NLO corrections to the $\Delta F=2$ Hamiltonian in the MSSM with non-degenerate squarks
Javier Virto
We present the next-to-leading strong interaction corrections to the $\Delta F=2$ Hamiltonian in the MSSM with exact diagonalization of the squark mass matrices. These results allow phenomenological studies of neutral meson mixing in scenarios with non-degenerate squarks, with control over the renormalization scale and scheme dependence.
ProceedingsSUSY09.tex
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\title{NLO corrections to the $\Delta F=2$ Hamiltonian in the MSSM with non-degenerate squarks}

\classification{11.30Pb, 12.60Jv, 12.38Bx, 12.15Ff.}
\keywords      {Supersymmetry, perturbative calculations, neutral meson mixing.} 

\author{Javier Virto}{
  address={INFN, Sezione di Roma, I-00185 Rome, Italy} }


\begin{abstract}
We present the next-to-leading strong interaction corrections to the $\Delta F=2$ Hamiltonian in the MSSM with exact diagonalization of the squark mass matrices. These results allow phenomenological studies of neutral meson mixing in scenarios with non-degenerate squarks, with control over the renormalization scale and scheme dependence.
\end{abstract}

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Flavor changing low-energy processes such as weak meson decays or the mixing of neutral mesons, are unique for indirect new physics searches because they are very sensitive to heavy degrees of freedom in loop amplitudes. This is due to the suppression of flavor-changing neutral currents in the SM, in contrast to the enormous flavor violation typical of new physics scenarios with generic flavor structure. Precise measurements --specially those related to $K$ and $B$ mesons-- have put stringent constraints on either the new physics scale or the flavor non-universality of the new couplings \cite{Antonelli:2009ws}. This is explicitly clear in SUSY models, and in particular in the MSSM, which is the paradigmatic extension of the SM.

In the MSSM, the leading source of flavor violation arises from a misalignment between quark and squark mass eigenbases induced by soft SUSY-breaking terms: in the basis for the superfields in which the quark mass matrices are diagonal (the so called super-CKM basis), the squark mass matrices contain non-zero non-diagonal elements (mass insertions), which are responsible for the flavor transition. Extensive phenomenological studies have been performed which constrain strongly the size of these mass insertions, based on FCNC processes \cite{Ciuchini:1998ix,Becirevic:2001jj,Silvestrini:2007yf,Ciuchini:2007cw,Crivellin:2009ar}, vacuum stability requirements \cite{hep-ph/9507294,hep-ph/9606237} and charged-current processes \cite{arXiv:0810.1613}. 

However, the increasing precision with which these quantities must be determined requires theoretical calculations of flavor violating processes at increasing order in perturbation theory, as well as more precise determinations of non-perturbative parameters. Here we focus on the calculation of matching conditions (Wilson coefficients at the SUSY scale) for the $\Delta F=2$ Hamiltonian, which are required for the theoretical determination of $K-\bar K$, $D-\bar D$ and $B_{d,s}-\bar B_{d,s}$ mixing amplitudes. The case of $B_s-\bar B_s$ mixing has recently caused some excitement in relation with a deviation of the measured mixing phase relative to the SM expectation \cite{arXiv:0712.2397,arXiv:0802.2255,arXiv:0803.0659}, and if such deviation is confirmed, a precise calculation of that phase in different models will be very convenient.

%******************************************************************
%%%Figure 1
%******************************************************************
\begin{figure}[t]
 \centering
 \psfrag{sb}{\small $\bar s$}\psfrag{bb}{\small $\bar b$}
 \psfrag{s}{\small $s$}\psfrag{b}{\small $b$} \psfrag{a}{\small $(a)$} \psfrag{c}{\small $(b)$}
 \psfrag{g}{\small $\tilde g$}\psfrag{qi}{\small $\tilde q_i$} \psfrag{qj}{\small $\tilde q_j$}
  \includegraphics[height=3.5cm,width=4.5cm]{LObox.eps}\hspace{1cm}
  \includegraphics[height=3.5cm,width=9cm]{NLObox.eps}
 \caption{A sample of the diagrams contributing to the MSSM matching conditions for $B_s-\bar B_s$ mixing at (a) leading order, and (b) next-to-leading order in $\alpha_s$.}
\label{fig1}
\end{figure}
%******************************************************************

Leading order (LO) strong interaction matching conditions in the MSSM have been computed in Refs.~\cite{Gerard:1984bg,hep-ph/9604387,Hagelin:1992tc}, and arise from squark-gluino box diagrams (Fig.~\ref{fig1}.a). The corresponding next-to-leading order (NLO) corrections arise from two loop diagrams such as those shown in Fig.~\ref{fig1}.b, and have been computed in Ref.~\cite{hep-ph/0606197} within the degenerate Mass Insertion Approximation (that is, at the leading order in an expansion in mass insertions, and assuming that the diagonal elements of the squark mass matrix are equal). Here we report on the calculation of the NLO strong interaction corrections for non-degenerate squark masses, that is, with exact diagonalization of the squark mass matrices. This calculation was performed in Ref.~\cite{Virto:2009wm}, extending the known results beyond the Mass Insertion Approximation (MIA), and the full expressions for the Wilson coefficients can be found in that paper.

These NLO corrections valid for non-degenerate squark masses are important for two reasons:

\begin{enumerate}

\item At LO, the renormalization scale and scheme cannot be specified for the strong coupling, leading to a large uncertainty related to scale and scheme ambiguities. At NLO, however, scheme independent results and NLO scale invariance are accomplished. The reduction of this uncertainty is numerically important due to the large anomalous dimensions of the $\Delta F=2$ operators involved. The analysis of Ref.~\cite{hep-ph/0606197} shows that this uncertainty is reduced from 10-15\% down to a few percent.  

