Massive Propagator Research Articles

Nonperturbative contributions to the massive propagator in a class of strong interactions

Nonperturbative contributions to the massive propagator in a class of strong interactions

Double nonperturbative gluon exchange: An update on the soft-Pomeron contribution to pp scattering

We employ a set of recent, theoretically motivated, fits to non-perturbative unquenched gluon propagators to check in how far double gluon exchange can be used to describe the soft sector of pp scattering data (total and differential cross section). In particular, we use the refined Gribov--Zwanziger gluon propagator (as arising from dealing with the Gribov gauge fixing ambiguity) and the massive Cornwall-type gluon propagator (as motivated from Dyson-Schwinger equations) in conjunction with a perturbative quark-gluon vertex, next to a model based on the non-perturbative quark-gluon Maris-Tandy vertex, popular from Bethe-Salpeter descriptions of hadronic bound states. We compare the cross sections arising from these models with "older" ISR and more recent TOTEM and ATLAS data. The lower the value of total energy \sqrt{s}, the better the results appear to be.

Higher-twist effects in light-cone sum rule for the Brightarrow pi form factor

We calculate the higher-twist corrections to the QCD light-cone sum rule for the B rightarrow pi transition form factor. The light-cone expansion of the massive quark propagator in the external gluonic field is extended to include new terms containing the derivatives of the gluon-field strength. The resulting analytical expressions for the twist-5 and twist-6 contributions to the correlation function are obtained in a factorized approximation, expressed via the product of the lower-twist pion distribution amplitudes and the quark-condensate density. The numerical analysis reveals that new higher-twist effects for the B rightarrow pi form factor are strongly suppressed. This result justifies the conventional truncation of the operator product expansion in the light-cone sum rules up to twist-4 terms.

Gauge covariance of the fermion Schwinger–Dyson equation in QED

Any practical application of the Schwinger–Dyson equations to the study of n-point Green's functions in a strong coupling field theory requires truncations. In the case of QED, the gauge covariance, governed by the Landau–Khalatnikov–Fradkin transformations (LKFT), provides a unique constraint on such truncation. By using a spectral representation for the massive fermion propagator in QED, we are able to show that the constraints imposed by the LKFT are linear operations on the spectral densities. We formally define these group operations and show with a couple of examples how in practice they provide a straightforward way to test the gauge covariance of any viable truncation of the Schwinger–Dyson equation for the fermion 2-point function.

Gauge field spectrum in massive Yang-Mills theory with Lorentz violation

The spectrum of the massive CPT-odd Yang-Mills propagator with Lorentz violation is performed at tree-level. The modification is due to mass terms generated by the exigence of multiplicative renormalizability of Yang-Mills theory with Lorentz violation. The causality analysis is performed from group and front velocities for both, spacelike and timelike background tensors. It is show that, by demanding causality, it is always possible to define a physical sector for the gauge propagator. Hence, it is expected that the model is also unitary, if one takes the Faddeev-Popov ghost into account.

Analytical study of Yang–Mills theory in the infrared from first principles

Pure Yang–Mills SU(N) theory is studied in the Landau gauge and four dimensional space. While leaving the original Lagrangian unmodified, a double perturbative expansion is devised, based on a massive free-particle propagator. In dimensional regularization, all diverging mass terms cancel exactly in the double expansion, without the need to include mass counterterms that would spoil the symmetry of the Lagrangian. No free parameters are included that were not in the original theory, yielding a fully analytical approach from first principles. The expansion is safe in the infrared and is equivalent to the standard perturbation theory in the UV. At one-loop, explicit analytical expressions are given for the propagators and the running coupling and are found in excellent agreement with the data of lattice simulations. A universal scaling property is predicted for the inverse propagators and shown to be satisfied by the lattice data. Higher loops are found to be negligible in the infrared below 300 MeV where the coupling becomes small and the one-loop approximation is under full control.

