[Paper Review] On the consistency between CP violation in the K vs. Bd systems within the Standard Model

Diego Guadagnoli|arXiv (Cornell University)|Feb 14, 2011

Particle physics theoretical and experimental studies10 references3 citations

TL;DR

This paper investigates the consistency between CP violation in the neutral kaon (εK) and B⁰d (sin 2β) systems within the Standard Model, showing that a refined calculation of εK—including a 92% multiplicative correction κε due to phase and mixing effects—reduces the SM prediction for |εK| by ~20% compared to experiment. This discrepancy implies a 2.6σ tension between εK and sin 2β, challenging the SM's unitarity triangle consistency.

ABSTRACT

In the K and Bd systems, indirect CP violation is quantified by the parameters epsilon_K and sin 2beta respectively. Within the Standard Model, the uniqueness of the CP violating phase implies that the measurement of either between epsilon_K and sin 2beta permits to predict the other. Since both these parameters are very well measured, this turns into a powerful test of consistency. I discuss the status of this test, especially in the light of recent advances on the epsilon_K formula.

Motivation & Objective

• To test the consistency of the Standard Model's CKM mechanism for CP violation using the εK–sin 2β correlation.
• To assess the impact of subleading corrections in the εK formula on the SM prediction for indirect CP violation.
• To quantify the tension between the experimental values of εK and sin 2β in light of improved theoretical calculations.
• To evaluate the role of theoretical uncertainties, particularly in |Vcb| and B̂K, on the εK–sin 2β consistency test.
• To determine whether the observed discrepancy signals new physics or is due to underestimated theoretical errors.

Proposed method

• Uses the SM formula for εK, expressed as εK = κε × εK(φε=45°, ξ=0), where κε accounts for phase and mixing corrections.
• Applies a refined estimate of κε = 0.94 ± 0.02, derived from φε ≈ 43.5° and ξ ≠ 0, based on ϵ′/ϵ data and the ΔI=1/2 rule.
• Relies on the ϵ′/ϵ experimental value (1.65 ± 0.26)×10⁻³ to constrain ξ, linking it to the hadronic matrix element ratio Ω.
• Performs a phenomenological fit using ρ = 0.6 ± 0.3 to account for long-distance contributions, including G8² and η′ exchange effects.
• Evaluates theoretical errors in |εK|SM, identifying |Vcb| (10% error) and B̂K (5% error) as dominant uncertainties.
• Compares the SM prediction for sin 2β, derived from εK with κε, to the experimental value from ψKS decays.

Experimental results

Research questions

• RQ1 Does the inclusion of subleading corrections in the εK formula resolve the tension between εK and sin 2β in the SM?
• RQ2 What is the quantitative impact of the κε correction on the SM prediction for |εK|?
• RQ3 How do theoretical uncertainties in |Vcb| and B̂K affect the εK–sin 2β consistency test?
• RQ4 Is the observed discrepancy between εK and sin 2β statistically significant, and what does it imply for new physics?
• RQ5 How do different global fits (e.g., UTfit vs. CKMfitter) interpret the tension, and what role do theory error treatments play?

Key findings

• The inclusion of subleading corrections reduces the SM prediction for |εK| to 1.85×10⁻³, compared to the experimental value of 2.2×10⁻³.
• The multiplicative correction κε is estimated as 0.94 ± 0.02, primarily due to φε ≠ 45° and ξ ≠ 0, with both effects being negative.
• The dominant theoretical uncertainty in |εK|SM arises from |Vcb|, contributing a 10% error, followed by B̂K (5%) and Rₜ (8%).
• When enforcing the experimental |εK|, the SM predicts sin 2β ≈ 0.75, which exceeds the experimental value of 0.67 by about 2.6σ.
• The UTfit group confirms a 2.6σ tension between εK and sin 2β, while CKMfitter with conservative error treatment finds no discrepancy.
• The discrepancy is robust under variations of the renormalization scale and is not resolved by current theoretical error estimates.