In-Medium Pion Valence Distribution Amplitude

Abstract

After a brief review of the quark-based model for nuclear matter, and some pion properties in medium presented in our previous works, we report new results for the pion valence wave function as well as the valence distribution amplitude in medium, which are presented in our recent article. We find that both the in-medium pion valence distribution and the in-medium pion valence wave function, are substantially modified at normal nuclear matter density, due to the reduction in the pion decay constant.Keywords In-medium pion properties · Form Factors · Distribution Amplitude IntroductionOne of the most exciting and challenging topics in hadronic physics is to study the modifications of hadron properties in nuclear medium, and to study how such modifications give impact on observables in medium. Since hadrons are composed of quarks, antiquarks and gluons, one can naturally expect that hadron internal structure would change when they are immersed in nuclear medium [1; 2; 3; 4; 5]. This question, becomes particularly interesting when it comes to that of pion. To be able to answer it, one first needs, simpler, effective quark-antiquark models of pion, which are successful in describing its properties in vacuum. Among such models, light-front constituent quark model has been very successful in describing the electromagnetic form factors, electromagnetic radii and decay constants of pion and kaon [6; 7; 8; 9; 10; 11]. Recent advances in experiments, indeed suggest to make it possible to access to the pion properties in a nuclear medium [3; 4; 5; 12; 13].Among the all hadrons, pion is the lightest, and it is believed as a Nambu-Goldstone boson, which is realized in nature emerged by the spontaneous breaking of chiral symmetry. This Nambu-Goldstone boson, pion, plays very important and special roles in hadronic and nuclear physics. However, because of its special properties, particularly the unusually light mass, it is not easy to describe the pion properties in medium as well as in vacuum based on naive quark models, even though such models can be successful in describing the other hadrons.Recently, we studied the properties of pion in nuclear medium [12; 13; 14], namely, the electromagnetic form factor, charge radius and weak decay constant, distribution amplitude (DA) by using a Below, we first briefly review the QMC model, the quark-based model of nuclear matter, to study the pion properties in medium. The QMC model was invented by Guichon [15] to describe the nuclear matter based on the quark degrees of freedom. The self-consistent exchange of the scalar-isoscalar σ and vector-isoscalar ω mean fields coupled directly to the relativistic confined quarks, are the key and novelty for the new saturation mechanism of nuclear matter. The model was extended to finite nuclei [16], and has successfully been applied for various nuclear and hadronic phenomena [3].The effective Lagrangian density for a uniform, spin-saturated, and isospin-symmetric nuclear system (symmetric nuclear matter) at the hadronic level is given...

Valence-quark distributions of pions and kaons in a nuclear medium

“…Recently, the electromagnetic form factors of pions and kaons [24,33] as well as meson distribution amplitudes [34] in a nuclear medium were studied by combining the lightfront constituent quark model and the quark-meson coupling (QMC) model. In these publications, the QMC model was used to provide the in-medium light-quark properties, which were then used as inputs for studying the medium modifications of meson properties.…”

Study of the in-medium nucleon electromagnetic form factors using a light-front nucleon wave function combined with the quark-meson coupling model

“…[28] to be enhanced in medium contrary to the proton case, and demonstrate that our model result indeed agrees with the prediction. A similar approach as in the present study was already applied for the study of pion properties in symmetric nuclear matter [29][30][31][32]. Although there may be possible to have alternative explanations based on traditional nuclear physics approaches, our interest of this study is on the internal structure change of nucleon in a nuclear medium.…”

“…To be consistent and encouraged by the studies for the pion properties in a nuclear medium [29][30][31][32], we build the nuclear matter with the same u and d constituent quark mass Fig. 6 with m q = 220 MeV, it also decreases faster than that for m q = 5 MeV [4] as increasing nuclear matter density.…”

“…GeV from the fit to the nucleon magnetic moments and mean-square charge radii [33]. (We note that the same value of the up and down quark constituent mass m q = 0.22 GeV was also used for the studies of pion properties in vacuum [45], as well as in medium [29][30][31][32]. )…”

“…In the numerical evaluation of the form factors, we use a constituent quark mass value of m q = 0.22 GeV [33,58] as mentioned. This value was also used in the study of pion properties in vacuum as well as in medium [29][30][31][32] with a light-front constituent quark model. In addition, the model has three fitting parameters, the momentum scales β and β 1 , and the relative weight λ, or M H (see Eqs.…”