%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%                                        %
% ALPHA's "macros.sty" (status: 07/2009) %
%                                        %
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

% Definitions and abbreviations

% Roman letters in math formulae

\def\rmd{{\rm d}}
\def\rmD{{\rm D}}
\def\rme{{\rm e}}
\def\rmO{{\rm O}}
\def\Or{{\rm O}}
\def\rmR{{\rm R}}

% Real and integer numbers

\def\rz{\blackboardrrm}
\def\gz{\blackboardzrm}
\def\Im{{\rm Im}\,}
\def\Re{{\rm Re}\,}


\def\rmonetwo{{r_\mathrm{m}^{\lbrace \mathrm{u,nu}\rbrace}}}
\def\rmonethreethree{{r_\mathrm{m}^{\lbrace \mathrm{u;}Z,T/3\rbrace}}}
\def\rmtwothreethree{{r_\mathrm{m}^{\lbrace \mathrm{nu;}Z,T/3\rbrace}}}
\def\rmonethreefour{{r_\mathrm{m}^{\lbrace \mathrm{u;}Z,T/4\rbrace}}}
\def\rmtwothreefour{{r_\mathrm{m}^{\lbrace \mathrm{nu;}Z,T/4\rbrace}}}
\def\rmonethree{{r_\mathrm{m}^{\lbrace \mathrm{u;}Z\rbrace}}}
\def\rmtwothree{{r_\mathrm{m}^{\lbrace \mathrm{nu;}Z\rbrace}}}
\def\zthree{{Z^{\lbrace T/3 \rbrace}}}
\def\zfour{{Z^{\lbrace T/4 \rbrace}}}
% Expectation values

\newcommand{\MV}[1]{\langle#1\rangle}
\newcommand{\mvl}[1]{\left\langle#1\right\rangle}
\newcommand{\ket}[1]{|#1\rangle}
\newcommand{\bra}[1]{\langle#1|}
\newcommand{\braket}[2]{\langle#1|#2\rangle}
\newcommand{\ketbra}[3]{\langle#1|#2|#3\rangle}

% Special relations and symbols

\def\defeq{\mathrel{\mathop=^{\rm def}}}
\def\proof{\noindent{\sl Proof:}\kern0.6em}
\def\endproof{\hskip0.6em plus0.1em minus0.1em
\setbox0=\null\ht0=5.4pt\dp0=1pt\wd0=5.3pt
\vbox{\hrule height0.8pt
\hbox{\vrule width0.8pt\box0\vrule width0.8pt}
\hrule height0.8pt}}
% \def\frac#1#2{\hbox{$#1\over#2$}}
\def\dual{\mathstrut^*\kern-0.1em}
% \def\mod{\;\hbox{\rm mod}\;}
\def\ring{\mathaccent"7017}
\def\lvec#1{\setbox0=\hbox{$#1$}
    \setbox1=\hbox{$\scriptstyle\leftarrow$}
    #1\kern-\wd0\smash{
    \raise\ht0\hbox{$\raise1pt\hbox{$\scriptstyle\leftarrow$}$}}
    \kern-\wd1\kern\wd0}
\def\rvec#1{\setbox0=\hbox{$#1$}
    \setbox1=\hbox{$\scriptstyle\rightarrow$}
    #1\kern-\wd0\smash{
    \raise\ht0\hbox{$\raise1pt\hbox{$\scriptstyle\rightarrow$}$}}
    \kern-\wd1\kern\wd0}

% Lattice derivatives

\def\nab#1{{\nabla_{#1}}}
\def\nabstar#1{\nabla\kern-0.5pt\smash{\raise 4.5pt\hbox{$\ast$}}
               \kern-4.5pt_{#1}}
\def\drv#1{{\partial_{#1}}}
\def\drvstar#1{\partial\kern-0.5pt\smash{\raise 4.5pt\hbox{$\ast$}}
               \kern-5.0pt_{#1}}

% Lattice momenta

\def\momp#1#2{
    \setbox0=\hbox{${#1}$}\setbox1=\hbox{${#1}_{#2}$}
    {#1}_{#2}\kern-\wd1\kern\wd0
    \smash{\raise4.5pt\hbox{$\scriptscriptstyle +$}}}
\def\momm#1#2{
    \setbox0=\hbox{${#1}$}\setbox1=\hbox{${#1}_{#2}$}
    {#1}_{#2}\kern-\wd1\kern\wd0
    \smash{\raise4.5pt\hbox{$\scriptscriptstyle -$}}}
\def\mompm#1#2{
    \setbox0=\hbox{${#1}$}\setbox1=\hbox{${#1}_{#2}$}
    {#1}_{#2}\kern-\wd1\kern\wd0
    \smash{\raise4.5pt\hbox{$\scriptscriptstyle \pm$}}}
\def\smomp#1#2{
    \setbox0=\hbox{${#1}$}\setbox1=\hbox{${#1}_{#2}$}
    {#1}_{#2}\kern-\wd1\kern\wd0
    \smash{\raise3pt\hbox{$\scriptscriptstyle +$}}}
\def\smomm#1#2{
    \setbox0=\hbox{${#1}$}\setbox1=\hbox{${#1}_{#2}$}
    {#1}_{#2}\kern-\wd1\kern\wd0
    \smash{\raise3pt\hbox{$\scriptscriptstyle -$}}}
\def\smompm#1#2{
    \setbox0=\hbox{${#1}$}\setbox1=\hbox{${#1}_{#2}$}
    {#1}_{#2}\kern-\wd1\kern\wd0
    \smash{\raise3pt\hbox{$\scriptscriptstyle \pm$}}}

% Units

\def\MeV{{\rm MeV}}
\def\GeV{{\rm GeV}}
\def\TeV{{\rm TeV}}
\def\fm{{\rm fm}}

\def\fpi{F_{\pi}}

% Constants

\def\euler{\gamma_{\rm E}}
\newcommand{\hlf}{{\textstyle{\frac{1}{2}}}}

% Fields

\def\psibar{\bar{\psi}}
\def\psiclass{\psi_{\rm cl}}
\def\psibarclass{\psibar_{\rm cl}}
\def\psitilde{\widetilde{\psi}}
\def\rhoprime{\rho\kern1pt'}
\def\rhobar{\bar{\rho}}
\def\rhobarprime{\rhobar\kern1pt'}
\def\rhobartilde{\kern2pt\tilde{\kern-2pt\rhobar}}
\def\rhobartildeprime{\kern2pt\tilde{\kern-2pt\rhobar}\kern1pt'}
\def\etabar{\bar{\eta}}
\def\chibar{\overline{\chi}}
\def\phibar{\overline{\phi}}
\def\zetabar{\overline{\zeta}}
\def\zetaprime{\zeta\kern1pt'}
\def\zetabarprime{\zetabar\kern1pt'}
\def\zetar{\zeta_{\raise-1pt\hbox{\rm R}}}
\def\zetabarr{\zetabar_{\raise-1pt\hbox{\rm R}}}
\def\phieff{\phi_{\rm eff}}
\def\phiimpr{\phi_{\kern0.5pt{\rm I}}}
\def\phir{\phi_{{\rm R}}}
\def\psibars{\psibar_s}
\def\psid{\psi_d}
\def\ar{A_{{\rm R}}}
\def\vr{V_{{\rm R}}}
\def\pr{P_{{\rm R}}}
\def\sr{S_{{\rm R}}}
\def\aimpr{A_{{\rm I}}}
\def\pimpr{P_{{\rm I}}}
\def\vimpr{V_{{\rm I}}}

% Dirac matrices

\def\dirac#1{\gamma_{#1}}
\def\diracstar#1#2{
    \setbox0=\hbox{$\gamma$}\setbox1=\hbox{$\gamma_{#1}$}
    \gamma_{#1}\kern-\wd1\kern\wd0
    \smash{\raise4.5pt\hbox{$\scriptstyle#2$}}}

% Improvement coefficients

\def\csw{c_{\rm sw}}
\def\ca{c_{\rm A}}
\def\cv{c_{\rm V}}
\def\cs{c_{\rm s}}
\def\ct{c_{\rm t}}
\def\cttil{\widetilde{c}_{\rm t}}

