Browsing by Author "Gomez, Humberto"
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Item CHY loop integrands from holomorphic forms(Springer Verlag, 2017-03-01) Gomez, Humberto; Mizer, Sebastian; Zhang, GuojunRecently, the Cachazo-He-Yuan (CHY) approach for calculating scattering amplitudes has been extended beyond tree level. In this paper, we introduce a way of constructing CHY integrands for Φ3 theory up to two loops from holomorphic forms on Riemann surfaces. We give simple rules for translating Feynman diagrams into the corresponding CHY integrands. As a complementary result, we extend the Λ-algorithm, originally introduced in arXiv:1604.05373, to two loops. Using this approach, we are able to analytically verify our prescription for the CHY integrands up to seven external particles at two loops. In addition, it gives a natural way of extending to higher-loop orders. © 2017, The Author(s).Item Computation of contour integrals on ℳ0,n(Springer Verlag, 2016-04-01) Cachazo, Freddy; Gomez, HumbertoContour integrals of rational functions over (Formula presented.) , the moduli space of n-punctured spheres, have recently appeared at the core of the tree-level S-matrix of massless particles in arbitrary dimensions. The contour is determined by the critical points of a certain Morse function on (Formula presented.). The integrand is a general rational function of the puncture locations with poles of arbitrary order as two punctures coincide. In this note we provide an algorithm for the analytic computation of any such integral. The algorithm uses three ingredients: an operation we call general KLT, Petersen’s theorem applied to the existence of a 2-factor in any 4-regular graph and Hamiltonian decompositions of certain 4-regular graphs. The procedure is iterative and reduces the computation of a general integral to that of simple building blocks. These are integrals which compute double-color-ordered partial amplitudes in a bi-adjoint cubic scalar theory. © 2016, The Author(s).Item Cosmological Scattering Equations(2021) Gomez, Humberto; Lipinski Jusinskas, Renann; Lipstein, ArthurWe propose a world sheet formula for tree-level correlation functions describing a scalar field with arbitrary mass and quartic self-interaction in de Sitter space, which is a simple model for inflationary cosmology. The correlation functions are located on the future boundary of the spacetime and are Fourier-transformed to momentum space. Our formula is supported on mass-deformed scattering equations involving conformal generators in momentum space and reduces to the CHY formula for φ4 amplitudes in the flat space limit. Using the global residue theorem, we verify that it reproduces the Witten diagram expansion at four and six points, and sketch the extension to n points.Item Cross-ratio identities and higher-order poles of CHY-integrand(Springer Verlag, 2016-09-01) Cardona, Carlos A.; Feng, Bo; Gomez, Humberto; Huang, RijunThe evaluation of generic Cachazo-He-Yuan(CHY)-integrands is a big challenge and efficient computational methods are in demand for practical evaluation. In this paper, we propose a systematic decomposition algorithm by using cross-ratio identities, which provides an analytic and easy to implement method for the evaluation of any CHY-integrand. This algorithm aims to decompose a given CHY-integrand containing higher-order poles as a linear combination of CHY-integrands with only simple poles in a finite number of steps, which ultimately can be trivially evaluated by integration rules of simple poles. To make the method even more efficient for CHY-integrands with large number of particles and complicated higher-order pole structures, we combine the Λ-algorithm and the cross-ratio identities, and as a by-product it provides us a way to deal with CHY-integrands where the Λ-algorithm was not applicable in its original formulation. © 2016, The Author(s).Item Elliptic scattering equations(Springer Verlag, 2016-06-01) Cardona, Carlos A.; Gomez, HumbertoRecently the CHY approach has been extended to one loop level using elliptic functions and modular forms over a Jacobian variety. Due to the difficulty in manipulating these kind of functions, we propose an alternative prescription that is totally algebraic. This new proposal is based on an elliptic algebraic curve embedded in a ℂP 2 space. We show that for the simplest integrand, namely the n − gon, our proposal indeed reproduces the expected result. By using the recently formulated Λ−algorithm, we found a novel recurrence relation expansion in terms of tree level off-shell amplitudes. Our results connect nicely with recent results