Non-Abelian Electric Field Correlator at NLO for Dark Matter Relic Abundance and Quarkonium Transport

Abstract

We perform a complete next-to-leading order calculation of the non-Abelian electric field correlator in a SU(N c ) plasma, which encodes properties of the plasma relevant for heavy particle bound state formation and dissociation. The calculation is carried out in the real-time formalism of thermal field theory and includes both vacuum and finite temperature contributions. By working in the R ξ gauge, we explicitly show the results are gauge independent, infrared and collinear safe. The previous results on the renormalization of the electric field correlator are also confirmed. Our next-to-leading order calculation can be directly applied to any dipole singlet-adjoint transition of heavy particle pairs. For example, it can be used to describe dissociation and (re)generation of heavy quarkonia inside the quark-gluon plasma well below the melting temperature, as well as heavy dark matter pairs (or charged co-annihilating partners) in the early universe.

Quarkonium Suppression in the Open Quantum System Approach

“…I reviewed recent progress in applying the open quantum system framework to study quarkonium dynamics inside the QGP, with a focus on the QGP correlators of the chromoelectric fields that enter the Lindblad equations in both the quantum Brownian motion and the quantum optical limits. The same framework has also been applied to study Dark Matter bound state formation in the coannihilation scenario in the early universe [26]. Some problems of jet quenching in heavy ion collisions have also been studied in the open quantum system framework [31][32][33].…”

“…In the dynamics of open heavy quarks, the heavy quark carries color all the way, so the Wilson lines extend to both positive and negative infinite times. Perturbative calculations [26,29] showed that these two correlators agree in the temperature dependent part but differ by a finite constant at next-to-leading order. See also the discussions in Ref.…”

“…The KMS relation was first proved in Ref. [26] by using the parity and time-reversal transformations and assuming the density matrix of the QGP at thermal equilibrium is invariant under these transformations.…”

Impact of bound states on non-thermal dark matter production

“…This does not only make the mediator long-lived compared to the Hubble time around the cosmological production of χ but also implies a long lifetime in the lab today. The expected decay length in the lab is given by ∆x Γ t βγc (22) where γ is the Lorentz factor and β the velocity of the decaying particle in natural units. We have checked that for the values of λ χ preferred by freeze-in and with a realistic distribution of γ factors ∆x ≥ 100 m throughout the considered parameter space.…”

“…However, aside from the abundant production at colliders, the SM gauge interactions also give rise to large non-perturbative corrections to the annihilation rates of the mediators in the early Universe. While these effects have been investigated in DM freezeout before [16][17][18][19][20][21][22][23], they have not been considered in the context of non-thermal production and it is not clear how large their impact on the cosmologically preferred parameter space is.…”