Prospect for measurement of CP-violating parameters of $B_s^0 \to φγ$ at the Tera Z factory

TL;DR

This work assesses the feasibility of measuring CP-violating observables in the FCNC decay $B_s^0\to\phi\gamma$ at the CEPC Tera-Z facility. It combines fast detector simulation of a CEPC-like baseline detector with a cut-based selection supplemented by a boosted decision tree, and performs a time-dependent analysis that accounts for $B_s^0$-$\bar{B}_s^0$ mixing to extract $A_{\phi\gamma}^{\Delta}$, $C_{\phi\gamma}$, and $S_{\phi\gamma}$. Projected uncertainties are quantified, with statistical and systematic components, and 1$\sigma$ sensitivity boundaries for New Physics (via Wilson coefficients $C_7^{(\prime)}$) are established, showing competitive reach and strong sensitivity to right-handed NP. The study also links detector performance, notably PID $K/\pi$ separation and ECAL resolution, to the precision, providing practical guidance for CEPC detector design and flavor-physics goals. Overall, the results demonstrate CEPC Tera-Z’s potential to substantially advance SM tests and NP searches in $b\to s\gamma$ transitions, while acknowledging modeling limitations inherent to fast simulation and background studies.

Abstract

$b \to sγ$ transition is a critical flavor-changing neutral current (FCNC) process that could be used to probe CP violation (CPV) and new physics (NP). We quantify the anticipated precision for measuring $B_s^0 \to φγ$ at the CEPC Z pole operation, showing that the relative statistical uncertainty could be as low as 0.16\%, improved by approximately two orders of magnitude compared to existing measurements. Additionally, we perform a time-dependent analysis of the $B_s^0 \to φγ$ decay, accounting for $B_s^0/\bar{B}_s^0$ mixing extract the mixing-induced and CP-violating parameters $\boldsymbol{\mathcal{A}_{φγ}^Δ}$, $\boldsymbol{C_{φγ}}$ and $\boldsymbol{S_{φγ}}$. Using central value from LHCb measurement as input, we evaluate the anticipated accuracy of measurements of these parameters. The projected statistical uncertainties are $σ_{A_{φγ}^Δ{}^{\text{stat}}} = 0.021$, $σ_C^{\text{stat}} = 0.0092$ and $σ_S^{\text{stat}} = 0.0096$, and the systematic uncertainties are $σ_{A_{φγ}^Δ{}^{\text{syst}}} = 0.035$, $σ_C^{\text{syst}} = 0.0027$ and $σ_S^{\text{syst}} = 0.0064$. Furthermore, the 1$σ$ sensitivity boundaries for NP in this study are found to be $\mathcal{A}_{φγ}^Δ< -0.05$ or $\mathcal{A}_{φγ}^Δ> 0.15$, $\mathcal{C}_{φγ} < -0.02$ or $\mathcal{C}_{φγ} > 0.04$, and $\mathcal{S}_{φγ} < -0.04$ or $\mathcal{S}_{φγ} > 0.04$. We also conduct a relevant detector optimization study by establishing the correlation between the anticipated precision and the intrinsic resolution of the ECAL, as well as the performance of the PID system.

Figures (18)

• Figure 1: The $b \to s\gamma$ penguin diagram, mediated by SM particles (left) and new physics particles (right).
• Figure 2: The topology of $B_s^0 \to \phi\gamma$ decay at Z-pole.
• Figure 3: The PID performance by combining dE/dx and TOF at a momentum ranging from 12.0 GeV/c to 12.4 GeV/c and a $\text{cos}\theta$ ranging from 0.30 to 0.31 is shown on the left panel and the performance of $K^\pm$ identification with maximum efficiency times purity at different momentum and cosine polar angle combinations is shown on the right panel.
• Figure 4: Normalized $\chi^2$ (left) and $V_{\phi\to K^+K^-}$ (right) of signal and background distributions. The selected ranges are $\log_{10}(\chi^2)<1$ and $\log_{10}(\frac{V_{\phi\to K^+K^-}}{\mu m})>2.6$.
• Figure 6: Normalized signal and background distributions for $\theta_{\phi\gamma}$, $E_{\gamma}$, and $P_{B_s^0}$. The selected range are $\theta_{\phi\gamma}<1.0$, $E_{\gamma}>8\ GeV$, and $P_{B_s^0}>25\ GeV$.