\def\ba{b_{\rm A}}
\def\bp{b_{\rm P}}
\def\bm{b_{\rm m}}
\def\bg{b_{\rm g}}

% Correlation functions
 
\def\fa{f_{\rm A}}
\def\fp{f_{\rm P}}
\def\fas{f_{\rm A S}}
\def\ftps{\tilde f_{\rm P S}}
\def\gA{g_{\rm A}}
\def\gP{g_{\rm P}}
\def\lT{l_{\rm T}}
\def\lV{l_{\rm V}}
\def\fx{f_{X}}
\def\kx{k_{X}}
\def\faimpr{f_{\rm A}^{\rm I}}
\def\kvimpr{k_{\rm V}^{\rm I}}
\def\fximpr{f_{\rm X}^{\rm I}}

\def\etax{\eta_{X}}
\def\etaa{\eta_{\rm A}}
\def\etap{\eta_{\rm P}}

% Gauge group, parameters

\def\nf{N_{\rm f}}
\def\Nf{N_{\rm f}}
\def\NF{N_{\rm f}}

\def\NVAL{N_{\rm val}}

\def\SUtwo{{\rm SU(2)}}
\def\SUthree{{\rm SU(3)}}
\def\SUn{{\rm SU}(N)}
\def\tr{\,\hbox{tr}\,}
\def\Ad{{\rm Ad}\,}
\def\CF{C_{\rm F}}
\def\cf{C_{\rm F}}

% Lagrangian

\newcommand{\lag}[1]{{\mathcal{L}}_{\rm {#1}}}

% Action

\def\Sg{S_{\rm G}}
\def\Sf{S_{\rm F}}
\def\Seff{S_{\rm eff}}
\def\Simpr{S_{\rm impr}}
\def\Simprf{S_{\rm F\!,impr}}
\def\Zf{{\cal Z}_{\rm F}}
\def\op#1{{\mathcal O}_{\rm #1}}
\def\opprime#1{\setbox0=\hbox{${\cal O}$}\setbox1=\hbox{${\cal O}_{\rm #1}$}
    {\cal O}_{\rm #1}\kern-\wd1\kern\wd0
    \smash{\raise4.5pt\hbox{\kern1pt$\scriptstyle\prime$}}\kern1pt}
\def\ophat#1{\widehat{\cal O}_{\rm #1}}
\def\opbar#1{\overline{\mathcal O}_{\rm #1}}
\def\ophatprime#1{\setbox0=\hbox{$\widehat{\cal O}$}
    \setbox1=\hbox{$\widehat{\cal O}_{\rm #1}$}
    \widehat{\cal O}_{\rm #1}\kern-\wd1\kern\wd0
    \smash{\raise4.5pt\hbox{\kern1pt$\scriptstyle\prime$}}\kern1pt}
\def\opi#1#2{{\cal L}_{#1}^{(#2)}}
\def\opa#1#2{{\mathcal A}_{#1}^{(#2)}}
\def\bop#1{{\cal L}_{\rm #1}}
\def\bopprime#1{\setbox0=\hbox{${\cal O}$}\setbox1=\hbox{${\cal O}_{\rm #1}$}
    {\cal L}_{\rm #1}\kern-\wd1\kern\wd0
    \smash{\raise4.5pt\hbox{\kern1pt$\scriptstyle\prime$}}\kern1pt}
\def\blag#1{{\cal B}_{#1}}
\def\blagprime#1{\setbox0=\hbox{${\cal B}$}\setbox1=\hbox{${\cal B}_{#1}$}
    {\cal B}_{#1}\kern-\wd1\kern\wd0
    \smash{\raise5.2pt\hbox{\kern1pt$\scriptstyle\prime$}}\kern1pt}

% Renormalization schemes

\def\alphaSF{\alpha_{\rm SF}}
\def\alphaTP{\alpha_{\rm TP}}
\def\alphaMSbar{\alpha_{\msbar}}
\def\bMS{b^{\msbar}}
\def\dMS{d^{\msbar}}
\def\dSF{d^{\rm SF}}

\def\gms{g_{\ms}}
\def\gbar{\bar{g}}
\def\gbsq{\bar{g}^2}
\def\gosq{g_0^2} 
\def\gbarMS{\gbar_{\ms}}
\def\gbarMSbar{\gbar_{\msbar}}
\def\gbarSF{\gbar_{\rm SF}}
\def\gbsqSF{\overline{g}^2_{{\rm SF}}}
\def\gbarTP{\gbar_{\rm TP}}
\def\gr{g_{{{\rm R}}}}
\def\glat{g_{\lat}}
\def\gSF{g_{{{\rm SF}}}}
\def\gparisi{g_{{{\rm P}}}}

\def\mbare{m_0}
\def\mq{m_{\rm q}}
\def\mqtilde{\widetilde{m}_{\rm q}}
\def\mr{m_{{{\rm R}}}}
\def\mc{m_{\rm c}}
\def\mlat{m_{\lat}}
\def\mSF{m_{{\rm SF}}}
\def\m{m}
\def\mprime{m'}
\def\dm{\Delta m}
\def\r{r}
\def\s{s}
\def\rprime{r'}
\def\sprime{s'}
\def\M{M}
\def\Mprime{M'}
\def\dM{\Delta M}
\def\mbar{\kern1pt\overline{\kern-1pt m\kern-1pt}\kern1pt}
\def\avm{m_{\rm av}}

\def\za{Z_{\rm A}}
\def\zv{Z_{\rm V}}
\def\zp{Z_{\rm P}}
\def\zs{Z_{\rm S}}
\def\zss{Z_{\rm S}^{0}}
\def\zg{Z_{\rm g}}
\def\zm{Z_{\rm m}}
\def\zM{Z_{\rm M}}
\def\zgm{Z_{\rm g,m}}
\def\zphi{Z_{\phi}}
\def\zmSF{Z_{\rm m}^{\hbox{\rm SF}}}
\def\zmlat{Z_{\rm m}^{\rm lat}}
\def\zzeta{Z_{\zeta}}
\def\zzetah{Z_{\zeta_{\rm h}}}
\def\sigmap{\sigma_{\rm P}}
\def\rmsea{r_{\rm m}}

\def\xg{X_{\rm g}}
\def\xm{X_{\rm m}}

\def\gtilde{\tilde{g}_0}
\def\mtilde{\widetilde{m}_0}
\def\hop{\kappa}
\def\hopcr{\kappa_{\rm crit}}
\def\hopval{\kappa^{\rm val}}
\def\hopsea{\kappa^{\rm sea}}

\def\ms{{\rm MS}}
\def\msbar{{\rm \overline{MS\kern-0.05em}\kern0.05em}}
\def\lat{{\rm lat}}

% Blackbord bold types
% [02/01/91 202131045  MEMBER NAME  MACROS   (TEXT13)   M  TEX]
 
\def\blackboardrrm{\mathchoice
{\rm I\kern-0.21 em{R}}{\rm I\kern-0.21 em{R}}
{\rm I\kern-0.19 em{R}}{\rm I\kern-0.19 em{R}}}
 
\def\blackboardzrm{\mathchoice
{\rm Z\kern-0.32 em{Z}}{\rm Z\kern-0.32 em{Z}}
{\rm Z\kern-0.28 em{Z}}{\rm Z\kern-0.28 em{Z}}}
 
\def\blackboardh{\mathchoice
{\rm I\kern-0.14 em{H}}{\rm I\kern-0.14 em{H}}
{\rm I\kern-0.11 em{H}}{\rm I\kern-0.11 em{H}}}
 
\def\blackboardp{\mathchoice
{\rm I\kern-0.14 em{P}}{\rm I\kern-0.14 em{P}}
{\rm I\kern-0.11 em{P}}{\rm I\kern-0.11 em{P}}}
 
\def\blackboardt{\mathchoice
{\rm T\kern-0.52 em{T}}{\rm T\kern-0.52 em{T}}
{\rm T\kern-0.40 em{T}}{\rm T\kern-0.40 em{T}}}
  
\def\su{{\rm su}(N)}
\def\SU{{\rm SU}(N)}
\def\sutwo{{\rm su}(2)}
\def\suthree{{\rm su}(3)}

% Schroedinger functional, effective action, action
 
\def\schrodinger{{\cal Z}}
\def\effaction{\Gamma}
\def\chernsimons{S_{\rm CS}}
 
% Background field, quantum field
 
\def\bvalue{C}
\def\bfield{B}
\def\bfieldtensor{G}
\def\bfunc{b}
\def\bfieldparm{\eta}
\def\qfield{q}
\def\bvaluelat{W}
\def\bfieldlat{V}
\def\bfunclat{v}
 
