Search

We consider the frequency-domain LO and NLO post-Minkowskian (PM) waveforms obtained from the tree-level and one-loop amplitudes describing the scattering of two massive scalar objects and the emission of one graviton. We explicitly calculate their post-Newtonian (PN) limit obtaining an expansion up to the third subleading PN order in all ingredients: the tree-level amplitude, the odd and even parts of the real one-loop kernel, and the Compton or "rescattering" cuts, thus reaching 3PN precision for the latter. We provide explicit expressions for the multipole decomposition of these results in the center-of-mass frame and compare them with the results obtained from the classical Multipolar post-Minkowskian (MPM) method. We find perfect agreement between the two, once the BMS supertranslation frame is properly adjusted and the infrared divergences due to rescattering are suitably subtracted in dimensional regularization. This shows that the approach proposed in arXiv:2312.07452 can be applied beyond the soft-regime ensuring the agreement between amplitude-based and MPM results for generic frequencies., Comment: 17 pages, 2 ancillary files. v2: references updated, typos corrected. v3: published in Phys.Rev.D

In this short note, we address the calculation of the contribution to the one-loop gravitational waveform arising from the difference of the unitarity cuts associated to the $s$- and $s'$-channels recently pointed out in arXiv:2308.02125, providing its explicit expression for minimally-coupled massive scalars in momentum space., Comment: Addendum to arXiv:2303.07006 by the same authors. 4 pages + refs

We revisit the amplitude-based derivation of gravitational waveform for the scattering of two scalar black holes at subleading post-Minkowskian (PM) order. We take an eikonal-inspired approach to the two-massive-particle cut needed in the KMOC framework, as highlighted in arXiv:2308.02125, and show that its effect is to implement a simple change of frame. This clarifies one of the points raised in arXiv:2309.14925 when comparing with the post-Newtonian (PN) results. We then provide an explicit PM expression for the waveform in the soft limit, $\omega\to0$, including the first non-universal, $\omega\log\omega$, contribution. Focusing on this regime, we show that the small-velocity limit of our result agrees with the soft limit of the PN waveform of arXiv:2309.14925, provided that the two quantities are written in the same asymptotic frame. Performing the BMS supertranslation that, as discussed in arXiv:2201.11607, is responsible for the $\mathcal O(G)$ static contribution to the asymptotic field employed in the PN literature, we find agreement between the amplitude-based and the PN soft waveform up to and including $G^3/c^5$ order., Comment: 40 pages, v2: presentation improved

We revisit the space of gapped quantum field theories with a global O(N) symmetry in two spacetime dimensions. Previous works using S-matrix bootstrap revealed a rich space in which integrable theories such as the non-linear sigma model appear at special points on the boundary, along with an abundance of unknown models hinting at a non conventional UV behaviour. We extend the S-matrix set-up by including into the bootstrap form factors and spectral functions for the stress-energy tensor and conserved O(N) currents. Sum rules allow us to put bounds on the central charges of the conformal field theory (CFT) in the UV. We find that a big portion of the boundary can only flow from CFTs with infinite central charges. We track this result down to a particular behaviour of the amplitudes in physical kinematics and discuss its physical implications., Comment: 31 pages + appendices, 13 figures

This contribution discusses a new perception of the structure of compound nuclei by introducing intermediate states of the Feshbach formalism of nuclear reactions in the Interacting Boson Model of nuclear structure. The stake is to explore the manifestation of the unitary limit in heavy, even-even nuclei. Interactions that govern Feshbach resonances of cold and dilute atomic gases suggest the formulation of an IBM-compound Hamiltonian for scattering two neutrons (2n) from a heavy, even-even target (A). The solutions of the corresponding coupled channel equations host a 2n-IBM state resonance. It turns out that the unitary limit is measurable in a heavy A+2n compound nucleus at low temperatures. That measurement is feasible through the fluctuations of the cross-sections that tune the 2n-A scattering length., Comment: Contribution to 13th International Spring Seminar on Nuclear Physics Perspectives and Challenges in Nuclear Structure after 70 Years of Shell Model (ISS 2022) 14/05/2022 - 20/05/2022 Sant'Angelo, Italy

We calculate the inelastic $2\to3$ one-loop amplitude for the scattering of two point-like, spinless objects with generic masses involving the additional emission of a single graviton. We focus on the near-forward, or classical, limit. Our results include the leading and subleading orders in the soft-region expansion, which captures all non-analytic contributions in the transferred momentum and in the graviton's frequency. This allows us to check the first constraint arising from the inelastic exponentiation put forward in Refs. 2107.12891, 2112.07556, 2210.12118 and to calculate the $2\to3$ one-loop matrix element of the $N$-operator, linked to the $S$-matrix by $S = e^{iN}$, showing that it is real, classical and free of infrared divergences. We discuss how our results feature in the calculation of the $\mathcal O(G^3)$ corrections to the asymptotic waveform., Comment: 33 pages + refs. v2: Includes ref. to the addendum arXiv:2312.14710 by the same authors

