Caravel: A C++ framework for the computation of multi-loop amplitudes with numerical unitarity

10.1007/jhep07(2021)186 ◽

2021 ◽

Vol 2021 (7) ◽

Author(s):

Dean Carmi

Keyword(s):

Spectral Representation ◽

Tree Level ◽

Point Function ◽

Position Space ◽

Gross Neveu Model ◽

Abstract We continue the study of AdS loop amplitudes in the spectral representation and in position space. We compute the finite coupling 4-point function in position space for the large-N conformal Gross Neveu model on AdS3. The resummation of loop bubble diagrams gives a result proportional to a tree-level contact diagram. We show that certain families of fermionic Witten diagrams can be easily computed from their companion scalar diagrams. Thus, many of the results and identities of [1] are extended to the case of external fermions. We derive a spectral representation for ladder diagrams in AdS. Finally, we compute various bulk 2-point correlators, extending the results of [1].

One-loop string corrections to AdS amplitudes from CFT

10.1007/jhep03(2021)038 ◽

2021 ◽

Vol 2021 (3) ◽

Cited By ~ 2

Author(s):

J.M. Drummond ◽

H. Paul

Keyword(s):

Stress Tensor ◽

Analytic Structure ◽

Position Space ◽

Yang Mills ◽

String Corrections ◽

The One ◽

Abstract We consider α′ corrections to the one-loop four-point correlator of the stress- tensor multiplets in $$ \mathcal{N} $$ N = 4 super Yang-Mills at order 1/N4. Holographically, this is dual to string corrections of the one-loop supergravity amplitude on AdS5 × S5. While this correlator has been considered in Mellin space before, we derive the corresponding position space results, gaining new insights into the analytic structure of AdS loop amplitudes. Most notably, the presence of a transcendental weight three function involving new singularities is required, which has not appeared in the context of AdS amplitudes before. We thereby confirm the structure of string corrected one-loop Mellin amplitudes, and also provide new explicit results at orders in α′ not considered before.

ZH production in gluon fusion: two-loop amplitudes with full top quark mass dependence

10.1007/jhep03(2021)125 ◽

2021 ◽

Vol 2021 (3) ◽

Author(s):

Long Chen ◽

Gudrun Heinrich ◽

Stephen P. Jones ◽

Matthias Kerner ◽

Jonas Klappert ◽

...

Keyword(s):

Top Quark ◽

Quark Mass ◽

Gluon Fusion ◽

Top Quarks ◽

Mass Dependence ◽

Finite Part ◽

Top Quark Mass ◽

Helicity Amplitudes ◽

Quark Mass Dependence ◽

Abstract We present results for the two-loop helicity amplitudes entering the NLO QCD corrections to the production of a Higgs boson in association with a Z -boson in gluon fusion. The two-loop integrals, involving massive top quarks, are calculated numerically. Results for the interference of the finite part of the two-loop amplitudes with the Born amplitude are shown as a function of the two kinematic invariants on which the amplitudes depend.

Classical sub-subleading soft photon and soft graviton theorems in four spacetime dimensions

10.1007/jhep12(2020)070 ◽

2020 ◽

Vol 2020 (12) ◽

Author(s):

Biswajit Sahoo

Keyword(s):

Fourier Transformation ◽

Soft Photon ◽

Scattering Process ◽

Retarded Time ◽

Long Wavelength ◽

Macroscopic Objects ◽

Abstract Classical soft photon and soft graviton theorems determine long wavelength electromagnetic and gravitational waveforms for a general classical scattering process in terms of the electric charges and asymptotic momenta of the ingoing and outgoing macroscopic objects. Performing Fourier transformation of the electromagnetic and gravitational waveforms in the frequency variable one finds electromagnetic and gravitational waveforms at late and early retarded time. Here extending the formalism developed in [1], we derive sub-subleading electromagnetic and gravitational waveforms which behave like u−2(ln u) at early and late retarded time u in four spacetime dimensions. We also have derived the sub-subleading soft photon theorem analyzing two loop amplitudes in scalar QED. Finally, we conjectured the structure of leading non-analytic contribution to (sub)n-leading classical soft photon and graviton theorems which behave like u−n(ln u)n−1 for early and late retarded time u.

All-multiplicity one-loop amplitudes in Born-Infeld electrodynamics from generalized unitarity

10.1007/jhep03(2020)009 ◽

2020 ◽

Vol 2020 (3) ◽

Author(s):

Henriette Elvang ◽

Marios Hadjiantonis ◽

Callum R. T. Jones ◽

Shruti Paranjape

Keyword(s):

Multiplicity One ◽

Two-loop rational terms in Yang-Mills theories

10.1007/jhep10(2020)016 ◽

2020 ◽

Vol 2020 (10) ◽

Author(s):

Jean-Nicolas Lang ◽

Stefano Pozzorini ◽

Hantian Zhang ◽

Max F. Zoller

Keyword(s):

Scattering Amplitudes ◽

Gauge Theories ◽

A Posteriori ◽

Four Dimensions ◽

Yang Mills ◽

General Properties ◽

Finite Set ◽

Numerical Tools ◽

Abstract Scattering amplitudes in D dimensions involve particular terms that originate from the interplay of UV poles with the (D − 4)-dimensional parts of loop numerators. Such contributions can be controlled through a finite set of process-independent rational counterterms, which make it possible to compute loop amplitudes with numerical tools that construct the loop numerators in four dimensions. Building on a recent study [1] of the general properties of two-loop rational counterterms, in this paper we investigate their dependence on the choice of renormalisation scheme. We identify a nontrivial form of scheme dependence, which originates from the interplay of mass and field renormalisation with the (D−4)-dimensional parts of loop numerators, and we show that it can be controlled through a new kind of one-loop counterterms. This guarantees that the two-loop rational counterterms for a given renormalisable theory can be derived once and for all in terms of generic renormalisation constants, which can be adapted a posteriori to any scheme. Using this approach, we present the first calculation of the full set of two-loop rational counterterms in Yang-Mills theories. The results are applicable to SU(N) and U(1) gauge theories coupled to nf fermions with arbitrary masses.

On the computation of one-loop amplitudes with external fermions in 4D heterotic superstrings

Nuclear Physics B ◽

10.1016/0550-3213(95)00053-u ◽

1995 ◽

Vol 440 (3) ◽

pp. 441-494 ◽

Cited By ~ 7

Author(s):

Andrea Pasquinucci ◽

Kaj Roland

Keyword(s):

Two-loop leading colour QCD corrections to $$ q\overline{q} $$ → γγg and qg → γγq

10.1007/jhep04(2021)201 ◽

2021 ◽

Vol 2021 (4) ◽

Author(s):

Bakul Agarwal ◽

Federico Buccioni ◽

Andreas von Manteuffel ◽

Lorenzo Tancredi

Keyword(s):

Numerical Code ◽

Tree Level ◽

Partial Fraction ◽

Integration By Parts ◽

Analytic Expressions ◽

Partial Fraction Decomposition ◽

Abstract We present the leading colour and light fermionic planar two-loop corrections for the production of two photons and a jet in the quark-antiquark and quark-gluon channels. In particular, we compute the interference of the two-loop amplitudes with the corresponding tree level ones, summed over colours and polarisations. Our calculation uses the latest advancements in the algorithms for integration-by-parts reduction and multivariate partial fraction decomposition to produce compact and easy-to-use results. We have implemented our results in an efficient C++ numerical code. We also provide their analytic expressions in Mathematica format.