% Fluctuation operator, Faddeev-Popov operator
 
\def\deltazero{\Delta_0}
\def\deltazerohat{\hat{\Delta}_0}
\def\deltaone{\Delta_1}
\def\deltaonehat{\hat{\Delta}_1}
\def\deltaoneprime{\Delta\kern-1.0pt
    \smash{\raise 4.5pt\hbox{$\scriptstyle\prime$}}
    \kern-1.5pt_{1}}
\def\FP{{\rm FP}}
\def\deltaSone{\Delta^{{\rm S}^1}}
 
% Seeley-DeWitt expansion, zeta functions
 
\def\seeleycoeff#1#2{\alpha_{#1}({#2})}
\def\zetafunc#1#2{\zeta(#1|#2)}
% \def\zetaprime#1{\zeta'(0|#1)}
 
% Hamilton operator, Hilbert space, transfer matrix
 
\def\projector{\blackboardp}
\def\ham{\mathbb{H}}
\def\trans{\mathbb{T}}
\def\opX{{\,\mathbb{X}\,}}
\def\opA{{\,\mathbb{A}_0}}
\def\opAstat{{\,\mathbb{A}_0^{\rm stat}}}
\def\Tr{{\rm Tr}}
 
\def\initial{|\rm i_{0}\rangle} 
\def\final{\langle \rm f_{0}|} 
\def\initialt{\langle \rm i_{0}|} 
\def\finalt{| \rm f_{0}\rangle} 
\def\initialpi{|\rm i_{\pi}\rangle} 
\def\finalpi{\langle \rm f_{\pi}|} 
\def\initialpi{|\rm i_{\pi}\rangle} 
\def\initialpit{\langle \rm i_{\pi}|} 
\def\pf{{\cal Z}}
\def\vecp{{\bf p}}
% \def\vecsig{{\bf \sigma}}
% \def\vecsigma{{\bf \sigma}}
\def\vecsig{\fat{\sigma}}
\def\vecsigma{\fat{\sigma}}
\def\vecD{{\bf D}}
\def\vecB{{\bf B}}

% Plaquette field, covariant derivatives
 
\def\del#1{{\Delta_{#1}}}
\def\delstar#1{\Delta\kern-1.0pt\smash{\raise 4.5pt\hbox{$\ast$}}
               \kern-4.0pt_{#1}}
\def\nab#1{{\nabla_{#1}}}
\def\nabstar#1{\nabla\kern-0.5pt\smash{\raise 4.5pt\hbox{$\ast$}}
               \kern-4.5pt_{#1}}
\def\lnab#1{{\overleftarrow{\nabla}_{#1}}}
\def\lnabstar#1{\overleftarrow{\nabla}\kern-0.5pt\smash
             {\raise 4.5pt\hbox{$\ast$}}\kern-4.5pt_{#1}}
\def\cdev#1{D\kern-0.2pt\smash{\raise 4.2pt
            \hbox{$\scriptstyle\phantom{\ast}$}}
            \kern-4.8pt_{#1}}
\def\cdevstar#1{D\kern-0.2pt\smash{\raise 4.2pt
                \hbox{$\scriptstyle\ast$}}
                \kern-4.8pt_{#1}}
\def\plaq{P}
\def\dplaq{d^*\!P}
 
% Abelian background field
 
\def\angle{\phi^{\vphantom{\prime}}}
\def\angleprime{\phi'}
\def\anglevector{\Phi^{\vphantom{\prime}}}
\def\anglevectorprime{\Phi'}
\def\temptrans{\Theta}
\def\setS{{\cal S}}
\def\perm{\sigma}
 
% Group of gauge transformations, field space etc.
 
\def\gaugegroup{{\cal G}}
\def\largegaugegroup{\hat{\gaugegroup}}
\def\cartangroup{{\rm C}_N}
\def\gaugealgebra{{\cal L}}
\def\fluctuationspace{{\cal H}}
\def\ga#1{\gaugealgebra_{#1}}
\def\fs#1{\fluctuationspace_{#1}}
\def\gap#1{\ga{#1}({\bf p})}
\def\fsp#1{\fs{#1}({\bf p})}
\def\gaugefunction{F}

% Calculation of determinants
 
\def\amat{{\cal A}}
\def\bmat{{\cal B}}
\def\cmat{{\cal C}}
\def\solmat{M}
\def\phat{\hat{p}}
\def\cgh{\cos{\gamma\over2}}
\def\funcspace{{\cal F}}
\def\dim{d_{\funcspace}}
 
\newcommand{\Dsl}{D \kern-.65em/}

% Fermion determinants

\def\Om{\Omega}
\def\Oms{\Omega^{\ast}}
\def\dOm{\partial\Om}
\def\dOms{\partial\Oms}
\def\dOmsring{[\dOms]}
\def\DOm{D_{\Om}}
\def\DOms{D_{\Oms_{\vphantom{1}}}}
\def\DdOm{D_{\dOm}}
\def\DdOms{D_{\dOms_{\vphantom{1}}}}
\def\PdOms{P_{\dOms}}
\def\VdOms{V_{\dOms}}

% Abbreviations for equations, sections etc.

\newcommand{\be}{\begin{equation}}
\newcommand{\ee}{\end{equation}}
\newcommand{\beq}{\begin{equation}}
\newcommand{\eeq}{\end{equation}}
\newcommand{\bes}{\begin{eqnarray}}
\newcommand{\ees}{\end{eqnarray}}
\newcommand{\beqa}{\begin{eqnarray}}
\newcommand{\eeqa}{\end{eqnarray}}
\newcommand{\bea}{\begin{eqnarray}}
\newcommand{\eea}{\end{eqnarray}}
\newcommand{\bean}{\begin{eqnarray*}}
\newcommand{\eean}{\end{eqnarray*}}
\newcommand{\bal}{\begin{align}}
\newcommand{\eal}{\end{align}}
\newcommand{\bit}{\begin{itemize}}
\newcommand{\eit}{\end{itemize}}
\newcommand{\ben}{\begin{enumerate}}
\newcommand{\een}{\end{enumerate}}

\newcommand{\eq}[1]{eq.~(\ref{#1})}
\newcommand{\Eq}[1]{Eq.~(\ref{#1})}
\newcommand{\eqs}[1]{eqs.~(\ref{#1})}
\newcommand{\Eqs}[1]{Eqs.~(\ref{#1})}
% \newcommand{\fig}[1]{Fig.~\ref{#1}}
% \newcommand{\figs}[1]{Figs.~\ref{#1}}
\newcommand{\Fig}[1]{Figure~\ref{#1}}
\newcommand{\Figs}[1]{Figures~\ref{#1}}
% \newcommand{\sect}[1]{Sect.~\ref{#1}}
% \newcommand{\sects}[1]{Sects.~\ref{#1}}
\newcommand{\Sect}[1]{Section~\ref{#1}}
\newcommand{\Sects}[1]{Sections~\ref{#1}}
% \newcommand{\app}[1]{App.~\ref{#1}}
% \newcommand{\App}[1]{Appendix~\ref{#1}}
\newcommand{\APP}[1]{\ref{#1}}
% \newcommand{\tab}[1]{Table~\ref{#1}}
% \newcommand{\tabs}[1]{Tables~\ref{#1}}
\newcommand{\Tab}[1]{Table~\ref{#1}}
\newcommand{\Tabs}[1]{Tables~\ref{#1}}
% \newcommand{\Ref}[1]{Ref.~\cite{#1}}
% \newcommand{\Refs}[1]{Refs.~\cite{#1}}
% 
% Redefinitions complying with JHEP conventions 
%
\newcommand{\sect}[1]{section~\ref{#1}}
\newcommand{\sects}[1]{sections~\ref{#1}}
\newcommand{\App}[1]{appendix~\ref{#1}}
%\newcommand{\Ref}[1]{ref.~\cite{#1}} needed to do this for arxiv submission
%\newcommand{\Refs}[1]{refs.~\cite{#1}}
\newcommand{\fig}[1]{figure~\ref{#1}}
\newcommand{\figs}[1]{figures~\ref{#1}}
\newcommand{\tab}[1]{table~\ref{#1}}
\newcommand{\tabs}[1]{tables~\ref{#1}}

% One-loop coefficients, schemes, masses etc.