on the one-loop formulation of the scattering equations. In addition, this new proposal can be easily stretched out to hyperelliptic curves in order to compute higher genus. © 2016, The Author(s).Item Multiparticle Solutions to Einstein’s Equations(2021-10-29) Gomez, Humberto; Lipinski Jusinskas, RenannIn this Letter, we present the first multiparticle solutions to Einstein’s field equations in the presence of matter. These solutions are iteratively obtained via the perturbiner method, which can circumvent gravity’s infinite number of vertices with the definition of a multiparticle expansion for the inverse spacetime metric as well. Our construction provides a simple layout for the computation of tree level field theory amplitudes in spacetime dimensions involving any number of gravitons and matter fields, with or without supersymmetry. © 2021 Published by the American Physical SocietyItem New factorization relations for nonlinear sigma model amplitudes(American Physical Society, 2019-02-15) Bjerrum-Bohr, Niels Emil Jannik; Gomez, Humberto; Helset, AndreasWe obtain novel factorization identities for nonlinear sigma model amplitudes using a new integrand in the Cachazo-He-Yuan double-cover prescription. We find that it is possible to write very compact relations using only longitudinal degrees of freedom. We discuss implications for on shell recursion. © 2019 authors. Published by the American Physical Society. Published by the American Physical Society under the terms of the »https://creativecommons.org/licenses/by/4.0/» Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article's title, journal citation, and DOI. Funded by SCOAP 3 .Item New factorization relations for Yang-Mills amplitudes(American Physical Society, 2019-01-15) Bjerrum-Bohr, Niels Emil Jannik; Damgaard, Poul Henrik; Gomez, HumbertoA double-cover extension of the scattering equation formalism of Cachazo, He, and Yuan leads us to conjecture covariant factorization formulas of n-particle scattering amplitudes in Yang-Mills theories. Evidence is given that these factorization relations are related to Berends-Giele recursions through repeated use of partial fraction identities involving linearized propagators. © 2019 authors. Published by the American Physical Society.Item New recursion relations for tree-level correlators in anti-de Sitter spacetime(2022-12-15) Armstrong, Connor; Gomez, Humberto; Lipinski Jusinskas, Renann; Lipstein, Arthur; Mei, JiajieWe present for the first time classical multiparticle solutions in anti-de Sitter space (AdS) involving scalars, gluons, and gravitons. They are recursively defined through multiparticle currents which reduce to Berends-Giele currents in the flat space limit. This construction exposes a compact definition of tree-level boundary correlators using a general prescription that removes unphysical boundary contributions. Similarly to the flat space perturbiner, a convenient gauge choice leads to a scalar basis for all degrees of freedom, while the tensor structure is exclusively captured by field theory vertices. This provides a fully automated way to compute AdS boundary correlators to any multiplicity and cosmological wave function coefficients after Wick rotating to de Sitter space.Item Non-planar one-loop Parke-Taylor factors in the CHY approach for quadratic propagators(Springer Verlag, 2018-05-01) Ahmadiniaz, Naser; Gomez, Humberto; Lopez-Arcos, CristhiamIn this work we have studied the Kleiss-Kuijf relations for the recently introduced Parke-Taylor factors at one-loop in the CHY approach, that reproduce quadratic Feynman propagators. By doing this, we were able to identify the non-planar one-loop Parke-Taylor factors. In order to check that, in fact, these new factors can describe non-planar amplitudes, we applied them to the bi-adjoint Φ3 theory. As a byproduct, we found a new type of graphs that we called the non-planar CHY-graphs. These graphs encode all the information for the subleading order at one-loop, and there is not an equivalent of these in the Feynman formalism. © 2018, The Author(s).Item One-loop Parke-Taylor factors for quadratic propagators from massless scattering equations(Springer Verlag, 2017-10-01) Gomez, Humberto; Lopez-Arcos, Cristhiam; Talavera, PedroIn this paper we reconsider the Cachazo-He-Yuan construction (CHY) of the so called scattering amplitudes at one-loop, in order to obtain quadratic propagators. In theories with colour ordering the key ingredient is the redefinition of the Parke-Taylor factors. After classifying all the possible one-loop CHY-integrands we conjecture a new one-loop amplitude for the massless Bi-adjoint