Rare B decays using lattice QCD form factors

In this write-up we review and update our recent lattice QCD calculation of $B \to K^*$, $B_s \to \phi$, and $B_s \to K^*$ form factors [arXiv:1310.3722]. These unquenched calculations, performed in the low-recoil kinematic regime, provide a significant improvement over the use of extrapolated light cone sum rule results. The fits presented here include further kinematic constraints and estimates of additional correlations between the different form factor shape parameters. We use these form factors along with Standard Model determinations of Wilson coefficients to give Standard Model predictions for several observables [arXiv:1310.3887]. The modest improvements to the form factor fits lead to improved determinations of $F_L$, the fraction of longitudinally polarized vector mesons, but have little effect on most other observables

The Hindered M1 Radiative Decay Υ(2S) → ηb(1S)γ from Lattice NRQCD

We present a calculation of the hindered M$1$ $\Upsilon(2S) \to \eta_b(1S) \gamma$ decay rate using lattice non-relativistic QCD. The calculation includes spin-dependent relativistic corrections to the NRQCD action through $\mathcal{O}(v^6)$ in the quark's relative velocity, relativistic corrections to the leading order current which mediates the transition through the quark's magnetic moment, radiative corrections to the leading spin-magnetic coupling and for the first time a full error budget. We also use gluon field ensembles at multiple lattice spacing values, all of which include $u$, $d$, $s$ and $c$ quark vacuum polarisation. Our result for the branching fraction is $\mathcal{B}(\Upsilon(2S)\to\eta_b(1S)\gamma) = 5.4(1.8)\times 10^{-4}$, which agrees with the current experimental value.This is the author accepted manuscript. The final version is available from APS via http://dx.doi.org/10.1103/PhysRevD.92.09450

Improving the kinetic couplings in lattice nonrelativistic QCD

We improve the non-relativistic QCD (NRQCD) action by comparing the dispersion relation to that of the continuum through $\mathcal{O}(p^6)$ in perturbation theory. The one-loop matching coefficients of the $\mathcal{O}(p^4)$ kinetic operators are determined, as well as the scale at which to evaluate $\alpha_s$ in the $V$-scheme for each quantity. We utilise automated lattice perturbation theory using twisted boundary conditions as an infrared regulator. The one-loop radiative corrections to the mass renormalisation, zero-point energy and overall energy-shift of an NRQCD $b$-quark are also found. We also explore how a Fat$3$-smeared NRQCD action and changes of the stability parameter $n$ affect the coefficients. Finally, we use gluon field ensembles at multiple lattice spacing values, all of which include $u$, $d$, $s$ and $c$ quark vacuum polarisation, to test how the improvements affect the non-perturbatively determined $\Upsilon(1S)$ and $\eta_b(1S)$ kinetic masses, and the tuning of the $b$ quark mass

B, Bs, K and pi weak matrix elements with physical light quarks

Calculations of pseudoscalar decay constants of B, Bs, K and pi mesons with physical light quarks are presented. We use HISQ ensembles that include u,d,s and c sea quarks at three lattice spacings. HISQ is used for the valence light quarks and a radiatively improved NRQCD action for the heavy quarks. The key results are f_{B^+}=0.184(4)$ GeV, f_{B_s}=0.224(4) GeV, f_{B_s}/f_{B^+}=1.217(8), f_{K^+}/f_{pi^+}=1.1916(21), f_{K^+}=155.37(34) MeV, giving a significant improvement over previous results that required chiral extrapolation. We also calculate the Wilson flow scale w_0, finding w_0=0.1715(9) fm

