Proof of dispersion relations for the amplitude in theories with a compactified space dimension
- PDF / 393,114 Bytes
- 29 Pages / 595.276 x 841.89 pts (A4) Page_size
- 2 Downloads / 149 Views
Springer
Received: April 2, Revised: May 21, Accepted: June 3, Published: June 23,
2020 2020 2020 2020
Jnanadeva Maharana1 Institute of Physics, Bhubaneswar 751005, India Max-Planck Institute for Gravitational Physics, Albert Einstein Institute, Golm, Germany
E-mail: [email protected] Abstract: The analyticity properties of the scattering amplitude in the nonforward direction are investigated for a field theory in the manifold R3,1 ⊗ S 1 . The theory is obtained from a massive, neutral scalar field theory of mass m0 defined in flat five dimensional spacetime upon compactification on a circle, S 1 . The resulting theory is endowed with a massive scalar field which has the lowest mass, m0 , as of the original five dimensional theory and a tower of massive Kaluza-Klein states. We derive nonforward dispersion relations for scattering of the excited Kaluza-Klein states in the Lehmann-Symanzik-Zimmermann formulation of the theory. In order to accomplish this object, first we generalize the JostLehmann-Dyson theorem for a relativistic field theory with a compact spatial dimension. Next, we show the existence of the Lehmann-Martin ellipse inside which the partial wave expansion converges. The scattering amplitude satisfies fixed-t dispersion relations when |t| lies within the Lehmann-Martin ellipse. Keywords: Field Theories in Higher Dimensions, Large Extra Dimensions ArXiv ePrint: 2003.14330
1
Adjunct Professor, NISER, Bhubaneswar.
c The Authors. Open Access, Article funded by SCOAP3 .
https://doi.org/10.1007/JHEP06(2020)139
JHEP06(2020)139
Proof of dispersion relations for the amplitude in theories with a compactified space dimension
Contents 1 Introduction
1
4 4 6 11
3 Nonforward elastic scatting of n 6= 0 Kaluza-Klein states
13
4 Asymptotic behavior of the amplitude
20
5 Summary and discussions
24
1
Introduction
This article is a continuation of our investigation of the analyticity properties of scattering amplitude in scalar field theory defined in a manifold R3,1 ⊗ S 1 . First we consider a neutral, massive scalar field theory of mass m0 in a flat five dimensional Minkowski space. Subsequently, one spatial coordinate is compactified on a circle of radius R. The spectrum of the resulting theory consists of a neutral scalar of mass m0 (same as the mass of the original uncompactified theory) and a tower of massive Kaluza-Klein (KK) states carrying the KK charges. We adopt the Lehmann-Symanzik-Zimmermann (LSZ) [1] formalism to construct the amplitude and to study the analyticity property of the scattering amplitude. We had proved the forward dispersion relation for scattering of KK states in an earlier paper [2] (henceforth referred to as I). The present investigation brings our programme to a completion. The analyticity properties of scattering amplitude plays a very important role in our understanding of collisions of relativistic particle in the frame works of general field theories without appealing to any specific model. The scattering amplitude, F (s, t), is an analytic function of the cen
Data Loading...
