[Paper Review] BR(Bs to mu+ mu-) as an electroweak precision test

Diego Guadagnoli, Gino Isidori|arXiv (Cornell University)|Feb 15, 2013

Particle physics theoretical and experimental studies35 references26 citations

TL;DR

This paper uses an effective field theory approach to show that the rare decay $B_s \to \mu^+\mu^-$ provides a stringent electroweak precision test of new physics, particularly constraining modified Z-boson couplings to down-type quarks. Under minimal flavor violation (MFV) or generic partial compositeness (PC), the current LHCb measurement of $B(B_s \to \mu^+\mu^-)$ already sets bounds on the left-handed coupling $\delta g_L$ that are comparable to Z-peak observables, while for the right-handed coupling $\delta g_R$, the bound from $B_s \to \mu^+\mu^-$ is more than two orders of magnitude stronger than from Z decays, especially in PC models.

ABSTRACT

Using an effective-theory approach, we analyze the impact of BR(Bs to mu+ mu-) in constraining new-physics models that predict modifications of the Z-boson couplings to down-type quarks. Under motivated assumptions about the flavor structure of the effective theory, we show that the bounds presently derived from BR(Bs to mu+ mu-) on the effective Z-boson couplings are comparable (in the case of minimal flavor violation) or significantly more stringent (in the case of generic partial compositeness) with respect to those derived from observables at the Z peak.

Motivation & Objective

• To assess the sensitivity of the rare decay $B_s \to \mu^+\mu^-$ as a probe of new physics in Z-boson couplings to down-type quarks.
• To compare constraints on effective Z-boson couplings derived from $B_s \to \mu^+\mu^-$ with those from electroweak precision observables at the Z peak.
• To evaluate the impact of flavor structure assumptions—minimal flavor violation (MFV) and generic partial compositeness (PC)—on the correlation between flavor-diagonal and flavor-changing couplings.
• To determine whether $B_s \to \mu^+\mu^-$ can provide more stringent bounds than Z-peak data on new physics affecting $Z \to b\bar{b}$.

Proposed method

• An effective field theory framework is used to describe deviations in Z-boson couplings to down-type quarks via dimension-six operators.
• The effective Lagrangian includes operators $O^{1L}_{ij}, O^{1R}_{ij}, O^{2L}_{ij}$ that generate tree-level contributions to $B_s \to \mu^+\mu^-$ and $Z \to b\bar{b}$.
• Flavor structure is modeled under two assumptions: MFV, where couplings are correlated via CKM and Yukawa matrices, and PC, where couplings are proportional to mixing parameters with composite states.
• Constraints on $\delta g_{L,R}^{ij}$ are derived by relating them to the branching ratio $B(B_s \to \mu^+\mu^-)$ and Z-peak observables such as $R_b$, $A^b_{\text{FB}}$, and $\alpha_s(M_Z)$.
• The analysis uses state-of-the-art SM inputs, including $m_t = 173.2$ GeV, $\alpha_s(M_Z) = 0.1184$, and $M_H = 125$ GeV, to compute SM predictions and deviations.
• Projected improvements in $B(B_s \to \mu^+\mu^-)$ sensitivity (e.g., $\sigma = 0.3 \times 10^{-9}$) are used to estimate future bounds on $\delta g_{L,R}$.

Experimental results

Research questions

• RQ1 How do constraints on modified Z-boson couplings to down-type quarks from $B_s \to \mu^+\mu^-$ compare with those from Z-peak precision observables?
• RQ2 Under what flavor structure assumptions (MFV vs. PC) does $B_s \to \mu^+\mu^-$ provide stronger bounds on $\delta g_L$ and $\delta g_R$?
• RQ3 Can $B_s \to \mu^+\mu^-$ probe tiny new-physics effects in $Z \to b\bar{b}$ couplings that are invisible to Z-peak data?
• RQ4 What is the projected sensitivity of $B_s \to \mu^+\mu^-$ to $\delta g_L$ and $\delta g_R$ with future experimental precision?

Key findings

• The current experimental bound on $B(B_s \to \mu^+\mu^-)$, with a 3.5σ signal at $3.2^{+1.5}_{-1.2} \times 10^{-9}$, already provides a constraint on $\delta g_L$ that is comparable to the one from Z-peak observables under the MFV assumption.
• In the partial compositeness framework, the bound on $\delta g_R$ from $B_s \to \mu^+\mu^-$ is more than two orders of magnitude stronger than the one derived from Z-peak data.
• With a projected experimental error of $\pm 0.3 \times 10^{-9}$, the 95% CL bound on $\delta g_R$ in the PC model would be $< 3.3 \times 10^{-5}$, significantly improving over current limits.
• The bound on the effective scale $\Lambda$ from $\delta g_L$ in MFV models is $\Lambda > 2.6$ TeV, while in PC models it is $m_\rho > (g_\rho \epsilon^q_3) \times 2.6$ TeV.
• The bound on $\delta g_R$ in PC models, $m_\rho > 0.23 \, \text{TeV} / \epsilon^q_3$, becomes relevant when $\epsilon^q_3 \ll 1$, where the $\delta g_L$ bound weakens.
• Even in the absence of observed deviations in $B_s \to \mu^+\mu^-$, the MFV bound on $\delta g_R$ would become more stringent than the Z-peak constraint.