the details we consider
their predicted three-body binding energies as input to our EFT analysis.} The figure displays the typical quasi-periodic logarithmic
singularities of the {\it approximate} RG limit cycles for the two limiting $B_3$ inputs. The corresponding non-asymptotic scale factor,
$\lambda_n \lesssim \lambda_\infty$, may be obtained by considering the ratio of two successive cut-offs where the three-body coupling
vanishes, i.e., if $g_3\left(\Lambda^{(n)}_c\right)=g_3\left(\Lambda^{(n+1)}_c\right)=0$, then
\begin{figure
\centering
\includegraphics[width=11cm]{fig3.eps}
\caption{ The first three branches corresponding to the approximate RG limit cycle behavior of the three-body coupling $g_3$
          for the $\Xi^- nn$ system, as a function of cut-off scale $\Lambda_c$, obtained by solving the integral equations,
          Eq.~\eqref{eq:11} \& \eqref{eq:12}. The input three-body binding energies $B_3= 2.886$~MeV and $4.06$~MeV, are
          predictions from the Faddeev based potential models~\cite{Garcilazo:2015noa,Filikhin:2017fog}, and the input S-wave
          spin-isospin triplet $\Xi^- n$ scattering length $a^{(1)}_{\Xi n}=4.911$~fm, provided by the ESC08c Nijmegen
          potential model analyses~\cite{Nagels:2015dia,Rijken:2016uon}.}
\label{FIG-3}
\end{figure}
\begin{equation}
 \lambda_{n} = \frac{\Lambda_c^{(n+1)}}{\Lambda_c^{(n)}}\,\,; \quad n = 1,2,..,\infty\,\,,
\end{equation}
where $\Lambda_c^{(n)}$ is the cut-off corresponding to $n^{\rm th}$ zero of $g_3$. For example, Table~\ref{tab:2} displays the
estimated non-asymptotic scale factors $\lambda_n$ corresponding to successive pairs of zeros of the RG limit cycles, each for
the two input values of the binding energy $B_3$. In each case the scale factor $\lambda_n$ is obtained close to but less than the
asymptotic value $\lambda_\infty$. But, however, by progressively choosing larger pairs of the successive zeros of $g_3$, i.e.,
with $n \to \infty$, $\lambda_n$ is found to converge rapidly to $\lambda_\infty$.

\begin{table}[tbp]
\begin{center}
\caption{The approximate RG limit cycle behavior with scale factor, $\lambda_n\to \lambda_\infty$, obtained by solving
         the coupled integral equations, Eqs.~\eqref{eq:11} \& \eqref{eq:12} for the $\Xi^- nn$ system. Here, results
         for $n=1-4$ are only displayed which indicate a rapid convergence toward the asymptotic limit
         $\lambda_\infty=49.919712\cdots$. The input three-body binding energies $B_3= 2.886$~MeV and $4.06$~MeV, are
         predictions from the Faddeev based potential models~\cite{Garcilazo:2015noa,Filikhin:2017fog}, and the input
         S-wave spin-isospin triplet $\Xi^- n$ scattering length $a^{(1)}_{\Xi n}=4.911$~fm, provided by
         the ESC08c Nijmegen potential model analyses~\cite{Nagels:2015dia,Rijken:2016uon}. }

\vspace{0.4cm}

\label{tab:2}
\begin{tabular}{|c|c|c|c|c|}
\hline
Binding Energy & $n\in{\mathbb Z}$ & $n^{\rm th}$ zero of $g_3$ & $(n+1)^{\rm th}$ zero of $g_3$ & Scale factor\\
  $B_3$ (MeV)  &                   & $\Lambda_c^{(n)}$ (MeV)    & $\Lambda_c^{(n+1)}$ (MeV)      & $\lambda_n=\Lambda^{(n+1)}/\Lambda^{(n)}$ \\
\hline\hline
                                & 1 & 334.283      & 16344.134      & $48.893105\cdots$ \\
2.886 \cite{Filikhin:2017fog}   & 2 & 16344.134    & 815412.631     & $49.890232\cdots$ \\
                                & 3 & 815412.631   & 40704680.527   & $49.919119\cdots$ \\
                                & 4 & 40704680.527 & 2031965537.021 & $49.919702\cdots$ \\
\hline
                                & 1 & 465.937      & 22919.007      & $49.189069\cdots$ \\
4.06 \cite{Garcilazo:2015noa}   & 2 & 22919.007    & 1143628.429    & $49.898690\cdots$ \\
                                & 3 & 1143628.429  & 57089119.370   & $49.919290\cdots$ \\
                                & 4 & 57089119.370 & 2849872042.899 & $49.919706\cdots$ \\
\hline\hline
\end{tabular}
\end{center}
\end{table}

