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In the present paper, the process of inverse double-Compton (IDC) scattering is considered in the context of astrophysical applications. It is assumed that the two hard X-ray photons emitted from an astrophysical source are scattered on a free electron and converted into a single soft photon of optical range. Using the QED S-matrix formalism for the derivation of a cross-section of direct double-Compton (DDC) scattering and assuming detailed balance conditions, an analytical expression for the cross-section of the IDC process is presented. It is shown that at fixed energies of incident photons, the inverse cross-section has no infrared divergences, and its behavior is completely defined by the spectral characteristics of the photon source itself, in particular by the finite interaction time of radiation with an electron. Thus, even for the direct process, the problem of resolving infrared divergence actually refers to a real physical source of radiation in which photons are never actually plane waves. As a result, the physical frequency profile of the scattered radiation for DDC as well as for IDC processes is a function of both the intensity and line shape of the incident photon field.

We apply effective field theory (EFT) methods to compute the renormalization group improved effective potential for theories with a large mass hierarchy. Our method allows one to compute the effective potential in a systematic expansion in powers of the mass ratio, as well as to sum large logarithms of mass ratios using renormalization group evolution. The effective potential is the sum of one-particle irreducible diagrams (1PI) but information about which diagrams are 1PI is lost after matching to the EFT, since heavy lines get shrunk to a point. We therefore introduce a tadpole condition in place of the 1PI condition, and use the renormalization group improved value of the tadpole in computing the effective potential. We explain why the effective potential computed using an EFT is not the same as the effective potential of the EFT. We illustrate our method using the $O(N)$ model, a theory of two scalars in the unbroken and broken phases, and the Higgs-Yukawa model. Our leading-log result, obtained by integrating the one-loop $\beta$-functions, correctly reproduces the log-squared term in explicit two-loop calculations. Our method does not have a Goldstone boson infrared divergence problem., Comment: Added a section explaining why the EFT method does not suffer from the Goldstone boson infrared divergence problem. Typos fixed

The $$ \mathcal{N} $$ N = 4 superconformal Yang-Mills theory on flat four-dimensional Minkowski space is a de-confined gauge theory in the sense that the string tension for fundamental representation coloured quarks vanishes. In fact, static fundamental representation quarks which lie in certain half-BPS super-multiplets do not interact at all. An interesting question asks whether such quarks would carry a well-defined global colour charge which, when the gauge is fixed, should have the status of an internal symmetry. We shall present a simple paradigmatic model which suggests that the answer to this question lies in the way in which infrared divergences are dealt with.

We examine in detail the structure of the Regge limit of the (nonplanar) ${\cal N}=4$ SYM four-point amplitude. We begin by developing a basis of color factors $C_{ik}$ suitable for the Regge limit of the amplitude at any loop order, and then calculate explicitly the coefficients of the amplitude in that basis through three-loop order using the Regge limit of the full amplitude previously calculated by Henn and Mistlberger. We compute these coefficients exactly at one loop, through ${\cal O} (\epsilon^2)$ at two loops, and through ${\cal O} (\epsilon^0)$ at three loops, verifying that the IR-divergent pieces are consistent with (the Regge limit of) the expected infrared divergence structure, including a contribution from the three-loop correction to the dipole formula. We also verify consistency with the IR-finite NLL and NNLL predictions of Caron-Huot et al. Finally we use these results to motivate the conjecture of an all-orders relation between one of the coefficients and the Regge limit of the ${\cal N} =8$ supergravity four-point amplitude., Comment: 34 pages; v2: clarification added, minor typos corrected, published version

HepLib is a C++ Library for computations in High Energy Physics, it works on top of GiNaC, a well-established C++ library used to perform symbolic computations. HepLib combines serval well-known packages to get high efficiency, including Qgraf to generate Feynman aptitudes, FORM to perform Dirac/Color matrix related computations, and FIRE or KIRA for integration-by-parts (IBP) reduction. Another core feature of HepLib lies in the numerical evaluation of master integrals using sector decomposition, which is a general method widely used in high-order numerical computation and has been implemented in many public packages in many different languages, and we present another implementation in the language of C++ with many new features. We use GiNaC to handle the symbolic operations, and export the corresponding integrand into an optimized C++ code, that will be compiled internally and linked dynamically, a customizable numerical integrator is selected to perform the numerical integration, while the integrand can be evaluated in different float precisions, including the arbitrary precision supported by MPFR., Comment: 26 pages, 1 figure

