[Paper Review] Fitting in or odd one out? Pulls vs residual responses in $b o s \ell^+\ell^-$

Bernat Capdevila, Ursula Laa+1 more|arXiv (Cornell University)|Aug 9, 2019

Particle physics theoretical and experimental studies8 references4 citations

TL;DR

This paper evaluates the impact of new LHCb and Belle II measurements on global fits of $b \to s\ell^+\ell^-$ transitions using a framework from prior work (arXiv:1811.10793), showing that updated $R_K^{[1.1,6]}$ and $B_s\to\mu^+\mu^-$ data reduce uncertainty in $C_{10\mu}^{\text{NP}}$ without altering the global tension with the Standard Model. The analysis confirms a shift toward smaller $C_{10\mu}^{\text{NP}}$ values, validated by a new global fit, while maintaining strong evidence against the SM at ~5σ.

ABSTRACT

New results in processes with an underlying quark transition $b o s \ell^+\ell^-$ have been recently reported by the LHCb and Belle II collaborations. In this note we show how the main implications of a handful of new measurements can be understood with the tools introduced in our recent paper, arXiv:1811.10793, without the need to redo the global fits. We find that the main impact of the new results, due to $R_K^{[1.1,6]}$ from LHCb, is a decrease in $C_{10μ}^{NP}$ with a reduced uncertainty. We validate this conclusion by presenting the result of a new global fit.

Motivation & Objective

• To assess the impact of new $b\to s\ell^+\ell^-$ measurements on existing global fits without re-running the full fit.
• To validate the predictive power of the pull and residual response framework introduced in arXiv:1811.10793 for tracking changes in global fits.
• To determine whether updated $R_K$, $R_{K^*}$, and $B_s\to\mu^+\mu^-$ data alter the evidence for new physics in $b\to s\ell^+\ell^-$ transitions.
• To quantify shifts in Wilson coefficients $C_{i\ell}^{\text{NP}}$ and changes in uncertainties using singular value decomposition (SVD) of the Hessian matrix.

Proposed method

• Utilizes the pull metric $\text{Pull}(\text{BF})_i = (T_{\text{BF},i} - O_i)/\sqrt{\Delta_{\text{exp},i}^2 + \Delta_{\text{BF},i}^2}$ to assess deviation of measurements from the best-fit point.
• Applies the residual response framework to estimate shifts in Wilson coefficients without full re-fitting, using SVD decomposition of the Hessian matrix.
• Compares old and new global fits in $C_{9\mu}^{\text{NP}}$-$C_{10\mu}^{\text{NP}}$ and $C_{10\mu}^{\text{NP}}$-$C_{10'\mu}^{\text{NP}}$ planes to visualize changes.
• Treats $B_s\to\mu^+\mu^-$ branching ratio with two methods: a combined likelihood (Eq. 3) and a weighted average (Eq. 4), to assess sensitivity to treatment.
• Uses the SVD basis to identify dominant directions of change in parameter space, particularly $4^{-}$ and $5^{+}$, and quantifies shifts in $C_{10\mu}^{\text{NP}}$ and $C_{10'\mu}^{\text{NP}}$.
• Validates results via a new global fit (Eq. 9), confirming predictions from the pull/residual response method.

Experimental results

Research questions

• RQ1 How do recent LHCb and Belle II measurements affect the global fit of $b\to s\ell^+\ell^-$ transitions?
• RQ2 Can the pull and residual response framework accurately predict shifts in Wilson coefficients without a full re-fit?
• RQ3 Does the updated $R_K^{[1.1,6]}$ measurement reduce the tension with the Standard Model or alter the preferred new physics parameters?
• RQ4 What is the impact of the new $B_s\to\mu^+\mu^-$ branching ratio measurement on the uncertainty and central value of $C_{10\mu}^{\text{NP}}$?
• RQ5 How do systematic differences in treatment of $B_s\to\mu^+\mu^-$ data affect the fit outcome and residual responses?

Key findings

• The updated $R_K^{[1.1,6]}$ measurement reduces the pull from 0.13 to 1.11, indicating a shift toward the Standard Model but with reduced uncertainty.
• The new global fit confirms a decrease in $C_{10\mu}^{\text{NP}}$ from 0.35 to 0.33, with a reduced uncertainty, primarily driven by the $R_K^{[1.1,6]}$ update.
• The dominant change in parameter space is along the SVD direction $4^{-}$, corresponding to a reduction in $C_{10\mu}^{\text{NP}}$, with a minor shift along direction $5^{+}$.
• The uncertainty in $C_{10\mu}^{\text{NP}}$ is reduced primarily along direction $4$, increasing the correlation between $C_{9\mu}^{\text{NP}}$ and $C_{10\mu}^{\text{NP}}$.
• The treatment of $B_s\to\mu^+\mu^-$ as a combined likelihood (Eq. 3) leads to a small additional shift in $C_{10'\mu}^{\text{NP}}$ toward more negative values, though this is not captured in the validation fit using Eq. 4.
• The framework successfully predicts the new fit outcome using only pull and residual response metrics, validating its utility for rapid assessment of new data impacts.