text:
\section{Introduction}
\FloatBarrier

A long-standing puzzle in flavor physics is the discrepancy between the extractions of the CKM matrix element $|V_{ub}|$
from inclusive and exclusive $B$ meson semileptonic decays at the $B$ factories \cite{Kowalewski:2010zz, Mannel:2010zz,
Antonelli:2009ws, PDG2012}. The current average values determined by the Particle Data Group are \cite{PDG2012}
\begin{eqnarray}
 |V_{ub}|_{\rm incl.} &=& (4.41 \pm 0.15 ^{+0.15}_{-0.17} )\cdot 10^{-3}, \label{eq:Vubincl} \\
 |V_{ub}|_{\rm excl.} &=& (3.23 \pm 0.31 )\cdot 10^{-3}, \label{eq:Vubexcl}
\end{eqnarray}
where the exclusive determination is based on measurements of $\bar{B} \to \pi^+ \ell^- \bar{\nu}_\ell$ decays by the BABAR
and BELLE collaborations, and uses $\bar{B} \to \pi^+$ form factors computed in lattice QCD \cite{Bailey:2008wp, Dalgic:2006dt}.
To address the discrepancy between Eqs.~(\ref{eq:Vubincl}) and (\ref{eq:Vubexcl}), new and independent determinations of
$|V_{ub}|$ are desirable. At the Large Hadron Collider, measurements of $\bar{B} \to \pi^+ \ell^- \bar{\nu}_\ell$ branching fractions
are difficult because of the large pion background; therefore an attractive possibility is to use instead the baryonic mode
$\Lambda_b \to p\: \ell^- \bar{\nu}_\ell$, which has a more distinctive final state \cite{Egede}. In order to
determine $|V_{ub}|$ from this measurement, the $\Lambda_b \to p$ form factors need to be calculated in nonperturbative QCD.

The $\Lambda_b \to p$ matrix elements of the vector and axial vector $b\to u$ currents are parametrized in terms of six
independent form factors (see, e.g., Ref.~\cite{Hussain:1992rb}). In leading-order heavy-quark effective theory (HQET),
which becomes exact in the limit $m_b\to \infty$ and is a good approximation at the physical value of $m_b$,
only two independent form factors remain, and the matrix element with arbitrary Dirac matrix $\Gamma$ in the current
can be written as \cite{Mannel:1990vg, Hussain:1990uu, Hussain:1992rb}
\begin{equation}
\langle N^+(p', s') | \:\bar{u} \Gamma Q \: | \Lambda_Q(v, s) \rangle =
\overline{u}_N(p',s')\left[ F_1 + \slashed{v}\:F_2 \right] \Gamma\: u_{\Lambda_Q}(v, s). \label{eq:FFdef}
\end{equation}
Above, $v$ is the four-velocity of the $\Lambda_Q$ baryon, and the form factors $F_1$, $F_2$ are functions of $p'\cdot v$,
the energy of the proton in the $\Lambda_Q$ rest frame (we denote the heavy quark defined in HQET by $Q$, and we denote
the proton by $N^+$). Note that in leading-order soft-collinear effective theory, which applies in the limit of large $p'\cdot v$,
the form factor $F_2$ vanishes \cite{Feldmann:2011xf, Mannel:2011xg, Wang:2011uv}.

Calculations of $\Lambda_b \to p$ form factors have been performed using QCD sum rules \cite{Huang:1998rq, Carvalho:1999ia}
and light-cone sum rules \cite{Huang:2004vf, Wang:2009hra, Azizi:2009wn, Khodjamirian:2011jp}. Light-cone sum rules
are most reliable at low $q^2$ (corresponding to large proton momentum in the $\Lambda_b$ rest frame),
and even there the uncertainty of the best available calculations is of order 20\% \cite{Khodjamirian:2011jp}.
As we will see later, the $\Lambda_b \to p\: \ell^- \bar{\nu}_\ell$ differential decay rate
has its largest value in the high-$q^2$ (low hadronic recoil) region. This is also the region
where lattice QCD calculations can be performed with the highest precision.

Lattice QCD determinations of the form factors for the mesonic decay $\bar{B} \to \pi^+ \ell^- \bar{\nu}_\ell$
are already available \cite{Dalgic:2006dt, Bailey:2008wp}, and several groups are working on new calculations
\cite{Bahr:2012vt, Bouchard:2012tb, Kawanai:2012id}. We have recently published the first lattice QCD calculation of
$\Lambda_Q \to \Lambda$ form factors, which are important for the rare decay $\Lambda_b \to \Lambda\: \ell^+\ell^-$
\cite{Detmold:2012vy}. We performed this calculation at leading order in HQET, i.e., with static heavy quarks. The HQET
form factors $F_1$ and $F_2$ for the $\Lambda_Q \to \Lambda$ transition are defined as in Eq.~(\ref{eq:FFdef}), except
that the current is $\bar{s}\Gamma Q$ and the final state is the $\Lambda$ baryon.
In the following, we report the first lattice QCD determination of the $\Lambda_Q \to p$ form factors defined in
Eq.~(\ref{eq:FFdef}), building upon the analysis techniques developed in Ref.~\cite{Detmold:2012vy}. The calculation
uses dynamical domain wall fermions \cite{Kaplan:1992bt, Furman:1994ky, Shamir:1993zy} for the up-, down-, and strange
quarks, and is based on gauge field ensembles generated by the RBC/UKQCD collaboration \cite{Aoki:2010dy}.

In Sec.~\ref{sec:latticecalc}, we outline our extraction of the $\Lambda_Q \to p$ form factors from ratios of correlation
functions, and present the lattice parameters and form factor results for each data set.
In Sec.~\ref{sec:chiralcontinuumextrap}, we present our fits of the lattice-spacing-, quark-mass-, and $(p'\cdot v)$-dependence
of these results, and discuss systematic uncertainties. We compare the $\Lambda_Q \to p$ form factors
computed here to previous determinations of both $\Lambda_Q \to p$ and $\Lambda_Q \to \Lambda$ form factors in
Sec.~\ref{sec:FFcomparison}. Using our form factor results, we then calculate the differential decay rates of
$\Lambda_b \to p\: \ell^- \bar{\nu}_\ell$ for $\ell=e,\mu,\tau$ in Sec.~\ref{sec:Lambdabdecay}.
Finally, in Sec.~\ref{sec:conclusions} we discuss the impact of our results on future determinations of $|V_{ub}|$
from these decays, and the prospects for more precise lattice calculations.

\FloatBarrier
\section{\label{sec:latticecalc}Lattice calculation}
\FloatBarrier

We performed the calculation of the $\Lambda_Q \to p$ form factors with the same lattice actions and parameters as
used in our calculation of the $\Lambda_Q \to \Lambda$ form factors in Ref.~\cite{Detmold:2012vy}. That is,
we are using a domain-wall action for the up, down, and strange quarks  \cite{Kaplan:1992bt, Furman:1994ky, Shamir:1993zy},
the Iwasaki action \cite{Iwasaki:1983ck, Iwasaki:1984cj} for the gluons, and the Eichten-Hill action \cite{Eichten:1989kb}
with HYP-smeared gauge links \cite{DellaMorte:2005yc} for the static heavy quark. The Eichten-Hill action
requires that we work in the $\Lambda_Q$ rest frame, i.e.~with $v=(1,0,0,0)$. We compute ``forward'' and ``backward''
three-point functions
\begin{eqnarray}
 C^{(3)}_{\delta\alpha}(\Gamma,\:\mathbf{p'}, t, t') &=& \sum_{\mathbf{y}} e^{-i\mathbf{p'}\cdot(\mathbf{x}-\mathbf{y})}
 \left\langle N_{\delta}(x_0,\mathbf{x})\:\: J_\Gamma^{\dag}(x_0-t+t',\mathbf{y})
 \:\:\: \overline{\Lambda}_{Q\alpha} (x_0-t,\mathbf{y}) \right\rangle, \label{eq:threept} \\
C^{(3,\mathrm{bw})}_{\alpha\delta}(\Gamma,\:\mathbf{p'}, t, t-t') &=& \sum_{\mathbf{y}}
e^{-i\mathbf{p'}\cdot(\mathbf{y}-\mathbf{x})} \left\langle \Lambda_{Q\alpha}(x_0+t,\mathbf{y})\:\: J_\Gamma(x_0+t',\mathbf{y})
\:\:\: \overline{N}_{\delta} (x_0,\mathbf{x}) \right\rangle, \label{eq:threeptbw}
\end{eqnarray}
containing the baryon interpolating fields
\begin{eqnarray}
 \Lambda_{Q\alpha} &=& \epsilon^{abc}\:(C\gamma_5)_{\beta\gamma}\:\tilde{d}^a_\beta\:\tilde{u}^b_\gamma\: Q^c_\alpha, \label{eq:lambdaqinterpol} \\
 N_{\alpha} &=& \epsilon^{abc}\:(C\gamma_5)_{\beta\gamma}\:\tilde{u}^a_\beta\:\tilde{d}^b_\gamma\: \tilde{u}^c_\alpha, \label{eq:protoninterpol}
\end{eqnarray}
and the current
\begin{equation}
 J_{\Gamma} = U(m_b, a^{-1})\: \mathcal{Z}
 \left[ \left( 1  + c^{(m a)}_\Gamma\:\frac{m_u\:a}{1-(w_0^{\rm MF})^2}\right) \overline{Q} \Gamma  u
 + c^{(p a)}_\Gamma\:a\: \overline{Q} \Gamma \bs{\gamma}\cdot \bs{\nabla}  u   \right]. \label{eq:LHQETcurrent}
\end{equation}
In the baryon interpolating fields, the tilde on the up- and down-quark fields indicates Gaussian gauge-covariant smearing.
The coefficients $\mathcal{Z}$, $c^{(m a)}_\Gamma$, and $c^{(p a)}_\Gamma$ in the current (\ref{eq:LHQETcurrent}) provide an
$\mathcal{O}(a)$-improved matching from lattice HQET to continuum HQET in the $\overline{\rm MS}$ scheme; they have been computed
in one-loop perturbation theory in Ref.~\cite{Ishikawa:2011dd}. The factor $U(m_b, a^{-1})$ provides two-loop renormalization-group
running in continuum HQET from the scale $\mu=a^{-1}$ (where $a$ is the lattice spacing) to the desired scale $\mu=m_b$.

Note that, because Eq.~(\ref{eq:protoninterpol}) contains two up-quark fields, the $\Lambda_Q \to p$ three-point functions
contain two different types of contractions of quark propagators, one of which is not present in the $\Lambda_Q \to \Lambda$
three-point functions studied in Ref.~\cite{Detmold:2012vy}. This is also the case for the proton two-point functions.

