Constraints on kinetic mixing of dark photons from dilepton spectra

Dark photons, the hypothetical gauge bosons associated with an additional <a:math xmlns:a="http://www.w3.org/1998/Math/MathML"> <a:mrow> <a:mi>U</a:mi> <a:msup> <a:mrow> <a:mo>(</a:mo> <a:mn>1</a:mn> <a:mo>)</a:mo> </a:mrow> <a:mo>′</a:mo> </a:msup> </a:mrow> </a:math> symmetry, can couple to standard model particles through a small kinetic mixing parameter <b:math xmlns:b="http://www.w3.org/1998/Math/MathML"> <b:mi>ɛ</b:mi> </b:math> with the ordinary photon. This mechanism provides a portal between the dark sector and visible matter. In this study, we present a procedure to derive theoretical upper bounds on the kinetic mixing parameter <c:math xmlns:c="http://www.w3.org/1998/Math/MathML"> <c:mrow> <c:msup> <c:mi>ɛ</c:mi> <c:mn>2</c:mn> </c:msup> <c:mrow> <c:mo>(</c:mo> <c:msub> <c:mi>M</c:mi> <c:mi>U</c:mi> </c:msub> <c:mo>)</c:mo> </c:mrow> </c:mrow> </c:math> by analyzing dilepton spectra from heavy-ion collisions across a broad energy range, from SIS to LHC energies. Our analysis is based on the microscopic parton-hadron-string dynamics (PHSD) transport approach, which successfully reproduces the measured dilepton spectra in <d:math xmlns:d="http://www.w3.org/1998/Math/MathML"> <d:mrow> <d:mi>p</d:mi> <d:mo>+</d:mo> <d:mi>p</d:mi> </d:mrow> <d:mo>,</d:mo> <d:mo> </d:mo> <d:mrow> <d:mi>p</d:mi> <d:mo>+</d:mo> <d:mi>A</d:mi> </d:mrow> </d:math> , and <e:math xmlns:e="http://www.w3.org/1998/Math/MathML"> <e:mrow> <e:mi>A</e:mi> <e:mo>+</e:mo> <e:mi>A</e:mi> </e:mrow> </e:math> collisions across the same energy range. Besides the dilepton channels resulting from interactions and decays of standard model particles (such as mesons and baryons), the PHSD has been extended to include the decay of hypothetical dark photons into dileptons, <f:math xmlns:f="http://www.w3.org/1998/Math/MathML"> <f:mrow> <f:mi>U</f:mi> <f:mo>→</f:mo> <f:msup> <f:mi>e</f:mi> <f:mo>+</f:mo> </f:msup> <f:msup> <f:mi>e</f:mi> <f:mo>−</f:mo> </f:msup> </f:mrow> </f:math> . The production of these dark photons occurs via Dalitz decays of <g:math xmlns:g="http://www.w3.org/1998/Math/MathML"> <g:msup> <g:mi>π</g:mi> <g:mn>0</g:mn> </g:msup> <g:mo>,</g:mo> <g:mo> </g:mo> <g:mi>η</g:mi> <g:mo>,</g:mo> <g:mo> </g:mo> <g:mi>ω</g:mi> <g:mo>,</g:mo> <g:mo> </g:mo> <g:msup> <g:mi>η</g:mi> <g:mo>′</g:mo> </g:msup> </g:math> , and <h:math xmlns:h="http://www.w3.org/1998/Math/MathML"> <h:mi mathvariant="normal">Δ</h:mi> </h:math> resonances; direct decays of <j:math xmlns:j="http://www.w3.org/1998/Math/MathML"> <j:mi>ρ</j:mi> <j:mo>,</j:mo> <j:mo> </j:mo> <j:mi>ω</j:mi> </j:math> , and <k:math xmlns:k="http://www.w3.org/1998/Math/MathML"> <k:mi>ϕ</k:mi> </k:math> ; the kaon mode <l:math xmlns:l="http://www.w3.org/1998/Math/MathML"> <l:mrow> <l:msup> <l:mi>K</l:mi> <l:mo>+</l:mo> </l:msup> <l:mo>→</l:mo> <l:msup> <l:mi>π</l:mi> <l:mo>+</l:mo> </l:msup> <l:mi>U</l:mi> </l:mrow> </l:math> ; and thermal <m:math xmlns:m="http://www.w3.org/1998/Math/MathML"> <m:mrow> <m:mi>q</m:mi> <m:mover accent="true"> <m:mi>q</m:mi> <m:mo>¯</m:mo> </m:mover> </m:mrow> </m:math> annihilation in the quark-gluon plasma. Our results show that high-precision measurements of dilepton spectra in heavy-ion collisions provide a sensitive and competitive probe of dark photons in the MeV to multi-GeV mass range. Furthermore, we quantify the experimental accuracy required to constrain the remaining viable parameter space of kinetic mixing in dark photon scenarios.