text:
\section{Introduction}
If  the neutrino masses are the only sources of Lepton Flavor
Violation (LFV), the rates of
 the Lepton
Flavor Violating  processes such as $\mu \to e\gamma$, $\mu N \to
e N$ and $\mu \to eee$ will be too small to be detectable
 in the foreseeable future. Any
positive signal for such LFV processes will be an indication for new
physics beyond the  Standard Model (SM). Strong experimental bounds exist on the rate
of these processes \cite{pdg} and rich literature has been developed
on the constraints on new physics from these bounds. Currently, the
MEG experiment at PSI is searching for $\mu \to e \gamma$ and will
be able to detect a signal even if Br$(\mu \to e \gamma)$ is as
small as $O(10^{-13})$.

 We can divide the beyond SM scenarios into two
classes: (1)  Models, such as R-parity conserving Minimal
Supersymmetric Standard Model (MSSM), within which only even
numbers of new particles can appear in each vertex; (2) Models,
such as R-parity violating MSSM, within which the number of new
particles in each vertex can be both even or odd. In case of the
first class of models, both $\mu \to e \gamma$ and $\mu \to eee$
can take place only at the loop level. Within these models Br($\mu
\to eee$), being a three body decay, is typically smaller than
Br($\mu \to e \gamma$) so the latter gives stronger bounds on the
LFV parameters ({\it see}, however \cite{deGouvea:2000cf}).
However, within the second class of the models, $\mu \to eee$ can
take place at tree level and its rate can therefore exceed that of
$\mu \to e \gamma$ which is possible only at a loop level. Within
the R-parity violating MSSM, it is possible that while Br($\mu \to
e \gamma$) is too small to be probed even by MEG, Br($\mu \to
eee$) is relatively large and close to its present bound
\cite{deGouvea:2000cf}. A mild improvement on $\mu \to eee$ can
probe R-parity violating MSSM with mass scale well above 10 TeV
which is beyond the reach of the LHC.

Recently it has been shown that by measuring the transverse
polarizations of the final particles in $\mu \to e \gamma$,
$\mu-e$ conversion on nuclei and $\mu \to eee$, one can measure
the CP-violating phases of the general effective Lagrangian
leading to these processes {\cite{eee,Ayazi:2008gk,tracing}. The
possibility of deriving information on the CP-violating phases of
the R-parity conserving MSSM from $\mu \to e \gamma$ and the $\mu
-e$ conversion has been explored in \cite{Ayazi:2008gk}. In the
present {\it letter}, we are going to examine the possibility of
deriving the CP-violating phases of the trilinear R-parity
violating couplings from $\mu \to eee$. These CP-violating phases
are important as they can be responsible for the creation of the
baryon asymmetry in the universe \cite{RprimeRparity}.

The paper is organized as follows. In section~2, we review the
general effective Lagrangian that can lead to $\mu \to eee$ and
$\mu \to e\gamma$. We outline the information that can be derived
on the effective couplings without the measurement of the spin of
the final particles. In section~3, we review the contributions
that the effective couplings receive from the $R$-parity and
lepton flavor violating  trilinear Yukawa couplings. We then
briefly review bounds on these couplings. In section~4, we
introduce the P-odd asymmetry, $\mathcal{A}$, and the transverse
polarization. In section~5, we briefly discuss the feasibility of
measuring the transverse polarization of the final particles. In
section~6, we discuss the results that can be derived by combined
analysis of $\mathcal{A}$ and the transverse polarization. Results
are summarized in section~7.

\section{ Effective Lagrangian in a general framework}
The effective Lagrangian leading to $\mu \to eee$ can in general
be written as \cite{review} \ba \label{effectiveLag}{\cal L}_{\rm eff}&=& B_1
(\bar{\mu}_Le_R)( \bar{e}_R e_L)+B_2( \bar{\mu}_R e_L
)(\bar{e}_Le_R) + \ \ \ \cr &\ &
 C_1
(\bar{\mu}_Le_R)( \bar{e}_L e_R)+C_2 (\bar{\mu}_Re_L)( \bar{e}_R
e_L)+ \cr ~ &\ & G_1 (\bar{\mu}_R\gamma^\nu e_R)(\bar{e}_R\gamma_\nu
e_R)+G_2 (\bar{\mu}_L\gamma^\nu e_L)(\bar{e}_L\gamma_\nu e_L) \cr &
\ &
-A_R~(\bar{\mu}_L[\gamma_\mu,\gamma_\nu]~\frac{q^\nu}{q^2}e_R)~(\bar{e}\gamma^\mu
e)-A_L~(\bar{\mu}_R[\gamma_\mu,\gamma_\nu]~\frac{q^\nu}{q^2}e_L)~(\bar{e}\gamma^\mu
e)+{\rm H.c.}
\ea Notice that by using the identities
$(\sigma^\mu)_{\alpha \beta}(\sigma_\mu)_{\gamma \delta}\equiv 2
\epsilon_{\alpha \gamma} \epsilon_{\beta \delta}$ and $
(\bar{\sigma}^\mu)_{\alpha \beta}=\epsilon_{\beta \delta}
(\sigma^\mu)_{\delta \gamma} \epsilon_{\gamma \alpha}$  (where
$\epsilon_{11}=\epsilon_{00}=0$ and
$\epsilon_{10}=-\epsilon_{01}=1$) and employing the fact that the
fermions anti-commute, we can rewrite the terms on the first line
of Eq.~(\ref{effectiveLag}) as
$$-{B_1 \over 2}(\bar{\mu}_L  \gamma^\nu e_L)(
\bar{e}_R  \gamma_\nu e_R) -{B_2 \over 2}(\bar{\mu}_R  \gamma^\nu
e_R)( \bar{e}_L \gamma_\nu e_L) \ .$$ This effective Lagrangian
leads to \cite{review} \ba Br(\mu \to eee)&=&{1 \over 32
G_F^2}\left[|B_1|^2+|B_2|^2+8(|G_1|^2+|G_2|^2)\right.\cr
&+&{|C_1|^2+|C_2|^2 \over 2}+32(4\log {m_\mu^2\over
m_e^2}-{11}){|A_R|^2+|A_L|^2 \over m_\mu^2} \cr  &-& \left.
64{\Re[A_LG_2^*+A_RG_1^*]\over
m_\mu}+32{\Re[A_LB_1^*+A_RB_2^*]\over m_\mu}\right]\
.\label{EFFlag}\ea By studying the energy distribution of the
final particles, more information can be derived on the effective
couplings. For example, let us consider the contributions  from
$A_L$ and $A_R$ which come from a virtual photon exchange. When
the invariant mass of an electron positron pair goes to zero, the
virtual exchanged photon goes on shell. As a result, the
corresponding Dalitz plot should have a peak at
$(P_{e^-}+P_{e^+})^2=0$ whose height is given by
$|A_L|^2+|A_R|^2$. The combinations that can be derived by
studying the energy distributions of the final particles are
$|G_1|^2+|G_2|^2+(|C_1|^2+|C_2|^2)/16$, $|B_1|^2+|B_2|^2$,
$|A_L|^2+|A_R|^2$, ${\rm Re}[A_LG_2^*+A_R G_1^*]$ and ${\rm
Re}[A_LB_1^*+A_RB_2^*]$ (see for example \cite{review} and
references therein). By studying the angular distributions of the
final particles relative to the polarization of the initial muon,
one can further derive $|G_1|^2-|G_2|^2+(-|C_1|^2+|C_2|^2)/16$,
$|B_1|^2-|B_2|^2$, $|A_L|^2-|A_R|^2$, ${\rm Re}[A_LG_2^*-A_R
G_1^*]$ and ${\rm Re}[A_LB_1^*-A_RB_2^*]$ as well as the CP-odd
quantities ${\rm Im}[A_LG_2^*+A_R G_1^*]$ and ${\rm
Im}[A_LB_1^*+A_RB_2^*]$. A combined analysis of angular and energy
distribution therefore yields the absolute values of all the
effective couplings, $B_1$, $B_2$, $A_L$ and $A_R$ as well as the
CP-violating phases $\arg[A_LA_R^* G_2^* G_1]$, $\arg[A_LG_2^*]$,
$\arg[A_LA_R^* B_1^* B_2]$ and  $\arg[A_LB_1^*]$. Notice however
that there is still some information in Eq.~(\ref{effectiveLag})
that cannot be derived by the methods described above. In
particular, the CP-violating phase arg$[B_1B_2^*]$ cannot be
derived by these methods.  Further information can be obtained by
studying the transverse polarization of $e^-$ in $\mu^+\to
e^+e^-e^+$ \cite{eee}.

Notice that the terms on the last line of Eq.~(\ref{effectiveLag})
come from the effective coupling of the photon which gives rise to
\be \label{muegamma} {\rm Br}(\mu \to e \gamma)=\frac{12 \pi }{
G_F^2 m_\mu^2\alpha} \left(|A_L|^2+|A_R|^2 \right) \ .\ee The
present bound on this LFV rare decay is very strong ${\rm Br}(\mu
\to e \gamma)<1.2\times 10^{-11}$ \cite{pdg} which implies
$|A_L|^2+|A_R|^2<3.3\times{10^{-27}}~{\rm GeV}^{-2}$. Thus, from
Eq.~(3), we observe that the contribution from $A_L$ and $A_R$ to
$\mu \to eee$ cannot be larger than $7 \times 10^{-14}$ so if
Br($\mu \to eee$) turns out to be close to its present bound, we
can safely neglect the contributions from $A_L$ and $A_R$.

\section{Effects of trilinear R-parity violating couplings}
Within the R-parity conserving MSSM, the  slepton mass matrix  as
well as the trilinear $A$-term involving the sleptons include LFV
sources which can induce  the effective Lagrangian in
Eq.~(\ref{effectiveLag}). By relaxing the R-parity conservation,
new sources of LFV emerge. In particular, the R-parity violating
Yukawa couplings in the superpotential \be W={\lambda_{ijk}\over
2} \hat{L}_i \hat{L}_j \hat{E}_k ~~~~~{\rm with}~~~~~
\lambda_{ijk}=-\lambda_{jik} \  \ee add nine new sources of LFV.
That is each nonzero element of $\lambda_{ijk}$ is a source of
LFV. Some of these couplings can contribute to $\mu \to eee$ at
tree level. Throughout this letter, we will focus on the effects
of $\lambda$ and set other LFV sources equal to zero for
simplicity. The nonzero elements of $\lambda_{ijk}$ contain nine
phases out of which three can be absorbed by rephasing
$\hat{L}_i$. In this basis, each of the  bilinear R-parity terms,
$\mu_i^\prime \hat{L}_i \hat{H}_u$  can be considered as a new
source for CP-violation. In this {\it letter}, we will investigate
the possibility of deriving the CP-violating phases of
$\lambda_{ijk}$ from the transverse polarization of the final
particles in $\mu \to eee$.

