Dipole polarizabilities of charged pions
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ipole Polarizabilities of Charged Pions1 L. V. Fil’kova, * and V. L. Kashevarova, b a
bInstitut
Lebedev Physical Institute, Moscow, 119991 Russia für Kernphysik, Johannes Gutenberg-Universität Mainz, 55099 Mainz, Germany *e-mail: [email protected]
Abstract—We discuss main experimental works, where dipole polarizabilities of charged pions have been determined. Possible reasons for the differences between the experimental data are discussed. In particular, it is shown that the account of the σ -meson gives a significant correction to the value of the polarizability obtained in the latest experiment of the COMPASS collaboration. DOI: 10.1134/S1063779617010063
1. INTRODUCTION Pion polarizabilities are fundamental structure parameters characterizing the behavior of the pion in an external electromagnetic field. The dipole (α1 and β1) and quadrupole (α 2 and β 2 ) polarizabilities are defined [1, 2] through the expansion of the non-Born helicity amplitudes of the Compton scattering on the pion over t at the fixed s = μ 2 :
M ++ (s = μ , t ) 2 = πμ ⎡2(α1 − β1) + t (α 2 − β 2 )⎤ + 2(t ), ⎢⎣ ⎥ ⎦ 6 . (1) 2 M + (s = μ , t ) = π ⎡2(α1 + β1) + t (α 2 + β 2 )⎤ + 2(t 2 ), ⎥⎦ 6 μ ⎢⎣ where s (t ) is the square of the total energy (momentum transfer) in the γπ center of mass (c.m.) system, μ is the pion mass, α i and β i are electric and magnetic polarizabilities correspondingly. In the following the dipole polarizabilities are given in units 10–4 fm3. The values of the pion polarizabilities are very sensitive to predictions of different theoretical models. Therefore, an accurate experimental determination of these parameters is very important for testing the validity of such models. The most of experimental data obtained for the difference of the dipole polarizabilities of the charged pions are presented in table. The polarizabilities were determined by analyzing the processes of the high energy pions scattering in the Coulomb field of heavy nuclei (π − A → γπ − A ') via the Primakoff effect, radiative pion photoproduction from
proton (γ p → γπ + n), and two-photon production of pion pairs (γγ → ππ) . As seen from table, the data vary from 4 up to 40 and are in conflict even for experiments performed with the same method. In this paper we will consider possible reasons for such disagreements. 2. RADIATIVE PHOTOPRODYCTION OF THE π+-MESON FROM THE PROTON
2
An experiment on the radiative photoproduction π -meson from the proton (γ p → γπ + n) was carried out at the Mainz Microtron MAMI [3] in the kinematical region of 540 < E γ < 820 MeV and +
cm 140 ° ≤ θ cm γγ ≤ 180 °, where θγγ is a polar angle in the c.m. system of the outgoing photon and pion.
The theoretical calculations of the cross section for the reaction γ p → γπ + n show that the contribution of nucleon resonances is suppressed for photons scattered backward in the c.m. system of the reaction γπ → γπ . Moreover, integration over ϕ and θcm γγ essentially decreases the contribution of nucleon resonances from the crossed channels. In addition, the difference (α1 −
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