\newcommand{\cbar}{c_{1,1}}
\newcommand{\vbar}{\bar v}
\newcommand{\pbar}{p_{1,1}}
\newcommand{\bbar}{b_{0,1}}
\newcommand{\ctbar}{c_t^{(1,1)}}
\newcommand{\bzero}{b_0(n_f,0)}
\newcommand{\deltabar}{\delta_{1,1}}
\newcommand{\eps}{\epsilon}

\newcommand{\MSbar}{\overline{\rm MS}}
\newcommand{\MS}{\MSbar}
\newcommand{\alphaMS}{\alpha_{\MS}}
\newcommand{\Oa}{{\rm O}(a)}
\newcommand{\Oasq}{{\rm O}(a^2)}
\newcommand{\Lmax}{L_{\rm max}}
\newcommand{\Lstar}{L^{\ast}}

\newcommand{\proj}{{\cal P}}
\newcommand{\smear}{{\cal S}}
\newcommand{\Vbar}{\overline{V}}
\newcommand{\Ubar}{\overline{U}}

\newcommand{\tmin}{t_{\rm min}}
\newcommand{\tmax}{t_{\rm max}}
\newcommand{\vecr}{{\it \bf r}}
\newcommand{\vecd}{{\it \bf d}}
\newcommand{\vecu}{{\it \bf u}}
\newcommand{\vecv}{{\it \bf v}}
\newcommand{\vecx}{{\it \bf x}}
\newcommand{\vecy}{{\it \bf y}}
\newcommand{\vecz}{{\it \bf z}}
\newcommand{\rnod}{r_{0}}
\newcommand{\mbarscale}{1.436\,r_{0}}
\newcommand{\rI}{r_{\rm I}}

\newcommand{\sigplatt}{\Sigma_{\rm P}}
\newcommand{\Sigmap}{\Sigma_{\rm P}}
\newcommand{\sigpcont}{\sigma_{\rm P}}
\newcommand{\Fpi}{F_{\pi}}
\newcommand{\Gpi}{G_{\pi}}
\newcommand{\Fp}{F_{\rm PS}}
\newcommand{\Gp}{G_{\rm PS}}
\def\mp{m_{\rm PS}}
\newcommand{\Fk}{F_{\rm K}}
\newcommand{\Fb}{F_{\rm B}}
\newcommand{\Fbs}{F_{\rm B_{\rm s}}}
\newcommand{\Fbd}{F_{\rm B_{\rm d}}}
% \newcommand{\Fb}{f_{\rm B}}
% \newcommand{\Fbs}{f_{\rm B_{\rm s}}}
\newcommand{\Gk}{G_{\rm K}}
\newcommand{\mk}{m_{\rm K}}
% \newcommand{\mb}{m_{\rm B}}
\newcommand{\mkstar}{m_{\rm K^*}}
\newcommand{\Bk}{B_{\rm K}}
\newcommand{\mphi}{m_{\Phi}}
\newcommand{\mv}{m_{\rm V}}
\newcommand{\mpi}{m_{\pi}}
\newcommand{\mrho}{m_{\rho}}
\newcommand{\RWI}{R}
\newcommand{\Rwi}{R}
\newcommand{\mav}{m_{\rm av}}
\newcommand{\strange}{{\rm s}}
\newcommand{\up}{{\rm u}}
\newcommand{\down}{{\rm d}}
\newcommand{\Mlight}{\hat{M}}
\newcommand{\mlight}{\hat{m}}
\newcommand{\Mref}{M_{\rm ref}}
\newcommand{\mref}{m_{\rm ref}}
\newcommand{\mstrange}{m_{\strange}}
\newcommand{\Mstrange}{M_{\strange}}
\newcommand{\beauty}{{\rm b}}
\newcommand{\mbeauty}{m_{\rm b}}
\newcommand{\Mbeauty}{M_{\beauty}}
\newcommand{\Mh}{M_{\rm h}}
\newcommand{\mup}{m_{\up}}
\newcommand{\mdown}{m_{\down}}
\newcommand{\charm}{{\rm c}}
\newcommand{\Mcharm}{M_{\charm}}

\newcommand{\rrmm} {1.5736}
\newcommand{\blank}{\multicolumn{2}{c}{\mbox{}}}

% Abbreviations for text
 
\newcommand{\txtSF}{{Schr\"odinger functional }}
\newcommand{\ps}{{pseudoscalar }}
\newcommand{\stat}{{static effective field theory}}

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%                                               %
% ALPHA's "macros_static.sty" (status: 01/2009) %
%                                               %
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

% Decay constant

\newcommand{\fb}{F_{\rm B}}

% Static action

\def\Sstat{S_{\rm h}}
\def\Sastat{S_{\bar{\rm h}}}
\def\Shqet{S_{\rm HQET}}
\def\Srel{S_{\rm rel}}
\def\Lstat{{\cal L}_{\rm stat}}
\def\LQCD{{\cal L}_{\rm QCD}}
\def\LHQET{{\cal L}_{\rm HQET}}
\def\qcdpar{{\cal C}_{\nf}}
\def\qcdparred{{\cal C}_{\nf-1}}
\def\hqetpar{{\cal C}_{\rm HQET}}
\def\Nn{{N_{n}}}
\def\NHQET{{N_{\rm HQET}}}
\def\LD{\lag{}}
\def\Dop{{\cal D}}
\def\Lh{\lag{h}}
\def\Lhb{\lag{\bar h}}
\def\Lhhb{\lag{h \bar h}}
\def\vecg{\bf \gamma}
\def\Dg{D_k\gamma_k}

\newcommand{\Okin}{\cl{O}_{\rm kin}}
\newcommand{\Ospin}{\cl{O}_{\rm spin}}
\newcommand{\ckin}{c_{\rm kin}}
\newcommand{\csig}{c_{\sigma}}
\newcommand{\cspin}{c_{\rm spin}}
\newcommand{\omkin}{\omega_{\rm kin}}
\newcommand{\omsig}{\omega_{\sigma}}
\newcommand{\omspin}{\omega_{\rm spin}}
\newcommand{\lnu}[1]{{\cal L}^{(#1)}}
\newcommand{\lcoeff}[2]{\omega^{(#1)}_#2}
\newcommand{\acoeff}[2]{\alpha^{(#1)}_#2}
\newcommand{\minv}{1/m}

% Static approximation fields

\newcommand{\heavy}{\psi_{\rm h}}
\newcommand{\heavyb}{\overline{\psi}_{\rm h}}
\newcommand{\aheavy}{\psi_{\bar{\rm h}}}
\newcommand{\aheavyb}{\overline{\psi}_{\bar{\rm h}}}
\newcommand{\light}{{\psi}_{\rm l}}
\newcommand{\lights}{{\psi}_{\rm s}}
\newcommand{\lightb}{\overline{\psi}_{\rm l}}
\newcommand{\lightsb}{\overline{\psi}_{\rm s}}
\newcommand{\rhol}{\rho_{\rm l}}
\newcommand{\rholb}{\overline{\rho}_{\rm l}}
\newcommand{\rholprime}{\rho_{\rm l}\kern1pt'}
\newcommand{\rholbprime}{\overline{\rho}_{\rm l}\kern1pt'}
\newcommand{\rhoh}{\rho_{\rm h}}
\newcommand{\rhohbprime}{\overline{\rho}_{\rm h}\kern1pt'}
\newcommand{\zetal}{\zeta_{\rm l}}
\newcommand{\zetalb}{\overline{\zeta}_{\rm l}}
\newcommand{\zetalprime}{\zeta_{\rm l}\kern1pt'}
\newcommand{\zetaiprime}{\zeta_{i}\kern1pt'}
\newcommand{\zetajprime}{\zeta_{j}\kern1pt'}
\newcommand{\zetalbprime}{\overline{\zeta}_{\rm l}\kern1pt'}
\newcommand{\zetaibprime}{\overline{\zeta}_{i}\kern1pt'}
\newcommand{\zetajbprime}{\overline{\zeta}_{j}\kern1pt'}
\newcommand{\zetah}{\zeta_{\rm h}}
\newcommand{\zetahb}{\overline{\zeta}_{\rm h}}
\newcommand{\zetahprime}{\zeta_{\rm h}\kern1pt'}
\newcommand{\zetahbprime}{\overline{\zeta}_{\rm h}\kern1pt'}
\newcommand{\Astat}{A^{\rm stat}_0}
\newcommand{\Ahqet}{A^{\rm HQET}_0}
\newcommand{\Argi}{(A^{\rm RGI})_0}
\newcommand{\Argistat}{(A_{\rm RGI}^{\rm stat})_0}
\newcommand{\Aren}{(A^{\rm stat}_{\rm R})_0}
% \newcommand{\Aren}{(A^{\rm stat}_0)_{\rm R}}
\newcommand{\Vstat}{V^{\rm stat}_{k}}
\newcommand{\Vren}{(V^{\rm stat}_{\rm R})_0}
\newcommand{\ArenSF}{(A^{\rm stat}_{\rm SF})_0}
\newcommand{\ArenMSbar}{(A^{\rm stat}_{\overline{\rm MS}})_0}
\newcommand{\ArenLat}{(A^{\rm stat}_{\rm lat})_0}
\newcommand{\ArenCA}{(A_{\rm CA})_0}
\newcommand{\Astatimpr}{(A^{\rm stat}_{\rm I})_0}
\newcommand{\Vstatimpr}{(V^{\rm stat}_{\rm I})_0}