We study the Schwinger process in a uniform non-Abelian electric field using a dynamical approach in which we evolve an initial quantum state for gluonic excitations. We evaluate the spectral energy density and number density in the excitations as functions of time. The total energy density has an ultraviolet divergence which we argue gets tamed due to asymptotic freedom, leading to $g^4E^4t^4$ growth, where $g$ is the coupling and $E$ the electric field strength. We also find an infrared divergence in the number density of excitations whose resolution requires an effect such as confinement., Comment: Two columns, 9 pages. 4 figures. Numerical code submitted as ancillary files. Match journal version (PHYS. REV. D.)

We present the galaxy power spectrum in general relativity. Using a novel approach, we derive the galaxy power spectrum taking into account all the relativistic effects in observations. In particular, we show independently of survey geometry that relativistic effects yield no divergent terms (proportional to $k^{-4}P_m(k)$ or $k^{-2}P_m(k)$ on all scales) that would mimic the signal of primordial non-Gaussianity. This cancellation of such divergent terms is indeed expected from the equivalence principle, meaning that any perturbation acting as a uniform gravity on the scale of the experiment cannot be measured. We find that the unphysical infrared divergence obtained in previous calculations occurred only due to not considering all general relativistic contributions consistently. Despite the absence of divergent terms, general relativistic effects represented by non-divergent terms alter the galaxy power spectrum at large scales (smaller than the horizon scale). In our numerical computation of the full galaxy power spectrum, we show the deviations from the standard redshift-space power spectrum due to these non-divergent corrections. We conclude that, as relativistic effects significantly alter the galaxy power spectrum at $k\lesssim k_{eq}$, they need to be taken into account in the analysis of large-scale data., Comment: 29 pages, 10 figures, accepted for publication in JCAP

We study the Wigner function for the inflationary tensor perturbation defined in the real phase space. We compute explicitly the Wigner function including the contributions from the cubic self-interaction Hamiltonian of tensor perturbations. Then we argue that it is no longer an appropriate description for the probability distribution in the sense that quantum nature allows negativity around vanishing phase variables. This comes from the non-Gaussian wavefunction in the mixed state as a result of the non-linear interaction between super- and sub-horizon modes. We also show that this is related to the explicit infrared divergence in the Wigner function, in contrast to the trace of the density matrix., Comment: (v1) 24 pages, (v2) 27 pages, discussions expanded and references added, to appear in Journal of High Energy Physics

The explicit exact analytical expressions for the lowest-order radiative corrections to the semi-inclusive deep inelastic scattering of the polarized particles are obtained in the most compact, covariant form convenient for the numerical analysis. The infrared divergence from the real photon emission is extracted and cancelled using the Bardin-Shumeiko approach. The contribution of the exclusive radiative tail is presented.The analytic results obtained within the ultrarelativistic approximation are also show., Comment: 17 pages, 1 figure

We consider scattering of Faddeev-Kulish electrons in QED and study the entanglement between the hard and soft particles in the final state at the perturbative level. The soft photon spectrum naturally splits into two parts: i) soft photons with energies less than a characteristic infrared scale $E_d$ present in the clouds accompanying the asymptotic charged particles, and ii) sufficiently low energy photons with energies greater than $E_d$, comprising the soft part of the emitted radiation. We construct the density matrix associated with tracing over the radiative soft photons and calculate the entanglement entropy perturbatively. We find that the entanglement entropy is free of any infrared divergences order by order in perturbation theory. On the other hand infrared divergences in the perturbative expansion for the entanglement entropy appear upon tracing over the entire spectrum of soft photons, including those in the clouds. To leading order the entanglement entropy is set by the square of the Fock basis amplitude for real single soft photon emission, which leads to a logarithmic infrared divergence when integrated over the photon momentum. We argue that the infrared divergences in the entanglement entropy (per particle flux per unit time) in this latter case persist to all orders in perturbation theory in the infinite volume limit., Comment: 33 pages, added references and discussions; accepted in Physical Review D; added clarification, corrected typos

