FCFernando Febres Cordero

Fernando Febres Cordero

Florida State University
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Fernando Febres Cordero has a total of 29 co-authors. Here are the top co-authors by number of shared publications:

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    Erratum: Two-Loop Four-Graviton Scattering Amplitudes [Phys. Rev. Lett. 124 , 211601 (2020)]

    by S. Abreu, F. Febres Cordero, H. Ita, M. Jaquier, B. Page, M. S. Ruf, V. Sotnikov

    This corrects the article DOI: 10.1103/PhysRevLett.124.211601.

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    First Look at Quartic-in-Spin Binary Dynamics at Third Post-Minkowskian Order

    by Dogan Akpinar, Fernando Febres Cordero, Manfred Kraus, Alexander Smirnov, Mao Zeng

    We compute the conservative and radiation-reaction contributions to classical observables in the gravitational scattering between a spinning and a spinless black hole to the fourth order in spin and third order in the gravitational constant. The conservative results are obtained from two-loop amplitudes for the scattering process of a massive scalar with a massive spin- s field ( s = 0 , 1, 2) minimally coupled to gravity, employing the recently introduced spin interpolation method to resolve all spin-Casimir terms. The two-loop amplitude exhibits a spin-shift symmetry in both probe limits, which we conjecture to be a sign of yet unknown integrability of Kerr orbits through the quartic order in spin and to all orders in the gravitational constant. We obtain the radial action from the finite part of the amplitude and use it to compute classical observables, including the impulse and spin kick. This is done using the recently introduced covariant Dirac brackets, which allow for the computation of classical scattering observables for general (nonaligned) spin configurations. Finally, employing the radiation-reaction amplitude proposed by Alessio and Di Vecchia, together with the Dirac brackets, we obtain radiation-reaction contributions to observables at all orders in spin and beyond the aligned-spin limit. We find agreement with known results up to the quadratic order in spin for both conservative and radiation-reaction contributions. Our results advance the state of the art in the understanding of spinning binary dynamics in general relativity and demonstrate the power and simplicity of the Dirac bracket formalism for relating scattering amplitudes to classical observables.

    Cited by 47
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    Spinning black hole scattering at $ \mathcal{O} $(G3S2): Casimir terms, radial action and hidden symmetry

    by Dogan Akpinar, Fernando Febres Cordero, Manfred Kraus, Michael S. Ruf, Mao Zeng

    We resolve subtleties in calculating the post-Minksowskian dynamics of binary systems, as a spin expansion, from massive scattering amplitudes of fixed finite spin. In particular, the apparently ambiguous spin Casimir terms can be fully determined from the gradient of the spin-diagonal part of the amplitudes with respect to S 2 = −s(s+1)ħ 2, using an interpolation between massive amplitudes with different spin representations. From two-loop amplitudes of spin-0 and spin-1 particles minimally coupled to gravity, we extract the spin Casimir terms in the conservative scattering angle between a spinless and a spinning black hole at $$ \mathcal{O} $$ O (G 3 S 2), finding agreement with known results in the literature. This completes an earlier study [Phys. Rev. Lett. 130 (2023), 021601] that calculated the non-Casimir terms from amplitudes. We also illustrate our methods using a model of spinning bodies in electrodynamics, finding agreement between scattering amplitude predictions and classical predictions in a root-Kerr electromagnetic background up to $$ \mathcal{O} $$ O (α 3 S 2). For both gravity and electrodynamics, the finite part of the amplitude coincides with the two-body radial action in the aligned spin limit, generalizing the amplitude-action relation beyond the spinless case. Surprisingly, the two-loop amplitude displays a hidden spin-shift symmetry in the probe limit, which was previously observed at one loop. We conjecture that the symmetry holds to all orders in the coupling constant and is a consequence of integrability of Kerr orbits in the probe limit at the first few orders in spin.

    Cited by 41
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    Two-loop master integrals for leading-color $ pp\to t\overline{t}H $ amplitudes with a light-quark loop

    by F. Febres Cordero, G. Figueiredo, M. Kraus, B. Page, L. Reina

    We compute the two-loop master integrals for leading-color QCD scattering amplitudes including a closed light-quark loop in $$ t\overline{t}H $$ t t ¯ H production at hadron colliders. Exploiting numerical evaluations in modular arithmetic, we construct a basis of master integrals satisfying a system of differential equations in ϵ-factorized form. We present the analytic form of the differential equations in terms of a minimal set of differential one-forms. We explore properties of the function space of analytic solutions to the differential equations in terms of iterative integrals which can be exploited for studying the analytic form of related scattering amplitudes. Finally, we solve the differential equations using generalized series expansions to numerically evaluate the master integrals in physical phase space. As the first computation of a set of two-loop seven-scale master integrals, our results provide valuable input for analytic studies of scattering amplitudes in processes involving massive particles and a large number of kinematic scales.

