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Interpreting the results on exclusive $c\rightarrow sμν$ modes

D. Bečirević, M. Martines, S. Rosauro-Alcaraz, O. Sumensari

Abstract

We examine the $q^2$-binned distributions of the $D\to Kμν$ decay rate and of the corresponding forward-backward asymmetry which were recently measured by BESIII, showing a mild deviation from the Standard Model predictions. We point out that the proposed solution to remedy the discrepancy by turning on a complex-valued New Physics coupling is in tension with the constraints deduced from the LHC bounds on the high-$p_T$ tail of the relevant Drell-Yan process. We then show that there are several plausible scenarios that are compatible with both the measured low-energy and high-energy constraints but the selected couplings appear to be too small to be observed in the measurements of integrated observables, except for possibly the $q^2$-binned distribution of the angular observables relevant to $D_s\to φ(\to KK) μν$ or $Λ_c\to Λ(\to p π) μν$ modes.

Interpreting the results on exclusive $c\rightarrow sμν$ modes

Abstract

We examine the -binned distributions of the decay rate and of the corresponding forward-backward asymmetry which were recently measured by BESIII, showing a mild deviation from the Standard Model predictions. We point out that the proposed solution to remedy the discrepancy by turning on a complex-valued New Physics coupling is in tension with the constraints deduced from the LHC bounds on the high- tail of the relevant Drell-Yan process. We then show that there are several plausible scenarios that are compatible with both the measured low-energy and high-energy constraints but the selected couplings appear to be too small to be observed in the measurements of integrated observables, except for possibly the -binned distribution of the angular observables relevant to or modes.

Paper Structure

This paper contains 7 sections, 19 equations, 5 figures, 1 table.

Table of Contents

  1. Introduction
  2. Low energy effective theory
  3. Using the complex $g_S$
  4. SMEFT and LHC constraints
  5. Plausible scenarios
  6. Summary
  7. Acknowledgments

Figures (5)

  • Figure 1: $\chi^2$-test showing the cumulative $\Delta \chi^2=\chi^2_\text{SM}-\chi^2_\mathrm{min}$ as one moves from lower to larger $q^2$-bins, obtained by using the experimental data from Ref. BESIII:2026ydr and the SM prediction for which the LQCD form factors from Ref. Chakraborty:2021qav have been employed. We see that in both modes the $q^2$-binned forward-backward asymmetry is not increasing $\chi^2$, and the main increase arises from the large $q^2$-bins of the differential decay rate.
  • Figure 2: Accommodating the experimental data for the binned decay width and forward-backward asymmetry of $D\to K\mu \nu$BESIII:2026ydr by allowing $g_S = g_{S_L}+ g_{S_R}$ to be complex and non-zero. For that purpose the hadronic form factors obtained by three different LQCD Collaborations have been used: ETMC Lubicz:2017syv, FNAL/MILC FermilabLattice:2022gku and HPQCD Chakraborty:2021qav.
  • Figure 3: Low energy (gray and blue) and high energy (red) constraints on the complex coupling $g_S$ using the LQCD form factors from Ref. Chakraborty:2021qavParrott:2022rgu. See text.
  • Figure 4: Energy enhanced contribution from $\psi^4$ semileptonic operator to $pp\to\ell \nu$ (left panel) and from $\psi^2 DH^2$ Higgs-current operator to $pp\to W h$ (right panel).
  • Figure 5: Low-energy and high-energy constraints on various combinations of (real valued) couplings appearing in Lagrangian \ref{['eq:left']}. Black curve in each plot correspond to the region of couplings that satisfy all the constraints to $2\sigma$. Dashed curve is the projection to the precision expected after completion of the High-Luminosity LHC, i.e. $3~\mathrm{ab}^{-1}$.