Stueckelberg mechanism introduces a scalar field, known as Stueckelberg field, so that gauge symmetry is preserved in the massive abelian gauge theory. In this work, we show that the role of the Stueckelberg field is similar to the Kulish and Faddeev coherent state approach to handle infrared (IR) divergences. We expect that the light-front quantum electrodynamics (LFQED) with Stueckelberg field must be IR finite in the massless limit of the gauge boson. We have explicitly shown the cancellation of IR divergences in the relevant diagrams contributing to self-energy and vertex correction at leading order., Comment: 12 pages, 2 figures, references added

We investigate the low density limit of the Homogeneous Electron system, often called the Strictly Correlated regime. We begin with a systematic presentation of the expansion around infinite r S , based on the first quantized treatments suggested in the existing literature. We show that the expansion is asymptotic in the parameter r S 1 ∕ 4 and that the leading order result contains exponential corrections that are significant even for r S ∼ 100 . Thus, the systematic expansion is of limited utility. As a byproduct of this analysis, we find that there is no Wigner Crystal (WC) in one spatial dimension. This is an example of the Mermin–Wagner theorem, but was not appreciated in some earlier literature. More modern work (Schulz, 1993 [1] ) has come to conclusions identical to ours. Note that the long range Coulomb potential modifies the dispersion relation of phonons in one dimension, but still leads to the instability of the crystal, due to a very weak infrared divergence. We then propose a new approximation scheme based on renormalization group ideas. We show that the Wegner–Houghton–Wilson–Polchinski exact renormalization group equation reduces, in the low density limit, to a classical equation for scale dependent electron and plasmon fields. In principle, this should allow us to lower the wave number cutoff of the model to a point where Wigner’s intuitive argument for dominance of the classical Coulomb forces becomes rigorously correct.

Quantum field theory of equilibrium and nonequilibrium Bose-Einstein condensates is formulated so as to satisfy three basic requirements: the Hugenholtz-Pines relation; conservation laws; identities among vertices originating from Goldstone's theorem I. The key inputs are irreducible four-point vertices, in terms of which we derive a closed system of equations for Green's functions, three- and four-point vertices, and two-particle Green's functions. It enables us to study correlated Bose-Einstein condensates with a gapless branch of single-particle excitations without encountering any infrared divergence. The single- and two-particle Green's functions are found to share poles, i.e., the structure of the two-particle Green's functions predicted by Gavoret and Nozi\`eres for a homogeneous condensate at $T=0$ is also shown to persist at finite temperatures, in the presence of inhomogeneity, and also in nonequilibrium situations., Comment: 12 pages, 2 figures

We construct, in the closed bosonic string, the multiloop amplitude involving $N$ tachyons and one massless particle with $26 -D$ compactified directions, and we show that at least for $D>4$, the soft behaviors of the graviton and dilaton satisfy the same soft theorems as at the tree level, up to one additional term at the subsubleading order, which can only contribute to the dilaton soft behavior and which we show is zero at least at one loop. This is possible, since the infrared divergences due to the non-vanishing tachyon and dilaton tadpoles do not depend on the number of external particles and are therefore the same both in the amplitude with the soft particle and in the amplitude without the soft particle. Therefore this leaves unchanged the soft operator acting on the amplitude without the soft particle. The additional infrared divergence appearing for $D \leq 4$ depend on the number of external legs and must be understood on their own., 20 p. + 23 p. appendices. New version to match the published version; new appendix (A) added and dependence on compactification radii clarified

Recently the Casimir self-entropy of an electromagnetic $\delta$-function shell was considered by two different groups, with apparently discordant conclusions, although both had concluded that a region of negative entropy existed for sufficiently weak coupling. We had found that the entropy contained an infrared divergence, which we argued should be discarded on physical grounds. On the contrary, Bordag and Kirsten recently found a completely finite self-entropy, although they, in fact, have to remove an infrared divergence. Apart from this, the high- and low-temperature results for finite coupling agree precisely for the transverse electric mode, but there are significant discrepancies in the transverse magnetic mode. We resolve those discrepancies here. In particular, it is shown that coupling-independent terms do not occur in a consistent regulated calculation, they likely being an artefact of the omission of pole terms. The results of our previous analysis, especially, the existence of a negative entropy region for sufficiently weak coupling, are therefore confirmed. Finally, we offer some analogous remarks concerning the Casimir entropy of a thin electromagnetic sheet, where the total entropy is always positive. In that case, the origin of the analogous discrepancy can be explicitly isolated., Comment: 10 pages, 1 figure. Changed by including a new Appendix, with resolves the discrepancy with Bordag et al. Clarifications added. To be published in Phys. Rev. D