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

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 $B_s$ and $B_d$ mesons we find: $\hat{B}_{B_s}=1.232(53)$, $\hat{B}_{B_d}=1.222(61)$. Combining our results with lattice QCD calculations of the decay constants using HISQ quarks from the Fermilab/MILC collaboration and with experimental values for $B_s$ and $B_d$ oscillation frequencies allows determination of the CKM elements $V_{ts}$ and $V_{td}$. We find $V_{ts} = 0.04189(93)$, $V_{td} = 0.00867(23)$ and $V_{ts}/V_{td} = 0.2071(27)$. Our results agree well (within $2\sigma$) with values determined from CKM unitarity constraints based on tree-level processes (only). Using a ratio to $\Delta M$ in which CKM elements cancel in the Standard Model, we determine the branching fractions ${\text{Br}}(B_s\rightarrow \mu^+\mu^-) = 3.81(18) \times 10^{-9}$ and ${\text{Br}}(B_d\rightarrow \mu^+\mu^-) = 1.031(54) \times 10^{-10}$. We also give results for matrix elements of the operators $R_0$, $R_1$ and $\tilde{R}_1$ that contribute to neutral $B$-meson width differences.This work was funded by STFC, the Royal Society, the Wolfson Foundation and the US DOE and National Science Foundation

Surgery versus Watchful Waiting in Patients with Craniofacial Fibrous Dysplasia – a Meta-Analysis

Fibrous dysplasia (FD) is a benign bone tumor which most commonly involves the craniofacial skeleton. The most devastating consequence of craniofacial FD (CFD) is loss of vision due to optic nerve compression (ONC). Radiological evidence of ONC is common, however the management of this condition is not well established. Our objective was to compare the long-term outcome of patients with optic nerve compression (ONC) due to craniofacial fibrous dysplasia (CFD) who either underwent surgery or were managed expectantly.We performed a meta-analysis of 27 studies along with analysis of the records of a cohort of patients enrolled in National Institutes of Health (NIH) protocol 98-D-0145, entitled Screening and Natural History of Fibrous Dysplasia, with a diagnosis of CFD. The study group consisted of 241 patients; 122 were enrolled in the NIH study and 119 were extracted from cases published in the literature. The median follow-up period was 54 months (range, 6-228 months). A total of 368 optic nerves were investigated. All clinically impaired optic nerves (n = 86, 23.3%) underwent therapeutic decompression. Of the 282 clinically intact nerves, 41 (15%) were surgically decompressed and 241 (85%) were followed expectantly. Improvement in visual function was reported in fifty-eight (67.4%) of the clinically impaired nerves after surgery. In the intact nerves group, long-term stable vision was achieved in 31/45 (75.6%) of the operated nerves, compared to 229/241 (95.1%) of the non-operated ones (p = 0.0003). Surgery in asymptomatic patients was associated with visual deterioration (RR 4.89; 95% CI 2.26-10.59).Most patients with CFD will remain asymptomatic during long-term follow-up. Expectant management is recommended in asymptomatic patients even in the presence of radiological evidence of ONC

B →Vℓ+ℓ− in the Standard Model from light-cone sum rules

We present $B_q\to\rho$, $B_q\to\omega$, $B_q\to K^*$, $B_s\to K^*$ and $B_s\to \phi$ form factors from light-cone sum rules (LCSR) at $\mathcal{O}(\alpha_s)$ for twist-2 and 3 and $\mathcal{O}(\alpha_s^0)$ for twist-4 with updated hadronic input parameters. Three asymptotic light-cone distribution amplitudes of twist-$4$ (and $5$) are determined, necessary for the form factors to obey the equations of motion. It is argued that the latter constrain the uncertainty of tensor-to-vector form factor ratios thereby improving the prediction of zeros of helicity amplitudes of major importance for $B\to K^*\ell\ell$ angular observables. We provide easy-to-use fits to the LCSR results, including the full error correlation matrix, in all modes at low $q^2$ as well as combined fits to LCSR and lattice results covering the entire kinematic range for $B_q\to K^*$, $B_s\to K^*$ and $B_s\to \phi$. The error correlation matrix avoids the problem of overestimating the uncertainty in phenomenological applications. Using the new form factors and recent computations of non-factorisable contributions we provide Standard Model predictions for $B\to K^*\gamma$ as well as $B\to K^*\ell^+\ell^-$ and $B_s\to\phi\mu^+\mu^-$ at low dilepton invariant mass. Employing our $B \to (\rho,\omega)$ form factor results we extract the CKM element $|V_\mathrm{ub}|$ from the semileptonic decays $B\to(\rho,\omega) \ell\nu$ and find good agreement with other exclusive determinations.Comment: 64 pages, 7 figures, 15 tables. v3: Minor clarifications, numerics unchanged. Matches version published in JHE