<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"> <mml:mrow> <mml:mi>B</mml:mi> <mml:mo stretchy="false">→</mml:mo> <mml:mi>ρ</mml:mi> <mml:mo>ℓ</mml:mo> <mml:mover accent="true"> <mml:mrow> <mml:mi>ν</mml:mi> </mml:mrow> <mml:mrow> <mml:mo stretchy="false">¯</mml:mo> </mml:mrow> </mml:mover> </mml:mrow> </mml:math> Resonance Form Factors from <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"> <mml:mrow> <mml:mi>B</mml:mi> <mml:mo stretchy="false">→</mml:mo> <mml:mi>π</mml:mi> <mml:mi>π</mml:mi> <mml:mo>ℓ</mml:mo> <mml:mover accent="true"> <mml:mrow> <mml:mi>ν</mml:mi> </mml:mrow> <mml:mrow> <mml:mo stretchy="false">¯</mml:mo> </mml:mrow> </mml:mover> </mml:mrow> </mml:math> in Lattice QCD
Luka Leskovec, Stefan Meinel, Marcus Petschlies, John Negele, Srijit Paul, Andrew Pochinsky
Abstract
The decay B→ρℓν[over ¯] is an attractive process for determining the magnitude of the smallest Cabibbo-Kobayashi-Maskawa 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→ρ form factors V, A_{0}, A_{1}, and A_{12}. The unstable nature of the ρ resonance has prevented precise lattice QCD calculations of these form factors to date. Here, we present the first lattice QCD calculation of the B→ρ form factors in which the ρ is treated properly as a resonance in P-wave ππ scattering. To this end, we use the Lellouch-Lüscher finite-volume formalism to compute the B→ππ form factors as a function of both momentum transfer and ππ invariant mass, and then analytically continue to the ρ 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.