We revisit the evaluations for the spacelike and timelike $\rho \pi$ transition form factors $F_{\rho\pi}(Q^2)$ and $G_{\rho\pi}(Q^2)$ with the inclusion of the the next-to-leading order (NLO) QCD contributions in the framework of the $k_T$ factorization theorem. The infrared divergence is regularized by the transversal momentum carried by external valence quarks, and ultimately absorbed into the meson wave functions. In the region of $ Q^2 \leqslant 2 \, \textrm{GeV}^2 $, where PQCD factorization apporach applicable, the NLO contribution can bring no larger than $ 35\%$ enhancement to the spacelike form factor $F_{\rho\pi}(Q^2)$. For the timelike form factor derived under the kinematic exchanging symmetry, this contribution is also under control when the momentum transfer squared is large enough. We also prolong our prediction into the small $Q^2$ region by taking the Lattice QCD results into account, and subsequently obtain the coupling $g_{\rho\pi\gamma} = G_{\rho\pi}(0)=0.596$.

Within the standard V - A theory of weak interactions, Quantum Electrodynamics (QED) and the linear sigma-model (LsM) of strong low-energy hadronic interactions we analyse gauge properties of hadronic structure of the neutron and proton in the neutron radiative beta-decay. We show that the Feynman diagrams, describing contributions of hadronic structure to the amplitude of the neutron radiative beta-decay in the tree-approximation for strong low-energy interactions in the LsM, are gauge invariant. In turn, the complete set of Feynman diagrams, describing the contributions of hadron-photon interactions in the one-hadron-loop approximation, is not gauge invariant. In the infinite limit of the scalar sigma-meson, reproducing the current algebra results (Weinberg, Phys. Rev. Lett. 18, 188 (1967)), and to leading order in the large nucleon mass expansion the Feynman diagrams, violating gauge invariance, do not contribute to the amplitude of the neutron radiative beta-decay in agreement with Sirlin's analysis of strong low-energy interactions in neutron beta decays. We assert that the problem of appearance of gauge non-invariant Feynman diagrams of hadronic structure of the neutron and proton is related to the following. The vertex of the effective V-A weak interactions does not belong to the combined quantum field theory including the LsM and QED. We argue that gauge invariant set of Feynman diagrams of hadrons, coupled to real and virtual photons in neutron beta decays, can be obtained within the combined quantum field theory including the Standard Electroweak Model (SEM) and the LsM, where the effective V-A vertex of weak interactions is a result of the W^- - electroweak boson exchange., Comment: 31 pages, 9 figures

Stueckelberg QED with massive photon is known to be renormalizable. But the limit of the mass going to zero is interesting because it brings the resolution to infrared questions through the role of Stueckelberg field at null infinity in addition to providing new asymptotic symmetries. Such symmetries facilitate the soft photon theorems also., Comment: 14 pages, 1 fugure

Using a quantization of the nonassociative and noncommutative Snyder phi^4 scalar field theory in a Hermitian realization, we present in this article analytical formulas for the momentum-conserving part of the one-loop two-point function of this theory in D-, 4-, and 3-dimensional Euclidean spaces, which are exact with respect to the noncommutative deformation parameter beta. We prove that these integrals are regularized by the Snyder deformation. These results indicate that the Snyder deformation does partially regularize the UV divergences of the undeformed theory, as it was proposed decades ago. Furthermore, it is observed that different nonassociative phi^4 products can generate different momentum-conserving integrals. Finally most importantly, a logarithmic infrared divergence emerges in one of these interaction terms. We then analyze sample momentum nonconserving integral qualitatively and show that it could exhibit IR divergence too. Therefore infrared divergences should exist, in general, in the Snyder phi^4 theory. We consider infrared divergences at the limit p -> 0 as UV-IR mixings induced by nonassociativity, since they are associated to the matching UV divergence in the zero-momentum limit and appear in specific types of nonassociative phi^4 products. We also discuss the extrapolation of the Snyder deformation parameter beta to negative values as well as certain general properties of one-loop quantum corrections in Snyder phi^4 theory at the zero-momentum limit., 14 pages, 3 figures, version to be published in Phys. Rev. D

