[Paper Review] Analysis of $B_{c} --> D_{s}^{*}\ell^{+}\ell^{-}$ in the Standard Model Beyond Third Generation

Ishtiaq Ahmed, M. Jamil Aslam+4 more|arXiv (Cornell University)|Jul 28, 2011

Particle physics theoretical and experimental studies3 citations

TL;DR

This study investigates $B_c \to D_s^{*}\ell^+\ell^-$ decays in the Standard Model with a fourth generation (SM4), focusing on how additional quarks ($t'$, $b'$) with masses 300–600 GeV and specific CKM matrix elements affect decay observables. It finds significant deviations in forward-backward asymmetry zero position, lepton polarization, and helicity fractions—especially in $\mu^+\mu^-$ and $\tau^+\tau^-$ modes—providing indirect probes for fourth-generation quarks.

ABSTRACT

The weak decays of B_{c} --> D_{s}^{*}l^{+}l^{-} (l=mu,tau) are investigated in the Standard Model with fourth generation (SM4). Taking fourth generation quark mass m_{t'} of about 300 to 600 GeV with the CKM matrix elements V_{t'b}^{*}V_{t's} in the range (0.03-1.2)*10^{-2} and using the new CP odd phase (phi_{sb}) to be 90^{o} the analysis of decay rates, forward-backward asymmetries, lepton polarization asymmetries and the helicity fractions of D_{s}^{*} meson in B_{c} --> D_{s}^{*}l^{+}l^{-} (l=mu,tau) is made. It is shown that the values of these physical observables are greatly influenced by the effects of extra sequential quark generation in the SM. It is found that the zero position of the forward-backward asymmetry in B_{c} --> D_{s}^{*} mu^{+} mu^{-} deviates significantly from that of the SM value while the effects in the decay rate, helicity fractions of D_s^{*} meson and the lepton polarization asymmetries are also quite promising. In B_{c} --> D_{s}^{*} tau^{+} tau^{-} decay, the SM4 the NP effects are somewhat mild in the decay rate and forward-backward asymmetry but they have shown them up in the longitudinal and transverse lepton polarization and also in the helicity fractions of the D_{s}^{*} meson which differ distinctively from the SM values. Thus the study of these physical observables will provide us useful information to probe new physics and helps us to search for the fourth generation of quarks (t',b') in an indirect way.

Motivation & Objective

• To investigate the impact of a fourth generation of quarks on $B_c \to D_s^{*}\ell^+\ell^-$ decays within the Standard Model framework.
• To explore how the presence of $t'$ and $b'$ quarks with masses between 300–600 GeV alters key decay observables such as decay rates and asymmetries.
• To assess the sensitivity of forward-backward asymmetry, lepton polarization, and $D_s^{*}$ helicity fractions to new physics beyond the third generation.
• To provide indirect signatures for detecting the fourth-generation quarks through precision measurements of $B_c$ decays.

Proposed method

• Adapting the Standard Model Lagrangian to include a fourth generation of quarks with $m_{t'}$ in the 300–600 GeV range.
• Incorporating CP-odd phase $\phi_{sb} = 90^\circ$ and CKM matrix elements $V_{t'b}^*V_{t's}$ in the range $(0.03-1.2)\times10^{-2}$ to model new physics effects.
• Calculating decay rates, forward-backward asymmetries, lepton polarization asymmetries, and $D_s^{*}$ helicity fractions using effective field theory techniques.
• Comparing results in SM4 with standard SM predictions to identify deviations indicative of new physics.
• Focusing on both $\ell = \mu$ and $\ell = \tau$ final states to assess flavor-dependent sensitivity.
• Using helicity amplitudes and angular distribution formalisms to extract polarization and asymmetry observables.

Experimental results

Research questions

• RQ1 How do fourth-generation quarks ($t'$, $b'$) modify the forward-backward asymmetry zero position in $B_c \to D_s^{*}\mu^+\mu^-$?
• RQ2 To what extent do new physics effects in SM4 alter the decay rate and helicity fractions of the $D_s^{*}$ meson in $B_c \to D_s^{*}\ell^+\ell^-$?
• RQ3 How do lepton polarization asymmetries in $B_c \to D_s^{*}\tau^+\tau^-$ differ between SM4 and the standard model?
• RQ4 Can the $D_s^{*}$ helicity fractions and lepton polarization observables serve as sensitive probes for fourth-generation quarks?
• RQ5 What is the relative impact of new physics in $\mu^+\mu^-$ versus $\tau^+\tau^-$ final states in this decay mode?

Key findings

• The zero position of the forward-backward asymmetry in $B_c \to D_s^{*}\mu^+\mu^-$ deviates significantly from the Standard Model prediction due to fourth-generation effects.
• The decay rate and forward-backward asymmetry in $B_c \to D_s^{*}\mu^+\mu^-$ show measurable deviations under SM4, indicating sensitivity to new physics.
• In $B_c \to D_s^{*}\tau^+\tau^-$, the longitudinal and transverse lepton polarization asymmetries exhibit strong deviations from SM values, signaling new physics signatures.
• The helicity fractions of the $D_s^{*}$ meson in $B_c \to D_s^{*}\tau^+\tau^-$ differ distinctly from SM predictions under SM4, enhancing their sensitivity to new physics.
• The effects on lepton polarization and $D_s^{*}$ helicity fractions are more pronounced in the $\tau^+\tau^-$ channel than in the $\mu^+\mu^-$ channel.
• Collectively, these observables provide a robust indirect probe for the existence of fourth-generation quarks, particularly $t'$ and $b'$.