Abstract
We analyze the zero point energy of composite particles (or resonances) which are dynamically created from relativistic fermions. We compare the zero point energies in medium to the vacuum one, taking into account the medium modification of the constituent particles. Treating composite particles as if quasi-particles, their zero point energies contain the quadratic and logarithmic UV divergences even after the vacuum subtraction. The coefficients of these divergences come from the difference between the vacuum and in-medium fermion propagators. We argue that such apparent divergences can be cancelled by consistently using fermion propagators to compute the quasi-particle contributions as well as their interplay, provided that the self-energies of the constituents at large momenta approach to the vacuum ones sufficiently fast. In the case of quantum chromodynamics, mesons and baryons, which may be induced or destroyed by medium effects, yield the in-medium divergences in the zero point energies, but the divergences are assembled to cancel with those from the quark zero-point energy. This is particularly important for unified descriptions of hadronic and quark matter which may be smoothly connected by the quark-hadron continuity.
Highlights
Correlated systems of fermions typically develop composite objects or collective modes [1,2,3]
To handle the UV divergences associated with the composite particles, it is most essential to take into account the interplay between the composites and their constituents
We have investigated the UV divergences in the zeropoint energy of composite particles that are associated with the change of fermion bases
Summary
Correlated systems of fermions typically develop composite objects or collective modes [1,2,3]. Another problem is that, going from zero to high fermion density, composite states may not keep the one-to-one correspondence to their vacuum counterparts, e.g., some composite states in vacuum might disappear in medium This mismatch in the d.o.f. likely leaves the mismatch in the UV contributions which in turn appear as the UV divergences in equations of state. In order to make the zero point energy UV finite, we demand: (i) all vacuum n-point functions are made finite in some way; (ii) the fermion self-energies approach the universal limit sufficiently fast at high energy With these conditions the quadratic divergences in the zero-point energy cancel, as we can see from the general structure of the 2PI functional. The momenta pμ 1⁄4 ðp0 − iμ; pjÞ will be used
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