$B\to \pi \ell \ell$ form factors for new-physics searches from lattice QCD

Abstract

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 $etal.$, Phys. Rev. D 92, 014024 (2015)], these parameterize the hadronic contribution to $B\to \pi$ semileptonic decays in any extension of the Standard Model. We obtain the total branching ratio $\text{BR}(B^{+}\to {\pi }^{+}{\mu }^{+}{\mu }^{-})=20.4(2.1)\times 10^{-9}$ 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 $etal.$, JHEP 1212, 125 (2012)]. Note added: after this paper was submitted for publication, LHCb announced a new measurement of the differential decay rate for this process [T. Tekampe, talk at DPF 2015], which we now compare to the shape and normalization of the Standard-Model prediction.

V3: Corrected errors in results for Standard-Model differential and total decay rates in abstract, Fig. 3, Table IV, and outlook. Added new preliminary LHCb data to Fig. 3 and brief discussion after outlook. Replaced outdated correlation matrix in Table III with correct final version. Other minor wording changes and references added. 7 pages, 4 tables, 3 figures

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