IR Singularities Research Articles

Loop corrections versus marginal deformations in celestial holography

Four-dimensional all-loop amplitudes in quantum electrodynamics and gravity exhibit universal IR singularities with a factorization structure. This structure is governed by tree amplitudes and a universal IR-divergent factor representing the exchange of soft particles between external lines. This Letter offers a precise dual interpretation of these universal IR-divergent factors within celestial holography. Considering the tree amplitude as the foundation of the celestial conformal field theory (CCFT), these universal factors correspond to marginal deformations with a construction in the CCFT. Remarkably, a novel geometric representation of these deformations through topological gauging provides an exact description of transitions within bulk vacuum moduli spaces which extends the celestial holography beyond the perturbative level. Our findings establish a concrete dictionary for celestial holography and offer a holographic lens to understand loop corrections in scattering amplitudes. Published by the American Physical Society 2024

Monte-Carlo tool SANCphot for polarized γγ collision simulation

Our study of theoretical uncertainties for the four bosons processes at one-loop level including the case of the transverse polarization is presented. The calculations are based on helicity amplitudes approach for 4-boson SM interactions through a fermion and boson loops. The computation takes into account nonzero mass of loop particles. The obtained predictions are equally suitable for a wide range of energies and for arbitrary, including extreme, regions of the phase volume. Uncertainty estimates are received using the new Monte-Carlo tool SANCphot for γγ collision simulation with final states γγ, γZ, ZZ adapted for polarized γ beams. Program summaryProgram Title: sancphot-v1.01CPC Library link to program files:https://doi.org/10.17632/5sn9nywv2b.1Licensing provisions: LGPLProgramming language: Fortran, C, C++Nature of problem: Theoretical calculations at next-to-leading order in perturbation theory allow to compute higher precision amplitudes for Standard Model processes and decays, provided proper treatments of UV divergences and IR singularities are performed.Solution method: Numerical integration of the precomputed differential expressions for polarized photon-photon cross sections of four-boson interaction processes implemented as SANC modules [1].Additional comments including restrictions and unusual features: Uses subprograms Looptools [2], Cuba [3].The list of processes is limited to photon-photon, photon-Z and Z-Z collisions.

Field theories on ρ-deformed Minkowski space-time

We study one-loop perturbative properties of scalar field theories on the ρ-Minkowski space. The corresponding star-product, together with the involution are characterized from a combination of Weyl quantization and defining properties of the convolution algebra of the Euclidean group linked to the coordinate algebra of the ρ-Minkowski space. The natural integration measure linked to the Haar measure of the Euclidean group defines a trace for the star-product. One-loop properties of the 2-point and 4-point functions for families of complex-valued scalar field theories on ρ-Minkowski space are examined. For scalar theories with orientable interaction, the 2-point function is found to receive UV quadratically diverging one-loop corrections in 4 dimensions while no IR singularities generating UV/IR mixing appears. These however occur in the one-loop corrections to the 4-point function. As well, one-loop 2-point functions for theories with non-orientable interaction involve such IR singularities. These results are discussed.

