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Large Hadronic Effects in $B \to K^* μμ$?

Wolfgang Altmannshofer, Samuel G. Christensen, Peter Stangl

Abstract

Recent results from LHCb have confirmed the long-standing $P_5^\prime$ anomaly, an intriguing discrepancy in the angular distribution of the $B \to K^* μ^+μ^-$ decay that might be a sign of new physics. In addition, the new results hint at a non-zero value for $S_7$, another observable that characterizes the $B \to K^* μ^+μ^-$ angular distribution. We stress that a non-zero $S_7$ cannot be explained by heavy new physics but instead necessarily requires a sizable hadronic effect that introduces a strong phase. We argue that, under plausible assumptions, the hadronic effect is of the correct size to also explain $P_5^\prime$. The direct CP asymmetry in $B \to K^* μ^+μ^-$ emerges in principle as a clean probe of new physics in such a scenario. We show that a combined fit of hadronic parameters and Wilson coefficients retains sensitivity to new physics and we find strong bounds on imaginary parts of new physics Wilson coefficients.

Large Hadronic Effects in $B \to K^* μμ$?

Abstract

Recent results from LHCb have confirmed the long-standing anomaly, an intriguing discrepancy in the angular distribution of the decay that might be a sign of new physics. In addition, the new results hint at a non-zero value for , another observable that characterizes the angular distribution. We stress that a non-zero cannot be explained by heavy new physics but instead necessarily requires a sizable hadronic effect that introduces a strong phase. We argue that, under plausible assumptions, the hadronic effect is of the correct size to also explain . The direct CP asymmetry in emerges in principle as a clean probe of new physics in such a scenario. We show that a combined fit of hadronic parameters and Wilson coefficients retains sensitivity to new physics and we find strong bounds on imaginary parts of new physics Wilson coefficients.

Paper Structure

This paper contains 16 sections, 31 equations, 4 figures, 6 tables.

Table of Contents

  1. Introduction
  2. Theoretical Framework
  3. Effective Hamiltonian and Helicity Amplitudes
  4. Parameterization of Hadronic Effects
  5. Analytic Approximations for Observables
  6. The Angular Observables S7 and S8
  7. The Angular Anomalies: AFB and S5
  8. Probes of Right-Handed Currents: S3 and S9
  9. The direct CP Asymmetry ACP
  10. Numerical Results and Implications
  11. Fits of Hadronic Parameters to CP-Averaged Observables
  12. Probing CP Violating New Physics with B to Kstar mu mu
  13. Summary and Outlook
  14. Approximate New Physics Expressions for S7 and S8
  15. Correlation Matrices of the Hadronic Fit
  16. ...and 1 more sections

Figures (4)

  • Figure 1: The $B \to K^* \mu^+ \mu^-$ angular observables $S_7$ (top left), $S_8$ (top right), $S_5$ (center left), and $A_\text{FB}$ (center right), as well as the differential branching ratio $d\text{BR}/dq^2$ (bottom) as a function of $q^2$. We compare the finely binned experimental results from LHCb LHCb:2025mqb (black) to the SM predictions from flavio (orange) in the $q^2$ region below the $J/\psi$ resonance.
  • Figure 2: Predictions for the $B \to K^* \mu^+ \mu^-$ branching ratio (top left) and the CP-averaged angular observables $F_L$ (top right), $S_3$ (bottom left), and $S_4$ (bottom right) in the low $q^2$ region below the $J/\psi$ resonance. Our fit predictions (blue) are compared to the default flavio predictions (orange) and the LHCb data (black).
  • Figure 3: Predictions for the CP-averaged angular observables $S_5$ (top left), $A_\text{FB}$ (top right), $S_7$ (center left), $S_8$ (center right), and $S_9$ (bottom) in the low $q^2$ region below the $J/\psi$ resonance. Our fit predictions (blue) are compared to the default flavio predictions (orange) and the LHCb data (black).
  • Figure 4: Corner plot showing the Wilson coefficients in the combined fit of hadronic parameters and Wilson coefficients to the CP-averaged observables and CP asymmetries from LHCb configuration (iv). The diagonal panels show the one-dimensional marginalized distributions for each Wilson coefficient, while the off-diagonal panels show the corresponding two-dimensional joint distributions for all Wilson coefficient pairs with $1\sigma$ and $2\sigma$ contours.