\vspace{0.1cm}

Next, in Fig.~\ref{FIG-4} we display the cut-off variation of the binding energy $B_3$ excluding the 3BF term, i.e., with
$g_3=0$ in the integral equations. In particular, due to the ambiguities regarding the precise nature of the (1,1) $\Xi N$
sub-system interactions between the different existing phenomenological
analyses~\cite{Khaustov:1999bz,Hiyama:2019kpw,Aoki:1998sv,Ahn:2005jz,Yamaguchi:2001ip,Friedman:2007zza,Hiyama:2010zz,Haidenbauer:2015zqb,Li:2018tbt,Haidenbauer:2018gvg,Kohno:2009ny,Krishichayan:2010zza,Nagels:2015dia,Rijken:2016uon}, we consider here two representative
scenarios with contrasting perspectives, either of which formally may generate an Efimov-like bound state emerging from the
respective thresholds, as elucidated below:
\begin{figure}[ht]
\centering
\includegraphics[width=6.58cm]{fig4a.eps}~\includegraphics[width=6.58cm]{fig4b.eps}
    \caption{Cut-off ($\Lambda_c$) dependence of three-body binding energy of the $\Xi^- nn$ system, obtained by solving
             the coupled integral equation, Eqs.~\eqref{eq:11} \& \eqref{eq:12} excluding the three-body contact interaction.
             The left panel represents the result for the three-body binding energy $B_d=B_3-{\mathcal B}_2$, relative to
             the $n+u_1$ particle-dimer threshold ${\mathcal B}_2=1.47$~MeV, with input S-wave spin-isospin triplet
             $\Xi^- n$ scattering length $a^{(1)}_{\Xi n}=4.911$~fm, predicted by the ESC08c Nijmegen potential model
             analyses~\cite{Nagels:2015dia,Rijken:2016uon}. While the right panel represents the result for $B_3$ relative
             to the three-particle threshold, with input scattering length $a^{(1)}_{\Xi n}=-1.17$~fm, predicted by the
             chiral EFT analysis~\cite{Haidenbauer:2018gvg}. For comparison, the right panel displays the predictions for the
             $\Xi^- nn$ binding energy, namely, $B_3= 2.886$~MeV and $4.06$~MeV, from the Faddeev analysis based
             models~\cite{Garcilazo:2015noa,Filikhin:2017fog}, both relying on the ESC08c Nijmegen model inputs. }
\label{FIG-4}
\end{figure}
\begin{itemize}
\item
First, the scenario with $a^{(1)}_{\Xi n}=4.911$~fm, as predicted by the updated ESC08c Nijmegen potential model analyses in
Ref.~\cite{Nagels:2015dia,Rijken:2016uon}, suggests a strongly attractive ${}^3S_1$ $\Xi^- n$ sub-system commensurate with the
likely existence of a two-body threshold bound state, such as the $D^*$~\cite{Garcilazo:2016ams,Filikhin:2017fog}. Consequently,
in the three-body sector with a pair of likely bound $(\Xi^- n)_t$ sub-systems and a virtual bound $nn$ sub-system, the
$\Xi^- nn$ assumes a halo-bound ({\it samba} configuration~\cite{Yamashita:2004pv}) structure emerging from the particle-dimer
break-up threshold at the CM energy $E=-{\mathcal B}_2$. This corresponds to the solid line curve (left panel) in
Fig.~\ref{FIG-4}, representing the regulator dependence of the {\it relative} three-body binding energy $B_d=B_3-{\mathcal B}_2$,
for an Efimov-like ($n=0$) ground state which appear at the {\it critical cut-off} scale $\Lambda^{(0)}_{\rm crit}\approx 80$~MeV.
\item
Second, the scenario with $a^{(1)}_{\Xi n}=-1.17$ fm, as predicted by the chiral EFT analysis up to next-to-leading-order (NLO) in
Ref.~\cite{Haidenbauer:2018gvg}, suggests a weakly attractive ${}^3S_1$ $\Xi^- n$ sub-system that is unlikely to exhibit a two-body
threshold bound state. Consequently, in the three-body sector with none of the two-body sub-systems bound, the $\Xi^- nn$ assumes a
bound {\it borromean} structure~\cite{Yamashita:2004pv} emerging from the three-particle break-up threshold $E=0$. This corresponds
to the dashed line curve (right panel) in Fig.~\ref{FIG-4}, representing the cut-off variation of $B_3$ for the corresponding
Efimov-like ground state which appears at the scale $\Lambda^{(0)}_{\rm crit} \approx 1940$~MeV.
\end{itemize}
Evidently, the large value of the critical cut-off in the latter scenario is not amenable to our EFT framework, and hence the
resulting Efimov-like state is unlikely to physically manifest as a bound $\Xi$-hypernuclus. In contrast, the small value of the
critical cut-off in the former scenario lies well within the realm of our EFT, indicating an encouraging prospect of a potentially
feasible $\Xi^- nn$ Efimov-bound state. Thus, we shall henceforth discuss our results only pertaining to the former choice of
$\Xi ^- nn$ system.

\vspace{0.1cm}

In the absence of the three-body contact interactions for renormalization our results for the three-body binding energy exhibit
considerable sensitivity to the cut-off variations. Figure~\ref{FIG-4} also compares our results with the regulator independent
predictions for the $\Xi^- nn$ binding energy from the potential models~\cite{Garcilazo:2015noa,Filikhin:2017fog} which also rely on
the two-body inputs from the Nijmegen ESC08c model analyses~\cite{Nagels:2015dia,Rijken:2016uon}. Our EFT eigenenergies reproduce the
model predictions $B_3=2.886$~MeV of Ref.~\cite{Filikhin:2017fog} and $B_3=4.06$~MeV of Ref.~\cite{Garcilazo:2015noa} at the cut-off
scales $\Lambda_c\approx 334$~MeV and $\Lambda_c\approx 465$~MeV respectively. The situation is clearly elucidated in Fig.~\ref{FIG-5},
where we plot the variation of $B_3$ as function of the input scattering length $a^{(1)}_{\Xi n}$ for several fixed cut-off values.
The potential model predicted binding energy $B_3$, namely, in the range $2.886-4.06$~MeV, as demarcated by the horizontal band in the
figure, is well constrained within the regulator range of $\Lambda_c\approx 334-465$~MeV. In particular, Table~\ref{tab:3} summarizes
the $\Lambda_c$ values at which our EFT solutions reproduce several of the existing Faddeev calculations based model predictions for
the $\Xi^- nn$ binding energy~\cite{Garcilazo:2015noa,Garcilazo:2016ylj,Garcilazo:2016ams,Filikhin:2017fog}. Although such a regulator
range apparently seems well beyond the expected EFT hard scale, $\Lambda_H\sim m_\pi$, the potential model results may still be
accommodated within the framework of a halo EFT having an extended domain of validity than standard ${}^{{\pi}\!\!\!/}$EFT.
Consequently, such a modified EFT should have a larger breakdown scale, say, $\widetilde{\Lambda}_H\lesssim 500$~MeV, where
interactions between the $\Xi$-hyperon and neutron are possibly dominated by two-pion ($\pi\pi$) or sigma ($\sigma$) meson exchange
mechanisms, since one-pion-exchanges are naturally ruled out by isospin invariance in strong processes.
\begin{figure}[h]
\centering
\includegraphics[width=11cm]{fig5.eps}
    \caption{Variation of the three-body binding energy $B_3$ of the ($I=3/2, J={1/2}$) $\Xi^- nn$ system as a function
             of input values of the S-wave ${}^3S_1$ $\Xi^- n$ scattering length, $a^{(1)}_{\Xi n}>0$, for fixed cut-offs
             $\Lambda_c$ excluding three-body interactions. The horizontal shaded band represents our benchmark range of
             values of $B_3$ considered between the limits, $B_3=2.886$~MeV and $4.06$~MeV, predicted by the Faddeev
             calculations based potential model analyses~\cite{Garcilazo:2015noa,Filikhin:2017fog}. The vertical dotted
             line indicates the S-wave spin-isospin triplet $\Xi^- n$ scattering length $a^{(1)}_{\Xi n} = 4.911$~fm,
             predicted by the updated ESC08c Nijmegen model analyses~\cite{Nagels:2015dia,Rijken:2016uon}.   }
\label{FIG-5}
\end{figure}
\begin{figure}[h]
\centering
\includegraphics[width=6.58cm]{fig6a.eps}~\includegraphics[width=6.58cm]{fig6b.eps}
    \caption{Regulator ($\Lambda_c$) dependence of the ($I=3/2, J={1/2}$) $\Xi^- nn$ or $n-(\Xi^-n)_t$ S-wave elastic three-body
             scattering length $a_{3}$. They are obtained by solving the coupled integral equation, Eqs.~\eqref{eq:11} \&
             \eqref{eq:12}, excluding the three-body coupling, i.e., $g_3=0$ (left panel) and including the three-body coupling,
             i.e., $g_3(\Lambda_c)\neq 0$ (right panel). For the later, $g_3$ is determined by the respective RG limit cycles (cf.
             Fig.~\ref{FIG-3}) corresponding to the two three-body inputs $B_3= 2.886$~MeV and $4.06$~MeV, taken from the potential
             models~\cite{Garcilazo:2015noa,Filikhin:2017fog}. The S-wave spin-isospin triplet $\Xi^- n$ scattering length
             $a_{\Xi n}=4.911$~fm, is taken from the updated ESC08c Nijmegen model~\cite{Nagels:2015dia,Rijken:2016uon}. Our
             predictions, namely, $a_{3}^{\infty}= 4.860$~fm and $2.573$~fm (right panel), correspond to the asymptotic limits of
             the renormalized plots. }
\label{FIG-6}
\end{figure}