We multiply the forward- and backward three-point functions and form the ratio \cite{Detmold:2012vy}
\begin{equation}
 \mathcal{R}(\Gamma, \mathbf{p'}, t, t') = \frac{4 \:\mathrm{Tr}\left[  C^{(3)}(\Gamma,\:\mathbf{p'}, t, t')
 \:\: C^{(3,\mathrm{bw})}(\Gamma,\:\mathbf{p'}, t, t-t') \right] }{ \mathrm{Tr}[ C^{(2,N)}(\mathbf{p'}, t)]
 \:\mathrm{Tr}[ C^{(2,\Lambda_Q)}(t) ] }, \label{eq:doubleratio}
\end{equation}
where $C^{(2,N)}(\mathbf{p'}, t)$ and $C^{(2,\Lambda_Q)}(t)$ are the proton and the $\Lambda_Q$ two-point functions, and
the traces are over spinor indices. The ratio is computed using the statistical bootstrap method. As explained in
Ref.~\cite{Detmold:2012vy}, we then form the combinations
\begin{eqnarray}
 \mathcal{R}_+(\mathbf{p'}, t, t') &=& \frac14 \left[ \mathcal{R}(1, \mathbf{p'}, t, t') + \mathcal{R}(\gamma^2\gamma^3, \mathbf{p'}, t, t')
 + \mathcal{R}(\gamma^3\gamma^1, \mathbf{p'}, t, t') + \mathcal{R}(\gamma^1\gamma^2, \mathbf{p'}, t, t') \right],  \label{eq:curlyRplus} \\
 \mathcal{R}_-(\mathbf{p'}, t, t') &=& \frac14 \left[ \mathcal{R}(\gamma^1, \mathbf{p'}, t, t') + \mathcal{R}(\gamma^2, \mathbf{p'}, t, t')
 + \mathcal{R}(\gamma^3, \mathbf{p'}, t, t') + \mathcal{R}(\gamma_5, \mathbf{p'}, t, t') \right],  \label{eq:curlyRminus}
\end{eqnarray}
which, upon inserting Eq.~(\ref{eq:FFdef}) into the transfer matrix formalism, yield
\begin{eqnarray}
 \mathcal{R}_+(\mathbf{p'}, t, t') &=& \frac{ E_N+m_N}{E_N} [F_1 + F_2]^2 + \hdots, \label{eq:RGammap}\\
 \mathcal{R}_-(\mathbf{p'}, t, t') &=& \frac{ E_N-m_N}{E_N} [F_1 - F_2]^2 + \hdots. \label{eq:RGammam}
\end{eqnarray}
Here, the ellipses denote excited-state contributions that decay exponentially with the Euclidean time separations, and
$F_1$, $F_2$ are the form factors at the given values of the proton momentum $\mathbf{p'}$, the lattice spacing, and the
quark masses. Throughout the remainder of this paper, we will use the following names for the combinations of form factors
that appear in Eqs.~(\ref{eq:RGammap}), (\ref{eq:RGammam}):
\begin{equation}
F_+ = F_1 + F_2, \hspace{4ex} F_- = F_1 - F_2.
\end{equation}
For a given value of $|\mathbf{p'}|^2$, we further average Eqs.~(\ref{eq:curlyRplus}) and (\ref{eq:curlyRminus}) over the
direction of $\mathbf{p'}$, and we denote the resulting quantities as $\mathcal{R}_\pm (|\mathbf{p'}|^2, t, t')$.
As a consequence of the symmetric form of the ratio (\ref{eq:doubleratio}), at a given source-sink separation $t$,
the contamination from excited states is smallest at the mid-point $t'=t/2$. We therefore construct the following functions
\begin{eqnarray}
 R_+(|\mathbf{p'}|^2, t) &=& \sqrt{\frac{E_N}{E_N+m_N} \mathcal{R}_+(|\mathbf{p'}|^2,\: t,\: t/2)}, \label{eq:Rplus}\\
 R_-(|\mathbf{p'}|^2, t) &=& \sqrt{\frac{E_N}{E_N-m_N} \mathcal{R}_-(|\mathbf{p'}|^2,\: t,\: t/2)}, \label{eq:Rminus}
\end{eqnarray}
which, according to Eqs.~(\ref{eq:RGammap}), (\ref{eq:RGammam}), become equal to the form factors $F_+$ and $F_-$
for large source-sink separation, $t$.

We performed the numerical calculations for the six different sets of parameters shown in Table \ref{tab:params}.
When evaluating Eqs.~(\ref{eq:Rplus}) and (\ref{eq:Rminus}), we used the lattice results for the proton mass, $m_N$, obtained
from fits to the proton two-point function in the same data set. These results are also given in Table \ref{tab:params}.
Unlike in Ref.~\cite{Detmold:2012vy}, here we calculated the energies at nonzero momentum using the relativistic continuum
dispersion relation $E_N=\sqrt{m_N^2 + |\mathbf{p'}|^2}$. The energies calculated in this way are consistent with the
energies obtained directly from fits to the proton two-point functions at nonzero momentum, but using the relativistic
dispersion relation reduces the uncertainty. We computed $R_\pm(|\mathbf{p'}|^2, t)$ for proton momenta in the range
$0 \leq |\mathbf{p'}|^2 \leq 9\cdot (2\pi/L)^2$, where $L=N_s a \approx 2.7$ fm is the spatial size of the lattice.
We performed the calculation for all source-sink separations from $t/a=4$ to $t/a=15$ at the coarse lattice spacing
(data sets \texttt{C14}, \texttt{C24}, \texttt{C54}), and for $t/a=5$ to $t/a=20$ at the fine lattice spacing
(data sets \texttt{F23}, \texttt{F43}, \texttt{F63}). This wide range of source-sink separations allows us to reliably
extract the ground-state form factors \cite{Detmold:2012vy}. Because the statistical uncertainties grow exponentially
with $t$, in practice the upper limit of $t/a$ we can use is somewhat smaller, especially at larger momentum.

A plot of example numerical results for $R_\pm(|\mathbf{p'}|^2, t)$ as a function of the source-sink separation $t$ is
shown in Fig.~\ref{fig:textrap_L24_005_psqr4}. The results are qualitatively similar to those obtained for the $\Lambda$
final state in Ref.~\cite{Detmold:2012vy} (the $t'$-dependence of $\mathcal{R}_\pm (|\mathbf{p'}|^2, t, t')$ is also
similar to that seen in Ref.~\cite{Detmold:2012vy}). It can be seen that there is contamination from excited states
which decays exponentially with $t$. At $|\mathbf{p'}|^2\neq0$ we perform fits of the $t$-dependence using the functions
\begin{equation}
R^{i,n}_\pm(t) = F^{i,n}_\pm + A^{i,n}_\pm \:\exp[-\delta^{i,n}\:t], \label{eq:tdepsepcoupled}
\end{equation}
which account for the leading excited-state contamination \cite{Detmold:2012vy}. Above, we use an abbreviated notation
where $n$ specifies the squared momentum of the proton [we write $|\mathbf{p'}|^2 = n\cdot (2\pi/L)^2$], and
$i=\mathtt{C14}, \mathtt{C24}, ..., \mathtt{F63}$ specifies the data set. To enforce the positivity of the energy gaps
$\delta^{i,n}$, we rewrite them as $\delta^{i,n} /(1\: {\rm GeV}) = \exp(l^{i,n})$. The fit parameters in
Eq.~(\ref{eq:tdepsepcoupled}) are then $F^{i,n}_\pm$, $A^{i,n}_\pm$, and $l^{i,n}$. Note that we perform coupled fits of
$R^{i,n}_+$ and $R^{i,n}_-$ with common energy gap parameters, which improves the statistical precision of the fits
\cite{Detmold:2012vy}. As a check, we have also performed independent fits with separate energy gap parameters $l^{i,n}_+$
and $l^{i,n}_-$ and found that $l^{i,n}_+$ and $l^{i,n}_-$ are in agreement within statistical uncertainties.

\begin{table}
\begin{tabular}{cccccccccccccccccccccc}
\hline\hline
Set & \hspace{1ex} & $\beta$ & \hspace{1ex} & $N_s^3\times N_t\times N_5$ & \hspace{1ex} & $a m_5$ & \hspace{1ex} & $am_{s}^{(\mathrm{sea})}$
& \hspace{1ex} & $am_{u,d}^{(\mathrm{sea})}$   & \hspace{1ex} & $a$ (fm) & \hspace{1ex} & $am_{u,d}^{(\mathrm{val})}$
& \hspace{1ex} & $m_\pi^{(\mathrm{val})}$ (MeV) & \hspace{1ex} & $m_N^{(\mathrm{val})}$ (MeV) & \hspace{1ex} & $N_{\rm meas}$ \\
\hline
\texttt{C14} && $2.13$ && $24^3\times64\times16$ && $1.8$ && $0.04$ && $0.005$ && $0.1119(17)$ && $0.001$ && 245(4) && 1090(21) && 2672 \\
\texttt{C24} && $2.13$ && $24^3\times64\times16$ && $1.8$ && $0.04$ && $0.005$ && $0.1119(17)$ && $0.002$ && 270(4) && 1103(20) && 2676 \\
\texttt{C54} && $2.13$ && $24^3\times64\times16$ && $1.8$ && $0.04$ && $0.005$ && $0.1119(17)$ && $0.005$ && 336(5) && 1160(19) && 2782 \\
\texttt{F23} && $2.25$ && $32^3\times64\times16$ && $1.8$ && $0.03$ && $0.004$ && $0.0849(12)$ && $0.002$ && 227(3) && 1049(25) && 1907 \\
\texttt{F43} && $2.25$ && $32^3\times64\times16$ && $1.8$ && $0.03$ && $0.004$ && $0.0849(12)$ && $0.004$ && 295(4) && 1094(18) && 1917 \\
\texttt{F63} && $2.25$ && $32^3\times64\times16$ && $1.8$ && $0.03$ && $0.006$ && $0.0848(17)$ && $0.006$ && 352(7) && 1165(23) && 2782 \\
\hline\hline
\end{tabular}
\caption{\label{tab:params} Lattice parameters.
The data sets \texttt{C14}, \texttt{C24} and \texttt{C54}
all correspond to the same ``coarse'' ensemble of gauge fields with gauge coupling $\beta=6/g^2=2.13$ and sea-quark masses
$am_{s}^{(\mathrm{sea})}=0.04$, $am_{u,d}^{(\mathrm{sea})}=0.005$; these data sets differ only in the values of the
valence-quark mass, $am_{u,d}^{(\mathrm{val})}$, used for the domain wall propagators. At the ``fine'' lattice spacing,
the propagators in the \texttt{F23} and \texttt{F43} data sets are from one common ensemble of gauge fields, but the
\texttt{F63} data set is obtained from a different ensemble with heavier sea-quark masses. In each case, we also list
the valence pion and proton masses, $m_\pi^{(\mathrm{val})}$ and $m_N^{(\mathrm{val})}$, and the number of light-quark
propagators, $N_{\rm meas}$, used for our analysis. The ensembles of gauge fields have been generated by the RBC/UKQCD
collaboration; see Ref.~\cite{Aoki:2010dy} for further details.}
\end{table}

\begin{figure}
\vspace{10ex}
 \includegraphics[height=6cm]{fig1.pdf}
 \caption{\label{fig:textrap_L24_005_psqr4}Example of numerical results for $R_\pm(|\mathbf{p'}|^2, t)$, plotted as
 a function of the source-sink separation $t$, along with a fit using Eq.~(\ref{eq:tdepsepcoupled}).
The data shown here are from the \texttt{C54} set and at $|\mathbf{p'}|^2=4\cdot(2\pi/L)^2$. As explained in
Ref.~\protect\cite{Detmold:2012vy}, at each value of $|\mathbf{p'}|^2$, the fit is performed simultaneously
for the six data sets.}
\vspace{10ex}
\end{figure}

At a given momentum-squared $n$, we perform the fits using Eq.~(\ref{eq:tdepsepcoupled}) simultaneously for the six
different data sets $i=\mathtt{C14}, \mathtt{C24}, ..., \mathtt{F63}$. Because the lattice size, $L$ (in physical units),
is equal within uncertainties for all data sets, the squared momentum $|\mathbf{p'}|^2= n\cdot (2\pi/L)^2$ for a given
$n$ is also equal within uncertainties for all data sets. To improve the stability of the fits, we augment the $\chi^2$ function
by adding a term that limits the variation of $l^{i,n}$ across the data sets to reasonable values \cite{Detmold:2012vy}.

At $\mathbf{p'}=0$, we can only compute $R^{i,0}_+(t)$, and we find that the $t$-dependence of $R^{i,0}_+(t)$ is weak.
In this case we are unable to perform exponential fits, and we instead perform constant fits, excluding a few points
at the shortest $t$.