We present an integrability-based conjecture for the three-point functions of single-trace operators in planar $\mathcal{N}=4$ super-Yang-Mills theory at finite coupling, in the case where two operators are protected. Our proposal is based on the hexagon representation for structure constants of long operators, which we complete to incorporate operators of any length using data from the TBA/QSC formalism. We perform various tests of our conjecture, at weak and strong coupling, finding agreement with the gauge theory through 5 loops for the shortest three-point function and with string theory in the classical limit., Comment: 6 pages, 4 figures, 1 appendix

We compute epsilon-expansions around 4 dimensions of a complete set of master integrals for momentum space five-loop massless propagator integrals in dimensional regularization, up to and including the first order with contributions of transcendental weight nine. Our method is the glue-and-cut technique from Baikov and Chetyrkin, which proves extremely effective in that it determines all expansion coefficients to this order in terms of recursively one-loop integrals and only one further integral. We observe that our results are compatible with conjectures that predict $\pi$-dependent contributions., Comment: 20 pages, 8 figures

We computed a set of structures which appear in the four-point function of protected operators of dimension two in $\mathcal{N}=4$ Super Yang Mills with $SU(N)$ gauge group, at any order in a large $N$ expansion. They are determined only by leading order CFT data. By focusing on a specific limit, we made connection with the dual supergravity amplitude in flat space, where such structures correspond to iterated $s$-cuts. We made several checks and we conjecture that the same interpretation holds for supergravity amplitudes on $AdS_5 \times S^5$., Comment: 43 pages, Ancillary files contains various results presented in the paper. V2: Corrected typos, added references and modified figure. V3: reformatted for J.Phys. A, accepted version

In this manuscript, which is to appear in the proceedings of the conference "MathemAmplitude 2019" in Padova, Italy, we provide an overview of the module intersection method for the the integration-by-parts (IBP) reduction of multi-loop Feynman integrals. The module intersection method, based on computational algebraic geometry, is a highly efficient way of getting IBP relations without double propagator or with a bound on the highest propagator degree. In this manner, trimmed IBP systems which are much shorter than the traditional ones can be obtained. We apply the modern, Petri net based, workflow management system GPI-Space in combination with the computer algebra system Singular to solve the trimmed IBP system via interpolation and efficient parallelization. We show, in particular, how to use the new plugin feature of GPI-Space to manage a global state of the computation and to efficiently handle mutable data. Moreover, a Mathematica interface to generate IBPs with restricted propagator degree, which is based on module intersection, is presented in this review., Comment: 19 pages, 5 figures. To appear in the proceedings of "MathemAmplitudes 2019: Intersection Theory & Feynman Integrals", held in Padova 18-20 December 2019

The purpose of this paper is to introduce the unitary limit as applied in systems of cold atoms into collective states of heavy, even-even nuclei and to identify a related physical example. This is accompanied by the determination of observables of conformal symmetry in nuclear structure. A Hamiltonian is defined that governs the scattering process of an incident pair of two slow neutrons onto a heavy, even-even target nucleus in the framework of the Interacting Boson Model of nuclear structure. A unitary pair-collective state interaction is introduced along with the effective range expansion of a pair-collective state scattering length. The solutions to the coupled channels equations provide a scattering state for the two neutrons that couples with intermediate states of the $A+2n$ compound nucleus. The unitary limit manifests itself when the intermediate states correspond to pair-collective state resonances the positions of which coincide with the energies of IBM states of the closed channels. The position and the width of each resonance is measurable via the fluctuation of the cross section which tunes the pair-collective state scattering length. Conformal symmetry is represented in a tower of equally spaced states that emerges at the unitary limit from two-boson excitations on the IBM state of the closed channel. These tower states are experimentally testable as a regularity pattern of fluctuations of the cross section, in terms of regular positions and widths. The manifestation of the unitary limit and conformal symmetry via fluctuations of the cross section indicates the $A+2n$ compound nucleus as a physical laboratory for the examination of the BCS-BEC crossover, of an underlying critical point and of algebras with infinite number of generators.

