Mirko Serino

Graviton vertices and the mapping of anomalous correlators to momentum space for a general conformal field theory

A bstractWe investigate the mapping of conformal correlators and of their anomalies from configuration to momentum space for general dimensions, focusing on the anomalous correlators TOO, TVV — involving the energy-momentum tensor (T) with a vector (V) or a scalar operator (O) — and the 3-graviton vertex TTT. We compute the TOO, TVV and TTT one-loop vertex functions in dimensional regularization for free field theories involving conformal scalar, fermion and vector fields. Since there are only one or two independent tensor structures solving all the conformal Ward identities for the TOO or TVV vertex functions respectively, and three independent tensor structures for the TTT vertex, and the coefficients of these tensors are known for free fields, it is possible to identify the corresponding tensors in momentum space from the computation of the correlators for free fields. This works in general d dimensions for TOO and TVV correlators, but only in 4 dimensions for TTT, since vector fields are conformal only in d = 4. In this way the general solution of the Ward identities including anomalous ones for these correlators in (Euclidean) position space, found by Osborn and Petkou is mapped to the ordinary diagrammatic one in momentum space. We give simplified expressions of all these correlators in configuration space which are explicitly Fourier integrable and provide a diagrammatic interpretation of all the contact terms arising when two or more of the points coincide. We discuss how the anomalies arise in each approach. We then outline a general algorithm for mapping correlators from position to momentum space, and illustrate its application in the case of the VVV and TOO vertices. The method implements an intermediate regularization — similar to differential regularization — for the identification of the integrands in momentum space, and one extra regulator. The relation between the ordinary Feynman expansion and the logarithmic one generated by this approach are briefly discussed.

Gravity and the neutral currents: Effective interactions from the trace anomaly

We present a complete study of the one graviton-two neutral gauge bosons vertex at 1-loop level in the electroweak theory. This vertex provides the leading contribution to the interaction between the Standard Model and gravity, mediated by the trace anomaly, at first order in the inverse Planck mass and at second order in the electroweak expansion. At the same time, these corrections are significant for precision studies of models with low scale gravity at the LHC. We show, in analogy with previous results in the QED and QCD cases, that the anomalous interaction between gravity and the gauge current of the Standard Model, due to the trace anomaly, is mediated, in each gauge invariant sector, by effective massless scalar degrees of freedom. We derive the Ward and Slavnov-Taylor identities characterizing the vertex. Our analysis includes the contributions from the improvements of the scalar sector, induced by a conformally coupled Higgs sector in curved space.

Dilaton interactions and the anomalous breaking of scale invariance of the Standard Model

A bstractWe discuss the main features of dilaton interactions for fundamental and effective dilaton fields. In particular, we elaborate on the various ways in which dilatons can couple to the Standard Model and on the role played by the conformal anomaly as a way to characterize their interactions. In the case of a dilaton derived from a metric compactification (graviscalar), we present the structure of the radiative corrections to its decay into two photons, a photon and a Z, two Z gauge bosons and two gluons, together with their renormalization properties. We prove that, in the electroweak sector, the renormalization of the theory is guaranteed only if the Higgs is conformally coupled. For such a dilaton, its coupling to the trace anomaly is quite general, and determines, for instance, an enhancement of its decay rates into two photons and two gluons. We then turn our attention to theories containing a non-gravitational (effective) dilaton, which, in our perturbative analysis, manifests as a pseudo-Nambu Goldstone mode of the dilatation current (JD). The infrared coupling of such a state to the two-photons and to the two-gluons sector, and the corresponding anomaly enhancements of its decay rates in these channels, is critically analyzed.

BCFW recursion for TMD parton scattering

A bstractWe investigate the application of the BCFW recursion relation to scattering amplitudes with one off-shell particle in a Yang-Mills theory with fermions. We provide a set of conditions of applicability of the BCFW recursion, stressing some important differences with respect to the pure on-shell case. We show how the formulas for Maximally-Helicity-Violating (MHV) configurations with any number of partons, which are well known in the fully on-shell case, are generalized to this kinematic regime. We also derive analytic expressions for all the helicity configurations of the 5-point color-stripped tree-level amplitudes for any of the partons being off the mass shell.

Solving the conformal constraints for scalar operators in momentum space and the evaluation of Feynman’s master integrals

A bstractWe investigate the structure of the constraints on three-point correlation functions emerging when conformal invariance is imposed in momentum space and in arbitrary space-time dimensions, presenting a derivation of their solutions for arbitrary scalar operators. We show that the differential equations generated by the requirement of symmetry under special conformal transformations coincide with those satisfied by generalized hyper-geometric functions (Appell’s functions). Combined with the position space expression of this correlator, whose Fourier transform is given by a family of generalized Feynman (master) integrals, the method allows to derive the expression of such integrals in a completely independent way, bypassing the use of Mellin-Barnes techniques, which have been used in the past. The application of the special conformal constraints generates a new recursion relation for this family of integrals.

