Infrared finiteness of a complete theory of charged scalars and fermions at finite temperature
- PDF / 1,371,628 Bytes
- 33 Pages / 595.276 x 790.866 pts Page_size
- 23 Downloads / 173 Views
Regular Article - Theoretical Physics
Infrared finiteness of a complete theory of charged scalars and fermions at finite temperature Pritam Sen1,2,a , D. Indumathi1,2,b , Debajyoti Choudhury3,c 1
The Institute of Mathematical Sciences, Chennai, India Homi Bhabha National Institute, Mumbai, India 3 Department of Physics and Astrophysics, University of Delhi, Delhi 110 007, India
2
Received: 20 December 2018 / Accepted: 26 September 2020 © The Author(s) 2020
Abstract It is known that the infrared (IR) divergences accruing from pure fermion–photon interactions at finite temperature cancel to all orders in perturbation theory. The corresponding infrared finiteness of scalar thermal QED has also been established recently. Here, we study the IR behaviour, at finite temperature, of theories where charged scalars and fermions interact with neutrals that could potentially be dark matter candidates. Such thermal field theories contain both linear and sub-leading logarithmic divergences. We prove that the theory is IR-finite to all orders in perturbation, with the divergences cancelling order by order between virtual and real photon corrections, when both absorption and emission of photons from and into the heat bath are taken into account. The calculation follows closely the technique used by Grammer and Yennie for zero temperature field theory. The result is generic and applicable to a variety of models, independent of the specific form of the neutral-fermion–scalar interaction vertex.
1 Introduction We are interested here in addressing the infrared (IR) behaviour of theories with both charged scalars and fermions, interacting with neutral singlets or doublets, at finite temperature. The study is motivated by simple models of dark matter (DM), described by a Lagrangian density of the type [1], 1 1 / − m f f + χ i ∂/ − m χ χ Fμν F μν + f i D 4 2 † + Dμφ Dμ φ − m 2φ φ † φ + λ χ PL f − φ + + h.c. . (1)
L=−
a e-mail:
[email protected]
b e-mail:
[email protected] (corresponding author)
c e-mail:
[email protected]
0123456789().: V,-vol
This is an extension of the Standard Model (SM), containing a charged lepton f , with an additional charged scalar φ + , along with the SU (2) × U (1) singlet neutral Majorana fermion χ which is usually the dark matter candidate. Note that we have written only the part of the lagrangian that is relevant to our analysis, suppressing the rest. For example, if f is part of the usual left-handed doublet, then so must φ + be. Similarly, we could have f to be a quark field, with φ now being a charged colored scalar. However, this would necessitate the discussion of QCD interactions, which, while being analogous to the electromagnetic interactions, is associated with additional computational complexity that is not germane to the issue at hand. It might seem that the Lagrangian of Eq. 1 is too specific and too simplistic a choice. However, not only is it a perfectly viable stand-alone model by itself (modulo the rest of the SM fields), but it also captures t
Data Loading...
