We investigate the partonic structure of the <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>ρ</mi></math> meson, the lightest spin-1 vector meson, within the light-front quark model (LFQM). To explore the sensitivity to model assumptions, we employ two distinct types of spin wave functions in the LFQM. Using light-front helicity wave functions, we derive explicit expressions for the leading-twist and subleading-twist quark parton distribution functions (PDFs), and evolve the leading-twist PDFs to higher scales with next-to-leading order (NLO) Dokshitzer-Gribov-Lipatov-Altarelli-Parisi (DGLAP) evolution. We have also calculated the Mellin moment from the evolved PDFs using a simple neural network frame and compared with available theoretical predictions. Furthermore, we compute the full set of nine leading-twist transverse-momentum-dependent distributions (TMDs) for the valence quark in the <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>ρ</mi></math> meson, including three tensor TMDs that arise from spin-1 tensor polarization of the hadron. Positivity constraints for the PDFs and TMDs are examined within this framework. Our findings highlight the crucial role of tensor polarization in shaping the three-dimensional partonic structure of vector mesons.

India

Satyajit Puhan

Russia

Shubham Sharma

Narinder Kumar

Harleen Dahiya

Valence quark distribution of the rho meson using a light-front quark model

We have studied the chiral-odd generalized parton distributions (GPDs) for the octet baryons within the framework of diquark spectator model, emphasizing the difference arising from different quark flavors of proton <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>p</mi></math> and light hyperons <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msup><mi mathvariant="normal">Σ</mi><mo>+</mo></msup></math> and <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msup><mi mathvariant="normal">Ξ</mi><mn>0</mn></msup></math>. The equation of quark-quark correlator for the tensor current has been solved to investigate the transversely polarized quark dynamics using light-cone wave functions. In the forward limit, transversity distributions of all the constituent quark flavors of proton, <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msup><mi mathvariant="normal">Σ</mi><mo>+</mo></msup></math> and <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msup><mi mathvariant="normal">Ξ</mi><mn>0</mn></msup></math>, have been studied. Additionally, the first moment of GPD <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi>H</mi><mi>T</mi></msub></math> and the combination of GPDs <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi>E</mi><mi>T</mi></msub></math> and <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mover accent="true"><mi>H</mi><mo stretchy="false">˜</mo></mover><mi>T</mi></msub></math> have also been investigated. Our results are comparable with other available model predictions and lattice data for the proton. Furthermore, we have presented a comparative analysis of tensor charges and anomalous tensor magnetic moments for all the constituent quark flavors of the considered baryons, comparing them with available data obtained from different approaches.

Navpreet Kaur

Chiral-odd generalized parton distributions for the low-lying octet baryons

We investigate the properties of pseudoscalar <italic>D</italic> and vector <inline-formula><tex-math id='TM0004' notation='LaTeX'>$D^{*}$</tex-math></inline-formula> mesons in an isospin asymmetric nuclear medium using a hybrid approach that integrates the light-front quark model with the chiral SU(3) quark mean-field model. The influence of the isospin asymmetric nuclear medium is examined by utilizing the in-medium quark masses derived from the chiral SU(3) quark mean-field model as an input in the light-front quark model to study the medium modification of <italic>D</italic> mesons. We examine the impact of isospin asymmetry and baryon density at zero and finite temperature on the effective masses, weak decay constants, and distribution amplitudes of the pseudoscalar mesons <inline-formula><tex-math id='TM0006' notation='LaTeX'>$D^0$</tex-math></inline-formula>, <inline-formula><tex-math id='TM0007' notation='LaTeX'>$D^+$</tex-math></inline-formula>, <inline-formula><tex-math id='TM0008' notation='LaTeX'>$D_s$</tex-math></inline-formula>, and the vector mesons <inline-formula><tex-math id='TM0009' notation='LaTeX'>$D^{0*}$</tex-math></inline-formula>, <inline-formula><tex-math id='TM0010' notation='LaTeX'>$D^{+*}$</tex-math></inline-formula>, and <inline-formula><tex-math id='TM0011' notation='LaTeX'>$D_s^{*}$</tex-math></inline-formula>. Our results indicate significant medium-induced changes for pseudoscalar <italic>D</italic> and vector <inline-formula><tex-math id='TM0013' notation='LaTeX'>$D^{*}$</tex-math></inline-formula> mesons with <inline-formula><tex-math id='TM0014' notation='LaTeX'>$u/d$</tex-math></inline-formula> as one of their constituent quarks, while a comparatively reduced effect is observed for mesons containing a strange quark. In contrast to temperature and isospin asymmetry, changes in the baryon density of the nuclear medium have a larger effect on different properties of <italic>D</italic> and <inline-formula><tex-math id='TM0016' notation='LaTeX'>$D^{*}$</tex-math></inline-formula> mesons.