\item Scenarios with large squark mass splittings can give rise to a quite different pattern of correlations between $\Delta F=1$ and $\Delta F=2$ observables, such that $\Delta F=2$ processes can be affected very differently by the experimental bounds on $\Delta F=1$ processes. An example of how this comes about in a hierarchical scenario is given in Ref.~\cite{arXiv:0812.3610}, where it is shown that the bounds from $B\to X_s\gamma$ can be partially evaded allowing a large $B_s$ mixing phase.

\end{enumerate}

From the results with exact diagonalization of the squark mass matrices presented here and in Ref.~\cite{Virto:2009wm}, it is possible to recover the Wilson coefficients in the MIA. This is done by relating the rotation matrices to the mass insertions, expanding to lowest order in the mass insertion expansion and taking the limit of equal diagonal elements of the mass matrices. The corresponding expressions agree with the results of Ref.~\cite{hep-ph/0606197}, verifying the correctness of their calculation. Moreover, in order to provide a clear comparison between the degenerate and non-degenerate scenarios, it is convenient to expand the exact results to lowest order in the mass insertion expansion but keeping the squark masses non-degenerate. This scheme might be called the \emph{non-degenerate mass insertion approximation} (NDMIA). 

In order to get an idea of the size of the new contributions, we consider a particular scenario in the NDMIA for the case of $B_s-\bar B_s$ mixing. This scenario is based on the ``hierarchical'' setup of Ref.~\cite{arXiv:0812.3610}, in which the first two generation squarks are given a common mass $\tilde m_{12}$, different from a common mass $\tilde m_3$ for the third generation squarks. Moreover, $\tilde m_3$ is assumed to be near the electroweak scale in order to ensure naturalness, while $\tilde m_{12}$ could be well above (thus reducing the conflict with kaon physics data, for example).

%******************************************************************
%%%Figure 2
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\begin{figure}
\centering
\psfrag{xh}{$x_h$} \psfrag{C2NLO}{\hspace{-0.5cm}$\stackrel{1\ +\ C_2^{\rm \sss NLO}/C_2^{\rm \sss LO}}{}$}
\psfrag{C3NLO}{$\stackrel{\hspace{-0.5cm}1\ +\ C_3^{\rm \sss NLO}/C_3^{\rm \sss LO}}{}$}
\includegraphics[width=6cm]{PlotC2NLO.eps}\qquad\quad
\includegraphics[width=6cm]{PlotC3NLO.eps}
\vspace{-0.5cm}
\caption{Relative importance of the full NLO result with respect to the LO, for the Wilson coefficients $C_2$ and $C_3$, as a function of $x_h\equiv \tilde m_{12}^2/m_{\tilde g}^2$, where $\tilde m_{12}$ is a common mass for first and second generation squarks. The dashed lines correspond to the degenerate (MIA) scenario. We have chosen $400~{\rm GeV}$ for third generation squark masses and $m_{\tilde g}=\mu=350~{\rm GeV}$, where $\mu$ is the matching scale.}
\label{fig2}
\end{figure}
%******************************************************************

The plots in Fig.~\ref{fig2} illustrate the relative importance of the NLO corrections, as a function of the mass splitting between the light and heavy squarks. The NLO correction is typically a $\sim 10\%$ effect in the degenerate case, but its importance increases with the mass splitting. For heavy squarks of about a TeV, the NLO contribution to $C_3$ can be up to a $\sim 25\%$ correction.

In order to analyze more closely the role of the mass splittings in the NLO corrections, we consider $C_1, C_4$ and $C_5$ as a function $x_l\equiv\tilde m_3^2/m_{\tilde g}^2$, for different splittings between $x_l$ and $x_h=\tilde m_{12}^2/m_{\tilde g}^2$. This is shown in Fig.~\ref{fig3}, where the dashed lines correspond to $x_l=x_h$ (that is, the degenerate case), and --departing smoothly from that limit-- the solid lines show increasing values of $x_h/x_l$. In these plots we take the dimensionless mass insertions $\delta_{L,R}=\delta_{R,L}=0$ and $m_{\tilde g}=\mu=350~{\rm GeV}$. We see that increasing the heavy scale tends to reduce systematically the size of the NLO contribution, being largest in the degenerate case.

However, caution must be taken when interpreting these results, since the NLO Wilson coefficients are renormalization scale and scheme dependent. These results correspond to the renormalization scheme adopted in Ref.~\cite{Virto:2009wm} (NDR with some subtleties), and will vary in other schemes. Of course, the scheme dependence cancels in physical amplitudes (against the scheme dependence of the matrix elements of the operators), so the true impact of these NLO corrections can only be established by analyzing their effect on observables. A full phenomenological analysis of these corrections and their impact on the bounds on the mass insertions (beyond the mass insertion approximation) will be presented in the future.



