Pseudoscalar meson transition form factors in nonperturbative QCD approach

Abstract

In this communication we discuss few topics related with modern experimental data on the physics of light pseudoscalar mesons. It includes the contribution of the pseudoscalar mesons to the muon anomalous magnetic moment (AMM), g − 2, the rare decays of light pseudoscalar mesons to lepton pair, the transition form factors of pseudoscalar mesons at large momentum transfer, the pion transversity form factor.Measuring the muon anomalous magnetic moment g −2 and the rare decays of light pseudoscalar mesons into lepton pair P → l + l − serve as important test of the standard model. To reduce the theoretical uncertainty in the standard model predictions the data on the transition form factors of light pseudoscalar mesons play significant role. Recently new data on behavior of these form factors at large momentum transfer was supplied by the BABAR collaboration. Within the nonlocal chiral quark model it shown how to describe these data and how the meson distribution amplitude evolves as a function of the dynamical quark masses and meson masses.

Limit on the pion distribution amplitude

“…Let us find the small x behavior of φ π x ( ) by using the Schwinger representation (12). We also make the following approximation for the denominators of the integrand Similarly we obtain the Laplace transform of the factor Σ ( ) ( ) Next we substitute these expressions in (12) keeping in mind that we are interested in the → x 0 behavior.…”

“…Some papers claim that other transition form factors of heavier mesons are compatible among themselves and with the saturation required by factorization theorems obtained from pQCD [13,22]. However, for heavier mesons than the pion the DA may be more peaked away from the end points [12]. A common statement in all papers is the need for more data to settle this problem.…”

“…As a consequence of these experiments there were many theoretical papers speculating why the data should (or not) obey the BL limit [9][10][11][12][13][14][15][16][17][18][19]. The first attempt to explain the BaBar result can be found in [20].…”

Exclusive production of pions and the pion distribution amplitude

“…These experiments originated several theoretical papers speculating why the data should (or not) obey the BL limit [5][6][7][8][9][10][11][12][13][14][15]. Some of these and recent proposals also claimed that the pion distribution amplitude (DA) at high momentum transfer was not given by the asymptotic form [16] ϕ as…”

“…but should be replaced by a broad concave distribution [17,18] or a flatter one [5,6,8,12,[19][20][21][22]. Available information indicates that the above asymptotic distribution is a poor approximation to the pion distribution amplitude even at large momentum scales [17].…”