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Understanding large localized CP violation in $B^\pm\to K^\pmπ^+π^-$ using dispersive methods

L. A. Heuser, A. Reyes-Torrecilla, C. Hanhart, B. Kubis, P. C. Magalhães, T. Mannel, J. R. Peláez

Abstract

We utilize the universality of pion-pion ($ππ$) final-state interactions at small invariant masses to understand the enhanced localized CP violation in $B^\pm\to K^\pmπ^+π^-$, using a dispersive approach. From a fit to the integrated CP-asymmetry data, we successfully predict the Dalitz-plot kinematic distribution of the asymmetry in the low-energy $ππ$ region, including the large localized CP violation recently observed by LHCb. An essential role is played by the contributions of isospin 2. This formalism, whose parameters have a physical meaning, can be adapted straightforwardly to other systems with CP violation enhanced by final-state interactions.

Understanding large localized CP violation in $B^\pm\to K^\pmπ^+π^-$ using dispersive methods

Abstract

We utilize the universality of pion-pion () final-state interactions at small invariant masses to understand the enhanced localized CP violation in , using a dispersive approach. From a fit to the integrated CP-asymmetry data, we successfully predict the Dalitz-plot kinematic distribution of the asymmetry in the low-energy region, including the large localized CP violation recently observed by LHCb. An essential role is played by the contributions of isospin 2. This formalism, whose parameters have a physical meaning, can be adapted straightforwardly to other systems with CP violation enhanced by final-state interactions.

Paper Structure

This paper contains 2 sections, 13 equations, 6 figures.

Table of Contents

  1. Fit details
  2. Dalitz-plot distribution

Figures (6)

  • Figure 1: Typical topologies for quark-level decays of $B^+\to K^+\pi^+\pi^-$ (a) with and (b) without charm loop. The gray box represents the flavor-changing weak decay process, which contains the CKM elements and CPV phase. For $q=s$, the operator in diagram (a) provides a $\bar{s}s$ source, for $q=u$ or $d$ a $\bar{u}u$ or $\bar{d}d$ source. The red line indicates the cut that generates an imaginary part. Diagram (b) provides a $\bar{u}u$ source.
  • Figure 2: Fit to the projected event distributions defined in Eq. \ref{['eq:observables']}, versus LHCb data LHCb:2022fpg (supplemental material). We show (a) the angle-symmetric sum of yields, (b) the angle-asymmetric sum of yields, (c) the angle-symmetric CP-violating difference of yields, and (d) the angle-asymmetric CP-violating difference of yields.
  • Figure 3: The most relevant contributions to the projected (a) $\Delta\Gamma_\text{CP}^{(+)}(s)$ and (b) $\Delta\Gamma_\text{CP}^{(-)}(s)$ distributions. Note the relevance of the $S2$ wave.
  • Figure 4: $B^\pm\to K^\pm\pi^+\pi^-$ CP asymmetry, distributed over the Dalitz plot section $m_{\pi^+\pi^-}^2\leq 1\,\text{GeV}^2$. (a) LHCb binned raw asymmetry ${\cal A}_\text{CP}$, cropped and enlarged from Fig. 3 in Ref. LHCb:2022fpg. (b) ${\cal A}_\text{CP}$ from our analysis.
  • Figure 5: Pulls of our fit, corresponding to the four panels in Fig. \ref{['fig:DeltaK']}.
  • ...and 1 more figures