%******************************************************************
%%%Figure 3
%******************************************************************
\begin{figure}
\centering
\psfrag{xl}{$x_l$} \psfrag{C1NLO}{\hspace{-0.5cm}\small $C_1^{\rm \sss NLO}\ {\scriptstyle (\times 10^{8})}$}
\psfrag{C4NLO}{\hspace{-0.5cm}\small $C_4^{\rm \sss NLO}\ {\scriptstyle (\times 10^{6})}$}
\psfrag{C5NLO}{\hspace{-0.5cm}\small $C_5^{\rm \sss NLO}\ {\scriptstyle (\times 10^{7})}$}
\includegraphics[width=4.5cm,height=3.5cm]{PlotC1NLO.eps}\quad
\includegraphics[width=4.5cm,height=3.5cm]{PlotC4NLO.eps}\quad
\includegraphics[width=4.5cm,height=3.5cm]{PlotC5NLO.eps}
\vspace{-0.5cm}
\caption{NLO Wilson coefficients $C_1^{NLO}$, $C_4^{NLO}$ and $C_5^{NLO}$ as a function of $x_l\equiv \tilde m_{3}^2/m_{\tilde g}^2$, where $\tilde m_{3}$ is a common mass for third generation squarks. The plots are in units of $(\alpha_s^3/\pi) \delta_{LL}^2$ and $(\alpha_s^3/\pi) \delta_{LL}\delta_{RR}$ for $C_1$ and $C_{4,5}$ respectively. The different lines correspond to different values of $x_h\equiv \tilde m_{12}^2/m_{\tilde g}^2$, and range from the MIA case, $x_h=x_l$ (dashed) to $x_h=1.5 x_l, 2 x_l,3 x_l, 4 x_l, 5 x_l, 6 x_l$.}
\label{fig3}
\end{figure}

\begin{theacknowledgments}
I would like to thank Luca Silvestrini, Enrico Franco and Marco Ciuchini for discussions on topics related to this work. I would like to thank as well the organizers and the attendees to the SUSY'09 conference for a very stimulating workshop. ~J.V. is associated to the Dipartimento di Fisica, Universita di Roma `La Sapienza'. 
\end{theacknowledgments}


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\begin{thebibliography}{9}

\bibitem{Antonelli:2009ws}
  M.~Antonelli {\it et al.},
  %``Flavor Physics in the Quark Sector,''
  arXiv:0907.5386 [hep-ph].
  %%CITATION = ARXIV:0907.5386;%%

\bibitem{Ciuchini:1998ix}
  M.~Ciuchini {\it et al.},
  %``Delta M(K) and epsilon(K) in SUSY at the next-to-leading order,''
  JHEP {\bf 9810}, 008 (1998)
  %[arXiv:hep-ph/9808328].
  %%CITATION = JHEPA,9810,008;%%
  
  \bibitem{Becirevic:2001jj}
  D.~Becirevic {\it et al.},
  %``$B_d - \bar{B}_d$ mixing and the $B_d \to J/\psi K_s$ asymmetry in general
  %SUSY models,''
  Nucl.\ Phys.\  B {\bf 634}, 105 (2002)
  %[arXiv:hep-ph/0112303].
  %%CITATION = NUPHA,B634,105;%%
  
  \bibitem{Silvestrini:2007yf}
  L.~Silvestrini,
  %``Searching for new physics in $b \to s$ hadronic penguin decays,''
  Ann.\ Rev.\ Nucl.\ Part.\ Sci.\  {\bf 57}, 405 (2007)
  %[arXiv:0705.1624 [hep-ph]].
  %%CITATION = ARNUA,57,405;%%
  
  \bibitem{Ciuchini:2007cw}
  M.~Ciuchini, E.~Franco, D.~Guadagnoli, V.~Lubicz, M.~Pierini, V.~Porretti and L.~Silvestrini,
  %``$D$ - $\bar{D}$ mixing and new physics: General considerations and
  %constraints on the MSSM,''
  Phys.\ Lett.\  B {\bf 655}, 162 (2007)
  %[arXiv:hep-ph/0703204].
  %%CITATION = PHLTA,B655,162;%%
  
  \bibitem{Crivellin:2009ar}
  A.~Crivellin and U.~Nierste,
  %``Chirally enhanced corrections to FCNC processes in the generic MSSM,''
  arXiv:0908.4404 [hep-ph].
  %%CITATION = ARXIV:0908.4404;%%


\bibitem{hep-ph/9507294}
  J.~A.~Casas, A.~Lleyda and C.~Munoz,
  %``Strong constraints on the parameter space of the MSSM from charge and color
  %breaking minima,''
  Nucl.\ Phys.\  B {\bf 471}, 3 (1996)
  %[arXiv:hep-ph/9507294].
  %%CITATION = NUPHA,B471,3;%%

\bibitem{hep-ph/9606237}
  J.~A.~Casas and S.~Dimopoulos,
  %``Stability bounds on flavor-violating trilinear soft terms in the MSSM,''
  Phys.\ Lett.\  B {\bf 387}, 107 (1996)
  %[arXiv:hep-ph/9606237].
  %%CITATION = PHLTA,B387,107;%%
 
\bibitem{arXiv:0810.1613}
  A.~Crivellin and U.~Nierste,
  %``Supersymmetric renormalisation of the CKM matrix and new constraints on the
  %squark mass matrices,''
  Phys.\ Rev.\  D {\bf 79}, 035018 (2009)
  %[arXiv:0810.1613 [hep-ph]].
  %%CITATION = PHRVA,D79,035018;%% 

 
 \bibitem{arXiv:0712.2397}
  T.~Aaltonen {\it et al.}  [CDF Collaboration],
  %``First Flavor-Tagged Determination of Bounds on Mixing-Induced CP Violation
  %in $B^0_{s} \to J/\psi \phi$ Decays,''
  Phys.\ Rev.\ Lett.\  {\bf 100}, 161802 (2008)
  %[arXiv:0712.2397 [hep-ex]].
  %%CITATION = PRLTA,100,161802;%%
 
