Exploring nucleon structure and the proton mass problem through holographic QCD

Understanding the internal structure of the proton—including the distributions of quarks and gluons and their contributions to proton properties such as mass—remains a central challenge in quantum chromodynamics (QCD). While quark generalized parton distributions (GPDs) have been studied extensively, a consistent approach that simultaneously extracts quark parton distribution functions (PDFs), gravitational form factors (GFFs), and gluon GPDs from experimental constraints is still lacking. Moreover, the role of gluons in proton mass generation, particularly through the trace anomaly mechanism, requires deeper theoretical and phenomenological exploration. In this study, we begin by extracting quark GPDs in protons using a parametrization method based on the electromagnetic form factors provided by light-front holographic QCD (LFHQCD), from which we derive both quark PDFs and their GFFs. Our contribution lies in adopting a distinct functional form for <a:math xmlns:a="http://www.w3.org/1998/Math/MathML" display="inline"> <a:mrow> <a:mi>w</a:mi> <a:mo stretchy="false">(</a:mo> <a:mi>x</a:mi> <a:mo>,</a:mo> <a:mi>t</a:mi> <a:mo stretchy="false">)</a:mo> </a:mrow> </a:math> and extending this approach to model gluon GPDs. Our calculations show consistency with experimental data and lattice QCD results and successfully reproduce soft Pomeron behavior. Furthermore, we investigate near-threshold <e:math xmlns:e="http://www.w3.org/1998/Math/MathML" display="inline"> <e:mi>J</e:mi> <e:mo>/</e:mo> <e:mi>ψ</e:mi> </e:math> production using gauge/string duality to quantify the contribution of the trace anomaly to the proton mass. Our results indicate that the parametrization method provides a consistent framework for describing both quark and gluon structure, bridging GPDs, PDFs, and GFFs. The analysis of <g:math xmlns:g="http://www.w3.org/1998/Math/MathML" display="inline"> <g:mi>J</g:mi> <g:mo>/</g:mo> <g:mi>ψ</g:mi> </g:math> production confirms that the trace anomaly contributes significantly ( <i:math xmlns:i="http://www.w3.org/1998/Math/MathML" display="inline"> <i:mo>∼</i:mo> <i:mn>24</i:mn> <i:mo>%</i:mo> </i:math> ) to the proton mass, with the calculated cross-section dependence on momentum transfer <k:math xmlns:k="http://www.w3.org/1998/Math/MathML" display="inline"> <k:mi>t</k:mi> </k:math> in agreement with experimental observations. This work advances the understanding of proton structure by integrating quark and gluon degrees of freedom and elucidating the origin of proton mass within QCD.