Hadron-hadron collision mode in ReneSANCe-v1.3.0

We report an implementation of the hadron-hadron (pp and pp¯) collision mode to the Monte Carlo event generator ReneSANCe — the code that was previously developed for e+e− collisions. The described extension of ReneSANCe currently contains neutral and charged current Drell-Yan processes pp[pp¯]→ZX→ℓ+ℓ−X, pp[pp¯]→W+X→ℓ+νℓX and pp[pp¯]→W−X→ℓ−ν¯ℓX. We take into account complete one-loop electroweak (EW) and one-loop QCD corrections to these processes. The calculation is based on the SANC (Support for Analytic and Numeric Calculations for experiments at colliders) modules. The generator is constructed in such a way that new processes can be easily added. The paper contains a theoretical description of the SANC approach, numerical validations and a manual. Program summaryProgram Title:ReneSANCe version 1.3.0CPC Library link to program files:https://doi.org/10.17632/wp36f7t3ft.2Licensing provisions: GPLv3Programming language: FORTRAN 77/90, C, C++External routines: ROOT (https://root.cern.ch), LHAPDF (https://lhapdf.hepforge.org)Journal reference of previous version: Comput. Phys. Commun. 256 (2020) 107445Does the new version supersede the previous version?: Yes.Reasons for the new version: Implementation of the hadron-hadron collision mode.Summary of revisions: Added support of the pp and pp¯ collision modes. Implemented neutral and charged current Drell-Yan processes.Nature of problem: Theoretical calculations at next-to-leading order in perturbation theory allow to compute higher precision amplitudes for Standard Model processes and decays. Proper treatments of UV divergences and IR singularities are performed.Solution method: Numerical integration of the precomputed differential expressions for cross sections of certain processes implemented as SANC modules [1,2].Additional comments including restrictions and unusual features:ReneSANCe homepage https://renesance.hepforge.org. The SANC modules and codes also available at http://sanc.jinr.ru. The list of processes in the hadron-hadron collision mode is limited to pp[pp¯]→ZX→ℓ+ℓ−X, pp[p¯]→W+X→ℓ+νℓX and pp[p¯]→W−X→ℓ+ν¯ℓX.

UV graviton scattering and positivity bounds from IR dispersion relations

Scattering amplitudes mediated by graviton exchange display IR singularities in the forward limit. This obstructs standard application of positivity bounds based on twice subtracted dispersion relations. Such divergences can be cancelled only if the UV limit of the scattering amplitude behaves in a specific way, which implies a very non-trivial connection between the UV and IR behaviors of the amplitude. We show that this relation can be expressed in terms of an integral transform, obtaining analytic results when $t \log{s}\rightarrow 0$. Carefully applying this limit to dispersion relations, we find that infinite arc integrals, which are usually taken to vanish, can give a non-trivial contribution in the presence of gravity, unlike in the case of finite negative $t$. This implies that gravitational positivity bounds cannot be trusted unless the size of this contribution is estimated in some way, which implies assumptions on the UV completion of gravitational interactions. We discuss the relevance of these findings in the particular case of QED coupled to gravity.

Resurgence and semiclassical expansion in two-dimensional large-N sigma models

The resurgence structure of the 2d O(N) sigma model at large N is studied with a focus on an IR momentum cutoff scale a that regularizes IR singularities in the semiclassical expansion. Transseries expressions for condensates and correlators are derived as series of the dynamical scale Λ (nonperturbative exponential) and coupling λμ renormalized at the momentum scale μ. While there is no ambiguity when a > Λ, we find for a < Λ that the nonperturbative sectors have new imaginary ambiguities besides the well-known renormalon ambiguity in the perturbative sector. These ambiguities arise as a result of an analytic continuation of transseries coefficients to small values of the IR cutoff a below the dynamical scale Λ. We find that the imaginary ambiguities are cancelled each other when we take all of them into account. By comparing the semiclassical expansion with the transseries for the exact large-N result, we find that some ambiguities vanish in the a → 0 limit and hence the resurgence structure changes when going from the semiclassical expansion to the exact result with no IR cutoff. An application of our approach to the ℂPN−1 sigma model is also discussed. We find in the compactified model with the ℤN twisted boundary condition that the resurgence structure changes discontinuously as the compactification radius is varied.

The Fundamental Scale of QCD

There are several scales in the QCD as the theory of strong interaction: the vacuum gluonic condensate (as the divergence of the dilatation current), the nucleon mass as the basic mass scale in our universe, which is connected to the string tension $\sigma$, and the perturbative QCD scale $\Lambda_{\rm QCD}$, which defines the scale of the renormalized perturbative expansions. In this paper we connect all these scales to the vacuum condensate, using the field correlator method, where the string tension is expressed in terms of nonlocal field correlators, which are connected to the local condensates, while the perturbative $\Lambda_V$ is connected to $\sigma$ in the framework of the Background Perturbation Theory (BPT). We also demonstrate how the IR singularities and IR renormalons disappear in BPT making the resulting theory internally consistent.