The numerical results for the form factors $F^{i,n}_\pm$ are listed in Tables \ref{tab:Fplus} and \ref{tab:Fminus}.
The uncertainties shown there are the quadratic combination of the statistical uncertainty and an estimate of the
systematic uncertainty associated with the choice of fit range for Eq.~(\ref{eq:tdepsepcoupled}). To estimate this
systematic uncertainty, we calculated the changes in the fitted $F^{i,n}_\pm$ when excluding the data points with
the shortest source-sink separation \cite{Detmold:2012vy}. These changes fluctuate as a function of the momentum,
and here we conservatively took the maximum of the change over all momenta as the systematic uncertainty for each
data set. In Tables \ref{tab:F1} and \ref{tab:F2}, we additionally list the corresponding results for
$F^{i,n}_1 = (F^{i,n}_+ + F^{i,n}_-)/2$ and $F^{i,n}_2=(F^{i,n}_+ - F^{i,n}_-)/2$, where the uncertainties
take into account the correlations between $F^{i,n}_+$ and $F^{i,n}_-$.

\begin{table}[h]
\begin{tabular}{cccccccccccccc}
\hline\hline
$|\mathbf{p'}|^2/(2\pi/L)^2$ & \hspace{1ex} & $F_+^\mathtt{C14}$ & \hspace{1ex} & $F_+^\mathtt{C24}$ & \hspace{1ex} &
$F_+^\mathtt{C54}$  & \hspace{1ex} & $F_+^\mathtt{F23}$ & \hspace{1ex} & $F_+^\mathtt{F43}$ & \hspace{1ex} & $F_+^\mathtt{F63}$ \\
\hline
0 && $1.148(53)$ && $1.126(39)$ && $1.119(39)$ && $1.125(74)$ && $1.117(52)$ && $1.069(62)$ \\
1 && $1.030(50)$ && $1.026(37)$ && $1.023(38)$ && $1.037(68)$ && $1.027(48)$ && $0.993(61)$ \\
2 && $0.926(51)$ && $0.923(38)$ && $0.924(38)$ && $0.922(67)$ && $0.921(47)$ && $0.892(64)$ \\
3 && $0.828(53)$ && $0.843(39)$ && $0.842(39)$ && $0.843(69)$ && $0.845(48)$ && $0.814(64)$ \\
4 && $0.776(51)$ && $0.775(38)$ && $0.772(39)$ && $0.795(70)$ && $0.792(49)$ && $0.761(63)$ \\
5 && $0.693(51)$ && $0.719(38)$ && $0.716(39)$ && $0.754(70)$ && $0.747(50)$ && $0.710(63)$ \\
6 && $0.648(52)$ && $0.673(39)$ && $0.664(39)$ && $0.702(72)$ && $0.700(51)$ && $0.673(64)$ \\
8 && $0.578(56)$ && $0.606(41)$ && $0.610(40)$ && $0.632(75)$ && $0.621(55)$ && $0.624(65)$ \\
9 && $0.549(60)$ && $0.568(45)$ && $0.573(42)$ && $0.604(77)$ && $0.590(59)$ && $0.605(67)$ \\
\hline\hline
\end{tabular}
\caption{\label{tab:Fplus} Lattice results for the form factor $F_+$.}
\end{table}

\begin{table}[h]
\begin{tabular}{cccccccccccccc}
\hline\hline
$|\mathbf{p'}|^2/(2\pi/L)^2$ & \hspace{1ex} & $F_-^\mathtt{C14}$ & \hspace{1ex} & $F_-^\mathtt{C24}$ & \hspace{1ex} &
$F_-^\mathtt{C54}$  & \hspace{1ex} & $F_-^\mathtt{F23}$ & \hspace{1ex} & $F_-^\mathtt{F43}$ & \hspace{1ex} & $F_-^\mathtt{F63}$ \\
\hline
1 && $1.80(12)$ && $1.861(98)$ && $1.874(66)$ && $1.70(18)$ && $1.709(93)$   && $1.755(99)$   \\
2 && $1.60(11)$ && $1.615(91)$ && $1.625(63)$ && $1.52(17)$ && $1.540(89)$   && $1.541(98)$   \\
3 && $1.46(12)$ && $1.502(10)$ && $1.513(71)$ && $1.48(18)$ && $1.433(90)$   && $1.415(99)$   \\
4 && $1.17(11)$ && $1.181(85)$ && $1.265(62)$ && $1.29(17)$ && $1.281(89)$   && $1.270(96)$   \\
5 && $1.07(10)$ && $1.110(86)$ && $1.169(63)$ && $1.15(17)$ && $1.177(88)$   && $1.179(95)$   \\
6 && $1.00(11)$ && $1.046(87)$ && $1.101(65)$ && $1.02(17)$ && $1.079(88)$   && $1.115(96)$   \\
8 && $0.82(11)$ && $0.878(88)$ && $0.915(65)$ && $0.89(18)$ && $0.955(90)$   && $0.965(97)$   \\
9 && $0.80(11)$ && $0.814(90)$ && $0.863(69)$ && $0.84(17)$ && $0.93(10)\phantom{0}$ && $0.94(10)\phantom{0}$ \\
\hline\hline
\end{tabular}
\caption{\label{tab:Fminus} Lattice results for the form factor $F_-$.}
\end{table}

\begin{table}[h]
\begin{tabular}{cccccccccccccc}
\hline\hline
$|\mathbf{p'}|^2/(2\pi/L)^2$ & \hspace{1ex} & $F_1^\mathtt{C14}$ & \hspace{1ex} & $F_1^\mathtt{C24}$ & \hspace{1ex} &
$F_1^\mathtt{C54}$  & \hspace{1ex} & $F_1^\mathtt{F23}$ & \hspace{1ex} & $F_1^\mathtt{F43}$ & \hspace{1ex} & $F_1^\mathtt{F63}$ \\
\hline
1 && $1.417(64)$ && $1.444(56)$ && $1.448(41)$ && $1.368(98)$ && $1.368(47)$ && $1.374(67)$ \\
2 && $1.263(61)$ && $1.269(53)$ && $1.274(41)$ && $1.220(90)$ && $1.231(43)$ && $1.216(69)$ \\
3 && $1.144(62)$ && $1.172(58)$ && $1.177(44)$ && $1.160(92)$ && $1.139(44)$ && $1.115(69)$ \\
4 && $0.975(56)$ && $0.978(50)$ && $1.018(39)$ && $1.041(90)$ && $1.037(43)$ && $1.016(68)$ \\
5 && $0.879(55)$ && $0.914(50)$ && $0.942(40)$ && $0.951(89)$ && $0.962(42)$ && $0.944(67)$ \\
6 && $0.824(56)$ && $0.860(51)$ && $0.883(41)$ && $0.861(91)$ && $0.890(43)$ && $0.894(67)$ \\
8 && $0.699(59)$ && $0.742(51)$ && $0.763(40)$ && $0.760(95)$ && $0.788(46)$ && $0.795(68)$ \\
9 && $0.672(63)$ && $0.691(52)$ && $0.718(41)$ && $0.722(96)$ && $0.760(52)$ && $0.770(71)$ \\
\hline\hline
\end{tabular}
\caption{\label{tab:F1} Lattice results for the form factor $F_1$.}
\end{table}

\begin{table}[h]
\begin{tabular}{cccccccccccccc}
\hline\hline
$|\mathbf{p'}|^2/(2\pi/L)^2$ & \hspace{1ex} & $F_2^\mathtt{C14}$ & \hspace{1ex} & $F_2^\mathtt{C24}$ & \hspace{1ex} &
$F_2^\mathtt{C54}$  & \hspace{1ex} & $F_2^\mathtt{F23}$ & \hspace{1ex} & $F_2^\mathtt{F43}$ & \hspace{1ex} & $F_2^\mathtt{F63}$ \\
\hline
1 && $-0.387(60)$ && $-0.418(43)$ && $-0.425(29)$ && $-0.332(86)$ && $-0.341(47)$ && $-0.381(37)$ \\
2 && $-0.337(56)$ && $-0.346(38)$ && $-0.350(27)$ && $-0.297(82)$ && $-0.309(46)$ && $-0.325(34)$ \\
3 && $-0.316(59)$ && $-0.330(44)$ && $-0.335(31)$ && $-0.317(86)$ && $-0.294(48)$ && $-0.300(35)$ \\
4 && $-0.199(54)$ && $-0.203(36)$ && $-0.247(27)$ && $-0.247(85)$ && $-0.245(48)$ && $-0.254(34)$ \\
5 && $-0.186(54)$ && $-0.196(37)$ && $-0.226(28)$ && $-0.197(82)$ && $-0.215(48)$ && $-0.235(34)$ \\
6 && $-0.176(55)$ && $-0.187(37)$ && $-0.219(29)$ && $-0.159(82)$ && $-0.190(48)$ && $-0.221(35)$ \\
8 && $-0.121(57)$ && $-0.136(41)$ && $-0.153(31)$ && $-0.128(85)$ && $-0.167(50)$ && $-0.171(36)$ \\
9 && $-0.124(60)$ && $-0.123(43)$ && $-0.145(35)$ && $-0.117(82)$ && $-0.170(59)$ && $-0.165(39)$ \\
\hline\hline
\end{tabular}
\caption{\label{tab:F2} Lattice results for the form factor $F_2$.}
\end{table}

\FloatBarrier
\section{\label{sec:chiralcontinuumextrap}Fits of the form factors as functions of $E_N-m_N$, $m_{u,d}$, and $a$}
\FloatBarrier

In this section we present fits that smoothly interpolate the $E_N$-dependence of our $\Lambda_Q \to p$ form factor
results, including corrections to account for the dependence on the lattice spacing and the light-quark mass. In principle,
the form of this dependence can be predicted in a low-energy effective field theory combining heavy-baryon chiral
perturbation theory for the proton \cite{Jenkins:1991ne, Jenkins:1990jv} with heavy-hadron chiral perturbation theory
\cite{Yan:1992gz, Cho:1992cf} for the $\Lambda_Q$. However, there are a number of issues that limit the usefulness of
this approach for our work. One limitation is that chiral perturbation theory breaks down for momenta $|\mathbf{p'}|$
comparable to or larger than the chiral symmetry breaking scale. Another limitation is that the effective theory also
needs to include the $\Sigma_Q$ and $\Delta$ baryons in the chiral loops, which is expected to lead to additional
unknown low-energy constants associated with the matching of the $Q \to u$ current to the $\Sigma_Q \to p$,
$\Lambda_Q \to \Delta$, and $\Sigma_Q \to \Delta$ currents in the effective theory. Finally, some of the data sets
used here are partially quenched (with valence-quark masses lighter than the sea-quark masses), which further increases
the complexity of the effective theory. As in Ref.~\cite{Detmold:2012vy}, we therefore use a simple model that
successfully describes the dependence of the form factors on $E_N$, $m_{u,d}$, and $a$, at the present level of
uncertainty. It is given by
\begin{eqnarray}
 F_\pm^{i,n} &=& \frac{Y_\pm}{(X_\pm^i+E_N^{i,n}-m_N^i)^2}\cdot [1 + d_\pm (a^i E_N^{i,n})^2], \label{eq:dipole}
\end{eqnarray}
where the position of the pole depends on the pion mass,
\begin{equation}
X_\pm^i = X_\pm + c_\pm \cdot \left[ (m_\pi^i)^2-(m_\pi^{{\rm phys}})^2\right], \label{eq:polemqdep}
\end{equation}
and the term $[1 + d_\pm (a^i E_N^{i,n})^2]$ models the lattice discretization artifacts, which are assumed to
increase with the proton energy. As discussed above, we calculate the proton energies using the relativistic
dispersion relation $E_N^{i,n}=\sqrt{(m_N^i)^2+n\cdot(2\pi/L)^2}$, where $m_N^i$ is the lattice proton mass for
the data set $i$. The free fit parameters in Eq.~(\ref{eq:dipole}) are $Y_{\pm}$, $X_\pm$, $d_\pm$, and $c_\pm$.
Note that here we do not include dependence on the strange-quark mass, because none of the hadrons involved
contain a valence strange quark. The fits of $F_\pm^{i,n}$ using Eq.~(\ref{eq:dipole}) are shown in
Fig.~\ref{fig:qsqrasqrextrapall}, and give the results listed in Table \ref{tab:dipolefitresults}. We have also
performed independent fits of the data for $F^{i,n}_1 = (F^{i,n}_+ + F^{i,n}_-)/2$ and
$F^{i,n}_2=(F^{i,n}_+ - F^{i,n}_-)/2$, using the functions
\begin{eqnarray}
 F_{1,2}^{i,n} &=& \frac{Y_{1,2}}{(X_{1,2}^i+E_N^{i,n}-m_N^i)^2}\cdot [1 + d_{1,2} (a^i E_N^{i,n})^2], \label{eq:dipoleF1F2}
\end{eqnarray}
with $X_{1,2}^i = X_{1,2} + c_{1,2} \cdot \left[ (m_\pi^i)^2-(m_\pi^{{\rm phys}})^2\right]$. These fits
are shown in Fig.~\ref{fig:qsqrasqrextrapallF1F2}, and the resulting values of the parameters are given
in Table \ref{tab:dipolefitresultsF1F2}.