It is widely known that the primordial curvature perturbation $\zeta$ has several universal properties in the infrared (IR) such as the soft theorem, which is also known as the consistency relation, and the conservation in time. They are valid in rather general single clock models of inflation. It has been argued that these universal properties are deeply related to the large gauge transformations in inflationary spacetime. However, the invariance under the large gauge transformations is not sufficient to show these IR properties. In this paper, we show that the locality condition is crucial to show the consistency relation and the conservation of $\zeta$. This argument also can apply to an interacting system with the inflaton and heavy fields which have arbitrary integer spins, including higher spin fields, which may be motivated from string theory. We will also show that the locality condition guarantees the cancellation of the IR divergences in a certain class of variables whose correlation functions resemble cosmologically observable quantities., Comment: 34 pages. v2: fixed typos and added refs

Phenomenological aspects of radiation by relativistic electrons in external field, in matter or the vicinity of matter are reviewed, among which: infrared divergence, coherence length effects, shadowing, enhancement in aligned crystals, quantum recoil and spin effects, electron side-slipping, photon impact parameter and the presence of tunnelling in the radiation process., 15 pages, 1 figure. Talk given at 6th International Conference - Channeling 2014 Charged & Neutral Particles Channeling Phenomena October 5-10, 2014 Capri (Naples) Italy

A space-periodic ground state is shown to exist for lattices of smeared ions in ${R}^3$ coupled to the Schrodinger and scalar fields. The elementary cell is necessarily neutral. The one-dimensional (1D), two-dimensional (2D), and three-dimensional (3D) lattices in ${R}^3$ are considered, and a ground state is constructed by minimizing the energy per cell. The case of a 3D lattice is rather standard, because the elementary cell is compact, and the spectrum of the Laplacian is discrete. In the cases of 1D and 2D lattices, the energy functional is differentiable only on a dense set of variations, due to the presence of the continuous spectrum of the Laplacian that causes the infrared divergence of the Coulomb bond. Respectively, the construction of electrostatic potential and the derivation of the Schrodinger equation for the minimizer in these cases require an extra argument. The space-periodic ground states for 1D and 2D lattices give the model of the nanostructures similar to the carbon nanotubes and grap...

Ultraviolet divergences are widely discussed in studies of entanglement entropy. Also present, but much less understood, are infrared divergences due to zero modes in the field theory. In this note, we discuss the importance of carefully handling zero modes in entanglement entropy. We give an explicit example for a chain of harmonic oscillators in 1D, where a mass regulator is necessary to avoid an infrared divergence due to a zero mode. We also comment on a surprising contribution of the zero mode to the UV-scaling of the entanglement entropy., v2: 12 pages, 8 figures. Minor changes and typos fixed. Figure and details added on the UV behavior of the giant eigenvalue in the limit of large system size. Discussion added of relation to other work

Electromagnetic effects in the leptonic decay rates $\pi^+ \to \mu^+ \nu$ and $K^+ \to \mu^+ \nu$ are evaluated for the first time on the lattice. Following a method recently proposed in Ref. [1] the emission of virtual photons at leading order in the electromagnetic coupling is evaluated on the lattice and the infrared divergence computed for a point-like meson at finite lattice volume is subtracted. The physical decay rate is then obtained by adding the emission of real and virtual photons regularised with a photon mass. Using the gauge ensembles produced by the European Twisted Mass Collaboration with $N_f = 2 + 1 + 1$ dynamical quarks the feasibility of our approach is demonstrated. Preliminary results for the electromagnetic corrections to charged (neutral) pion and kaon masses as well as to the leptonic decay rates of charged pions and kaons are presented., Comment: 7 pages, 4 figures, 1 table, proceedings of the 34th annual International Symposium on Lattice Field Theory, 24-30 July 2016, University of Southampton (UK)

The problem of infrared divergence of the effective electromagnetic field produced by elementary charges is revisited using the model of an electron freely evolving in a photon bath. It is shown that for any finite travel time, the effective field of the electron is infrared-finite, and that in each order of perturbation theory the radiative contributions grow without bound in the large-time limit. Using the Schwinger-Keldysh formalism, factorization of divergent contributions in multi-loop diagrams is proved, and summation of the resulting infinite series is performed. It is demonstrated that the effective electromagnetic field of the electron vanishes in the large-time limit, and that this vanishing respects the total charge conservation and the Gauss law. It is concluded that the physical meaning of infrared singularity in the effective field is the existence of a peculiar irreversible spreading of electric charges, caused by their interaction with the photon field. This spreading exists in vacuum as well as at finite temperature, and shows itself in a damping of the off-diagonal elements of the momentum-space density matrix of electron, but does not affect its momentum probability distribution. It precludes preparation of spatially localized particle states at finite times by operating with free particle states in the remote past. Relationship of the obtained results to the Bloch-Nordsieck theorem is established, and discussed from the standpoint of measurability of the electromagnetic field. The effect of irreversible spreading on the electron diffraction in the classic two-slit experiment is determined, and is shown to be detectable in principle by modern devices already at room temperature., 26 pages, 11 figures

