$B\to \pi ll$ Form Factors for New Physics Searches from Lattice QCD

The rare decay $B\to \pi {\ell }^{+}{\ell }^{-}$ arises from $b\to d$ flavor-changing neutral currents and could be sensitive to physics beyond the standard model. Here, we present the first ab initio QCD calculation of the $B\to \pi$ tensor form factor $f_T$. Together with the vector and scalar form factors $f_{+}$ and $f_0$ from our companion work [J. A. Bailey et al., Phys. Rev. D 92, 014024 (2015)], these parametrize the hadronic contribution to $B\to \pi$ semileptonic decays in any extension of the standard model. We obtain the total branching ratio $\mathrm{BR}(B^{+}\to {\pi }^{+}{\mu }^{+}{\mu }^{-})=20.4(2.1)\times {10}^{-9}$ in the standard model, which is the most precise theoretical determination to date, and agrees with the recent measurement from the LHCb experiment [R. Aaij et al., J. High Energy Phys. 12 (2012) 125].

Figure 1

Error budget for $f_T$ as a function of $q^2$ for the range of simulated lattice momenta. The filled bands show the relative size of each error contribution to the total. The quadrature sum is shown on the left $y$ axis and the error itself, in percent, on the right.

Figure 2

Ab initio result for $f_T(q^2)$ from lattice QCD.

Figure 3

Partial branching fractions for $B^{+}\to {\pi }^{+}{\mu }^{+}{\mu }^{-}$ (upper panel) and $B^{+}\to {\pi }^{+}{\tau }^{+}{\tau }^{-}$ (lower panel) outside the resonance regions. Different patterns (colors) show the contributions from the main sources of uncertainty; those from the remaining sources are too small to be visible. For $B^{+}\to {\pi }^{+}{\mu }^{+}{\mu }^{-}$, new measurements from LHCb [73], which were announced after our Letter appeared, are overlaid.