\begin{table}
\begin{tabular}{ccc}
\hline\hline
Parameter & \hspace{1ex} & Result \\
\hline
$Y_+$  && $3.24 \pm 0.62$ ${\rm GeV}^2$  \\
$X_+$  && $1.66 \pm 0.15$ ${\rm GeV}^{\phantom{2}}$  \\
$Y_-$  && $2.92 \pm 0.62$ ${\rm GeV}^2$ \\
$X_-$  && $1.19 \pm 0.13$ ${\rm GeV}^{\phantom{2}}$  \\
\hline\hline
\end{tabular}
\caption{\label{tab:dipolefitresults} Results for the form factor normalization and shape parameters $Y_\pm$ and $X_\pm$
from fits of the lattice QCD results for $F_\pm^{i,n}$, using Eq.~(\protect\ref{eq:dipole}). The covariances of the
parameters needed in Eq.~(\ref{eq:Fplusminusphysical}) are ${\rm Cov}(Y_+,X_+)=0.090\:\:{\rm GeV}^3$ and
${\rm Cov}(Y_-,X_-)=0.080\:\:{\rm GeV}^3$. The results for the parameters describing the quark mass and lattice
spacing dependence are $c_+=0.38(35)\:\:{\rm GeV}^{-1}$, $d_+=-0.031(81)$, $c_-=-0.22(35)\:\:{\rm GeV}^{-1}$,
and $d_-=-0.025(94)$.}
\end{table}

\begin{table}
\begin{tabular}{ccc}
\hline\hline
Parameter & \hspace{1ex} & Result \\
\hline
$Y_1$  && $\wm2.97 \pm 0.50$ ${\rm GeV}^2$  \\
$X_1$  && $\wm1.36 \pm 0.12$ ${\rm GeV}^{\phantom{2}}$  \\
$Y_2$  && $  -0.28 \pm 0.11$   ${\rm GeV}^2$ \\
$X_2$  && $\wm0.81 \pm 0.17$ ${\rm GeV}^{\phantom{2}}$  \\
\hline\hline
\end{tabular}
\caption{\label{tab:dipolefitresultsF1F2} Results for the form factor normalization and shape parameters $Y_{1,2}$ and
$X_{1,2}$ from fits of the lattice QCD results for $F_{1,2}^{i,n}$, using Eq.~(\protect\ref{eq:dipoleF1F2}).
The covariances of the parameters needed in Eq.~(\ref{eq:F12physical}) are
${\rm Cov}(Y_1,X_1)=0.057\:\:{\rm GeV}^3$ and ${\rm Cov}(Y_2,X_2)=-0.018\:\:{\rm GeV}^3$.
The results for the parameters describing the quark mass and lattice spacing dependence are $d_1=-0.038(70)$,
$c_1=-0.04(30)\:\:{\rm GeV}^{-1}$, $d_2=0.05(22)$, and $c_2=-0.53(54)\:\:{\rm GeV}^{-1}$.}
\end{table}

By construction, Eqs.~(\ref{eq:dipole}) and (\ref{eq:dipoleF1F2}) reduce to
\begin{eqnarray}
 F_\pm &=& \frac{Y_\pm}{(X_\pm+E_N-m_N)^2} \label{eq:Fplusminusphysical}, \\
 F_{1,2} &=& \frac{Y_{1,2}}{(X_{1,2}+E_N-m_N)^2} \label{eq:F12physical}
\end{eqnarray}
in the continuum limit and at the physical pion mass. These functions are shown at the bottom of Figs.~\ref{fig:qsqrasqrextrapall}
and \ref{fig:qsqrasqrextrapallF1F2}. In the range of $E_N-m_N$ considered here, the numerical results for
Eqs.~(\ref{eq:Fplusminusphysical}) and (\ref{eq:F12physical}) are consistent with the relations $F_+=F_1+F_2$ and
$F_-=F_1-F_2$ within the statistical uncertainties, as expected. In the plots at the bottom of Figs.~\ref{fig:qsqrasqrextrapall}
and \ref{fig:qsqrasqrextrapallF1F2}, the statistical/fitting uncertainty is indicated using the inner error bands. The
outer error bands additionally include estimates of the total systematic uncertainty, arising from the following sources:
the matching of the lattice HQET to continuum HQET current, the finite lattice volume, the unphysical light-quark
masses, and the non-zero lattice spacing. We discuss these uncertainties below.

As explained in Sec.~\ref{sec:latticecalc}, the lattice HQET to continuum HQET matching is performed using one-loop
perturbation theory at the scale $\mu=a^{-1}$, followed by a two-loop renormalization-group evolution from $\mu=a^{-1}$
to the scale of the $b$-quark mass. To estimate the uncertainty resulting from this use of perturbation theory, we vary
the scale from $\mu=a^{-1}$ to $\mu=2a^{-1}$. For the $\Lambda_Q \to p$ form factors, this results in a change by 7\%
at the coarse lattice spacing, and 6\% at the fine lattice spacing (these relative changes are approximately the same
as for $\Lambda_Q \to \Lambda$ \cite{Detmold:2012vy}; any difference in the size of the effect has to come from the
$\mathcal{O}(a)$-improvement terms, but their contribution is small). Thus, we take the matching uncertainty for the
continuum-extrapolated form factors to be 6\%. Finite-volume effects are also estimated in the same way as in
Ref.~\cite{Detmold:2012vy}; based on the values of $\exp(-m_\pi L)$ for each data set we estimate the finite-volume
effects in the extrapolated form factors to be of order 3\%. The extrapolations to the physical pion mass and the
continuum limit using our simple fit models (\ref{eq:dipole}) and (\ref{eq:dipoleF1F2}) with a small number of
parameters cannot be expected to completely remove the errors associated with the unphysical light-quark masses
and nonzero lattice spacing. As discussed above, we did not use chiral perturbation theory, and we ignored the fact
that some of our lattice results are partially quenched. Similarly, our fit models assume a particular $E_N$-dependence
of the lattice-spacing errors, which was not derived from effective field theory. Following Ref.~\cite{Detmold:2012vy},
we estimate the resulting systematic uncertainties by comparing the form factor results from our standard fits to those
from fits with the parameters $c_\pm$, $c_{1,2}$ or $d_\pm$, $d_{1,2}$ set to zero. In the energy range
$0\leq E_N-m_N\leq 0.7$ GeV, the maximum changes when setting $c_\pm=0$, $c_{1,2}=0$ are 3\% for $F_+$, 3\% for $F_-$,
1\% for $F_1$, and 13\% for $F_2$. In the same range, the maximum changes when setting $d_\pm=0$, $d_{1,2}=0$ are 2\% for
$F_+$, 2\% for $F_-$, 3\% for $F_1$, and 4\% for $F_2$. None of these changes are statistically significant; nevertheless
we add these percentages in quadrature to the uncertainties from the current matching and from the finite-volume effects.

In summary, we obtain the following estimates of the total systematic uncertainties (valid for $0\leq E_N-m_N\leq 0.7$ GeV):
\begin{eqnarray}
 F_+: && \hspace{4ex} \sqrt{(6\%)^2 + (3\%)^2 + (3\%)^2 + (2\%)^2 } \approx 8\%, \label{eq:Fplussysterr} \\
 F_-: && \hspace{4ex} \sqrt{(6\%)^2 + (3\%)^2 + (3\%)^2 + (2\%)^2 } \approx 8\%, \label{eq:Fminussysterr} \\
 F_1: && \hspace{4ex} \sqrt{(6\%)^2 + (3\%)^2 + (1\%)^2 + (3\%)^2 } \approx 7\%, \label{eq:F1systerr} \\
 F_2: && \hspace{4ex} \sqrt{(6\%)^2 + (3\%)^2 + (13\%)^2 + (4\%)^2 } \approx 15\% \label{eq:F2systerr}.
\end{eqnarray}
Note that in contrast to Ref.~\cite{Detmold:2012vy}, here we choose to only evaluate the form factors in the
energy region where we have lattice data, and Eqs.~(\ref{eq:dipole}) and (\ref{eq:dipoleF1F2}) interpolate this data
in $E_N-m_N$. While we have investigated extrapolations into the large-energy region, such extrapolations necessarily
introduce model dependence (similar to that seen in Ref.~\cite{Detmold:2012vy}) and will not aid in a precision
extraction of $|V_{ub}|$ from experiment.

\begin{figure}
\includegraphics[width=0.465\linewidth]{fig2a.pdf}\hfill\includegraphics[width=0.465\linewidth]{fig2b.pdf} \\
\includegraphics[width=0.465\linewidth]{fig2c.pdf}\hfill\includegraphics[width=0.465\linewidth]{fig2d.pdf} \\
\includegraphics[width=0.465\linewidth]{fig2e.pdf}\hfill\includegraphics[width=0.465\linewidth]{fig2f.pdf} \\
\centerline{\includegraphics[height=5.65cm]{fig2g.pdf}}
\caption{\label{fig:qsqrasqrextrapall}Fits of the form factor data for $F_+$ and $F_-$ using Eq.~(\ref{eq:dipole}).
In the upper six plots, we show the lattice results together with the fitted functions evaluated at the corresponding
values of the pion mass and lattice spacing. In the lower plot, we show the fitted functions evaluated at the
physical pion mass and in the continuum limit. There, the inner shaded bands indicate the statistical/fitting
uncertainty, and the outer shaded bands additionally include the estimates of the systematic uncertainty given
in Eqs.~(\ref{eq:Fplussysterr}) and (\ref{eq:Fminussysterr}).}
\end{figure}

\begin{figure}
\includegraphics[width=0.48\linewidth]{fig3a.pdf}\hfill\includegraphics[width=0.48\linewidth]{fig3b.pdf} \\
\includegraphics[width=0.48\linewidth]{fig3c.pdf}\hfill\includegraphics[width=0.48\linewidth]{fig3d.pdf} \\
\includegraphics[width=0.48\linewidth]{fig3e.pdf}\hfill\includegraphics[width=0.48\linewidth]{fig3f.pdf} \\
\centerline{\includegraphics[height=5.65cm]{fig3g.pdf}}
\caption{\label{fig:qsqrasqrextrapallF1F2}Fits of the form factor data for $F_1$ and $F_2$ using Eq.~(\ref{eq:dipoleF1F2}).
In the upper six plots, we show the lattice results together with the fitted functions evaluated at the corresponding
values of the pion mass and lattice spacing. In the lower plot, we show the fitted functions evaluated at the physical
pion mass and in the continuum limit. There, the inner shaded bands indicate the statistical/fitting uncertainty,
and the outer shaded bands additionally include the estimates of the systematic uncertainty given in
Eqs.~(\ref{eq:F1systerr}) and (\ref{eq:F2systerr}).}
\end{figure}

\FloatBarrier
\section{\label{sec:FFcomparison}Comparison with other form factor results}
\FloatBarrier

It is interesting to compare our results for the $\Lambda_Q \to p$ form form factors to the corresponding results
for the $\Lambda_Q \to \Lambda$ transition obtained in Ref.~\cite{Detmold:2012vy}. This comparison is shown for
$F_1$ and $F_2$ in Fig.~\ref{fig:protonvsLambda}, where we plot the form factors vs.~$E_N - m_N$ and
$E_\Lambda - m_\Lambda$ as before. This choice of variables on the horizontal axis ensures that the points of
zero spatial momentum of the final-state hadron (in the $\Lambda_Q$ rest frame) coincide. As can be seen in the
figure, when compared in this way, the $\Lambda_Q \to p$ form factors have a larger magnitude than the
$\Lambda_Q \to \Lambda$ form factors. This difference is statistically most significant at zero recoil, and becomes
less well resolved at higher energy, where our relative uncertainties grow. For the ratio $F_2/F_1$, we are unable
to resolve any difference between $\Lambda_Q \to p$ and $\Lambda_Q \to \Lambda$, as shown on the right-hand side
of Fig.~\ref{fig:protonvsLambda}.

\begin{figure}[!t]
\includegraphics[height=7cm]{fig4a.pdf} \hfill \includegraphics[height=7cm]{fig4b.pdf}
\caption{\label{fig:protonvsLambda}Left: comparison of the form factors $F_1$ and $F_2$ for the $\Lambda_Q \to p$
transition to the analogous form factors for the $\Lambda_Q \to \Lambda$ transition \cite{Detmold:2012vy}, all
calculated using the same actions and parameters in lattice QCD. Right: comparison of the ratio $|F_2/F_1|$.
Only the statistical error bands are shown here for clarity.}
\end{figure}

It is also interesting to compare our QCD calculation of the $\Lambda_Q \to p$ form form factors with calculations
using sum rules \cite{Huang:1998rq, Carvalho:1999ia} or light-cone sum rules
\cite{Huang:2004vf, Wang:2009hra, Azizi:2009wn, Khodjamirian:2011jp}. However, most of these studies worked with the
relativistic form factors, and focused on the region of high proton momentum (low $q^2$), where our results would involve
extrapolation and hence model dependence. Only Ref.~\cite{Huang:1998rq} explicitly includes results for the HQET form
factors $F_1$ and $F_2$ in an energy region that overlaps with the region where we have lattice data. For example,
at $E_N-m_N=0.7$ GeV, the results obtained in Ref.~\cite{Huang:1998rq} for three different values of the Borel
parameter used in that work are $F_1\approx (0.46, 0.47, 0.50)$ and $F_2\approx (-0.13, -0.18, -0.27)$, while our
lattice QCD calculation gives
\begin{eqnarray}
 F_1(E_N-m_N=0.7\:{\rm GeV}) &=& 0.703 \pm 0.045 \pm 0.049,  \\
 F_2(E_N-m_N=0.7\:{\rm GeV}) &=& -0.124 \pm 0.025 \pm 0.019,
\end{eqnarray}
where the first uncertainty is statistical and the second uncertainty is systematic.