\vspace{0.1cm}

Finally as a simple demonstration of predictability of our EFT framework, we attempt a naive estimation of the ($I=3/2, J={1/2}$)
$\Xi^- nn$ three-body scattering length or more precisely the $n-(\Xi^- n)_t$ elastic S-wave scattering length $a_3$ by utilizing the
three-body information on the binding energies predicted by the erstwhile potential
models~\cite{Garcilazo:2015noa,Garcilazo:2016ylj,Garcilazo:2016ams,Filikhin:2017fog}. Here we need to solve our coupled integral
equations, Eqs.~\eqref{eq:11} and \eqref{eq:12}, in the kinematical scattering domain for the elastic on-shell renormalized amplitude
$t^{(R)}_A$ and then consider its threshold limit (i.e., $k\to 0$) [cf. Eq.~\eqref{eq:a3}]. Solving the integral equations with the 3BF
terms excluded (i.e., with $g_3=0$) leads to strong regulator dependence with the resulting amplitude displaying quasi-periodic
singularities akin to the limit cycle behavior (see left panel of Fig.~\ref{FIG-6}). Such divergences are renormalized by
introducing the scale-dependent 3BF counterterms with running coupling $g_3(\Lambda_c)$ which is already fixed from the RG limit cycle
behavior (cf. Fig.~\ref{FIG-3}) once the binding energy ($B_3$) model inputs are considered.

\vspace{0.1cm}

Figure~\ref{FIG-6} (right panel) depicts the regulator dependence of the three-body scattering length $a_{3}(\Lambda_c)$ renormalized
by the 3BF terms. As mentioned, the scale dependence of $g_3$ is fixed using the RG limit cycles corresponding to the model inputs for
the three-body binding energy~\cite{Garcilazo:2015noa,Filikhin:2017fog}. Each renormalized plot still displays a residual regulator
dependence stemming from the scale dependent counterterms, especially at low cut-off scales owing to the decoupling of most underlying
physics. However, for large enough values of the cut-off, say $\Lambda_c\gtrsim 400$~MeV, most of the underlying low-energy three-body
dynamics are well captured by our solutions to the integral equations. Consequently, the renormalization of $a_3$ by the counterterms
becomes more effective at large $\Lambda_c$ leading to a well-defined asymptotic limit:
\begin{equation}
    a^\infty_3=\lim_{\Lambda_c\to \infty} a_{3}(\Lambda_c) \,.
\end{equation}
Thus, in each case of a different three-body input ($B_3$), a constant value $a^\infty_3$ is obtained, as demanded by renormalization
invariance, which represents our predicted three-body scattering length. In particular, our limiting inputs $B_3=2.886$~MeV and
$4.06$~MeV, lead to $a_{3}^{\infty}= 4.860$~fm and $2.573$~fm respectively. In addition, Table~\ref{tab:3} displays the other
intermediate results corresponding to two more existing model inputs, namely, $B_3=3.89$~MeV and $3.00$~MeV, from the Faddeev analyses,
Refs.~\cite{Garcilazo:2016ylj,Garcilazo:2016ams}. In this context, we note that for a possible negative choice of the
${}^3S_1$ $\Xi^- n$ scattering length, e.g., the NLO chiral EFT prediction $a^{(1)}_{\Xi n}=-1.17$~fm~\cite{Haidenbauer:2018gvg}, the
$(\Xi^- n)_t$ sub-system is unbound with an undefined kinematical particle-dimer scattering domain, i.e.,
$-{\mathcal B}_2\leq E \leq 0$. In this case the scattering domain is only definable above the three-particle break-up threshold, i.e.,
$E>0$, which is beyond the interest of our work. It is also noteworthy from the table that $a^\infty_{3}$ decreases with increasing
$B_3$, as anticipated by our naive expectation $a^\infty_{3}\sim 1/\sqrt{2\mu_{n(\Xi n)} B_3}$.
\begin{table}[t]
\begin{center}
\caption{Summary of our EFT results with two different input S-wave spin-isospin triplet $\Xi^- n$ scattering lengths, namely,
         $a^{(1)}_{\Xi n}=4.911$~fm, taken from the updated ESC08c Nijmegen model analyses~\cite{Nagels:2015dia,Rijken:2016uon}, and
         $a^{(1)}_{\Xi n}=-1.17$~fm, taken from the NLO chiral EFT analysis~\cite{Haidenbauer:2018gvg}. Displayed are the cut-off
         scales ($\Lambda_c$) at which the level energy for the Efimov-like ground state (excluding three-body contact interactions)
         reproduce several existing potential model predictions of the three-body binding energies $B_3$ of the ($I=3/2,\,J=1/2$)
         $\Xi^- nn$ system~\cite{Garcilazo:2015noa,Garcilazo:2016ylj,Garcilazo:2016ams,Filikhin:2017fog}. Also summarized are our
         predicted three-body scattering length $a^\infty_3$ corresponding to each model input for $B_3$, with the three-body
         coupling $g_3(\Lambda_c)$ determined by the respective RG limit cycles. Our results corresponding to the case,
         $a^{(1)}_{\Xi n}=-1.17$~fm, has an undefined particle-dimer scattering domain and is unlikely to support a $\Xi^- nn$ bound
         state.}

\vspace{0.4cm}

\label{tab:3}
\begin{tabular}{|c|c|c|c|}
\hlin
Two-body scattering                                 & Three-body binding             & Cut-off             & Three-body scattering \\
length $a^{(1)}_{\Xi n}$(fm)                        & energy $B_3$ (MeV)             & $\Lambda_{c}$ (MeV) & length $a^\infty_{3}$ (fm) \\
\hline\hline
                                                    & 2.886~\cite{Filikhin:2017fog}  & 334                 &  4.860 \\
                                                    & 2.89~\cite{Garcilazo:2016ylj}  & 335                 &  4.849 \\
4.911 (ESC08c)~\cite{Nagels:2015dia,Rijken:2016uon}  & 3.00~\cite{Garcilazo:2016ams}  & 348                 &  4.562 \\
                                                    & 4.06~\cite{Garcilazo:2015noa}  & 465                 &  2.573 \\
\hline
                                                    & 2.886~\cite{Filikhin:2017fog}  & 2333                &  - \\
                                                    & 2.89~\cite{Garcilazo:2016ylj}  & 2334                &  - \\
-1.17 (Chiral EFT)~\cite{Haidenbauer:2018gvg}       & 3.00~\cite{Garcilazo:2016ams}  & 2345                &  - \\
                                                    & 4.06~\cite{Garcilazo:2015noa}  & 2440                &  - \\
\hline\hline
\end{tabular}
\end{center}
\end{table}\\

