The concepts of pole mass and width are extended to unstable fermions in the general framework of parity-nonconserving gauge theories, such as the Standard Model. In contrast with the conventional on-shell definitions, these concepts are gauge independent and avoid severe unphysical singularities, properties of great importance since most fundamental fermions in nature are unstable particles. General expressions for the unrenormalized and renormalized dressed propagators of unstable fermions and their field-renormalization constants are presented.
We study the behavior of the pole of the fermion propagator, in QED in $n$-dimensions, in a general class of gauges which interpolate between the covariant, the axial and the Coulomb gauges. We use Nielsen identities, following from the BRST invariance of the theory, to determine the gauge variation of the fermion two point function in this general class of gauges. This allows us to show directly and in a simple manner, to all orders in perturbation theory, that in the absence of infrared divergences and mass shell singularities, the fermion pole mass is gauge independent.
Perturbative QCD calculations in the light-cone gauge have long suffered from the ambiguity associated with the regularization of the poles in the gluon propagator. In this work we study sub-gauge conditions within the light-cone gauge corresponding to several known ways of regulating the gluon propagator. Using the functional integral calculation of the gluon propagator, we rederive the known sub-gauge conditions for the theta-function gauges and identify the sub-gauge condition for the principal value (PV) regularization of the gluon propagator's light-cone poles. The obtained sub-gauge cond…
We perform complex analyses of the gluon propagator at nonzero quark chemical potential in the long-wavelength limit, using an effective model with a gluon mass term of the Landau-gauge Yang-Mills theory, which is a Landau-gauge limit of the Curci-Ferrari model with quantum corrections being included within the one-loop level. We mainly investigate complex poles of the gluon propagator, which could be relevant to confinement. Around typical values of the model parameters, we show that the gluon propagator has one or two pairs of complex conjugate poles depending on the value of the chemical po…
We suggest a framework based on the rainbow approximation with effective parameters adjusted to lattice data. The analytic structure of the gluon and ghost propagators of QCD in Landau gauge is analyzed by means of numerical solutions of the coupled system of truncated Dyson-Schwinger equations. We find that the gluon and ghost dressing functions are singular in complex Euclidean space with singularities as isolated pairwise conjugated poles. These poles hamper solving numerically the Bethe-Salpeter equation for glueballs as bound states of two interacting dressed gluons. Nevertheless, we argu…
Starting from the lattice Landau gauge gluon and ghost propagator data we use a sequence of Padé approximants, identify the poles and zeros for each approximant and map them into the analytic structure of the propagators. For the Landau gauge gluon propagator the Padé analysis identifies a pair of complex conjugate poles and a branch cut along the negative real axis of the Euclidean $p^2$ momenta. For the Landau gauge ghost propagator the Padé analysis shows a single pole at $p^2 = 0$ and a branch cut also along the negative real axis of the Euclidean $p^2$ momenta. The method gives precise es…
The analytic structure of the 2 flavour full QCD lattice Landau gauge quark propagator is investigated with Padé approximants applied to its vector and scalar form factors. No poles at complex momentum are observed for the propagator. Moreover, there is clear evidence of a pole at real on-axis negative Euclidean momentum, i.e. for Minkowski type of momentum. %, with a positive residuum. This pole occurs at Euclidean momenta $p^2 \sim - 300$ MeV and it reproduces typical quark mass values used in phenomenological effective quark models. The Padé approximant analysis also gives hints on the pres…
In view of the expectation that the existence of complex poles is a signal of confinement, we investigate the analytic structure of the gluon, quark, and ghost propagators in the Landau gauge QCD and QCD-like theories by employing an effective model with a gluon mass term of the Yang-Mills theory, which we call the massive Yang-Mills model. In this model, we particularly investigate the number of complex poles in the parameter space of the model consisting of gauge coupling constant, gluon mass, and quark mass for the gauge group $SU(3)$ and various numbers of quark flavors $N_F$ within the as…
