[Paper Review] The $\Lambda_b o \Lambda\ ( o p \pi^-)\mu^+\mu^-$ decay in the $ ext{RS}_{c}$ model

Aqsa Nasrullah, Faisal Munir Bhutta+1 more|arXiv (Cornell University)|May 3, 2018

Particle physics theoretical and experimental studiesPhysics and Astronomy97 references4 citations

TL;DR

This study investigates the rare baryonic decay Λb → Λ(→pπ⁻)μ⁺μ⁻ within the Randall-Sundrum model with custodial protection (RSc), using stringent constraints from LHC data, electroweak precision tests, and Higgs signal strengths. Despite small deviations in Wilson coefficients due to Kaluza-Klein gluon exchanges, the model cannot explain the large discrepancies between Standard Model predictions and LHCb measurements in angular observables and branching fractions.

ABSTRACT

We study the four body decay $\Lambda_b ightarrow \Lambda ( ightarrow p \pi^-) \mu^{+} \mu^{-}$ in the Randall-Sundrum model with custodial protection $( ext{RS}_c)$. By considering the constraints coming from the direct searches of the lightest Kaluza-Klein (KK) excitation of the gluon, electroweak precision tests, the measurements of the Higgs signal strengths at the LHC and from $\Delta F=2$ flavor observables, we perform a scan of the parameter space of the $ ext{RS}_c$ model and obtain the maximum allowed deviations of the Wilson coefficients $\Delta C^{(\prime)}_{7,\; 9,\; 10}$ for different values of the lightest KK gluon mass $M_{g^{(1)}}$. Later, their implications on the observables such as differential branching fraction, longitudinal polarization of the daughter baryon $\Lambda$, forward-backward asymmetry with respect to leptonic, hadronic and combined lepton-hadron angles are discussed where we present the analysis of these observables in different bins of di-muon invariant mass squared $s\;(= q^2)$. It is observed that with the current constraints the Wilson coefficients in $ ext{RS}_c$ model show slight deviations from their Standard Model values and hence can not accommodate the discrepancies between the Standard Model calculations of various observables and the LHCb measurements in $\Lambda_b$ decays.

Motivation & Objective

• To assess whether the RSc model can explain observed deviations in Λb → Λ(→pπ⁻)μ⁺μ⁻ decay from SM predictions.
• To constrain the parameter space of the RSc model using LHC data, electroweak precision tests, and Higgs signal strengths.
• To compute Wilson coefficients and angular observables (differential branching fraction, polarization, asymmetries) in the RSc framework.
• To evaluate whether the model can account for the large tensions seen in LHCb measurements of RK, RK*, and angular distributions.

Proposed method

• Performs a global scan of the RSc model parameter space under constraints from direct searches of the lightest KK gluon (Mg(1)), electroweak precision tests, and LHC Higgs signal strengths.
• Uses complex 5D Yukawa coupling matrices instead of real ones, leading to complex Wilson coefficients.
• Applies helicity formalism for Λb → Λ transition matrix elements and incorporates the latest lattice QCD form factors.
• Calculates differential branching fraction, longitudinal polarization (FL), and forward-backward asymmetries (AℓFB, AΛFB, AℓΛFB) in multiple q² bins.
• Compares predictions across SM and RSc model for observables in 5 bins of di-muon invariant mass squared (s).
• Uses experimental data from LHCb (2018) for comparison, including branching fractions and angular observables with uncertainties.

Experimental results

Research questions

• RQ1 Can the RSc model explain the observed deviations in Λb → Λ(→pπ⁻)μ⁺μ⁻ decay from SM predictions?
• RQ2 How large are the deviations in Wilson coefficients C7, C9, C10 in the RSc model under current experimental constraints?
• RQ3 Do the angular observables (FL, AℓFB, AΛFB, AℓΛFB) in the RSc model show significant deviations from SM values in different s bins?
• RQ4 Can the RSc model account for the large tensions in RK, RK*, and angular distributions observed by LHCb?
• RQ5 What is the impact of using complex Yukawa couplings and updated lattice QCD form factors on the model's phenomenology?

Key findings

• For Mg(1) = 4.8 TeV, the RSc model predicts a differential branching fraction of 0.190⁺⁰.¹²⁰₋₀.¹¹⁹ in the [1.1, 6] GeV² bin, 1.9σ below the LHCb measurement of 0.09⁺⁰.⁰⁶¹₋₀.⁰⁵¹.
• In the low-recoil bin [15, 20] GeV², the RSc model predicts a branching fraction of 0.807⁺⁰.⁰⁶⁹₋₀.⁰⁶⁹, 4.1σ above the LHCb measurement of 0.61⁺⁰.¹¹⁴₋₀.¹⁴³.
• The longitudinal polarization FL in the [0.1, 2] GeV² bin is predicted at 0.552⁺⁰.⁰⁶⁹₋₀.⁰⁸⁴ in RSc, only 0.02σ from the LHCb value of 0.56⁺⁰.²⁴⁴₋₀.⁵⁶⁶.
• For AℓFB in the [15, 20] GeV² bin, the RSc model gives -0.332⁺⁰.⁰⁰⁸₋₀.⁰⁰⁹, 3.0σ from the LHCb measurement of -0.05⁺⁰.⁰⁹⁵₋₀.⁰⁹⁵.
• The AΛFB in the [15, 20] GeV² bin is predicted at -0.247⁺⁰.⁰¹¹₋₀.⁰¹¹ in RSc, deviating by 0.5σ from the LHCb value of -0.29⁺⁰.⁰⁷⁶₋₀.⁰⁸¹.
• All angular observables in the RSc model remain close to SM predictions, with deviations too small to explain the observed tensions in LHCb data.