    Cited by 59
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    Numerical Unitarity for Binary Dynamics

    by Fernando Febres Cordero

    We present a calculation of the conservative two-body Hamiltonian of a compact binary system including a spinning black hole. We include up-to third order corrections in Newton's constant $G$, all orders in velocity, and linear and quadratic terms in spin. The results are obtained from the classical limit of two-loop scattering amplitudes involving two massive scalars and two massive spin-1 particles minimally coupled to gravity. We discuss the usage of numerical techniques in our computation. In particular we show how the numerical unitarity method is well suited to obtain results of relevance to the physics program of current and future gravitational wave observatories.

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    Numerical Unitarity for Binary Dynamics

    by Fernando Febres Cordero

    We present a calculation of the conservative two-body Hamiltonian of a compact binary system including a spinning black hole. We include up-to third order corrections in Newton's constant $G$, all orders in velocity, and linear and quadratic terms in spin. The results are obtained from the classical limit of two-loop scattering amplitudes involving two massive scalars and two massive spin-1 particles minimally coupled to gravity. We discuss the usage of numerical techniques in our computation. In particular we show how the numerical unitarity method is well suited to obtain results of relevance to the physics program of current and future gravitational wave observatories.

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    Conservative Binary Dynamics with a Spinning Black Hole at $\mathcal{O}(G^3)$ from Scattering Amplitudes

    by Fernando Febres Cordero, Manfred Kraus, Guanda Lin, Michael S. Ruf, Mao Zeng

    We compute the conservative two-body Hamiltonian of a compact binary system with a spinning black hole through $\mathcal{O}(G^3)$ to all orders in velocity, including linear and quadratic spin terms. To obtain our results we calculate the classical limit of the two-loop amplitude for the scattering of a massive scalar particle with a massive spin-1 particle minimally coupled to gravity. We employ modern scattering amplitude and loop integration techniques, in particular numerical unitarity, integration-by-parts identities, and the method of regions. The conservative potential in terms of rest-frame spin vectors is extracted by matching to a non-relativistic effective field theory. We also apply the Kosower-Maybee-O'Connell (KMOC) formalism to calculate the impulse in the covariant spin formalism directly from the amplitude. We work systematically in conventional dimensional regularization and explicitly evaluate all divergent integrals that appear in full- and effective-theory amplitudes, as well as in the phase-space integrals that arise in the KMOC formalism.

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    Conservative Binary Dynamics with a Spinning Black Hole at O(G3) from Scattering Amplitudes

    by Fernando Febres Cordero, Manfred Kraus, Guanda Lin, Michael S. Ruf, Mao Zeng

    We compute the conservative two-body Hamiltonian of a compact binary system with a spinning black hole through O(G3) to all orders in velocity, including linear and quadratic spin terms. To obtain our results we calculate the classical limit of the two-loop amplitude for the scattering of a massive scalar particle with a massive spin-1 particle minimally coupled to gravity. We employ modern scattering amplitude and loop integration techniques, in particular numerical unitarity, integration-by-parts identities, and the method of regions. The conservative potential in terms of rest-frame spin vectors is extracted by matching to a nonrelativistic effective field theory. We also apply the Kosower-Maybee-O’Connell (KMOC) formalism to calculate the impulse in the covariant spin formalism directly from the amplitude. We work systematically in conventional dimensional regularization and explicitly evaluate all divergent integrals that appear in full- and effective-theory amplitudes, as well as in the phase-space integrals that arise in the KMOC formalism.

    Cited by 181
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    Computational Challenges for Multi-loop Collider Phenomenology

    by Fernando Febres Cordero, Andreas von Manteuffel, Tobias Neumann

    Cited by 31
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    Leading-color two-loop amplitudes for four partons and a W boson in QCD

    by S. Abreu, F. Febres Cordero, H. Ita, M. Klinkert, B. Page, V. Sotnikov

    We present the leading-color two-loop QCD corrections for the scattering of four partons and a W boson, including its leptonic decay. The amplitudes are assembled from the planar two-loop helicity amplitudes for four partons and a vector boson decaying to a lepton pair, which are also used to determine the planar two-loop amplitudes for four partons and a Z/γ∗ boson with a leptonic decay. The analytic expressions are obtained by setting up a dedicated Ansatz and constraining the free parameters from numerical samples obtained within the framework of numerical unitarity. The large linear systems that must be solved to determine the analytic expressions are constructed to be in Vandermonde form. Such systems can be very efficiently solved, bypassing the bottleneck of Gaussian elimination. Our results are expressed in a basis of one-mass pentagon functions, which opens the possibility of their efficient numerical evaluation.

    Cited by 133
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