Radiation from Secondary Planar Surfaces Sources in Quantum Field Theory

In quantum optics (optical coherence) theorem, many sources are employed in the laboratory are secondary planar sources. A source of this kind is usually an aperture in an opaque planar surface screen, illuminated either directly or via an optical system with primary sources. The expression following into the formulation of the radiation in radiant intensity which, analytical solution has not given the time evolution of amplitude. In this research, we consider this problem in quantum field theory (QFT) view point. By using the method of study based on a configuration space for explaining characteristic of the complete process, which begins and ends with the vacuum state so-called vacuum-to-vacuum transition amplitude between emitters and detectors. Propose in this research, we attend and explain the radiation for radiant intensity with time evolution process. To calculation amplitude transition of massive quantum particles propagator stimulated emission by secondary planar surface sources in space-time. Finally, we use the mathematical program for corresponding numerical evaluations between quantum optics and quantum field theory situation.

BRST-symmetry breaking and Bose-ghost propagator in lattice minimal Landau gauge

The Bose-ghost propagator has been proposed as a carrier of the confining force in Yang-Mills theories in minimal Landau gauge. We present the first numerical evaluation of this propagator, using lattice simulations for the SU(2) gauge group in the scaling region. Our data are well described by a simple fitting function, which is compatible with an infrared-enhanced Bose-ghost propagator. This function can also be related to a massive gluon propagator in combination with an infrared-free (Faddeev-Popov) ghost propagator. Since the Bose-ghost propagator can be written as the vacuum expectation value of a BRST-exact quantity and should therefore vanish in a BRST-invariant theory, our results provide the first numerical manifestation of BRST-symmetry breaking due to restriction of gauge-configuration space to the Gribov region.

Callan-Symanzik approach to infrared Yang-Mills theory

Dyson-Schwinger equations are the most common tool for the determination of the correlation functions of Landau gauge Yang-Mills theory in the continuum, in partic- ular in the infrared regime. We shall argue that the use of Callan-Symanzik renormaliza- tion group equations has distinctive advantages over the Dyson-Schwinger equations, in particular for the vertex functions. We present a generalization of the infrared safe renor- malization scheme proposed by Tissier and Wschebor in 2011. The comparison with the existing lattice data for the gluon and ghost propagators can be used to determine the most appropriate renormalization scheme. Dyson-Schwinger equations have given access to the deep infrared (IR) regime of Landau gauge Yang-Mills theory. The first solutions found show a scaling behavior of the propagators in the IR (1). Several years later, another type of solutions of the same equations was discovered (2), with a massive gluon propagator and a finitely enhanced ghost propagator in the IR (decoupling solutions). To date, Dyson-Schwinger equations are still the main tool for the (semi-)analytical exploration of the IR regime of Yang-Mills theory. In a parallel development that actually initiated much earlier with Gribov's observation of the existence of gauge copies in his famous 1978 paper (3) and was later worked out in great detail by Zwanziger (4), the theoretical foundations of IR Yang-Mills theory were laid. While this so-called Gribov-Zwanziger scenario seemed to confirm the existence of the scaling solutions, a more recent refinement (5) favors the decoupling type of solutions. Finally, the results of simulations of Yang- Mills theory in the Landau gauge on huge lattices (6) have been interpreted by most workers in the field as confirming the realization of the decoupling type of solutions in three and four space-time dimensions. In this contribution, we will present a different technique for the exploration of the IR regime of Yang-Mills theory. We intend to reproduce the results of lattice simulations in the Landau gauge that restrict the gauge field configurations to the (first) Gribov region, but make no attempt to reach the fundamental modular region. The restriction to the Gribov region implies the breaking of BRST invariance in the continuum formulation (4). The most important consequence of the broken BRST invariance for the IR regime is the appearance of a mass term for the gluon field (5). Indeed, the addition of a gluonic mass term to the Yang-Mills action has been shown to reproduce all the solutions (two types of scaling solutions and the decoupling solution) found before with the help of Dyson- Schwinger equations when solving the Callan-Symanzik equations for this theory in the IR regime in

