Ultraviolet Divergences Research Articles

Light scalars at the cosmological collider

We study the self-energies of weakly interacting scalar fields in de Sitter space with one field much lighter than the Hubble scale. We argue that self-energies drastically simplify in this light limit. We illustrate this in theories with two scalar fields, one heavy and one light, interacting with one another through either cubic or quartic interactions. To regulate infrared divergences, we compute these self-energies in Euclidean de Sitter space and then carefully analytically continue to Lorentzian signature. In particular, we do this for the most general renormalizable theory of two scalar fields with even interactions to leading order in the coupling and the mass of the light field. These self-energies are determined by de Sitter sunset diagrams, whose analytic structure and UV divergences we derive. Even at very weak couplings, the light field can substantially change how the heavy field propagates over long distances. The light field’s existence may then be inferred from how it modifies the heavy field’s oscillatory contribution to the primordial bispectrum in the squeezed limit, i.e. its cosmological collider signal.

Dynamics of heavy quarks in the Fock space

This paper concerns a method of describing hadrons that starts with the canonical front form Hamiltonian of QCD. The method is developed in the relatively simple context of QCD with only heavy quarks. We regulate its canonical Hamiltonian by introducing a vanishingly small gluon mass mg. For positive mg, the small-x gluon divergences become ultraviolet and hence they are renormalized in the same way the ultraviolet transverse divergences are. This is done using the renormalization group procedure for effective particles. Up to the second order of expansion of the renormalized Hamiltonian in powers of the quark-gluon coupling constant g, only the quark mass-squared and gluon-exchange divergences require counterterms. In these circumstances, we calculate an effective potential between quarks in heavy quarkonia in an elementary way, replacing all the quarkonium-state components with gluons of mass mg by only one component with just one gluon that is assigned a mass mG, comparable to or exceeding the scale of typical relative momenta of bound quarks. In the limit of mg→0 and large mG two results are obtained. (1) While the color-singlet quarkonium mass eigenvalue stays finite and physically reasonable in that limit, the eigenvalues for single quarks and octet quarkonia are infinite. (2) Besides the coulomb terms, the effective quark-antiquark potential is quadratic as a function of the distance and spherically symmetric for typical separations between quarks but becomes logarithmic and no longer spherically symmetric for large separations. Our conclusion indicates how to systematically improve upon the approximations made in this paper. Published by the American Physical Society 2024

Corrected calculation for the non-local solution to the g − 2 anomaly and novel results in non-local QED

We provide the corrected calculation of the (g − 2)μ in non-local QED previously done in the literature. In specific, we show the proper technique for calculating loops in non-local QED and use it to find the form factors F1(q2) and F2(q2) in non-local QED. We also utilize this technique to calculate some novel results in non-local QED, including calculating the correction to the photon self-energy, the modification to the classical Coulomb potential, the modification to the energy levels of the hydrogen atom, and the contribution to the Lamb shift. We also discuss charge dequantization through non-locality, and show that the experimental bounds on the electric charge on Dirac neutrinos, translate into strong flavor-dependent bounds on the scale on non-locality that range between 105−1010 TeV. We also discuss the inconsistencies of unrenormalized non-local Quantum Field Theories (QFTs) and the need for renormalizing them, even when they are free from UV divergences.

Forward production of a Drell-Yan pair and a jet at small x at next-to-leading order

We perform the analytical next-to-leading order calculation of the process p + A γ∗ + jet + X, at forward rapidities and low x. These kinematics justify a hybrid approach, where a quark from the ‘projectile’ proton scatters off the gluon distribution of the ‘target’, which can be a nucleus or a highly boosted proton. By using the Color Glass Condensate effective theory approach, this gluon distribution is allowed to be so dense that the quark undergoes multiple scattering. Moreover, large high-energy logarithms in the ratio of the hard scale and the center-of-mass energy are resummed by the Balitsky, Kovchegov, Jalilian-Marian, Iancu, McLerran, Weigert, Leonidov, Kovner or BK-JIMWLK evolution equations. We demonstrate that all ultraviolet divergences encountered in the calculation cancel, while the high-energy divergences are absorbed into BK-JIMWLK. The remaining singularities are collinear in nature and can be either absorbed into the Dokshitzer-Gribov-Lipatov-Altarelli-Parisi evolution of the incoming quark, when they stem from initial-state radiation, or else can be treated by a jet function in case they are caused by final-state emissions. The resulting cross section is completely finite and expressed in function of only a small set of color operators.

Holographic quantum distances and replica trick

This paper gives concrete examples to exhibit how to use the replica trick to calculate the quantum (quasi-)distances holographically. First, we consider the fidelity and relative entropy between thermal states that are dual to the Schwarzschild-AdS black holes. Then we generalize our method into the RN-AdS black holes by adding a U(1) gauge field. We also investigate the fidelity between states excited by scalar operator in probe limit. In this case, it is surprising that the fidelity in standard quantization will suffer from new UV divergence though the usual holographic renormalization has been applied. We call for deep understanding for such divergence in the future. We also discover a holographic method to check whether the density matrices of two holographic states are commutative.

