Spectral and chiral properties of hot QCD matter around the crossover and the photon emissivity of the Quark-Gluon Plasma from lattice QCD
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Abstract
In this work, we explore thermal strongly interacting matter across the chiral crossover using the lattice regularization of Quantum Chromodynamics (QCD). While finite temperature is naturally implemented in lattice QCD, the extraction of real-time observables from Monte Carlo data remains a significant challenge.
In the first part, we investigate the properties of the pion quasiparticle along a coarse temperature scan around the finite temperature crossover.
Using simulations with $\mathcal{O}(a)$-improved Wilson quarks and physical up, down and strange quark masses,
we study the properties of thermal QCD matter at the temperatures $T=\{128,154,192\}$\,MeV with a fixed lattice spacing $a=0.064$\,fm and volume $V=(6.1\,\text{fm})^3$.
At low momenta, the dispersion relation of the pion quasiparticle is governed by a \gls{rgi} parameter $u(T)$, which is directly accessible on the lattice from screening quantities. This temperature-dependent parameter plays a dual role: it predicts the modified dispersion relation and relates the (\textit{static}) screening mass to the (\textit{dynamic}) pole mass.
We find that the pion quasiparticle---defined via the low-energy pole of the axial charge two-point function---becomes lighter with increasing temperature. We argue, based on hydrodynamic considerations, that this pole becomes purely diffusive above the chiral crossover.
We further analyze the thermal modifications of the isovector vector and axial-vector spectral functions using the Backus-Gilbert method. The vector channel shows enhancement at low energies and depletion around 1\,GeV,
while the axial-vector channel exhibits a larger enhancement below 1\,GeV.
These findings are consistent with spectral sum rules.
Additionally, we study several chiral symmetry restoration order parameters, with particular focus on the vector–axial-vector correlator difference, which is phenomenologically relevant and found to be suppressed by over an order of magnitude at the crossover.
The second part of this thesis addresses the photon emissivity of the quark-gluon plasma (QGP). Estimating the full energy-differential photon emissivity from lattice QCD requires solving a numerically ill-posed inverse problem. However, energy-integrated quantities---such as energy moments---can be accessed without this inversion by evaluating spatially transverse Euclidean correlators $H_E(\omega_n)$ at imaginary spatial momenta.
We compute the first energy moment $H_E(\omega_1)$ of the thermal electromagnetic spectral function $\sigma_{\text{em}}(\omega)$ across the same three $N_{\mathrm{f}} = 2+1$ ensembles used in the pion study. Our results indicate that $H_E(\omega_1)$ already reaches values typical of the high-temperature phase near the chiral crossover, suggesting substantial photon emission in the late stages of heavy-ion collisions (HICs).
Apart from this, we examine the first two energy-moments, this time at a fixed temperature in the chirally restored phase using three $N_{\mathrm{f}}=2$ ensembles with lattice spacings in the range of $0.033-0.049$\,fm. Utilizing stochastic momentum wall sources, we improve statistical precision on the relevant correlators by a factor of up to $\approx 40$ compared to our previous analysis using point sources. This allows for a controlled continuum extrapolation of the first two energy moments and a detailed assessment of systematic uncertainties related to large source-sink separations.
Our result for the difference of these two moments---sensitive to photon energies $\omega\gtrsim \pi T$---is below, but compatible with, the value obtained from integrating the leading-order weak-coupling photon spectrum.
These findings contribute to the ongoing effort to resolve the \textit{direct photon puzzle} in HIC phenomenology, where current models struggle to simultaneously account for both photon yield and azimuthal anisotropy.
Finally, we take a first look at the challenging third Matsubara sector and provide a conservative upper bound on the third energy-moment.