Finite Temperature Corrections to Dark Matter Annihilation Cross Sections using Thermal Field Theory [HBNI Th272]

Prabhat Butola

dc.contributor.author	Prabhat Butola
dc.date.accessioned	2026-04-02T05:48:20Z
dc.date.available	2026-04-02T05:48:20Z
dc.date.issued	2025
dc.date.submitted	2025-07
dc.identifier.uri	https://dspace.imsc.res.in/xmlui/handle/123456789/913
dc.description.abstract	The finite temperature higher order corrections to the annihilation cross section of Majorana and Dirac type dark matter candidates are presented considering a model in which the dark matter, χ, annihilates to Standard Model fermion pairs via a scalar portal having Yukawa interaction, L ⊃ (λ χPL f − ϕ+ + h.c.). The finite temperature corrections are computed for virtual photon corrections to the cross section for the process χχ → f f at next-to-leading order in the QED coupling constant as well as to real photon emission and absorption process χχ → f f (γ). Techniques of thermal field theory are used in order to calculate these finite temperature corrections. At finite temperature there are no ultraviolet divergences due to the presence of the Bose-Einstein or Fermi-Dirac distribution functions which act as a regulator; however, infra-red and collinear divergences are still present. The generalized technique of Grammer and Yennie is used to factorise the photon propagator into an infra-red-safe and infra-red-divergent part in order to deal with the soft divergences. The cancellation of infra-red divergences among complementary diagrams between the virtual photon correction and real photon correction to the dark matter annihilation process at next-to-leading order (at O(α)) is shown. It is noted that the thermal correction in the virtual case appears due to the finite temperature terms in the photon and fermion propagators whereas the thermal correction in the real photon case appears due to finite temperature terms in the phase space factors. In this study, the mediator scalar is considered to be heavy compared to the dark matter particles and fermions mϕ > mχ ≫ m f. The cross section at both leading and next-to-leading order is found to be helicity suppressed for Majorana dark matter, whereas helicity suppression is lifted for Dirac dark matter. Finally, the dominant thermal corrections to the dark matter annihilation cross section at this order are presented, keeping terms up to quadratic order in fermion mass m²f at O(T²).	en_US
dc.description.tableofcontents	Chapter 1: Introduction and Motivation 1.1 Introduction and Background 1.2 A Brief Introduction to the Standard Model 1.3 A Brief Introduction to Cosmology 1.4 Evidence for Dark Matter 1.4.1 The CMB Power Spectrum 1.4.2 Lyman Alpha and 21 cm Spectral Lines 1.4.3 Evidence from Galaxies and Galaxy Clusters 1.5 Models and Production Mechanisms of Dark Matter 1.5.1 Thermal Production 1.5.2 Non-thermal Production of Dark Matter 1.6 Detection Techniques of Dark Matter 1.6.1 Indirect Detection 1.6.2 Direct Detection 1.6.3 Collider Searches 1.7 Motivation of the Study Chapter 2: Quantum Field Theory at Finite Temperature 2.1 Real-Time Formalism of Thermal Field Theory 2.2 Choice of Contour 2.3 The Scalar Field Thermal Propagator 2.4 Feynman Rules in Thermal Field Theory 2.4.1 Some Identities at Finite Temperature 2.5 Phase Space Integrals Chapter 3: Infra-red Divergences: Grammer and Yennie Technique 3.1 Separation of IR Divergent and IR Safe Parts at T = 0 3.2 The Grammer and Yennie Technique at Finite Temperature 3.2.1 Insertion of Virtual K Photons 3.2.2 Insertion of Real K Photons 3.2.3 The Factorised Cross Section Chapter 4: Virtual Thermal Corrections to Dark Matter Annihilation Cross Section 4.1 The Dark Matter Annihilation Cross Section at Leading Order (LO) 4.1.1 Thermal Corrections to the Cross Section at LO 4.2 Virtual Thermal Corrections to the Cross Section at Next-to-Leading Order (NLO) 4.2.1 NLO Thermal Virtual Contribution from Diagram 1 4.2.2 Thermal Contribution from Diagrams 1–3 4.2.3 Thermal Contribution from Diagrams 4–5 4.2.4 Thermal Contribution from Diagrams 6–7 4.3 Total Thermal NLO Contributions to the Cross Section 4.4 Collinear Divergences 4.5 Additional Virtual Diagrams Chapter 5: Real Photon Thermal Corrections at Next-to-Leading Order 5.1 Real Thermal Corrections to the Cross Section at NLO 5.1.1 Kinematics of χχ → f f (γ) 5.2 Real Photon Matrix Elements 5.2.1 Thermal Photon Contribution and IR Divergences 5.2.2 Virtual–Real Photon Correspondence 5.2.3 Collinear Divergences 5.2.4 Cancellation of Collinear Divergences 5.2.5 Finite Remainder and Real Thermal Photon Cross Section Chapter 6: Conclusions and Outlook Appendix A: Imaginary Time Formalism of Thermal Field Theory A.1 Introduction to Path Integral Formalism A.2 Spectral Function ρ(k₀) A.3 Imaginary-Time Propagator A.4 Time-Ordered Propagator A.5 Finite Temperature Field Theory for Scalar Fields	en_US
dc.publisher.publisher	The Institute of Mathematical Sciences
dc.subject	Thermal Field Theory	en_US
dc.subject	Finite Temperature	en_US
dc.subject	Dark Matter Annihilation	en_US
dc.title	Finite Temperature Corrections to Dark Matter Annihilation Cross Sections using Thermal Field Theory [HBNI Th272]	en_US
dc.type.degree	Ph.D	en_US
dc.type.institution	HBNI	en_US
dc.description.advisor	D. Indumathi
dc.description.pages	163p.	en_US
dc.type.mainsub	Physics	en_US
dc.type.hbnibos	Physical Sciences	en_US