Perturbative renormalization of weak Hamiltonian four-fermion operators with overlap fermions

Abstract

The renormalization of the most general dimension-six four-fermion operators without power subtractions is studied at one loop in lattice perturbation theory using overlap fermions. As expected, operators with different chirality do not mix among themselves and parity-conserving and parity-violating multiplets renormalize in the same way. The renormalization constants of unimproved and improved operators are also the same. These mixing factors are necessary to determine physical matrix elements relevant to many phenomenological applications of weak interactions. The most important are the K 0 −K 0 and B 0 −B 0 mixings in the Standard Model and beyond, the ∆I = 1/2 rule and ǫ ′ /ǫ.

Artifacts and⟨A2⟩power corrections: ReexaminingZψ(p2)Boucaud1, Soto2, Leroy3 et al. 2006Phys. Rev. D380190View full textAdd to dashboardCite

“…But in fact, already in lattice perturbation theory, the tendency is that the one-loop corrections to Z and Z V are large because of a very large tadpole contribution to the self-energy [37,38] (while g 1 remains close to 1 as we find nonpertubatively). The net effect is already large at 6:0, for the usual s 0:4: Z V 1:247, and still larger for our s 0: Z V 1:444; we use Table 1 of Ref.…”

“…The net effect is already large at 6:0, for the usual s 0:4: Z V 1:247, and still larger for our s 0: Z V 1:444; we use Table 1 of Ref. [37] for the analytical expressions (the definition of Z is different, but by a negligible amount); the numbers are quoted assuming a boosted perturbation theory (BPT) boosted coupling with g 2 BPT 1:68 (see Ref. [38] under Eq.…”

Perturbative renormalization for overlap fermions

“…The parity-conserving part of C m ± is then quadratically divergent 2 . The Z ± factors in (5) are simple linear combinations of Z S , Z V and Z ψ [8]. The C m ± coefficients are not needed for the physical K → ππ matrix elements; if K → π amplitudes are used, they can be determined by a 2-loop calculation or non-perturbatively using K → 0 matrix elements.…”

“…The Z's for ρ = 1.9 are indeed smaller than for ρ = 1.0, and closer to the Wilson results (see Table 1). The renormalization of the four-fermion operators of the ∆F = 2 and ∆S = 1 effective weak Hamiltonians has been studied together with L. Giusti [8]. They describe physics like the K 0 -K 0 and B 0 -B 0 mixings, the ∆I = 1/2 rule (octet enhancement) and the CP violation parameter ǫ ′ /ǫ.…”

Light hadron weak matrix elements

“…The renormalization of quark bilinears and fourquark operators, for domain-wall fermions, has been performed non-perturbatively in the RI scheme [22]. The same renormalization, for operators which have no power-divergences, has been performed at one loop for Neuberger fermions [23,24].…”