[Paper Review] Hadronic form factors for rare semileptonic $B$ decays

J. M. Flynn, Andreas Jüttner+3 more|arXiv (Cornell University)|Nov 20, 2015

Particle physics theoretical and experimental studies28 references3 citations

TL;DR

This paper presents first lattice QCD computations of short-distance contributions to hadronic form factors for rare semileptonic $B$ and $B_s$ decays, specifically $B\to K^*\ell^+\ell^-$ and $B_s\to\phi\ell^+\ell^-$. Using $N_f=2+1$ domain-wall fermions and relativistic heavy quarks on coarse ensembles, the authors extract seven form factors with good statistical signals, providing a crucial independent check on existing predictions and enabling precision tests of the Standard Model and new physics beyond it.

ABSTRACT

We discuss first results for the computation of short distance contributions to semileptonic form factors for the rare $B$ decays $B o K^{*} \ell^+\ell^-$ and $B_s o ϕ\ell^+ \ell^-$. Our simulations are based on RBC/UKQCD's $N_f=2+1$ ensembles with domain wall light quarks and the Iwasaki gauge action. For the valence $b$-quark we chose the relativistic heavy quark action.

Motivation & Objective

• To compute short-distance contributions to hadronic form factors for rare semileptonic $B$ decays, which are key inputs for testing the Standard Model and probing new physics.
• To provide independent lattice QCD results for form factors in $B\to K^*\ell^+\ell^-$ and $B_s\to\phi\ell^+\ell^-$ decays, reducing theoretical uncertainties in flavor physics.
• To validate a computational framework using domain-wall fermions and relativistic heavy quarks on RBC/UKQCD $N_f=2+1$ ensembles for rare decay form factors.
• To enable future chiral and continuum extrapolations by generating data across multiple sea and valence quark masses and lattice spacings.

Proposed method

• Simulations are performed on $N_f=2+1$ domain-wall fermion ensembles with Iwasaki gauge action, using a coarse lattice spacing of $a^{-1} \approx 1.785$ GeV.
• Valence $b$-quarks are treated with the relativistic heavy quark action, nonperturbatively tuned, while light and strange quarks use domain-wall fermions.
• Three-point functions are computed using Gaussian-smeared $b$-quark sources and point sources for light quarks to suppress excited-state contamination.
• Form factors are extracted via correlated fits to plateaus in the 3-point function time dependence, with source-sink separations optimized for signal-to-noise.
• The hadronic matrix elements are parametrized by seven form factors: $f_V, f_{A_0}, f_{A_1}, f_{A_2}, f_{T_1}, f_{T_2}, f_{T_3}$, corresponding to vector, axial-vector, and tensor currents.
• Renormalization factors are being computed using a mostly nonperturbative scheme, with plans to extend to finer ensembles and physical quark masses.

Experimental results

Research questions

• RQ1 What are the leading short-distance contributions to the hadronic form factors in $B_s\to\phi\ell^+\ell^-$ decays, as computed via lattice QCD?
• RQ2 How well can the form factors be extracted from lattice 3-point functions with controlled systematic errors using domain-wall fermions and relativistic heavy quarks?
• RQ3 What is the signal-to-noise behavior of the 3-point functions across different source-sink separations, and which configuration yields the most stable plateau?
• RQ4 How do the extracted form factors vary with $q^2$ and light quark mass, and what is their behavior across different ensembles?
• RQ5 Can the lattice results be used to perform a combined chiral and continuum extrapolation using heavy meson chiral perturbation theory?

Key findings

• The form factor $f_{A_1}$ for $B_s\to\phi\ell^+\ell^-$ at zero momentum shows consistent values across four source-sink separations ($t_{\text{sink}} = 18, 20, 22, 24$), with the best signal-to-noise ratio at $t_{\text{sink}} = 20$.
• All seven form factors—$f_V, f_{A_0}, f_{A_1}, f_{A_2}, f_{T_1}, f_{T_2}, f_{T_3}$—are successfully extracted with good statistical precision from correlated fits to plateaus on the coarse ensembles.
• The extracted form factors show stable plateaus over multiple time slices, indicating effective suppression of excited-state contamination.
• The results are obtained on two coarse ensembles with $am_l = 0.005$ and $am_l = 0.010$, and $M_\pi \approx 338$ MeV and $434$ MeV, respectively.
• The authors confirm the viability of their computational setup for future extrapolations, with plans to include finer ensembles ($a^{-1} = 2.38$ GeV) and physical quark masses.
• The work provides a foundation for future $z$-expansion kinematical extrapolations to $q^2 = 0$ and for precision comparisons with experimental data and other lattice collaborations.