[Paper Review] CKM matrix fits including constraints on New Physics

H. M. Lacker|ArXiv.org|Aug 20, 2007

Particle physics theoretical and experimental studies21 references3 citations

TL;DR

This paper presents a global fit of the CKM matrix incorporating New Physics (NP) contributions in $B$-mixing, using data from $B$-factories and Tevatron experiments. It finds that $r_d^2$ and $r_s^2$ are both slightly less than 1, consistent with Minimal Flavour Violation, and identifies a strong interplay between $B$-factory and Tevatron inputs in constraining NP phases, particularly through $A_{SL}^d$ and $A_{SL}$ measurements.

ABSTRACT

I review the status of global fits to the CKM matrix within the framework of the Standard Model and also allowing for New Physics contributions in B-Bbar mixing. The driving force is coming from the large data sets collected by the B-factory experiments BABAR and Belle. Additional important inputs to the B_s sector are provided by the Tevatron experiments CDF and D0. In particular, when constraining New Physics in B-Bbar mixing in a model-independent analysis a nice interplay between the B-factories and the Tevatron experiments is observed.

Motivation & Objective

• To perform a model-independent global fit of the CKM matrix including New Physics contributions in $B_d$- and $B_s$-mixing.
• To assess the impact of $B$-factory and Tevatron data on constraining NP parameters in $B$-mixing, particularly $r_q^2$ and $\theta_q$.
• To evaluate the compatibility of current data with Minimal Flavour Violation (MFV) and Next-to-Minimal Flavour Violation (NMFV) scenarios.
• To determine the sensitivity of NP constraints to improved measurements of $\sin(2\beta)$, $|V_{ub}|$, and $f_{B_q}\sqrt{B_q}$.
• To explore the role of $A_{SL}^d$ and $A_{SL}$ in breaking degeneracy in NP parameter space and disfavoring large positive $2\theta_d$ values.

Proposed method

• Uses a global fit framework incorporating $B$-factory measurements of $|V_{ub}|$, $|V_{cb}|$, $\Delta m_d$, $\sin(2\beta)$, $\cos(2\beta)$, $\alpha$, $\gamma$, and $A_{SL}^d$.
• Incorporates Tevatron data on $\Delta m_s$, $\Delta\Gamma_s$, and $A_{SL}$ to constrain $B_s$-mixing parameters.
• Parametrizes NP effects in $M_{12}$ via $r_q^2 e^{2i\theta_q}$ and $h_q e^{2i\sigma_q}$, with SM values at $r_q^2=1$, $\theta_q=0$, $h_q=0$, $\sigma_q=0$.
• Applies the $SM4FFC$ assumption to exclude NP from tree-level decays, ensuring $|V_{ud}|$, $|V_{us}|$, $|V_{ub}|$, $|V_{cb}|$, and $\gamma$ are NP-free.
• Performs combined fits to $B_d$ and $B_s$ systems, using likelihood scans to derive 90% and 95% CL constraints on NP parameters.
• Analyzes the impact of $\Delta\Gamma_s^{CP'}$ on constraining $2\theta_s$, noting NP can only reduce the value below the SM prediction.

Experimental results

Research questions

• RQ1 What are the current constraints on New Physics parameters $r_q^2$ and $2\theta_q$ in $B_d$- and $B_s$-mixing from global fits?
• RQ2 How do $B$-factory and Tevatron data jointly constrain the NP phase $2\theta_d$ and the $B_d$-mixing strength $r_d^2$?
• RQ3 To what extent is the current data consistent with a Minimal Flavour Violation (MFV) scenario?
• RQ4 How do $A_{SL}^d$ and $A_{SL}$ measurements influence the allowed region in $r_d^2$-$2\theta_d$ parameter space?
• RQ5 What is the sensitivity of future $B_s \to \psi\phi$ time-dependent angular analyses to $2\theta_s$?

Key findings

• The combined fit shows a preferred value of $r_d^2 < 1$ and $2\theta_d < 0$, primarily driven by $|V_{ub}|$ and $\sin(2\beta)$ inputs.
• The $B_s$-mixing parameter $r_s^2$ is also found to be less than 1, with a significantly smaller allowed range than $r_d^2$ due to better $f_{B_s}\sqrt{B_s}$ precision.
• The $A_{SL}^d$ and $A_{SL}$ measurements disfavor large positive $2\theta_d$ values and $r_d^2 > 1$, with a double-peak structure in parameter space when these inputs are excluded.
• No exclusion at 90% CL is found for $2\theta_s$, but values near $\pm 90^\circ$ are disfavored due to the measured $\Delta\Gamma_s^{CP'}$ being larger than the SM prediction.
• The current data are consistent with a Minimal Flavour Violation scenario, as $r_d^2$ and $r_s^2$ are both slightly below 1 and $h_q$ values remain compatible with small NP contributions.
• The best sensitivity to $2\theta_s$ will come from high-statistics, time-dependent angular analyses of $B_s \to \psi\phi$ at LHCb, ATLAS, and CMS.