[Paper Review] Flavor SU(3) and $\Lambda_b$ decays

Michael Gronau, Jonathan L. Rosner|arXiv (Cornell University)|Dec 19, 2013

Quantum Chromodynamics and Particle Interactions10 citations

TL;DR

This paper develops flavor SU(3) symmetry relations among penguin amplitudes in charmless Λb baryon decays to pseudoscalar-baryon final states, enabling extraction of penguin contributions from measurable decay rates. It derives amplitude relations that lead to triangle inequalities among decay rates, offering a method to test penguin dominance in Λb → K−p and access CP violation through rare decay measurements like Λb → π−Σ+, K+Ξ−, and K0Λ.

ABSTRACT

Some flavor SU(3) results are presented for decays of the $\Lambda_b$ baryon into non-charmed final states $PB$, where $P$ is a pseudoscalar mesons and $B$ is a spin-1/2 baryon. Although these relations are among amplitudes and hence not yet subject to direct experimental test, they can form the basis for triangle inequalities among decay rates.

Motivation & Objective

• To establish flavor SU(3) relations among penguin amplitudes in Λb → PB decays.
• To provide a framework for isolating penguin contributions in Λb → K−p, where pQCD calculations fail.
• To suggest measurable rare decay modes (e.g., Λb → π−Σ+, K+Ξ−, K0Λ) to test penguin dominance.
• To enable future extraction of CP-violating observables via polarization and rate measurements.
• To address the challenge of penguin amplitude underestimation in perturbative QCD by using SU(3) symmetry constraints.

Proposed method

• Uses SU(3) flavor symmetry to relate amplitudes of Λb decays into S = −1 and S = 0 final states.
• Expresses penguin amplitudes in terms of SU(3) singlet (A1), octet (F, D) coupling constants.
• Derives amplitude combinations such as (2A(K−p) − A(π−Σ+) − A(K+Ξ−))/3 = −1/√6 (3F + D), linking to A(K0Λ).
• Constructs relations involving r = V∗td/V∗ts to connect amplitudes across different final states.
• Proposes experimental strategies to detect rare decays via displaced vertices, kink signatures, and V-type topologies.
• Suggests using rate inequalities and polarization to disentangle S- and P-wave contributions and probe CP violation.

Experimental results

Research questions

• RQ1 Can flavor SU(3) symmetry relations be used to extract penguin amplitudes in Λb decays despite theoretical uncertainties?
• RQ2 How can the penguin amplitude in Λb → K−p be constrained if pQCD calculations underestimate its rate?
• RQ3 What rare Λb decay modes are accessible experimentally and can serve as probes of penguin dynamics?
• RQ4 Can triangle inequalities among decay rates be derived from SU(3) amplitude relations to test penguin dominance?
• RQ5 What experimental signatures can be used to identify and measure elusive decays like Λb → π−Σ+ and Λb → K0Λ?

Key findings

• The amplitude relation 1/3[2A(K−p) − A(π−Σ+) − A(K+Ξ−)] = −1/√6(3F + D) links the K−p amplitude to A(K0Λ), enabling indirect extraction of penguin parameters.
• A relation proportional to F + D is derived: 1/3[A(K−p) − A(π−Σ+)] = −1/√6 r−1 A(π−p), connecting K−p and π−p amplitudes via the CKM ratio r.
• The rate for Λb → K0Λ is suppressed by r² = |Vtd/Vts|² ≈ 0.05 compared to S = −1 final states, making it challenging but measurable.
• Decays Λb → π−Σ+, K+Ξ−, and K0Λ are proposed as viable experimental probes for penguin amplitude extraction.
• The paper suggests that LHCb may have sensitivity to Λb → π−Σ+ via displaced vertices, kinks, and π⁰ → γγ signatures.
• Polarization measurements in these decays could help separate S- and P-wave contributions and enable CP violation studies.