$B\to \rho \ell \bar{\nu }$ resonance form factors from $B\to \pi \pi \ell \bar{\nu }$ in lattice QCD

Abstract

The decay $B\to \rho \ell \bar{\nu }$ is an attractive process for determining the magnitude of the smallest CKM matrix element, $|V_{ub}|$, and can provide new insights into the origin of the long-standing exclusive-inclusive discrepancy in determinations of this Standard-Model parameter. This requires a nonperturbative QCD calculation of the $B\to \rho$ form factors $V$, $A_0$, $A_1$, and $A_{12}$. The unstable nature of the $\rho$ resonance has prevented precise lattice QCD calculations of these form factors to date. Here, we present the first lattice QCD calculation of the $B\to \rho$ form factors in which the $\rho$ is treated properly as a resonance in $P$-wave $\pi \pi$ scattering. To this end, we use the Lellouch-Lüscher finite-volume formalism to compute the $B\to \pi \pi$ form factors as a function of both momentum transfer and $\pi \pi$ invariant mass, and then analytically continue to the $\rho$ resonance pole. This calculation is performed with $2+1$ dynamical quark flavors at a pion mass of approximately 320 MeV, and demonstrates a clear path toward results at the physical point.

8 pages, 2 figures, ancillary files, updated to published version

References in corpus (21)

• Averages of $b$-hadron, $c$-hadron, and $\tau$-lepton properties as of 2021
• Form Factors from Light-Cone Sum Rules with B-Meson Distribution Amplitudes
• Bayesian model averaging for analysis of lattice field theory results
• Study of B --> pi l nu and B --> rho l nu Decays and Determination of |V_ub|
• $B\to \pi \ell \nu$ and $B_s\to K\ell \nu$ form factors and $|V_{ub}|$ from 2+1-flavor lattice QCD with domain-wall light quarks and relativistic heavy quarks
• Multichannel one-to-two transition amplitudes in a finite volume
• Branching fraction and form-factor shape measurements of exclusive charmless semileptonic B decays, and determination of |V_{ub}|
• Relativistic Heavy Quark Effective Action
• Bottomonium spectrum at order v^6 from domain-wall lattice QCD: precise results for hyperfine splittings
• Challenges in Semileptonic B Decays
• Non-perturbatively Determined Relativistic Heavy Quark Action
• Form factors of $B\to \pi \ell \nu$ and a determination of $|V_{ub}|$ with Möbius domain-wall-fermions
• New ways to search for right-handed current in B -> rho ell nu decay
• Timelike-helicity $B\to \pi \pi$ form factor from light-cone sum rules with dipion distribution amplitudes
• QCD Factorization for $B\to \pi \pi \ell \nu$ Decays at Large Dipion Masses
• Constraining $1+\mathcal{J}\to 2$ coupled-channel amplitudes in finite-volume
• $B\to \rho l\bar{\nu }$ and $\omega l\bar{\nu }$ in and beyond the Standard Model: Improved predictions and $|V_{ub}|$
• Measurement of the Branching Fraction of the Decay ${\mathbf{B}}^{+}\to {\mathbf{\pi }}^{+}{\mathbf{\pi }}^{-}{\mathbf{\ell }}^{+}{\mathbf{\nu }}_{\mathbf{\ell }}$ in Fully Reconstructed Events at Belle
• Toward a complete description of $b\to u{\ell }^{-}\bar{\nu }$ decays within the Weak Effective Theory
• Finite-volume matrix elements in multi-boson states
• Role of $\rho -\omega$ interference in semileptonic $B\to {\pi }^{+}{\pi }^{-}\ell {\bar{\nu }}_{\ell }$ decays

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