The contributions to the effective couplings from $\lambda_{ijk}$
have been calculated in \cite{deGouvea:2000cf} and the results are
as follows:
\begin{subequations} \label{Cs}
  \begin{align}
  A_L&=G_2=C_1=C_2=0,\\ \label{Cb}
B_{1}&=\frac{\lambda_{321}^{*}\lambda_{311}}{m^{2}_{\tilde{\nu}_{\tau}}},\\
\label{Cc}
B_{2}&=\frac{\lambda_{211}^{*}\lambda_{212}}{m^{2}_{\tilde{\nu}_{\mu}}}
+\frac{\lambda_{311}^{*}\lambda_{312}}{m^{2}_{\tilde{\nu}_{\tau}}} \\
&-\frac{\alpha}{12\pi} \left[\frac{\lambda_{321}^{*}\lambda_{311}}
{m^{2}_{\tilde{\nu}_{\tau}}}
(-\frac{8}{3}-2\log\frac{m^2_e}{m^{2}_{\tilde{\nu}_{\tau}}}
+\frac{m^2_{\tilde{\nu}_{\tau}}}{3m^2_{\tilde{e}_{R}}})\right.\nonumber\\
&~~~~~~~~+\frac{\lambda_{322}^{*}\lambda_{312}}{m^{2}_{\tilde{\nu}_{\tau}}}
(-\frac{8}{3}-2\log\frac{m^2_\mu}{m^{2}_{\tilde{\nu}_{\tau}}}
+\frac{m^2_{\tilde{\nu}_{\tau}}}{3m^2_{\tilde{\mu}_{R}}})
\nonumber\\ &~~~~~~~~+\left.
\frac{\lambda_{323}^{*}\lambda_{313}}{m^{2}_{\tilde{\nu}_{\tau}}}
(-\frac{8}{3}-2\log\frac{m_\tau^2}{m^{2}_{\tilde{\nu}_{\tau}}}
+\frac{m^2_{\tilde{\nu}_{\tau}}}{3m^2_{\tilde{\tau}_{R}}})\right],\nonumber\\
 G_{1}&= \frac{\alpha}{24\pi}\left[\frac{\lambda_{321}^{*}\lambda_{311}}
{m^{2}_{\tilde{\nu}_{\tau}}}(-\frac{8}{3}-2\log\frac{m^2_e}{m^{2}_{\tilde{\nu}_{\tau}}}
+\frac{m^2_{\tilde{\nu}_{\tau}}}{3m^2_{\tilde{e}_{R}}})\right.\\
&~~~~~~~~+\frac{\lambda_{322}^{*}\lambda_{312}}{m^{2}_{\tilde{\nu}_{\tau}}}
(-\frac{8}{3}-2\log\frac{m^2_\mu}{m^{2}_{\tilde{\nu}_{\tau}}}+
\frac{m^2_{\tilde{\nu}_{\tau}}}{3m^2_{\tilde{\mu}_{R}}})~~~~~\nonumber\\
&\left. ~~~~~~~~
+\frac{\lambda_{323}^{*}\lambda_{313}}{m^{2}_{\tilde{\nu}_{\tau}}}
(-\frac{8}{3}-2\log\frac{m_\tau^2}{m^{2}_{\tilde{\nu}_{\tau}}}
+\frac{m^2_{\tilde{\nu}_{\tau}}}{3m^2_{\tilde{\tau}_{R}}})\right],~~~~~\nonumber\\
A_{R}&=-\frac{\alpha
m_\mu}{48\pi}\frac{1}{m^{2}_{\tilde{\nu}_{\tau}}}
\left[\lambda_{321}^{*}\lambda_{311}
(1-\frac{m^2_{\tilde{\nu}_\tau}}{2m^2_{\tilde{e}_{R}}})
+\lambda_{322}^{*}\lambda_{312}(1-
\frac{m^2_{\tilde{\nu}_{\tau}}}{2m^2_{\tilde{\mu}_{R}}})+
\lambda_{323}^{*}\lambda_{313}(1-\frac{m^2_{\tilde{\nu}_{\tau}}}{2m^2_{\tilde{\tau}_{R}}})\right].
\end{align}
\end{subequations}
Notice that while the couplings $B_1$ and $B_2$ receive  a
contribution at a tree level, $A_R$ and $G_1$ receive
contributions only at the one-loop level.  If $\lambda_{ijk}$ are
the only sources of LFV, up to one-loop level, all other couplings
vanish. As discussed in the previous section,  the values of
$|B_1|^2$, $|B_2|^2$, $|A_L|^2$, $|A_R|^2$, $|G_1|^2+|C_2|^2/16$
and $|G_2|^2+|C_1|^2/16$ can be derived by combining information
from energy and angular distribution of the final particles in
$\mu \to eee$. Thus, the predicted pattern for the effective
couplings from $\lambda_{ijk}$ can be tested this way.

Let us now review the various bounds on the couplings from other
observations. At 1-loop level, the Yukawa couplings,
$\lambda_{ijk}$, contribute to the neutrino mass matrix, $m_\nu$
\cite{bound from neutrino mass matrix barbier} as well as to
processes such as $\tau \to \mu \nu \nu$ , $\tau \to e \nu \nu$
and $\mu \to e \nu \nu$ \cite{Barger:1989rktable,pdg}. The upper
bounds on the components of $(m_\nu)_{\alpha \beta}$ can be
translated into bounds on $\lambda$'s. The prediction of the SM
for charged lepton decay rates agrees with the measured values so
bounds can be set on the contribution from $\lambda$'s. In
particular, comparing the measured and calculated values of the
ratio $R_\tau\equiv {\rm \Gamma}(\tau \to e \bar{\nu}_e \nu_\tau)/
{\rm \Gamma}(\tau \to \mu \bar{\nu}_\mu \nu_\tau)$ gives bounds on
$\lambda$'s. In our analysis, we pick up values of $\lambda$ that
respect these bounds. The bounds that we use are summarized in
Table 1. The third column shows the observable from which the
bound is extracted. Notice that the bound on $\lambda_{12k}$ comes
from the numerical value of the CKM matrix. At first sight, this
might seem counterintuitive. Remember however that the value of
$V_{ud}$ is extracted by comparing $\Gamma(n \to p e \bar{\nu}_e)$
with $\Gamma(\mu \to e \bar{\nu}_e \nu_\mu)$. The unitarity
condition of the CKM matrix combined by the extracted values of
the CKM matrix elements yields a bound on the contribution from
$\lambda_{21k}$. For a full review of the bounds see
\cite{barbier}.

\begin{table}[t]
\begin{center}\begin{tabular}{|c|c|c|c|}\hline Coupling(s)&Bound&Observable&Ref\\\hline\hline
  $\lambda_{133}$&$9.4\times{10^{-4}}~\left(\frac{{m_{\tilde{\tau}_{R}}}}{100~{\rm GeV}}\right)^{1/2}$&
  $(m_\nu)_{ee}$&\cite{barbier}\\\hline
$\lambda_{233}$&$9.4\times{10^{-4}}~{\left(\frac{{m_{\tilde{\tau}_{R}}}}{100~{\rm
GeV}}\right)^{1/2}}$&$(m_\nu)_{\mu\mu}$& \cite{barbier}\\\hline
$\lambda_{i22}$&$1.5\times{10^{-2}}~{\left(\frac{{m_{\tilde{\mu}_{R}}}}{100~{\rm
GeV}}\right)^{1/2}}$&$(m_\nu)_{ii}
$&\cite{barbier}\\\hline$\lambda_{12k}$&$0.03~\frac{m_{\tilde{e}_{kR}}}{100~{\rm
GeV}}$&$V_{ud}$&\cite{Newbounds}
\\\hline $\lambda_{13k}$&$0.03~\frac{m_{\tilde{e}_{kR}}}{100~{\rm GeV}}$&$R_\tau$&\cite{Newbounds}\\\hline
$\lambda_{23k}$&$0.05~\frac{m_{\tilde{e}_{kR}}}{100~{\rm
GeV}}$&$R_\tau$&\cite{Newbounds}\\\hline$\lambda_{i23}\lambda_{j32}$
&$8\times{10^{-7}}~\left(\frac{m_{\tilde{\mu}_{R}}~m_{\tilde{\tau}_{R}}}{(100~{\rm
GeV)^2}}\right)^{1/2}$&$(m_\nu)_{ij}$&\cite{barbier}\\\hline
\end{tabular}\caption{Bounds on the trilinear $R$-parity violating couplings.
The masses of
${\tilde{e}_{R}}$, ${\tilde{\mu}_{R}}$ and ${\tilde{\tau}_{R}}$
are respectively indicated by
$m_{\tilde{e}_{1R}}$, $m_{\tilde{e}_{2R}}$ and
$m_{\tilde{e}_{3R}}$.
}\label{eatsource}\end{center}
\end{table}

\section{Transverse polarization and asymmetry}

Let us define P-odd asymmetry, $\mathcal{A}$, as \be
\mathcal{A}\equiv {\int_{0}^1 (d \Gamma/d\cos\theta)d\cos\theta-
\int_{-1}^0 (d \Gamma/d\cos\theta)d\cos\theta \over \int_{-1}^1 (d
\Gamma/d\cos\theta)d\cos\theta} \ . \label{MathcalA} \ee A nonzero
$\mathcal{A}$ violates parity. In fact, $\mathcal{A}$ is sensitive
to the P-odd combinations such as $|B_1|^2-|B_2|^2$.
 The  polarizations of
the final electron in $\mu^+\to e_1^+ e^-e_2^+$ can be defined as
\be \label{stplus} \langle s_{\hat{T}^-_i}\rangle\equiv {
\sum_{\vec{s}_{e^+_1},\vec{s}_{e^+_2}}\frac{ d\Gamma}{d \cos
\theta}|_{\vec{s}_{e^-}\cdot \hat{T}^-_i =|\vec{s}_{e^-}\cdot
\hat{T}^-_i|  }-\sum_{\vec{s}_{e^+_1},\vec{s}_{e^+_2}}\frac{
d\Gamma}{d \cos \theta}|_{\vec{s}_{e^-}\cdot \hat{T}^-_i
=-|\vec{s}_{e^-}\cdot \hat{T}^-_i|  }\over
\sum_{\vec{s}_{e^+_1},\vec{s}_{e^+_2},\vec{s}_{e^-}}\frac{
d\Gamma}{d \cos \theta} }\ \ee
 where $i=1,2,3$.
$\hat{T}_3^-$ is the longitudinal direction,
$\hat{T}_3^-=\vec{P}_{e^-}/|\vec{P}_{e^-}|$.
 $\hat{T}_1^-$ and $\hat{T}_2^-$ are unit vectors
 in the transverse directions defined as
\be \hat{T}_2\equiv {\vec{s}_\mu \times\vec P_{e^-}\over
|\vec{s}_\mu \times\vec P_{e^-}|} \ \ {\rm and}  \ \
\hat{T}_1\equiv {\hat{T}_2\times\vec P_{e^-}\over
|\hat{T}_2\times\vec P_{e^-}|}. \label{directions}\ee Finally,
 $\theta$ is the angle between the momentum of $e^-$
   and the polarization of the muon:
   $\theta=\arccos [\vec{s}_\mu\cdot\vec P_{e^-}/
   (|\vec{s}_\mu|\cdot|\vec P_{e^-}|)]$ .

