Effects of Quenching and Partial Quenching on Penguin Matrix Elements

In the calculation of non-leptonic weak decay rates, a "mismatch" arises when the QCD evolution of the relevant weak hamiltonian down to hadronic scales is performed in unquenched QCD, but the hadronic matrix elements are then computed in (partially) quenched lattice QCD. This mismatch arises because the transformation properties of penguin operators under chiral symmetry change in the transition from unquenched to (partially) quenched QCD. Here we discuss QCD-penguin contributions to $\Delta S=1$ matrix elements, and show that new low-energy constants contribute at leading order in chiral perturbation theory in this case. In the partially quenched case (in which sea quarks are present), these low-energy constants are related to electro-magnetic penguins, while in the quenched case (with no sea quarks) no such relation exists. As a simple example, we give explicit results for $K^+\to\pi^+$ and $K^0\to vacuum$ matrix elements, and discuss the implications for lattice determinations of $K\to\pi\pi$ amplitudes from these matrix elements.Comment: 10 pages, minor corrections, ref. added, to appear in JHE

The strong coupling regime of twelve flavors QCD

We summarize the results recently reported in Ref.[1] [A. Deuzeman, M.P. Lombardo, T. Nunes da Silva and E. Pallante,"The bulk transition of QCD with twelve flavors and the role of improvement"] for the SU(3) gauge theory with Nf=12 fundamental flavors, and we add some numerical evidence and theoretical discussion. In particular, we study the nature of the bulk transition that separates a chirally broken phase at strong coupling from a chirally restored phase at weak coupling. When a non-improved action is used, a rapid crossover is observed at small bare quark masses. Our results confirm a first order nature for this transition, in agreement with previous results we obtained using an improved action. As shown in Ref.[1], when improvement of the action is used, the transition is preceded by a second rapid crossover at weaker coupling and an exotic phase emerges, where chiral symmetry is not yet broken. This can be explained [1] by the non hermiticity of the improved lattice Transfer matrix, arising from the competition of nearest-neighbor and non-nearest neighbor interactions, the latter introduced by improvement and becoming increasingly relevant at strong coupling and coarse lattices. We further comment on how improvement may generally affect any lattice system at strong coupling, be it graphene or non abelian gauge theories inside or slightly below the conformal window.Comment: 7 pages, 7 figures, Proceedings of the 30th International Symposium on Lattice Field Theory, June 24 - 29, 2012, Cairns, Australi