arXiv subjects

Pierpaolo Mastrolia

Publications and source records attributed to Pierpaolo Mastrolia.

72 records · Page 4Linked to original sources

arXiv2010

Modern Feynman Diagrammatic One-Loop Calculations

In this talk we present techniques for calculating one-loop amplitudes for multi-leg processes using Feynman diagrammatic methods in a semi-algebraic context. Our approach combines the advantages of the different methods allowing for a fast evaluation of the amplitude while monitoring the numerical stability of the calculation. In phase space regions close to singular kinematics we use a method avoiding spurious Gram determinants in the calculation. As an application of our approach we report on the status of the calculation of the amplitude for the process $pp\to b\bar{b}b\bar{b}+X$.

hep-ph↗

arXiv2010

Unitarity-Cuts, Stokes' Theorem and Berry's Phase

Two-particle unitarity-cuts of scattering amplitudes can be efficiently computed by applying Stokes' Theorem, in the fashion of the Generalised Cauchy Theorem. Consequently, the Optical Theorem can be related to the Berry Phase, showing how the imaginary part of arbitrary one-loop Feynman amplitudes can be interpreted as the flux of a complex 2-form.

hep-ph↗

arXiv2009

NLO QED Corrections to Hard-Bremsstrahlung Emission in Bhabha Scattering

In this paper we present a numerical implementation of the one-loop QED corrections to the hard-bremsstrahlung process e- e+ \to e- e+ gamma. These corrections can be included in the Monte Carlo event generators employed for simulating Bhabha scattering events at low-energy high-luminosity electron-positron colliders. The calculation is performed by employing the reduction method developed by Ossola, Papadopoulos and Pittau. Our results are implemented in a modular code for the numerical evaluation of the scattering amplitudes for any given phase-space point. In a similar way, we also evaluate the one-loop QED corrections to e- e+ \to mu- mu+ gamma, which represents an interesting application of the method in the presence of two different mass scales in the loops.

hep-ph↗

arXiv2009

One-loop Higgs plus four gluon amplitudes: Full analytic results

We consider one-loop amplitudes of a Higgs boson coupled to gluons in the limit of a large top quark mass. We treat the Higgs as the real part of a complex field phi that couples to the self-dual field strengths and compute the one-loop corrections to the phi-NMHV amplitude, which contains one gluon of positive helicity whilst the remaining three have negative helicity. We use four-dimensional unitarity to construct the cut-containing contributions and a hybrid of Feynman diagram and recursive based techniques to determine the rational piece. Knowledge of the phi-NMHV contribution completes the analytic calculation of the Higgs plus four gluon amplitude. For completeness we also include expressions for the remaining helicity configurations which have been calculated elsewhere. These amplitudes are relevant for Higgs plus jet production via gluon fusion in the limit where the top quark is large compared to all other scales in the problem.

hep-ph↗

arXiv2009

Unitarity-Cuts and Berry's Phase

Elaborating on the observation that two-particle unitarity-cuts of scattering amplitudes can be computed by applying Stokes' Theorem, we relate the Optical Theorem to the Berry Phase, showing how the imaginary part of arbitrary one-loop Feynman amplitudes can be interpreted as the flux of a complex 2-form.

hep-ph↗

arXiv2009

Double-Cut of Scattering Amplitudes and Stokes' Theorem

We show how Stokes' Theorem, in the fashion of the Generalised Cauchy Formula, can be applied for computing double-cut integrals of one-loop amplitudes analytically. It implies the evaluation of phase-space integrals of rational functions in two complex-conjugated variables, which are simply computed by an indefinite integration in a single variable, followed by Cauchy's Residue integration in the conjugated one. The method is suitable for the cut-construction of the coefficients of 2-point functions entering the decomposition of one-loop amplitudes in terms of scalar master integrals.

hep-ph↗

arXiv2008

On the Cuts of Scattering Amplitudes

The use of complex analysis for computing one-loop scattering amplitudes is naturally induced by generalised unitarity-cut conditions, fulfilled by complex values of the loop variable. We report on two techniques: the cut-integration with spinor-variables as contour integrals of rational functions; and the use of the Discrete Fourier Transform to optimize the reduction of tensor-integrals to master scalar integrals.

hep-ph↗

arXiv2008

One-loop phi-MHV amplitudes using the unitarity bootstrap: the general helicity case

We consider a Higgs boson coupled to gluons via the five-dimensional effective operator H tr G_{μν}G^{μν}. We treat H as the real part of a complex field phi that couples to the selfdual gluon field strengths and compute the one-loop corrections to the phi-MHV amplitudes involving phi, two negative helicity gluons and an arbitrary number of positive helicity gluons. Our results generalise earlier work where the two negative helicity gluons were constrained to be colour adjacent. We use four-dimensional unitarity to construct the cut-containing contributions and the recently developed recursion relations to obtain the rational contribution for an arbitrary number of external gluons. We solve the recursion relations and give explicit results for up to four external gluons. These amplitudes are relevant for Higgs plus jet production via gluon fusion in the limit where the top quark mass is large compared to all other scales in the problem.