The power spectrum of a stationary process may be calculated in terms of the autocorrelation function using the Wiener-Khinchin theorem. We here generalize the Wiener-Khinchin theorem for nonstationary processes and introduce a time-dependent power spectrum $\ensuremath{\langle}{S}_{{t}_{m}}(\ensuremath{\omega})\ensuremath{\rangle}$ where ${t}_{m}$ is the measurement time. For processes with an aging autocorrelation function of the form $\ensuremath{\langle}I(t)I(t+\ensuremath{\tau})\ensuremath{\rangle}={t}^{\mathrm{\ensuremath{\Upsilon}}}{\ensuremath{\phi}}_{\mathrm{EA}}(\ensuremath{\tau}/t)$, where ${\ensuremath{\phi}}_{\mathrm{EA}}(x)$ is a nonanalytic function when $x$ is small, we find aging $1/{f}^{\ensuremath{\beta}}$ noise. Aging $1/{f}^{\ensuremath{\beta}}$ noise is characterized by five critical exponents. We derive the relations between the scaled autocorrelation function and these exponents. We show that our definition of the time-dependent spectrum retains its interpretation as a density of Fourier modes and discuss the relation to the apparent infrared divergence of $1/{f}^{\ensuremath{\beta}}$ noise. We illustrate our results for blinking-quantum-dot models, single-file diffusion, and Brownian motion in a logarithmic potential.

In this work we study the decay constants of $B$ and $B_s$ mesons based on the wave function obtained in the relativistic potential model. Our results are in good agreement with experimental data which enables us to apply this method to the investigation of $B$-meson distribution amplitudes. A very compact form of the distribution amplitude is obtained. We also investigate the one-loop QCD corrections to the pure leptonic decays of $B$ mesons. We find that, after subtracting the infrared divergence in the one-loop corrections using the factorization method, the QCD one-loop corrections to the hard amplitude of leptonic decay will be zero., Comment: 26 pages, 8 figures, 2 tables. Comments are welcomed; version to appear in Phys.Rev.D

A scheme is presented here to cancel out the topologically unfactorized infrared divergences in the inclusive production of heavy quarkonia, which affect the NRQCD factorization of these processes. The heavy quarkonia are defined as resonance states of QCD instead of color singlet heavy quark pair. Thus the final heavy quark pair is nor necessarily to be color singlet. In addition, the heavy quarkonia are reconstructed by their decay products. As the result, transition between states containing containing heavy quarks caused by exchanges of soft gluons are also taken into account here. Such cancellation is crucial for the NRQCD factorization of these processes., 17 pages, 26 figures

We consider quantum electrodynamics quantized on the light front in Feynman gauge and regulated in the ultraviolet by the inclusion of massive, negative-metric Pauli--Villars (PV) particles in the Lagrangian. The eigenstate of the electron is approximated by a Fock-state expansion truncated to include one photon. The Fock-state wave functions are computed from the fundamental Hamiltonian eigenvalue problem and used to calculate the anomalous magnetic moment, as a point of comparison. Two approaches are considered: a sector-dependent parameterization, where the bare parameters of the Lagrangian are allowed to depend on the Fock sectors between which the particular Hamiltonian term acts, and the standard choice, where the bare parameters are the same for all sectors. Both methods are shown to require some care with respect to ultraviolet divergences; neither method can allow all PV masses to be taken to infinity. In addition, the sector-dependent approach suffers from an infrared divergence that requires a nonzero photon mass; due to complications associated with this divergence, the standard parameterization is to be preferred. We also show that the self-energy effects obtained from a two-photon truncation are enough to bring the standard-parameterization result for the anomalous moment into agreement with experiment within numerical errors. This continues the development of a method for the nonperturbative solution of strongly coupled theories, in particular quantum chromodynamics., Comment: 28 pages, 2 figures, LaTeX with elsarticle.cls

It is shown that the usual quantum field theory leads to an ultraviolet divergence in the vacuum energies and an infrared divergence in the two-point functions of the massive and massless vector fields. Using a new method of quantization it is shown that the vacuum energies converge, and the normal ordering procedure is not necessary. Also the propagators are calculated, which are automatically renormalied.