\newcommand{\zetalone}{\zeta_1}
\newcommand{\zetalbtwo}{\overline{\zeta}_2}
\newcommand{\zetalbprimeone}{\overline{\zeta}_1\kern1pt'}
\newcommand{\zetalprimetwo}{\zeta_2\kern1pt'}

\newcommand{\zh}{Z_{\rm h}}

\newcommand{\chiAstatSFMSbar}{\chi_{\rm A}^{\rm stat}}
\newcommand{\chiAstat}{(\chi_{\rm A}^{\rm stat})}
\newcommand{\chiAstatMSbarLat}{(\chi_{\rm A}^{\rm stat})_{\msbar,\rm lat}}
\newcommand{\chiAstatMSbarLatOne}{(\chi_{\rm A}^{\rm stat})_{\msbar,\rm lat}^{(1)}}
\newcommand{\chiAstatSFMSbarOne}{(\chi_{\rm A}^{\rm stat})^{(1)}}

\newcommand{\SigmaAstat}{\Sigma_{\rm A}^{\rm stat}}
\newcommand{\sigmaAstat}{\sigma_{\rm A}^{\rm stat}}
\newcommand{\sigmaAzerostat}{\sigma_{\rm A,0}^{\rm stat}}
\newcommand{\sigmaAonestat}{\sigma_{\rm A,1}^{\rm stat}}
\newcommand{\sigmaAtwostat}{\sigma_{\rm A,2}^{\rm stat}}
\newcommand{\sigmaAnstat}{\sigma_{{\rm A},n}^{\rm stat}}

\newcommand{\gamSF}{\gamma^{\rm SF}}
\newcommand{\gamMSbar}{\gamma^{\overline{\rm MS}}}

\newcommand{\latstep}{\Sigma_{\rm A}^{\rm stat}}
\newcommand{\contstep}{\sigma_{\rm A}^{\rm stat}}

% Static approximation correlation functions

\newcommand{\fastat}{f_{\rm A}^{\rm stat}}
\newcommand{\fakin}{f_{\rm A}^{\rm kin}}
\newcommand{\faspin}{f_{\rm A}^{\rm spin}}
\newcommand{\kvstat}{k_{\rm V}^{\rm stat}}
\newcommand{\fastatimpr}{f_{\rm A}^{\rm stat, I}}
\newcommand{\fdeltaAstat}{f_{\delta\rm A}^{\rm stat}}
\newcommand{\fonestat}{f_{1}^{\rm stat}}
\newcommand{\fonehh}{f_{1}^{\rm hh}}
\newcommand{\fonekin}{f_{1}^{\rm kin}}
\newcommand{\fonespin}{f_{1}^{\rm spin}}
\newcommand{\fastatren}{(f_{\rm A}^{\rm stat})_{\rm R}}
\newcommand{\fonestatren}{(f_{1}^{\rm stat})_{\rm R}}
\newcommand{\Xbare}{X_{\rm bare}}
\newcommand{\Xren}{X_{\rm R}}
\newcommand{\XLat}{X_{\rm lat}}
\newcommand{\Xmatch}{X_{\rm match}}
\newcommand{\Xnew}{\Xi}
\def\caa{C_{\rm AA}}
\def\caahqet{C_{\rm AA}^{\rm HQET}}
\def\daa{D_{\rm AA}}

% Light-light correlation functions

\newcommand{\fone}{f_1}
\newcommand{\kone}{k_1}

% Masses

\newcommand{\mcrit}{m_{\rm c}}
\newcommand{\mcritone}{m_{\rm c}^{(1)}}
% \newcommand{\mMSbar}{\overline{m}_{2,\overline{\rm MS}}}
\newcommand{\mMSbar}{\overline{m}_{\overline{\rm MS}}}

% Matrices appearing in the correlation functions

\newcommand{\Hlight}{H_{\rm l}}
\newcommand{\Hheavy}{H_{\rm h}}
\newcommand{\Klight}{K_{\rm l}}
\newcommand{\Kheavy}{K_{\rm h}}

% Static approximation renormalizations

\newcommand{\zastat}{Z_{\rm A}^{\rm stat}}
\newcommand{\zahqet}{Z_{\rm A}^{\rm HQET}}
\newcommand{\zastatSF}{Z_{\rm A, SF}^{\rm stat}}
\newcommand{\zastatMSbar}{Z_{\rm A, \overline{\rm MS}}^{\rm stat}}
\newcommand{\zastatLat}{Z_{\rm A, lat}^{\rm stat}}
\newcommand{\ZdeltaA}{Z_{\delta\rm A}}
\newcommand{\BAstat}{B_{\rm A}^{\rm stat}}
\newcommand{\zvstat}{Z_{\rm V}^{\rm stat}}
\def\dmstat{\delta m}

% Light quark renormalizations

\newcommand{\zmMSbar}{Z_{\rm m, \overline{\rm MS}}}

% Static approximation improvement coefficients

\def\castat{c_{\rm A}^{\rm stat}}
\def\cahqet{c_{\rm A}^{\rm HQET}}
\def\cstat{c_{\rm h}}
\def\dastat{d_{\rm A}^{\rm stat}}
\def\bastat{b_{\rm A}^{\rm stat}}
\def\bstat{b_{\rm h}}
\def\cvstat{c_{\rm V}^{\rm stat}}
\def\bvstat{b_{\rm V}^{\rm stat}}

% Martin Kurth's stuff

\newcommand{\ola}{\overleftarrow}
\newcommand{\vectq}{{\it \bf q}}
\newcommand{\vectp}{{\it \bf p}}
\newcommand{\vectn}{{\it \bf 0}}

\newcommand{\cttilde}{\widetilde{c}_{\rm t}}

\newcommand{\gbarLat}{\bar{g}_{\rm lat}}
\newcommand{\gLat}{g_{\rm lat}}

\newcommand{\fonehhtree}{f_1^{\rm hh,(0)}}
\newcommand{\fonehhoneloop}{f_1^{\rm hh,(1)}}
\newcommand{\zastattree}{Z_{\rm A}^{\rm stat,(0)}}
\newcommand{\zastatoneloop}{Z_{\rm A}^{\rm stat,(1)}}
\newcommand{\SigmaAstatoneloop}{\Sigma_{\rm A}^{\rm stat,(1)}}
\newcommand{\sigmaAstatoneloop}{\sigma_{\rm A}^{\rm stat,(1)}}
\newcommand{\sigmaAstattwoloop}{\sigma_{\rm A}^{\rm stat,(2)}}
\newcommand{\sigmaAstatnloop}{\sigma_{\rm A}^{{\rm stat,}(n)}}
% \newcommand{\deltaAstat}{\delta}
\newcommand{\deltaAstat}{\delta\Astat}
\newcommand{\deltaAstatoneloop}{\delta^{(1)}}