\vspace{-1.42cm}

Our predicted range of three-body scattering lengths represents a naive ballpark estimate based on the induced universal three-body
correlations which is expected to manifest themselves in a halo-bound $\Xi^- nn$ system, despite the approximations considered in this
analysis. To further elucidate the universal aspects, it is worth demonstrating the $B_3$ versus $a^\infty_3$ correlations with our
preferred choice of the input $\Xi^- n$ scattering length, namely, $a^{(1)}_{\Xi n}=4.911$~fm~\cite{Nagels:2015dia,Rijken:2016uon}.
This yields the well-known Phillips line plot for the $\Xi^- nn$ system, as depicted in Fig.~\ref{FIG-7}. The curve diverges as
$B_3\to {\mathcal B}_2=1.47$~MeV, the $n-(\Xi^- n)_t$ particle-dimer threshold, whenever an Efimov-like bound state emerges at
zero-energy threshold (i.e., with $B_d=B_3-{\mathcal B}_2=0$). A second virtual bound three-body state with large negative value of
$a^\infty_3$ is expected to emerge around $B^{\rm (virt)}_3=e^{\pi/s_0}{\mathcal B}_2\approx 70$~MeV, where the Phillips line diverges
again. However, the latter state lies outside the domain of validity of standard ${}^{{\pi}\!\!\!/}$EFT with an estimated breakdown
energy $B_3\approx 14$~MeV, as determined by the three-body binding momentum of the order of the pion mass, i.e.,
$\gamma_3=\sqrt{2\mu_{n(\Xi n)}B_3}\gtrsim m_\pi$. The four data points displayed in the figure correspond to the $B_3$ predictions
from the potential model analyses~\cite{Garcilazo:2015noa,Garcilazo:2016ylj,Garcilazo:2016ams,Filikhin:2017fog}, all of which rely on
the same input two-body scattering length $a^{(1)}_{\Xi n}=4.911$~fm~\cite{Nagels:2015dia,Rijken:2016uon} (cf. Table~\ref{tab:3}).
Evidently, the Phillips plot clearly demonstrates the compatibility of the model inputs with our EFT description.
\begin{figure}[tbp]
\centering
    \includegraphics[width=11cm]{fig7.eps}
    \caption{Phillips line correlation plot for the ($I=3/2,\,J=1/2$) $\Xi^-nn$ system corresponding to the input
             ${}^3S_1$ $\Xi^- n$ scattering length $a^{(1)}_{\Xi n}=4.911$~fm, as predicted by updated ESC08c Nijmegen
             model analyses~\cite{Nagels:2015dia,Rijken:2016uon}. The data points correspond to the input values of the
             three-body binding energy $B_3= 2.886~{\rm MeV},\, 2.89~{\rm MeV},\, 3.00~{\rm MeV}$ and $4.06$~MeV,
             predicted by the potential model
             analyses~\cite{Garcilazo:2015noa,Garcilazo:2016ylj,Garcilazo:2016ams,Filikhin:2017fog}. The vertical dotted
             line on the left represent the $n-(\Xi^- n)_t$ particle-dimer threshold at $B_3=\mathcal{B}_2=1.47$~MeV,
             while the hashed region, $B_3\gtrsim  14$~MeV, represents the expected breakdown region of our EFT
             description. }
\label{FIG-7}
\end{figure}

\section{Summary and Conclusions}\label{sec:4}
A knowledge of few-body dynamics in light ($S=-2$) $\Xi$-hypernuclei can serve as essential input to determine the correct EoS for
neutron star matter for possible explanation of the stability of neutron stars with masses close to or above $2M_{\odot}$. In this
regard, the ($I=3/2, J^P={1/2}^+$) $\Xi^- nn$ three-body system is one of the simplest systems to investigate the nature of the
underlying 3BF, owing to the stability of this channel against strong decays and to the Coulomb-free dynamics. However, the
impracticability of performing $\Xi$-hyperon scattering experiments and the lack of empirical data thereof have so far eluded rigorous
determination of essential observables. Thus, a general qualitative approach relying solely on low-energy universality is demanded to
illuminate specific characteristics of the underlying interactions that may reflect the emergence of exotic bound states.

\vspace{0.1cm}

Here we used the framework of leading order halo ${}^{{\pi}\!\!\!/}$EFT in a speculative study to explore the feasibility of $\Xi^- nn$
to be Efimov-bound. Notably, the presence of the predominantly repulsive ${}^1S_0$ $\Xi^- n$ sub-system channel potentially leads to the
generation of anomalously deep two- and three-body bound states beyond the breakdown scale of the ${}^{{\pi}\!\!\!/}$EFT. In our current
simplistic approach, as the first step such unphysical contributions are avoided, albeit non-systematically, by explicitly decoupling
this channel in the construction of our coupled integral equations in momentum space. In a more systematic (realistic) approach which
includes both the repulsive ${}^1S_0$ and attractive ${}^3S_1$ $\Xi^- n$ sub-system channels, one perhaps requires a modification of the
dibaryon formalism, {\it vis-a-vis} the halo ${}^{{\pi}\!\!\!/}$EFT power counting~\cite{Bedaque:1998kg,Bedaque:1999ve}. For example,
a simultaneous perturbative and non-perturbative expansion schemes in the singlet and triplet $\Xi^- n$ channels respectively, may be
incorporated. However, such a modified EFT analysis is beyond the scope of the current work and must be explored in the future as a
possible next step. Our asymptotic analysis of the $\Xi^- nn$ integral equations revealed the formal appearance of Efimov states in the
unitary limit associated with a RG limit cycle with a discrete scale factor, $\lambda_\infty=e^{\pi/s_0^{\infty}}\approx 50$. This factor
is, however, quite different from the expected scaling based on the universality of three-particle mass
ratios~\cite{Braaten:2004rn}, namely, $\lambda_{\exp}=e^{\pi/(s_0^{\infty})_{\rm exp}}\approx 20$, owing to the neglect of the
${}^1S_0$ $\Xi^- n$ channel. Such scaling differences are certainly going to affect our numerical predictions in the low-energy
non-asymptotic domain, but the general qualitative features are unlikely to change substantially even with both the $\Xi^- n$ spin
channels included.\footnote{In either cases we expect to find remnant universal features like the quasi-periodic RG limit cycle nature of
the leading order three-body coupling $g_3(\Lambda_c)$. However, the inclusion of the repulsive ${}^1S_0$ $\Xi^- n$ channel interactions
is likely to shift the RG limit cycles towards higher cut-off values. Although, this reduces the likelihood of a viable Efimov-like state
in the valid EFT domain, this does not pre-empt the possibility that the aforementioned scale shift toward higher values is partially or
wholly compensated by the corresponding decrease in the scale factor $\lambda_\infty$ from 50 to 20.}