Hybrid renormalization for quasi distribution amplitudes of a light baryon

We develop a hybrid scheme to renormalize quasi distribution amplitudes of a light baryon on the lattice, which combines the self-renormalization and ratio scheme. By employing self-renormalization, the UV divergences and linear divergence at large spatial separations in quasi distribution amplitudes are removed without introducing extra nonperturbative effects, while making a ratio with respect to the zero-momentum matrix element can properly remove the UV divergences in small spatial separations. As a specific application, distribution amplitudes of the Λ baryon made of uds are investigated, and the requisite equal-time correlators, which define quasi distribution amplitudes in coordinate space, are perturbatively calculated up to the next-to-leading order in strong coupling constant αs. These perturbative equal-time correlators are used to convert lattice QCD matrix elements to the continuum space during the renormalization process. Subsequently, quasi distribution amplitudes are matched onto lightcone distribution amplitudes by integrating out hard modes and the corresponding hard kernels are derived up to next-to-leading order in αs including the hybrid counterterms. These results are valuable in the lattice-based investigation of the lightcone distribution amplitudes of a light baryon from the first principles of QCD.

Fusion of conformal defects in interacting theories

We study fusion of two scalar Wilson defects. We propose that fusion holds at a quantum level by showing that bare one-point functions are the same. This is an expected result as the path integral is invariant under fusion of the two defects. The difference instead lies in renormalization of local quantities on the defects. Those on the fused defect takes into account UV divergences in the fusion limit when the two defects approach eachother, in addition to UV divergences in the coincident limit of defect-local fields and in the near defect limits of bulk-local fields. At the fixed point of the corresponding RG flow the two conformal defects have fused into a single conformal defect identical to one of the original scalar Wilson defects.Parts of this paper was first presented in my thesis [1].

The [formula omitted] vertex in a left–right model

We consider the one-loop corrections to the Zbb¯ vertex in a CP-conserving left–right model (LRM), viz. a model with gauge group SU(2)L×SU(2)R×U(1). We allow the gauge coupling constants of SU(2)L and SU(2)R to be different. The spontaneous symmetry breaking is accomplished only by doublets and/or singlets of SU(2)L and SU(2)R. The lightest massive neutral gauge boson of our LRM is assumed to have the same Yukawa couplings to bottom-quark pairs as the Z of the Standard Model (SM); this assumption has the advantage that, then, the infrared divergences automatically cancel down in the subtraction of the Zbb¯ vertex in the SM from the same vertex in the LRM. We effect a proper renormalization of the Zbb¯ vertex and check explicitly both its gauge invariance and the cancellation of all the ultraviolet divergences. We find out that a LRM with the above assumptions cannot achieve a better fit to the Zbb¯ vertex than a multi-Higgs extension of the SM, viz. both models can only achieve a decent fit when one admits scalar particles with very low masses ≲50 GeV. This is true even when we allow for markedly different gauge coupling constants of SU(2)L and SU(2)R.

On the gravitational diagram technique in the discrete setup

This paper is in the spirit of our work on the consequences of the Regge calculus, where some edge length scale arises as an optimal initial point of the perturbative expansion after functional integration over connection. Now consider the perturbative expansion itself. To obtain an algorithmizable diagram technique, we consider the simplest periodic simplicial structure with a frozen part of the variables (“hypercubic”). After functional integration over connection, the system is described by the metric [Formula: see text] at the sites. We parameterize [Formula: see text] so that the functional measure becomes Lebesgue. The discrete diagrams are free from ultraviolet divergences and reproduce (for ordinary, non-Planck external momenta) those continuum counterparts that are finite. We give the parametrization of [Formula: see text] up to terms, providing, in particular, additional three-graviton and two-graviton-two-matter vertices, which can give additional one-loop corrections to the Newtonian potential. The edge length scale is [Formula: see text], where [Formula: see text] defines the free factor [Formula: see text] in the measure and should be a large parameter to ensure the true action after integration over connection. We verify the important fact that the perturbative expansion does not contain increasing powers of [Formula: see text] if its initial point is chosen close enough to the maximum point of the measure, thus justifying this choice. Discrete propagators depend on the Barbero–Immirzi parameter [Formula: see text], which determines the ratio of timelike and spacelike elementary length scales. The existing estimates of [Formula: see text] allow the propagator poles to have real energy for any (real) spatial momenta.

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.