\bibitem{arXiv:0802.2255}
  V.~M.~Abazov {\it et al.}  [D0 Collaboration],
  %``Measurement of $B0_{s}$ mixing parameters from the flavor-tagged decay
  %$B0_{s} \to J/\psi \phi$,''
  Phys.\ Rev.\ Lett.\  {\bf 101}, 241801 (2008)
  %[arXiv:0802.2255 [hep-ex]].
  %%CITATION = PRLTA,101,241801;%%
  
  \bibitem{arXiv:0803.0659}
  M.~Bona {\it et al.}  [UTfit Collaboration],
  %``First Evidence of New Physics in $b \longleftrightarrow s$ Transitions,''
  arXiv:0803.0659 [hep-ph].
  %%CITATION = ARXIV:0803.0659;%%

 
 \bibitem{Gerard:1984bg}
  J.~M.~Gerard, W.~Grimus, A.~Raychaudhuri and G.~Zoupanos,
  %``Super Kobayashi-Maskawa CP Violation,''
  Phys.\ Lett.\  B {\bf 140}, 349 (1984).
  %%CITATION = PHLTA,B140,349;%%
  
  \bibitem{hep-ph/9604387}
  F.~Gabbiani, E.~Gabrielli, A.~Masiero and L.~Silvestrini,
  %``A complete analysis of FCNC and CP constraints in general SUSY extensions
  %of the standard model,''
  Nucl.\ Phys.\  B {\bf 477}, 321 (1996)
  %[arXiv:hep-ph/9604387].
  %%CITATION = NUPHA,B477,321;%%
  
  \bibitem{Hagelin:1992tc}
  J.~S.~Hagelin, S.~Kelley and T.~Tanaka,
  %``Supersymmetric flavor changing neutral currents: Exact amplitudes and
  %phenomenological analysis,''
  Nucl.\ Phys.\  B {\bf 415}, 293 (1994).
  %%CITATION = NUPHA,B415,293;%%
 

\bibitem{hep-ph/0606197}
  M.~Ciuchini, E.~Franco, D.~Guadagnoli, V.~Lubicz, V.~Porretti and L.~Silvestrini,
  %``Next-to-leading order strong interaction corrections to the Delta(F) =  2
  %effective hamiltonian in the MSSM,''
  JHEP {\bf 0609}, 013 (2006)
  %[arXiv:hep-ph/0606197].
  %%CITATION = JHEPA,0609,013;%%
  
  \bibitem{Virto:2009wm}
  J.~Virto,
  %``Exact NLO strong interaction corrections to the Delta F=2 effective
  %Hamiltonian in the MSSM,''
  arXiv:0907.5376 [hep-ph].
  %%CITATION = ARXIV:0907.5376;%%
  
  \bibitem{arXiv:0812.3610}
  G.~F.~Giudice, M.~Nardecchia and A.~Romanino,
  %``Hierarchical Soft Terms and Flavor Physics,''
  Nucl.\ Phys.\  B {\bf 813}, 156 (2009)
  %[arXiv:0812.3610 [hep-ph]].
  %%CITATION = NUPHA,B813,156;%%
   

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     \typeout{*}
     \typeout{* The aip-arlo.clo file which is part of the aipproc distribution}
     \typeout{* must be installed in a directory which is searched by LaTeX.}
     \typeout{*}
     \typeout{* Please install this file and retry.}
     \typeout{*}
     \stop
}
\fi

\typeout{*}
\typeout{* Looking for fixltx2e.sty ... }
\IfFileExists{fixltx2e.sty}
    {
     \typeout{* ... ok }
    }
    {
     \typeout{* ... not found, trying fix2col.sty instead ... }
     \typeout{*}
     \IfFileExists{fix2col.sty}
         {
          \typeout{* ... ok }
         }
         {
          \typeout{* ... not found! }
          \typeout{*}
          \typeout{* Sorry this is a fatal error:}
          \typeout{*}
          \typeout{* Your LaTeX distribution contains neither fixltx2e.sty}
          \typeout{* nor fix2col.sty.}
          \typeout{*}
          \typeout{* This means that it is either too old or incompletely}
          \typeout{* installed.}
          \typeout{*}
          \typeout{* fixltx2e.sty is part of the standard LaTeX distribution}
          \typeout{* since 1999; fix2col.sty is an earlier version of this}
          \typeout{* package.}
          \typeout{*}
          \typeout{* Best solution is to get the latest LaTeX distribution.}
          \typeout{* If this is impossible for you, download fix2col.sty.}
          \typeout{* You can get this software from a CTAN host.}
          \typeout{* Refer to http://www.ctan.org and search for "fix2col".}
          \typeout{*}
          \typeout{* After you have updated your LaTeX distribution}
          \typeout{* retry processing this guide.}
          \stop
     }
}

\typeout{*}
\typeout{* Looking for fontenc.sty ... }
\IfFileExists{fontenc.sty}
    {
     \typeout{* ... ok }
    }
    {
     \typeout{* ... not found! }
     \typeout{*}
     \typeout{* Sorry this is a fatal error:}
     \typeout{*}
     \typeout{* The fontenc package, which is part of standard LaTeX}
     \typeout{* (base distribution) has to be installed at the site to}
     \typeout{* run the aipproc class.}
     \typeout{*}
     \typeout{* The fact that it cannot be found either means that}
     \typeout{* this LaTeX release is too old or that it was installed}
     \typeout{* improperly.}
     \typeout{*}
     \typeout{* Please make sure that your version of LaTeX is okay}
     \typeout{* before attempting to use this class. The LaTeX distribution}
     \typeout{* contains the file "ltxcheck.tex" which can be used to}
     \typeout{* test the basic functionality and integrity of your installation.}
     \typeout{*}
     \stop
    }

