Investigation of the chiral anomalyγ→3πin pion pair production by pion in the nuclear Coulomb field

Abstract

The vertex y + 3~ has been investigated in the reaction of pion pair production by pions in the nuclear Coulomb field, rii-+ ( Z , A 1-r-+no+ (2, A ) , in the region of low-invariant-mass r -T O pairs. The experiment has been carried out in the 40-GeV pion beam of the I H E P accelerator (Serpukhov) with the SIGMA spectrometer. We have measured for the first time the cross section of the reaction in the region of momentum transfer squared q 2 < 2 X 1 0 -' (~e V / c )~, U / Z ' = 1.63k0.2310.13 nb, and the y -3 r coupling constant F'"= 12.9k0.9iO. 5 G~V P ' , where the first (second) error is statistical (systematic). The obtained result agrees with the calculations based on the Wess-Zumino-Witten effective Lagrangian. The hypothesis of chiral anomalies and the color-SU(3) quark symmetry are confirmed.

Extracting the chiral anomaly fromγπ→ππ

“…where C r 2 (µ) is an O(p 6 ) low-energy constant (LEC), and Im f (6) 1 (s) denotes the one-loop imaginary part…”

“…Assuming that the amplitude were solely given by Eq. (1), the Primakoff experiment in the threshold region performed at Serpukhov [6] led to F 3π = (12.9 ± 0.9 ± 0.5) GeV −3 , suggesting some tension with the low-energy theorem. Subsequently, it was shown that neither the oneloop [7] and two-loop [8] corrections, nor the inclusion of vector mesons [9] can fully resolve this discrepancy, while a treatment based on dispersion relations was found to suffer from the occurrence of unknown free parameters [10].…”

“…Presently, a Primakoff measurement of γπ − → π − π 0 is being analyzed at COMPASS, with the aim of determining the cross section not only in the low-energy regime as in the Serpukhov experiment [6], but also for centerof-mass energies well beyond, in particular including the peak generated by the ρ(770) resonance [15]. However, the chiral amplitude will only be valid in the low-energy region, so that most of the data would be lost for the anomaly extraction.…”

Electromagnetic corrections toγπ±→π0π±

“…In this section, we discuss electromagnetic effects in f (0) (s, cos θ) and in f (1) (s, cos θ) for the reaction γπ ± → π 0 π ± , which is the channel of interest for the Serpukhov experiment [6], but also for forthcoming experiments [17,18,19]. To this end, we use the formalism of ChPT in the situation where virtual photons are also present [20,21].…”

“…In the Serpukhov experiment [6], the interaction is mediated by a virtual photon with momentum q = p 2 + p 0 − p 1 , whose virtuality is small enough, q 2 max ≤ 2 × 10 −3 GeV 2 ≪ M 2 π , so that it can be considered as a real photon. This experiment measured the total cross-section σ total for the reaction (1.6) on different targets, and with pion pairs produced with a squared invariant mass…”