[Paper Review] CP violation induced by the interference of scalar and vector resonances in three-body decays of bottom mesons

Zhen-Hua Zhang, Xin‐Heng Guo+1 more|arXiv (Cornell University)|Aug 23, 2013

Particle physics theoretical and experimental studies3 citations

TL;DR

This paper proposes a mechanism for large, localized CP violation in three-body decays of bottom mesons via interference between scalar (f₀(500)) and vector (ρ⁰(770)) resonances. The model explains the LHCb observation of CP asymmetry >30% in B±→K±π+π− when m(π+π−)≈f₀(500), with the asymmetry depending on the relative strong phase δ̃, which must lie between 200° and 249° to match data.

ABSTRACT

Large CP violation is an interesting phenomenon both theoretically and experimentally. Last year, LHCb Collaboration found in some three-body decays of bottom mesons that large CP violations appear in regions of the Dalitz plots that are not dominated by contributions from narrow resonances. In this paper, we present a mechanism which can induce such kind of large CP violations. In this mechanism, large localized CP asymmetries in phase space can be induced by the interference of two intermediate resonances with different spins. We also apply this mechanism to the decay channel $B^\pm o K^\pm π^+π^-$.

Motivation & Objective

• To explain the large, localized CP asymmetries observed by LHCb in B±→K±π+π− decays, particularly in regions not dominated by narrow resonances.
• To investigate whether interference between scalar and vector resonances can generate significant CP violation in three-body B meson decays.
• To determine the required strong phase between interfering amplitudes to reproduce experimental CP asymmetry data in the K±π± system.
• To simplify the theoretical description by reducing free parameters compared to previous models of similar decays.

Proposed method

• Uses a general amplitude expansion in Legendre polynomials in the invariant mass squared of the final-state particles, with coefficients depending on the spin of intermediate resonances.
• Models the decay amplitude as a sum of contributions from two resonances with different spins (J=0 and J=1), leading to interference terms that can induce CP violation.
• Applies the formalism to B±→K±π+π−, focusing on the region where m(π+π−)≈f₀(500), treating ρ⁰(770) and f₀(500) as the dominant intermediate states.
• Parametrizes the amplitude using form factors and a single free parameter—the relative strong phase δ̃—to minimize model complexity.
• Compares theoretical differential CP asymmetry as a function of g(sK±π±) with LHCb data, using the monopole approximation for form factors.
• Fixes form factors at zero recoil (F₁(B→K)(0)=0.35, A₀(B→ρ)(0)=0.28, F₀(B→f₀)(0)=0.3) and assumes pole masses around 5–6 GeV.

Experimental results

Research questions

• RQ1 Can interference between scalar and vector resonances explain the large, localized CP asymmetries observed in B±→K±π+π− by LHCb?
• RQ2 What is the required range of the relative strong phase δ̃ between the f₀(500) and ρ⁰(770) amplitudes to reproduce the experimental CP asymmetry data?
• RQ3 How does the CP asymmetry vary with the invariant mass of the K±π∓ system when m(π+π−) is near f₀(500)?
• RQ4 Why is the CP asymmetry large only in specific regions of the Dalitz plot, and not in others, despite the absence of dominant narrow resonances?
• RQ5 Can a simplified model with only one free parameter (δ̃) successfully describe the observed CP asymmetry pattern in this decay?

Key findings

• The interference between f₀(500) and ρ⁰(770) resonances can generate large, localized CP asymmetries in the Dalitz plot of B±→K±π+π−, even without dominant narrow resonances.
• The differential CP asymmetry becomes large (exceeding 30%) when g(sK±π∓) > 0.5, corresponding to low invariant masses of the K±π∓ system.
• The CP asymmetry is small when g(sK±π∓) < 0, corresponding to high invariant masses of the K±π∓ system, matching the LHCb observation of near-zero asymmetry in that region.
• The relative strong phase δ̃ must lie between 200° and 249° to reproduce the experimental data, with δ̃=220° providing a good fit to the asymmetry pattern.
• The model reduces the number of free parameters to one (δ̃), making it significantly simpler than previous models for similar decays.
• The theoretical prediction for the CP asymmetry as a function of g(sK±π∓) shows a clear transition from small to large asymmetry, consistent with the LHCb data.