Scale of non-locality for a system of $n$ particles

Scalar dark matter (DM) in a theory introduces hierarchy problems, and suffers from the inability to predict the preferred mass range for the DM. In a WIMP-like minimal scalar DM set-up we show that the infinite derivative theory can predict DM mass and its coupling. The scale of non-locality (M) in such a theory in its lower-most limit (constrained by LHC) implies a DM mass $\sim$ TeV and a coupling with the Standard Model (SM) Higgs $\lambda_\mathrm{HS} \sim 10^{-2}$. Plann...

It is possible to formulate theories with many Lee-Wick particles such that a limit exists where the low-energy theory approaches the form of a ghost-free nonlocal theory. Such asymptotically nonlocal quantum field theories have a derived regulator scale that is hierarchically smaller than the lightest Lee-Wick resonance; this has been studied previously in the case of asymptotically nonlocal scalar theories, Abelian and non-Abelian gauge theories, and linearized gravity. Her...

We study a novel class of higher derivative theories for interacting massless gravitons in Minkowski spacetime. These theories were first discussed by Wald decades ago, and are characterized by scattering amplitudes essentially different from general relativity and many of its modifications. We discuss various aspects of these higher derivative theories, including the Lagrangian construction, violation of asymptotic causality, scattering amplitudes, non-renormalization, and p...

In this paper we will consider quantum aspects of a non-local, infinite-derivative scalar field theory - a $\it toy \, model$ depiction of a covariant infinite-derivative, non-local extension of Einstein's general relativity which has previously been shown to be free from ghosts around the Minkowski background. The graviton propagator in this theory gets an exponential suppression making it $\it asymptotically \, free$, thus providing strong prospects of resolving various cla...

We discuss an alternative approach to studying the low energy limit of quantum general relativity. We investigate the low energy limit of a scattering cross-section for two massive scalar particles. Unlike calculations involving the reconstruction of the gravitational potential, our approach avoids ambiguities and is applicable in any frame. Our results are in agreement with both relativistic and non-relativistic calculations. The non-analytic parts of scattering amplitudes t...

In the effective field theory of quantum gravitation coupled to N_s scalars, N_f fermions, and N_V vectors, tree unitarity is violated at an energy squared of E_{CM}^2 = 20(G_N N)^{-1}, where N = {2/3}N_s + N_f + 4N_V and G_N is Newton's constant. This is related to radiative corrections proportional to G_N N E^2 (where E is the typical energy), due to loops of such particles. New physics must enter before E_{CM}=5.6 x 10^{18} GeV in the standard model, and 4.6 x 10^{18} GeV ...

We propose a renormalization scheme for non-local Quantum Field Theories (QFTs) with infinite derivatives inspired by string theory. Our Non-locality Renormalization Scheme (NRS) is inspired by Dimensional Regularization (DR) in local QFTs and is shown to significantly improve the UV behavior of non-local QFTs. We illustrate the scheme using simple examples from the phi3 and phi4 theories, then we evaluate the viability of NRS-enhanced non-local QFTs to solve the hierarchy pr...

In this thesis massive higher derivative gravity theories are analyzed in some detail. One-particle scattering amplitude between two covariantly conserved sources mediated by a graviton exchange is found at tree-level in $D$ dimensional (Anti)-de Sitter and flat spacetimes for the most general quadratic curvature theory augmented with the Pauli-Fierz mass term. From the amplitude expression, the Newtonian potential energies are calculated for various cases. Also, from this am...

A number of gravitation-motivated theories, as well as theories with new coloured fermions predict heavy particle towers with spectral densities $\rho(m^2)$ growing faster than $e^{m}$, a characteristic of nonlocalizable theories. It is shown that if a light scalar, like the Higgs boson, interacts strongly with a heavy scalar particle tower with exponentially rising degeneracy, then the local low-energy theory is equivalent to an effective nonlocal scalar QFT. For energies ap...

Local gravitational theories with more than four derivatives are superrenormalizable, and also may be unitary in the Lee-Wick sense. Thus, it is relevant to study the low-energy properties of these theories, especially to identify observables which might be useful for experimental detection of higher derivatives. Using an analogy with the neutrino Physics, we explore the possibility of a gravitational seesaw mechanism, in which several dimensional parameters of the same order...