\section{\label{sec:Lambdabdecay}The decay $\Lambda_b \to p\: \ell^-\, \bar{\nu}_\ell$}

In this section, we use the form factors determined above to calculate the differential decay rates of
$\Lambda_b \to p\: \ell^-\, \bar{\nu_\ell}$ with $\ell=e,\mu,\tau$ in the Standard Model. The effective weak Hamiltonian
for $b \to u \:\ell^-\, \bar{\nu}_\ell$ transitions is
\begin{equation}
\mathcal{H}_{\rm eff} = \frac{G_F}{\sqrt{2}}V_{ub}\: \bar{u} \gamma_\mu(1-\gamma_5)b\: \bar{l} \gamma^\mu (1-\gamma_5) \nu,
\end{equation}
with the Fermi constant $G_F$ and the CKM matrix element $V_{ub}$ \cite{Cabibbo:1963yz, Kobayashi:1973fv, Wilson:1969zs}.
Higher-order electroweak corrections are neglected. The resulting amplitude for the decay
$\Lambda_b \to p\: \ell^-\, \bar{\nu}_\ell$ can be written as
\begin{eqnarray}
\nonumber \mathcal{M}&=&-i\,\langle N^+(p',s')\:\ell^-(p_-,s_-)\:\bar{\nu}(p_+,s_+) | \mathcal{H}_{\rm eff} | \Lambda_b(p,s) \rangle \\
 &=& -i \frac{G_F}{\sqrt{2}}V_{ub}\: A_\mu \:\bar{u}_{\ell}(p_-,s_-)\gamma^\mu(1-\gamma_5) v_{\bar{\nu}}(p_+,s_+),
\end{eqnarray}
where $A_\mu$ is the hadronic matrix element
\begin{equation}
A_\mu = \langle N^+(p',s')| \: \bar{u} \gamma_\mu(1-\gamma_5)b\: | \Lambda_b(p,s) \rangle.  \label{eq:hadMEqcd}
\end{equation}
Because we have computed the form factors in HQET, we need to match the QCD current $\bar{u} \gamma_\mu(1-\gamma_5)b$ in
Eq.~(\ref{eq:hadMEqcd}) to the effective theory. This gives (at leading order in $1/m_b$)
\begin{equation}
A_\mu = \sqrt{m_{\Lambda_b}} \langle N^+(p',s')| \big( c_\gamma\: \bar{u} \gamma_\mu Q + c_v\: \bar{u} v_\mu Q
- c_\gamma\: \bar{u} \gamma_\mu\gamma_5 Q + c_v\: \bar{u} v_\mu \gamma_5 Q  \big) | \Lambda_Q(v,s) \rangle,  \label{eq:hadMEHQET1}
\end{equation}
where $Q$ is the static heavy-quark field, and to one loop, the matching coefficients are given by \cite{Eichten:1989zv}
\begin{eqnarray}
c_\gamma &=& 1-\frac{\alpha_s(\mu)}{\pi}\left[ \frac{4}{3} + \ln\left( \frac{\mu}{m_b} \right) \right], \\
c_v      &=& \frac{2}{3} \frac{\alpha_s(\mu)}{\pi}.
\end{eqnarray}
Here we set $\mu=m_b$. We can now use Eq.~(\ref{eq:FFdef}) to express the matrix element $A_\mu$ in terms of the form
factors $F_1$ and $F_2$:
\begin{equation}
A_\mu = \bar{u}_N(p',s')\Big(F_1+\slashed{v} F_2\Big)\Big( c_\gamma \gamma_\mu + c_v \: v_\mu
- c_\gamma \: \gamma_\mu\gamma_5 +  c_v\: v_\mu\gamma_5  \Big) \sqrt{m_{\Lambda_b}} u_{\Lambda_Q}(v,s). \label{eq:hadMEHQET2}
\end{equation}
The factor of $\sqrt{m_{\Lambda_b}}$ in Eqs.~(\ref{eq:hadMEHQET1}) and (\ref{eq:hadMEHQET2}) results from the HQET
convention for the normalization of the state $| \Lambda_Q(v,s) \rangle$ and the spinor $u_{\Lambda_Q}(v,s)$. We can make
the replacement $\sqrt{m_{\Lambda_b}}\:u_{\Lambda_Q}(v, s) = u_{\Lambda_b}(p,s)$, where $p=m_{\Lambda_b} v$, and the
spinor $u_{\Lambda_b}(p,s)$ has the standard relativistic normalization. A straightforward calculation then gives the
following differential decay rate,
\begin{eqnarray}
\nonumber \frac{d\Gamma}{d q^2} &=& \frac{|V_{ub}|^2 G_F^2}{768 \pi^3 q^6 m_{\Lambda_b}^5} (q^2 - m_\ell^2)^2
\sqrt{((m_{\Lambda_b}+m_N)^2-q^2)((m_{\Lambda_b}-m_N)^2-q^2)}\\
&& \times \Bigg[  (4 c_\gamma^2+4 c_\gamma c_v+2c_v^2) m_\ell^2 \mathcal{F}\, \mathcal{I}+
\Big( 2 c_\gamma^2 (\mathcal{I}+3 q^2 m_{\Lambda_b}^2) + c_v (2 c_\gamma+c_v)(\mathcal{I}- 3 q^2 m_{\Lambda_b}^2) \Big)
q^2\mathcal{F} +4 c_\gamma (c_{\gamma}+c_v) \mathcal{K} \Bigg], \hspace{3ex}
\end{eqnarray}
where we have defined the combinations
\begin{eqnarray}
 \mathcal{F}&=&((m_{\Lambda_b}+m_N)^2-q^2)F_+^2+((m_{\Lambda_b}-m_N)^2-q^2) F_-^2, \\
 \mathcal{I} &=& m_{\Lambda_b}^4-2 m_N^2 (m_{\Lambda_b}^2+q^2)+q^2 m_{\Lambda_b}^2+m_N^4+q^4, \\
 \mathcal{K} &=& (2 m_\ell^2+q^2) ((m_{\Lambda_b}+m_N)^2-q^2)((m_{\Lambda_b}-m_N)^2-q^2)
   (m_{\Lambda_b}^2-m_N^2+q^2)  F_+ F_-,
\end{eqnarray}
and, as before, $F_\pm=F_1\pm F_2$. To evaluate this, we use $F_+$ and $F_-$ from the fits to our lattice QCD results,
which are parametrized by Eq.~(\ref{eq:dipole}) with the parameters in Table \ref{tab:dipolefitresults}. At a given
value of $q^2$, we evaluate the form factors at
\begin{equation}
 E_{N}-m_N = p'\cdot v-m_N = \frac{m_{\Lambda_b}^2+m_N^2-q^2}{2m_{\Lambda_b}}-m_N, \label{eq:E_N}
\end{equation}
with the physical values of the baryon masses (which we take from Ref.~\cite{PDG2012}).

In Fig.~\ref{fig:dGamma}, we show plots of $|V_{ub}|^{-2}\mathrm{d}\Gamma/\mathrm{d}q^2$ for the decays
$\Lambda_b \to p\: \mu^- \bar{\nu}_\mu$ and $\Lambda_b \to p\: \tau^- \bar{\nu}_\tau$ in the kinematic range where we
have lattice QCD results (in this range, the results for the electron final state look identical to the results for the
muon final state and are therefore not shown). The inner error bands in Fig.~\ref{fig:dGamma} originate from the total
uncertainty (statistical plus systematic) in the form factors $F_+$ and $F_-$. The use of leading-order HQET for the
$b$-quark introduces an additional systematic uncertainty in the differential decay rate, which is included in the outer
error band in Fig.~\ref{fig:dGamma}. At zero hadronic recoil, this uncertainty is expected to be of order
$\Lambda_{\rm QCD}/m_b$. At non-zero hadronic recoil, one further expects an uncertainty of order $|\mathbf{p'}|/m_b$,
because the proton momentum constitutes a new relevant scale. We add these two uncertainties in quadrature, and hence
estimate the systematic uncertainty in $|V_{ub}|^{-2}\mathrm{d}\Gamma/\mathrm{d}q^2$ that is caused by the use of
leading-order HQET to be
\begin{equation}
 \sqrt{\frac{\Lambda_{\rm QCD}^2}{m_b^2}+\frac{|\mathbf{p'}|^2}{m_b^2}},
\end{equation}
where we take $\Lambda_{\rm QCD}=500$ MeV.

\begin{figure}
\includegraphics[height=6.5cm]{fig5a.pdf} \hfill \includegraphics[height=6.5cm]{fig5b.pdf}
\caption{\label{fig:dGamma}Our predictions for the differential decay rates of $\Lambda_b \to p\: \mu^- \bar{\nu}_\mu$ (left)
and $\Lambda_b \to p\: \tau^- \bar{\nu}_\tau$ (right), divided by $|V_{ub}|^2$. We only show the kinematic region where
we have lattice QCD results for the form factors $F_+$ and $F_-$. The inner error band originates from the statistical
plus systematic uncertainty in $F_\pm$. The outer error band additionally includes an estimate of the uncertainty caused
by the use of leading-order HQET for the $b$ quark. The plot for $\Lambda_b \to p\: e^- \bar{\nu}_e$ is indistinguishable
from $\Lambda_b \to p\: \mu^- \bar{\nu}_\mu$ and is therefore not shown.}
\end{figure}

We also provide the following results for the integrated decay rate in the kinematic range of our lattice calculation,
$ 14\:{\rm GeV}^2 \leq q^2 \leq q^2_{\rm max}$ [where $q^2_{\rm max}=(m_{\Lambda_b}-m_N)^2$],
\begin{equation}
\label{eq:Gamma} \frac{1}{|V_{ub}|^2}\int_{14\:{\rm GeV}^2}^{q^2_{\rm max}}
\frac{\mathrm{d}\Gamma (\Lambda_b \to p\: \ell^- \bar{\nu}_\ell)}{\mathrm{d}q^2} \mathrm{d} q^2
 = \left\{ \begin{array}{ll} 15.3 \pm 2.4 \pm 3.4 \:\: \rm{ps}^{-1} & \hspace{1ex}{\rm for}\hspace{2ex}\ell=e, \\
                             15.3 \pm 2.4 \pm 3.4 \:\: \rm{ps}^{-1} & \hspace{1ex}{\rm for}\hspace{2ex}\ell=\mu, \\
                             12.5 \pm 1.9 \pm 2.7 \:\: \rm{ps}^{-1} & \hspace{1ex}{\rm for}\hspace{2ex}\ell=\tau.
            \end{array} \right.
\end{equation}
Here, the first uncertainty originates from the form factors, and the second uncertainty originates from the use of the static
approximation for the $b$-quark. With future experimental data, Eq.~(\ref{eq:Gamma}) can be used to determine $|V_{ub}|$.

