Lattice extraction of K → ππ amplitudes to next-to-leading order in partially quenched and in full chiral perturbation theory

Jack Laiho, Amarjit Soni

Research output: Contribution to journalArticle

20 Scopus citations

Abstract

We show that it is possible to construct ε1/ε to next-to-leading order (NLO) using partially quenched chiral perturbation theory (PQChPT) from amplitudes that are computable on the lattice. We demonstrate that none of the needed amplitudes require 3-momentum on the lattice for either the full theory or the partially quenched theory; nondegenerate quark masses suffice. Furthermore, we find that the electro-weak penguin (ΔI = 3/2 and 1/2) contributions to ε1/ε in PQChPT can be determined to NLO using only degenerate (mK = mπ) K → π computations without momentum insertion. Issues pertaining to power divergent contributions, originating from mixing with lower dimensional operators, are addressed. Direct calculations of K → ππ at unphysical kinematics are plagued with enhanced finite volume effects in the (partially) quenched theory, but in simulations when the sea quark mass is equal to the up and down quark mass the enhanced finite volume effects vanish to NLO in PQChPT. In embedding the QCD penguin left-right operator onto PQChPT an ambiguity arises, as first emphasized by Golterman and Pallante. With one version [the "PQS" (patially quenched singlet)] of the QCD penguin, the inputs needed from the lattice for constructing K → ππ at NLO in PQChPT coincide with those needed for the full theory. Explicit expressions for the finite logarithms emerging from our NLO analysis to the above amplitudes also are given.

Original languageEnglish (US)
Article number014021
Pages (from-to)014021-1-014021-28
JournalPhysical Review D - Particles, Fields, Gravitation and Cosmology
Volume71
Issue number1
DOIs
StatePublished - Jan 2005
Externally publishedYes

ASJC Scopus subject areas

  • Nuclear and High Energy Physics
  • Physics and Astronomy (miscellaneous)

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