arXiv subjects

Alexander Ochirov

Publications and source records attributed to Alexander Ochirov.

27 records · Page 2Linked to original sources

arXiv2017

One-loop monodromy relations on single cuts

The discovery of colour-kinematic duality has led to significant progress in the computation of scattering amplitudes in quantum field theories. At tree level, the origin of the duality can be traced back to the monodromies of open-string amplitudes. This construction has recently been extended to all loop orders. In the present paper, we dissect some consequences of these new monodromy relations at one loop. We use single cuts in order to relate them to the tree-level relations. We show that there are new classes of kinematically independent single-cut amplitudes. Then we turn to the Feynman diagrammatics of the string-theory monodromy relations. We revisit the string-theoretic derivation and argue that some terms, that vanish upon integration in string and field theory, provide a characterisation of momentum-shifting ambiguities in these representations. We observe that colour-dual representations are compatible with this analysis.

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arXiv2017

Full Colour for Loop Amplitudes in Yang-Mills Theory

We present a general method to account for full colour dependence Yang-Mills amplitudes at loop level. The method fits most naturally into the framework of multi-loop integrand reduction and in a nutshell amounts to consistently retaining the colour structures of the unitarity cuts from which the integrand is gradually constructed. This technique has already been used in the recent calculation of the two-loop five-gluon amplitude in pure Yang-Mills theory with all positive helicities, arXiv:1507.08797. In this note, we give a careful exposition of the method and discuss its connection to loop-level Kleiss-Kuijf relations. We also explore its implications for cancellation of nontrivial symmetry factors at two loops. As an example of its generality, we show how it applies to the three-loop case in supersymmetric Yang-Mills case.

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arXiv2015

Color-Kinematics Duality for QCD Amplitudes

We show that color-kinematics duality is present in tree-level amplitudes of quantum chromodynamics with massive flavored quarks. Starting with the color structure of QCD, we work out a new color decomposition for n-point tree amplitudes in a reduced basis of primitive amplitudes. These primitives, with k quark-antiquark pairs and (n-2k) gluons, are taken in the (n-2)!/k! Melia basis, and are independent under the color-algebra Kleiss-Kuijf relations. This generalizes the color decomposition of Del Duca, Dixon, and Maltoni to an arbitrary number of quarks. The color coefficients in the new decomposition are given by compact expressions valid for arbitrary gauge group and representation. Considering the kinematic structure, we show through explicit calculations that color-kinematics duality holds for amplitudes with general configurations of gluons and massive quarks. The new (massive) amplitude relations that follow from the duality can be mapped to a well-defined subset of the familiar BCJ relations for gluons. They restrict the amplitude basis further down to (n-3)!(2k-2)/k! primitives, for two or more quark lines. We give a decomposition of the full amplitude in that basis. The presented results provide strong evidence that QCD obeys the color-kinematics duality, at least at tree level. The results are also applicable to supersymmetric and D-dimensional extensions of QCD.

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arXiv2015

Pure Gravities via Color-Kinematics Duality for Fundamental Matter

We give a prescription for the computation of loop-level scattering amplitudes in pure Einstein gravity, and four-dimensional pure supergravities, using the color-kinematics duality. Amplitudes are constructed using double copies of pure (super-)Yang-Mills parts and additional contributions from double copies of fundamental matter, which are treated as ghosts. The opposite-statistics states cancel the unwanted dilaton and axion in the bosonic theory, as well as the extra matter supermultiplets in supergravities. As a spinoff, we obtain a prescription for obtaining amplitudes in supergravities with arbitrary non-self-interacting matter. As a prerequisite, we extend the color-kinematics duality from the adjoint to the fundamental representation of the gauge group. We explain the numerator relations that the fundamental kinematic Lie algebra should satisfy. We give nontrivial evidence supporting our construction using explicit tree and loop amplitudes, as well as more general arguments.

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arXiv2015

A Complete Two-Loop, Five-Gluon Helicity Amplitude in Yang-Mills Theory

We compute the integrand of the full-colour, two-loop, five-gluon scattering amplitude in pure Yang-Mills theory with all helicities positive, using generalized unitarity cuts. Tree-level BCJ relations, satisfied by amplitudes appearing in the cuts, allow us to deduce all the necessary non-planar information for the full-colour amplitude from known planar data. We present our result in terms of irreducible numerators, with colour factors derived from the multi-peripheral colour decomposition. Finally, the leading soft divergences are checked to reproduce the expected infrared behaviour.

