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Computation of spin-resummed observables in post-Minkowskian dynamics typically involve evaluation of Feynman integrals deformed by an exponential factor, where the exponent is a linear sum of the momenta being integrated. Such integrals can be viewed as tensor integral generating functions, which provide alternative approaches to tensor reduction of Feynman integrals. We develop a systematic method to evaluate tensor integral generating functions using conventional multiloop integration techniques. The spin-resummed aligned-spin eikonal at second post-Minkowskian order is considered as a phenomenologically relevant example where evaluation of tensor integral generating functions is necessary., Comment: 10 pages, 4 figures

We consider the covariant proposal for the gravitational Compton amplitude for a Kerr black hole. Employing the covariant three- and four-point Compton amplitudes, we assemble the classical one-loop integrand on the maximal cut at all orders in spin, utilizing the method of unitarity. Expanding in powers of spin, we evaluate the one-loop amplitude up to $\mathcal O(G^2 a^8)$. Supplemented with extra contact contributions derived from the far-zone data of the Teukolsky solutions, the one-loop amplitude is in agreement with results available in the literature. We showcase the classical eikonal in the aligned-spin case at $\mathcal O(G^2 a^7)$., Comment: 16 pages + appendices

In this paper, we address the problem of estimating the rotational extrinsics, as well as the scale factors of two gyroscopes rigidly mounted on the same device. In particular, we formulate the problem as a least-squares minimization and introduce a direct algorithm that computes the estimated quantities without any iterations, hence avoiding local minima and improving efficiency. Furthermore, we show that the rotational extrinsics are observable while the scale factors can be determined up to global scale for general configurations of the gyroscopes. To this end, we also study special placements of the gyroscopes where a pair, or all, of their axes are parallel and analyze their impact on the scale factors' observability. Lastly, we evaluate our algorithm in simulations and real-world experiments to assess its performance as a function of key motion and sensor characteristics.

In this paper we revisit the gravitational eikonal amplitudes of two scattering spinning particles and inspect their scrambling power in the spin spaces that is quantified through the tripartite information. We found that in the non-relativistic limit and a special high-energy limit the leading contribution is a quantity that is universal and theory independent. The minimal coupling is singled out with minimal scrambling in a different high momenta limit. We also inspected the initial state dependence of entanglement generation and found that the spin coherent state with vanishing spin may not necessarily be the hardest to entangle. Interestingly, among a family of mixed states, the only P-rep state there known to be the best approximation of classical mixed states was singled out as one with minimal entanglement generated., Comment: 24 pages + appendix, 4 figures

We investigate the worldline quantum field theory (WQFT) formalism for scalar-QED and observe that a generating function emerges from WQFT, from which the scattering angle ensues. This generating function bears important similarities with the radial action in that it requires no consideration of exponentiation of lower-order contributions. We demonstrate the computations of this generating function and the resulting scattering angle of a binary system coupled to electromagnetic field up to the third order in the Post-Minkowskian expansion (3PM).expansion (3PM)., Comment: 4 pages + appendices, typos fixed, references added

Kinematic numerators of Yang-Mills scattering amplitudes possess a rich Lie algebraic structure that suggest the existence of a hidden infinite-dimensional kinematic algebra. Explicitly realizing such a kinematic algebra is a longstanding open problem that only has had partial success for simple helicity sectors. In past work, we introduced a framework using tensor currents and fusion rules to generate BCJ numerators of a special subsector of NMHV amplitudes in Yang-Mills theory. Here we enlarge the scope and explicitly realize a kinematic algebra for all NMHV amplitudes. Master numerators are obtained directly from the algebraic rules and through commutators and kinematic Jacobi identities other numerators can be generated. Inspecting the output of the algebra, we conjecture a closed-form expression for the master BCJ numerator up to any multiplicity. We also introduce a new method, based on group algebra of the permutation group, to solve for the generalized gauge freedom of BCJ numerators. It uses the recently introduced binary BCJ relations to provide a complete set of NMHV kinematic numerators that consist of pure gauge., Comment: 45pages + appx./refs

