QCD-Enhancement of |ΔI| = ½ Transitions

Conference paper


The origin of the empirically observed enhancement of strangeness-changing non-leptonic weak amplitudes with isospin transfer |ΔI| = ½ is a long-standing question in particle physics, which has not yet been given a satisfactory explanation within the framework of the standard model. The short-distance analysis of the product of weak hadronic currents [1–6] results in an effective ΔS = 1 Hamiltonian which is a sum of local four-quark operators, constructed with the light (u,d,s) quark fields only, modulated by Wilson coefficients which are functions of the heavy (W,t,b,c) masses and an overall renormalization scale µ:
$$ \matrix{ {{H^{\Delta S = 1}}} \hfill & = \hfill & { - {{{}^GF} \over {\sqrt 2 }}{s_1}{c_1}{c_3}\{ {c_ + }(\mu ) {q_ + } + {c_ - }(\mu ) {q_ - } + {c_6}(\mu ){\rm{ }}{q_6} + \ldots \} } \hfill \cr {{Q_ \pm }} \hfill & = \hfill & {4\{ ({{\bar s}_L}{\gamma ^\mu }{u_L})({{\bar u}_L}{\gamma _\mu }{d_L}) \pm ({{\bar s}_L}{\gamma ^\mu }{d_L})({{\bar u}_L}{\gamma _\mu }{d_L})\} } \hfill \cr {{Q_6}} \hfill & = \hfill & { - {8_{q = {u^\Sigma },d,s}}({{\bar s}_L}{q_R})({{\bar q}_R}{d_L}).} \hfill \cr } $$
Here, GF is the Fermi coupling constant and si = sinθi and ci = cosθi are the conventional Cabibbo-Kobayashi-Maskawa factors.


Anomalous Dimension Renormalization Scale Perturbative Calculation Hadronic Matrix Element Anomalous Dimension Matrix 
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Copyright information

© Springer-Verlag Berlin Heidelberg 1989

Authors and Affiliations

  • A. Pich
    • 1
  1. 1.Theoretical Physics DivisionCERNGeneva 23Switzerland

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