Looking for chiral anomaly in pion photoproduction on kaons
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oking for Chiral Anomaly in Pion Photoproduction on Kaons1 M. I. Vysotskya, b, c and E. V. Zhemchugova, c, * a
b
Alikhanov Institute for Theoretical and Experimental Physics, Moscow, 117218 Russia Moscow Institute of Physics and Technology, Dolgoprudny, Moscow oblast, 141700 Russia c Moscow Engineering Physics Institute, Moscow, 115409 Russia *e-mail: [email protected]
Abstract⎯In an experiment currently being performed at the Institute for High Energy Physics, Serpukhov, Russia, a beam of charged kaons is directed on a copper target. In the electromagnetic field of the target nuclei, two reactions occur: K + γ → K + π 0 and K + γ → K 0 π + . A peculiar distinction between these two reactions is that there is a chiral anomaly contribution in the former reaction, but not in the latter. This contribution can be directly seen through comparison of the cross sections of these reactions near the threshold. In Ref. [1] expressions for these cross sections are derived taking into account the anomaly and the contribution of the lightest vector mesons. In this talk an overview of the derivation is provided and cross sections numerical values near the threshold are presented. DOI: 10.1134/S1063779617060600
1. INTRODUCTION An experiment is currently being performed at the Institute for High-Energy Physics at Serpukhov, Russia, in which a beam of charged kaons with the energy of 17 . 7 GeV is scattered by a copper target [2]. Two reactions occur in the electromagnetic field of copper nuclei: K + γ → K + π 0 and K + γ → K 0π + . A theoretical prediction of the results of the experiment is the subject of [1]. This experiment is in a way a continuation of a similar experiment performed earlier at the same facility [3]. Then a beam of charged pions with the energy of 40 GeV was directed at various targets, and cross section of the π − γ → π − π 0 reaction near the threshold was measured. From the theoretical point of view both experiments are interesting because they allow for observation of the chiral anomaly. 2. PIONS Let us consider first what research has been done in the case of pions. Let
A(π − γ → π −π 0 ) = h(s, t, u)ε μαβγ Aμ∂ α π −∂ βπ +∂ γ π 0 (1) be the amplitude of the π − γ → π − π 0 reaction, where h(s, t, u) is some function of Mandelstam variables. At
s = t = u = 0 , in the absence of the chiral anomaly, h(0) ≡ h(0, 0, 0) = 0 . However, through the connection of (1) to the π 0 → γγ amplitude it was obtained in [4, 5] that h(0) ≡ h(0, 0, 0) =
e = 9 . 8 GeV −3, 4π 2Fπ3
where Fπ = 92 . 2 MeV is the π → ν decay constant. This expression is also contained in the Wess–Zumino anomalous lagrangian term [6], and it can be calculated from diagrams like the one in Fig. 1. The fact that h(0) ≠ 0 is the manifestation of the chiral anomaly. The value h(0) cannot be directly measured in an experiment, because no experiment can measure an amplitude at s = t = u = 0 . However, h(s, t, u) can be measured near the threshold and then extrapolated to the point s = t = u = 0 with the help of some phenomenological model. Using
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