We study the four point function of the superconformal primary of the stress-tensor multiplet in four dimensional $\mathcal{N}=4$ Super Yang Mills, at large 't Hooft coupling and in a large $N$ expansion. This observable is holographically dual to four graviton amplitudes in type IIB supergravity on $AdS_5 \times S^5$. We construct the most trascendental piece of the correlator at order $N^{-6}$ and compare it with the flat space limit of the corresponding two loops amplitude. This comparison allows us to conjecture structures of the correlator/amplitude which should be present at any loop order., Comment: 7 pages. V2: reformatted for Phys. Rev. D, accepted version

We introduce an algebro-geometrically motived integration-by-parts (IBP) reduction method for multi-loop and multi-scale Feynman integrals, using a framework for massively parallel computations in computer algebra. This framework combines the computer algebra system Singular with the workflow management system GPI-Space, which is being developed at the Fraunhofer Institute for Industrial Mathematics (ITWM). In our approach, the IBP relations are first trimmed by modern algebraic geometry tools and then solved by sparse linear algebra and our new interpolation methods. These steps are efficiently automatized and automatically parallelized by modeling the algorithm in GPI-Space using the language of Petri-nets. We demonstrate the potential of our method at the nontrivial example of reducing two-loop five-point nonplanar double-pentagon integrals. We also use GPI-Space to convert the basis of IBP reductions, and discuss the possible simplification of IBP coefficients in a uniformly transcendental basis., Comment: minor corrections; We encourage researchers in high energy community to send us IBP reduction problems (mailto: alessandro.georgoudis@physics.uu.se)

The Interacting Boson Model of nuclear structure is introduced to the unitarity limit. Non relativistic conformal symmetry creates a scale invariant state from which the stationary states of atomic nuclei are obtained. A brief discussion of the nature of the conformal field theory is included along with the BCS-BEC crossover and hydrodynamic properties.

We obtain all planar four-point correlators of half-BPS operators in $\mathcal{N}=4$ SYM up to five loops. The ansatz for the integrand is fixed partially by imposing light-cone OPE relations between different correlators. We then fix the integrated correlators by comparing their asymptotic expansions with simple data obtained from integrability. We extract OPE coefficients and find a prediction for the triple wrapping correction of the hexagon form factors, which contributes already at the five-loop order., Comment: 26 pages, 3 figures; ancillary files with results. v2: Published version and corrected typo in triple wrapping result. v3: Corrected error in citations from v2

We present the powerful module-intersection integration-by-parts (IBP) method, suitable for multi-loop and multi-scale Feynman integral reduction. Utilizing modern computational algebraic geometry techniques, this new method successfully trims traditional IBP systems dramatically to much simpler integral-relation systems on unitarity cuts. We demonstrate the power of this method by explicitly carrying out the complete analytic reduction of two-loop five-point non-planar hexagon-box integrals, with degree-four numerators, to a basis of $73$ master integrals., Comment: minor corrections, updated references

We develop a method to obtain $\epsilon$-expansions of massless two-point integrals in position space, based on the constraints implied by symmetries of the asymptotic expansion of conformal four-point integrals. Together with parametric integration, we are able to fix the expansions of 170 genuine five-loop master integrals. In particular, we computed the expansions of all planar master integrals up to transcendental weight 9., Comment: 16 pages + references; results included in ancillary files

Integration-by-parts identities between loop integrals arise from the vanishing integration of total derivatives in dimensional regularization. Generic choices of total derivatives in the Baikov or parametric representations lead to identities which involve dimension shifts. These dimension shifts can be avoided by imposing a certain constraint on the total derivatives. The solutions of this constraint turn out to be a specific type of syzygies which correspond to logarithmic vector fields along the Gram determinant formed of the independent external and loop momenta. We present an explicit generating set of solutions in Baikov representation, valid for any number of loops and external momenta, obtained from the Laplace expansion of the Gram determinant. We provide a rigorous mathematical proof that this set of solutions is complete. This proof relates the logarithmic vector fields in question to ideals of submaximal minors of the Gram matrix and makes use of classical resolutions of such ideals., Comment: 12 pages, two-column format, 3 figures. Added example with internal masses; minor corrections; journal version

Scattering amplitudes computed at a fixed loop order, along with any other object computed in perturbative quantum field theory, can be expressed as a linear combination of a finite basis of loop integrals. To compute loop amplitudes in practice, such a basis of integrals must be determined. We discuss Azurite (A ZURich-bred method for finding master InTEgrals), a publicly available package for finding bases of loop integrals. We also discuss Cristal (Complete Reduction of IntegralS Through All Loops), a future package that produces the complete integration-by-parts reductions., Comment: 7 pages, 3 figures. Contribution to the proceedings of RADCOR 2017, 25-29 September 2017, St. Gilgen, Austria