Thermal analysis of photon-like particles in rainbow gravity

This work is devoted to study the thermodynamic behavior of photon-like particles within the rainbow gravity formalism. To to do this, we chose two particular ansatzs to accomplish our calculations. First, we consider a dispersion relation which avoids UV divergences, getting a positive effective cosmological constant. We provide numerical analysis for the thermodynamic functions of the system and bounds are estimated. Furthermore, a phase transition is also expected for this model. Second, we consider a dispersion relation employed in the context of Gamma Ray Bursts. Remarkably, for this latter case, the thermodynamic properties are calculated in an analytical manner and they turn out to depend on the harmonic series Hn, gamma Γ(z), polygamma ψn(z) and zeta Riemann functions ζ(z).

Gravitational form factors of a kink in 1 + 1 dimensional ϕ4 model

We calculate the one-loop correction to the distribution of energy-momentum tensor around a kink in 1 + 1 dimensional ϕ4 model. We employ the collective coordinate method to eliminate the zero mode that gives rise to infrared divergence. The ultraviolet divergences are removed by vacuum subtraction and mass renormalization. We obtain an analytic result that is finite and satisfies the momentum conservation. The total energy of the kink obtained from the spatial integral of energy density reproduces the known result. Our result obtained on a finite space has a spatially-uniform term that is inversely proportional to the spatial length.

Color-Dual Fates of F^{3}, R^{3}, and N=4 Supergravity.

We find that the duality between color and kinematics can be used to inform the high energy behavior of effective field theories. Namely, we demonstrate that the massless gauge theory of Yang-Mills deformed by a higher-derivative F^{3} operator cannot be tree level color dual while consistently factorizing without a tower of additional four-point counterterms with rigidly fixed Wilson coefficients that reaches to the ultraviolet (UV). We find through explicit calculation a suggestive resummation, namely that their amplitudes are consistent with the α^{'} expansion of those generated by the (DF)^{2}+YM theory, a known color-dual theory where the F^{2} term has been given a mass squared proportional to 1/α^{'}. As a result, considering consistent double-copy construction as a physical principle implies that an F^{3}-based color-dual resolution of the UV divergence in N=4 supergravity comes at the cost of field-theoretic locality. Similarly, when double copying F^{3} with itself, double-copy consistency lifts R^{3} gravity to a family of gravity theories with an all-order tower of higher-derivative corrections, which includes the closed bosonic string as a standard adjoint-type double copy.

Running vacuum in QFT in FLRW spacetime: the dynamics of rho _{textrm{vac}}(H) from the quantized matter fields

Phenomenological work in the last few years has provided significant support to the idea that the vacuum energy density (VED) is a running quantity with the cosmological evolution and that this running helps to alleviate the cosmological tensions afflicting the Lambda CDM. On the theoretical side, recent devoted studies have shown that the properly renormalized rho _{textrm{vac}} in QFT in FLRW spacetime adopts the ‘running vacuum model’ (RVM) form. While in three previous studies by two of us (CMP and JSP) such computations focused solely on scalar fields non-minimally coupled to gravity, in the present work we compute the spin-1/2 fermionic contributions and combine them both. The calculation is performed using a new version of the adiabatic renormalization procedure based on subtracting the UV divergences at an off-shell renormalization point M. The quantum scaling of rho _{textrm{vac}} with M turns into cosmic evolution with the Hubble rate, H. As a result the ‘cosmological constant’ Lambda appears in our framework as the nearly sustained value of 8pi G(H)rho _{textrm{vac}}(H) around (any) given epoch H, where G(H) is the gravitational coupling, which is also running, although very mildly (logarithmically). We find that the VED evolution at present reads delta rho _textrm{vac}(H)sim nu _{textrm{eff}}, m_{textrm{Pl}}^2 left( H^2-H_0^2 right) (|nu _{textrm{eff}}|ll 1). The coefficient nu _{textrm{eff}} receives contributions from all the quantized fields, bosons and fermions, which we compute here for an arbitrary number of matter fields. Remarkably, there also exist higher powers mathcal{O}(H^{6}) which can trigger inflation in the early universe. Finally, the equation of state (EoS) of the vacuum receives also quantum corrections from bosons and fermion fields, shifting its value from − 1. The striking consequence is that the EoS of the quantum vacuum may nowadays effectively appears as quintessence.

Resummation and renormalization of kinematical effects in inclusive P-wave quarkonium production

We investigate the renormalization properties of the shape function formalism for inclusive production of P-wave heavy quarkonia, which arises from resumming a class of corrections coming from kinematical effects associated with the motion of the heavy quark and antiquark pair relative to the quarkonium. Such kinematical effects are encoded in the nonperturbative shape functions, which are normalized to the corresponding nonrelativistic QCD long-distance matrix elements. By using the known ultraviolet divergences in the matrix elements, we derive the large-momentum asymptotic behavior of the shape functions. This strongly constrains the form of the shape functions and significantly reduces the dependence on the nonperturbative model. Based on these results we show that the shape function formalism at loop level can be useful in taming the threshold logarithms at large transverse momentum, and at small transverse momentum the kinematical corrections reduce the sizes of χc and χb cross sections which may improve agreement with measurements.

