[Paper Review] Probing CP violation in $B^0_s ightarrow K^{0}_{ m S} \pi^{+}\pi^{-}$ decays

T. Gershon, T. Latham+1 more|arXiv (Cornell University)|Nov 7, 2014

Particle physics theoretical and experimental studies19 references3 citations

TL;DR

This paper investigates the sensitivity of various Dalitz plot analysis methods—untagged decay-time-integrated, untagged decay-time-dependent, and tagged decay-time-dependent—for probing CP violation in $B^0_s \to K^0_S \pi^+\pi^-$ decays. Using a toy model with $K^*(892)$, $K^*_0(1430)$, $\rho(770)$, and $f_0(980)$ resonances, it demonstrates that untagged methods can achieve good precision on CP-violating parameters, though flavour tagging significantly improves sensitivity to the weak phase $\phi_s$, with a factor of ~2.5 improvement even at 5% tagging efficiency.

ABSTRACT

The three-body charmless hadronic decay $B^0_s ightarrow K^{0}_{ m S} \pi^{+}\pi^{-}$ provides a number of novel possibilities to search for CP violation effects and test the Standard Model of particle physics. These include fits to the Dalitz-plot distributions of the decay-time-integrated final state, decay-time-dependent (but without initial state flavour tagging) fits to the Dalitz-plot distribution, as well as full decay-time-dependent and flavour tagged fits. The relative sensitivities of these different approaches are investigated.

Motivation & Objective

• . To compare the relative sensitivity of untaged and tagged decay-time-dependent Dalitz plot analyses for probing CP violation in $B^0_s \to K^0_S \pi^+\pi^-$ decays.
• . To evaluate the feasibility of measuring CP-violating parameters without initial-flavour tagging, leveraging effective lifetime measurements.
• . To assess the impact of flavour tagging on the precision of weak phase $\phi_s$ and relative phase measurements in $B^0_s$ decays.
• . To provide a framework for future amplitude analyses at Belle II and LHCb using existing and upcoming data.

Proposed method

• . Uses a toy model with resonant contributions from $K^*(892)$, $K^*_0(1430)$, $\rho(770)$, and $f_0(980)$ in the $B^0_s \to K^0_S \pi^+\pi^-$ decay.
• . Implements the Laura++ Dalitz-plot fitting package to simulate and fit the decay-time-dependent amplitude distributions.
• . Applies three analysis strategies: (i) untagged decay-time-integrated, (ii) untagged decay-time-dependent, and (iii) tagged decay-time-dependent fits.
• . Defines CP-violation parameters via the complex parameter $\lambda_f = \bar{A}_f / A_f$, with $S_f$, $C_f$, and $A^{\Delta\Gamma_s}_f$ encoding CP-odd and CP-even asymmetries.
• . Uses a signal sample of 2000 events per pseudoexperiment to assess statistical uncertainties and bias in parameter estimation.
• . Compares results across methods under various CP-violation scenarios, including $ACP = 50\%$, $\Delta\delta = 3\pi/4$, and $\phi_s = -2\beta_s$.

Experimental results

Research questions

• RQ1 . How does the sensitivity to CP-violating parameters in $B^0_s \to K^0_S \pi^+\pi^-$ decay compare between untagged and tagged Dalitz plot analyses?
• RQ2 . Can effective lifetime measurements (untagged, decay-time-dependent) provide meaningful constraints on CP violation in $B^0_s$ decays despite lacking flavour tagging?
• RQ3 . What is the improvement in precision for measuring the weak phase $\phi_s$ when flavour tagging is applied, even at low efficiency?
• RQ4 . How do the uncertainties on the $K^*\pm(892)$ isobar coefficients (amplitude and phase) scale across different analysis methods?
• RQ5 . Can the relative phase between $B^0_s$ and $B^0_s$ decays to $\rho^0(770)$ be measured effectively with untagged vs. tagged approaches?

Key findings

• . The untagged decay-time-integrated method achieves good precision on $K^*\pm(892)$ CP-violating parameters, with statistical uncertainties only slightly larger than those from tagged methods.
• . The untagged decay-time-dependent method shows similar precision to the untagged decay-time-integrated method, indicating that the $A^{\Delta\Gamma_s}_f$ term contributes little additional sensitivity.
• . Flavour tagging improves the precision on the weak phase $\phi_s$ by a factor of approximately 2.5 even at a realistic tagging efficiency of ~5%, compared to untagged methods.
• . The precision on $\phi_s$ improves by an order of magnitude with perfect tagging, highlighting the value of tagging for phase measurements.
• . The method of fixing $\phi_s = -2\beta_s$ and floating the $\rho^0(770)$ resonance phase $\Delta y_j$ yields consistent results, confirming the robustness of the tagging advantage.
• . All CP-violation scenarios—including $ACP = 50\%$, $\Delta\delta = 3\pi/4$, and $\phi_s = -2\beta_s$—are retrieved with minimal bias and good precision across all methods, validating the analysis framework.