\FloatBarrier
\section{\label{sec:conclusions}Discussion}
\FloatBarrier

We have obtained precise lattice QCD results for the $\Lambda_Q \to p$ form factors defined in the heavy-quark limit.
These results are valuable in their own right, as they can be compared to model-dependent studies performed in the same limit,
and eventually to future lattice QCD calculations at the physical $b$ quark mass.
For the $\Lambda_b \to p\: \ell^- \bar{\nu}_\ell$ differential decay rate, the static approximation introduces
a systematic uncertainty that is of order $\Lambda_{\rm QCD}/m_b\sim10\%$ at zero recoil and grows as the momentum
of the proton in the $\Lambda_b$ rest frame is increased. The total uncertainty for the integral of the differential decay
rate from $q^2=14\:{\rm GeV}^2$ to $q^2_{\rm max}=(m_{\Lambda_b}-m_N)^2$, which is the kinematic range where we have
lattice data, is about 30\%. Using future experimental data, this will allow a novel determination of the CKM matrix element
$|V_{ub}|$ with about 15\% theoretical uncertainty (the experimental uncertainty will also contribute to the overall extraction).
The theoretical uncertainty is already smaller than the difference between the values of $|V_{ub}|$ extracted from inclusive
and exclusive $B$ meson decays [Eqs.~(\ref{eq:Vubincl}) and (\ref{eq:Vubexcl})], and can be reduced further by performing
lattice QCD calculations of the full set of $\Lambda_b \to p$ form factors at the physical value of the $b$-quark mass.
In such calculations, the $b$ quark can be implemented using for example a Wilson-like action
\cite{ElKhadra:1996mp, Aoki:2001ra, Christ:2006us}, lattice nonrelativistic QCD \cite{Lepage:1992tx}, or higher-order
lattice HQET \cite{Blossier:2012qu}. Once the uncertainty from the static approximation is eliminated, other systematic
uncertainties need to be reduced. In the present calculation, the second-largest source of systematic uncertainty is the
one-loop matching of the lattice currents to the continuum current; ideally, in future calculations this can be replaced
by a nonperturbative method. We expect that after making these improvements, the theoretical uncertainty in the value of
$|V_{ub}|$ extracted from $\Lambda_b \to p\: \ell^- \bar{\nu}_\ell$ decays will be of order 5\%, and comparable to the
theoretical uncertainty for the analogous $\bar{B} \to \pi^+ \ell^- \bar{\nu}_\ell$ decays.

\FloatBarrier

\begin{acknowledgments}
We thank Ulrik Egede for a communication about the possibility of measuring $\Lambda_b \to p\: \mu^- \bar{\nu}_\mu$ at LHCb.
We thank the RBC and UKQCD collaborations for providing the gauge field configurations. This work has made use of the Chroma
software system for lattice QCD \cite{Edwards:2004sx}. WD and SM are supported by the U.S.~Department of Energy under
cooperative research agreement Contract Number DE-FG02-94ER40818. WD is also supported by U.S.~Department of Energy
Outstanding Junior Investigator Award DE-S{C0}0{0-17}84. CJDL is supported by Taiwanese NSC Grant Number 99-2112-M-009-004-MY3,
and MW is supported by STFC. Numerical calculations were performed using machines at NICS/XSEDE (supported by National
Science Foundation Grant Number OCI-1053575) and at NERSC (supported by U.S.~Department of Energy Grant Number DE-AC02-05CH11231).
\end{acknowledgments}

redpajama_set_name: RedPajamaArXiv


text:
The Facts of Life Reboot in the Works
By Andy Swift / August 3 2018, 12:11 PM PDT
Courtesy of Columbia Pictures Television
You take the good, you take the bad, you take 'em both, and there you have… yet another reboot of a classic TV series.
TV Reboots and Revivals: A Complete Guide
An updated take on The Facts of Life is currently in development, our sister site Deadline reports, with Leonardo DiCaprio's Appian Way and Jessica Biel's Iron Ocean Films in talks to produce.
The original Facts of Life, which aired on NBC from 1979 to 1988, followed a group of girls — Blair (Lisa Whelchel), Natalie (Mindy Cohn), Jo (Nancy McKeon), Tootie (Kim Fields) and a revolving door of other characters — living at Eastland School, an all-girls boarding academy in Peekskill, N.Y. Under the tutelage of the wise Edna Garrett (Charlotte Rae), they learned… well, exactly what the title suggested. The show was a spinoff of Diff'rent Strokes, on which Mrs. Garrett served as the Drummonds' housekeeper.
The Facts of Life joins a slew of other classic series currently being redeveloped for a modern audience. Earlier this week, TVLine exclusively reported that a reboot of ALF is in the works at Warner Bros. TV.
Your thoughts on a new Facts of Life? Drop 'em in a comment below. And good luck getting this theme song out of your head…
TAGS: The Facts of Life
GET MORE: Revivals and Reboots

redpajama_set_name: RedPajamaCommonCrawl


text:
Q: What information does "Top" output while using MPI I am trying to figure out how much memory my program which uses MPI needs. It was suggested to use the function "top" to obtain the usage of memory. However, I am unclear on what the information means.
I wish to know how to estimate the system memory and how much it utilizes?
top - 13:52:41 up 208 days, 19:50,  1 user,  load average: 0.68, 0.15, 0.05
Tasks:  86 total,   6 running,  80 sleeping,   0 stopped,   0 zombie
Cpu(s): 98.5% us,  0.6% sy,  0.0% ni,  0.8% id,  0.0% wa,  0.0% hi,  0.1% si
Mem:   1024708k total,   225144k used,   799564k free,   104232k buffers
Swap:        0k total,        0k used,        0k free,    37276k cached

PID   USER      PR  NI  VIRT RES  SHR  S %CPU  %MEM  TIME+  COMMAND
12052 amohan    16   0  9024 4756 5504 R 99.0  0.5   0:09.65 greet
12054 amohan    16   0  9024 4756 5504 R 99.0  0.5   0:09.64 greet
12055 amohan    16   0  9024 4752 5504 R 98.7  0.5   0:09.65 greet
12053 amohan    16   0  9024 4760 5504 R 98.7  0.5   0:09.63 greet

This question is related to an earlier post Fatal Error in MPI_Irecv: Aborting Job

A: The standard information displayed by top is, in order:

*

*The Process ID

*The owning username

*The kernel-assigned process priority (higher is "lower" priority)

*The "niceness" of the process (higher is "nicer" to other processes and gives the process a "lower" priority)

*The virtual memory allocated for the process in KiB

*The resident memory in use by the process (the memory that has been malloc()ed and is not swapped out) in KiB

*The shared memory (the memory that is accessible to both the running process, its sibling processes, and any other processes that have been granted access) accessible to the process in KiB

*The run state (R is running, Z is zombie, S is sleeping, etc.)

*The % of CPU in use (obviously)

*The % of memory in use relative to total system memory

*The cumulative time that the process has been in a Run state

More detailed information should be available in man top.
In particular, the memory that MPI likely uses is contained in the shared memory area. More detailed information can be pulled from the /proc/ directory, but I don't know the specifics off the top of my head.

redpajama_set_name: RedPajamaStackExchange


The Q-SAFE practical driving test is an important step in Queensland's graduated licensing system. The practical driving test helps identify drivers who are ready to progress to a different licence class and drive safely on their own.
Find more information about driver tests.
This manual is used to guide Driver Examiner's through the requirements and procedures of the Q-SAFE practical driving test. Learner drivers can also read this guide to help them prepare for their Q-SAFE practical driving test.


text:
The newsletter of the Emassy of the Republic of South Africa is published on a monthly basis and features political, economic, touristic and cultural information on South Africa as well as on South Africa in Germany.
By clicking on the links below, you can:
|+| Subscribe to the Newsletter
|+| Unsubscribe from the Newsletter
|+| Minister Lindiwe Sisulu welcomes decision by EU countries to remove South Africa from red lists
|+| President Cyril Ramaphosa Delivered Eulogy at the Funeral Service of Archbishop Emeritus Desmond Mpilo Tutu
|+| President Honours Anglican Archbishop Emeritus Desmond Tutu with Special Official Funeral Category 1
|+| President Cyril Ramaphosa: Message on the passing of Anglican Archbishop Emeritus Desmond Mpilo Tutu
|+| Statement on the passing of Archbishop Emeritus Desmond Mpilo Tutu 26 December 2021


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Founded in 1995, the Elephant Theatre Company has long been a Los Angeles creative mainstay. Mounting World Premieres, West Coast Premieres and Los Angeles Premieres, the company and its Co-Artistic Directors David Fofi and Lindsay Allbaugh are committed to fostering new and groundbreaking works. Featuring the plays of artists such as Timothy McNeil, Stephen Adly Guirgis, Kevin King, Mark Roberts, Kate Fodor, Tony Foster, Louis Douglas Jacobs and Tom Stanczyk, the Elephant Theatre Company has won and been nominated for numerous awards, including the Garland, LADCC, Ovation and LA Weekly and has been described as "superb" and "gem-like" by the Los Angeles Times and "piping-hot" by Variety. Voted Favorite Theatre Company to see and to work with in Back Stage for the last three years, the Elephant continues to grow and solidify its reputation as one of the best Los Angeles theatre companies. The company recently announced a partnership with New York's LAByrinth Theater Company.
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If you're waiting to see if mortgage rates are going to come down any further you may have to wait a long time. Historically, rates have never been as low as they are now and the pressure for rates to increase is growing, albeit slowly. As recently as the middle of August the RBC (Royal Bank of Canada) raised some of its fixed rates and in particular the Special Offer 5-year fixed rate, rose 20 bps to 3.69% on August 21st. Of course this is only one lender and time will tell if there is an upward trend in interest rates on mortgages and borrowing in general.
That's not to say that every other lender will do the same, or be forced to do the same, but it may well be an indication to the market that the continuous downward trend of Canadian mortgage rates may be coming to an end. It may be that fixed rate mortgages will be available at these historically low rates for quite some time to come as the market continues to drag itself out of recession. However, if that is the case, it could be paving the way for more restrictions and less flexibility than we have seen of late.
The point is that if you are considering re-mortgaging or taking the plunge for the first time now is as good a time as any to do so. Real estate values continue to remain fairly buoyant, although there are geographical differences to be expected. Certain sectors of the market remain at risk but in the main it appears that Canadian real estate is faring extremely well given the weakness of the global economy as a whole. As the global economy recovers and evolves (as it surely will) the gains you make on real estate investment stand to be very healthy indeed.
If you're in the market for a short term loan then fixed Canadian mortgage rates are great value; however, if you're in it for the long term maybe a variable rate is best for you but don't worry, if rates do subsequently decrease and the rate you get now is not as competitive as say, in one year's time, do what every wise borrower does – re-mortgage at the new lower fixed rate. My belief is that low interest rates and new, emerging mortgage deals are here for a while longer.
It's time to take advantage of all those juicy Canadian mortgage rates to raise your standard of living as a whole.


text:
Helge BergerIMFBlog2020-01-09T11:58:55-05:00
Helge Berger is an Assistant Director in the IMF's Research Department. He is also an adjunct professor of monetary economics at Free University of Berlin. He was educated in Munich, Germany, where he received his Ph.D. and the venia legendi for economics. Previously, he taught at Princeton University as a John Foster Dulles Visiting Lecturer, helped to coordinate the Munich-based CESifo network as its research director, and served as full professor (tenured) at Free University Berlin.
Latest Post:
Chart of the Week: Grading the G-20 on its Growth Goals
The Euro Area Needs a Fiscal Union
Taming government debt—it can be done, but it ain't easy


text:
NASHVILLE — The Sons of Confederate Veterans and City of Memphis argued before the Tennessee Court of Appeals on Tuesday about what should come next in determining the legality of the city's process of removing Confederate statues.
The Memphis City Council in December 2017 approved for $1,000 each the sale of Health Sciences Park and Fourth Bluff Park to Memphis Greenspace, a nonprofit that had been formed by Shelby County Commissioner Van Turner. The decision, the city has argued, allowed them to have have the statues legally removed.
The Tennessee Heritage Protection Act requires that a public entity obtain a waiver approving the removal or relocation of historic monuments, which the state historic commission had repeatedly denied to Memphis.
Hours after the sale, the nonprofit removed Confederate statues located in the parks — monuments to Confederate Gen. Nathan Bedford Forrest, President Jefferson Davis and Capt. J. Harvey Mathes — and stored them offsite.
The nonprofit has said it is interested in moving them to a location where they can be displayed in proper context, but has no plans to destroy the statues.
"We presented ample evidence of why we did that, and it wasn't because we are alien to history or converse to Confederate monuments," said Allan Wade, an attorney representing Memphis, while speaking to a panel of three judges at the appellate hearing.
"We had legitimate reasons for not expending sacred resources to defend inanimate objects, using police resources when we have public safety issues in our city."
According to a 2017 report from the Memphis Police Department, the city spent tens of thousands of dollars on police patrol at the statue
Chris Vescovo, an attorney representing Memphis Greenspace, used a portion of the city's time to argue that the statues weren't subject to the heritage protection provisions after the sale.
"They became private property, and at that point, they could be removed because it's only memorials on public property that may not be removed," Vescovo said.
While the 2018 Heritage Protection Act prohibits the sale of historic statues, there was no such language in the 2016 version of the act, which applied at the time Memphis sold the park land to Greenspace and prevents the removal of monuments.
Davidson County Chancellor Ellen Hobbs Lyle last year lifted an injunction that prevented the relocation of the statues, but then issued a stay in order to give SCV more time to appeal and seek a new injunction.
Doug Jones, the attorney representing SCV, asked the court to rule to keep the monuments in place until the Tennessee Historic Commission can make a determination on whether the sale of the statues to a private group constituted a violation of the Heritage Protection Act, though no such hearing has taken place.
"We would ask that the court protect these monuments," Jones said. "This is American history, whether you like Confederates or southern history. It's American history."
Vescovo argued that the historic commission does not have jurisdiction to make that determination and has "no authority whatsoever to hear" the case.
The judges, Richard H. Dinkins, Frank G. Clement Jr. and W. Neal McBrayer, will consider the sides' arguments and issue a ruling.
Reach Natalie Allison at nallison@tennessean.com. Follow her on Twitter at @natalie_allison.
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More:Memphis among cities where future of Confederate statues remains unclear