hep-ph↗

arXiv2008

Closed-Form Decomposition of One-Loop Massive Amplitudes

We present formulas for the coefficients of 2-, 3-, 4- and 5-point master integrals for one-loop massive amplitudes. The coefficients are derived from unitarity cuts in D dimensions. The input parameters can be read off from any unitarity-cut integrand, as assembled from tree-level expressions, after simple algebraic manipulations. The formulas presented here are suitable for analytical as well as numerical evaluation. Their validity is confirmed in two known cases of helicity amplitudes contributing to gg -> gg and gg -> gH, where the masses of the Higgs and the fermion circulating in the loop are kept as free parameters.

hep-ph↗

arXiv2007

Feynman Diagrams and Differential Equations

We review in a pedagogical way the method of differential equations for the evaluation of D-dimensionally regulated Feynman integrals. After dealing with the general features of the technique, we discuss its application in the context of one- and two-loop corrections to the photon propagator in QED, by computing the Vacuum Polarization tensor exactly in D. Finally, we treat two cases of less trivial differential equations, respectively associated to a two-loop three-point, and a four-loop two-point integral. These two examples are the playgrounds for showing more technical aspects about: Laurent expansion of the differential equations in D (around D=4); the choice of the boundary conditions; and the link among differential and difference equations for Feynman integrals.

hep-ph↗

arXiv2007

Unitarity cuts and reduction to master integrals in d dimensions for one-loop amplitudes

We present an alternative reduction to master integrals for one-loop amplitudes using a unitarity cut method in arbitrary dimensions. We carry out the reduction in two steps. The first step is a pure four-dimensional cut-integration of tree amplitudes with a mass parameter, and the second step is applying dimensional shift identities to master integrals. This reduction is performed at the integrand level, so that coefficients can be read out algebraically.

hep-ph↗

arXiv2006

On Triple-Cut of Scattering Amplitudes

It is analysed the triple-cut of one-loop amplitudes in dimensional regularisation within spinor-helicity representation. The triple-cut is defined as a difference of two double-cuts with the same particle content, and a same propagator carrying, respectively, causal and anti-causal prescription in each of the two cuts. That turns out into an effective tool for extracting the coefficients of the three-point functions (and higher-point ones) from one-loop-amplitudes. The phase-space integration is oversimplified by using residues theorem to perform the integration over the spinor variables, via the holomorphic anomaly, and a trivial integration on the Feynman parameter. The results are valid for arbitrary values of dimensions.

hep-th↗

arXiv2006

Twistors and Unitarity

We review on the recent developments for the computation of scattering amplitudes, with attention to the on-shell formalisms and unitarity-based methods.

hep-ph↗

arXiv2006

D-dimensional unitarity cut method

We develop a unitarity method to compute one-loop amplitudes with massless propagators in d=4-2*epsilon dimensions. We compute double cuts of the loop amplitudes via a decomposition into a four-dimensional and a -2*epsilon-dimensional integration. The four-dimensional integration is performed using spinor integration or other efficient techniques. The remaining integral in -2*epsilon dimensions is cast in terms of bubble, triangle, box, and pentagon master integrals using dimensional shift identities. The method yields results valid for arbitrary values of epsilon.

hep-ph↗

arXiv2006

Unitarity Cuts: NLO Six-Gluon Amplitudes in QCD

We report on a technique for evaluating finite unitarity cut for one-loop amplitudes in gauge theories, and discuss its application to the cut-constructible part of six-gluon amplitude in QCD.

hep-ph↗

arXiv2006

The Cut-Constructible Part of QCD Amplitudes

Unitarity cuts are widely used in analytic computation of loop amplitudes in gauge theories such as QCD. We expand upon the technique introduced in hep-ph/0503132 to carry out any finite unitarity cut integral. This technique naturally separates the contributions of bubble, triangle and box integrals in one-loop amplitudes and is not constrained to any particular helicity configurations. Loop momentum integration is reduced to a sequence of algebraic operations. We discuss the extraction of the residues at higher-order poles. Additionally, we offer concise algebraic formulas for expressing coefficients of three-mass triangle integrals. As an application, we compute all remaining coefficients of bubble and triangle integrals for nonsupersymmetric six-gluon amplitudes.

hep-ph↗

arXiv2005

CSW Diagrams and Electroweak Vector Bosons

Based on the joined work performed together with Z. Bern, D. Forde, and D. Kosower [1], in this talk it is recalled the (twistor-motivated) diagrammatic formalism describing tree-level scattering amplitudes presented by Cachazo, Svrček and Witten, and it is discussed an extension of the vertices and accompaining rules to the construction of vector-boson currents coupling to an arbitrary source.

hep-ph↗

arXiv2005

Twistor-Inspired Construction of Electroweak Vector Boson Currents

We present an extension of the twistor-motivated MHV vertices and accompanying rules presented by Cachazo, Svrvcek and Witten to the construction of vector-boson currents coupling to an arbitrary source. In particular, we give rules for constructing off-shell vector-boson currents with one fermion pair and n gluons of arbitrary helicity. These currents may be employed directly in the computation of electroweak amplitudes. The rules yield expressions in agreement with previously-obtained results for Z,W,γ^* --> qbar q + n gluons (analytically up to n=3, beyond via the Berends--Giele recursion relations). We also confirm that the contribution to a seven-point amplitude containing the non-abelian triple vector-boson coupling obtained using the next-to-MHV currents matches the previous result in the literature.

hep-ph↗