\typeout{*}
\typeout{* Looking for calc.sty ... }
\IfFileExists{calc.sty}
    {
     \typeout{* ... ok }
    }
    {
     \typeout{* ... not found! }
     \typeout{*}
     \typeout{* Sorry this is a fatal error:}
     \typeout{*}
     \typeout{* The calc package, which is part of standard LaTeX}
     \typeout{* (tool distribution) has to be installed at the site}
     \typeout{* to run the aipproc class.}
     \typeout{*}
     \typeout{* The fact that it cannot be found either means that}
     \typeout{* this LaTeX release is too old or that it was installed}
     \typeout{* only in parts.}
     \typeout{*}
     \typeout{* Please make sure that the tools distribution of LaTeX}
     \typeout{* is installed before attempting to use this class.}
     \typeout{*}
     \typeout{* (You might be able to get calc.sty separately for your}
     \typeout{* installation if you are unable to upgrade to a recent}
     \typeout{* distribution for some reason.)}
     \typeout{*}
     \stop
    }

\typeout{*}
\typeout{* Looking for varioref.sty ... }
\IfFileExists{varioref.sty}
    {
     \typeout{* ... ok }
     \gdef\variorefoptionifavailable{varioref,}
    }
    {
     \typeout{* ... not found! }
     \typeout{*}
     \typeout{* Problem detected:}
     \typeout{*}
     \typeout{* The varioref package, which is part of standard LaTeX}
     \typeout{* (tool distribution) is not installed at this site.}
     \typeout{*}
     \typeout{* The fact that it cannot be found either means that}
     \typeout{* this LaTeX release is too old or that it was installed}
     \typeout{* only in parts.}
     \typeout{*}
     \typeout{* You can use the aipproc class without this package but }
     \typeout{* you cannot make use of the options "varioref" or "nonvarioref".}
     \typeout{*}
     \typeout{* Please also note that the aipguide.tex documentation}
     \typeout{* normally uses the "varioref" option to show its}
     \typeout{* effects (which  will now fail).}
     \typeout{*}
     \typein{* Type <return> to continue ...}
     \problemtrue
     \gdef\variorefoptionifavailable{}
     \let\vpageref\pageref
     \let\vref\ref
    }

\typeout{*}
\typeout{* Looking for times.sty ... }
\IfFileExists{times.sty}
    {
     \begingroup
% load times and forget it immediately again
       \RequirePackage{times}
       \global\expandafter\let\csname ver@times.sty\endcsname\relax    
       \long\def\next{ptm}
       \ifx\rmdefault\next
         \typeout{* ... ok }
         \gdef\psnfssproblemoption{}
         \endgroup
         \timesoktrue
       \else
         \endgroup
     \typeout{* ... obsolete! }
     \typeout{*}
     \typeout{* Serious problem detected:}
     \typeout{*}
     \typeout{* The times package, which is part of standard LaTeX}
     \typeout{* (psnfss distribution) is obsolete at this site.}
     \typeout{*}
     \typeout{* The fact that it contains incorrect code either means that}
     \typeout{* this LaTeX release is too old or that it was installed}
     \typeout{* only in parts with old files remaining!}
     \typeout{*}
     \typeout{* You can use the aipproc class without this package but}
     \typeout{* you have to specify the option "cmfonts" which result in}
     \typeout{* documents which are not conforming to the AIP layout specification!}
     \typeout{*}
     \typeout{* You can also try using the class in the following way:}
     \typeout{*}
     \typeout{* \space\space \string\documentclass[cmfonts]{aipproc}}
     \typeout{* \space\space \string\usepackage{times}}
     \typeout{* \space\space ...}
     \typeout{*}
     \typeout{* With luck this will result in Times Roman output but chances}
     \typeout{* are that you will get a larger number of error messages in}
     \typeout{* which case you have to remove the \string\usepackage declaration.}
     \typeout{*}
     \typein{* Type <return> to continue ...}
          \problemtrue
          \gdef\psnfssproblemoption{cmfonts}
          \def\textdegree{$^\circ$}            % used below but now
                                               % not setup
       \fi
    }
    {
     \typeout{* ... not found! }
     \typeout{*}
     \typeout{* Serious problem detected:}
     \typeout{*}
     \typeout{* The times package, which is part of standard LaTeX}
     \typeout{* (psnfss distribution) can not be found.}
     \typeout{*}
     \typeout{* The fact that this package cannot be found either means that}
     \typeout{* this LaTeX release is too old or that it was installed}
     \typeout{* only in parts!}
     \typeout{*}
     \typeout{* You can use the aipproc class without this package but }
     \typeout{* you have to specify the option "cmfonts" which result in}
     \typeout{* documents which are not conforming to the AIP layout specification!}
     \typeout{*}
     \typein{* Type <return> to continue ...}
     \problemtrue
     \gdef\psnfssproblemoption{cmfonts,}
    }

\iftimesok % don't bother testing other font options if times already
           % bad