\vspace{0.1cm}

Evidently, the absence of any three-body datum to fix the scale dependence of the three-body coupling $g_3(\Lambda_c)$ is a major drawback
of our approach which prevents robust predictions. Thus, we relied on several Faddeev calculations based
models~\cite{Garcilazo:2015noa,Garcilazo:2016ylj,Garcilazo:2016ams,Filikhin:2017fog} for the input three-body binding energy $B_3$ in the
range, $2.886-4.06$~MeV. Moreover, the ${}^{{\pi}\!\!\!/}$EFT formalism also requires two-body inputs, for which we considered the following
S-wave scattering lengths: the ${{}^1S_0}$ $nn$ scattering length $a_{nn}=-18.63$~\cite{Zyla:2020zbs}, and the ${}^3S_1$ $\Xi^- n$
scattering length $a^{(1)}_{\Xi n}$. For the latter, we considered two contrasting choices, namely,
$a_{\Xi n}^{(1)}=4.911$~fm~\cite{Nagels:2015dia,Rijken:2016uon} and $-1.17$~fm~\cite{Haidenbauer:2018gvg}, given the current uncertainty
regarding the exact nature of the spin-isospin triplet (1,1) $\Xi^- n$ interaction. However, with the input, $a^{(1)}_{\Xi n}=-1.17$~fm,
our investigations hinted at a predominantly unbound $\Xi^-nn$ system. While the input, $a_{\Xi n}^{(1)}=4.911$~fm, indicated favourable
prospects of the $\Xi^-nn$ system to be physically realized as an Efimov-like ground state, with the proviso that the validity domain of
our EFT could be augmented (with $\widetilde{\Lambda}_H\gtrsim 500$~MeV) to accommodate interactions mediated by $\pi\pi$ or $\sigma$-meson
exchanges. Specifically, our leading order solutions to the integral equations excluding the 3BF terms could reproduce the aforementioned
range of model binding energies ($B_3$) for cut-offs in the range $\Lambda_c\approx 335-464$ MeV.

\vspace{0.1cm}

Finally, as a simple demonstration of the predictive power of our EFT formalism, we evaluated the three-body S-wave $n-(\Xi^- n)_t$
scattering length in the range, $a^{\infty}_3\approx 2.6-4.9$~fm, by including our estimated $g_3(\Lambda_c)$ fixed from the RG limit
cycles corresponding to the model $B_3$. Given the very speculatory nature of this work and the indeterminable scattering length
$a^\infty_3$ from present day emulsion or production experiments, the numerical figures displayed in this work are by all means ballpark
estimates. Nevertheless, they are indicative of the emergent features of a prospective bound $\Xi^- nn$ system which induce universal
three-body correlations like the Phillips line. Such three-body correlations are apparently robust against ambiguities in the two-body
description provided the $B_3$ inputs do not change substantially. Thus, it is not entirely wishful to surmise similar qualitative
features to arise from a more rigorous future investigation even including the $^1S_0$ $\Xi^- n$ sub-system channel. Needless to say
that the above conclusions tacitly rely on our assumed halo-bound structure of the $\Xi^- nn$ system, {\it viz.} a sufficiently
attractive ${}^3S_1$ $\Xi^- n$ sub-system that is ostensibly bound, and a repulsive ${}^1S_0$ $\Xi^- n$ sub-system with small but
positive scattering length.

\vskip 2mm \noindent
\section{ Acknowledgements}
We wish to acknowledge the support of the Department of Physics, Indian Institute of Technology Guwahati. We thank Bipul Bhuyan
for useful discussions.

\vskip 3mm \noindent

redpajama_set_name: RedPajamaArXiv


In 2003 I decided to become a Locksmith as research to inform my art practice. When many of my friends and colleagues found out about this they encouraged me to do diabolical actions such as, stealing things or breaking into places, and then frame the action as "art". Instead, the body of artwork that came out of this research yielded pieces that were by and large about liberation and breaking free of keys. At the same time that I became a Locksmith I also started practicing yoga. I did this to compare how we lock and guard our spaces to how we lock and guard our bodies. The two bodies of research informed one and other and many of Locksmithing pieces borrowed from yogic philosophy to explicate the "attachment" that many people experience regarding keys and the relationships, places, and things that their keys allow them to access. Eventually I decided that my next career/research-project was going to be as a yoga instructor. After 4 years of schooling and apprenticing I started teaching yoga. I taught for almost 3 years and then stopped. When asked why I usually site various reasons ranging from "I wasn't good at it" to "it was ruining my personal yoga practice." During this time I was also making artwork about being a yoga teacher. Again, many people had suggestions and desires about the kind of art pieces that could come out of this research. Many thought that I would make pieces about liberation and helping people, similar to the Locksmithing projects. Instead my research as a yoga instructor yielded works or art that were thematically similar to the Locksmithing pieces but used subtle (and not-so-subtle), passive-aggressive, forced-coercion tactics to herd or manipulate the viewer into doing things they would not normally do in public. Though in each of the Locksmithing pieces I was increasingly aware that I was deliberately posturing students into awkward and vulnerable positions in public, the yoga-teaching pieces were much less subtle and were often directly confrontational. This is what drove me away from yoga teaching. The power dynamic that exists in the yoga studio was too intense and seemed far too easy for me to manipulate (though I never did). I realized that what interested me most about my locksmithing research and yoga teaching was that both examinations explicated the ways that each of us create (or are forced to create) very private moments in very public ways. So, I began an investigation into how we share public space and maintain our privacy outside the confines of our own homes (please see the body of work entitled "Contractor" for more information.) The pieces in this section were directly born from my research as a yoga instructor. Most physically taxed my body in ways facilitated by yoga my practice and pushed the boundaries of audience members personal space.


