Chiral corrections and lattice QCD results for f/f and Δm/Δm

Abstract

It has been argued recently that the inclusion of the chiral logarithms in extrapolation of the lattice data can shift the value of the hadronic parameter ξ = f Bs B Bs /f B d B B d , from 1.16(6) to 1.32(10) and even higher. If true, that would considerably change the theoretical estimate for the ratio of oscillation frequencies in the B 0 s -and B 0 d -systems, and would affect the standard CKM unitarity triangle analysis. In this letter we show that f Bs /f B d ≈ f K /f π , and thus the uncertainty due to the missing chiral logs is smaller than previously thought. By combining the NLO chiral expansion with the static heavy quark limit we obtain ξ = 1.22(8). Uncertainty in ∆mThe K 0 −K 0 and B 0 −B 0 mixing amplitudes are the main ingredients in the standard unitarity triangle analysis [1]. They overconstrain the apex of the CKM triangle in the (ρ,η)-plane. Confronting such an overconstrained triangle with the directly measured sin(2β) [2] allows for the consistency check from which we hope to either see the effects of the non-Standard Model physics, or simply to confirm the validity of Standard Model at the accessible accuracy [3]. One of the essential constraints is provided by the ratio of oscillation frequencies ∆m

Status of lattice calculations of B-meson decays and mixing

“…In ref. [13] it was argued that the chiral logarithms in / and /f π are nearly of the same size, so that one would expect / ≈ /f π = 1.22, which is compatible with [11], but closer to previous global estimates. The key question for any future determination is whether or not the quark masses used in the simulation are light enough so that ChPT at NLO gives a good description.…”

“…In order to make contact with the chiral regime, one currently relies on extrapolations in the light quark mass, using Chiral Perturbation Theory (ChPT) as a guide. It has only been realised relatively recently that this can introduce large uncertainties, since chiral logarithms are not necessarily under control [11][12][13].…”

An exploratory lattice study of ΔI=3/2 K→ππ decays at next-to-leading order in the chiral expansi

“…for good fits. more general context, it has been argued that one may combine the behaviour expected in chiral perturbation theory at low masses with the observed polynomial dependence on the kinematical parameters in lattice simulations [63,64]. We now attempt to perform such a matching.…”

Non-factorizable effects in $B - \overline{B}$ mixing

“…The decay constants f B d and f Bs were also given in [7], but are listed also here for com- The values for the f B 's and especially for the ratio f Bs /f B d (and ξ) in (75) are a bit low [3,33]. There might be at least three reasons for this.…”