\typeout{*}
\typeout{* Looking for t1ptm.fd or T1ptm.fd ... }
\IfFileExists{t1ptm.fd}
    {
     \typeout{* ... ok }
    }
    {
     \typeout{* ... not found, trying T1ptm.fd ... }
     \IfFileExists{T1ptm.fd}
          {
           \typeout{* ... ok }
          }
          {
           \typeout{* ... not found}
           \typeout{* Serious problem detected:}
           \typeout{*}
           \typeout{* The times package, which is part of standard LaTeX}
           \typeout{* (psnfss distribution) is available but the corresponding}
           \typeout{* .fd file (defining how to load Times Roman) is missing.}
           \typeout{*}
           \typeout{* The fact that this package is only partially installed}
           \typeout{* means that you LaTeX installation is unable to use Times}
           \typeout{* Roman fonts!}
           \typeout{*}
           \typeout{* You can use the aipproc class without this package but }
           \typeout{* you have to specify the option "cmfonts" which result in}
           \typeout{* documents which are not conforming to the AIP layout}
           \typeout{* specification!}
           \typeout{*}
           \typein{* Type <return> to continue ...}
           \problemtrue
           \timesokfalse
           \gdef\psnfssproblemoption{cmfonts,}
          }
    }

\fi


\newcommand\CheckFDFile[3]{%
  \typeout{*}
  \typeout{* Looking for #1#3.fd or #2#3.fd ... }
  \IfFileExists{#1#3.fd}
    {
     \typeout{* ... ok }
    }
    {
     \IfFileExists{#2#3.fd}
      {
       \typeout{* ... ok }
      }
      {\problemtrue
       \typeout{* ... not found! }
      }
    }
}

\iftimesok % don't bother testing other font options if Times already bad

%\CheckFDFile{ot1}{OT1}{ot1ztmcm}
%\CheckFDFile{oml}{OML}{omlztmcm}
%\CheckFDFile{oms}{OMS}{omsztmcm}
%\CheckFDFile{omx}{OMX}{omxztmcm}

\typeout{*}
\typeout{* Looking for mathptm.sty ... }
\IfFileExists{mathptm.sty}
    {
     \typeout{* ... ok }
     \CheckFDFile{ot1}{OT1}{ptmcm}
     \CheckFDFile{oml}{OML}{ptmcm}
     \CheckFDFile{oms}{OMS}{pzccm}
     \CheckFDFile{omx}{OMX}{psycm}
     \ifproblem
      \typeout{*}
      \typeout{* Problem detected:}
      \typeout{*}
      \typeout{* The mathptm package, which is part of standard LaTeX}
      \typeout{* (psnfss distribution) was found but some or all of its}
      \typeout{* support files describing which fonts to load are missing!}
      \typeout{*}
      \typeout{*}
      \typeout{* The fact that this package is only partially installed}
      \typeout{* means that the mathptm package cannot be used!}
      \typeout{*}
      \typeout{* You can use the aipproc class without this package but }
      \typeout{* you have to specify the option "nomathfonts" so that}
      \typeout{* math formulas will be typeset using Computer Modern.}
      \typeout{*}
      \typein{* Type <return> to continue ...}
      \problemtrue
      \gdef\psnfssproblemoption{nomathfonts,}
     \else
      \typeout{*}
      \typeout{* Looking for mathptmx.sty ... }
      \IfFileExists{mathptmx.sty}
       {
        \typeout{* ... ok }
        \CheckFDFile{ot1}{OT1}{ztmcm}
        \CheckFDFile{oml}{OML}{ztmcm}
        \CheckFDFile{oms}{OMS}{ztmcm}
        \CheckFDFile{omx}{OMX}{ztmcm}
        \ifproblem
          \typeout{*}
          \typeout{* Problem detected:}
          \typeout{*}
          \typeout{* The mathptmx package, which is part of standard LaTeX}
          \typeout{* (psnfss distribution) was found but some or all of its}
          \typeout{* support files describing which fonts to load are missing!}
          \typeout{*}
          \typeout{*}
          \typeout{* The fact that this package is only partially installed}
          \typeout{* means that the mathptmx package cannot be used!}
          \typeout{*}
          \typeout{* You can use the aipproc class without this package but }
          \typeout{* you have to specify the option "mathptm" (no x) so that}
          \typeout{* math formulas use the older version with upright greek letters.}
          \typeout{*}
          \typein{* Type <return> to continue ...}
          \problemtrue
          \gdef\psnfssproblemoption{mathptm,}
        \fi
       }
       {
        \typeout{* ... not found! }
        \typeout{*}
        \typeout{* Problem detected:}
        \typeout{*}
        \typeout{* The mathptmx package, which is part of standard LaTeX}
        \typeout{* (psnfss distribution) can not be found.}
        \typeout{*}
        \typeout{* This is unfortunate but not a disaster as the older}
        \typeout{* version of the package "mathptm" (no x) seems to exist.}
        \typeout{*}
        \typeout{* You can use the aipproc class without this package but }
        \typeout{* you have to specify the option "mathptm" so that}
        \typeout{* math formulas use the older version with upright greek letters.}
        \typeout{*}
        \typein{* Type <return> to continue ...}
        \problemtrue
        \gdef\psnfssproblemoption{mathptm,}
       }
      \fi
    }
    {
     \typeout{* ... not found! }
     \typeout{*}
     \typeout{* Problem detected:}
     \typeout{*}
     \typeout{* The mathptm package, which is part of standard LaTeX}
     \typeout{* (psnfss distribution) can not be found.}
     \typeout{*}
     \typeout{* The fact that this package cannot be found either means that}
     \typeout{* this LaTeX release is too old or that it was installed}
     \typeout{* only in parts!}
     \typeout{*}
     \typeout{* You can use the aipproc class without this package but }
     \typeout{* you have to specify the option "nomathfonts" so that}
     \typeout{* math formulas will be typeset using Computer Modern.}
     \typeout{*}
     \typein{* Type <return> to continue ...}
     \problemtrue
     \gdef\psnfssproblemoption{nomathfonts,}
    }