We examine the coexistence of spherical and $\gamma$-unstable deformed nuclear shapes, described by an SO(5)-invariant Bohr Hamiltonian, along the critical-line. Calculations are performed in the Algebraic Collective Model by introducing two separate bases, optimized to accommodate simultaneously different forms of dynamics. We demonstrate the need to modify the $\beta$-dependence of the moments of inertia, in order to obtain an adequate description of such shape-coexistence., Comment: 6 pages, 4 figures, Proc. 12th Int. Spring Seminar on Nuclear Physics "Current Problems and Prospects for Nuclear Structure", May 15-19, 2017, Sant'Angelo d'Ischia, Italy

We use the method of asymptotic expansions to study the OPE limit of a four-point function of protected operators in N=4 SYM. We use a new method for evaluating the resulting propagator-type integrals and then extract the OPE coefficient with Konishi at the five loop order., Comment: 12 pages

For any given Feynman graph, the set of integrals with all possible powers of the propagators spans a vector space of finite dimension. We introduce the package {\sc Azurite} ({\bf A ZUR}ich-bred method for finding master {\bf I}n{\bf TE}grals), which efficiently finds a basis of this vector space. It constructs the needed integration-by-parts (IBP) identities on a set of generalized-unitarity cuts. It is based on syzygy computations and analyses of the symmetries of the involved Feynman diagrams and is powered by the computer algebra systems {\sc Singular} and {\sc Mathematica}. It can moreover analytically calculate the part of the IBP identities that is supported on the cuts., Comment: Version 1.1.0 of the package Azurite, with parallel computations. It can be downloaded from https://bitbucket.org/yzhphy/azurite/raw/master/release/Azurite_1.1.0.tar.gz

We show that for a class of two-loop diagrams, the on-shell part of the integration-by-parts (IBP) relations correspond to exact meromorphic one-forms on algebraic curves. Since it is easy to find such exact meromorphic one-forms from algebraic geometry, this idea provides a new highly efficient algorithm for integral reduction. We demonstrate the power of this method via several complicated two-loop diagrams with internal massive legs. No explicit elliptic or hyperelliptic integral computation is needed for our method., Comment: minor changes: more references added

The Deformation Dependent Mass (DDM) Kratzer model is constructed by considering the Kratzer potential in a Bohr Hamiltonian, in which the mass is allowed to depend on the nuclear deformation, and solving it by using techniques of supersymmetric quantum mechanics (SUSYQM), involving a deformed shape invariance condition. Analytical expressions for spectra and wave functions are derived for separable potentials in the cases of gamma-unstable nuclei, axially symmetric prolate deformed nuclei, and triaxial nuclei, implementing the usual approximations in each case. Spectra and B(E2) transition rates are compared to experimental data. The dependence of the mass on the deformation, dictated by SUSYQM for the potential used, moderates the increase of the moment of inertia with deformation, removing a main drawback of the model., Comment: 27 pages, 6 figures, 8 tables. arXiv admin note: text overlap with arXiv:1103.5935

A conformal factor in the Bohr model embeds Bohr space in six dimensions, revealing the $O(6)$ symmetry and its contraction to the $E(5)$ at infinity. Phenomenological consequences are discussed after the re-formulation of the Bohr Hamiltonian in six dimensions on a five sphere.

Analytical expressions for spectra and wave functions are derived for a Bohr Hamiltonian, describing the collective motion of deformed nuclei, in which the mass is allowed to depend on the nuclear deformation. Solutions are obtained for separable potentials consisting of a Davidson potential in the beta variable, in the cases of gamma-unstable nuclei, axially symmetric prolate deformed nuclei, and triaxial nuclei, implementing the usual approximations in each case. The solution, called the Deformation Dependent Mass (DDM) Davidson model, is achieved by using techniques of supersymmetric quantum mechanics (SUSYQM), involving a deformed shape invariance condition. Spectra and B(E2) transition rates are compared to experimental data. The dependence of the mass on the deformation, dictated by SUSYQM for the potential used, reduces the rate of increase of the moment of inertia with deformation, removing a main drawback of the model., Comment: 23 pages, 2 figures, 5 tables

The Bohr Hamiltonian describing the collective motion of atomic nuclei is modified by allowing the mass to depend on the nuclear deformation. Exact analytical expressions are derived for spectra and wave functions in the case of a gamma-unstable Davidson potential, using techniques of supersymmetric quantum mechanics. Numerical results in the Xe-Ba region are discussed., Comment: 13 pages, LaTeX, 3 eps figures