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On long backpacking trips sometimes I have thoughts. Some are important and I keep those to myself. Others are silly and I share them here. Here are 10 of those "thoughts in progress" from my trek through Olympic National Park and the wilderness coast in July of 2016. Enjoy!
Oftentimes while on solo trips I get weirdly introspective. This post is from a recently found note written on the last day of a weeklong backpacking trip through Olympic National Park in July of 2016. Straight from my notebook and published without revisions.


text:
Q: Open huge text file and perform regex searching I'm trying to open a huge text file (1 GB) and perform some text mining.
I'm willing to perform some regex searching.
When I'm using the read() function, I'm getting the error:
File "C:\Python33\lib\encodings\latin_1.py", line 26, in decode
return codecs.latin_1_decode(input,self.errors)[0]
MemoryError

My code is:
dataFile = open('data/AllData_2000001_3000000.txt', 'r', encoding="latin-1")
print(dataFile.read())

What will be the best way to open the text, in order to perform regex search?
Thanks!

A: By doing print(dataFile.read()) you're loading the whole file in memory, that's why you're getting the error. A better way to do it would be line by line:
dataFile = open('data/AllData_2000001_3000000.txt', 'r', encoding="latin-1")
for line in dataFile:
    #perform regex searching in each line here
    print(line)

Hope this helps!

A: Depends on what you want to do:
If you really want to perform a regex search on the whole 1GB in one piece, you don't have a lot of options. Switching to 64-bit Python might be one if you're using a 32-bit version right now.
Is your text file organized in lines or something the like? In that case you can read one line, process it, go to the next and so on. Of course this works with any kind of 'chunk' that you can isolate.


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text:
Estate Planning After Divorce Or Separation
Family Law Agreements
Children's Family Law Issues
Collaborative Family Law
Mobility in Family Law Part 2
On behalf of Henderson Heinrichs LLP on Monday, September 22, 2014.
Joseph Broadhurst of our firm has recently achieved success in both a BC Supreme Court trial (A.B. v. C.D., 2014 BCSC 1081) and an appeal from Provincial Court to BC Supreme Court (C.M.B. v. B.D.G., 2014 BCSC 780) on the issue of mobility. This is the second part of our three part series explaining the law when one parent wants to move and the other wants to stay. The first part is available here. We previously discussed the different standards and different laws applied in determining mobility. Next we are going to look at exactly how the Court approaches the question of what is in the best interests of the Child. The Supreme Court of Canada case Gordon v. Goertz, [1996] 2 SCR 27 sets out the relevant factors that the court should consider for married couples. They are as follows:
the existing custody arrangement and relationship between the child and the custodial parent;
the existing access arrangement and the relationship between the child and the access parent;
the desirability of maximizing contact between the child and both parents;
the views of the child;
the custodial parent's reason for moving, only in the exceptional case where it is relevant to that parent's ability to meet the needs of the child;
disruption to the child of a change in custody;
disruption to the child consequent on removal from family, schools, and the community he or she has come to know.
For unmarried parties the factors are a little different and are set out in the Family Law Act. The relevant factors for unmarried parties are:
the child's health and emotional well-being;
the child's views, unless it would be inappropriate to consider them;
the nature and strength of the relationships between the child and significant persons in the child's life; the history of the child's care;
the child's need for stability, given the child's age and stage of development;
the ability of each person who is a guardian or seeks guardianship of the child, or who has or seeks parental responsibilities, parenting time or contact with the child, to exercise his or her responsibilities;
the impact of any family violence on the child's safety, security or well-being, whether the family violence is directed toward the child or another family member;
whether the actions of a person responsible for family violence indicate that the person may be impaired in his or her ability to care for the child and meet the child's needs;
the appropriateness of an arrangement that would require the child's guardians to cooperate on issues affecting the child, including whether requiring cooperation would increase any risks to the safety, security or well-being of the child or other family members;
any civil or criminal proceeding relevant to the child's safety, security or well-being.
While these factors are a little bit different, in practical application they are very similar and will generally lead to the same results.
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Family law: Some vaccination debates end up in court
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We're constantly on the look out for bright, shiny, enthusiastic folk with a zest for life, love of good food and a work ethic that would shame a beaver. We're more interested in your potential and what you're about to do than what you've already done so don't worry if your CV is a bit rusty.
It's fair to say that Olives Et Al is no ordinary place to work. It can be fun, challenging, frustrating and rewarding all in equal measure and we think it's really important to give everyone who works here the opportunity to develop and shine. Of course, like most jobs, it can also be boring, repetitive, and very hard work. Whilst we all have proper job descriptions, Olives Et Al is still a team operation and if there's a job to be done then sleeves get rolled up and everyone pitches in. We try hard not to have too many demarcation lines and office politics; we don't have too much hierarchy either, so you'll never be asked to do something that nobody else is prepared to do.
If all this sounds like you and you'd like to find out more then drop us a line and we can go from there.
We arrange to have an initial chat over the phone to see whether what we've got matches what your after and vice versa. If that works out this is followed by coming in to meet us and have a good look around the place to see if we both like what we see and finally a decent interview to explore each other in more depth. No weird questions. No staged emergencies and no confrontation – just a smooth series of conversations in a friendly environment which is exactly what it's supposed to be all about. Let's chat.


text:
Kongsberg, Thales Ink New Protector Weapon Systems Agreement
Kongsberg Defence and Aerospace has partnered with Thales UK to support the British armed forces' Protector Remote Weapon Systems (RWS) program.
Under the agreement, the companies will work on various capabilities for the maturation of the Protector weapon system in the UK military and foreign markets.
The memorandum of agreement builds on an existing collaboration signed by the companies in 2007.
Kongsberg and Thales have promoted the Protector RWS globally, integrating approximately 1,000 of the weapon systems into the British defense.
"I am delighted to be re-signing this memorandum of agreement that consolidates our existing partnership over 20 years," Thales UK Managing Director Stephen McCann explained.
"A partnership that has secured a major role within the UK Army's Boxer Strategic Pipeline and has grown from strength to strength."
"I look forward to extending the reach and scope of a partnership in the UK and throughout Europe and supporting Kongsberg in the United States of America."
Expanding Collaboration
According to Kongsberg, the Protector RWS was selected by the UK Ministry of Defence for its high accuracy, sensor performance, system modularity, and flexibility.
A Nexter VBCI 2 fitted with Kongsberg's medium-calibre turret and Protector remote weapon system at the DIMDEX exhibition in Doha, Qatar. Source: Kongsberg
The Protector family includes light machine guns, light cannons, and medium-caliber cannons that can be mounted on land vehicles and stationed platforms.
In the past 20 years, over 20,000 Protector RWS have been delivered to 28 nations.
"PROTECTOR Programmes, projects and capability areas KONGSBERG and Thales UK aspire to collaborate in have steadily grown since we signed the last agreement in 2017," Kongsberg Executive Vice President of Land Systems Eirik Tord Jensen said.
See also Ukraine Warns of Fresh Russian Missile Strikes
"Both companies have expressed a high level of ambition to expand our relationship over the coming 5 years."
Latest Protector Contracts
Kongsberg's most recent Protector RWS milestone was a $1.5 billion contract to extend its supply to the US Army.
Another achievement was a Mechanized Infantry Vehicle agreement for the British Army's Protector RS4 variant Boxer armored multirole vehicle.
Tags: Agreement, Ink, Kongsberg, Protector, Systems, Thales, Weapon
Previous British Army Investing $109M in Advanced Communication System
Next US Approves $323 Million Missile Sale to Finland


text:
M&S plans closure of 14 more UK stores
British retailer Marks & Spencer said on Wednesday six UK stores would close by the end of April, while a further eight had been identified for closure.
M&S said in November 2016 it would reposition about 25 percent of its clothing and home space through a combination of closures, downsizes, relocations and conversions to food-only stores. In November last year it said it was accelerating this programme.
The group said all staff from the six stores closing in April will move to nearby stores. It said 468 employees would be affected at the eight stores proposed for closure and will now enter a period of consultation.
M&S also said it had reassessed and reduced its "Simply Food" opening programme, and now only plans to open a total of 36 owned and franchise stores over the next six months.
It said these stores would create 1,200 jobs.
#retail, #uk, Other
Bargain retail chain has eyes on Northern Ireland expansion
Dubai launches world's first floating drive-thru


text:
The Threat of Terrorism from Western Foreign Fighters in Syria and Iraq
Be Afraid. Be A Little Afraid: The Threat of Terrorism from Western Foreign Fighters in Syria and Iraq
Listen To Audio Download the Audio Download
10:00 AM EST - 11:30 AM EST
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Twitter Join the conversation on Twitter using #foreignfighters
As many as 3,000 foreign fighters from Europe and North America have gone to Syria and Iraq to become soldiers, most often fighting for jihadist groups such as ISIS and Al-Nusra. Western foreign fighters have traveled to conflicts in the Islamic world in the past—in Afghanistan, in Iraq and in Somalia, for example—but never in such numbers. U.S. and European officials have expressed fears that this unprecedented flow of foreign fighters creates a serious threat that some of them will someday return and commit terrorist acts in their country of origin.
On January 12, the Center on the United States and Europe and the Center on Middle East Policy launched a new policy paper by Senior Fellow Daniel Byman and Fellow Jeremy Shapiro that examines the threat that Western foreign fighters pose to their homelands. The paper argues that although the threat of foreign fighters to the West is real, it has also been exaggerated and that Western security services have the knowledge and capacity to deal with the problem.
Following opening remarks, Daniel Benjamin, Norman E. McCulloch Jr. Director of the John Sloan Dickey Center for International Understanding at Dartmouth and former Coordinator for Counterterrorism at the U.S. State Department offered comments. Brookings Fellow Will McCants moderated the discussion.
Join the conversation on Twitter using #foreignfighters
Daniel L. Byman
Senior Fellow - Foreign Policy, Center for Middle East Policy
Twitter dbyman
Nonresident Senior Fellow - Foreign Policy, Strobe Talbott Center for Security, Strategy, and Technology, The Intelligence Project
Center on the United States and Europe
Center for Middle East Policy
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text:
Q: How to write the correct relative path to the file I'm doing an exercise where it picks and displays three random cards from a file of card images stored in lib/cards/cards of the project. Card images are named from 1.png to 52.png.
My java file is in src which has the same level with lib
Here's the code I used.
Random rd = new Random();
int[] card = new int[3];
//randomize cards
card[0] = rd.nextInt(52) + 1;
card[1] = rd.nextInt(52) + 1;
card[2] = rd.nextInt(52) + 1;
ImageView image_0 = new ImageView("lib/cards/cards/"+ Integer.toString(card[0]) + ".png");
ImageView image_1 = new ImageView("D:/Visual Studio/New/Test/lib/cards/cards/"+ Integer.toString(card[1]) + ".png");
ImageView image_2 = new ImageView("D:/Visual Studio/New/Test/lib/cards/cards/"+ Integer.toString(card[2]) + ".png");

Absolute path works just fine for image_1 and image_2, and relative path doesn't work for image_0. I wonder if I can use relative path for this, and if I can how to write the correct relative path for this to work.