We study the Post-Minkowskian (PM) and Post-Newtonian (PN) expansions of the gravitational three-body effective potential. At order 2PM a formal result is given in terms of a differential operator acting on the maximal generalized cut of the one-loop triangle integral. We compute the integral in all kinematic regions and show that the leading terms in the PN expansion are reproduced. We then perform the PN expansion unambiguously at the level of the integrand. Finding agreement with the 2PN three-body potential after integration, we explicitly present new $G^2v^4$-contributions at order 3PN and outline the generalization to $G^2v^{2n}$. The integrals that represent the essential input for these results are obtained by applying the recent Yangian bootstrap directly to their $\epsilon$-expansion around three dimensions. The coordinate space Yangian generator that we employ to obtain these integrals can be understood as a special conformal symmetry in a dual momentum space., Comment: 15 pages, 5 figures, 1 ancillary machine-readable file, v2: minor improvements and additions, title adapted to journal title

We construct the gravitational theory emerging from the double-copy of massive scalar quantum chromodynamics in general dimensions. The resulting two-form-dilaton-gravity theory couples to flavored massive scalars gravitationally and via the dilaton. It displays scalar self-interaction terms of arbitrary even order in the fields but quadratic in derivatives. We work out the emerging Lagrangian explicitly up to the sixth order in scalar fields and propose an all order form., Comment: 6 pages, 1 figure, v2: References added, simple resummed form of the action added via field redefinitions

The duality between color and kinematics present in scattering amplitudes of Yang-Mills theory strongly suggest the existence of a hidden kinematic Lie algebra that controls the gauge theory. While associated BCJ numerators are known on closed forms to any multiplicity at tree level, the kinematic algebra has only been partially explored for the simplest of four-dimensional amplitudes: up to the MHV sector. In this paper we introduce a framework that allows us to characterize the algebra beyond the MHV sector. This allows us to both constrain some of the ambiguities of the kinematic algebra, and better control the generalized gauge freedom that is associated with the BCJ numerators. Specifically, in this paper, we work in dimension-agnostic notation and determine the kinematic algebra valid up to certain ${\cal O}\big((\varepsilon_i \cdot \varepsilon_j)^2\big)$ terms that in four dimensions compute the next-to-MHV sector involving two scalars. The kinematic algebra in this sector is simple, given that we introduce tensor currents that generalize standard Yang-Mills vector currents. These tensor currents controls the generalized gauge freedom, allowing us to generate multiple different versions of BCJ numerators from the same kinematic algebra. The framework should generalize to other sectors in Yang-Mills theory., Comment: 43 pages, 4 figures

We demonstrate that a recently proposed classical double copy procedure to construct the effective action of two massive particles in dilaton-gravity from the analogous problem of two color charged particles in Yang-Mills gauge theory fails at next-to-next-to-leading orders in the post-Minkowskian (3PM) or post-Newtonian (2PN) expansions., Comment: v3: typos fixed, version published in PRD

In previous works, we devised a differential operator for evaluating typical integrals appearing in the Cachazo-He-Yuan (CHY) forms and in this paper we further streamline this method. We observe that at tree level, the number of free parameters controlling the differential operator depends solely on the number of external lines, after solving the constraints arising from the scattering equations. This allows us to construct a reduction matrix that relates the parameters of a higher-order differential operator to those of a lower-order one. The reduction matrix is theory-independent and can be obtained by solving a set of explicitly given linear conditions. The repeated application of such reduction matrices eventually transforms a given tree-level CHY-like integral to a prepared form. We also provide analytic expressions for the parameters associated with any such prepared form at tree level. We finally give a compact expression for the multidimensional residue for any CHY-like integral in terms of the reduction matrices. We adopt a dual basis projector which leads to the CHY-like representation for the non-local Bern-Carrasco-Johansson (BCJ) numerators at tree level in Yang-Mills theory. These BCJ numerators are efficiently computed by the improved method involving the reduction matrix., Comment: 20 pages. Citations added. Typo fixed

