Photon emissivity of the quark-gluon plasma: a lattice QCD analysis of the transverse channel

We present results for the thermal photon emissivity of the quark-gluon plasma derived from spatially transverse vector correlators computed in lattice QCD at a temperature of 250 MeV. The analysis of the spectral functions, performed at fixed spatial momentum, is based on continuum-extrapolated correlators obtained with two flavors of dynamical Wilson fermions. We compare the next-to-leading-order perturbative QCD correlators, as well as the <math display="inline"><mrow><mi mathvariant="script">N</mi><mo>=</mo><mn>4</mn></mrow></math> supersymmetric Yang-Mills correlators at infinite coupling, to the correlators from lattice QCD and find them to lie within <math display="inline"><mo>∼</mo><mn>10</mn><mo>%</mo></math> of each other. We then refine the comparison, performing it at the level of filtered spectral functions obtained model-independently via the Backus-Gilbert method. Motivated by these studies, for frequencies <math display="inline"><mi>ω</mi><mo>≲</mo><mn>2.5</mn><mtext> </mtext><mtext> </mtext><mi>GeV</mi></math> we use fit Ansätze to the spectral functions that perform well when applied to mock data generated from the NLO QCD or from the strongly coupled SYM spectral functions, while the high-frequency part, <math display="inline"><mi>ω</mi><mo>≳</mo><mn>2.5</mn><mtext> </mtext><mtext> </mtext><mi>GeV</mi></math>, is matched to NLO QCD. We compare our results for the photon emissivity to our previous analysis of a different vector channel at the same temperature. We obtain the most stringent constraint at photon momenta around <math display="inline"><mi>k</mi><mo>≃</mo><mn>0.8</mn><mtext> </mtext><mtext> </mtext><mi>GeV</mi></math>, for which we find a differential photon emission rate per unit volume of <math display="inline"><mi mathvariant="normal">d</mi><msub><mi mathvariant="normal">Γ</mi><mi>γ</mi></msub><mo>/</mo><msup><mi mathvariant="normal">d</mi><mn>3</mn></msup><mi>k</mi><mo>=</mo><mo stretchy="false">(</mo><msub><mi>α</mi><mrow><mi>em</mi></mrow></msub><mo>/</mo><mo stretchy="false">(</mo><mi>exp</mi><mo stretchy="false">(</mo><mi>k</mi><mo>/</mo><mi>T</mi><mo stretchy="false">)</mo><mo>-</mo><mn>1</mn><mo stretchy="false">)</mo><mo stretchy="false">)</mo><mo>×</mo><mo stretchy="false">(</mo><mn>2.2</mn><mo>±</mo><mn>0.8</mn><mo stretchy="false">)</mo><mo>×</mo><msup><mn>10</mn><mrow><mo>-</mo><mn>3</mn></mrow></msup><mtext> </mtext><mtext> </mtext><mi>GeV</mi></math>.