[Paper Review] Lattice computation of $B o D^*,\;D^{**}\ell u$ form factors at finite heavy masses

Mariam Atoui|arXiv (Cornell University)|May 2, 2013

Quantum Chromodynamics and Particle Interactions1 references7 citations

TL;DR

This lattice QCD study computes form factors for B → D∗∗ℓν semileptonic decays using realistic, finite-mass charm quarks for the first time, employing three-point correlation functions and twisted-mass fermions on two ensembles (β = 3.90, 4.05). Key results show non-zero axial current matrix elements at zero recoil for the 3P0 state and a branching fraction estimate of (7.4 ± 4.9) × 10⁻³ for B → D(2+) → D∗π at mB ≈ 2.9 GeV, indicating finite charm mass effects may resolve the 1/2 vs. 3/2 puzzle.

ABSTRACT

We propose a strategy to compute form factors entering the semileptonic decay channel of $B$ mesons into orbitally excited (P wave) $D^{**}$ charmed mesons on the lattice using, for the first time, realistic charm quarks having a finite mass. We present preliminary results about the extracted transition amplitudes and form factors at different recoils and at three different $b$ quark masses.

Motivation & Objective

• To compute semileptonic B → D∗∗ℓν form factors using realistic, finite-mass charm quarks, avoiding the infinite heavy quark mass approximation.
• To address the persistent 1/2 vs. 3/2 puzzle in B → D∗∗ℓν decays by including finite-mass effects in lattice QCD.
• To extract transition amplitudes and form factors for scalar (3P0) and tensor (3P2) D∗∗ states at different recoil energies and b-quark masses.
• To compare results with the infinite mass limit and assess the impact of finite charm mass on branching ratios and matrix elements.

Proposed method

• Use of three-point correlation functions to extract matrix elements of vector and axial currents between B and D∗∗ states.
• Employment of twisted-mass fermions with maximal twist to simulate light, charm, and heavy quarks on two Lattice QCD ensembles (β = 3.90, 4.05).
• Application of ratio method (R(t)) to isolate form factors by combining two- and three-point functions and removing exponential time dependence.
• Extraction of form factors ˜u₊, ˜u₋ for the 3P0 state and ˜k, ˜b₊, ˜b₋ for the 3P2 state via fitting effective mass plateaus.
• Extrapolation of F₀(1) to physical b-quark mass using data from three b-quark masses at each β, with renormalization via ZA from [9].
• Comparison of finite-mass results with infinite-mass limit predictions using known relations from heavy quark effective theory (HQET).

Experimental results

Research questions

• RQ1 How do finite charm quark masses affect the axial current matrix element ⟨D∗∗|A₀|B⟩ at zero recoil, particularly for the 3P0 state?
• RQ2 What is the magnitude of the form factor ˜k for the 3P2 state in the finite-mass regime, and how does it compare to the infinite-mass limit?
• RQ3 To what extent do finite-mass effects alter the predicted branching ratios for B → D(2+) → D∗π compared to the infinite mass limit?
• RQ4 Can lattice QCD with realistic charm quarks resolve the 1/2 vs. 3/2 puzzle in B → D∗∗ℓν decays?
• RQ5 How do the extracted form factors F₀(1) for B → D∗ℓν compare with previous lattice results and QCD sum rules?

Key findings

• The axial current matrix element ⟨3P0|A₀|B⟩ at zero recoil is non-zero, contradicting the infinite mass limit prediction and indicating finite-mass effects are non-negligible.
• For the 3P2 state, the ratio of finite-mass to infinite-mass three-point functions for ˜k is found to be 2.88 ± 3.82 at the highest b-quark mass (aµ = 0.67), suggesting a significant enhancement in the finite-mass regime.
• The estimated branching fraction for B → D(2+) followed by D(2+) → D∗π is (7.4 ± 4.9) × 10⁻³ at mB ≈ 2.9 GeV, indicating a possible resolution to the 1/2 vs. 3/2 puzzle.
• F₀(1) for B → D∗ℓν is found to be 0.827(53) at β = 4.05 and aµb = 0.5757, with an extrapolated value of 0.871(43), which is higher than previous QCD sum rule estimates.
• Statistical uncertainties are large at high b-quark masses due to increased noise in effective mass plateaus, suggesting the need for higher statistics in future studies.
• The results indicate that finite charm quark mass effects are crucial for accurate predictions and that lattice QCD with realistic quarks can provide new insights into the 1/2 vs. 3/2 puzzle.