% Rainer Sommer's stuff

\newcommand{\fhh}{f^{\rm hh}}
\newcommand{\zastathh}{Z_{\rm A, SF,hh}^{\rm stat}}
\newcommand{\gamhh}{\gamma^{\rm SF,hh}}
\newcommand{\Fhatstat}{ {\Phi}^{\rm stat} }
\newcommand{\FhatstatRGI}{\Phi^{\rm stat}_{\rm RGI}}
\newcommand{\simas}[1]{\raisebox{-.1ex}{
            $\stackrel{\small{#1}}{\sim}$}}
\newcommand{\toas}[1]{\raisebox{-.1ex}{
            $\stackrel{\small{#1}}{\longrightarrow}$}}
\newcommand{\Toas}[1]{\raisebox{-.1ex}{
            $\stackrel{\small{#1}}{\Longrightarrow}$}}
\newcommand{\equalas}[1]{\raisebox{-.1ex}{
            $\stackrel{\small{#1}}{=}$}}
\newcommand{\equivas}[1]{\raisebox{-.1ex}{
            $\stackrel{\small{#1}}{\equiv}$}}

% Jochen Heitger's stuff

\newcommand{\mumatch}{\mu_{\rm m}}
\newcommand{\muhad}{\mu_{\rm had}}
\newcommand{\mupert}{\mu_{\rm pert}}

\newcommand{\psib}{\psi_{\rm b}}
\newcommand{\bpsid}{\overline{\psi}_{\rm d}}
\newcommand{\mbMSbar}{m_{{\rm b},\MS}}
\newcommand{\mB}{m_{\rm B}}
\newcommand{\mBstat}{m_{\rm B}^{\rm stat}}
\newcommand{\mBstar}{m_{\rm B^*}}
\newcommand{\Mb}{M_{\rm b}}
\newcommand{\Fbbare}{F_{\rm B}^{\rm bare}}
\newcommand{\Fbsstat}{F_{{\rm B}_{\rm s}}^{\rm stat}}
\newcommand{\Fbstat}{F_{{\rm B}}^{\rm stat}}
\newcommand{\Aistat}{(A^{\rm stat}_{\rm I})_{0}}
\newcommand{\Arstat}{(A_{\rm R}^{\rm stat})_{0}}

\newcommand{\oldSF}{{\rm old}}
\newcommand{\newSF}{{\rm new}}
\newcommand{\gamSFold}{\gamma^{{\rm SF},\oldSF}}
\newcommand{\zastatold}{Z_{{\rm A},\oldSF}^{{\rm stat}}}
\newcommand{\SigmaAstatold}{\Sigma_{{\rm A},\oldSF}^{{\rm stat}}}

\newcommand{\Phibare}{\Phi_{\rm bare}}
\newcommand{\PhiSF}{\Phi_{\rm SF}}
\newcommand{\PhiRGI}{\Phi_{\rm RGI}}
\newcommand{\PhiMSbar}{\Phi_{\overline{\rm MS}}}
\newcommand{\Phimatch}{\Phi_{\rm match}}
\newcommand{\FhatRGI}{\hat{F}_{\rm RGI}}
\newcommand{\FhatMSbar}{\hat{F}_{\overline{\rm MS}}}
\newcommand{\FhatSF}{\hat{F}_{\rm SF}}
\newcommand{\ZPhi}{Z_{\rm RGI}}
\newcommand{\Ztil}{\widetilde{Z}}
\newcommand{\Cmatch}{C_{\rm match}}
\newcommand{\Cpshat}{\widehat{C}_{\rm PS}}
\newcommand{\Cvhat}{\widehat{C}_{\rm V}}
\newcommand{\Crhat}{\widehat{C}_{\rm R}}
\newcommand{\Cpsvhat}{\widehat{C}_{{\rm PS}/{\rm V}}}
\newcommand{\Cmaghat}{\widehat{C}_{\rm mag}}
\newcommand{\Cspinhat}{\widehat{C}_{\rm spin}}
\newcommand{\Cps}{C_{\rm PS}}
\newcommand{\Cv}{C_{\rm V}}
\newcommand{\Cr}{C_{\rm R}}
\newcommand{\Cpsv}{C_{{\rm PS}/{\rm V}}}
\newcommand{\Cx}{C_{\rm X}}
\newcommand{\Cspin}{C_{\rm spin}}
\newcommand{\Cmag}{C_{\rm mag}}
\newcommand{\Ckin}{C_{\rm kin}}
\newcommand{\Cmass}{C_{\rm mass}}
\newcommand{\gammatch}{\gamma^{\rm match}}
\newcommand{\gamonematch}{\gamma_1^{\rm match}}
\newcommand{\gamtwomatch}{\gamma_2^{\rm match}}
\newcommand{\gamspin}{\gamma^{\rm spin}}

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%                                               %
% various further definitions (status: 07/2009) %
%                                               %
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

% (Lattice) derivatives in directions mu,nu

\newcommand{\Pmu}{\partial_{\mu}}
\newcommand{\Pnu}{\partial_{\nu}}
\newcommand{\Pz}{\partial_{0}}
\newcommand{\Dmu}{D_{\mu}}
\newcommand{\dmu}[1]{\nabla^{{\rm (#1)}}_{\mu}}
\newcommand{\Cmu}{\nabla_{\mu}}
\newcommand{\Lmu}{\triangle_{\mu}}
\newcommand{\Lnu}{\triangle_{\nu}}
\newcommand{\Smu}{\tilde{\partial}_{\mu}}
\newcommand{\Snu}{\tilde{\partial}_{\nu}}
\newcommand{\Sz}{\tilde{\partial}_{0}}
% \newcommand{\lnab}[1]{\overleftarrow{\nabla}_{#1}}
% \newcommand{\lnabstar}[1]{{\overleftarrow{\nabla}\kern-0.5pt\smash
%                           {\raise 4.5pt\hbox{$\ast$}}\kern-4.5pt_{#1}}}

% Dirac matrices etc.

\newcommand{\gmu}{\gamma_{\mu}}
\newcommand{\gfv}{\gamma_5}
\newcommand{\gzr}{\gamma_0}
\newcommand{\gen}{{\textstyle{\frac{1}{2}}}\,\tau^a}
\newcommand{\smunu}{\sigma_{\mu\nu}}

% Boldface spatial momenta

\newcommand{\mbx}{\mathbf{x}}
\newcommand{\mby}{\mathbf{y}}
\newcommand{\mbz}{\mathbf{z}}
\newcommand{\mbu}{\mathbf{u}}
\newcommand{\mbv}{\mathbf{v}}
\newcommand{\mbw}{\mathbf{w}}
\newcommand{\mbp}{\mathbf{p}}
\newcommand{\mbn}{\mathbf{0}}

\newcommand{\bx}{\mbx}
\newcommand{\by}{\mby}
\newcommand{\bz}{\mbz}
\newcommand{\bu}{\mbu}
\newcommand{\bv}{\mbv}
\newcommand{\bw}{\mbw}
% \newcommand{\bp}{\mbp}
\newcommand{\bn}{\mbn}
\newcommand{\bxs}{\bx}
\newcommand{\bys}{\by}
\newcommand{\bzs}{\bz}
\newcommand{\bus}{\bu}
\newcommand{\bvs}{\bv}
\newcommand{\bws}{\bw}
% \newcommand{\bps}{\bp}
\newcommand{\bns}{\bn}

% Fields

\newcommand{\amu}{A_{\mu}^a}
\newcommand{\az}{A_0^a}
\newcommand{\p}{P^a}

\newcommand{\ob}{\mathcal{O}}
\newcommand{\obi}{\mathcal{O}^a}
\newcommand{\obf}{\mathcal{O}'^a}
\newcommand{\qbi}{\mathcal{Q}^a_k}
\newcommand{\qbf}{\mathcal{Q}'^a_k}
\newcommand{\obir}{\mathcal{O}^a_{\rm R}}
\newcommand{\obfr}{\mathcal{O}'^a_{\rm R}}
\newcommand{\qbir}{(\mathcal{Q}^a_k)_{\rm R}}
\newcommand{\qbfr}{(\mathcal{Q}'^a_k)_{\rm R}}
\newcommand{\zeb}{\bar{\zeta}}
\newcommand{\zer}{\zeta_{\rm R}}
\newcommand{\zebr}{\bar{\zeta}_{\rm R}}
\newcommand{\zeu}{\zeta_{\rm u}}
\newcommand{\zed}{\zeta_{\rm d}}
\newcommand{\zeub}{\bar{\zeta}_{\rm u}}
\newcommand{\zedb}{\bar{\zeta}_{\rm d}}
\newcommand{\rhb}{\bar{\rho}}