\typeout{*}
\typeout{* Looking for mathtime.sty ... }
\IfFileExists{mathtime.sty}
    {
     \typeout{* ... ok }
    }
    {
     \typeout{* ... not found! }
     \typeout{*}
     \typeout{* The mathime package can not be found.}
     \typeout{*}
     \typeout{* This is not a real problem but an observation,}
     \typeout{* because this package is only of interest}
     \typeout{* if you own the commerical MathTime fonts.}
     \typeout{*}
     \typeout{* You can use the aipproc class without this package but }
     \typeout{* you cannot use the "mathtime" option of the class.}
     \typeout{*}
     \observationtrue
    }
\typeout{*}
\typeout{* Looking for mtpro.sty ... }
\IfFileExists{mtpro.sty}
    {
     \typeout{* ... ok }
    }
    {
     \typeout{* ... not found! }
     \typeout{*}
     \typeout{* The mtpro package can not be found.}
     \typeout{*}
     \typeout{* This is not a real problem but an observation,}
     \typeout{* because this package is only of interest}
     \typeout{* if you own the commerical MathTime Professional fonts.}
     \typeout{*}
     \typeout{* You can use the aipproc class without this package but }
     \typeout{* you cannot use the "mtpro" option of the class.}
     \typeout{*}
     \observationtrue
    }
\else
\fi % iftimesok

\typeout{*}
\typeout{* Looking for graphicx.sty ... }
\IfFileExists{graphicx.sty}
    {
     \typeout{* ... ok }
    }
    {
     \typeout{* ... not found! }
     \typeout{*}
     \typeout{* Problem detected:}
     \typeout{*}
     \typeout{* The graphics package, which is part of standard LaTeX}
     \typeout{* (graphics distribution) can not be found.}
     \typeout{*}
     \typeout{* The fact that this package cannot be found either means that}
     \typeout{* this LaTeX release is too old or that it was installed}
     \typeout{* only in parts!}
     \typeout{*}
     \typeout{* You can use the aipproc class without this package but }
     \typeout{* you cannot use commands like \protect\includegraphics
                or \protect\resizebox}
     \typeout{* in this case.}
     \typeout{*}
     \typeout{* Please note that you will get a further error message below}
     \typeout{* about: "graphicx.sty not found" because the class will try}
     \typeout{* to load this package! Type return in response to that error.}
     \typeout{*}
     \typeout{* As a result the illustrations in aipguide will look strange.}
     \typeout{*}
     \typein{* Type <return> to continue ...}

     \gdef\resizebox##1##2{}
     \gdef\includegraphics{\textbf{graphics package missing:}}
     \problemtrue
    }

\typeout{*}
\typeout{* Looking for textcomp.sty ... }
\IfFileExists{textcomp.sty}
    {
     \typeout{* ... ok }
    }
    {
     \typeout{* ... not found! }
     \typeout{*}
     \typeout{* Problem detected:}
     \typeout{*}
     \typeout{* The textcomp package, which is part of standard LaTeX}
     \typeout{* (base distribution) can not be found.}
     \typeout{*}
     \typeout{* The fact that this package cannot be found either means that}
     \typeout{* this LaTeX release is too old or that it was installed}
     \typeout{* only in parts!}
     \typeout{*}
     \typeout{* You can use the aipproc class without this package but }
     \typeout{* you will always get the error: "textcomp.sty not found"}
     \typeout{* because the class will try to load this package!}
     \typeout{* Type return in response to that error.}
     \typeout{*}
     \typein{* Type <return> to continue ...}

     \def\textdegree{$^\circ$}         % used below but now
                                       % not set up
     \problemtrue
    }


\typeout{*}
\typeout{* Looking for url.sty ... }
\IfFileExists{url.sty}
    {
     \typeout{* ... ok }
    }
    {
     \typeout{* ... not found! }
     \typeout{*}
     \typeout{* Problem detected:}
     \typeout{*}
     \typeout{* The url package, which should be part of a good LaTeX}
     \typeout{* distribution, can not be found.}
     \typeout{*}
     \typeout{* Without this package you will not be able to use the \string\url}
     \typeout{* command. Try to download this package from a CTAN  host.}
     \typeout{* Refer to http://www.ctan.org and search for "url".}
     \typeout{*}
     \typein{* Type <return> to continue ...}

     \problemtrue
    }


\typeout{*}
\typeout{* Looking for textcase.sty ... }
\IfFileExists{textcase.sty}
    {
     \typeout{* ... ok }
    }
    {
     \typeout{* ... not found! }
     \typeout{*}
     \typeout{* Problem detected:}
     \typeout{*}
     \typeout{* The textcase package, which should be part of a good LaTeX}
     \typeout{* distribution, can not be found.}
     \typeout{*}
     \typeout{* Without this package you should be careful not to put math}
     \typeout{* formulas into \noexpand\section headings as these headings are}
     \typeout{* converted to UPPERCASE and might spoil your formulas.}
     \typeout{* Try to download this package from a CTAN  host.}
     \typeout{* Refer to http://www.ctan.org and search for "url".}
     \typeout{*}
     \typein{* Type <return> to continue ...}

