[Paper Review] Hints and challenges in heavy flavor physics

S. Hashimoto|arXiv (Cornell University)|Feb 25, 2019

Particle physics theoretical and experimental studies61 references10 citations

TL;DR

This paper reviews the current status and challenges in lattice QCD calculations for heavy flavor physics, focusing on precision determinations of B-meson decay constants, form factors, and matrix elements relevant to new physics searches. It highlights a 1% precision calculation of the B-meson decay constant by Fermilab/MILC using the HISQ action and discusses critical issues like discretization effects, long-distance contributions in $B\to K\ell^+\ell^-$, and violations of factorization in non-leptonic decays.

ABSTRACT

Heavy flavor physics entered a new era when the Belle II experiment observed its first collision. There are several hints found so far by BaBar, Belle, and LHCb in particular, that suggest the physics beyond the Standard Model appearing in the loop processes at short distances. They will be further tested by higher precision experiments in the coming years, while the role of lattice QCD is to understand the long-distance physics quantitatively so that one can unambiguously isolate the short-distance physics from the experimental data. I summarize the status towards this goal and then look at the challenges we are facing.

Motivation & Objective

• To summarize the current status of lattice QCD in addressing precision challenges in heavy flavor physics, particularly in isolating short-distance new physics effects.
• To address the difficulty in disentangling long-distance QCD effects from short-distance new physics contributions in rare $B$ decays like $B\to K\ell^+\ell^-$.
• To evaluate the role of lattice QCD in resolving discrepancies such as the $R(K^{(*)})$ anomaly and the $B\to D^{(*)}\tau\nu$ tension.
• To explore the limitations of factorization in non-local matrix elements and the need for non-perturbative QCD calculations in exclusive decays.
• To assess the feasibility and challenges of extending lattice methods to inclusive decays and QED corrections in semi-leptonic processes.

Proposed method

• Utilizes the Highly Improved Staggered Quark (HISQ) action for both light and heavy quarks to reduce discretization errors in lattice QCD simulations.
• Employs simulations at physical pion masses and fine lattice spacings down to $a = 0.042$ fm to improve control over systematic uncertainties.
• Applies Heavy Quark Effective Theory (HQET) and the Fermilab interpretation to estimate and correct for $O(\alpha_s a^2 m^2)$ discretization effects in $b$ quark systems.
• Performs non-local matrix element calculations involving bilocal operators, such as $\langle K|J_{\mu}^{(em)}(x){\cal H}(0)|B\rangle$, to model $B\to K\ell^+\ell^-$ decays.
• Tests the validity of factorization in matrix elements by comparing products of form factors and decay constants against full lattice results.
• Extends lattice techniques to include QED corrections and forward-scattering matrix elements for inclusive $B$ decays.

Experimental results

Research questions

• RQ1 To what extent can lattice QCD achieve 1% precision in $B$-meson decay constants, and what are the dominant systematic uncertainties?
• RQ2 How do discretization effects in the $b$ quark sector impact the reliability of lattice results, and can they be quantitatively controlled?
• RQ3 To what degree does factorization fail in non-leptonic $B$ decays, particularly in the $B\to K\ell^+\ell^-$ mode, and what are the implications for new physics searches?
• RQ4 What is the role of long-distance contributions, such as those from $B\to \psi^{(\prime)}K$ intermediate states, in the $B\to K\ell^+\ell^-$ decay rate, and how can they be quantified?
• RQ5 Can lattice QCD provide a reliable non-perturbative framework for calculating QED corrections and inclusive decay rates in $B$ meson decays?

Key findings

• The Fermilab/MILC collaboration achieved a 1% precision in the $B$-meson decay constant, reporting $f_B = 189.4 \pm 1.4$ MeV, marking a significant improvement over previous averages.
• Discretization effects for the $b$ quark remain substantial, with a rough estimate of 7% for a 3 GeV fictitious $b$ quark, indicating that $am_b \ll 1$ is not yet satisfied.
• Factorization is well satisfied for the operator $\mathcal{O}_1 = (\bar{c}\gamma_\mu P_L c)(\bar{s}\gamma_\mu P_L b)$, but shows $O(1)$ violation for $\mathcal{O}_2 = (\bar{c}\gamma_\mu P_L b)(\bar{s}\gamma_\mu P_L c)$, with lattice data suggesting a ratio near zero instead of 1/3.
• The matrix element for $B\to K\ell^+\ell^-$ is sensitive to non-local current insertions and rescattering effects, which are not captured by simple factorization.
• Preliminary lattice results indicate that the $B\to K\ell^+\ell^-$ decay rate is lower than experimental data away from charmonium resonances, suggesting possible long-distance contributions not yet fully quantified.
• Lattice QCD is advancing toward the precision frontier necessary to test new physics in $B\to D^{(*)}\tau\nu$ and $R(K^{(*)})$ anomalies, but challenges in controlling hadronic uncertainties remain central.