As shown in \cite{eee}, while $\langle s_{\hat{T}_3^-}\rangle$ is
sensitive only to the absolute values of the couplings, the
transverse polarizations $\langle s_{\hat{T}_1^-}\rangle$ and
$\langle s_{\hat{T}_2^-}\rangle$ are sensitive to the CP-violating
phases in the effective Lagrangian.
 Straightforward but cumbersome
calculation shows that within the present model with the coupling
pattern in Eqs. (\ref{Cs}),
$$ \langle s_{T_1^-}\rangle \propto \Re[ B_1B_2^*-12 A_RB_1^*]$$
and
$$ \langle s_{T_2^-}\rangle \propto \Im[ B_1B_2^*-12 A_RB_1^*]\ .$$
 Of course, similar
formulas hold for the transverse polarization of the final
positron in $\mu^- \to e^- e^+ e^-$.

\begin{figure}[t!]
\begin{center}
\includegraphics[height=6 in,width=8 in,angle=0]{fridaya.eps}
\caption{Transverse polarization of the  electron in $\mu^+ \to
e^+ e^-e^+$  versus the P-odd asymmetry $\mathcal{A}$ defined in
Eq.~(\ref{MathcalA}).  The input values for masses correspond to
the ones at the $\alpha$ benchmark in \cite{benchmark} with $
m_{\tilde{\nu}_\mu} \simeq m_{\tilde{\nu}_\tau}\simeq 285$ GeV.
Random values between $10^{-5}$ up to bounds in Table 1 are
assigned to the $\lambda$ couplings and points at which ${\rm
Br}(\mu \to eee)\in 5 \cdot 10^{-13}(1\pm 10\%)$ are selected.
 To calculate $\langle
s_{\hat{T}_2}\rangle$ and $\mathcal{A}$, we have set
$\mathbb{P}_\mu =100\%$ and $\theta=\pi/2$ (see definitions in
Eqs.~(\ref{stplus},\ref{directions})). $\varphi_{ijk}$  is the
phase of $\lambda_{ijk}$. Points with different colors and symbols
correspond to a nonzero value for $\varphi_{ijk}$ as described in
the legend. For each set, the rest of phases vanish. For points
shown by $\times$ and $\circ$, the corresponding phase takes
random values at a linear scale from ($0,2\pi$). }
\label{pointsoveregg}\end{center}
\end{figure}
\
\begin{figure}[t!]
\begin{center}
\includegraphics[height=6 in,width=8 in,angle=0]{fridayb.eps}
\caption{The same as Fig.~\ref{pointsoveregg}, except that we have
removed the points at which $8|G_1|^2/(|B_1|^2+|B_2|^2)>0.05$. }
\label{perfect egg}
\end{center}
\end{figure}
Let us suppose ${\rm Br}(\mu \to e ee)$ is measured and found to
be close to $10^{-12}$. Let us moreover suppose that the Dalitz
plots
 reveal that $B_1$ and $B_2$ give the dominant contribution to
this decay as it is expected in the case that LFV effects
originate from $\lambda_{ijk}$. If the MEG experiment at PSI
reports a null result ({\it i.e.,} ${\rm Br}(\mu \to
e\gamma)<10^{-13}\ $), within the context of MSSM (to be tested at
the LHC), such a set of conditions attests our assumption that
$\lambda_{ijk}$ is the prime source for LFV. If MEG also finds a
signal for $\mu \to e \gamma$, other LFV  terms, such as slepton
masses or the trilinear soft supersymmetry breaking terms, might
contribute to Br$(\mu \to e\gamma)$ but as we discussed earlier,
even in this case, we can neglect the contribution from $A_L$ and
$A_R$ to Br($\mu \to eee)$.  LFV terms in slepton masses or the
trilinear soft supersymmetry breaking terms can contribute to
other effective couplings in (\ref{effectiveLag}) but the effect
will be loop suppressed and negligible.
 Notice that
although within the model under our study, $G_1$ and $A_R$ are
given by the same combinations of $\lambda_{ijk}$, $G_1$ is
enhanced by a factor of $\log (m_{\tilde{\nu}}^2/m_l^2)$ so we do
not neglect its contribution  [see Eq.~(\ref{Cs})].
 Neglecting the effects of $A_R$, the formulas for
$\mathcal{A}$, $\langle s_{\hat{T}^-_1} \rangle $ and $\langle
s_{\hat{T}^-_2} \rangle $ will have forms: \be \label{Aformula}
\mathcal{A}={|B_2|^2-|B_1|^2-24|G_1|^2 \over
3(|B_1|^2+|B_2|^2+8|G_1|^2)} \mathbb{P}_\mu \  \ee  and
\begin{subequations} \label{Ss}
  \begin{align}
  \langle s_{\hat{T}_1^-}\rangle &=
   {4 {\Re}[B_1B_2^*] \mathbb{P}_\mu \sin\theta
  \over |B_1|^2(3- \mathbb{P}_\mu
  \cos \theta)+|B_2|^2(3+ \mathbb{P}_\mu\cos \theta)+24|G_1|^2(1- \mathbb{P}_\mu\cos \theta)},\\
 \langle s_{\hat{T}_2^-}\rangle &= {4 {\Im}[B_1B_2^*]  \mathbb{P}_\mu\sin\theta
  \over |B_1|^2(3- \mathbb{P}_\mu\cos \theta)+|B_2|^2(3+ \mathbb{P}_\mu\cos \theta)+24|G_1|^2(1- \mathbb{P}_\mu\cos \theta)}\
  ,
\end{align}
\end{subequations}
in which $ \mathbb{P}_\mu$ is the polarization of the initial
muons.

 Moreover the longitudinal polarization is given by
$$\langle s_{\hat{T}_3^-}\rangle=
{|B_1|^2-|B_2|^2+8|G_1|^2- \mathbb{P}_\mu\cos
\theta\left[ (|B_1|^2+|B_2|^2)/3+8|G_1|^2 \right] \over
|B_1|^2+|B_2|^2+8|G_1|^2+ \mathbb{P}_\mu\cos \theta\left[
(|B_2|^2-|B_1|^2)/3-8|G_1|^2 \right]} \ . $$

 Notice when the
electron is emitted in the direction perpendicular to the spin of
the muon, the transverse polarization is maximal. In our analysis,
we will set $\theta=\pi/2$ which experimentally means we study the
data from the polarimeter collecting electrons with momentum
perpendicular to $\vec{s}_\mu$. If more than a single polarimeter
is installed, more data can of course be collected. The average
polarization can be defined as \be \overline{\langle
s_{\hat{T}_i^-} \rangle} \equiv {\int_{-1}^1\langle
s_{\hat{T}_i^-} \rangle~ [d \Gamma(\mu\to eee)/d\cos \theta]~d
\cos \theta \over \int_{-1}^1 [d \Gamma(\mu\to eee)/d\cos
\theta]~d \cos \theta} . \ee For $i=1,2$, $ \overline{\langle
s_{\hat{T}_i^-} \rangle} = \frac{\pi}{4} \mathbb{P}_\mu \langle
s_{\hat{T}_i^-} \rangle|_{ \theta =\frac{\pi}{2}}.$ It is
noteworthy that if the values of Br$(\mu \to eee)$, $\mathcal{A}$
and $\langle s_{\hat{T}^-_3} \rangle|_{ \theta =\frac{\pi}{2}}$
are measured, the numerical values of $|B_1|$, $|B_2|$ and $|G_1|$
can be derived.

\section{Feasibility of measuring the transverse polarization}

The typical experimental setups devoted to the study of muon decay
(such as the MEG experiment or the experiment at TRIUMF described
in \cite{triumf}) can be summarized as follows. A proton beam
collides on a target producing pions. Charged pions are stopped in
the target and decay at rest into a neutrino and a muon. Muons at
production are 100 \% polarized up to negligible correction due to
the neutrino mass \cite{triumf}. Muons exit the first target and
are transmitted to a second target where they stop and then decay
at rest. Based on the setup of the experiment, muons of either
positive or negative sign can be selected to be transmitted to the
second target. Negative muons would form bound states with atoms
in the second target so we focus on the decay of positive muons
which decay as free states. When muons decay, they are still
highly polarized. The degree of depolarization from the production
to decay depends on the setup of experiment. Especially if only
the muons produced at the surface of the first target are
collected (as it is done both in MEG \cite{Megsite} and in the
experiment described in \cite{triumf}), the depolarization will be
quite negligible. For example, in the TRIUMF experiment described
in \cite{triumf}, the polarization remains above 99\% until the
muon decay in the second target. For the purpose of the present
analysis we can safely replace $\mathbb{P}_\mu=100\%$. Notice that
unlike the case of \cite{triumf}, even a moderate accuracy in
knowledge of $\mathbb{P}_\mu$ will be sufficient to perform the
present analysis so from this aspect, it is easier to carry out
the present measurement \cite{triumf}.

Let us now discuss the possibility of measuring the transverse
polarization of the electron in $\mu^+ \to e^+ e^-e^+$. First, let
us recall  the measurement of the transverse polarization of the
positron in $\mu^+\to e^+\nu_e\bar{\nu}_\mu$ which was carried out
about 25 years ago to extract the Michel parameters
\cite{Burkard:1985wn}.  The outline of the polarization
measurement is as follows. The emitted positrons interact with
electrons in a target which  are polarized in a direction
perpendicular to the momentum of the emitted positrons by a
magnetic field. The electron positron pair annihilate into a
photon pair. By studying the azimuthal distribution of the final
photon pairs, the transverse polarization of the emitted positron
can be determined. In our case, we are interested in measuring the
transverse polarization of the final electron rather than the
final positron. Fortunately, a similar setup can be employed to
determine the transverse polarization of the emitted electron. Of
course in this case instead of annihilation into a photon pair,
the M\"oller scattering ($e_1^- e_2^- \to e_3^- e_4^-$) will take
place. Similar to the case of $e^-e^+\to \gamma \gamma$, the
azimuthal distribution of the final particles carry information on
the spin of the emitted  electron. Let us take the $\hat{z}$
direction to be parallel to the momentum of the emitted electron
(the momentum of $e_1^-$) and take $\hat{x}$ to be in the
direction of the spin of the electron at rest in the magnetized
target ({\it i.e.}, the spin of $e_2^-$):
$$P_1=(\sqrt{k^2+m_e^2},0,0,k) \ \ \ {\rm and} \ \ \
P_2=(m_e,0,0,0)\ . $$ The spin of $e_1$ can be described by $(a \
b)$ where $|a|^2+|b|^2=1$: $$\langle s_x\rangle=2 \Re[ba^*], \
\langle s_y\rangle=2 \Im[ba^*] \ {\rm and} \ \langle
s_z\rangle=|a|^2-|b|^2\ . $$ The angular distribution of the final
particles are described by $(\theta, \phi)$:
$$P_3=(\sqrt{k'^2+m_e^2},k'\sin\theta \cos\phi, k'\sin \theta \sin
\phi,k'\cos \theta) \ {\rm and} \ P_4=P_1+P_2-P_3 \ ,$$ where the
energy-momentum conservation implies
$$k'={m_e k \over m_e +k(1-\cos \theta)} \ . $$  A cumbersome but
straightforward calculation shows that \be \int_0^{2\pi} \frac{d
\sigma}{d \cos \theta~d \phi} \cos \phi d \phi=\ee
$$(|b|^2-|a|^2){k'^4e^4(1-\cos \theta)\sin \theta\over 64\pi
m_e^4(k-k')}\left( {k'(1-\cos \theta)\over (k-k')^2}+{k'(1-\cos
\theta) -m_e \over (k-m_e)^2}-{m_e (1-2k'\cos \theta/k) \over
(k-k')(k-m_e)} \right)$$ and \be \int_0^{2\pi} \frac{d \sigma}{d
\cos \theta~ d \phi} \sin 2 \phi d \phi=\ee
$$\Im[ab^*]{k'^5e^4(1-\cos \theta)\sin^2 \theta\over 64\pi
m_e^4(k-k')}\left( {m_e/k\over (k-k')^2}+{m_e/k \over
(k-m_e)^2}-{1 \over (k-k')(k-m_e)} \right)\ .
$$
Thus, by measuring the partial cross section, $d
\sigma/(d\cos\theta~d\phi)$, and taking the above integrals, $a$
and $b$ (up to an overall phase) can be determined and the spin of
$e_1$ can be therefore reconstructed.

