Abstract
The exclusive semileptonic decay $B \rightarrow \pi \ell \nu$ is a key process for the determination of the Cabibbo-Kobayashi-Maskawa matrix element $V_{ub}$ from the comparison of experimental rates as a function of $q^2$ with theoretically determined form factors. The sensitivity of the form factors to the $u/d$ quark mass has meant significant systematic uncertainties in lattice QCD calculations at unphysically heavy pion masses. Here we give the first lattice QCD calculations of this process for u/d quark masses going down to their physical values, calculating the $f_0$ form factor at zero recoil to 3\%. We are able to resolve a long-standing controversy by showing that the soft-pion theorem result $f_0(q^2_{max}) = f_B/f_{\pi}$ does hold as $m_{\pi} \rightarrow 0$. We use the Highly Improved Staggered Quark formalism for the light quarks and show that staggered chiral perturbation theory for the $m_{\pi}$ dependence is almost identical to continuum chiral perturbation theory for $f_0$, $f_B$ and $f_{\pi}$. We also give results for other processes such as $B_s \rightarrow K \ell \nu$.
Highlights
The exclusive semileptonic process B → πlν is a key one for flavor physics because it gives access to the Cabibbo-Kobayashi-Maskawa matrix element Vub from a process involving two “gold-plated” mesons, B and π
The exclusive semileptonic decay B → πlν is a key process for the determination of the CabibboKobayashi-Maskawa matrix element Vub from the comparison of experimental rates as a function of q2 with theoretically determined form factors
In this paper we have laid to rest a long-standing controversy over the relationship between the form factor f0 at zero recoil in B → π decay and the ratio fB=fπ from lattice QCD results
Summary
The exclusive semileptonic process B → πlν is a key one for flavor physics because it gives access to the Cabibbo-Kobayashi-Maskawa matrix element Vub from a process involving two “gold-plated” (stable in QCD) mesons, B and π. Vub is determined by comparing the experimental rate for the process to that determined from theoretical calculations of hadronic parameters known as form factors which are functions of the squared 4-momentum transfer, q2, between the B and the π. If the calculations of the form factors are done in lattice QCD, the full effect of QCD interactions that keep the quarks bound inside the mesons is taken into account. Lattice QCD calculations for this process are difficult, because the results are sensitive to the mass of the u=d quarks that form the π meson. Existing lattice QCD calculations have used u=d quarks that have heavier masses than in the real world, and results have to be extrapolated to the physical point. The value of the u=d quark masses, and the π mass, affects the q2 value for a given π spatial momentum and, since the form factors are strongly varying functions of q2, this gives
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