Anshu Gautam

Dhananjay Singh

Suneel Dutt

Arvind Kumar

<italic>D</italic> and <italic>D*</italic> Mesons in an Isospin Asymmetric Nuclear Medium

In this work, we have investigated the valence quark structure through chiral-even vector quark generalized parton distributions (GPDs) of light <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>ρ</mi></math> and heavy <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>J</mi><mo>/</mo><mi>ψ</mi></math> vector mesons using the light-cone quark model. By solving the quark-quark correlator, we have represented the quark GPDs in the light-front wave function (LFWFs) form. The charge, magnetic, and quadrupole form factors of these particles have been derived from the vector quark GPDs and compared with available theoretical predictions and lattice simulation data. The structure functions corresponding to the Rosenbluth scattering cross section of these mesons have also been calculated and compared with available NJL model predictions. All the results of our calculations are found to follow a similar trend to other model results. We have also calculated the parton distribution functions (PDFs) of these particles in the forward limit of GPDs. The calculated PDFs have also been evolved to <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mrow><mn>5</mn><mtext> </mtext><mtext> </mtext><msup><mrow><mi>GeV</mi></mrow><mrow><mn>2</mn></mrow></msup></mrow></math> through next to next to leading order Dokshitzer-Gribov-Lipatov-Altarelli-Parisi (DGLAP) evolutions.

 Tanisha

Anurag Yadav

Valence quark distribution of light <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>ρ</mi></math> and heavy <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>J</mi><mo>/</mo><mi>ψ</mi></math> vector mesons in a light-cone quark model

We investigate the internal structure of the pion using generalized transverse momentum-dependent parton distributions (GTMDs) within the light-cone quark model. By solving the quark–quark correlator, we derive the twist-2, 3, and 4 quark GTMDs in terms of light-front wave functions. Out of the 16 possible GTMDs, 12 are found to be nonzero. Furthermore, we extract the valence quark transverse momentum-dependent parton distributions and generalized parton distributions from their corresponding GTMDs. Additionally, we compute the valence quark electromagnetic form factors and parton distribution functions up to twist-4. The elastic charge radius of the pion is determined to be 0.558 fm. Our results exhibit a qualitative agreement with predictions from other theoretical models like the Nambu–Jona-Lasinio model, light-front holographic model, and spectator model at the leading twist. This study provides a comprehensive insight into the internal structure of the pion.

Understanding the Valence Quark Structure of the Pion through Generalized Transverse Momentum-Dependent Parton Distributions

We calculate the possible scalar, vector, and tensor form factors (FFs) for pion and kaon in the light-cone quark model (LCQM). These FFs are calculated from the leading and subleading twist generalized parton distribution functions (GPDs) of the pion and kaon. The vector and tensor FFs correspond to twist-2 GPDs, whereas the scalar FFs correspond to twist-3 scalar GPDs. We calculate the FFs from the GPDs quark-quark correlator and express them in the form of light-front wave functions. The behavior of these FFs was found to be in agreement with experimental data, other model predictions, and lattice simulation results. We have also calculated the charge radii corresponding to different FFs and compared them with other models, lattice simulation results, and experimental data. The scalar radii of the pion and kaon of our model are found to be 0.528 and 0.409 fm, respectively.

Scalar, vector, and tensor form factors of pion and kaon

We calculate the valence quark generalized parton distributions (GPDs) of the lightest pseudoscalar meson, pion, in an isospin asymmetric nuclear matter at zero temperature by employing a light-cone quark model. The medium modifications in the unpolarized GPDs have been incorporated by taking inputs from the chiral SU(3) quark mean field model. The electromagnetic form factors (EMFFs) and charge radii have been calculated for both the vacuum and in-medium cases. These results are found to be in agreement with the available experimental data and other model predictions.

