Nonperturbative photon qq¯ light front wave functions from a contact interaction model

We propose a method to calculate the <a:math xmlns:a="http://www.w3.org/1998/Math/MathML" display="inline"><a:mi>q</a:mi><a:mover accent="true"><a:mi>q</a:mi><a:mo stretchy="false">¯</a:mo></a:mover></a:math> light front wave functions (LFWFs) of photons at low virtuality, i.e., the light front amplitude of <e:math xmlns:e="http://www.w3.org/1998/Math/MathML" display="inline"><e:msup><e:mi>γ</e:mi><e:mo>*</e:mo></e:msup><e:mo stretchy="false">→</e:mo><e:mi>q</e:mi><e:mover accent="true"><e:mi>q</e:mi><e:mo stretchy="false">¯</e:mo></e:mover></e:math> at low <j:math xmlns:j="http://www.w3.org/1998/Math/MathML" display="inline"><j:msup><j:mi>Q</j:mi><j:mn>2</j:mn></j:msup></j:math>, based on a light front projection approach. We exemplify this method using a contact interaction model within Dyson-Schwinger equations formalism and obtain the nonperturbative photon <l:math xmlns:l="http://www.w3.org/1998/Math/MathML" display="inline"><l:mi>q</l:mi><l:mover accent="true"><l:mi>q</l:mi><l:mo stretchy="false">¯</l:mo></l:mover></l:math> LFWFs. In this case, we find the nonperturbative effects are encoded in the enhanced quark mass and a dressing function of covariant quark-photon vertex, as compared to the leading order quantum electrodynamics photon <p:math xmlns:p="http://www.w3.org/1998/Math/MathML" display="inline"><p:mi>q</p:mi><p:mover accent="true"><p:mi>q</p:mi><p:mo stretchy="false">¯</p:mo></p:mover></p:math> LFWFs. We then use nonperturbative-effect modified photon <t:math xmlns:t="http://www.w3.org/1998/Math/MathML" display="inline"><t:mi>q</t:mi><t:mover accent="true"><t:mi>q</t:mi><t:mo stretchy="false">¯</t:mo></t:mover></t:math> LFWFs to study the inclusive deep inelastic scattering HERA data in the framework of the color dipole model. The results demonstrate that the theoretical description of data at low <x:math xmlns:x="http://www.w3.org/1998/Math/MathML" display="inline"><x:msup><x:mi>Q</x:mi><x:mn>2</x:mn></x:msup></x:math> can be significantly improved once the nonperturbative corrections are included in the photon LFWFs. Published by the American Physical Society 2024