UV/IR mixing in noncommutative SU(N) Yang\u2013Mills theory

We show that there are one-loop IR singularities arising from UV/IR mixing in noncommutative SU(N) Yang–Mills theory defined by means of the theta -exact Seiberg–Witten map. This is in spite of the fact that there are no ordinary U(1) gauge fields in the theory and this is at variance with the noncommutative U(N) case, where the two-point part of the effective action involving the ordinary SU(N) fields do not suffer from those one-loop IR singularities.

Locally finite two-loop amplitudes for off-shell multi-photon production in electron-positron annihilation

We study the singularity structure of two-loop QED amplitudes for the production of multiple off-shell photons in massless electron-positron annihilation and develop counterterms that remove their infrared and ultraviolet divergences point by point in the loop integrand. The remainders of the subtraction are integrable in four dimensions and can be computed in the future with numerical integration. The counterterms capture the divergences of the amplitudes and factorize in terms of the Born amplitude and the finite remainder of the one-loop amplitude. They consist of simple one- and two-loop integrals with at most three external momenta and can be integrated analytically in a simple manner with established methods. We uncover novel aspects of fully local IR factorization, where vertex and self energy subdiagrams must be modified by new symmetrizations over loop momenta, in order to expose their tree-like tensor structures and hence factorization of IR singularities prior to loop integration. This work is a first step towards isolating locally the hard contributions of generic gauge theory amplitudes and rendering them integrable in exactly four dimensions with numerical methods.

Polarized NLO EW [formula omitted] cross section calculations with ReneSANCe-v1.0.0

In this paper we present a new Monte Carlo event generator ReneSANCe for simulation of processes at electron–positron colliders. In the current release of the generator the Bhabha scattering (e+e−→e−e+) and Higgs-strahlung (e+e−→ZH) process are implemented. Based on the SANC (Support for Analytic and Numeric Calculations for experiments at colliders) modules, the new generator takes into account complete one-loop and some higher-order electroweak radiative corrections with finite particle masses and polarizations. The new generator effectively operates in the collinear region and at the ZH production threshold. It is constructed in such a way that new processes can be easily added. The paper contains a theoretical description of the SANC approach, numerical validations and manual. Program summaryProgram Title: ReneSANCe-v1.0.0Program Files doi:http://dx.doi.org/10.17632/wp36f7t3ft.1Licensing provisions: GPLv3Programming language: Fortran, C, C++Supplementary material: Looptools [1], FOAM [2]Nature of problem: Theoretical calculations at next-to-leading order in perturbation theory allow to compute higher precision amplitudes for Standard Model processes and decays, provided proper treatments of UV divergences and IR singularities are performed.Solution method: Numerical integration of the precomputed differential expressions for cross sections of certain processes implemented as SANC modules [3,4].Restrictions: The list of processes is limited to e+e−→e−e+ and e+e−→ZH.

\u03ba-Poincar\xe9 invariant orientable field theories at one-loop

We consider a family of κ-Poincaré invariant scalar field theories on 4-d κ-Minkowski space with quartic orientable interaction, that is for which ϕ and its conjugate ϕ† alternate in the quartic interaction, and whose kinetic operator is the square of a Uκ(iso(4))-equivariant Dirac operator. The formal commutative limit yields the standard complex ϕ4 theory. We find that the 2-point function receives UV linearly diverging 1-loop corrections while it stays free of IR singularities that would signal occurrence of UV/IR mixing. We find that all the 1-loop planar and non-planar contributions to the 4-point function are UV finite, stemming from the existence of the particular estimate for the propagator partly combined with its decay properties at large momenta, implying formally vanishing of the beta-functions at 1-loop so that the coupling constants stay scale-invariant at 1-loop.