Effect of nuclear medium on the spatial distribution of pions

This work primarily focuses on determining the magnetic moments of <inline-formula><tex-math id='TM0002' notation='LaTeX'>$\frac{1}{2}^-$</tex-math></inline-formula> baryon resonances in the presence of hot and dense hadronic matter. In the chiral <inline-formula><tex-math id='TM0003' notation='LaTeX'>$SU(3)$</tex-math></inline-formula> quark mean field model approach, we have essentially accounted for the effects on in-medium scalar meson fields to investigate the impact of high densities on the in-medium baryon masses and their constituent quarks. In light of the chiral constituent quark model <inline-formula><tex-math id='TM0004' notation='LaTeX'>$\chi$</tex-math></inline-formula>CQM, we have calculated the magnetic moments of <inline-formula><tex-math id='TM0005' notation='LaTeX'>$\frac{1}{2}^-$</tex-math></inline-formula> baryon resonances and scrutinized the effects due to its internal constituents: the valence quarks, sea quarks, and the orbital moment of sea quarks. Furthermore, we have investigated the effective baryonic magnetic moments for the finite magnitudes of isospin asymmetry and strangeness fraction.

Abhinaba Upadhyay

Magnetic Moments of ½ &#8211; Baryon Resonances in Strange Hadronic Matter at High Densities

The role of asymmetric nuclear medium on the properties of kaon is investigated at zero and finite temperature employing a hybrid approach integrating the light cone quark model and the chiral SU(3) quark mean field model. The in-medium quark masses are calculated within the chiral SU(3) quark mean field model and are used as inputs to study the medium modifications in the kaon properties. In particular, we have analyzed the impact of baryonic density, isospin asymmetry, and temperature on the weak decay constant, distribution amplitudes, and parton distribution functions (PDFs) of valence quarks of kaon. The effects of isospin asymmetry on the kaon doublet <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mrow><mi>K</mi><mo>=</mo><mrow><mo stretchy="false">(</mo><mfrac linethickness="0"><mrow><msup><mrow><mi>K</mi></mrow><mrow><mo>+</mo></mrow></msup></mrow><mrow><msup><mrow><mi>K</mi></mrow><mrow><mn>0</mn></mrow></msup></mrow></mfrac><mo stretchy="false">)</mo></mrow></mrow></math> and antikaon doublet <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mrow><mover accent="true"><mrow><mi>K</mi></mrow><mrow><mo stretchy="false">¯</mo></mrow></mover><mo>=</mo><mo stretchy="false">(</mo><msup><mrow><mi>K</mi></mrow><mrow><mo>−</mo></mrow></msup><mo>,</mo><msup><mrow><mover accent="true"><mrow><mi>K</mi></mrow><mrow><mo stretchy="false">¯</mo></mrow></mover></mrow><mrow><mn>0</mn></mrow></msup><mo stretchy="false">)</mo></mrow></math> are also studied. In order to compare with future experiments, we have also evolved the in-medium PDFs of kaons to <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msup><mi>Q</mi><mn>2</mn></msup><mo>=</mo><mn>16</mn><mtext> </mtext><mtext> </mtext><msup><mrow><mi>GeV</mi></mrow><mrow><mn>2</mn></mrow></msup></math>. As compared to the temperature and isospin asymmetry, change in baryonic density of the nuclear medium makes more significant changes to the distribution amplitudes and PDFs of kaons.

Manpreet Kaur

Effect of an asymmetric nuclear medium on the valence quark structure of the kaons

We investigated the ground state (1S), radially excited states (2S) and (3S), and orbitally excited state (1P) for the heavy charmonia (  $ c \bar c $  ) and bottomonia (  $ c \bar c $  ) mesons in the light-front quark model (LFQM). The light-front wave functions have been successful in explaining various physical properties of meson states in the past, especially for the 1S and 2S states. However, the radially excited state 3S and orbitally excited state 1P have rarely been investigated. In this study, we considered these two excited states and investigated the electromagnetic form factors (EMFFs), charge radii, decay constants, parton distribution functions (PDFs), and the distribution amplitudes (DAs) for the quarkonia system. For the sake of completeness, we also studied the ground and the first excited states of quarkonia mesons. We also illustrated the 3D wave functions for the radially excited states to study their nodal structures.