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SUMMARY:Large N_c QCD and Weak Matrix Elements
DTSTART;VALUE=DATE-TIME:19990310T153000Z
DTEND;VALUE=DATE-TIME:19990310T163000Z
DTSTAMP;VALUE=DATE-TIME:20260703T041734Z
UID:indico-event-1116@indico.ific.uv.es
DESCRIPTION:The first part of my talk will be an overview of the progress 
 made and the problems which remain in deriving an effective Lagrangian whi
 ch describes the non--leptonic weak interactions of the Nambu--Goldstone d
 egrees 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 curr
 ents\, while those of the strong sector (QCD only) are more simply related
  to the coefficients of the Taylor expansions of QCD Green's functions. Th
 e study of these issues within the framework of the $1/N_c$ expansion\, an
 d in the {\\it lowest meson dominance} approximation described in ref.~\\c
 ite{PPdeR98}\, seems a very promising path.\nThe second part of my talk wi
 ll be dedicated to a review of the properties of the $\\Pi_{LR}(Q^2)$ corr
 elation function in the large--$N_c$ limit as recently discussed in ref.~\
 \cite{KdeR97}. This is the correlation function which governs the {\\it el
 ectroweak} $\\pi^{+}-\\pi^{0}$ mass difference. Following the discussion o
 f ref.~\\cite{KPdeR98}\, I shall show how the calculation of this observab
 le\, which requires non--trivial contributions from next--to--leading term
 s in the $1/N_c$ expansion\, provides an excellent theoretical laboratory 
 for studying issues of long-- and short-- distance matching in calculation
 s of weak matrix elements of four--quark operators.\nThe third part of my 
 talk will be dedicated to recent work reported in ref~\\cite{KPdeR98d}\, w
 here it is shown that the $K\\rightarrow\\pi\\pi$ matrix elements of the f
 our--quark operator $Q_7$\, generated by the electroweak penguin--like dia
 grams of the Standard Model\, can be calculated to first non--trivial orde
 r in the chiral expansion and in the $1/N_c$ expansion. I shall compare th
 e results to recent numerical evaluations from lattice--QCD.\n\\begin{theb
 ibliography}{12}\n\\bibitem{PPdeR98} S.~Peris\, M.~Perrottet and E.~de Raf
 ael\, JHEP {\\bf 05} (1998) 011. \\bibitem{KdeR97} M.~Knecht and E.~de Raf
 ael\, Phys. Lett. {\\bf B424} (1998) 335. \\bibitem{KPdeR98} M.~Knecht\, S
 .~Peris and E.~de Rafael\, Phys. Lett.{\\bf B443} (1998) 255. \\bibitem{KP
 deR98d} M.~Knecht\, S.~Peris and E.~de Rafael\, hep-ph/9812471.\n\\end{the
 bibliography}\n\nhttps://indico.ific.uv.es/event/1116/
LOCATION:Dpto. de Fisica Teorica (UVEG) Sala Seminarios
URL:https://indico.ific.uv.es/event/1116/
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