On the one loop γ ∗ → q q ¯ $$ {\gamma}^{\left(\ast \right)}\to q\overline{q} $$ impact factor and the exclusive diffractive cross sections for the production of two or three jets

We present the calculation of the impact factor for the $\gamma^{(*)}\to q\bar{q}$ transition with one loop accuracy in arbitrary kinematics. The calculation was done within Balitsky's high energy operator expansion. Together with our previous result for the $\gamma^{(*)}\to q\bar{q} g$ Born impact factor it allows one to derive cross-sections for 2- (one loop) and 3-jet (Born) difractive electroproduction. We write such cross sections for the 2 and 3 jet exclusive diffractive electroproduction off a proton in terms of hadronic matrix elements of Wilson lines. For the 2-jet cross section we demonstrate the cancellation of IR, collinear and rapidity singularities. Our result can be directly exploited to describe the recently analyzed data on exclusive dijet production at HERA and used for the study of jet photoproduction in ultraperipheral proton or nuclear scattering.

Closed star product on noncommutative ℝ 3 and scalar field dynamics

We consider the noncommutative space $\mathbb{R}^3_\theta$, a deformation of $\mathbb{R}^3$ for which the star product is closed for the trace functional. We study one-loop IR and UV properties of the 2-point function for real and complex noncommutative scalar field theories with quartic interactions and Laplacian on $\mathbb{R}^3$ as kinetic operator. We find that the 2-point functions for these noncommutative scalar field theories have no IR singularities in the external momenta, indicating the absence of UV/IR mixing. We also find that the 2-point functions are UV finite with the deformation parameter $\theta$ playing the role of a natural UV cut-off. The possible origin of the absence of UV/IR mixing in noncommutative scalar field theories on $\mathbb{R}^3_\theta$ as well as on $\mathbb{R}^3_\lambda $, another deformation of $\mathbb{R}^3$, is discussed.

SCET approach to regularization-scheme dependence of QCD amplitudes

We investigate the regularization-scheme dependence of scattering amplitudes in massless QCD and find that the four-dimensional helicity scheme (FDH) and dimensional reduction (DRED) are consistent at least up to NNLO in the perturbative expansion if renormalization is done appropriately. Scheme dependence is shown to be deeply linked to the structure of UV and IR singularities. We use jet and soft functions defined in soft-collinear effective theory (SCET) to efficiently extract the relevant anomalous dimensions in the different schemes. This result allows us to construct transition rules for scattering amplitudes between different schemes (CDR, HV, FDH, DRED) up to NNLO in massless QCD. We also show by explicit calculation that the hard, soft and jet functions in SCET are regularization-scheme independent.

RG flows in 6D N = (1,0) SCFT from SO(4) half-maximal 7D gauged supergravity

We study $N=2$ seven-dimensional gauged supergravity coupled to three vector multiplets with $SO(4)$ gauge group. The resulting gauged supergravity contains 10 scalars consisting of the dilaton and 9 vector multiplet scalars parametrized by $SO(3,3)/SO(3)\times SO(3)$ coset manifold. The maximally supersymmetric $AdS_7$ vacuum with unbroken $SO(4)$ symmetry is identified with a $(1,0)$ SCFT in six dimensions. We find one new supersymmetric $AdS_7$ critical point preserving $SO(3)_{\textrm{diag}}\subset SO(3)\times SO(3)\sim SO(4)$ and study a holographic RG flow interpolating between the $SO(4)$ and the new $SO(3)$ supersymmetric critical points. The RG flow is driven by a vacuum expectation value of a dimension-four operator and describes a deformation of the UV $(1,0)$ SCFT to another supersymmetric fixed point in the IR. In addition, a number of non-supersymmetric critical points are identified, and some of them are stable with all scalar masses above the BF bound. RG flows to non-conformal $N=(1,0)$ Super Yang-Mills with $SO(2)\times SO(2)$ and $SO(2)$ symmetries are also investigated. Some of these flows have physically acceptable IR singularities since the scalar potential is bounded above. These provide physical RG flows from $(1,0)$ SCFT to non-conformal field theories in six dimensions.

