Effects of Quenching and Partial Quenching on Penguin Matrix Elements.pdfVIP

Effects of Quenching and Partial Quenching on Penguin Matrix Elements Maarten Golterman1 ∗ Department of Physics, Washington University, St. Louis, MO 63130, USA 1 0 Elisabetta Pallante2 0 2 SISSA, Via Beirut 2–4, I-34013 Trieste, Italy t c O 0 3 Abstract 2 v In the calculation of non-leptonic weak decay rates, a “mismatch” arises when 0 1 the QCD evolution of the relevant weak hamiltonian down to hadronic scales is per- 0 formed in unquenched QCD, but the hadronic matrix elements are then computed 8 in (partially) quenched lattice QCD. This mismatch arises because the transforma- 0 tion properties of penguin operators under chiral symmetry change in the transition 1 from unquenched to (partially) quenched QCD. Here we discuss QCD-penguin con- 0 tributions to ∆S = 1 matrix elements, and show that new low-energy constants / t contribute at leading order in chiral perturbation theory in this case. In the partially a l- quenched case (in which sea quarks are present), these low-energy constants are re- p lated to electro-magnetic penguins, while in the quenched case (with no sea quarks) e no such relation exists. As a simple example, we give explicit results for K+ → π+ h and K0 → vacuum matrix elements, and discuss the implications for lattice deter- : v minations of K → ππ amplitudes from these matrix elements. i X r a ∗ address after Sept. 1: Dept. of Physics, San Francisco State University, San Francisco, CA 94132,