     \problemtrue
    }


\makeatletter

\typeout{*}
\typeout{* Looking for natbib.sty ... }
\IfFileExists{natbib.sty}
    {
     \IfStandaloneCheck
       {\begingroup
        \let\@listi\relax
        \let\thebibliography\@empty
        \let\bibstyle\@empty
        \RequirePackage{natbib}
        \@ifpackagelater{natbib}{1999/05/29}
          {
           \typeout{* ... ok }
          }{
           \typeout{* ... might be too old! }
           \typeout{*}
           \typeout{* Your version of the natbib package might be too}
           \typeout{* old to be usable. This class was designed to}
           \typeout{* work with the version 7.0 dated 1999/05/28}
           \typeout{*}
           \typeout{* If problems occur download a}
           \typeout{* recent version from a CTAN host.}
           \typeout{*}
           \typeout{* Refer to http://www.ctan.org and search for "natbib".}
           \typeout{*}
           \typein{* Type <return> to continue ...}

           \global\problemtrue
          }
        \endgroup
        }{}
    }
    {
     \typeout{* ... not found! }
     \typeout{*}
     \typeout{* Serious problem detected:}
     \typeout{*}
     \typeout{* The natbib package, which should be part of a good LaTeX}
     \typeout{* distribution, can not be found.}
     \typeout{*}
     \typeout{* Without this package you will not be able to use certain}
     \typeout{* citation styles. See the aipguide documentation!}
     \typeout{*}
     \typeout{* Especially the layout for ARLO requires this package!}
     \typeout{*}
     \typeout{* Try to download this package from a CTAN  host.}
     \typeout{* Refer to http://www.ctan.org and search for "natbib".}
     \typeout{*}
     \typein{* Type <return> to continue ...}

     \problemtrue
    }

\makeatother


\typeout{*}
\typeout{* ... finished testing}
\typeout{*}
\ifproblem
\typeout{* The tests have revealed some problems in your TeX installation.}
\typeout{*}
\typeout{* Please review the above comments carefully and read the file}
\typeout{* README for further information.}
\typeout{*}
\typeout{*****************************************************************}
\typein{* Type <return> to continue ...}
\else
 \ifobservation
  \typeout{****************************************************************}
  \typeout{*}
  \typeout{* The tests have reveiled no problems in your TeX installation,}
  \typeout{* but some observations have been made; see above.}
  \typeout{*}
  \typeout{****************************************************************}
 \else
  \typeout{****************************************************************}
  \typeout{*}
  \typeout{* The tests have reveiled no problems in your TeX installation.}
  \typeout{*}
  \typeout{****************************************************************}
 \fi
\fi


% if this file is run standalone stop otherwise continue

\makeatletter
\IfStandaloneCheck
 {
\typeout{*}
\typeout{* This document only produces terminal output.}
\typeout{*}
\stop
 }
 {
\AtBeginDocument{\relax\ifx\xfm@address@loop\@undefined
  \typeout{***************************}
  \typeout{* Oooops ... you seem to have picked up an obsolete}
  \typeout{* aipproc.cls file from a previous installation!}
  \typeout{*}
  \typeout{* Please check that LaTeX finds the right one.}
  \typeout{*}
  \typeout{* Sorry have to give up ....}
  \typeout{***************************}
  \stop
 \fi}
 }
\makeatother

\endinput

%%% Local Variables: 
%%% mode: latex
%%% TeX-master: t
%%% End: 

0909.3277.extracted_bib
\begin{thebibliography}{9}

\bibitem{Antonelli:2009ws}
  M.~Antonelli {\it et al.},
  %``Flavor Physics in the Quark Sector,''
  arXiv:0907.5386 [hep-ph].
  %%CITATION = ARXIV:0907.5386;%%

\bibitem{Ciuchini:1998ix}
  M.~Ciuchini {\it et al.},
  %``Delta M(K) and epsilon(K) in SUSY at the next-to-leading order,''
  JHEP {\bf 9810}, 008 (1998)
  %[arXiv:hep-ph/9808328].
  %%CITATION = JHEPA,9810,008;%%
  
  \bibitem{Becirevic:2001jj}
  D.~Becirevic {\it et al.},
  %``$B_d - \bar{B}_d$ mixing and the $B_d \to J/\psi K_s$ asymmetry in general
  %SUSY models,''
  Nucl.\ Phys.\  B {\bf 634}, 105 (2002)
  %[arXiv:hep-ph/0112303].
  %%CITATION = NUPHA,B634,105;%%
  
  \bibitem{Silvestrini:2007yf}
  L.~Silvestrini,
  %``Searching for new physics in $b \to s$ hadronic penguin decays,''
  Ann.\ Rev.\ Nucl.\ Part.\ Sci.\  {\bf 57}, 405 (2007)
  %[arXiv:0705.1624 [hep-ph]].
  %%CITATION = ARNUA,57,405;%%
  
  \bibitem{Ciuchini:2007cw}
  M.~Ciuchini, E.~Franco, D.~Guadagnoli, V.~Lubicz, M.~Pierini, V.~Porretti and L.~Silvestrini,
  %``$D$ - $\bar{D}$ mixing and new physics: General considerations and
  %constraints on the MSSM,''
  Phys.\ Lett.\  B {\bf 655}, 162 (2007)
  %[arXiv:hep-ph/0703204].
  %%CITATION = PHLTA,B655,162;%%
  
  \bibitem{Crivellin:2009ar}
  A.~Crivellin and U.~Nierste,
  %``Chirally enhanced corrections to FCNC processes in the generic MSSM,''
  arXiv:0908.4404 [hep-ph].
  %%CITATION = ARXIV:0908.4404;%%


\bibitem{hep-ph/9507294}
  J.~A.~Casas, A.~Lleyda and C.~Munoz,
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\end{thebibliography}