text:
Patent, Trademark & Registered Design Attorneys
Please contact us to find out how we can help you secure strong protection for your intellectual property.
Patentable Subject Matter in Singapore 2016
(For a downloadable version of this note, click here.)
On 16 May 2016 the Intellectual Property Office of Singapore (IPOS) issued a revised version of the Examination Guidelines for Patent Applications at IPOS (the "Guidelines"), available here. The Guidelines include a revised Chapter 8 on Patentable Subject Matter and Industrial Applicability.
The modern Singapore Patents Act came into force only in the mid-1990s. It has always been heavily influenced by the UK Patents Act 1977. At the time of its introduction, this version of the Singapore Act included a list of statutory exclusions from patentability:
(a) a discovery, scientific theory or mathematical method;
(b) a literary, dramatic, musical or artistic work or any other aesthetic creation whatsoever;
(c) a scheme, rule or method for performing a mental act, playing a game or doing business, or a program for a computer; or
(d) the presentation of information.
This was subject to the usual qualifier, that the exclusions related only to the extent that a patent/application related to these things "as such". These exclusions corresponded with exclusions still present to this day in UK legal code. Not long afterwards, the relevant sub-section of the Singapore Act specifying these exclusions was repealed (i.e. it was deleted/removed from the Singapore Act). From that time, it seemed to be the case in practice that anything and everything was "patent eligible" in Singapore. IPOS is now seeking to change this.
The new position
In summary, in the revised Guidelines, IPOS identifies developments in these areas (a) – (d) as being, from now on, not considered "inventions". That is, IPOS is taking the position that these subject matter areas are again not "patent eligible". IPOS states that the new Chapter 8 applies to national applications (or any divisional application derived from these) with a filing date on or after 16 May 2016, and to any international applications entering the national phase in Singapore (or any divisional applications derived from these) on or after that date.
Further context
The revised version of the Guidelines has been a long time coming. A public consultation process was initiated, and a lively debate between IPOS and the Singapore patent attorney profession ensued. The main reason for the debate is that there is a school of thought the current legal code in force in Singapore does not support IPOS's new position. As noted above, these exclusions were repealed from Singapore law around 20 years ago. They have not been reintroduced into the Singapore Act, and we are not aware of any plan for them to be reintroduced.
IPOS specifically identifies the "actual contribution" test (from the UK decision in Aerotel Ltd v Telco Holdings Ltd & Ors Rev 1 [2007] RPC 7) as being relevant in assessing whether an invention is patent eligible. It is worth noting the Aerotel/Macrossan decision is one in a very long line of decisions –spanning decades – from the UK based on exclusions no longer present in Singapore law. Aerotel/Macrossan related to challenges the invention of that patent was excluded from patentability under the business method and computer program exclusions, neither of which are in the current Singapore legal code.
Practical effect
It is very early days and, at this stage, the full impact this is going to have is difficult to predict. The new Chapter 8 does not give an enormous amount of guidance on what is a complex and controversial subject. Despite this, one section in particular may turn out to be helpful, at least in the area of computer-implemented inventions.
Our initial thinking is that if it can be demonstrated technical features of an invention operate together to "address a specific problem" (citing from section 8.7 of the new Guidelines) then the invention is arguably patent eligible. Interestingly, this section 8.7 does not specify that the problem being solved must be a technical problem, a requirement in other jurisdictions when assessing such matters. However, and as always, each case will have to be considered on its own merits.
If – or more likely when – IPOS begins issuing rejections under these new guidelines, it will not be a great surprise if patent applicants start appealing these rejections to the Court.
This is provided for information only and does not constitute legal advice. Please contact us for detailed advice if you have any specific questions. We should be very happy to answer any questions that you may have.

