Electromagnetic form factors of the pion and kaon from the instanton vacuum

Abstract

We investigate the pion and kaon ( þ , K þ , K 0 ) electromagnetic form factors in the spacelike region: Q 2 & 1 GeV, based on the gauged low-energy effective chiral action from the instanton vacuum in the large N c limit. Explicit flavor SU(3) symmetry breaking is taken into account. The nonlocal contributions turn out to be crucial to reproduce the experimental data. While the pion electromagnetic form factor is in good agreement with the data, the kaon one seems underestimated. We also calculate the electromagnetic charge radii for the pion and kaon: hr 2 i þ ¼ 0:455 fm 2 , hr 2 i K þ ¼ 0:534 fm 2 , and hr 2 i K 0 ¼ À0:060 fm 2 without any adjustable free parameter except for the average instanton size and interinstanton distance, and they are compatible with the experimental data.

Fragmentation functions and parton distribution functions for the pion with the nonlocal interactions

“…This model is motivated from the dilute instanton liquid model [40][41][42][43][44]. We note that, to date, various nonperturbative QCD properties have been well studied in terms of the instanton vacuum configuration and the results are comparable with experiments and LQCD simulations [45][46][47][48]. In that model, nonperturbative QCD effects are deciphered by the nontrivial quark-instanton interactions in the dilute instanton ensemble.…”

“…The reason for this discrepancy can be understood as follows: Within NLChQM (and also the instanton model), the value of F π turns out to be about 20% smaller than its empirical value, if the mass-derivative terms, i.e. ∂M k /∂|k|, are ignored [40][41][42][43][44][45][46][47][48]. Note that these terms are originated by considering the (axial) vector current conservation for the relevant hadronic matrix elements [41,57,58].…”

“…p T = 0. Note that the value of M 0 can be fixed self-consistently within the instanton model [40][41][42][43][44][45][46][47][48] with the phenomenological (anti)instanton parametersρ ≈ 1/3 fm andR ≈ 1 fm, resulting in M 0 ≈ 350 MeV by the following self-consistent equation, defined in Euclidean (E) space:…”

“…It is worth mentioning that, NLChQM have successfully produced results for various nonperturbative QCD quantities which are in agreement with experiments as well as lattice QCD (LQCD) simulations. [45][46][47][48][49][50].…”

QCD topological susceptibility from the nonlocal chiral quark model

“…Furthermore, we observe that χ t < χ QL t in general in according to Eq. (32). It means that the dynamical quark contributions reduce the topological susceptibility by (10 ∼ 20) % within NLχQM.…”