A: try adding ./ in the beginning of the path if the image in the same folder as the file u are in ex if your current file is in lib and the image is in lib type ./nameOfImage
if u want to go one level app (AKA if the image in the parent folder ) add ../ to the beginning of the path ex if your current file is in lib and your image is in the Test folder to go to it your file will be ../nameOfImage


text:
If you want to purchase just one movie from the Rocky series, this one captures it all.
Genre(s): Drama, Sport
Director: Sylvester Stallone
Actors: Sylvester Stallone, Talia Shire, Burt Young, Carl Weathers, Tony Burton, Brigitte Nielsen, Dolph Lundgren, Michael Pataki
Rocky IV embodies the best and worst qualities of the Rocky series. As such, it's as fun to make fun of as it is genuinely enjoyable. The movie is wrapped around the soundtrack like an elaborate music video, but with songs this good and villains this bad, it's impossible not to get caught up in the action. What it lacks in substance, Rocky IV makes up in scale. As they say in Scarface, "Nothing exceeds like excess."
After his win against Clubber Lang, Rocky truly has it all. His family is happy, and they're so wealthy they make Richie Rich look like a schmo. After all, did Richie Rich ever have a robot that could serve birthday cake, bring you the phone, and pump out cool 80's music? I think not. Rocky's only lament is that with the glory days behind him, he's becoming a regular person.
All of this changes when Soviet powerhouse Ivan Drago (Dolph Lundgren) challenges Rocky to a fight on national television. Apollo sees the challenge as he's watching T.V. in the pool, then hightails it to Rocky's house. He's got the brilliant idea to fight Drago first, and orchestrates the show of shows. Remember the crazy display of patriotism at the original fight in Rocky ? Well multiply it tenfold, and you've got a pretty good idea of what you're about to see.
Rocky rolls his eyes as James Brown sings "Living in America" live, but the mood at this overblown extravaganza quickly changes once the fight begins. Drago must be some sort of superhuman science experiment, because he has no limits and no mercy. The fight intended to be the grand finale of Apollo's career quickly turns into the grand finale of Apollo's life.
Inundated with death threats and hate mail, Drago's wife (Brigitte Nielsen) makes her poetic you-have-this-belief speech: "You have this belief, that Americans are so very good. You have this belief that the Soviets are so very bad. You have this belief that Americans are so very fair. You have this belief…" You get the picture. She prattles on about how her husband is a fighter, not a soldier, as if he's the poor baby that needs protecting. They return to the U.S.S.R. to ensure their personal safety, but Rocky is determined to avenge Apollo's death. Naturally Adrian begs him not to follow in Apollo's footsteps.
Torn, Rocky climbs into his sports car and reflects upon his life as "No Easy Way Out" by Robert Tepper blares from the stereo. Through flashbacks, we relive Adrian and Rocky's first kiss, the birth of Rocky Jr., various runs up the museum steps, and lots of fun with Apollo. If you want to purchase just one movie from the Rocky series, this one captures it all.
You can probably guess that all this rumination leads Rocky to pack up Paulie and head to Siberia. He must take a stand for Apollo's sake! Once there, he carries logs while walking through knee-deep snow, pulls a sleigh like a demented sled dog, does crazy full-body sit-ups, climbs a mountain, and grows a beard. Even his hired minders in their fancy car can't keep up with him. Meanwhile Drago trains at a bizarre government facility like some sort of lab rat. His punches are calibrated by machine, and clock in at thousands of pounds. He may be a giant, but we know the man will win, especially with Adrian by his side.
On the night of the fight, Ivan Drago steps into the ring wearing a disgusting black mouthguard, and declaring, "If he dies, he dies." Staring Rocky in the face, he hisses, "I must break you." Ew! Not even, "I will break you" or "I want to break you," but "I must", like before I do anything else at all. He's taller, and his reach is longer, but he's just fighting. Rocky is standing up for his fallen friend, for the United States, for the common man, for all that is just and good. Soon even the Soviet people are chanting his name, much to the chagrin of Mrs. Drago. Apparently people will always root for a hardworking, pure-hearted underdog regardless of nationality – especially when he's this good-looking and brings along such excellent American music.


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I've made a scarf that I'd like to add fringe to the edge, is there any way to know how many beads I will need to order for this project? And what types of seed beads are best for fringe?
The amount of beads you will need is determined by the size bead you choose and the length of your fringe. Seed beads make nice fringe. Because they range in size and come in many different colors and finishes, it's easy to find the right bead for the project. The size seed bead that you should use is dependent on the size of thread, cord or yarn that you would like to use on the scarf, as well as if you want a delicate fringe or a more sizable full fringe. For a finer thread or cording and a more delicate styled fringe, you could use a size 11/0 seed bead. A size 6/0 seed bead would work well with a heavier gauge cording or fine yarn and will make a fuller fringe. The ''Wire Gauge to Inches and Millimeters Conversion Chart'' converts to inches or millimeters and will help you to determine the size beads that will fit onto your thread.
Once you have these parameters figured out, determine the size of the seed bead based on the "Seed Bead Sizes and Holes Sizes" chart. Lay your scarf on a plain piece of paper then sketch how long you want the fringe to be. Sketch in the seed beads as close to their true size as possible to then determine how many beads you will need for each fringe. Then sketch in the fringe across the end of the scarf to determine how many fringes are needed for one end. The final formula will look like this: # of seed beads x # of fringe x 2 = seed beads needed.


text:
Axel Bühler (* 13. Februar 1966 in Freiburg im Breisgau) ist ein deutscher Politiker der Grün-Alternativen Liste (GAL) und ehemaliges Mitglied der Hamburgischen Bürgerschaft.

Leben
Axel Bühler besuchte die Schule im Saarland und in Hannover. Sein Abitur machte er dann in Karlsruhe. Es folgte ein Studium der Physik an der Universität Hamburg. Während dieser Zeit arbeitete er als EDV-Berater und Fachübersetzer.

Politik
Zur Politik kam Bühler über die kirchliche Jugendarbeit, Friedensbewegung und die studentische Selbstverwaltung. In die GAL trat er 1995 ein.

Er war für die GAL Mitglied der Hamburgischen Bürgerschaft in der 16. Wahlperiode von 1997 bis 2001. Für seine Fraktion übernahm er die Aufgabe als energiepolitischer Sprecher und saß im Ausschuss für Europa und Städtepartnerschaften, im Umweltausschuss, im Haushaltsausschuss sowie im Wirtschaftsausschuss.

Ähnlich wie Joschka Fischer, der 1985 in Turnschuhen im Hessischen Landtag erschien und damit für Wirbel sorgte, war Bühler 1999 in kurzen Hosen in der Bürgerschaft erschienen. Die Aktion hatte zwar kein weiteres Nachspiel, wurde aber auch nicht wiederholt.

Literatur
 Bürgerhandbuch – Bürgerschaft der Freien und Hansestadt Hamburg, 16. Wahlperiode (Stand August 1997), S. 32.

Einzelnachweise

Mitglied der Hamburgischen Bürgerschaft
Bündnis-90/Die-Grünen-Mitglied
Politiker (20. Jahrhundert)
Deutscher
Geboren 1966
Mann

redpajama_set_name: RedPajamaWikipedia


text:
Q: Align button at the bottom of div I am having trouble trying to get the button in each div ".inductees" to sit at the bottom it. The height of the div is set after the document is loaded via a javascript that takes the largest height and sets the rest equal to it. Thus my problem of how to get it to the bottom. I have tried several methods but they all break the Bootstrap columns.
jsfiddle
CSS
.inductees {
    margin-bottom: 50px;
    padding-bottom: 10px;
    background-color: #FFF;
}
.inductees .info-text {
    color: #494743;
    padding: 10px;
}
.center {
    text-align: center;
}

HTML

Shelmer Doyle Blackburn Jr.

Year Inducted: 2014

Blackburn established The Blackburn Family Foundation Charitable Organization. He is the former Chairman of Adult Enrichment Services of Wilkes County and was instrumental in the establishment of the Ruby Pardue Blackburn Adult Day Care.

<button class="btn btn-primary btn-lg">See More</button>

Zachary Knight Galifianakis

Year Inducted: 2014

Galifianakis' career began on television, and he currently thrives in the film industry as an award-winning supporting actor.

<button class="btn btn-primary btn-lg">See More</button>

Shelmer Doyle Blackburn Jr.

Year Inducted: 2014

Blackburn established The Blackburn Family Foundation Charitable Organization. He is the former Chairman of Adult Enrichment Services of Wilkes County and was instrumental in the establishment of the Ruby Pardue Blackburn Adult Day Care.

<button class="btn btn-primary btn-lg">See More</button>

Zachary Knight Galifianakis

Year Inducted: 2014

Galifianakis' career began on television, and he currently thrives in the film industry as an award-winning supporting actor.

<button class="btn btn-primary btn-lg">See More</button>

Any suggestions?

A: You could add another class that absolute positions the parent div of the button. Then set bottom: 0, and the width 100% to allow to still center.
For instance something like:
.alignBottom {
  position:absolute;
  bottom: 0;
  width: 100%;
}

JSFiddle here to see it working:
https://jsfiddle.net/5hd7ow7p/2/

A: You just need to add 2 css
.inductees{
    position:relative;
}
.inductees .btn{
    position:absolute;
    bottom:15px;
    left: 50%;
    transform: translateX(-50%);
    -webkit-transform: translateX(-50%);
    -moz-transform: translateX(-50%);
}

A: You were closing the inductee info text div tags after the button, so the button was layering ontop.
Make sure the text div is seperate to the button. This is the updated version, edit the margin and padding for the info-text divs and button divs to center them. But this answers your question.
HTML:

Shelmer Doyle Blackburn Jr.

Year Inducted: 2014

Blackburn established The Blackburn Family Foundation Charitable Organization. He is the former Chairman of Adult Enrichment Services of Wilkes County and was instrumental in the establishment of the Ruby Pardue Blackburn Adult Day Care.

<button class="btn btn-primary btn-lg">See More</button>

Zachary Knight Galifianakis

Year Inducted: 2014

Galifianakis' career began on television, and he currently thrives in the film industry as an award-winning supporting actor.

<button class="btn btn-primary btn-lg">See More</button>

Shelmer Doyle Blackburn Jr.

Year Inducted: 2014

Blackburn established The Blackburn Family Foundation Charitable Organization. He is the former Chairman of Adult Enrichment Services of Wilkes County and was instrumental in the establishment of the Ruby Pardue Blackburn Adult Day Care.

<button class="btn btn-primary btn-lg">See More</button>

Zachary Knight Galifianakis

Year Inducted: 2014

Galifianakis' career began on television, and he currently thrives in the film industry as an award-winning supporting actor.

<button class="btn btn-primary btn-lg">See More</button>

CSS:
.wrapper {
    background-color: black;
    width: 100%;
    overflow:auto;
    padding: 20px 0;
}
.inductees {
    margin-bottom: 50px;
    padding-bottom: 10px;
    background-color: #FFF;
}
.inductees .info-text {
    color: #494743;
}
.center {
    vertical-align:center;
    text-align: center;
    margin-top:0;
    margin-bottom:10px;
}

.center button {height:100%;}

http://jsfiddle.net/8ta32wa0/3/


'Crystal Blue' is a 78.74ft /24m motor yacht, custom built in 2007 by Evolution Yachts. She is a great choice for your next charter vacation with friends and family.
Crystal Blue's interior layout sleeps up to 8 guests in 4 rooms, including a master suite, 1 double cabin. She is also capable of carrying up to 2 crew onboard to ensure a relaxed luxury yacht experience. Timeless styling, beautiful furnishings and sumptuous seating feature throughout to create an elegant and comfortable atmosphere.
Her leisure and entertainment facilities make her perfect for entertaining friends and family on your charter vacation. There's ample space for enjoying an alfresco lunch, delicious dinner on deck, or simply lounging in the sunshine and topping up your tan.
Sleek, sporty and luxurious, the designers of this yacht have used lavish furnishings and a added a delightful finish, sure to provide you with the most luxurious of charter vacations.


Now hiring Cashiers at Murphy USA in Springfield, TN!
Murphy USA offers competitive benefits such as: healthcare coverage (medical and dental), competitive pay, paid time off and more.
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On Tuesday October 31st St. Stephen will be having a jack-o-lantern raffle, where students can win pumpkins prepared and decorated by classes in the school. Tickets are .50 cents each, or three for a dollar. The draw will be held on Tuesday afternoon.