Four-jet production in single- and double-parton scattering within high-energy factorization

A bstractWe perform a first study of 4-jet production in a complete high-energy factorization (HEF) framework. We include and discuss contributions from both single-parton scattering (SPS) and double-parton scattering (DPS). The calculations are performed for kinematical situations relevant for two experimental measurements (ATLAS and CMS) at the LHC. We compare our results to those reported by the ATLAS and CMS collaborations for different sets of kinematical cuts. The results of the HEF approach are compared with their counterparts for collinear factorization. For symmetric cuts the DPS HEF result is considerably smaller than the one obtained with collinear factorization. The mechanism leading to this difference is of kinematical nature. We conclude that an analysis of inclusive 4-jet production with asymmetric pT -cuts below 50 GeV would be useful to enhance the DPS contribution relative to the SPS contribution. In contrast to the collinear approach, the HEF approach nicely describes the distribution of the ΔS variable, which involves all four jets and their angular correlations.

Constraining the double gluon distribution by the single gluon distribution

Abstract We show how to consistently construct initial conditions for the QCD evolution equations for double parton distribution functions in the pure gluon case. We use to momentum sum rule for this purpose and a specific form of the known single gluon distribution function in the MSTW parameterization. The resulting double gluon distribution satisfies exactly the momentum sum rule and is parameter free. We also study numerically its evolution with a hard scale and show the approximate factorization into product of two single gluon distributions at small values of x , whereas at large values of x the factorization is always violated in agreement with the sum rule.

Search for optimal conditions for exploring double-parton scattering in four-jet production: kT-factorization approach

In the present paper we discuss how to maximize the double-parton scattering (DPS) contribution in four-jet production by selecting kinematical cuts. Here both single-parton and doubleparton scattering effects are calculated in the kT-factorization approach, following our recent developments of relevant methods and tools. Several differential distributions are shown and discussed in the context of future searches for DPS effects, such as rapidity of jets, rapidity distance, and azimuthal correlations between jets. The dependences of the relative DPS amount is studied as function of those observables. The regions with an enhanced DPS contribution are identified. Future experimental explorations could extract more precise values of sef f and its potential dependence on kinematical variables.

The conformal anomaly and the neutral currents sector of the Standard Model

Abstract We elaborate on the structure of the graviton–gauge–gauge vertex in the electroweak theory, obtained by the insertion of the complete energy–momentum tensor (T) on 2-point functions of neutral gauge currents ( V V ′ ). The vertex defines the leading contribution to the effective action which accounts for the conformal anomaly and related interaction between the Standard Model and gravity. The energy–momentum tensor is derived from the curved spacetime Lagrangian in the linearized gravitational limit, and with the inclusion of the term of improvement of a conformally coupled Higgs sector. As in the previous cases of QED and QCD, we find that the conformal anomaly induces an effective massless scalar interaction between gravity and the neutral currents in each gauge invariant component of the vertex. This is described by the exchange of an anomaly pole. We show that for a spontaneously broken theory the anomaly can be entirely attributed to the poles only for a conformally coupled Higgs scalar. In the exchange of a graviton, the trace part of the corresponding interaction can be interpreted as due to an effective dilaton, using a local version of the effective action. We discuss the implications of the anomalous Ward identity for the T V V ′ correlator for the structure of the gauge/gauge/effective dilaton vertex in the effective action. The analogy between these effective interactions and those related to the radion in theories with large extra dimensions is pointed out.

Three and four point functions of stress energy tensors in D = 3 for the analysis of cosmological non-gaussianities

A bstractWe compute the correlation functions of 3 and 4 stress energy tensors (T) in D = 3 in free field theories of scalars, abelian gauge fields, and fermions, which are relevant in the analysis of cosmological non-gaussianities. These correlators appear in the holographic expressions of the scalar and tensor perturbations derived for holographic cosmological models. The result is simply adapted to describe the leading contributions in the gauge coupling to the same correlators also for a non abelian SU(N) gauge theory. In the case of the bispectrum, our results are mapped and shown to be in full agreement with the corresponding expressions given in a recent holographic study by Bzowski, McFadden and Skenderis. In the 4-T case we present the completely traced amplitude plus all the contact terms. These are expected to appear in a fourth order extension of the holographic formulas for the 4-point functions of scalar metric perturbations.