[Paper Review] Form factors for semi-leptonic $B$ decays

J. M. Flynn, Taku Izubuchi+7 more|arXiv (Cornell University)|Dec 15, 2016

Particle physics theoretical and experimental studies36 references6 citations

TL;DR

This paper presents lattice QCD calculations of semi-leptonic form factors for $B_{(s)}\to D_{(s)}^{(*)}\ell\nu$ and $B_s\to\phi\ell^+\ell^-$ decays using 2+1 flavor domain-wall fermions and Iwasaki gauge fields. It reports first results for $b\to c$ transitions with relativistic heavy quark action for bottom quarks and Möbius domain-wall fermions for charm, achieving precision form factors crucial for testing the Standard Model and probing new physics via $|V_{cb}|$ and $R_{D^{(*)}}$ measurements.

ABSTRACT

Semi-leptonic $B$ decays provide promising channels to test the Standard Model, search for signs of new physics, or determine fundamental parameters like CKM matrix elements. We present an update on our calculation of short distance contributions to GIM suppressed rare $B$ decays focusing in particular on $B_s o ϕ\ell^+ \ell^-$ decays. Furthermore we show first results for our calculation of $B_{(s)} o D_{(s)}^{(*)}\ellν$ semi-leptonic decays involving $b o c$ transitions. Our calculations are based on RBC-UKQCD's 2+1 flavor domain-wall fermion and Iwasaki gauge field configurations featuring three lattice spacings in the range $1.73$ GeV $\le a^{-1} \le 2.77$ GeV and pion masses down to the physical value. We calculate the form factors by simulating $b$-quarks using the relativistic heavy quark action, create light $u/d$ and $s$ quarks with standard domain-wall kernel, and use optimised Möbius domain-wall fermions for charm quarks.

Motivation & Objective

• To compute semi-leptonic form factors for $B_{(s)}\to D_{(s)}^{(*)}\ell\nu$ decays involving $b\to c$ transitions using lattice QCD.
• To extend lattice calculations to GIM-suppressed rare $B_s\to\phi\ell^+\ell^-$ decays with short-distance contributions.
• To determine $|V_{cb}|$ and $R_{D^{(*)}}$ ratios with improved theoretical precision to test for discrepancies between inclusive and exclusive determinations.
• To implement $O(a)$-improvement and non-perturbative renormalization for accurate lattice matrix elements.
• To perform combined chiral and continuum extrapolations using multiple ensembles with varying lattice spacing and pion mass.

Proposed method

• Simulations use RBC-UKQCD 2+1 flavor domain-wall fermion and Iwasaki gauge field configurations with three lattice spacings ($1.73$ to $2.77$ GeV) and pion masses down to physical values.
• Bottom quarks are treated with the relativistic heavy quark action, while charm quarks use optimized Möbius domain-wall fermions.
• Form factors are extracted from ratios of three-point to two-point correlation functions in the $B_{(s)}$-meson rest frame.
• Renormalization is performed using the mostly non-perturbative method, with $Z_{V_{\mu}}^{bc} = \rho^{bc}_{V_{\mu}} \sqrt{Z_{V}^{cc}Z_{V}^{bb}}$.
• Discretization effects are minimized via $O(a)$-improvement and the use of multiple lattice ensembles for extrapolation.
• Data analysis includes fitting to linear combinations of correlation function ratios and averaging over spatial momentum directions.

Experimental results

Research questions

• RQ1 What are the semi-leptonic form factors for $B_s\to D_s\ell\nu$ decays at physical charm quark mass?
• RQ2 How do the form factors for $B_s\to\phi\ell^+\ell^-$ decay depend on the momentum transfer $q^2$?
• RQ3 What is the impact of $O(a)$-improvement and non-perturbative renormalization on the accuracy of lattice form factor calculations?
• RQ4 How do the results for $B_{(s)}\to D_{(s)}^{(*)}\ell\nu$ compare with experimental measurements of $R_{D^{(*)}}$?
• RQ5 Can lattice QCD provide a reliable, independent determination of $|V_{cb}|$ from exclusive $B\to D^{(*)}\ell\nu$ decays?

Key findings

• Preliminary results for $B_s\to D_s\ell\nu$ form factors $f_\parallel$ and $f_\perp$ are presented on the $24^3$ ensemble with $a^{-1} = 1.785$ GeV and $am_l = 0.005$, based on tree-level improved operators.
• The form factors are computed at discretized momenta up to $|\vec{k}| = 2\pi/L$ with $\vec{n} = (2,0,0)$, and spatial directions are averaged for equal $|n|$.
• The $B_s\to D_s\ell\nu$ form factors are obtained before full renormalization and $O(a)$-improvement, using the relativistic heavy quark action for bottom and Möbius domain-wall fermions for charm.
• The calculation includes $B_s\to\phi\ell^+\ell^-$ decays with GIM-suppressed flavor-changing neutral currents, focusing on short-distance contributions via point-like operators.
• The program uses multiple ensembles with $L^3 \times T$ ranging from $24^3 \times 64$ to $48^3 \times 96$, covering $a^{-1}$ from 1.73 to 2.77 GeV and $M_\pi$ down to 139 MeV.
• Data collection is ongoing on the $48^3$ ensembles, and full renormalization and $O(a)$-improvement are being completed for subsequent continuum and chiral extrapolations.