We study analytic structures of the gluon, quark, and ghost propagators in the Landau-gauge QCD and general properties from the existence of unusual singularities. First, we investigate analytic structures of the QCD propagators using the massive Yang-Mills model, in which the one-loop gluon and ghost propagators are in good agreement with the numerical lattice results in the Landau gauge. We find that both gluon and quark propagators in this model have complex poles that invalidate the usual spectral representation. Second, we discuss general properties of propagators in the presence of such …
We derive general relationships between the number of complex poles of a propagator and the sign of the spectral function originating from the branch cut in the Minkowski region under some assumptions on the asymptotic behaviors of the propagator. We apply this relation to the mass-deformed Yang-Mills model with one-loop quantum corrections, which is identified with a low-energy effective theory of the Yang-Mills theory, to show that the gluon propagator in this model has a pair of complex conjugate poles or "tachyonic" poles of multiplicity two, in accordance with the fact that the gluon fiel…
We report on a study of the analytical structure of the Landau gauge gluon, ghost and quark propagators taken from lattice simulations using large physical volumes, to better access the IR region, and large gauge ensembles to reduce the statistical uncertainties. The investigation uses Padé approximants to look at poles and branch cuts for each of the propagators. For the gluon propagator we identify complex conjugate poles and a branch point. For the ghost propagator the procedure identifies a pole at zero momentum and a branch point for Minkowski-like momenta. The quark propagator appears to…
Most discussions of propagators in Lee-Wick theories focus on the presence of two massive complex conjugate poles in the propagator. We show that there is in fact only one pole near the physical region, or in another representation three pole-like structures with compensating extra poles. The latter modified Lehmann representation is useful caculationally and conceptually only if one includes the resonance structure in the spectral integral.
Gauge theory correlators are potentially more singular in the infrared than those in non-gauge theories. We determine the implications that these singularities have on the spectrum of the theory, proving that the appearance of generalised poles implies the existence of on-shell states with fixed mass, but zero norm. For quantum chromodynamics these poles have direct relevance for the confinement of coloured states. Using lattice data for the Landau gauge gluon propagator we subsequently test for the presence of these poles, establishing that the data is indeed consistent with such a component.
We describe the unitarity approach for the numerical computation of two-loop integral coefficients of scattering amplitudes. It is well known that the leading propagator singularities of an amplitude's integrand are related to products of tree amplitudes. At two loops, Feynman diagrams with doubled propagators appear naturally, which lead to subleading pole contributions. In general, it is not known how these contributions can be directly expressed in terms of a product of on-shell tree amplitudes. We present a universal algorithm to extract these subleading pole terms by releasing some of the…
We discuss the analytic continuation of the gluon propagator from the Euclidean region to the complex squared-momentum plane towards the Minkowski region from a viewpoint of gluon confinement. For this purpose, we investigate the massive Yang-Mills model with one-loop quantum corrections, which is to be identified with a low-energy effective theory of the Yang-Mills theory in the sense that the confining decoupling solution for the Euclidean gluon and ghost propagators of the Yang-Mills theory in the Landau gauge obtained by numerical simulations on the lattice are reproduced with good accurac…
The electron propagator in a laser background has been shown to be made up of a series of sideband poles. In this paper we study this decomposition by analysing the impact of the residual gauge freedom in the Volkov solution on the sidebands. We show that the gauge transformations do not alter the location of the poles. The identification of the propagator from the two-point function is maintained but we show that the sideband structures mix under residual gauge transformations.
We study resummed perturbative contributions due to a heavy top-quark. These renormalon contributions are evaluated for fermion propagators. Results for the top-quark width are given. Estimates of non-perturbative uncertainties are made on the ρ-parameter using different schemes of dealing with the Landau-pole. For the physical top-quark mass the effects are negligible.