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arXiv2014

Scattering amplitudes in gauge theories with and without supersymmetry

This thesis aims at providing better understanding of the perturbative expansion of gauge theories with and without supersymmetry. At tree level, the BCFW recursion relations are analyzed with respect to their validity for general off-shell objects in Yang-Mills theory, which is a significant step away from their established zone of applicability. Unphysical poles constitute a new potential problem in addition to the boundary behavior issue, common to the on-shell case as well. For an infinite family of massive fermion currents, both obstacles are shown to be avoided under the certain conditions, which provides a natural recursion relation. At one loop, scattering amplitudes can be calculated from unitarity cuts through their expansion into known scalar integrals with free coefficients. A powerful method to obtain these coefficients, namely spinor integration, is discussed and rederived in a somewhat novel form. It is then used to compute analytically the infinite series of one-loop gluon amplitudes in N = 1 super-Yang-Mills theory with exactly three negative helicities. The final part of this thesis concerns the intriguing relationship between gluon and graviton scattering amplitudes, which involves a beautiful duality between the color and kinematic content of gauge theories. This BCJ duality is extended to include particles in the fundamental representation of the gauge group, which is shown to relieve the restriction of the BCJ construction to factorizable gravities and thus give access to amplitudes in generic (super-)gravity theories.

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arXiv2014

BCJ duality and double copy in the closed string sector

This paper is focused on the loop-level understanding of the Bern-Carrasco-Johansson double copy procedure that relates the integrands of gauge theory and gravity scattering amplitudes. At four points, the first non-trivial example of that construction is one-loop amplitudes in N=2 super-Yang-Mills theory and the symmetric realization of N=4 matter-coupled supergravity. Our approach is to use both field and string theory in parallel to analyze these amplitudes. The closed string provides a natural framework to analyze the BCJ construction, in which the left- and right-moving sectors separately create the color and kinematics at the integrand level. At tree level, in a five-point example, we show that the Mafra-Schlotterer-Stieberger procedure gives a new direct proof of the color-kinematics double copy. We outline the extension of that argument to n points. At loop level, the field-theoretic BCJ construction of N=2 SYM amplitudes introduces new terms, unexpected from the string theory perspective. We discuss to what extent we can relate them to the terms coming from the interactions between left- and right-movers in the string-theoretic gravity construction.

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arXiv2013

All one-loop NMHV gluon amplitudes in N=1 SYM

We compute the next-to-maximally-helicity-violating one-loop n-gluon amplitudes in N=1 super-Yang-Mills theory. These amplitudes contain three negative-helicity gluons and an arbitrary number of positive-helicity gluons, and constitute the first infinite series of amplitudes beyond the simplest, MHV, amplitudes. We assemble ingredients from the N=4 NMHV tree super-amplitude into previously unwritten double cuts and use the spinor integration technique to calculate all bubble coefficients. We also derive the missing box coefficients from quadruple cuts. Together with the known formula for three-mass triangles, this completes the set of NMHV one-loop master integral coefficients in N=1 SYM. To facilitate further use of our results, we provide their Mathematica implementation.

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arXiv2012

On-shell recursion for massive fermion currents

We analyze the validity of BCFW recursion relations for currents of n - 2 gluons and two massive quarks, where one of the quarks is off shell and the remaining particles are on shell. These currents are gauge-dependent and can be used as ingredients in the unitarity-based approach to computing one-loop amplitudes. The validity of BCFW recursion relations is well known to depend on the so-called boundary behavior of the currents as the momentum shift parameter goes to infinity. With off-shell currents, a new potential problem arises, namely unphysical poles that depend on the choice of gauge. We identify conditions under which boundary terms are absent and unphysical poles are avoided, so that there is a natural recursion relation. In particular, we are able to choose a gauge in which we construct a valid shift for currents with at least n - 3 gluons of the same helicity. We derive an analytic formula in the case where all gluons have the same helicity. As by-products, we prove the vanishing boundary behavior of general off-shell objects in Feynman gauge, and we find a compact generalization of Berends-Giele gluon currents with a generic reference spinor.

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