Φ3 theory. The prescription directly reproduces the quadratic propagators of the traditional Feynman approach. © 2017, The Author(s).Item Quadratic Feynman loop integrands from massless scattering equations(American Physical Society, 2017-05-17) Gomez, HumbertoRecently, the Cachazo-He-Yuan (CHY) approach has been extended to the loop level, but the resulting loop integrand has propagators that are linear in the loop momentum unlike Feynman’s. In this paper, we present a new technique that directly produces quadratic propagators identical to Feynman’s from the CHY approach. This paper focuses on the Φ 3 theory, but extensions to other theories are briefly discussed. In addition, our proposal has an interesting geometric meaning; we can interpret this new formula as a unitary cut on a higher genus Riemann surface.Item Scattering equations and a new factorization for amplitudes. Part I. Gauge theories(Springer Verlag, 2019-05-01) Gomez, HumbertoIn this work we show how a double-cover (DC) extension of the Cachazo, He and Yuan formalism (CHY) can be used to provide a new realization for the factorization of the amplitudes involving gluons and scalar fields. First, we propose a graphic representation for a color-ordered Yang-Mills (YM) and special Yang-Mills-Scalar (YMS) amplitudes within the scattering equation formalism. Using the DC prescription, we are able to obtain an algorithm (integration-rules) which decomposes amplitudes in terms of three-point building-blocks. It is important to remark that the pole structure of this method is totally different to ordinary factorization (which is a consequence of the scattering equations). Finally, as a byproduct, we show that the soft limit in the CHY approach, at leading order, becomes trivial by using the technology described in this paper. © 2019, The Author(s).Item Scattering equations and a new factorization for amplitudes. Part II. Effective field theories(Springer Verlag, 2019-05-01) Gomez, Humberto; Helset, AndreasWe continue the program of extending the scattering equation framework by Cachazo, He and Yuan to a double-cover prescription. We discuss how to apply the double-cover formalism to effective field theories, with a special focus on the non-linear sigma model. A defining characteristic of the double-cover formulation is the emergence of new factorization relations. We present several factorization relations, along with a novel recursion relation. Using the recursion relation and a new prescription for the integrand, any non-linear sigma model amplitude can be expressed in terms of off-shell three-point amplitudes. The resulting expression is purely algebraic, and we do not have to solve any scattering equation. We also discuss soft limits, boundary terms in BCFW recursion, and application of the double-cover prescription to other effective field theories, like the special Galileon theory. © 2019, The Author(s).Item Two-loop superstring five-point amplitude and S -duality(American Physical Society, 2016-02-24) Gomez, Humberto; Mafra, Carlos R.; Schlotterer, OliverThe low-energy limit of the massless two-loop five-point amplitudes for both type IIA and type IIB superstrings is computed with the pure spinor formalism and its overall coefficient determined from first principles. For the type IIB theory, the five-graviton amplitude is found to be proportional to its tree-level counterpart at the corresponding order in α ′ . Their ratio ties in with expectations based on S-duality since it matches the same modular function E 5 / 2 which relates the two-loop and tree-level four-graviton amplitudes. For R-symmetry violating states, the ratio between tree-level and two-loop amplitudes at the same α ′ -order carries an additional factor of − 3 / 5 . Its S -duality origin can be traced back to a modular form derived from E 5 / 2 .Item Λ scattering equations(Springer Verlag, 2016-06-01) Gomez, HumbertoAbstract: The CHY representation of scattering amplitudes is based on integrals over the moduli space of a punctured sphere. We replace the punctured sphere by a double-cover version. The resulting scattering equations depend on a parameter Λ controlling the opening of a branch cut. The new representation of scattering amplitudes possesses an enhanced redundancy which can be used to fix, modulo branches, the location of four punctures while promoting Λ to a variable. Via residue theorems we show how CHY formulas break up into sums of products of smaller (off-shell) ones times a propagator. This leads to a powerful way of evaluating CHY integrals of generic rational functions, which we call the Λ algorithm. © 2016, The Author(s).