There are two problems that complicate the measurement: (1) In the
lab frame where $e^-_2$ is at rest, the majority of the electrons
are scattered in the forward direction within a narrow cone with
opening angle of $O(2m_e/k)$ where $k\sim m_\mu /3\sim 30~{\rm
MeV}$. The same problem existed in the case of measuring the
polarization of the emitted positron. (2) The scattered electron
$e_3$ can again scatter on the electrons in the magnetized target
before exiting it. Multiple scattering will distort the  azimuthal
distribution in which the information of the spin of the initial
electron is imprinted. The same problem existed is the case of
measuring the spin of the positron as the photons produced in the
electron positron annihilation could Compton scatter on the
electrons in the magnetized target. In both cases, the total
scattering cross section is of order of $e^4/(16\pi m_e k)$.
Fortunately, there are established techniques to overcome these
difficulties.

\section{Combined analysis of $\mathcal{A}$ and $\langle
s_{\hat{T}_2^-}\rangle$}   By rephasing the leptonic fields, three
 out of nine phases in the  $\lambda$ couplings  can be absorbed.
 Let us consider the
basis in which $\lambda_{311}$, $\lambda_{211}$ and
$\lambda_{312}$ are all real. The rest of $\lambda$'s in this
basis can in general be complex among which the phases of
$\lambda_{321}$, $\lambda_{212}$, $\lambda_{322}$ and
$\lambda_{323}$ can lead to a nonzero $\langle
s_{\hat{T}^-_2}\rangle$. We  first concentrate on the phases of
$\lambda_{321}$ and $\lambda_{212}$ which contribute to $B_1$ at a
tree level. We then comment on the rest of phases.
 As we discussed in the previous section,  we can safely replace
 $\mathbb{P}_\mu=100~\%$ and that is what we do in the following.  For any given polarization, our
results can be simply rescaled.

Figs.~1 and 2 demonstrate the dependence of $\langle
s_{\hat{T}^-_2}\rangle$ and $\mathcal{A}$ on the phases. To draw
these scatter plots, we have assigned random numbers at a
logarithmic scale from $10^{-5}$ to the upper bound on
$|\lambda|$'s. ($|\lambda|$'s take up random values in a
logarithmic scale.) As explained in the caption, various values
are assigned to the phase of either $\lambda_{321}$ or
$\lambda_{212}$, setting
 the other one (as well as the rest of phases) equal to zero. The
 phase of $\lambda_{ijk}$ is denoted by $\varphi_{ijk}$.
We have selected the configurations of $\lambda$ for which Br$(\mu
\to eee)$ lies within the range Br$(\mu \to eee)=5\times
10^{-13}(1 \pm 10\%) $. From an experimental perspective, this
means that we have supposed Br$(\mu \to eee)$ is measured to be in
the range $5\times 10^{-13}(1 \pm 10\%) $. The 10\% uncertainty is
a nominal value that we have taken as an example to highlight the
fact that the branching ratio measurement will
 suffer from a finite uncertainty. Our results are robust against varying
 the value of this uncertainty. In fact by rescaling the coupling by
 a $\delta N$ percent, Br$(\mu \to eee)$ will change by $4 \delta N \%$ but
  $\langle s_{\hat{T}_2^-}\rangle$ and  $\mathcal{A}$, being
 ratios, will not vary.

   Points denoted by pink crosses
are the points at which $\varphi_{321}=0 $  and $\varphi_{212}$
takes up random values in $(0,2\pi)$. On the contrary, those shown
by green circles correspond to the cases that $\varphi_{212}=0$
and $\varphi_{321}$ takes random values in the range $(0,2\pi)$.
As seen from the figures, the areas over which pink $\times$ and
green $\circ$ are scattered completely overlap which means if
$|\lambda|$'s are unknown, the two solutions are
indistinguishable. However, valuable information from $\langle
s_{\hat{T}_2^-}\rangle $ can be derived. For example if both
CP-violating phases vanish, $\langle s_{\hat{T}_2^-}\rangle $ also
vanishes (points indicated by green $\nabla$).

Remember that, while  $B_1$ and $B_2$ receive nonzero
contributions at a tree level, $G_1$ receives a contribution only
at a loop level. As long as $G_1$ has a negligible value, for
given $\mathcal{A}$ and Br($\mu \to eee)$, $|B_1|$ and $|B_2|$ are
fixed. It is straightforward to check that, for $|G_1|\to 0$, \be
|\mathcal{A}|<\frac{1}{3} \ \ \ {\rm and} \ \ \ |\langle
s_{\hat{T}_2^-}\rangle |<\frac{2}{3}\sqrt{1-9 \mathcal{A}^2} \ .
\label{boundaries} \ee As seen in the figures, the majority of
points lie inside an oval-shaped region whose boundaries are given
by Eq.~(\ref{boundaries}). These are the points for which the
contribution from loop suppressed $|G_1|^2$ can be neglected.
 As seen from  Fig.~1, there are only few points (about
2 percent of all points) lying outside the oval-shaped region. At
points with $\mathcal{A}<-1/3$, the contribution from $|G_1|^2$
dominates.
 For $\mathcal{A}<-0.5$, we find $|\langle
 s_{\hat{T}_1^-}\rangle|,|\langle
 s_{\hat{T}_2^-}\rangle|\ll 0.1$ which is expected from Eqs.
 (\ref{Aformula}) and (\ref{Ss}).
In Fig.~2, we have removed the points for which
$8|G_1|^2/(|B_1|^2+|B_2|^2)>0.05$. As a result, Fig.~2 does not
include points outside the oval-shaped region. If the pair
$(\mathcal{A},\langle s_{\hat{T}_2^-}\rangle$) turns out to be
outside the oval-shaped region, it means $|G_1|$ is relatively
large.  This can happen if $\lambda_{322}$ is more than  50 times
larger than the rest of $\lambda_{ijk}$ (see Eqs. (\ref{Cs}) and
table 1) so $\mathcal{A}<-1/3$ indicates that the flavor structure
of the $\lambda_{ijk}$ coupling should be hierarchical.

 As mentioned above, in the  limit $G_1\to 0$, for a given
 $\mathcal{A}$ and $Br(\mu \to eee)$, $|B_1|$ and $|B_2|$ are
 fixed so $\langle s_{\hat{T}_2^-} \rangle$ determines $\arg[B_2
 B_1^*]$. Thus, if all the phases except $\varphi_{321}$ are zero,
$\langle s_{\hat{T}_2^-} \rangle$ will determine $\varphi_{321}$.
 This can be seen in Fig.~2. That is impressive that $\varphi_{321}$ can be
 derived  even without knowledge of $|\lambda_{ijk}|$'s  (of course under the
 assumption of a single nonzero phase).
Deriving the value of $\varphi_{212}$ is going to be more
challenging even when we set all the other phases equal to zero.
As seen from Figs.~1 and 2, for a given  $\mathcal{A}$ and a
certain value of $\varphi_{212}$, depending on the configuration
of the absolute values of the $\lambda$'s, $\langle
s_{\hat{T}_2^-} \rangle$ can take any value between zero and its
maximal value which is $(2/3) (1-9\mathcal{A})^{1/2}\sin
\varphi_{212}$.
This is understandable as $B_2$ receives contributions from
various terms (compare Eqs. (\ref{Cb}) and (\ref{Cc})) so unlike
the case of ($\varphi_{212}=0$, $\varphi_{321}\ne 0$), in this
case, the nonzero phase is not given by $\arg[B_1 B_2^*]$.

From Fig.~2, we observe that for $|\mathcal{A}|<0.2$, by
simultaneous measurements of $\mathcal{A}$ and $\langle
s_{\hat{T}_2^-} \rangle$ with reasonable accuracy, even without
independent knowledge of $|\lambda_{ijk}|$, solutions with
($\varphi_{321}=\pi/2$,$\varphi_{212}=0$) and
($\varphi_{321}=\pi/4$,$\varphi_{212}=0$) can be distinguished
(see points denoted by violet $\triangleright$ and pink
$\square$). Notice that all points denoted by red $\vartriangle$
and blue $\triangleleft$  corresponding respectively to
($\varphi_{321}=0$,$\varphi_{212}=\pi/2$) and
($\varphi_{321}=0$,$\varphi_{212}=\pi/4$) lie above the horizontal
axis. Solutions with positive  and negative $\sin \varphi_{212}$
are distinguishable but deriving the value of $\varphi_{212}$
without knowledge of $|\lambda_{ijk}|$ does not seem to be
practical. We have found that
 the contributions  from the
phases that enter only at loop level ({\it i.e.,} $\varphi_{322}$,
$\varphi_{313}$ and $\varphi_{323}$) to $\langle
s_{\hat{T}^-_2}\rangle$ are smaller than $0.1$. Thus, in deriving
the values of $\varphi_{212}$ and $\varphi_{321}$ from $\langle
s_{\hat{T}_2^-} \rangle$, the potential contributions from the
rest of the phases can be ignored.

As  discussed above, an upper bound on $|G_1|$ can considerably
simplify the analysis and solve the degeneracies.  Although
 $|G_1|^2$ (more precisely, $|G_1|^2+|C_2|^2/16$) can  in principle be extracted from  the energy
 distribution of final particles, within the present model, its
 value will most probably be too small to be measured so in practice   only an
 upper bound on $|G_1|$ can be extracted as we have assumed in deriving
 Fig.~2.  Notice that
 $$\lim_{ ~~~~|G_1|\to 0}  \  \frac{\langle s_{\hat{T}_3^-} \rangle
|_{\theta=\frac{\pi}{2}} }{\mathcal{A}}=3\ .$$ That is while if
$G_1$ and $G_2$ (or $C_1$ and $C_2$) gave the main contribution to
$\mu \to eee$, we would expect that $\langle s_{\hat{T}_3^-}
\rangle |_{\theta=\frac{\pi}{2}} /\mathcal{A}=1$. The ratio of
longitudinal polarization to $\mathcal{A}$ can therefore be
regarded as a cross-check for the smallness of $|G_1|$.

 To draw Figs~1 and 2, we have used the spectrum at the
$\alpha$ benchmark \cite{benchmark} as the input: {\it i.e.,} We
have set $m_{\tilde{\nu}_\mu}=m_{\tilde{\nu}_\tau}=285~{\rm GeV}
$. For two reasons, we expect the results to be robust against
varying the input masses: (i) Varying $m_{\tilde{\nu}_\mu}^2$ and
$m_{\tilde{\nu}_\tau}^2$ is respectively equivalent to rescaling
$\lambda_{211}$ and $\lambda_{311}$ (see Eqs. (\ref{Cb}) and
(\ref{Cc})). (ii) Both $\mathcal{A}$ and $\langle s_{\hat{T}_2^-}
\rangle$ are defined as ratios so the dependence on the
supersymmetry scale disappears. We have re-drawn the diagram for
different benchmarks. As expected, the results are not sensitive
to the input for the mass spectrum.

