Valence quark distribution of the pion inside a medium with finite baryon density: A Nambu--Jona-Lasinio model approach

TL;DR

This work develops a hybrid light-cone quark model–Nambu–Jona-Lasinio approach to study the valence structure of the pion in a medium with finite baryon density. By obtaining density-dependent constituent quark masses from the NJL gap equation and encoding them into the pion's light-cone wave function, the authors compute in-medium DA, EMFF, and PDF, then evolve PDFs to a perturbative scale using NLO DGLAP. Key findings include a decreasing $m^*$ with density, a flattened DA and reduced decay constant, suppressed EMFF at intermediate $Q^2$, and a shift of the PDF to higher longitudinal momentum fractions, with Mellin moments showing minor density dependence. The results illuminate the separation between non-perturbative medium effects and perturbative evolution and provide benchmarks against experimental and lattice data for pion structure in nuclear matter.

Abstract

We calculate the in-medium valence quark distribution of the pion immersed in a finite baryon density using the light-cone quark model. The medium-modified pion properties are obtained by using the constituent quark mass-dependent light cone wave functions. To obtain the constituent quark masses at finite baryon density, we employ the two-flavor Nambu--Jona-Lasinio model. We primarily focus on the in-medium electromagnetic form factor, distribution amplitude, and the parton distribution function of the pion. The parton distribution functions are also evolved from the model scale to a perturbative scale using next to leading order Dokshitzer-Gribov-Lipatov-Altarelli-Parisi evolution equations. Furthermore, our calculated form factors are compared with available experimental measurements and lattice quantum chromodynamics studies. We also examine the Mellin moments derived from our parton distribution functions in comparison with existing extractions and theoretical model predictions.

Figures (6)

• Figure 1: The constituent quark mass has been plotted as a function of baryonic density $\rho_B/\rho_0$.
• Figure 2: (Color online) The DA has been plotted with respect to baryonic density up to $\rho_B/\rho_0=1$ in the interval of $0.25$ in Fig. (a) and up to baryonic density $\rho_B/\rho_0=4$ in the interval of $1$ in Fig. (b). In Fig. (c), we have plotted the ratio of the in-medium decay constant and the vacuum decay constant with respect to the baryonic density $\rho_B/\rho_0$. Here all the results are at model scale, i.e, 0.20 GeV$^2$.
• Figure 3: (Color online) The electro-magnetic form factor of pion has been plotted with respect to $Q^2$ GeV$^2$ at different baryonic densities up to $\rho_B/\rho_0=1$ in Fig. (a) and (b). Both the in-medium and vacuum FFs have been compared with available vacuum experimental data NA7:1986vavJeffersonLabFpi:2007virJeffersonLabFpi-2:2006yshJeffersonLabFpi:2000nlcDally:1982zk in Fig. (c) along with lattice simulations QCDSFUKQCD:2006gmgDing:2024lfj in Fig. (d) and (e).
• Figure 4: (Color online) (Color online) The pion FFs have been plotted with respect to $Q^2$ GeV$^2$ at different baryonic densities up to $\rho_B/\rho_0=4$ in Fig. (a) and (b). Both the in-medium and vacuum FFs have been compared with available vacuum experimental data NA7:1986vavJeffersonLabFpi:2007virJeffersonLabFpi-2:2006yshJeffersonLabFpi:2000nlcDally:1982zk in Fig. (c) along with lattice simulations QCDSFUKQCD:2006gmgDing:2024lfj in Fig. (d) and (e). Fig. (f) shows the variation of the in-medium pion charge radius along with the squared charge radius with respect to the baryonic density $\rho_B/\rho_0$.
• Figure 5: (Color online) The unpolarized pion PDFs $f_1(x)$ have been plotted at different baryonic densities with respect to $x$ in Fig. (a) and (b) at the model scale. In Fig. (c), we have plotted the in-medium evolved PDFs at 25 $GeV^2$ using the NLO DGLAP equation.