A scalar quantum field model defined on a pseudo Riemann manifold is considered. The model is unitarily transformed the one with a variable mass. By means of a Feynman-Kac-type formula, it is shown that when the variable mass is short range, the Hamiltonian has no ground state. Moreover the infrared divergence of the expectation values of the number of bosons in the ground state is discussed., The title is revised

We have developed an efficient algorithm for the subtraction of infrared divergences that arise in the evaluation of QED corrections to the anomalous magnetic moment of lepton ( g − 2 ). By incorporating this new algorithm, we have extended the automated code-generating system developed previously to deal with diagrams without internal lepton loops (called q-type), which produced convergent integrals when applied to diagrams that have only ultraviolet-divergent subdiagrams of vertex type. The new system produces finite integrals for all q-type diagrams, including those that contain self-energy subdiagrams and thus exhibit infrared-divergent behavior. We have thus far verified the system for the sixth- and eighth-order cases. We are now evaluating 6354 vertex diagrams of q-type that contribute to the tenth-order lepton g − 2 .

Regularities and higher order regularities of ground states of quantum field models are investigated through the fact that asymptotic annihilation operators vanish ground states. Moreover, a sufficient condition for the absence of a ground state is given.

Regularities and higher order regularities of ground states of quantum field models are investigated through the fact that asymptotic annihilation operators vanish ground states. Moreover, a sufficient condition for the absence of a ground state is given.

Institute of Theoretical Physics, University of Wroclaw,pl. M. Borna 9, 50–204 Wroclaw, Poland(Received January 4, 2007)We briefly review some issues of the nilpotent objects in theoretical physics using simple modelsas an illustration. Nilpotent elements appear at quantum and classical level in several ways. On theone hand there are celebrated BRST operators, external derivative and related with them cohomolo-gy theory, on the other hand there are dual numbers which are a less known structure than complexnumbers but important in many approaches, then there are commuting nilpotent variables, some-how generalizing the nilpotent but anticommuting Grassmann variables used in super-mathematicsand SUSY models. As an interesting fact we note that nilpotent variables demand the use of thegeneralized light-cone geometry with the metric of the null signature.Key words: infrared divergence, hydrodynamical approach, renormalization.PACS number(s): 11.30.Pb, 45.20.JjI. INTRODUCTION

The $H\to gg$ amplitude relevant for Higgs production via gluon fusion is computed in the four-dimensional helicity scheme (FDH) and in dimensional reduction (DRED) at the two-loop level. The required renormalization is developed and described in detail, including the treatment of evanescent $\epsilon$-scalar contributions. In FDH and DRED there are additional dimension-5 operators generating the $H g g$ vertices, where $g$ can either be a gluon or an $\epsilon$-scalar. An appropriate operator basis is given and the operator mixing through renormalization is described. The results of the present paper provide building blocks for further computations, and they allow to complete the study of the infrared divergence structure of two-loop amplitudes in FDH and DRED.

We study the ``Higgs'' amplitude mode in the relativistic quantum $\mathrm{O}(N)$ model in two space dimensions. Using the nonperturbative renormalization group and the Blaizot--M\'endez-Galain--Wschebor approximation (which we generalize to compute four-point correlation functions), we compute the $\mathrm{O}(N)$-invariant scalar susceptibility at zero temperature in the vicinity of the quantum critical point. In the ordered phase, we find a well-defined Higgs resonance for $N=2$ and 3 and determine its universal properties. No resonance is found for $N\ensuremath{\ge}4$. In the disordered phase, the spectral function exhibits a threshold behavior with no Higgs-like peak. We also show that for $N=2$, the Higgs mode manifests itself as a very broad peak in the longitudinal susceptibility in spite of the infrared divergence of the latter. We compare our findings with results from quantum Monte Carlo simulations and $\ensuremath{\epsilon}=4\ensuremath{-}(d+1)$ expansion near $d=3$.