\newcommand{\bpsi}{\overline{\psi}}
\newcommand{\psiu}{\psi_{\rm u}}
% \newcommand{\bpsiu}{\overline{\psi}_{\rm u}}
\newcommand{\bpsiu}{\overline{u}}
\newcommand{\psil}{\psi_{\rm l}}
% \newcommand{\bpsil}{\overline{\psi}_{\rm l}}
\newcommand{\bpsil}{\overline{\ell}}
% \newcommand{\psic}{\psi_{\rm c}}
\newcommand{\psic}{c}
% \newcommand{\psis}{\psi_{\rm s}}
\newcommand{\psis}{s}
% \newcommand{\bpsis}{\overline{\psi}_{\rm s}}
\newcommand{\bpsis}{\overline{s}}
\newcommand{\bpsib}{\overline{\psi}_{\rm b}}

% Masses

\newcommand{\moi}[1]{m_{0,#1}}
\newcommand{\mzi}{m_{0,i}}
\newcommand{\mzl}{m_{0,{\rm l}}}
\newcommand{\mzh}{m_{0,{\rm h}}}
\newcommand{\mri}[1]{m_{{\rm R},#1}}
\newcommand{\mij}[1]{m_{#1}}
\newcommand{\mqi}{m_{{\rm q},i}}
\newcommand{\mqj}{m_{{\rm q},j}}
\newcommand{\mql}{m_{{\rm q},{\rm l}}}
\newcommand{\mqs}{m_{{\rm q},{\rm s}}}
\newcommand{\mqc}{m_{{\rm q},{\rm c}}}
\newcommand{\mqh}{m_{{\rm q},{\rm h}}}
\newcommand{\mqn}[1]{m_{{\rm q},#1}}
\newcommand{\mqitil}{\widetilde{m}_{{\rm q},i}}
\newcommand{\mqltil}{\widetilde{m}_{{\rm q},{\rm l}}}
\newcommand{\mqhtil}{\widetilde{m}_{{\rm q},{\rm h}}}
\newcommand{\mqtil}{\widetilde{m}_{\rm q}}
\newcommand{\muq}{\mu_{\rm q}}
\newcommand{\muqtil}{\widetilde{\mu}_{\rm q}}

\newcommand{\Mq}{M_{\rm q}}

\newcommand{\mbbar}{\overline{m}_{\rm b}}
\newcommand{\mhbar}{\overline{m}_{\rm h}}
\newcommand{\mb}{m_{\rm b}}
\newcommand{\mbstat}{m_{\rm b}^{\rm stat}}
\newcommand{\ml}{m_{\rm l}}
\newcommand{\mh}{m_{\rm h}}
\newcommand{\mQ}{m_{\rm Q}}
\newcommand{\mhMSbar}{m_{{\rm h},\MS}}
\newcommand{\mhbarMSbar}{\overline{m}_{{\rm h},\MS}}
\newcommand{\msbMS}{\overline{m}_{\rm s}^{\,\overline{\rm MS}}}
\newcommand{\mcbMS}{\overline{m}_{\rm c}^{\,\overline{\rm MS}}}
\newcommand{\mbbMS}{\overline{m}_{\rm b}^{\,\overline{\rm MS}}}
\newcommand{\mbMS}{m_{\rm b}^{\,\overline{\rm MS}}}
\newcommand{\mhbMS}{\overline{m}_{\rm h}^{\,\overline{\rm MS}}}
% \newcommand{\mbSF}{\overline{m}^{\rm SF}}
\newcommand{\mbSF}{\overline{m}_{\rm SF}}

\newcommand{\md}{m_{\rm d}}
\newcommand{\mU}{m_{\rm u}}
\newcommand{\mUb}{\overline{m}_{\rm u}}
\newcommand{\mS}{m_{\rm s}}
\newcommand{\msb}{\overline{m}_{\rm s}}
\newcommand{\mC}{m_{\rm c}}
\newcommand{\mcb}{\overline{m}_{\rm c}}
\newcommand{\Mu}{M_{\rm u}}
\newcommand{\Ms}{M_{\rm s}}
\newcommand{\Md}{M_{\rm d}}
% \newcommand{\Ml}{M_{\rm l}}
\newcommand{\Ml}{M_{\ell}}
\newcommand{\Mc}{M_{\rm c}}

\newcommand{\kapc}{\kappa_{\rm c}}
\newcommand{\kapu}{\kappa_{\rm u}}
\newcommand{\kapd}{\kappa_{\rm d}}
\newcommand{\kaps}{\kappa_{\rm s}}
\newcommand{\kapl}{\kappa_{\rm l}}
\newcommand{\kaph}{\kappa_{\rm h}}

% Correlators

\newcommand{\fX}{f_{\rm X}}
\newcommand{\kv}{k_{\rm V}}
\newcommand{\kt}{k_{\rm T}}

% Improvement coefficients

\newcommand{\bP}{b_{{\rm P}}}
\newcommand{\bV}{b_{{\rm V}}}

% Hadronic observables

\newcommand{\PS}{{\rm PS}}
\newcommand{\mps}{m_{\rm PS}}
\newcommand{\Fps}{F_{\rm PS}}
\newcommand{\Fd}{F_{\rm D}}
\newcommand{\Fds}{F_{\rm D_{\rm s}}}
\newcommand{\mD}{m_{\rm D}}
\newcommand{\mDs}{m_{\rm D_{\rm s}}}

% B-Physics

\newcommand{\Cstat}{C_{\rm stat}}
\newcommand{\Estat}{E_{\rm stat}}
\newcommand{\Eeff}{E_{\rm eff}}
\newcommand{\Ekin}{E_{\rm kin}}
\newcommand{\Ekinhat}{\hat{E}_{\rm kin}}
\newcommand{\Espin}{E_{\rm spin}}
\newcommand{\delE}{\Delta E}
\newcommand{\delstat}{\Delta^{\rm stat}}
\newcommand{\mhbare}{m_{\rm bare}}
\newcommand{\mhpole}{m_{\rm pole}}
\newcommand{\Xr}{X_{\rm R}}
\newcommand{\XRGI}{X_{\rm RGI}}
\newcommand{\XRGIspin}{X_{\rm RGI}^{\rm spin}}
\newcommand{\Yr}{Y_{\rm PS}}
\newcommand{\Yv}{Y_{\rm V}}
\newcommand{\Yx}{Y_{\rm X}}
\newcommand{\Rr}{R_{\rm }}
\newcommand{\gamrel}{\Gamma_{\rm rel}}
\newcommand{\gamstat}{\Gamma_{\rm stat}}
\newcommand{\gamonestat}{\Gamma_1^{\rm stat}}
\newcommand{\gamonekin}{\Gamma_1^{\rm kin}}
\newcommand{\gamps}{\Gamma_{\rm PS}}
\newcommand{\gamv}{\Gamma_{\rm V}}
\newcommand{\gamav}{\Gamma_{\rm av}}
\newcommand{\gamdifstat}{\Xi_{\rm stat}}
\newcommand{\gamdifone}{\Xi_{\rm kin}}
\newcommand{\gamdif}{\Xi}
\newcommand{\gamx}{\Gamma_{\rm X}}
\newcommand{\delgam}{{\Delta}_{\Gamma}}
\newcommand{\Omps}{\Omega_{\rm PS}}
\newcommand{\Omv}{\Omega_{\rm V}}
\newcommand{\Omav}{\Omega_{\rm av}}
\newcommand{\Omx}{\Omega_{\rm X}}
\newcommand{\omps}{\omega_{\rm PS}}
\newcommand{\omv}{\omega_{\rm V}}
\newcommand{\omav}{\omega_{\rm av}}
\newcommand{\omx}{\omega_{\rm X}}
\newcommand{\zb}{z_{{\rm b}}}
\newcommand{\Bs}{{\rm B}_{\rm s}}
\newcommand{\mBs}{m_{{\rm B}_{\rm s}}}
\newcommand{\Bb}{B_{\rm B}}