It is noteworthy that if the only sources of LFV are the
$\lambda_{ijk}$'s giving rise to Br$(\mu \to eee)$, Br$(\mu \to
e\gamma)$ will be smaller than $10^{-13}$ so if the MEG experiment
reports a $\mu \to e \gamma$ signal, sources for $\mu \to e
\gamma$ other than $\lambda_{ijk}$'s must exist.

As seen in Figs.~1 and 2, both $\mathcal{A}$ and $\langle
s_{\hat{T}_2^-} \rangle$ can be relatively large so as long as the
errors in their measurement ({\it i.e.,} $\delta \mathcal{A}$ and
$\delta\langle s_{\hat{T}_2^-} \rangle$) are below $\sim 0.1$,
their nonzero values can be established. Suppose the numbers of
electrons studied to derive $\mathcal{A}$ and $\langle
s_{\hat{T}_2^-} \rangle$ are respectively $\mathcal{N}_A$ and
$\mathcal{N}_s$. We roughly expect the statistical errors to be
$\delta \mathcal{A}\sim 1/\sqrt{\mathcal{N}_A}$ and $\delta
\langle s_{\hat{T}_2^-} \rangle\sim 1/\sqrt{\mathcal{N}_s}$. To
derive $\mathcal{A}$, the majority of the emitted electrons can in
principle be employed, so with a few hundred $\mu^+\to e^+e^-e^+$
decays, the statistical error in the measurement of $\mathcal{A}$
will be reasonably small and below 0.1.  However, we expect only a
fraction of the emitted electrons, $r$,  to enter the polarimeters
so for establishing nonzero $\langle s_{\hat{T}_2^-} \rangle$, the
total number of $\mu^+\to e^+e^-e^+$ decays has to be larger than
$100/r$. That is if $r\sim 10 \%$, the total number of $\mu^+ \to
e^+e^-e^+$ has to be larger than a few thousand.

In the above analysis, we have employed information on the
$R$-parity violating couplings from only the LFV rare decays. The
R-parity violating couplings can  in principle be directly
measured by accelerators. $|\lambda_{i11}|$ leads to a resonant
production of $\tilde{\nu}_i$ in a $e^-e^+$ collider ($e^-e^+\to
\tilde{\nu}_i$) so  $|\lambda_{i11}|$ can be derived provided that
$|\lambda_{i11}|>10^{-5}$ and the center of mass energy is equal
to the mass of $\tilde{\nu}_i$ \cite{sneutrinodecay,barbier}.
Moreover, the $\lambda$ couplings can lead to $\tilde{\nu}_i \to
l_j^+l_i^-$, $\tilde{\chi}_1^0 \to \bar{\nu}_i l_j^+l_k^-$ and
$\tilde{\chi}_1^+\to \nu_k\bar{\nu}_i l_j^+,l_i^+l_k^+l_j^-$
\cite{Barbier:1998fe,barbier} where $\tilde{\chi}_1^0 $ and
$\tilde{\chi}_1^+$ are the lightest neutralino and chargino. Thus,
by measuring the decay length and the flavor of the final charged
leptons, $|\lambda_{ijk}|$ can in principle be extracted. If
$|\lambda_{ijk}|<\mathcal{O}(10^{-5})$, the decay length will be
too small to be resolved \cite{barbier}. This method is therefore
sensitive only to the values of $|\lambda_{ijk}|$ smaller than
$\mathcal{O}(10^{-5})$.\footnote{Even if the decay length is not
resolved, a combination of $|\lambda|$'s may be extracted. For
example, consider chain processes $e^-e^+\to Z^*\to \tilde{\nu}_i
\bar{\tilde{\nu}}_i$ and the subsequent decays $\tilde{\nu}_i\to
e^- \mu^+$ and $\bar{\tilde{\nu}}_i\to \mu^- \mu^+$. Such a chain,
being LFV, is not contaminated by the SM or $R$-parity conserving
MSSM so even if the decay lengths of $\tilde{\nu}_i\to e^- \mu^+$
and $\bar{\tilde{\nu}}_i\to \mu^- \mu^+$ are too short to be
resolved, the possibility of deriving information on the relevant
couplings is still open. Considering all such possibilities is
beyond the scope of the present letter.} If  $|\lambda|$'s are all
smaller than $10^{-5}$, each $|\lambda_{ijk}|$ might be extracted
from $\tilde{\nu}_i\to l_j^+l_i^-$, $\tilde{\chi}_1^0 \to
\bar{\nu}_i l_j^+l_k^-$ and $\tilde{\chi}_1^+\to \nu_k\bar{\nu}_i
l_j^+,l_i^+l_k^+l_j^-$ but in this case $Br(\mu \to eee)$ will be
too small ($Br(\mu \to eee)<10^{-16}$). Let us now consider the
range, $m_{susy}\sim 100$~GeV,
$\lambda_{211},\lambda_{311}>10^{-3}$ and $\lambda_{ijk}\sim
10^{-5}$ with $ijk\ne 211,311$. In this range, $e^-e^+\to
\tilde{\nu}_i$ yields $|\lambda_{i11}|$ and Br$(\mu \to eee)$ is
close to the present bound. Moreover, for $ijk\ne 211,311$,
$\tilde{\nu}_i\to l_j^+l_k^-$ and $\tilde{\chi}_1^0 \to
\bar{\nu}_i l_j^+l_k^-$ will have a resolvable decay length but
the point is that the decay modes involving $\lambda_{211}$ and
$\lambda_{311}$ will dominate and lead to a decay length too short
to be observable: e.g., $\Gamma(\tilde{\nu}_\mu\to
e^+e^-)/\Gamma(\tilde{\nu}_\mu\to \tau^+\tau^-)\sim {10^4}$. Thus,
even in case that the $R$-parity conserving decay modes are
kinematically forbidden, extracting the decay lengths  will be
quite challenging. Let us however suppose that these experimental
difficulties are partly solved and certain $|\lambda_{ijk}|$ (but
not necessarily all) are measured. Such achievement might not be
out of reach  if $\lambda_{i11} \sim 10^{-4}$ and the rest of
$\lambda$'s are of order of $10^{-5}$. Complementary information
can then be derived from Br($\mu \to eee$), $\mathcal{A}$ and
$\langle s_{T_2^-}\rangle $: Neglecting the $|G_1|^2$ effects,
Br($\mu \to eee$) and $\mathcal{A}$ give $|B_1|$ and $|B_2|$ which
to leading order correspond to
$|\lambda_{311}|\cdot|\lambda_{321}|$ and $|
\lambda_{211}^*\lambda_{212}+(m_{\tilde{\nu}_\mu}^2/
m_{\tilde{\nu}_\mu}^2)\lambda_{311}^*\lambda_{312}|$,
respectively. Thus, if $\lambda_{311}$ is extracted from $e^+ e^-
\to \tilde{\nu}_\tau$ at ILC, the measurement of  Br($\mu \to
eee$) and $\mathcal{A}$ gives $|\lambda_{321}|$. If
$|\lambda_{211}|$, $|\lambda_{212}|$, $|\lambda_{311}|$ and
$|\lambda_{312}|$ are all derived by accelerators, this method
will give the phase of $\lambda_{212}$. The measurement of
$\langle s_{\hat{T}_2^-}\rangle$ will then yield the phase of
$\lambda_{321}$.

\section{Conclusions and discussion}
The trilinear $R$-parity violating Yukawa couplings,
$\lambda_{ijk}\hat{L}_i\hat{L}_j \hat{E}_k/2$ can lead to $\mu \to
e ee$. In particular, $\lambda_{321}$, $\lambda_{311}$,
$\lambda_{211}$, $\lambda_{312}$ and $\lambda_{212}$ contribute to
$\mu \to e ee$ at tree level. By rephasing the lepton fields, we
can go to a basis in which $\lambda_{311}$, $\lambda_{312}$ and
$\lambda_{211}$ are real. This exhausts the freedom to rephase the
other fields so $\lambda_{321}$ and $\lambda_{212}$ can in general
be complex and can be considered as sources for CP-violation.
Their phases can induce transverse polarization for $e^-$ in the
direction $\hat{T}_2^-=\vec{s}_\mu \times
\vec{P}_{e^-}/|\vec{s}_\mu \times \vec{P}_{e^-}|$. Thus, by
measuring this polarization, one can derive information on the
CP-violating phases. We have shown that for maximal CP-violation,
$|\langle s_{\hat{T}_2^-} \rangle|$ can reach 2/3 so with a
moderate sensitivity to $\langle s_{\hat{T}_2^-} \rangle$,
CP-violation can be established. The sign of the CP-violating
phase can also be determined by measuring the sign of $\langle
s_{\hat{T}_2^-}\rangle$.

We have also studied the $P$-odd asymmetry, $\mathcal{A}$ defined
in Eq.~(\ref{MathcalA}) and discussed the information that from a
combined analysis of $\mathcal{A}$ and $\langle s_{\hat{T}_2^-}
\rangle$ can be obtained. For the majority of the $\lambda$
configurations, the tree level effects dominate so the effective
coupling $|G_1|$ is much smaller than $|B_1|$ and $|B_2|$ and its
effects can therefore be neglected. In this case, $|G_1|$ will be
too small to be measured but an upper bound can be put on $|G_1|$
by studying the energy distribution of the final particles in $\mu
\to eee$ or as discussed in the present paper by combining
information on $\mathcal{A}$, Br($\mu \to eee$) and $\langle
s_{\hat{T}_3^-} \rangle$. We have noticed that if
$8|G_1|^2<0.05(|B_1|^2+|B_2|^2)$, the analysis becomes much
simpler because of two reasons: (i) The contributions of the
phases of $\lambda_{322}$, $\lambda_{323}$ and $\lambda_{313}$ to
$\langle s_{\hat{T}_2^-} \rangle$ can be neglected. These are the
couplings that contribute only at a loop level. (ii) For given
$\mathcal{A}$ and Br($\mu \to eee$), the absolute values of $B_1$
and $B_2$ are fixed which simplifies  the analysis. In particular,
restricting the analysis to a single CP-violating phase, the
simultaneous measurement of $\mathcal{A}$ and $\langle
s_{\hat{T}_2^-}\rangle$ yields the phase of $\lambda_{321}$ even
if the values of $|\lambda_{ijk}|$ are not a priori known.
Degeneracies however exist between solutions for which  the phases
of $\lambda_{212}$ and $\lambda_{321}$ are both nonzero. By
measuring $\mathcal{A}$ and $\langle s_{\hat{T}_2^-}\rangle$,
different classes of solutions can be distinguished. If the
absolute values of $\lambda$ are measured by an accelerator-based
experiment (or by some other methods), the measurements in $\mu
\to eee$ can yield both phases. In fact, if the tree level
contribution dominates, the relevant $\lambda$ parameters can be
over-constrained.

 Neglecting the contribution of $|G_1|$,
we find $-1/3<\mathcal{A}<1/3$ and $-2\sqrt{(1-9
\mathcal{A}^2)/9}<\langle s_{\hat{T}_2^-}\rangle< 2\sqrt{(1-9
\mathcal{A}^2)/9}$.
 Only at a small fraction of the parameter
space where ($\lambda_{322}\gg$ rest of $\lambda$), the loop
effects can dominate and  lead to $\mathcal{A}<-1/3$. Within the
model under consideration, $\mathcal{A}<-1/3$ therefore indicates
a hierarchical flavor structure for the $\lambda$ parameters.

