[Paper Review] Flavor physics with $Λ_b$ baryons

Stefan Meinel|Jan 13, 2014

Particle physics theoretical and experimental studies3 citations

TL;DR

This paper presents new relativistic lattice QCD calculations of $Λ_b \to p$, $Λ_b \to \Lambda$, and $Λ_b \to \Lambda_c$ form factors using a relativistic heavy-quark action, significantly reducing theoretical uncertainties compared to prior static $b$-quark approximations. The improved form factors enable more precise predictions for $\Lambda_b \to p\mu^-\bar{\nu}_\mu$ and $\Lambda_b \to \Lambda\ell^+\ell^-$ decays, with the potential to determine $|V_{ub}|$ at the LHC with theory uncertainty below 7%.

ABSTRACT

At the LHC, bottom baryons are being produced in unprecedented quantities, which opens up a new field for flavor physics. For example, the decay $Λ_b o p μ^- \barν$ can be used to obtain a novel determination of the CKM matrix element $|V_{ub}|$, and the decay $Λ_b o Λμ^+ μ^-$ probes the weak interactions at the loop level. The first lattice calculations of the relevant $Λ_b o p$ and $Λ_b o Λ$ form factors have recently been performed using domain-wall light quarks and static $b$ quarks. To further reduce the theoretical uncertainty, one has to go beyond the static approximation. Here I present new calculations of $Λ_b o p$, $Λ_b o Λ$, and $Λ_b o Λ_c$ form factors using a relativistic heavy-quark action.

Motivation & Objective

• To reduce theoretical uncertainties in $\Lambda_b$ decay observables by moving beyond the static $b$-quark approximation in lattice QCD.
• To enable precise determination of the CKM matrix element $|V_{ub}|$ from $\Lambda_b \to p\mu^-\bar{\nu}_\mu$ at the LHC.
• To enhance sensitivity to new physics in $\Lambda_b \to \Lambda\ell^+\ell^-$, a flavor-changing neutral current decay with high loop-level sensitivity.
• To provide complete sets of relativistic form factors for $\Lambda_b \to p$, $\Lambda_b \to \Lambda$, and $\Lambda_b \to \Lambda_c$ decays using improved lattice actions.
• To control excited-state contamination in three-point functions through large source-sink separations, improving accuracy in form factor extraction.

Proposed method

• Employing a relativistic heavy-quark action to describe the $b$ quark, replacing the prior static approximation and eliminating $\mathcal{O}(\Lambda/m_b)$ errors.
• Performing lattice QCD calculations with domain-wall light quarks and relativistic $b$ quarks at nonzero lattice spacing and unphysical light-quark masses.
• Using three-point correlation functions with large source-sink separations to suppress excited-state contamination in form factor determinations.
• Fitting the time dependence of correlation functions with exponential forms $R(t) = f + A e^{-\delta t}$, including constraints on parameter variation across data sets.
• Applying $\mathcal{O}(a)$-improvement and renormalization to reduce lattice artifacts before chiral and continuum extrapolations.
• Using a wide range of momentum transfers to map form factor shapes and enabling extrapolation to physical light-quark masses and continuum limit.

Experimental results

Research questions

• RQ1 Can relativistic $b$-quark actions in lattice QCD reduce theoretical uncertainties in $\Lambda_b$ decay form factors compared to the static approximation?
• RQ2 To what extent can improved form factors enhance the precision of $|V_{ub}|$ determination from $\Lambda_b \to p\mu^-\bar{\nu}_\mu$ at the LHC?
• RQ3 How do the form factors for $\Lambda_b \to \Lambda\ell^+\ell^-$ decay constrain new physics in $b \to s\ell^+\ell^-$ transitions?
• RQ4 What is the impact of excited-state contamination on form factor extraction, and can it be effectively controlled in $\Lambda_b$ decays?
• RQ5 How do the new relativistic form factors compare to previous static-approximation results in terms of stability and convergence?

Key findings

• The new relativistic form factor calculations reduce the theory uncertainty in the $\Lambda_b \to p\mu^-\bar{\nu}_\mu$ decay rate by at least a factor of two compared to the static approximation.
• The improved form factors enable a potential determination of $|V_{ub}|$ at the LHC with a theory uncertainty of 7% or lower, significantly reducing the current 30% discrepancy between inclusive and exclusive $B$-meson measurements.
• The form factor shapes for $\Lambda_b \to \Lambda$, $\Lambda_b \to p$, and $\Lambda_b \to \Lambda_c$ are presented in preliminary results at nonzero lattice spacing and unphysical light-quark masses, with stable fits across multiple data sets.
• Excited-state contamination is effectively controlled due to the use of large source-sink separations, which is a key advantage over typical nucleon form factor calculations.
• The results demonstrate that the $\mathcal{O}(\Lambda/m_b)$ errors from the static approximation have been removed, shifting the dominant uncertainty to light-quark mass extrapolation and chiral behavior.
• Future calculations at the physical point are planned to eliminate light-quark mass extrapolation uncertainties, further improving precision for $|V_{ub}|$ and new physics searches.