arXiv subjects

Avijit Sen Majumder

Publications and source records attributed to Avijit Sen Majumder.

4 recordsLinked to original sources

arXiv2026

Effect of $ξRϕ^2$ non-minimal coupling on gravitational light bending

We investigate the bending of massless fields by a massive object in the presence of a curvature-scalar $\sqrt{-g}ξR ϕ^2$ non-minimal coupling up to one loop, using the perturbative quantum gravity computations. It is well known that without such coupling a self interacting scalar field theory cannot be renormalised in the presence of gravity. The massive object is modelled by a massive scalar $ϕ$, and it is assumed to be non-relativistic, e.g., a star. We compute the 2-2 scattering of massless scalar and photons off this object via graviton exchanges. Assuming both $ξ$ and the bending angle to be small, we use the eikonal approximation to compute the angle up to ${\cal O}(ξG^2)$. At tree level $({\cal O}(ξG))$ we find no bending, and hence the ${\cal O}(ξG^2)$ result happens to be leading in this case. The non-minimal vertices are qualitatively different from that of the standard minimal ones, e.g. $ \sqrt{G} h_{μν} T^{μν}$, as the former contains explicit momenta of the gravitons instead of the scalar, complementing the second. The bending angle is found to behave like $\sim b^{-7}$, where $b$ is the impact parameter. We have emphasised the qualitative differences of our results from that of the well studied minimal case.

hep-th↗

arXiv2026

Scattering of massive spin-2 field via graviton exchanges with different spin fields and the long range gravitational potential

In this work, we compute the graviton mediated scattering amplitude of a massive spin-2 Fierz-Pauli field with various other massive spin fields, and in the non-relativistic limit, find out the corresponding two-body gravitational potentials. The massive spin-2 field does not represent gravity here. The theory of gravity is taken to be the usual massless general relativity, and the massive spin-2 field is taken as a test quantum field coupled to gravity via the standard minimal prescription. We first compute the tree level 2-2 scattering of a massive spin-2 field with massive scalar, spin-1, and spin-1/2 fields with one graviton exchanges. Leading Newton potential, as well as the subleading spin or polarisation dependent terms at ${\cal O}(G)$ have been computed. We also consider the next to the leading order (${\cal O}(G^2)$) scattering of the massive spin-2 field with a massive scalar, and demonstrate the spin independent, spherically symmetric leading part of the two body gravitational potential. The present paper can be considered as an attempt to compute the gravitational potential in the context of a higher spin field theory.

hep-th↗

arXiv2026

$ξRϕ^2$ non-minimal coupling, and the long range gravitational potential for different spin fields from 2-2 scattering amplitudes

In this paper we investigate the long range gravitational effect of curvature-scalar field non-minimal coupling, in the form of $ξR ϕ^2$, in the perturbative quantum gravity framework. Such coupling is most naturally motivated from the renormalisation of a scalar field theory with a quartic self interaction in a curved spacetime background. This coupling results in two scalar-$n$ graviton vertices which contain no explicit momenta of the scalar, qualitatively different from the usual, e.g. $κh^{μν}T_{μν}$-type minimal matter-graviton vertices. Assuming the dimensionless coupling parameter $ξ$ to be small, we compute the 2-2 scattering Feynman amplitudes between such scalars up to ${\cal O}(G^2 ξ)$. From the non-relativistic limit of these amplitudes, we compute the corresponding long range gravitational potential. There exists no tree level contribution $({\cal O}(ξG))$ here, and hence the one loop ${\cal O}(G^2 ξ)$ result is leading. Recently, the effect of a cosmological constant in such non-minimal interaction and the subsequent gravitational potential was computed. In this work we take the cosmological constant to be vanishing. The resulting potential is found to have $r^{-4}$ leading behaviour. We further extend these results for scalar-massive spin-1 and massive spin-1/2 scattering. Spin and polarisation dependence of the two body potential have been explicitly demonstrated. We discuss some possible physical implications of these results.

hep-th↗

arXiv2026

$ξR ϕ^2$ coupling, cosmological constant and quantum gravitational correction to Newton's potential

This letter investigates the contribution of the $\sqrt{-g}ξRϕ^2$ interaction to the long range gravitational potential for massive scalar fields, from the non-relativistic limit of the 2-2 scattering amplitude with graviton exchanges. Such coupling is naturally motivated from the renormalisation of a scalar field theory with quartic self interaction in a curved spacetime. This is qualitatively different from the minimal ones like $ \sqrt{G} h^{μν}T_{μν}$, as the vertices corresponding to the former do not explicitly contain any scalar momenta, but instead explicitly contains the momentum carried by graviton line. For the minimal vertex, the long range gravitational potential up to one loop $({\cal O}(G), {\cal O}(G^2))$ was obtained earlier from the terms non-analytic in the transfer momentum, $q^{-2},\ q^{-1},\ \ln q^2 $, yielding potentials respectively like $r^{-1}$, $r^{-2}$, $r^{-3}$. However owing to the aforesaid explicit appearance of transfer momentum for the non-minimal vertices, the leading contribution in this case comes at ${\cal O}(ξG^2)$, and turns out to be subleading compared to even $r^{-3}$. To complement this `screening' effect, we consider the three graviton vertex generated by the $\sim Λ\sqrt{-g}/G$ term in the action, where $Λ$ is the cosmological constant. This vertex does not explicitly contain any graviton momentum. With this vertex, and assuming short scale scattering much small compared to the Hubble horizon, we compute the seagull, the vacuum polarisation and the fish diagrams and obtain the 2-2 scattering amplitudes. The leading gravitational potential at ${\cal O}(ξΛG^2 )$ behaves like $ r^{-1}$, even though it is much subleading compared to Newton's potential due to the appearance of $Λ$. We also discuss the scenario where this potential dominates the aforesaid ${\cal O}(ξG^2)$ one.

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