Semileptonic $B\to D^{\ast \ast }$ decays in Lattice QCD : a feasibility study and first results

Abstract

We compute the decays $B\to D_0^{\ast }$ and $B\to D_2^{\ast }$ with finite masses for the $b$ and $c$ quarks. We first discuss the spectral properties of both the $B$ meson as a function of its momentum and of the $D_0^{\ast }$ and $D_2^{\ast }$ at rest. We compute the theoretical formulae leading to the decay amplitudes from the three-point and two-point correlators. We then compute the amplitudes at zero recoil of $B\to D_0^{\ast }$ which turns out not to be vanishing contrary to what happens in the heavy quark limit. This opens a possibility to get a better agreement with experiment. To improve the continuum limit we have added a set of data with smaller lattice spacing. The $B\to D_2^{\ast }$ vanishes at zero recoil and we show a convincing signal but only slightly more than 1 sigma from 0. In order to reach quantitatively significant results, we plan to fully exploit smaller lattice spacings as well as another lattice regularization.

31 pages with 15 figures ; sections 5 and 6 revised and updated

References in corpus (9)

• On the generalized eigenvalue method for energies and matrix elements in lattice field theory
• Twisted mass lattice QCD
• Observation of new resonances decaying to $D\pi$ and $D^{\ast }\pi$ in inclusive $e^{+}{e}^{-}$ collisions near $\sqrt{s}=$10.58 GeV
• Electromagnetic form factor of the pion from twisted-mass lattice QCD at Nf=2
• Lattice QCD with two light Wilson quarks and maximally twisted mass
• Proposal to study $B_s\to {\bar{D}}_{sJ}$ transitions
• Neutral meson oscillations in the Standard Model and beyond from Nf=2 Twisted Mass Lattice QCD
• Twisted mass lattice computation of charmed mesons with focus on $D^{\ast \ast }$
• In Memoriam Nikolai Uraltsev : Uraltsev's and other Sum Rules, Theory and Phenomenology of $D^{\ast \ast }$'s

Cited by in corpus (7)

• A review of the open charm and open bottom systems
• Masses of $D$ mesons, $D_s$ mesons and charmonium states from twisted mass lattice QCD
• Continuum limit of the $D$ meson, $D_s$ meson and charmonium spectrum from $N_f=2+1+1$ twisted mass lattice QCD
• Progress on semi-leptonic $B_{(s)}$ decays
• Quark Flavor Physics Review
• In Memoriam Nikolai Uraltsev : Uraltsev's and other Sum Rules, Theory and Phenomenology of $D^{\ast \ast }$'s
• $B\to D^{\ast \ast }$ -- puzzle 1/2 vs 3/2