Non-local massive gravity

We present a general covariant action for massive gravity merging together a class of “non-polynomial” and super-renormalizable or finite theories of gravity with the non-local theory of gravity recently proposed by Jaccard, Maggiore and Mitsou (Phys. Rev. D 88 (2013) 044033). Our diffeomorphism invariant action gives rise to the equations of motion appearing in non-local massive gravity plus quadratic curvature terms. Not only the massive graviton propagator reduces smoothly to the massless one without a vDVZ discontinuity, but also our finite theory of gravity is unitary at tree level around the Minkowski background. We also show that, as long as the graviton mass m is much smaller the todayʼs Hubble parameter H0, a late-time cosmic acceleration can be realized without a dark energy component due to the growth of a scalar degree of freedom. In the presence of the cosmological constant Λ, the dominance of the non-local mass term leads to a kind of “degravitation” for Λ at the late cosmological epoch.

Stability of the Landau–Fermi Liquid Theory

The stability of the Landau–Fermi liquid theory is investigated. It has been shown that if the interaction function of the Fermi system is a finite function of the angle between the momenta of two particles at the Fermi surface, then the liquid can be stable. We have shown that the absolute value of the expansion coefficients of the interaction functions in Legendre polynomials are decreasing function of the coefficients indices. We solve the stability condition for one photon exchange (OPE) in an electron gas. The results show that we must use the massive boson propagator (higher order corrections to the photon propagator). Similar to previous works (Abrikosov et al. in Method of Quantum Field Theory in Statistical Physics, Pergamon, Elmsford, 1965), our result is proportional to g2. The density and temperature dependence of results is occulted in the effective mass of the system.

Fine splitting in the charmonium spectrum with a channel coupling effect

We study the fine splitting in the charmomium spectrum in the quark model with the channel coupling effect, including DD, DD*, D*D* and DsDs, DsDs*, Ds*Ds* channels. The interaction for channel coupling is constructed from the current-current Lagrangian related to the color confinement and the one- gluon exchange potentials. By adopting the massive gluon propagator from the lattice calculation in the nonperturbative region, the coupling interaction is further simplified to four-fermion interaction. The numerical calculation still prefers the assignment 1++ of X(3872).

Running gluon mass from a Landau gauge lattice QCD propagator

The interpretation of the Landau gauge lattice gluon propagator as a massive-type bosonic propagator is investigated. Three different scenarios are discussed: (i) an infrared constant gluon mass; (ii) an ultraviolet constant gluon mass; (iii) a momentum-dependent mass. We find that the infrared data can be associated with a massive propagator up to momenta ∼500 MeV, with a constant gluon mass of 723(11) MeV, if one excludes the zero momentum gluon propagator from the analysis, or 648(7) MeV, if the zero momentum gluon propagator is included in the data sets. The ultraviolet lattice data are not compatible with a massive-type propagator with a constant mass. The scenario of a momentum-dependent gluon mass gives a decreasing mass with the momentum, which vanishes in the deep ultraviolet region. Furthermore, we show that the functional forms used to describe the decoupling-like solution of the Dyson–Schwinger equations are compatible with the lattice data with similar mass scales.

On the massive gluon propagator, the PT-BFM scheme and the low-momentum behaviour of decoupling and scaling DSE solutions

We study the low-momentum behaviour of Yang-Mills propagators obtained from Landau-gauge Dyson-Schwinger equations (DSE) in the PT-BFM scheme. We compare the ghost propagator numerical results with the analytical ones obtained by analyzing the low-momentum behaviour of the ghost propagator DSE in Landau gauge, assuming for the truncation a constant ghost-gluon vertex and a simple model for a massive gluon propagator. The asymptotic expression obtained for the regular or decoupling ghost dressing function up to the order ${\cal O}(q^2)$ is proven to fit pretty well the numerical PT-BFM results. Furthermore, when the size of the coupling renormalized at some scale approaches some critical value, the numerical PT-BFM propagators tend to behave as the scaling ones. We also show that the scaling solution, implying a diverging ghost dressing function, cannot be a DSE solution in the PT-BFM scheme but an unattainable limiting case.

