[SEMINARI]: Prof. De Rafael: Large N_c QCD and Weak Matrix Elements

[Arcadi Santamaria]

------------ próxima parte ------------
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                              S E M I N A R I

            [Image]    Departament de Física Teòrica     [Image]
                          Universitat de València
                      46100 Burjassot (València) Spain

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                      Large N_c QCD and Weak Matrix Elements

                              Eduardo de Rafael

                               (CPT Marseille)

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                     Aula de Seminaris de Física Teòrica
                 Wednesday 10 of March of 1999 at 04:00 PM
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                                    Resum

 The first part of my talk will be an overview of the progress made and the
  problems which remain in deriving an effective Lagrangian which describes
   the non--leptonic weak interactions of the Nambu--Goldstone degrees of
     freedom ($K$, $\pi$ and $\eta$) of the spontaneous $SU(3)_{L}\times
   SU(3)_{R}$ symmetry breaking in the Standard Model. I shall show, with
   examples, how the coupling constants of the $\vert\Delta S\vert=1$ and
  $\vert\Delta S\vert=2$ effective low energy Lagrangian are given by {\it
 integrals} of Green's functions of QCD currents and density currents, while
    those of the strong sector (QCD only) are more simply related to the
coefficients of the Taylor expansions of QCD Green's functions. The study of
 these issues within the framework of the $1/N_c$ expansion, and in the {\it
   lowest meson dominance} approximation described in ref.~\cite{PPdeR98},
seems a very promising path. The second part of my talk will be dedicated to
  a review of the properties of the $\Pi_{LR}(Q^2)$ correlation function in
 the large--$N_c$ limit as recently discussed in ref.~\cite{KdeR97}. This is
        the correlation function which governs the {\it electroweak}
       $\pi^{+}-\pi^{0}$ mass difference. Following the discussion of
  ref.~\cite{KPdeR98}, I shall show how the calculation of this observable,
  which requires non--trivial contributions from next--to--leading terms in
   the $1/N_c$ expansion, provides an excellent theoretical laboratory for
 studying issues of long-- and short-- distance matching in calculations of
  weak matrix elements of four--quark operators. The third part of my talk
 will be dedicated to recent work reported in ref~\cite{KPdeR98d}, where it
  is shown that the $K\rightarrow\pi\pi$ matrix elements of the four--quark
 operator $Q_7$, generated by the electroweak penguin--like diagrams of the
 Standard Model, can be calculated to first non--trivial order in the chiral
   expansion and in the $1/N_c$ expansion. I shall compare the results to
 recent numerical evaluations from lattice--QCD. \begin{thebibliography}{12}
  \bibitem{PPdeR98} S.~Peris, M.~Perrottet and E.~de Rafael, JHEP {\bf 05}
  (1998) 011. \bibitem{KdeR97} M.~Knecht and E.~de Rafael, Phys. Lett. {\bf
  B424} (1998) 335. \bibitem{KPdeR98} M.~Knecht, S.~Peris and E.~de Rafael,
Phys. Lett.{\bf B443} (1998) 255. \bibitem{KPdeR98d} M.~Knecht, S.~Peris and
            E.~de Rafael, hep-ph/9812471. \end{thebibliography}

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