Accelerating Unruh-DeWitt detectors coupled with a spinor field

The behavior of accelerating Unruh-DeWitt detectors coupled with a spinor field in (3+1)-dimensional spacetime is investigated. For a single point-like detector with Gaussian switching function, the transition probability increases with the acceleration and thus the antiUnruh effect effect cannot occur. Due to the spinor structure of the Dirac field, UV divergences are encountered in the calculation of the entanglement between the detectors. After introducing some UV cutoff Λ, the negativity of detectors is shown to behave nonmonotonically with respect to the acceleration. Besides, the negativity increases with the cutoff Λ and decreases with the distance between the detectors. The mutual information between the two detectors is also discussed.

Deformation of d = 4, mathcal{N} ≥ 5 supergravities breaks nonlinear local supersymmetry

We study d = 4, mathcal{N} ≥ 5 supergravities and their deformation via candidate counterterms, with the purpose to absorb UV divergences. We generalize the earlier studies of deformation and twisted self-duality constraint to the case with unbroken local mathcal{H} -symmetry in presence of fermions. We find that the deformed action breaks nonlinear local supersymmetry. We show that all known cases of enhanced UV divergence cancellations are explained by nonlinear local supersymmetry.This result implies, in particular, that if mathcal{N} = 5 supergravity at five loop will turn out to be UV divergent, the deformed theory will be BRST inconsistent. If it will be finite, it will be a consequence of nonlinear local supersymmetry and E7-type duality.

Heat statistics in the relaxation process of the Edwards-Wilkinson elastic manifold.

The stochastic thermodynamics of systems with a few degrees of freedom has been studied extensively so far. We would like to extend the study to systems with more degrees of freedom and even further-continuous fields with infinite degrees of freedom. The simplest case for a continuous stochastic field is the Edwards-Wilkinson elastic manifold. It is an exactly solvable model of which the heat statistics in the relaxation process can be calculated analytically. The cumulants require a cutoff spacing to avoid ultraviolet divergence. The scaling behavior of the heat cumulants with time and the system size as well as the large deviation rate function of the heat statistics in the large size limit is obtained.

Approach to Equilibrium of Statistical Systems: Classical Particles and Quantum Fields Off-Equilibrium

Non-equilibrium evolution at absolute temperature T and approach to equilibrium of statistical systems in long-time (t) approximations, using both hierarchies and functional integrals, are reviewed. A classical non-relativistic particle in one spatial dimension, subject to a potential and a heat bath (hb), is described by the non-equilibrium reversible Liouville distribution (W) and equation, with a suitable initial condition. The Boltzmann equilibrium distribution Weq generates orthogonal (Hermite) polynomials Hn in momenta. Suitable moments Wn of W (using the Hn’s) yield a non-equilibrium three-term hierarchy (different from the standard Bogoliubov–Born–Green–Kirkwood–Yvon one), solved through operator continued fractions. After a long-t approximation, the Wn’s yield irreversibly approach to equilibrium. The approach is extended (without hb) to: (i) a non-equilibrium system of N classical non-relativistic particles interacting through repulsive short range potentials and (ii) a classical ϕ4 field theory (without hb). The extension to one non-relativistic quantum particle (with hb) employs the non-equilibrium Wigner function (WQ): difficulties related to non-positivity of WQ are bypassed so as to formulate approximately approach to equilibrium. A non-equilibrium quantum anharmonic oscillator is analyzed differently, through functional integral methods. The latter allows an extension to relativistic quantum ϕ4 field theory (a meson gas off-equilibrium, without hb), facing ultraviolet divergences and renormalization. Genuine simplifications of quantum ϕ4 theory at high T and large distances and long t occur; then, through a new argument for the field-theoretic case, the theory can be approximated by a classical ϕ4 one, yielding an approach to equilibrium.

Self-Adjointness of a Class of Multi-Spin–Boson Models with Ultraviolet Divergences

We study a class of quantum Hamiltonian models describing a family of N two-level systems (spins) coupled with a structured boson field of positive mass, with a rotating-wave coupling mediated by form factors possibly exhibiting ultraviolet divergences. Spin–spin interactions which do not modify the total number of excitations are also included. Generalizing previous results in the single-spin case, we provide explicit expressions for the self-adjointness domain and the resolvent of these models, both of them carrying an intricate dependence on the spin–field and spin–spin coupling via a family of concatenated propagators. This construction is also shown to be stable, in the norm resolvent sense, under approximations of the form factors via normalizable ones, for example an ultraviolet cutoff.