redpajama_set_name: RedPajamaCommonCrawl


I'm beginning to think Doug Ross is never going to give me my gold, and that in fact, he never had any intention of fulfilling his promise to give a one-ounce Krugerrand to any progressive who can send him "a documented lie repeated by Fox News reporters."
Yesterday, I pointed out  that Fox had repeatedly falsely reported that Supreme Court nominee Elena Kagan had "banned" military recruiters from Harvard Law School's campus when she was dean, and asked Ross to pay me. After he replied, challenging my facts, I noted  that the source he was citing to bolster Fox's position was actually bolstering mine, and asked him to pay me. He's since responded  with what he calls the "final word" on the matter, a quote from Sen. Jeff Sessions in which Sessions agrees with me -- he says Kagan denied recruiters "equal access to campus" compared to other recruiters, not that she banned them from campus, as Fox falsely reported.
The crux of Ross' position appears to be that the words "banned" and "stonewalled" mean the same thing. They do not. Military recruiters were "stonewalled" by Office of Career Services officials -- they received no help from them. They were not "banned" from campus, as Fox claimed; they could still come on campus, and recruit through the Harvard Law School Veterans Association. Did they receive the same treatment as other recruiters? No -- but that's not what Fox reported. What Fox reported was that they were banned from campus, and that's not true.
While I'm sure Ross has other sources he could cite that support my position and not his, I'm going to move on now to a few more of Fox News' "documented lie[s]." Ross' criteria remove a lot of the most  obvious  lies , but this is what we call a target-rich environment.
Fox News reporters claimed that by potentially using a legislative procedure known as the "self-executing rule" to finalize health care reform in the House, Democrats would be passing health care reform "without actually voting for it." That's false -- in fact, so false that those reporters were often corrected by other Fox News reporters.
Fox News reporters claimed that stolen emails "reveal that scientists use, quote, 'tricks' to hide evidence of a decline in global temperature." That's false.
Fox News reporters claimed that by passing health care reform using the reconciliation process, Democrats would be "changing the rules" and using the "nuclear option." That's false.
Do I anticipate that Ross will actually acknowledge that Fox News lied in these cases and pay me what he owes me? Not really. The examples above are Fox News lies, but they are lies that favor conservatives. As Ross' response to the Kagan example indicates, conservatives have a way of inventing their own facts when the actual facts are against them.
Nonetheless, it would be nice for Ross to demonstrate some of that personal responsibility for which I'm told conservatives are so famous.
Fox Lie: Dems Planned To Pass Health Care Without "A Single Vote"
Definition of "Self-Executing" Rule. One of the newer types is called a "self-executing" rule; it embodies a "two-for-one" procedure. This means that when the House adopts a rule it also simultaneously agrees to dispose of a separate matter, which is specified in the rule itself. For instance, self-executing rules may stipulate that a discrete policy proposal is deemed to have passed the House and been incorporated in the bill to be taken up. The effect: neither in the House nor in the Committee of the Whole will lawmakers have an opportunity to amend or to vote separately on the "self-executed" provision. It was automatically agreed to when the House passed the rule. Rules of this sort contain customary, or "boilerplate," language, such as: "The amendment printed in [section 2 of this resolution or in part 1 of the report of the Committee on Rules accompanying this resolution] shall be considered as adopted in the House and in the Committee of the Whole."
Almost every major bill must obtain a special rule, or resolution, from the Rules Committee permitting immediate floor consideration. The resolution also specifies the amount of general debate time and what amendments will be allowed. A special rule also may contain other bells, whistles, gizmos and gadgets.One of these optional attachments is a self-executing provision, which decrees a specified amendment to have been adopted upon the rule's passage [emphasis added]. In other words, once the House adopts the special rule it effectively has adopted the amendment before the bill has even been called up for consideration [emphasis added].
This example is particularly egregious because after Fox's anchors falsely claimed that the self-executing rule would pass the bill without a vote, they were often corrected by other Fox News reporters, analysts, or guests. Nonetheless, the same anchors would go on to repeat the same false claims in subsequent segments.
SCOTT: Carl, how would this work? You pass a bill without voting on it?
ALI VELSHI: Okay. It's true that this debate has taught all of us a legislative lexicon that most of us never wanted to learn. Reconciliation is a prime example, but not the latest one or the most controversial. That gets me back to what exactly House members will be voting on this week.
CNN's Brianna Keilar joins me now to break it all down. I don't know even where to start. You are introducing us to new terminology that most of us never thought we'd never need to learn, Brianna.
BRIANNA KEILAR, CNN CONGRESSIONAL CORRESPONDENT: Yes. Add this to your lexicon. it's called deem and pass, and this right now is the prevailing strategy for Democrats in the House while they try to pass their health care reform package.
Here's what they're facing, and I've broken this down, honestly, so I don't confuse myself and certainly not you. House Democrats need to pass the Senate bill, but they want to pass changes to the Senate bill, so they would pass it separately in the changes bill.
But the problem is for Democrats there's a lot of vulnerable Democrats who say, "I really do not want to vote on this Senate bill because it's got a whole lot of stuff in it that I don't like." For instance, the so-called Cornhusker kickback, that sweetheart deal worked out in the Senate with the state of Nebraska, or a tax on Cadillac, the so-called Cadillac, high-end health care plans. They want to pare it down with the changes bill.
So, what they are doing, Ali, is taking something called a rule. This is, sort of a procedural vote. Normally, it doesn't do a whole lot. Members of Congress vote on it and they say, hey, we're going to debate for this long. But what they're doing is they're rolling the Senate bill into the rule, and here I'm going to -- I'll staple it together, right? So that we can make it official. It's stuck in there.
And then they would vote on the rule, which would deem that the Senate bill is passed, and then they could emphasize this changes bill. Republicans are screaming about this, Ali, and they say that they're going to force a vote this week about whether or not this tactic should even go forward, Ali.
VELSHI: All right. So, let's keep it in mind. The rule thing. Until now, we thought rule was a four-letter word. But it's actually a methodology, something that they can use to get the bill through. Republican representative Virginia Foxx had something to say about this. She's from North Carolina, let's listen to this together.
REP. VIRGINIA FOXX (R), NORTH CAROLINA: I serve on the Rules committee. They are planning to bring a rule that say if you vote for the rule, you've voted for the bill. That's never happened in the history of this country, and, again, it undermines the rule of law, and the American people will not stand for it.
VELSHI: Now, it's not entirely true. In fact, it's not true at all that it hasn't happened in the history of the country. We've found a few examples of where it's happened in 1993, in 1999. But clearly, the Republicans are not interested in this.
KEILAR: Yes, this has happened many times, if you're talking about the folding in, we call it a self-executing rule. You pass the rule, and whatever's embedded in it will then pass. This has happened, I believe, dozens of times in the last decade. Actually, most recently in February.
And members of Congress, Republicans and Democrats, have done it to give themselves political cover for votes, which is the whole point of this, right? I mean, in February, they did it with the debt ceiling, which was obviously something the Democrats need to pass to increase the debt ceiling. But it's not popular, and so they put it in the rule and it gives them a little cover.
But what you have, Ali, is Republicans going, don't trick us, don't try to fool us. In the rule, we know it's the Senate bill, and we're going to hit Democrats for passing the Senate bill with a lot of unpopular stuff in it. But Democrats standing by it, saying look at the overall package we are passing, not the Senate bill. We're changing this bill.
"Hide the decline" refers to unreliable tree-ring data, not actual temperature readings. The Morning Call of Allentown, Pennsylvania, reported  that Penn State scientist Michael Mann -- whose "trick" was referenced in an email  from Phil Jones, head of the Climatic Research Unit at the University of East Anglia -- "said his trick, or 'trick of the trade,' for the Nature chart was to combine data from tree-ring measurements, which record world temperatures from 1,000 years ago until 1960, with actual temperature readings for 1961 through 1998" because "scientists have discovered that, for temperatures since 1960, tree rings have not been a reliable indicator." Jones has also stated  that it is "well known" that tree ring data "does not show a realistic trend of temperature after 1960," and the Climatic Research Unit at the University of East Anglia has said that "[t]he 'decline' in this set of tree-ring data should not be taken to mean that there is any problem with the instrumental temperature data."
Temperature records show there was no "decline" in actual temperatures to hide. In a December 8, 2009, London Times column , Andrew Watson, research professor at the University of East Anglia explained, "The tree-ring measure declines, but the actual temperatures after 1960 go up." Jones has similarly explained  that "it was absolutely necessary to remove the incorrect impression given by the tree rings that temperatures between about 1960 and 1999 (when the email was written) were not rising, as our instrumental data clearly showed they were." Indeed, measurements from each of the major  climate  centers  show the clear warming trend.
Scientists have stated that the word "trick" is being misinterpreted. Scientists say the word "trick" is a commonly used expression and does not indicate deception. Bob Ward, director of policy and communications at the Grantham Research Institute on Climate Change and the Environment at the London School of Economics, is quoted in a Guardian article  as saying of Jones' email: "Scientists say 'trick' not just to mean deception. They mean it as a clever way of doing something -- a short cut can be a trick." RealClimate also explained  that "[s]cientists often use the term 'trick' to refer to ... 'a good way to deal with a problem', rather than something that is 'secret', and so there is nothing problematic in this at all." Further, Penn State concluded  in an investigation of charges against Mann that they "were not falsifying data; they were trying to construct an understandable graph for those who were not experts in the field. The so-called 'trick' was nothing more than a statistical method used to bring two or more different kinds of data sets together in a legitimate fashion by a technique that has been reviewed by a broad array of peers in the field."
ANDERSON COOPER: John, you know, you read these e-mails, and there's a lot of them. But many of them, I mean, they don't look good.
JOHN ROBERTS: Yes, and even the man who wrote them, Phil Jones, admit that some of them don't look good at the first reading. For example, take this e-mail from 16th of November, 1999. Phil Jones writes, quote, "I've just completed Mike's Nature trick of adding in the real temperatures to each series for the last 20 years to hide the decline."
Now, if you're a skeptic of global warming, you take a look at that e-mail, and you say, "Well, wait a minute. They're trying to manipulate the data, here. They're trying to hide things. They're using a trick to do it."
But I talked to the person that this e-mail was addressed to, and he said no, no, no. What, indeed, Phil Jones was trying to do was he had two different data streams, and one ended at a certain point. And then the other one began, and he was just trying to put the two of them together."
Fox Lie: The Reconciliation Process Is The "Nuclear Option"
The reconciliation process is not  the "nuclear option." "Nuclear option" was a term coined by then-Republican Sen. Trent Lott in 2005 to refer to a possible Republican attempt to change Senate filibuster rules. Reconciliation is a part of the congressional budget process -- no rule change is needed to exercise it. In fact, the procedure was repeatedly used by Republicans to pass President Bush's agenda, including the 2001 and 2003 tax cuts.
JOSH LEVS, CNN CORRESPONDENT: Yes, it's one of those complicated procedures, as we were just hearing there, reported from Washington. So, this is one of those times we kind of stop through a little bit of "Schoolhouse Rock" here for you at the Magic Wall.
We just want everyone to understand why this is even possible and how it would work in the first place. And so we have some fun pictures.
Check this out. This is -- thanks to our graphics designers upstairs, this is what we have to represent a filibuster. Now, as you know, the way it works in the Senate, you need 60 votes to break a filibuster. So, you see a lawmaker here, blah, blah, blah, keeps talking. As a rule, you need these 60 votes; right?
Well, this is what's different now. In budgets, you can do this thing called a budget reconciliation, if you're able to get it inside the budget. And for this year, as CNN reported in the spring, we did. For the 2010 budget, tucked inside of this, we have this, a health care reconciliation.
Now, you can get these reconciliations in. They are debated. And this one was controversial at the time, but it did pass as part of the budget.
Once you have that reconciliation in here, all you need is this, a simple majority in the Senate. So, now, the Senate would only need 51 votes, Drew, to pass this reconciliation.
So, the theory here is, if they cannot get those 60 votes they would usually need to break a filibuster, this is a whole other way to circumvent it and say, you know what? Let's not even worry about. Let's use that reconciliation, get a simple majority of 51 votes, potentially pass the bill.
GRIFFIN: Josh, is that the nuclear option we've heard about in the past?
LEVS: It's actually not. Right, we've heard the "nuclear option" term used, and that was used in the context of trying to get through some judicial nominees against a filibuster. In a way, it's a similar concept, but we're not talking about that term here. That's not the term that's being used. Instead, it's about this specific thing, a reconciliation that got inside that 2010 budget.
Come on, Ross. Pay me my money.


