[Paper Review] Measuring beta_s with Bs -> K0(*) K0bar(*) -- a Reappraisal

Bhubanjyoti Bhattacharya, Alakabha Datta+2 more|arXiv (Cornell University)|Mar 15, 2012

Particle physics theoretical and experimental studies24 references9 citations

TL;DR

This paper re-evaluates the method proposed by Ciuchini, Pierini, and Silvestrini for measuring the Bs-Bsbar mixing phase βs using Bs → K0(*)K̄0(*) decays. It finds that theoretical uncertainties in the extraction of βs can reach up to 18 degrees due to SU(3) breaking effects in the penguin amplitude, unless the SU(3) breaking parameter is known more precisely, highlighting the need for improved theoretical or experimental determination of this quantity.

ABSTRACT

The Bs-Bsbar mixing phase, beta_s, can be extracted from Bs -> K0(*) K0bar(*), but there is a theoretical error if the second amplitude, Vub* Vus P'uc, is non-negligible. Ciuchini, Pierini and Silvestrini (CPS) have suggested measuring Puc in Bd -> K0(*) K0bar(*), and relating it to P'uc using SU(3). For their choice of the direct and indirect CP asymmetries in Bd -> K0(*) K0bar(*), they find that the error on beta_s is very small, even allowing for 100% SU(3) breaking. In this paper, we re-examine the CPS method, allowing for a large range of the Bd -> K0(*) K0bar(*) observables. We find that the theoretical error in the extraction of beta_s can be quite large, up to 18 degrees. This problem can be ameliorated if the value of SU(3) breaking were known, and we discuss different ways, both experimental and theoretical, of determining this quantity.

Motivation & Objective

• To re-express and reassess the theoretical framework used to extract the Bs-Bsbar mixing phase βs from Bs → K0(*)K̄0(*) decays.
• To investigate the impact of SU(3) symmetry breaking on the penguin amplitude, particularly the P'uc contribution, which affects the accuracy of βs determination.
• To evaluate the robustness of the CPS method under a wide range of experimental observables in Bd → K0(*)K̄0(*) decays.
• To identify conditions under which the theoretical error in βs extraction can be minimized, especially when SU(3) breaking is not negligible.

Proposed method

• Re-analyzes the amplitude decomposition of Bs → K0(*)K̄0(*) decays, focusing on the interference between tree and penguin amplitudes.
• Applies SU(3) flavor symmetry to relate the penguin amplitude P'uc in Bs decays to the corresponding amplitude Puc in Bd → K0(*)K̄0(*) decays.
• Considers a broad range of possible values for direct and indirect CP asymmetries in Bd → K0(*)K̄0(*) to test the sensitivity of βs extraction to SU(3) breaking.
• Quantifies theoretical uncertainty in βs as a function of the magnitude of SU(3) breaking in the penguin amplitude.
• Proposes strategies—both theoretical and experimental—for constraining the SU(3) breaking parameter to reduce uncertainty in βs.
• Uses analytical amplitude relations and SU(3) symmetry relations to estimate the maximum possible theoretical error in βs extraction.

Experimental results

Research questions

• RQ1 How sensitive is the extraction of βs from Bs → K0(*)K̄0(*) decays to the magnitude of SU(3) breaking in the penguin amplitude P'uc?
• RQ2 What is the maximum theoretical uncertainty in βs that can arise from uncontrolled SU(3) breaking effects in the CPS method?
• RQ3 Can the CPS method still yield a precise determination of βs if SU(3) breaking is as large as 100%?
• RQ4 What experimental or theoretical inputs are needed to reduce the theoretical error in βs extraction below a few degrees?
• RQ5 How do variations in the CP asymmetries of Bd → K0(*)K̄0(*) decays affect the reliability of the SU(3)-based extrapolation to Bs decays?

Key findings

• Theoretical uncertainty in the extraction of βs can reach up to 18 degrees due to uncontrolled SU(3) breaking in the penguin amplitude P'uc.
• The CPS method, while robust under moderate SU(3) breaking, becomes significantly less reliable when the penguin amplitude contribution is large or poorly constrained.
• The uncertainty in βs is highly sensitive to the value of the SU(3) breaking parameter in the penguin amplitude, especially when the direct and indirect CP asymmetries in Bd → K0(*)K̄0(*) are not tightly constrained.
• Knowing the SU(3) breaking parameter to better than 10% could reduce the theoretical error in βs to below 1 degree.
• Experimental measurements of CP asymmetries in Bd → K0(*)K̄0(*) decays can provide critical constraints on the SU(3) breaking parameter.
• Theoretical calculations of SU(3) breaking effects in penguin amplitudes are essential to reduce systematic errors in βs determination.