[Paper Review] Comparative Study of $B_{c} o D_{s}^{*}\ell^{+}\ell^{-}$ Decays in Standard Model and Supersymmetric Models

Aqeel Ahmed, Ishtiaq Ahmed+4 more|arXiv (Cornell University)|Aug 4, 2011

Particle physics theoretical and experimental studies51 references3 citations

TL;DR

This study compares rare $B_c \to D_s^{*}\ell^+\ell^-$ decays in the Standard Model (SM) and supersymmetric models (MSSM and SUSY SO(10) GUT), using QCD sum rules for form factors. It finds significant SUSY effects—especially in forward-backward asymmetry and polarization asymmetries—due to new Wilson coefficients, offering strong constraints on SUSY parameter spaces beyond the SM.

ABSTRACT

A comparative study of the exclusive rare $B_{c} ightarrow D_{s}^{\ast}\ell^{+}\ell^{-}$ ($\ell=\mu, au$) decays has been made in the minimal supersymmetric models (MSSM) and the SUSY SO(10) GUT models. In this context, various physical observables such as branching ratios $(\mathcal{BR})$, forward-backward asymmetries $(\mathcal{A}_{FB})$, lepton polarization asymmetries $(P_{L,N,T})$ and helicity fractions ($f_{L,T}$) of $D_{s}^{\ast}$ meson by using the the QCD sum rules form factors have been investigated. It is found that the SUSY effects are characteristically prominent to that of the SM values for these observables. For instance, in SUSY I and SUSY II, the forward-backward asymmetry does not cross zero which is mainly due to the same sign of the $C_{7}^{eff}$ and $C_{9}^{eff}$ Wilson coefficients. Similarly in SUSY SO(10) GUT models due to the complex nature of the new Wilson coefficients -- corresponding to the new operators arising due to the contribution of neutral Higgs bosons (NHBs) -- the above mentioned observables are sizably affected. Therefore the analysis of said observables in charmed semileptonic $B$ meson decays can put some stringent constraints on the parameter space of SUSY variants and can serve as a windowpane to look beyond the SM.

Motivation & Objective

• To investigate the impact of supersymmetry on exclusive rare $B_c \to D_s^{*}\ell^+\ell^-$ decays beyond the Standard Model.
• To analyze how SUSY contributions—particularly from neutral Higgs bosons—modify key observables such as branching ratios and asymmetries.
• To compare predictions from minimal supersymmetric models (MSSM) and SUSY SO(10) GUT models with those of the Standard Model.
• To assess the sensitivity of observables like forward-backward asymmetry and lepton polarization to new physics via effective Wilson coefficients.
• To establish whether these decays can serve as probes for constraining the parameter space of supersymmetric models.

Proposed method

• Employed QCD sum rules to calculate the form factors for the $B_c \to D_s^*$ transition, essential for computing decay rates.
• Calculated physical observables including branching ratios, forward-backward asymmetry ($\mathcal{A}_{FB}$), lepton polarization asymmetries ($P_L, P_N, P_T$), and helicity fractions ($f_L, f_T$) of $D_s^*$.
• Derived effective Hamiltonians including new Wilson coefficients ($C_7^{\text{eff}}, C_9^{\text{eff}}$) from SUSY contributions, particularly from neutral Higgs boson exchanges.
• Analyzed the complex structure of new Wilson coefficients in SUSY SO(10) GUT models, which significantly alter decay observables compared to SM.
• Compared results across SM, MSSM (SUSY I and II), and SUSY SO(10) GUT models to isolate SUSY signatures.
• Used lepton flavor ($\ell = \mu, \tau$) dependence to probe differences in SUSY contributions across final states.

Experimental results

Research questions

• RQ1 How do supersymmetric models (MSSM and SUSY SO(10) GUT) modify the branching ratio of $B_c \to D_s^{*}\ell^+\ell^-$ compared to the Standard Model?
• RQ2 What is the impact of new physics contributions—especially from neutral Higgs bosons—on the forward-backward asymmetry in $B_c \to D_s^{*}\ell^+\ell^-$ decays?
• RQ3 How do lepton polarization asymmetries and helicity fractions of the $D_s^*$ meson differ in SUSY models versus the SM?
• RQ4 Why does the forward-backward asymmetry fail to cross zero in certain SUSY scenarios, and what does this imply about the sign of effective Wilson coefficients?
• RQ5 Can the observed deviations in observables from SM predictions constrain the parameter space of supersymmetric models?

Key findings

• SUSY effects significantly alter the forward-backward asymmetry in $B_c \to D_s^{*}\ell^+\ell^-$ decays, with the asymmetry not crossing zero in SUSY I and SUSY II due to same-sign $C_7^{\text{eff}}$ and $C_9^{\text{eff}}$ Wilson coefficients.
• In SUSY SO(10) GUT models, the complex nature of new Wilson coefficients—arising from neutral Higgs boson contributions—leads to sizable modifications in all studied observables.
• Lepton polarization asymmetries ($P_L, P_N, P_T$) and helicity fractions ($f_L, f_T$) of the $D_s^*$ meson show distinct deviations from SM predictions in SUSY scenarios.
• The branching ratios in SUSY models are modified compared to the SM, with the extent of modification depending on the specific SUSY model and the final-state lepton flavor.
• The forward-backward asymmetry remains non-zero and sign-stable in SUSY models, contrasting with the SM behavior, indicating a clear signature of new physics.
• These observables collectively provide strong, model-dependent constraints on the parameter space of both MSSM and SUSY SO(10) GUT models.