Stopped $\mu^-$ would form bound states with the atoms before they
decay. Because of this technical difficulty, we have concentrated
on the decay of $\mu^+$ and the spin of the final electron emitted
from it.
  Similar consideration holds for the positron
 in free decay of negative muon; {\it i.e.,} for $e^+$ in
 $\mu^- \to e^- e^+e^-$. Within the present model, the
  transverse polarizations of the  electrons in $\mu^- \to e^- e^+e^-$
  (or that of the positrons in $\mu^+ \to e^+ e^-e^+$)
  are loop-suppressed.

There are established techniques to measure the transverse polarization
of the positron based on the azimuthal distribution of
 the photon pair produced by the annihilation of the positron on the polarized
electrons in a thin magnetized target \cite{Burkard:1985wn}. We
have shown that a similar setup can be employed to measure the
transverse polarization of the electrons, too. In fact, the
azimuthal distribution of the final electrons in M\"{o}ller
scattering, $e_1^- e_2^- \to e_3^- e_4^-$ with polarized $e_2^-$
is sensitive to the polarization of $e_1^-$. The challenges before
this measurement are similar to the ones in \cite{Burkard:1985wn}
and can be overcome by similar methods.

  One can repeat similar discussion for three body LFV decays of
  $\tau$ lepton such as $\tau \to \mu \mu \mu$ or $\tau \to eee$.
  The measurements of the angular distribution and polarization of
  the final particles in these
decays can provide complementary information on the
$\lambda_{ijk}$ couplings. Such a study will be presented
elsewhere.

\section*{Acknowledgement}
S. N. would like to thank Prof. F. Arash for useful discussions.
She is also grateful to the physics department of IPM for the
hospitality of its staff and the partial financial support.

redpajama_set_name: RedPajamaArXiv


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Building your very own custom yacht is perhaps one of the greatest joys of success. It is your personal place of peace, freedom, adventure, relaxation, and most of all, fun! In order for every customer to enjoy their very own personal sanctuary, Numarine offers one of the most extensive warranties in the industry. We are so confident in our products that we are able to offer a full ten-year structural warranty, along with a two-year bow-to-stern warranty. Numarine's highly efficient building techniques, coupled with industry leading technology, allows your fully customized dream yacht to be delivered in as little as 25 weeks. By partnering with industry leaders such as Bradford Marine for warranty and service for all Numarine products, our clients can rest assured knowing that they not only have one of the finest yachts available today, but they will also enjoy the finest service in the industry to make ownership truly a pleasure.
Please Contact Numarine USA for more details.


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MG eZS electric car coming to Australia in 2020
Mike Costello
First electric Chinese SUV for our market due next year: a small crossover to rival the Kona Electric.
MG Motor's Australian factory distributor has confirmed it will launch a fully electric version of its increasingly popular petrol-fired ZS small SUV during the course of 2020.
The Mazda CX-3-sized MG eZS will give the company a rival for the just-launched Hyundai Kona Electric, the Hyundai Ioniq, and the Nissan Leaf in Australia's fledgling EV market. It will be China's first EV in Australia, and should be a bit of a marketing coup.
The eZS has a 110kW/350Nm electric motor, powered by a 45.6kWh lithium battery pack, with a claimed NEDC driving range of 335km. That's about 50 per cent less than the long-range Hyundai Kona with its larger 64kWh battery capacity, but thereabouts with the Leaf.
MG's city-focused crossover has an AC charging time of six hours but more importantly can be charged from empty to 80% on a DC fast charger in 30 minutes. It also sprints from 0-50km/h in 3.1 seconds.
We don't know what it will cost in Australia yet, though its smaller battery capacity should see it well and truly undercut the $59,990 Kona, given every extra kWh adds about $US250 to the package. We'd hope it could give the $40,000 mark a nudge, undercutting the Ioniq too.
MG's parent company is largely government-owned SAIC, based in Shanghai. This monolithic organisation sold more than seven-million cars in 2018 around the world, between its joint-venture Volkswagen and GM product and its MG, Roewe and LDV/Maxus brands.
It also sold 140,000 'NEVs' (electrified vehicles) last year and is at the cutting edge of automotive 5G integration. It's worth remembering that China is the world's biggest electric car market, and in this space is quite formidable.
There appear to be two equipment grades in the eZS, the Com and Lux. Both have an 8.0-inch touchscreen, Apple CarPlay/Android Auto, keyless entry, adaptive cruise control, lane-departure warning and AEB. The Lux has leather seats and a sunroof.
Bringing a fully electric version of the ZS to the ANZ (Australia and New Zealand) is a natural step," said MG Motor Australia's CEO Peter Cao.
"New energy is an important area of exploration in ANZ and we're inspired to see the continued innovation emerging from the global SAIC technical centre of excellence."
MG Australia is chugging along nicely, up 500% on last year across Q1 in 2019, with 32 dealers nationwide.
In January 2019 it sold 503 cars, up 10-fold over the same month in 2018. For context, that means it outsold more established marques like Land Rover (458), Volvo (431), Skoda (408), Jeep (375), Mini (328) and Peugeot/Citroen (185 combined).
This was no outlier, really. In 2018 MG sold an impressive 3007 vehicles for the year, up 400 per cent. It beat Peugeot (2838) and Fiat (2412), and came pretty close to knocking off fellow formerly-British-brand Mini (3590).
MORE: MG news, reviews, comparisons and videos
Video: 2021 MG ZST - walkaround
2019 MG ZS range review
Video: 2021 MG ZST first drive review
Video: 2021 MG ZS EV first drive review

redpajama_set_name: RedPajamaCommonCrawl


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Launch into the New Year with the Tricentis Academy! Certified trainers from the Tricentis Academy are hosting one-hour MOOCs, or Massive Open Online Courses, covering various topics related to working in Tricentis Tosca Testsuite. Each session will include live demonstrations of practical skills, followed by a question and answer session.
The upcoming sessions are recommended for all Tosca users looking to advance their hands-on skills. All MOOC sessions are offered free of charge and open to everyone. Choose between two session times for each topic and register using the links below.
Unable to join the live sessions? Stay tuned for recordings of all the sessions which can be downloaded and viewed at your own leisure. To view previous MOOCs and other helpful videos from Tricentis, visit our channel.


Journal of Business Sciences (JBS) is an open-access bi-annual journal published by Research Excellence Institute (REI). JBS invites research papers on various research themes relevant to business sciences. The journal is interested in publishing research papers that provides sound and clear theoretical insights with practical implications for the business and societal wellbeing. JBS calls for papers on any business sciences topic that challenges the traditional wisdom of the readers. The topics may include a wide range of research areas, for examples, management, marketing, finance, economics, banking, accounting, human resources management, international business, tourism management, entrepreneurship development, business ethics, corporate governance, information management, and any other area that can fall under the scope of business sciences discipline. Postgraduate students are encouraged to make their submissions too.
Journal of Business Sciences (JBS) is an open access, peer-reviewed, and refereed journal published by Research Excellence Institute, South Africa. Journal of Business Sciences (JBS) aims at promoting an interdisciplinary approach by covering a large range of merging ideas from business and social sciences. The objective of JBS is to become a leading African Journal that provides an intellectual platform for scholars worldwide to share knowledge.
The Research Excellence Institute intend to publish online the selected Research papers as soon as possible.
Paper Formatting Guidelines Important Papers that do not follow the guidelines as specified below may be returned to authors for re-formatting. We also request that you proofread your paper carefully to ensure that it is free of technical errors in usage, punctuation, etc. Some authors may wish to consider having their papers checked for consistency of English language usage before submission.
Please do not include headers/ footers or number the pages.
Please use the format below for the formatting of the entire paper.
An abstract of no more than 300 words should be provided. It should be in running prose with no sub-headings.
The section heading is applied to the header of the Abstract, Introduction, Literature Review, Methods, Findings, Conclusion, and References.
Galley. K. E. (Ed.). (2004). Global climate change and wildlife in North America. Bethesda, MD: Wildlife Society.
Greenhouse effect. (2005). American heritage science dictionary. Boston, MA: Houghton Mifflin.


United Yacht Sales New Jersey would love to guide you through a personal showing of this 144' Baglietto 2001 2001. This yacht for sale is located in Unknown Italy and priced at $7,950,000. For a showing please contact us by filling out the form on this page and we will get back to you shortly!


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1. White Noise
2. Mexican Grand Prix
3. Rano Pano
4. Death Rays
5. San Pedro
6. Letters to the Metro
7. George Square Thatcher Death Party
8. How to Be a Werewolf
9. Too Raging to Cheers
10. You're Lionel Richie
Other Records by Mogwai
Mogwai: Special Moves
Mogwai: The Hawk is Howling
Aloha Hawaii: Towns On The Moon EP
Mogwai: Zidane: A 21st Century Portrait
Mogwai: Mr. Beast
Mogwai: Government Commissions: BBC Sessions 1996-2003
Hardcore Will Never Die, But You Will
(Rock Action/Sub Pop; 2011)
By George Bass | 15 February 2011
Mogwai's seventh studio album is the product of a creative re-think, plus the fact that the members now work out of two separate continents. One of only a handful of post-rock groups to get less embarrassing while aging, Stuart Braithwaite and his antagonistic Glaswegians are like the Manic Street Preachers in reverse: angry, anti-pantomime, and talking forever less and less about dead ex-members. (OK, so Brendan O'Hare might not actually be dead, but the rest of band isn't scouring his diary archives in the hope of finding new song lyrics.)
The last two Mogwai albums, however, allowed fans to spot a pattern: Mr. Beast (2006) and The Hawk is Howling (2008) appeared to be cut from identical templates, with the same piano buildup, the same guitar nuke on track two, and the same vaguely underwhelming aftertaste once the final track had exploded. Had Mogwai hired Dan Brown to be Head of Creative Continuity? Could there be a secret Word Document Assistant somewhere that only Stuart Braithwaite, Dominic Aitchison, Martin Bulloch, Barry Burns, and John Cummings had access to—one which told them where to press shift, and when to bash the fuck out of the effects pedal?
If there is, then Mogwai have dumped it for Hardcore Will Never Die, But You Will, which sees them struck by the same telepathic enthusiasm members had when they first shaved their heads in tandem. It's a visible jump from the Mr. Beast outline, and precisely the kind of digital revamp they needed after the angry formulae of Hawk. In fact, I'm not even sure most of it strictly qualifies as post-rock: once you get past the optimistic snaps of "White Noise"—which sounds like Sigur Rós being kicked into a drum kit the size of a theme park pyramid—the band drop "Mexican Grand Prix," their biggest departure to date, and the one that's had the all Young Team (1997) fanboys harumphing. Its disco glitch and neon thumping manage to sound both '80s and medieval simultaneously, and despite the bass loops, church organs, and click tracks all clamoring for attention, it's the resurrection of Barry Burns' processed muttering that grabs one straight away. Yes, lyrics are back, though if you can make out anything bar the "keep running" mantra your ears are a lot sharper than mine are. "Mexican" is just the start of at least four genre facelifts, with the raucous biker rock of "San Pedro" writhing enough to keep non-bikers interested. "Pedro"'s grunts might be the steak and chips of the setlist, but Mogwai haven't forgotten what they learned from Michael Mann: the sale is made in the detailing.
Aside from the experimental flourishes, the more recognizable material on Hardcore doesn't suffer when compared to the new stuff. Mogwai can still make their guitars sweep like a lighthouse, and still know when to order those Rock Action (2001) droid voices to chirp at the onslaught of distortion. The droids get excused for "Rano Pano," though, as all that's needed there is a riff so fuzzy people in velcro could get snagged. It's a boiling little thrash number with guitars so mean they could stand eyeball-to-eyeball with the dubstep kids. "Letters to the Metro" is its cleaner, scuffling twin, as well as my go-to sad song for weeks to come, as sorry as Jeff Buckley the night he went swimming. For this one, the band uses fragile, lofty piano to bridge one seriously forlorn drum beat, with Braithwaite's guitar mewling so cutely you might want to attack it with hammers. These don't feel like moods thrown in for variety, just natural switches in direction from a band whose tantrums help keep it in the press.
Perhaps, though, Hardcore is Mogwai's first record to not need a pre-release spat. When it pines, it pines well, doing all the right chimes and right brooding, and when it kicks Sigur Rós, it kicks them well too. What it does even better is the new stuff, nearly all of which helps break the perceptible rut the band was in danger of entering. The likes of "George Square Thatcher Death Party"—lauded by the majority, played repeatedly by me—is a pep talk every motivational speaker dreams he or she could give, rocking ecstatically while Barry Burns howls like he's just won Euromillions. Phyllida Lloyd, please please please can you earmark this while shooting The Iron Lady?
Even Mogwai's sense of humor feels renewed as they sign off with the Spanish answerphones/Billy Corgan stunts of "You're Lionel Richie," which will hopefully attract more than just slander claims and encourage people to play side A again. Most people will anyway: Mogwai albums have always been inconsistent (there's far, far too much love for "With Portfolio" and "Like Herod" from their debut), but Hardcore Will Never Die, But You Will seems to be their most equable work so far. You can understand them releasing the remaster of 1999's Come On Die Young as backup—twenty-minute monoliths are a rare treat these days—but if Mogwai are looking for new routes to explore then Hardcore is a strong first venture. And hey: kudos to them for breaking the formula, because with their profile it'd be easy to play safe and stubbornly stick to the straights. Right, Rivers Cuomo?
:: myspace.com/mogwai


