[Paper Review] B Semileptonic Decays at High Recoil Momentum

C. T. H. Davies, E. Follana+3 more|ArXiv.org|Oct 3, 2007

Particle physics theoretical and experimental studies4 references3 citations

TL;DR

This paper proposes using random-wall sources for light-quark propagators in lattice QCD simulations to reduce statistical noise in B→πlν semileptonic decays at high recoil momentum. By improving the signal-to-noise ratio by a factor of 3–4, especially at large pion momenta (e.g., $ap_\pi = \frac{2\pi}{L}(3,0,0)$), the method enables more precise extraction of form factors critical for determining $|V_{ub}|$, with significant improvements observed even at $q^2 \sim 10\,\text{GeV}^2$. The approach is validated on MILC coarse lattices using HISQ valence quarks and moving NRQCD for the b quark.

ABSTRACT

We explore the possibility of studying $B oπlν$ semileptonic decays at large recoil momentum. Our methods include the use of a random-wall source for the pion to reduce statistical errors, and different smearing functions are used for the B meson to improve the overlap with the ground state. We observe, in general, a factor of 3-4 improvement in the signal-to-noise ratio in correlation functions if random-wall propagators are used.

Motivation & Objective

• To address the challenge of exponentially growing statistical errors in lattice QCD simulations of B→πlν decays at high pion recoil momentum.
• To improve the signal-to-noise ratio in correlation functions for form factor extraction at low $q^2$ values, extending reach to $q^2 \sim 10\,\text{GeV}^2$.
• To test the efficacy of random-wall sources for light-quark propagators in enhancing ground-state overlap and reducing noise in 2- and 3-point functions.
• To enable more precise lattice determination of the CKM matrix element $|V_{ub}|$ by accessing experimental data in the low $q^2$ region.

Proposed method

• Use of a zero-momentum random-wall source for the pion, defined by a random complex unit vector $\vec{\eta}(x)$ on a time slice, to generate multiple effective source points and improve statistics.
• Construction of the pion 2-point function via $\frac{1}{N}\sum_y \tilde{g}^*(y)\tilde{g}(y)$, where $\tilde{g}(y) = \sum_x g(y,x)\vec{\eta}(x)$, to average over spatial sources.
• Incorporation of momentum-dependent phases $e^{\pm i\frac{k}{2}x}$ in the source for finite-momentum pion correlation functions.
• Adoption of the naïve-quark basis with $S(y,x) = g(y,x)\Omega(y)\Omega^\dagger(x)$ to compute matrix elements involving $\gamma_5$ currents.
• Use of a matrix fit to simultaneously analyze 2-point and 3-point functions with $N_\pi = N_B = 5$ exponentials to extract ground-state matrix elements.
• Application of Bayesian fitting techniques to extract energy eigenvalues and amplitudes with controlled uncertainties.

Experimental results

Research questions

• RQ1 Can random-wall sources significantly reduce statistical noise in lattice QCD correlation functions for B→πlν decays at high recoil momentum?
• RQ2 To what extent does the random-wall method improve the signal-to-noise ratio in 2- and 3-point functions compared to local sources?
• RQ3 Can the method enable reliable extraction of form factors at $q^2 \sim 10\,\text{GeV}^2$, where experimental data is available but lattice simulations are hindered by noise?
• RQ4 How does the performance of the random-wall method scale with increasing pion momentum, particularly at $ap_\pi = \frac{2\pi}{L}(3,0,0)$?

Key findings

• The random-wall source reduces statistical errors in pion 2-point functions by a factor of 2–3 for the ground state energy and amplitude compared to local sources.
• At $ap_\pi = (0,0,0)$, the random-wall method improves the signal-to-noise ratio by a factor of 5 compared to local sources.
• At $ap_\pi = \frac{2\pi}{L}(3,0,0)$, the signal-to-noise ratio is improved by a factor of 2–3, with the 3-point function showing a 3–4× improvement in accuracy.
• For the temporal vector current matrix element $v_{00}$, the random-wall method yields $v_{00} = 0.0597(7)$ at $ap_\pi = (0,0,0)$, compared to $0.0605(39)$ with local sources.
• At $ap_\pi = \frac{2\pi}{L}(3,0,0)$, the random-wall result $v_{00} = 0.043(33)$ is significantly more precise than the local result $v_{00} = 0.029(49)$.
• The method demonstrates robustness even at large momenta, with measurable improvements in signal quality despite residual noise, supporting its use in future high-precision lattice studies.