Smeerenburg is on a flat peninsula on the southeastern point of the island of Amsterdamøya in northwestern Spitsbergen. It is one of the only places in the area where the terrain allowed to build and to run a whaling station. It was the Dutch who took advantage of the place and built a station early in the 17th century (see page about 17th century whaling for more background information).
Smeerenburg, which translates as "blubber town", was one of the largest whaling stations in Spitsbergen and certainly the most famous one. Eight companies from different Dutch towns were active there and had at least one blubber oven and 2 buildings. Also a Danish company was involved at times. In its heydays, up to 200 men were working in Smeerenburg during the summer. Remains of the blubber ovens can still be seen, after 4 centuries.


text:
You want to add or remove CSS class names to your Ember Components based on properties of the component.

### Solution
Add property names to the `classNameBindings` property of subclassed components.

### Discussion

You can apply classes based on properties of the component, or even by properties bound to data passed into the component. This is done by binding the class attribute using `classNameBindings`.

```js
classNameBindings: ['active'],
active: true
```

You can also set the class name based on a computed property.

```js
classNameBindings: ['isActive'],
isActive: function() {
  return 'active';
}.property('someAttribute')
```

Another way would be to bind the class name to a bound property.

```js
classNameBindings: ['isRelated:relative'],
isRelatedBinding: "content.isRelated" // value resolves to boolean
```

redpajama_set_name: RedPajamaGithub


text:
Home » All Networks » H-Announce » Announcements
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Call for Abstracts: Archaeologies of Displacement: Heritage, Memory, Materiality
Announcement published by Nour A. Munawar on Tuesday, November 15, 2022
Subject Fields:
Cultural History / Studies, Humanities, Immigration & Migration History / Studies, Middle East History / Studies, Social Sciences
This call for abstracts invites interested researchers to send their abstracts of suggested chapters on the archaeologies of displacement, migration and humanitarian crises, their impact on societies, cultural identity, and collective memory of displaced people around the world.
Book Topic
Displacement and forced migrations were a major feature of the 20th century in many regions of the world and are increasing rather than decreasing in the second decade of the 21st century. Civil wars, conflicts and political unrest have all created movements of refugees and internally displaced people. Other people have fled their homes due to famine, environmental disasters, nuclear or chemical disasters, or major development projects, such as dam building.
Currently, the seemingly endless cycle of violence and conflicts in several areas across the world, such as the Middle East and North Africa (MENA) region, Eastern Europe, Southeast Asia, Central and South America, and Africa has served to create humanitarian catastrophes. In the context of the Middle East, more than 10 million people have left their homes and have been internally displaced or sought refuge in neighbouring countries. Others have made their way through the Mediterranean to reach Northern Europe, stirring up political tensions and debates about the rights of migrants and refugees. Similarly, in the past few months, images and videos highlighted a new wave of migration due to the warfare hostilities in Ukraine. Western media started immediately to report on the humanitarian crisis in Ukraine and how those refugees are "civilized", "educated", "know how to use Instagram", and "very different from the Middle Easterners or Africans" who sought refuge during the last decade. A growing number of activists on social media platforms ironically responded to the Western media double standards and narratives of refuge.
The concept of involuntary displacement offers a powerful tool with which to explore the identities of exiled groups. A close consideration of the mechanisms of forced migration allows us to understand how the decay and loss of material objects such as personal possessions and photographs, which are invested with individual memories, compromise the ability to recall or come to terms with a difficult past life.
Many displaced refugees and migrants seek to safeguard their cultural identities by attempting to maintain contact with their homeland. This can lead to the creation of 're-invented ethnicities' where nostalgic memories of a homeland are added to and embellished in a place of sanctuary. In some cases, the assertion of alien identities can lead to ethnic tensions and hinder integration into new communities. It can also lead to distrust and the segregation or ghettoization of incoming migrants and refugees.
This edited book aims to understand how and why the voices of displaced people are so often forgotten in the narratives of globalisation. We will focus on how the trauma of forced migration creates interconnections between material objects, memories, oral histories and people and explore the potential for creating sustainable archaeologies of displacement. Finally, we will examine how the authentic voices and testimonies of refugees can be used to revive the forgotten and unexplored narratives of global displacement.
We welcome cross-disciplinary proposals from individuals at different stages in their careers, including early and mid-career researchers, academics and practitioners and from a range of methodological and conceptual perspectives.
Please send abstracts (chapter proposals) of 300-400 words to the below emails by 28 February 2023
Editors
Dr. Nour A. Munawar: nour.munawar@dohainstitute.edu.qa
Doha Institute for Graduate Studies & Center for Conflict and Humanitarian Studies – Qatar
Prof. Dr. James Symonds: j.symonds2@uva.nl
University of Amsterdam (UvA) – Netherlands
nour.munawar@dohainstitute.edu.qa
https://chs-doha.org/en/News/Pages/Archaeologies-of-Displacement.aspx
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