[Paper Review] Probe the R-parity Violating Supersymmetry Effects in the $B^0_s-\bar{B}^0_s$ Mixing

Ru-Min Wang, G. R. Lu+2 more|arXiv (Cornell University)|Sep 27, 2006

Particle physics theoretical and experimental studies3 citations

TL;DR

This paper investigates R-parity violating (RPV) supersymmetry effects in $B^0_s$-$\bar{B}^0_s$ mixing using the latest CDF and DØ measurements of the mass difference $\Delta M_s$. By constraining the RPV coupling product $\lambda'_{i32}\lambda'^{*}_{i23}$ from $\Delta M_s$, it predicts significant reductions in the $B_s$ width difference $\Delta\Gamma_s$ and derives a tighter upper bound than previous constraints, improving limits by a factor of ~3 over existing bounds.

ABSTRACT

The recent measurements of the $B_s$ mass difference $ΔM_s$ by the CDF and DØ collaborations are roughly consistent with the Standard Model predictions, therefore, these measurements will afford an opportunity to constrain new physics scenarios beyond the Standard Model. We consider the impact of the R-parity violating supersymmetry in the $B^0_s-\bar{B}^0_s$ mixing, and use the latest experimental results of $ΔM_s$ to constrain the size of the R-parity violating tree level couplings in the $B^0_s-\bar{B}^0_s$ mixing. Then, using the constrained R-parity violating parameter space from $ΔM_s$, we show the R-parity violating effects on the $B_s$ width difference $ΔΓ_{s}$.

Motivation & Objective

• To constrain R-parity violating (RPV) supersymmetry couplings in $B^0_s$-$\bar{B}^0_s$ mixing using the latest experimental $\Delta M_s$ measurements.
• To examine the impact of these constrained RPV couplings on the $B_s$ width difference $\Delta\Gamma_s$.
• To derive a tighter bound on the RPV coupling product $\lambda'_{i32}\lambda'^{*}_{i23}$ by combining constraints from both $\Delta M_s$ and $\Delta\Gamma_s$.
• To assess the potential for future LHC data to further shrink or rule out the allowed parameter space for RPV couplings.

Proposed method

• Uses the measured $\Delta M_s = (17.31^{+0.33}_{-0.18} \pm 0.07)/\text{ps}$ from CDF and DØ to constrain the RPV coupling product $\lambda'_{i32}\lambda'^{*}_{i23}$.
• Applies the effective Hamiltonian formalism in the Standard Model and RPV SUSY to compute the mixing amplitude $M_{12}^{s,\text{SM}}$ and the RPV contribution $M_{12}^{s,\text{RPV}}$.
• Derives the $B_s$ width difference $\Delta\Gamma_s$ using the SM expression involving $V_{cb}V_{cs}^*$, $G(x_c)$, $G_2(x_c)$, and $1/m_b$ corrections.
• Performs a three-dimensional scatter plot analysis of $\Delta\Gamma_s$ as a function of $|\lambda'_{i32}\lambda'^{*}_{i23}|$ and $\phi_{\not R_p}$ to visualize the allowed parameter space.
• Combines the $\Delta M_s$ constraint with the experimental $\Delta\Gamma_s = (0.22 \pm 0.09)/\text{ps}$ to further restrict the allowed region of $\lambda'_{i32}\lambda'^{*}_{i23}$.
• Uses the $\tilde{\nu}_i$ slepton mass dependence to express bounds in terms of $m_{\tilde{\nu}_i}$, scaling as $1/m_{\tilde{\nu}_i}^2$.

Experimental results

Research questions

• RQ1 What is the allowed parameter space for the RPV coupling product $\lambda'_{i32}\lambda'^{*}_{i23}$ based on the latest $\Delta M_s$ measurements?
• RQ2 How do RPV SUSY contributions affect the $B_s$ width difference $\Delta\Gamma_s$ relative to the Standard Model prediction?
• RQ3 Can the combined constraints from $\Delta M_s$ and $\Delta\Gamma_s$ yield a tighter bound on $\lambda'_{i32}\lambda'^{*}_{i23}$ than $\Delta M_s$ alone?
• RQ4 What is the expected sensitivity of future LHC data to further constrain or rule out the RPV coupling space?

Key findings

• The upper bound on $|\lambda'_{i32}\lambda'^{*}_{i23}|$ is improved to $4.4 \times 10^{-7} \times (100~\text{GeV}/m_{\tilde{\nu}_i})^2$ from $\Delta M_s$ alone, a significant tightening over previous limits.
• The RPV contributions to $\Delta\Gamma_s$ can reduce the width difference below the SM prediction of $0.07 \pm 0.03$ ps, with $\Delta\Gamma_s$ ranging from 0.00 to 0.10 ps depending on the phase $\phi_{\not R_p}$.
• The phase $\phi_{\not R_p}$ in the range $[2\pi/3, 8\pi/9]$ can drive $\Delta\Gamma_s$ to zero, indicating strong interference effects.
• The combined constraint from $\Delta M_s$ and $\Delta\Gamma_s$ excludes the region $4.4 \times 10^{-7} < |\lambda'_{i32}\lambda'^{*}_{i23}| < 5.5 \times 10^{-7}$, leading to a stronger bound than from $\Delta M_s$ alone.
• The final allowed range for $|\lambda'_{i32}\lambda'^{*}_{i23}|$ is $[5.5, 13.1] \times 10^{-7} \times (100~\text{GeV}/m_{\tilde{\nu}_i})^2$, representing a tighter constraint than previous studies.
• Future LHC data with $10^{12}$ $b\bar{b}$ events per year are expected to significantly shrink or rule out the remaining allowed parameter space for $\lambda'_{i32}\lambda'^{*}_{i23}$.