In \cite{Chen:2016fgi} we proposed a differential operator for the evaluation of the multi-dimensional residues on isolated (zero-dimensional) poles.In this paper we discuss some new insight on evaluating the (generalized) Cachazo-He-Yuan (CHY) forms of the scattering amplitudes using this differential operator. We introduce a tableau representation for the coefficients appearing in the proposed differential operator. Combining the tableaux with the polynomial forms of the scattering equations, the evaluation of the generalized CHY form becomes a simple combinatoric problem. It is thus possible to obtain the coefficients arising in the differential operator in a straightforward way. We present the procedure for a complete solution of the $n$-gon amplitudes at one-loop level in a generalized CHY form. We also apply our method to fully evaluate the one-loop five-point amplitude in the maximally supersymmetric Yang-Mills theory; the final result is identical to the one obtained by Q-Cut., Comment: 34 pages, 10 figures

We propose a differential operator for computing the residues associated with a class of meromorphic $n$-forms that frequently appear in the Cachazo-He-Yuan form of the scattering amplitudes. This differential operator is conjectured to be uniquely determined by the local duality theorem and the intersection number of the divisors in the $n$-form. We use the operator to evaluate the tree-level amplitude of $\phi^3$ theory and the one-loop integrand of Yang-Mills theory from their CHY forms. The method can reduce the complexity of the calculation. In addition, the expression for the 1-loop four-point Yang-Mills integrand obtained in our approach has a clear correspondence with the Q-cut results., Comment: 37 pages

We study three-point correlation functions of local operators in planar $\mathcal{N}=4$ SYM at weak coupling using integrability. We consider correlation functions involving two scalar BPS operators and an operator with spin, in the so called SL(2) sector. At tree level we derive the corresponding structure constant for any such operator. We also conjecture its one loop correction. To check our proposals we analyze the conformal partial wave decomposition of known four-point correlation functions of BPS operators. In perturbation theory, we extract from this decomposition sums of structure constants involving all primaries of a given spin and twist. On the other hand, in our integrable setup these sum rules are computed by summing over all solutions to the Bethe equations. A perfect match is found between the two approaches., Comment: 2 figures

Null Polygon Wilson Loops (WL) in N=4 SYM can be computed using the Operator Product Expansion in terms of a transition amplitude on top of a color flux tube (FT). That picture is valid at any value of the 't Hooft coupling. So far it has been efficiently used at weak coupling (WC) in cases where only a single particle is flowing. At any finite value of the coupling however, an infinite number of particles are flowing on top of the color FT. A major open problem in this approach was how to deal with generic multi-particle states at WC. In this paper we study the propagation of any number of FT excitations at WC. We do this by first mapping the WL into a sum of two point functions of local operators. This map allows us to translate the integrability techniques developed for the spectrum problem back to the WL. E.g., the FT Hamiltonian can be represented as a simple kernel acting on the loop. Having an explicit representation for the FT Hamiltonian allows us to treat any number of particles on an equal footing. We use it to bootstrap some simple cases where two particles are flowing, dual to N2MHV amplitudes. The FT is integrable and therefore has other (infinite set of) conserved charges. The generating function of conserved charges is constructed from the monodromy (M) matrix between sides of the polygon. We compute it for some simple examples at leading order at WC. At strong coupling (SC), these Ms were the main ingredients of the Y-system solution. To connect the WC and SC computations, we study a case where an infinite number of particles are propagating already at leading order at WC. We obtain a precise match between the WC and SC Ms. That match is the WL analogue of the well known Frolov-Tseytlin limit where the WC and SC descriptions become identical. Hopefully, putting the WC and SC descriptions on the same footing is the first step in understanding the all loop structure., Comment: 52 pages, 14 figures, the abstract in the pdf is not encrypted and is slightly more detailed

We extend the Operator Product Expansion for Null Polygon Wilson loops to the Mason-Skinner-Caron-Huot super loop, dual to non MHV gluon amplitudes. We explain how the known tree level amplitudes can be promoted into an infinite amount of data at any loop order in the OPE picture. As an application, we re-derive all one loop NMHV six gluon amplitudes by promoting their tree level expressions. We also present some new all loops predictions for these amplitudes., Comment: 16 pages + appendices; 5 figures