Neutral B -meson mixing from full lattice QCD at the physical point

Abstract

We calculate the bag parameters for neutral B-meson mixing in and beyond the Standard Model, in full four-flavour lattice QCD for the first time. We work on gluon field configurations that include the effect of u, d, s and c sea quarks with the Highly Improved Staggered Quark (HISQ) action at three values of the lattice spacing and with three u/d quark masses going down to the physical value. The valence b quarks use the improved NRQCD action and the valence light quarks, the HISQ action. Our analysis was blinded. Our results for the bag parameters for all five operators are the most accurate to date. For the Standard Model operator between Bs and B d mesons we find: BB s = 1.232(53),BB d = 1.222(61). Combining our results with lattice QCD calculations of the decay constants using HISQ quarks from the Fermilab/MILC collaboration and with experimental values for Bs and B d oscillation frequencies allows determination of the CKM elements Vts and V td . We find Vts = 0.04189(93), V td = 0.00867(23) and Vts/V td = 0.2071(27). Our results agree well (within 2σ) with values determined from CKM unitarity constraints based on tree-level processes (only). Using a ratio to ∆M in which CKM elements cancel in the Standard Model, we determine the branching fractions Br(Bs → µ + µ − ) = 3.81(18) × 10 −9 and Br(B d → µ + µ − ) = 1.031(54) × 10 −10 . We also give results for matrix elements of the operators R0, R1 andR1 that contribute to neutral B-meson width differences.

∆Ms theory precision confronts flavour anomalies

“…Different determinations [12,13,21,[24][25][26]31] of the ratio ξ are compared in Fig. 4 and we observe good agreement.…”

“…The full basis of matrix elements has been determined with lattice simulations [12,25,31] and sum rules [23,24]. In [12] the combinations f 2 B s B i were determined and combined with the 2016 PDG average for the decay constants to extract the Bag parameters.…”

“…The relative uncertainties for f 2 B s B 1 are estimated as 3% [27] and 1.3% [37]. Given that the two latest lattice results [12,25] do not overlap within their uncertainties and differ by 15% we believe the latter estimate to be overly optimistic and assume the scenario of [27]. On the other hand the uncertainties in sum rule analyses are dominated by the one from the matching between QCD and Heavy Quark Effective Theory (HQET) matrix elements which can be reduced significantly by a perturbative two-loop matching calculation [21,22] or eliminated altogether by using QCD [38,39] instead of HQET sum rules.…”

“…We note that the CKM parameters are taken from the standard fit of the CKMfitter collaboration [75,89] which includes ∆M s and ∆M d as constraints. The FNAL/MILC [12] and HPQCD [25] collaborations instead use the result of CKMfitter's tree fit tree fit: V cb = (42.41 +0.40 −1.51 ) × 10−3 , (A.1) which uses only tree-level observables and is therefore independent of the mass differences. However, also a number of other observables are discarded in this approach.…”

Opportunities for Lattice QCD in quark and lepton flavor physics

“…4 (right)] typically also contributes to B (s) meson mixing, which could provide strong constraints [77]. The constraints are, however, currently limited by the theoretical errors on the hadronic mixing parameters, which are calculated in lattice QCD with uncertainties that are still an order of magnitude larger than experiment [78,79], leaving much room for improvement. On the other hand, as is well known, the ratio of the mass differences benefits from error cancellations that result in a significantly smaller theoretical uncertainty, and this ratio is therefore one of the strongest constraints on the CKM unitarity triangle analysis.…”