On a Wilson line approach to the study of jet quenching

We address the geometrical structure of the ‘skewed’ correlator of two space-like separated (almost) oppositely directed Wilson lines. Similar objects occur in the analysis of the transverse-momentum broadening probability function, the first moment of which is associated with the jet quenching parameter. We start from the Euclidean space formulation and then transform the result to the Minkowski light-cone geometry, arguing that this procedure is consistent in the leading order of the perturbative expansion. We discuss as well the issues of the UV, rapidity and IR singularities, and the possible use of the proposed approach in lattice simulations.

Model independent electromagnetic corrections in hadronicτdecays

The long distance correction to the total decay width of the $\tau^{\pm}\to K^{0}\pi^{\pm}\nu$ decay is calculated in a model independent approach where a discrimination of photons in the Bremmstrahlung process is assumed. This correction is completely free of UV and IR singularities and moreover, it satisfies electromagnetic gauge invariance. The result of this work can be applied on the tau decays: $\tau^{\pm}\to \pi^{\pm}\pi^{0}\nu, K^{\pm}\pi^{0}\nu$.

Soft gravitational effects in Kadanoff-Baym approach

In de Sitter space, the gravitational fluctuation at the super-horizon scale may make physical quantities time dependent by breaking the de Sitter symmetry. We adopt the Kadanoff-Baym approach to evaluate soft gravitational effects in a matter system at the sub-horizon scale. This investigation proves that only the local terms contribute to the de Sitter symmetry breaking at the one-loop level. The IR singularities in the non-local terms cancel after summing over degenerate states between real and virtual processes. The corresponding IR cut-off is given by the energy resolution like QED. Since the energy resolution is physical and independent of cosmic evolution, the non-local contributions do not induce the de Sitter symmetry breaking. We can confirm that soft gravitational effects preserve the effective Lorentz invariance.

NLO EW and QCD proton–proton cross section calculations with mcsanc-v1.01

mcsanc is a Monte Carlo tool based on the SANC (Support for Analytic and Numeric Calculations for experiments at colliders) modules for higher order calculations in hadron collider physics. It allows to evaluate NLO QCD and EW cross sections for Drell–Yan processes (inclusive), associated Higgs and gauge boson production and single-top quark production in s- and t-channels. The paper contains theoretical description of the SANC approach, numerical validations and manual. Program summaryProgram title: mcsanc-v1.01Catalogue identifier: AEPO_v1_0Program summary URL:http://cpc.cs.qub.ac.uk/summaries/AEPO_v1_0.htmlProgram obtainable from: CPC Program Library, Queen’s University, Belfast, N. IrelandLicensing provisions: Standard CPC licence, http://cpc.cs.qub.ac.uk/licence/licence.htmlNo. of lines in distributed program, including test data, etc.: 144207No. of bytes in distributed program, including test data, etc.: 1115648Distribution format: tar.gzProgramming language: Fortran, C, C++.Computer: x86(-64) architecture.Operating system: Linux.RAM: 2 GBClassification: 11.1, 11.6.External routines: LHAPDF [1]. LoopTools [2], Cuba [3] (included in the distribution file).Nature of problem:Theoretical calculations at next-to-leading order in perturbation theory allow the computation of higher precision amplitudes for Standard Model processes and decays, provided proper treatments of UV divergences and IR singularities are performed.Solution method:Numerical integration of the precomputed differential expressions for partonic cross sections of certain processes implemented as SANC modules [4].Restrictions:The list of processes is limited to Drell–Yan, associated Higgs and gauge boson production and single-top production in s- and t-channels.Running time:From hours to days depending on the requested precision and kinematic conditions. The example provided takes approximately 10–15 min.

BCJ duality and the double copy in the soft limit

We examine the structure of infrared singularities in QCD and quantum General Relativity, from the point of view of the recently conjectured double copy property which relates scattering amplitudes in non-Abelian gauge theories with gravitational counterparts. We show that IR divergences in both theories are consistent with the double copy procedure, to all orders in perturbation theory, thus providing all loop-level evidence for the conjecture. We further comment on the relevance, or otherwise, to the so-called dipole formula, a conjecture for the complete structure of IR singularities in QCD.