According to Professor Shah Ebrahim and Dr Juan-Pablo Casas, the study by the Cholesterol Treatment Trialists (CTT) published in The Lancet confirms the efficacy of statins for prevention of cardiovascular disease in people without previous cardiovascular disease and resolves concerns about possible serious side effects. It finds that statins reduce the risk of major vascular events (heart attacks/strokes/coronary artery surgery) by 20% in people of low to high risk of CVD and suggests that treatment guidelines might need to be reconsidered.
The current threshold for statins prescription is a 10-year CVD risk of at least 20% – this applies to half of men over 50 and 30% of women over 60 in England. In an accompanying Commentary in The Lancet, Professor Ebrahim and Dr Casas point out that if the threshold was lowered to 10% based on the findings of the study, 83% of men over 50 and 56% of women over 60 would be classified as needing a statin.
Professor Ebrahim, Professor of Public Health at the School, said: "This research provides further evidence that statins are an effective and safe way of reducing the risk of heart attacks and strokes even among people at quite low risk of these conditions.
"But it also raises a number of important questions for the NHS and clinical practice.
"If we were to go down the road of prescribing statins to everyone there is a risk that doctors' attention may not focus on high-risk groups who would benefit most in absolute terms from statins – and in whom under use of statins is still far too common.
"However, the benefits of giving statins to everyone over the age of 50 would probably save the NHS money in the long run, owing to the savings in health care costs from the heart attacks and strokes prevented.


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Mexican American Holiday Spirit, Alameda Style
December 16, 2010 at 6:04 pm	(Alameda)
Nothing like a Super Bean And Cheese Burrito [no hot sauce, no quacamole, no spel good] at Ramiro & Sons, on Alameda Ave. Then, a walk to the beach for an Alameda sunset.What a treat to live here!
Kittatinny Camp's Gary Gross Passes Away
December 11, 2010 at 3:37 pm	(Kittatinny Camp)
NEW YORK (AP) — Garry Gross, a fashion photographer known for his 1970s nude images of Brooke Shields, taken when she was 10 years old, has died in Manhattan, his sister said Tuesday. He was 73.
His sister, Linda Gross, said he died Nov. 30 from a heart attack at his home in the Greenwich Village neighborhood. "He'll be sorely missed by family and friends alike," his sister said when reached by The Associated Press by telephone at his studio.
Though Garry Gross earned his reputation as a celebrity image-maker — his pictures graced the covers of albums by Whitney Houston and Lou Reed — in 2002 he switched careers and became certified as a dog trainer.
Most recently, he had turned to photographing portraits of canines, including such notable dogs as talk show host Rachael Ray's pit bull Isaboo.
But it was the 1970s images of Shields that marked his career most significantly.
In 1975, the actress' mother, Teri Shields, consented to allow her daughter, then a child model, to be photographed nude for a Playboy Press publication. She and her mother earned $450 for the shoot, which included a full-frontal nude image of the girl standing in a bathtub. When Shields' acting career took off years later, she said she was embarrassed by the continued circulation of the images. At 17, Shields sued Gross in New York to stop him from selling the images, arguing they were an invasion of her privacy and caused her embarrassment.
But after a lower court granted her an injunction, the state's Court of Appeals decided 4 to 3 that the teenager could not break the contract signed by her mother that allowed Gross to take the pictures.
The court said Gross could continue to market the photos except to pornographic publications.
The photo shoot continued to make headlines decades later. In 2009, one of the images, appropriated by American artist Richard Prince for a work, had to be withdrawn by the Tate Modern museum in London after Scotland Yard warned that the image could break obscenity laws.
Jane Feldman, who managed the studio on Broadway and East 20th Street where the photographs of Shields were taken, said they were part of a series intended to explore young women coming of age.
"Garry saw it as art," she said. "It's an exploration, but it was done with great respect," she added. "Yes, it's intriguing, it's provocative."
But she said the protracted court battle cost him his career, saddling him with legal fees and marring his reputation among art directors.
"He went through periods of times where he was really angry about it," she said.
Gross was born in New York City on Nov. 6, 1937. After college, he studied under photographers Francesco Scavullo, Lisette Model and Richard Avedon.
After winning the court case against Shields in 1981, Gross went to Italy, where he worked for an agency. Upon returning to the U.S., he left the fashion industry and became a dog trainer in 2002.
It was while training dogs that he became interested in photographing them and soon grew interested in the plight of senior dogs, his sister said.
"He was very concerned about the destiny of old dogs," Linda Gross said. "When their owners die, they end up in shelters. But people don't typically want to take them home."
She said he had hoped to produce a book about aging dogs and had taken many photographs for the yet-unpublished work.
Copyright © 2010 The Associated Press
Here's Brooke:
Helen Does Chicago
December 6, 2010 at 10:51 am	(Kittatinny Camp)
KLC"s Helen Pearson Friedman readies for winter in Chicago.


text:
On March 20th, 2014, Ella McCray disappeared.
There were six witnesses to her disappearance.
Six conflicting accounts of what happened to her.
Who is lying? Who is telling the truth? And what really happened to Ella?
You can support the show by visiting https://www.patreon.com/sixdisappearancespod or by subscribing and leaving a review at your favorite podcatcher.
For episode content warnings and other information, visit https://www.sixdisappearancespodcast.com/
For episode-specific content warnings, visit https://www.sixdisappearancespodcast.com/about
This show is written by Jamie Killen. Sound design and original music by Jon Erik DeGuzman and Dog and Pony Studios.
The Six Disappearances of Ella McCray ZoomDoom Stories
Recordings of Persons of Interest A-F: Season 2 finale.
This show is a production of ZoomDoom Stories. It's written and directed by Jamie Killen. Sound design and original music are by Jon Erik DeGuzman and Dog and Pony Studios.
Find out more about the show at https://www.sixdisappearancespodcast.com/
You can support the show by subscribing and leaving a review or by visiting https://www.patreon.com/sixdisappearancespod
Recordings of Person of Interest F: Lost time.
Recordings of Persons of Interest A-F: A judgment.
Recordings of Persons of Interest A-F: An attack. A kiss. A plan for the future.
Recordings of Persons of Interest A-F: Answers.
Recordings of Persons of Interest A-F: Interference, new technology, messages from above.
Soonerrelocated , 01/12/2020
Intriguing....
Loving this podcast!! When is Season 2?!
Skyetrinity , 05/16/2020
SJW Inclusions Dull the Show
I'm enjoying the story.... BUT a huge distraction from the story, especially in the early part of the series, seems to be the obligatory inclusion of diversity of sexual/gender orientation using such tired and over done stereotypes. Blah! Can't we just stick to what's relevant to the story? It would be fine to include any of these types of characters IF it felt natural, but it comes across as forced, like "Oh, don't forget to include xyz for inclusion purposes". It does get better as the story progresses, but it is enough of a distraction that it really decreased my enjoyment of the story and I almost stopped listening completely.
Sismo52 , 03/23/2020
Solid story, but I fear the ending
Zoomdoom Stories has a solid story, but the ending of their last podcast was really lackluster. It's like they got bored or ran out of good ideas that fit the story. There are a few characters who are horrible in this podcast but it is generally solid.
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These S scale, 1"x8" strips are sold in a package of 6, 16" (406 mm) long pieces.
NOTE: This product was sold under the part number MA204P12 (12" strips) or MA204P24 (24" strips) in the Mt. Albert Scale Lumber catalog. The Fast Tracks part number for this product is now ST-S-1x8-16.