Some chirality-related properties of the 4D massive Dirac propagator and determinant in an arbitrary gauge field

For a 4-D massive Dirac field in the background of arbitrary gauge fields, we show that the Dirac propagator and functional determinant are completely determined by knowledge of the corresponding quantities for just one of the chirality sectors of the second-order Dirac operator. This generalizes the related, previously known, statements in (anti-)self-dual background gauge fields. The logarithms of the (renormalized) functional determinants from the two chirality sectors are shown to be different only by a term reflecting the integrated chiral anomaly.

Low-momentum ghost dressing function and the gluon mass

We study the low-momentum ghost propagator Dyson-Schwinger equation (DSE) in Landau gauge, assuming for the truncation a constant ghost-gluon vertex, as it is extensively done, and a simple model for a massive gluon propagator. Then, regular DSE solutions (the zero-momentum ghost dressing function not diverging) appear to emerge and we show the ghost propagator to be described by an asymptotic expression reliable up to the order ${\cal O}(q^2)$. That expression, depending on the gluon mass and the zero-momentum Taylor-scheme effective charge, is proven to fit pretty well the low-momentum ghost propagator obtained through big-volume lattice simulations.

THE LEE-WICK STANDARD MODEL

This article reviews some recent work on a version of the standard model (the Lee-Wick standard model) that contains higher derivative kinetic terms that improve the convergence of loop diagrams removing the quadratic divergence in the Higgs boson mass. Naively higher derivative theories of this type are not acceptable since the higher derivative terms either cause instabilities (from negative energies) or a loss of unitarity (from negative norm states). Lee and Wick provided an interpretation for such theories arguing that theories with higher derivative kinetic terms can be unitary and stable if the states associated with the massive propagator poles, that arise from the higher derivatives, have widths and hence decay and are not in the spectrum of the theory.

On the complete analytic structure of the massive gravitino propagator in four-dimensional de Sitter space

With the help of the general theory of the Heun equation, this paper completes previous work by the authors and other groups on the explicit representation of the massive gravitino propagator in four-dimensional de Sitter space. As a result of our original contribution, all weight functions which multiply the geometric invariants in the gravitino propagator are expressed through Heun functions, and the resulting plots are displayed and discussed after resorting to a suitable truncation in the series expansion of the Heun function. It turns out that there exist two ranges of values of the independent variable in which the weight functions can be divided into dominant and sub-dominant families.

Gluon mass and freezing of the QCD coupling

Infrared finite solutions for the gluon propagator of pure QCD are obtained from the gauge-invariant non-linear Schwinger-Dyson equation formulated in the Feynman gauge of the background field method. These solutions may be fitted using a massive propagator with the special characteristic that the effective ‘mass’ employed drops asymptotically as the inverse square of the momentum transfer, in agreement with general operator-product expansion arguments. Due to the presence of the dynamical gluon mass the strong effective charge extracted from these solutions freezes at a finite value, giving rise to an infrared fixed point for QCD.

On the gauge covariance of the fermion propagator in QED

We study the gauge covariance of the massive fermion propagator in three as well as four-dimensional quantum electrodynamics (QED). Starting from its knowledge at the lowest order in perturbation theory in the Landau gauge, we evaluate a non-perturbative expression for the propagator in arbitrary covariant gauge by means of its Landau-Khalatnikov-Fradkin (LKF) transformation. We compare the weak-coupling expansion of our findings with the known oneloop perturbative results and observe perfect agreement upto a gauge parameter independent term, a difference permitted by the structure of the LKF transformations.