Radiative resonance couplings in γπ→ππ

Abstract

Studies of the reaction γπ → ππ, in the context of the ongoing Primakoff program of the COM-PASS experiment at CERN, give access to the radiative couplings of the ρ(770) and ρ3(1690) resonances. We provide a vector-meson-dominance estimate of the respective radiative width of the ρ3, Γρ 3 →πγ = 48(18) keV, as well as its impact on the F -wave in γπ → ππ. For the ρ(770), we establish the formalism necessary to extract its radiative coupling directly from the residue of the resonance pole by analytic continuation of the γπ → ππ amplitude to the second Riemann sheet, without any reference to the vector-meson-dominance hypothesis.

Three-pion contribution to hadronic vacuum polarization

“…There is little phenomenological information on the ρ 3 πγ * coupling besides the ρ 3 → πω branching ratio. However, the fact that the corresponding ω-dominance estimate from [51] is in line with preliminary results from COMPASS [103] suggests that at least within [0, M 2 ω ] the q 2 -dependence should be approximately described by a(q 2 ). Here, we estimate a potential F -wave contribution by assuming that this approximation remains meaningful up to q 2 = 1.8 GeV.…”

“…where the coupling constants are set to the values from [51]. Numerically, we find that the interference between P -and F -waves gives a correction around 1% at q 2 = 1.8 GeV, while the pure F -wave contribution is suppressed by another two orders of magnitude.…”

“…with derivatives of the Legendre polynomials P ′ l (z s ). Since higher partial waves are completely irrelevant below the ρ 3 (1690) resonance [3,51] (see App. B for an estimate of the F -wave contribution), the discontinuity equation reduces to…”

“…Here, we extend this strategy to the 3π channel, which produces both the secondlargest contribution to the total HVP value and its uncertainty. Instead of the pion vector form factor, the underlying hadronic amplitude becomes γ * → 3π, which was studied in detail in the context of the pion-pole contribution to HLbL scattering [17,18,[48][49][50][51] and further emerges in the two-pion contributions via the left-hand cut in γ * γ * → ππ [52][53][54][55][56]. For an isoscalar-photon virtuality q 2 = M 2 ω , M 2 φ , this amplitude is directly related to the three-particle decays of ω and φ, and indeed the KT approach can be generalized to obtain a dispersive representation of the e + e − → 3π cross section, see Sect.…”

Resonances from lattice QCD

“…Given the important role played in the low-energy manifestation of QCD, it should not come as a surprised that this reaction plays an important role in a variety of processes, ranging from the chiral anomaly to the anomalous magnetic moment of the muon (see Refs. [87,88] for recent phenomenological studies of this amplitude).…”