\newcommand{\Obare}{O_{\rm bare}}
\newcommand{\OINP}{O_{\rm INP}}
\newcommand{\ZMS}{Z^{\,\overline{\rm MS}}}
\newcommand{\ZMSpole}{Z^{\,\overline{\rm MS}}_{\,\rm pole}}
\newcommand{\ZRGI}{Z_{\rm RGI}}
\newcommand{\ZINP}{Z_{\rm INP}}
\newcommand{\Zspin}{Z_{\rm spin}}
\newcommand{\Zkin}{Z_{\rm kin}}
\newcommand{\PhiINP}{\Phi_{{\rm INP}}}
\newcommand{\Phieff}{\Phi_{{\rm eff}}}
\newcommand{\PhistatMSbar}{\Phi^{\rm stat}_{\overline{{\rm MS}}}}
\newcommand{\PhiQCD}{\Phi^{\rm QCD}}
\newcommand{\PhiHQET}{\Phi^{\rm HQET}}
\newcommand{\Phiqcd}{\Phi^{\rm QCD}}
\newcommand{\Phihqet}{\Phi^{\rm HQET}}
\newcommand{\Phistat}{\Phi^{\rm stat}}
\newcommand{\Phikin}{\Phi^{\rm kin}}
\newcommand{\Phispin}{\Phi^{\rm spin}}
\newcommand{\Phibar}{\overline{\Phi}}
\newcommand{\Phibarkin}{\overline{\Phi}^{\rm kin}}
\newcommand{\Phibarspin}{\overline{\Phi}^{\rm spin}}
\newcommand{\Phirstat}{\Phi_{\rm R}^{\rm stat}}
\newcommand{\PhirHQET}{\Phi_{\rm R}^{\rm HQET}}
\newcommand{\PhirQCD}{\Phi_{\rm R}^{\rm QCD}}
\newcommand{\Phir}{\Phi_{{\rm R}}}

\newcommand{\sigm}{\sigma_{\rm m}}
\newcommand{\Sigm}{\Sigma_{\rm m}}
\newcommand{\sigkin}{\sigma^{\rm kin}}
\newcommand{\Sigkin}{\Sigma^{\rm kin}}
\newcommand{\sigx}{\sigma_{\rm X}}
\newcommand{\Sigx}{\Sigma_{\rm X}}

% Couplings and Lambda-parameters

\newcommand{\lQCD}{\Lambda_{\rm QCD}}
\newcommand{\lSF}{\Lambda_{\rm SF}}
\newcommand{\lMSbar}{\Lambda_{\overline{{\rm MS}}}}
\newcommand{\lMSbarq}{\Lambda_{\overline{{\rm MS}}}^{(0)}}

% Misc

\newcommand{\fns}{\footnotesize}
\newcommand{\sps}{\scriptsize}
\newcommand{\T}{\textstyle}
\newcommand{\D}{\displaystyle}
\newcommand{\cl}[1]{\mathcal{#1}}

\newcommand{\mrm}[1]{{\rm #1}}
\newcommand{\dts}[2]{#1_{{\rm #2}}}
\newcommand{\uts}[2]{#1^{{\rm #2}}}
\newcommand{\duts}[3]
           {#1_{{\rm #2}}^{{\rm #3}}}
\newcommand{\fat}[1]{\mbox{\boldmath$#1$}}
\newcommand{\sfat}[1]{{\small \mbox{\boldmath$#1$}}}
\newcommand{\tb}[1]{\textbf{#1}}

\newcommand{\lmax}{L_{\rm max}}
\newcommand{\alphs}{\alpha_{\rm s}}
\newcommand{\alphSF}{\alpha_{\rm SF}}
\newcommand{\MZ}{M_{\rm Z}}
\newcommand{\alphR}{\alpha_{\rm R}}
\newcommand{\alphTI}{\alpha_{\Box}}
\newcommand{\alphqqbar}{\alpha_{{\rm q}\overline{{\rm q}}}}
\newcommand{\alphMSbar}{\alpha_{\overline{{\rm MS}}}}
\newcommand{\mcost}{M_{\rm cost}}
\newcommand{\dcost}{D_{\rm cost}}
\newcommand{\nmd}{N_{\rm md}}
\newcommand{\Q}{\hat{Q}}
\newcommand{\Fm}{{\rm fm}}
\newcommand{\K}{{\rm K}}
% \newcommand{\D}{{\rm D}}
\newcommand{\Ds}{{\rm D}_{\rm s}}
\newcommand{\meff}{m_{{\rm eff}}}
\newcommand{\half}{{\textstyle{\frac{1}{2}}}}
\newcommand{\third}{{\textstyle{\frac{1}{3}}}}
\newcommand{\quart}{{\textstyle{\frac{1}{4}}}}
\newcommand{\threequart}{{\textstyle{\frac{3}{4}}}}
\newcommand{\nth}{{\textstyle{\frac{1}{N}}}}
\newcommand{\ts}{$\times$}
\newcommand{\crsp}{\hat{=}}
\newcommand{\oloop}{\rm 1-loop}
\newcommand{\ctop}{\dts{\chi}{top}}
\newcommand{\qtop}{\dts{Q}{top}}
\newcommand{\ctops}{\dtss{\chi}{top}}
\newcommand{\qtops}{\dtss{Q}{top}}
\newcommand{\tint}{\dts{\tau}{int}}
\newcommand{\texp}{\dts{\tau}{exp}}
\newcommand{\dt}{{\rm d}}
\newcommand{\Dt}{{\rm D}}
\newcommand{\Dc}{\cl{D}}
\newcommand{\Zc}{\cl{Z}}
\newcommand{\Oc}{\cl{O}}
\newcommand{\dsl}{D\hspace{-0.25cm}/\hspace{+0.075cm}}
\newcommand{\Exp}{{\rm e}}
\newcommand{\Mod}{{\rm mod\,}}
\newcommand{\Ep}{E_{\bps}}
\newcommand{\Eps}{E_{\bpss}}
\newcommand{\id}{\Bbb{I}}
\newcommand{\tfm}{\Bbb{T}}
\newcommand{\pro}{\Bbb{P}}
\newcommand{\cur}{\Bbb{X}}
% \newcommand{\opa}{\Bbb{A}}
\newcommand{\cpt}{\chi\mbox{PT}}
\newcommand{\SF}{{\rm SF}}
\newcommand{\MOM}{{\rm MOM}}
\newcommand{\lattice}{{\rm lattice}}
\newcommand{\QCD}{{\rm QCD}}
\newcommand{\HQET}{{\rm HQET}}
\newcommand{\citvoid}[1]{[\textbf{citation~#1}]}
\newcommand{\tabvoid}[1]{[\textbf{table~#1}]}
\newcommand{\figvoid}[1]{[\textbf{figure~#1}]}
\newcommand{\Alpha}{\hbox{\epsfxsize=0.75 true cm 
                          \epsfbox{plots/alpha_color_60.eps}}}
\newcommand{\ALPHA}{\hbox{\epsfxsize=0.875 true cm 
                          \epsfbox{plots/alpha_color_60.eps}}}

% Patrick Fritzsch's stuff

\def\rmi{{\rm i}}
\def\myt#1{\;\text{#1}}
\def\sdrv#1{{\widetilde{\partial}^{}_{#1}}}
\def\gotildesq{\widetilde{g}_{\kern0.1em 0}^{\kern0.1em 2}}
\def\hpo{\hphantom{0}}
\def\hpm{\hphantom{-}}
\def\hph#1{\hphantom{#1}}
\def\hphinv{^{\hph{-1}}}

\newcommand{\eee}[1]{\mathrm{e}^{#1}}  
\newcommand{\dd}[2]{\mathrm{d}^{#1}{#2}\;}
\newcommand{\intdd}[2]{\int\!\mathrm{d}^{#1}{#2}\,}
\newcommand{\evalbig}[1]{\big\langle#1\big\rangle}
\newcommand{\Ximp}{X_\mathrm{I}}
\newcommand{\lh}{_\mathrm{\,h}}
\newcommand{\RAP}{R_{\rm AP}}
\newcommand{\Rm}{R_{\rm m}}
\newcommand{\RAm}{R_{\rm Am}}
\newcommand{\Gamps}{\varGamma_{\rm PS}}
\newcommand{\clml}[1]{\multicolumn{1}{l}{#1}}
\newcommand{\clmc}[1]{\multicolumn{1}{c}{#1}}
\newcommand{\clmr}[1]{\multicolumn{1}{r}{#1}}
\newcommand{\MCC}[1]{\multicolumn{2}{c}{#1}}


% Other stuff

\newcommand{\cO}{{\cal O}}
