%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% % % % 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}}