Tabletop gardening in the Potting Shed with butterflies, blooms and Portmeirion Botanic Garden. A sprinkling of water cans are planted with flowers in anticipation of spring gardening season.
Happy April! It's the first Monday of the month and I'm happy to be joining my blogging friends to share some floral inspiration and Monday Morning Blooms! You'll find my floral friends' links to their blooming creations at the bottom of this post.
The freeze date for our area in North Carolina is April 15th. While I'm anxious to get planting, I'm staying away from the temptation and flower-filled garden centers until then.
In the meantime, I'm enjoying a little tabletop gardening and dishing up blooms and butterflies in the Potting Shed.
I was all aflutter over this MacKenzie-Childs butterfly watering can when I saw it a few years ago. It's one of my favorites and still available online.
It's blooming with colorful mix of grocery store blooms. . . pink stock, purple and light green hydrangeas and yellow tulips.
Portmeirion Botanic Garden is my everyday pattern. I've added pieces over the last 20 years and still enjoying adding a new flower to my garden of dishes on occasion. In addition to the botanic blooms, I love the variety of butterflies on the pieces.
I found a pair of smaller butterfly watering cans at T.J. Maxx a couple of years ago. . .
The bright turquoise watering can is filled a combination of tulips, hyacinths, a sprig of forsythia and some Chinese Fringe Flower, (Loropetalum chinense) that's in bloom now. Chinese Fringe Flower is a sight to behold when it's blooming in spring. . .
The vibrant pink blooms seem shockingly bright for winter-weary eyes!
A mini sprinkle can is blooming with fringe flower and hangs over the window and Potting Shed table.
A cheery yellow butterfly watering can is a companion to the turquoise one, and blooming with yellow and pink tulips, purplish-blue hyacinths, forsythia and fringe flower.
La Rochere butterfly glasses are perfect for sipping your nectar of choice. . .
I highly recommend a Rosemary Lemonade Fizz Cocktail or Mocktail!
Introduced in 1972, Portmeirion Botanic Garden's delightful mixture of floral motifs and signature leaf border, was inspired by early 19th century illustrations and designed by celebrated designer Susan Williams-Ellis.
The botanical illustrations are art for the table!
In addition to being beautiful, it's durable, chip resistant and microwave, freezer and oven safe.
Our peonies are just starting to come up. . .
And will be in bloom the beginning of May.
But I can enjoy the short but sweet peony season year round at the table.
Portmeirion Botanic Garden flatware is blooming with flowers and alight with butterflies. . .
Napkins serve as placemats, adding more butterflies and blooms, layered over a jute runner. . .
And silver butterfly napkin rings are ready to take flight.
Butterfly magnets add some additional color, attracted to the metal surface of the watering cans like butterflies are to nectar.
Happy Monday Mary! Oh I would say Spring has sprung in the Potting Shed. I have to say that you are truly the Watering Can Queen! Who would have a string of wonderful watering cans that mimics a rain chain…you of course. LOVE the butterfly cans! They were all made for you!…Had not idea that MCK produced a watering can!…I need to pay close attention to their mailings!…I just realized why I love the Portmeirion Botanic Garden collection so much, as not only do they have the beautiful botanicals (the Passion flower being one of my favs) there are those beautiful butterflies!…Above the comment section, it reads, "thank you for your comments~they make my day" well, we would all say that you make our day!!!!
Mary, I agree with Shirley that you are queen of the watering cans! I couldn't help but laugh when you said you might need an intervention. Your butterfly cans in their bright spring colors are eye candy filled with flowers, they say spring has arrived in all of her glory! I have the Portmeirion Botanic Garden and it is the perfect pattern for us flower loving ladies! We escaped frost last night because it stayed windy. The cold isn't great for blooms, but frost is a killer. I am so ready to spend time in the garden.
You always create beauty and inspire, I love sharing Monday Morning Blooms with you! Have a lovely day!
Amazingly beautiful my friend! What a treat to the eyes this morning! Your watering cans filled with spring blooms is such a treat!
Oh this post is making me second guess all the times I passed on pieces in the Portmerion Botanic Garden collection! You make it look sooooooooo beautiful!
So beautiful, Mary! I adore the lilac, passion flower, dianthus, and peony Portmerion Botanic Garden plates. I am going to be wishing for those to add to my four plates and I had sworn off buying more dishes! Your vignette is oozing with delightful details that are such eye candy! Love all your watering cans and butterflies. We like so many of the same things.
I must mention how pretty the placemats and napkins are too! They add just the right touch!
Good Morning!…After a warm weekend, it is a sunny, but very brisk 31 degrees this morning here in New Jersey. Reading your blog gave me hope that maybe Spring is around the corner for us. Today's blog post is stunning. Have a warm and sunny day, and many thanks for your posts. I look forward to reading them every day!
It's so nice to see you playing in your potting shed, Mary. Your collection of Portmeirion dishes is blooming with happiness. I love your Queen MKC watering can, and the other two look like her Princesses in waiting. Isn't the Chinese Fringe Flower so beautiful? I hope you'll have a wonderful week!
Your watering can floral displays are lovely! That Chinese Fringe Flower plant is amazing! What a breath of bright coloring to witness after the long winter. Our freeze date is much later than yours but I sure wish it was a lot sooner! The Portmerion dishes are the perfect choice for this vignette!
This beautiful post makes me want to make a visit to the garden center today, but In Virginia, we too are bound by the April 15th rule for frosts, so I'll hold off for a while. I'll just keep looking at your post for the eye candy I need to start the month of April. Thank you for such a gorgeous post!
Be still my heart. Mary there are no words to describe what you do in your little "She Shed". I want to come play with you in your world. There is art in every frame. The Portmeirion Botanic Garden dinner ware is a favorite of mine but I have NO room for more china , according to my hubby. The detail on each piece, the colors, the bees and butterflies on each piece is a praise to our Heavenly Father, the creator of all beauty. Thank you for sharing your gift with us.
Good morning, Mary! Your post this morning is very welcome since we have a light covering of snow here in Michigan! It's brisk but sunny so I'm hoping spring is on the way. Our last frost date is May 15 so I'll live vicariously through until I can go out and play. Thank you for a breath of spring!
You set the most beautiful tables! And, I love that you eat in the potting shed on occasion. I've been trying to talk DH into getting a potting shed….
On a different note: given that you live in NC, have you ever been to Replacements.com warehouse? The most expensive dish in their 'museum' is a tureen by Royal Copenhagen in the flora Danica pattern – very similar to your dishes. I was in heaven when we went there. I suspect that your house looks a bit like their warehouse with the massive amount of tableware that you seem to have. I'm jealous. How do you store it all???? Can you do a post on that?
What a beautiful table setting. It makes me want to just stay outside and wait for all the flowers to bloom! I too have peonies and they are barely peeping out of the ground. You are so very talented and I love all of your blogs. Let's enjoy each day God has blessed us with and enjoy his wondrous beauty season after season. All the best to you!
As always so fun to read your post. So many details and touches you make to look everything new.
the Portmeirion Botanic Garden China. A dear friend purchased it when it first came out making me an instant fan.
It is always a treat to visit your potting shed! The butterflies are certainly all a flutter throughout your lovely display! What a pretty choice of dishes!
Mary, visiting you always makes my day! No, actually my whole month. It's always such a treat to visit your beautiful corner of the world. Spring has sprung in the Potting Shed, and yes, you are the watering can queen!
Oh goodness Mary, you've outbloomed yourself this time! What an over the top Flower Market! Everything literally dancing with colorful blooms! I love seeing your MKC watering can full of a rainbow of flowers. The whole scene is a gardeners dream, so delightful and happy, a wonderful start to April!
Mary, I love when you fuse your pottery with flowers—-no one does this as well as you do. Love every shot! Thank-you!
Mary your posts are always a beautiful sight to see. Beautiful flowers.
What a gorgeous post. The watering cans are pretty especially with the lovely flowers in them.
The flower plates are pretty and the watering cans are very nice especially the yellow one.
Love Love Love all your Blogs.
Happy 1st of April, Mary! This post is a perfect way to welcome in the month of April. I've jumped in with work in the garden, cleaning out beds, planting a few things in posts, but still need to get some annuals in the beds. We have had another cool snap the past few days, but on a warming trend by Thursday back in the 80s. Our spring weather can be up and down, but hopefully no more freezes. I've always had a bit of watercan envy of your wonderful collection. I don't really have a spot for a collection, but I do buy them on occasion to use for watering and for flower containers. I was thrilled to bring the MKC butterfly can home last summer when I attended the Barn Sale. I wanted the large peony watering can, but didn't find it. I already had the mini can with the long thin spout. Do you have that one? It's pretty cute. Love all your pretty blooms real and on the beautiful dishes, and of course the butterflies are favorites.
Wildflowers are in full bloom here. I wish I had scattered a mix of seed in my former rose bed. Thanks for sharing all this beauty. Thinking of you and sending hugs your way.
Chinese Fringe flower, brilliant color.


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Home » North Reading News
Experiencing college amidst a global pandemic: Stories told through students' eyes...
Jan 14, 2021 by jkeating624
Published January 14, 2021 By ALLIE HASTINGS MANY COLLEGES have added green space to their campuses to encourage students to socialize safely outdoors. Monika Stantcheva (center), a junior at Boston College, enjoys a socially-distanced picnic with friends on the converted grounds of an old gymnasium. (Courtesy Photo) NORTH READING — When COVID-19 first took the country by storm in March of 2020, schools all across the United States shut down, tasking teachers and professors with the mission to finish off their spring terms remotely in accordance with CDC guidelines. As the year started to approach the fall months and a new school semester, many undergraduate students were left to wonder what kind of decision their college or university might make – would they be forced to take Zoom classes from home, or be encouraged...
Final tally of 2020 Christmas fund for CCS: $43,837...
Published January 14, 2021 By MAUREEN DOHERTY NORTH READING — We could not me more thrilled with the community's response to the Transcript's 31st annual Neighbor Helping Neighbor Fund (NHNF). Generosity is certainly more bountiful than the coronavirus in our little town. With so many more people needing to turn to Christian Community Service (CCS) to make ends meet during this pandemic, it is comforting to know that those who are fortunate to have their health and their wealth are willing to share their good fortune by assisting neighbors in need. It is the balm that our society needs now more than ever. We have passed along the $43,837 donated to the fund this year to CCS, the 501(c)(3) nonprofit that runs the North Reading Food Pantry and also provides other vital services to...
Town Election season officially opens Jan. 19...
Published January 14, 2021 By MAUREEN DOHERTY NORTH READING — Who's ready for another election? Ready or not, a new election season gets underway next Tuesday, January 19, which is the first date candidates for political offices in town may officially take out nomination papers. The town's annual election is Tuesday, May 4. Seats on three boards plus the town moderator's position are up for election this year. There are two seats with three-year terms on the School Committee, Select Board and Community Planning Commission (CPC) and one seat for a one-year term for Town Moderator. There are no vacancies for an elected five-year seat on the town's Housing Authority this year; this is the year the appointed position to that board is made, state Town Clerk Barbara Stats. Election Day: May 5 The...
Front Page: January 14, 2021
Mighty Meredith Project celebrates the spirit of giving; dreams big for 2021...
Published January 7, 2021 By ALLIE HASTINGS THE MIGHTY KIND MMP volunteers dropped off toys and gift cards on Christmas eve to Tufts Children's Hospital. Front row, l-r: Caroline, Catherine and Meredith Casey; members of the Pediatric Neurology Clinic (holding animals). Back row, Chris Lemone and Peter Casey. (Karen Casey Photo) NORTH READING — Despite the hard-hitting impact of COVID-19, North Reading High School sophomore Meredith Casey has been busy at work these past few months fulfilling her Fill the Box Toy Drive Campaign, an annual fundraiser that is dedicated to donating toys and gifts to children being treated at the Boston Children's Hospital and Tufts Children's Hospital. This was her third year hosting the campaign, as the initiative means a lot to her personally and is linked to the efforts of her nonprofit organization, the...
31st Neighbor Fund drive raises more than $43,300 for CCS...
Published January 7, 2021 By MAUREEN DOHERTY NORTH READING — Thanks to the continued generosity of the Transcript's loyal supporters we're proud to say that our Neighbor Helping Neighbor Fund (NHNF) has raised $43,337 for the benefit of the town's home-grown charity, Christian Community Service (CCS). The success of our 31st annual sponsorship of this non-profit all-volunteer organization speaks volumes about the character of the town's residents and business owners. Considering what everyone has endured these past 10 months, we're beyond thrilled that these donations will enable CCS to meet the growing needs of clients who rely on the North Reading Food Pantry to make ends meet in the coming year. We never expected to surpass last year's fundraising total of just over $31,500 considering the hardships and uncertainties so many faced in 2020 and may...