Students' Talks

STANDARD MODEL TERM PAPERS

Aug-Dec, 2018

Course Instructor: Prof. Aninda Sinha

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BCFW Recursion Relation: Understanding Boundary Contributions

Rhitaja Sengupta

Abstract

The BCFW on-shell recursion relation has made the calculation of tree-level gluon amplitudes in Yang-Mills theory easier and much more transparent. The BCFW recursion can also give insight into the understanding of different quantum field theories by looking at how the amplitudes behave when two of the momenta are taken to infinity in some complex direction, i.e., the boundary contribution. We discuss here the BCFW recursion relation along with the boundary contribution. We outline why in gauge theories the boundary contribution always goes to zero unlike the simpler scalar theories. We then demonstrate the working of the recursion for the case of gluon amplitudes considering both maximally helicity violating (MHV) and next-to-MHV (NMHV) amplitudes. Lastly, we review how to handle the boundary contributions in φ4 theory using the auxiliary field method and in scalar QCD theory.

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BCFW: Extensions and Applications

BCFW in AdS

Ahmadullah Zahed

Abstract

BCFW recursion relation has wider range of applications. Here we have presented extension of BCFW recursion relation for scalar theories. In scalar theories we have to handle the boundary terms carefully. We also see BCFW is a general feature of QFT by extending it in curved space. We have presented here the BCFW recursion relation in AdS for scalar theory.

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Generalized Unitarity

Abhijit Das

Abstract

The unitarity method is discussed which uses the expressibility of One-loop Feynman Integrals in terms of master integrals and the consequent relation between their cuts to evaluate them. Different methods for evaluating cut Feynman diagrams like Leray’s multivariate residues, and use of spinor-helicity formalism to find the coefficients of master integrals is discussed. Finally the generalization of unitary method to generalized unitarity is discussed.

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Scattering Amplitude in Twistor Space and MHV Vertex Expansion

Pronobesh Maity

Abstract

Twistor space structures of tree level Yang Mills amplitudes are surprisingly simple and more string-like, being supported on curves of various degrees. By twistor correspondence, these structures motivate an alternative method (MHV Vertex Expansion) for computing tree amplitides, where vertices are MHV amplitudes, continued off shell in a particular fashion. This formalism leads to new and relatively simple formulas for many amplitudes, which can be verified from their previous evaluations.

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Background Field Methods

Simran Singh

Abstract

Background field method is motivated from considering functional methods. The method is then applied to scalar fields to discuss vacuum stability after SSB. The method is then applied to Gauge fields where gauge invariance is discussed and the Yang-Mills β function is then calculated.

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Topology in Quantum Field Theory

Rishabh Thakkar

Abstract

The existence of non-perturbative and exact solution to some of the non-linear equation of motion gives rise to exciting physics. Here, we look at some of these scenario and try finding solutions that are localised and have finite energy.

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Topological vacua in the (1+1) dimensional Abelian Higgs model

Sipaz Sharma

Abstract

In (1+1) dimensions, the vacuum structure of Abelian Higgs model is different from the (3+1) dimensions' perturbative Higgs vacuum. This difference results because the topological effects associated with the finite Euclidean action solutions (instantons) of the equations of motion come into picture. Homotopic considerations are different in (1+1) dimensions. Features associated with Higgs phenomenon need not be present.

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CP Violation

Mani Chandra Jha

Abstract

CP violation is considered to be one of the main candidates for explaining matter-antimatter asymmetry in the universe. The smallness of the magnitude of the violation relative to what is actually required is one of the most important unsolved problems in Physics. A review of discrete symmetries and of the current understanding of CP violation is given, and two approaches that have been taken to solve the problem are presented. The first one involves modifying the Standard model symmetry group while the second one involves modifying the definition of the discrete symmetries. The successes and limitations of these approaches are elucidated.

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Baryogenesis

A Cosmological Perspective

Pratik Nandy

Abstract

Baryogenesis, the matter-antimatter asymmetry is a fundamental problem in cosmology and particle physics. In this report we address the problem of baryogenesis from cosmological perspective. We first review the early universe cosmology which is essential to understand baryogenesis. We see that standard cosmological model is inefficient to explain the dominace of matter over antimatter. In context of Standard Model we see that baryon number current is anomalous. We discuss Sakharov criteria, which are necessary for baryogenesis. Although Standard Model satisfy all the criteria but it also turns out to be ineffective. This invites us to consider beyond standard model physics. We briefly mention two other process, one is baryogenesis via leptogenesis and Affleck-Dine baryogenesis.

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Baryogenesis

In Electroweak Theory

M.S.A. Alam Khan

Abstract

Baryogenesis is one of the most interesting phenomena behind the existence of everything we see around us. Unfortunately, Standard Model of Particle Physics cannot explain the observed amount of asymmetry between matter and antimatter. In this report, we have tried to understand the phase transition in the electroweak theory and why it fails to reproduce the exact amount of asymmetry.

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Neutrino Oscillations

Abhiram Anand

Abstract

Neutrino oscillation is the phenomenon of change of neutrino flavor during propagation. Neutrino oscillations imply neutrinos are massive. QM and QFT derivations of neutrino oscillations are presented. The correction to this due to background matter is also discussed.

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Physics of Neutrinos

Venkata Lokesh Kumar Y

Abstract

Standard Model of Particle Physics has been successful in predicting many particles W and Z bosons, gluon, top and charm quarks before they were observed. But one of the serious lacking of the model is that it does not allow neutrinos to be massive. In this report we study multiple mechanisms of how neutrinos can acquire mass and how one could extend the Standard Model to accommodate massive neutrinos along with the existing particle content. Further, ways to explain the extremely tiny masses of neutrinos compared to other leptons are considered.

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S-Matrix Bootstrap

Kausik Ghosh

Abstract

This term paper is essentially a brief review of S-matrix bootstrap, a topic which has received a lot of attention in modern research. Since it is a review none of the part of this article is original work and the materials are heavily drawn from arxiv:1607.06110 and arxiv:1708.06765. We first start with numerical approach to S-matrix bootstrap in two dimensions. Then we analyse this case analytically. After discussing few interesting and exciting cases we review another numerical approach to this problem and finally comment briefly on its implementation in higher dimensions. All the figures except fig. 2 (in the report) are taken from arxiv:1607.06110.