Mirko Serino

The two point correlation function of the stress-energy-momentum tensor describes the propagation of a space-time "micro-earthquake" in the vacuum. In the framework of the path integral formulation of field theory in curved space-time, we derive the Ward-Takashi identity for two-point Green's function of the stress-energy-momentum tensor for a general case of a non-conformal theory. The identity constrains the longitudinal part of the correlator, with the vacuum expectation value of the stress-energy-momentum, non-zero in a non-conformal theory. The obtained formula is demonstrated on the free massive Dirac fermion theory, treated at the one-loop level. This example befits a class of phenomenological chiral quarks models which have been used successfully in numerous applications in the soft non-perturbative regime of strong interactions. We discuss the constraints following from the Ward-Takahashi identity for the correlation functions in these models. We also show how the temporal representation of the two-point correlators, which is an object amenable to lattice QCD, displays an expected exponential fall-off.

We present an explicit momentum space computation of the four-point function of the energy-momentum tensor in 4 spacetime dimensions for the free and conformally invariant theory of a scalar field. The result is obtained by explicit evaluation of the Feynman diagrams by tensor reduction. We work by embedding the scalar field theory in a gravitational background consistently with conformal invariance in order to derive all the terms the correlator consists of and all the Ward identities implied by the requirements of general covariance and anomalous Weyl symmetry. We test all these identities numerically in several kinematic configurations. Mathematica notebooks detailing the step-by-step computation are made publicly available through a GitHub repository. To the best of our knowledge, this is the first explicit result for the four-point correlation function of the energy-momentum tensor in a conformal and non supersymmetric field theory which is readily numerically evaluable in any kinematic configuration.

We present an explicit momentum space computation of the four-point function of the energy-momentum tensor in 4 spacetime dimensions for the free and conformally invariant theory of a scalar field. The result is obtained by explicit evaluation of the Feynman diagrams by tensor reduction. We work by embedding the scalar field theory in a gravitational background consistently with conformal invariance in order to derive all the terms the correlator consists of and all the Ward identities implied by the requirements of general covariance and anomalous Weyl symmetry. We test all these identities numerically in several kinematic configurations. Mathematica notebooks detailing the step-by-step computation are made publicly available through a GitHub repository (https://github.com/mirkos86/4-EMT-correlation-function-in-a-4d-CFT.). To the best of our knowledge, this is the first explicit result for the four-point correlation function of the energy-momentum tensor in a conformal and non supersymmetric field theory which is readily numerically evaluable in any kinematic configuration.

We calculate the transverse momentum dependent gluon-to-gluon splitting function within

A new calculation using off-shell matrix elements with TMD parton densities supplemented with a newly developed initial state TMD parton shower is describe