Respecting the group theoretical approach, it is debated that the theory of linear conformal gravity should be formulated through a tensor field of rank-3 and mixed symmetry \cite{binegar}. Pursuing this path, such a field equation was obtained in de Sitter space \cite{takook}. In present work, considering the de Sitter ambient space notation, a proper solution to the physical part of this field equation is obtained. We have also calculated the related two-point function, which is interestingly de Sitter invariant and free of infrared divergence., 10 pages

Extensive investigations show that ${\mathrm{QED}}_{3}$ exhibits dynamical fermion mass generation at zero temperature when the fermion flavor $N$ is sufficiently small. However, it seems difficult to extend the theoretical analysis to finite temperature. We study this problem by means of the Dyson-Schwinger equation approach after considering the effect of finite temperature or disorder-induced fermion damping. Under the widely used instantaneous approximation, the dynamical mass displays an infrared divergence in both cases. We then adopt a new approximation that includes an energy-dependent gauge boson propagator and obtain results for dynamical fermion mass that do not contain infrared divergence. The validity of the new approximation is examined by comparing it to the well-established results obtained at zero temperature.

The quantization scheme based on reduction of the physical states \cite{Park:2014tia} is extended to two gravity-matter systems and pure dS gravity. For the gravity-matter systems we focus on quantization in a flat background for simplicity, and renormalizability is established through gauge-fixing of matter degrees of freedom. Quantization of pure dS gravity has several new novel features. It is noted that the infrared divergence does not arise in the present scheme of quantization. The lapse function constraint plays a crucial role., Comment: 39 pages, 1 figure, refs and clarifications added, version to appear in IJGMMP

The strong phases and CP violation in the rare $\bar{B}^0\to K^+K^-$, $K^{*\pm}K^\mp$, $K^{*+}K^{*-}$ decays are investigated. As these decays proceed only via annihilation type diagrams in the standard model (SM), a dynamical gluon mass is introduced to avoid the infrared divergence in the soft endpoint regions. The Cutkosky rule is adopted to deal with a physical-region singularity of the on mass-shell quark propagators, which leads to a big imaginary part and hence a large strong phase. As a consequence, large CP asymmetries are predicted in those decay modes due to a big interference between the annihilation amplitudes from penguin and tree operators, which may be tested in future more precise experiments.

Resume Nous proposons des bases bi-orthogonales d'ondelettes qui resolvent le probleme de la divergence infra-rouge des series en ondelettes usuelles dans les espaces de Sobolev homogenes H ˙ s ( R n ) . Ces bases permettent de supprimer la divergence dans le cas s − n 2 ∉ N car elles sont aussi des bases de la realisation de H ˙ s ( R n ) . Dans le cas critique s − n 2 ∈ N , elles fournissent un confinement de la divergence infra-rouge sur un « petit » espace. Cette methode de confinement s'applique aussi au processus de Mumford. Pour citer cet article : B. Vedel, C. R. Acad. Sci. Paris, Ser. I 341 (2005).

In this Letter, we investigate the vertex corrections and spectator hard scattering contributions to B → χ c 0 , 2 K decays, which has no leading contribution from naive factorization scheme. A non-zero binding energy b = 2 m c − M is introduced to regularize the infrared divergence of the vertex part. The spectator diagrams also contain logarithmic and linear infrared divergences, for which we adopt a model dependent parametrization. If we neglect possible strong phases in the hard spectator contributions, we obtain a too small branching ratio for χ c 0 K while too large one for χ c 2 K , as can be seen from the ratio of the branching ratio of B + → χ c 2 K + to that of B + → χ c 0 K + , which is predicted to be 2.15 −0.76 +0.63 in our model, while experimentally it should be about 0.1 or even smaller. But a closer examination shows that, assuming large strong phases difference between the twist-2 and twist-3 spectator terms, together with a slightly larger spectator infrared cutoff parameter Λ h , it is possible to accommodate the experimental data. This shows that, for B → χ c 0 , 2 K decays with no factorizable contributions, QCDF seems capable of producing decay rates close to experiments, in contrast to the B → J / ψ K decay which is dominated by the factorizable contributions.

We present a factorization formula for valence quark distributions in a hadron in x-->1 limit. For the example of pion, we arrive at the form of factorization by analyzing momentum flow in the leading and high-order Feynman diagrams. The result confirms the well-known 1-x scaling rule to all orders in perturbation theory, providing the non-perturbative matrix elements for the infrared-divergence factors. We comment on re-summation of perturbative single and double logarithms in 1-x., 7 pages, 2 figures included