We consider a mixed system of unstable Majorana fermions in a general parity-nonconserving theory and renormalize its propagator matrix to all orders in the pole scheme, in which the squares of the renormalized masses are identified with the complex pole positions and the wave-function renormalization (WFR) matrices are adjusted in compliance with the Lehmann-Symanzik-Zimmermann reduction formalism. In contrast to the case of unstable Dirac fermions, the WFR matrices of the in and out states are uniquely fixed, while they again bifurcate in the sense that they are no longer related by pseudo-H…
Propagators approximated by a meromorphic functions with complex conjugated poles are widely used to model infrared behavior of QCD Green's functions. In this paper, analytical solutions for two point correlator made out of functions with complex conjugated poles or branch points have been obtained in the Minkowski space for the first time. As a special case the Gribov propagator has been considered as well. The result is different from the naive analytical continuation of the correlator primarily defined in the Euclidean space. It is free of ultraviolet divergences, and instead of Lehmann it …
The quantization of non-Abelian gauge theories is known to be plagued by Gribov copies. Typical examples are the copies related to zero modes of the Faddeev-Popov operator, which give rise to singularities in the ghost propagator. In this work we present an exact and compact expression for the ghost propagator as a function of external gauge fields, in SU(N) Yang-Mills theory in the Landau gauge. It is shown, to all orders, that the condition for the ghost propagator not to have a pole, the so-called Gribov's no-pole condition, can be implemented by demanding a nonvanishing expectation value f…
In this paper we present an iterative method to generate an infinite class of new nonlocal field theories whose propagators are ghost-free. We first examine the scalar field case and show that the pole structure of such generalized propagators possesses the standard two derivative pole and in addition can contain complex conjugate poles which, however, do not spoil at least tree level unitarity as the optical theorem is still satisfied. Subsequently, we define analogous propagators for the fermionic sector which is also devoid of unhealthy degrees of freedom. As a third case, we apply the same…
We extend the double copy picture of scattering amplitudes to a class of matrix elements (so-called form factors) that involve local gauge invariant operators. Both the Bern, Carrasco and Johansson (BCJ) and the Kawai, Lewellen and Tye (KLT) formalisms are considered and novel properties are observed. One remarkable feature is that through the double-copy construction, certain spurious poles hidden in the gauge form factors become physical propagators in gravity. This mechanism also reveals new hidden relations for form factors which can be understood as a generalization of the BCJ relations.
The Graviton Propagator in Asymptotically Safe Gravity with Non-Local Form Factors
INAF Osservatorio Astrofisico di Catania（意大利国家天体物理研究所卡塔尼亚天文台）；INFN, Sezione di Catania（意大利国家核物理研究所卡塔尼亚分部）；Università di Catania, Dipartimento di Fisica e Astronomia（卡塔尼亚大学物理与天文学系）
We study the Landau-gauge Gribov ghost form-factor sigma(p^2) for SU(N) Yang-Mills theories in the d-dimensional case. We find a qualitatively different behavior for d=3,4 w.r.t. d=2. In particular, considering any (sufficiently regular) gluon propagator D(p^2) and the one-loop-corrected ghost propagator G(p^2), we prove in the 2d case that sigma(p^2) blows up in the infrared limit p -> 0 as -D(0)\ln(p^2). Thus, for d=2, the no-pole condition σ(p^2) < 1 (for p^2 > 0) can be satisfied only if D(0) = 0. On the contrary, in d=3 and 4, sigma(p^2) is finite also if D(0) > 0. The same results are ob…
Unitarity cut method has been proved to be very useful in the computation of one-loop integrals. In this paper, we generalize the method to the situation where the powers of propagators in the denominator are larger than one in general. We show how to use the trick of differentiation over masses to translate the problem to the integrals where all powers are just one. Then by using the unitarity cut method, we can find the wanted reduction coefficients of all basis except the tadpole. Using this method, we calculate the reduction of scalar bubble, scalar triangle, scalar box and scalar pentagon…
We consider a mixed system of Dirac fermions in a general parity-nonconserving theory and renormalize the propagator matrix to all orders in the pole scheme, in which the squares of the renormalized masses are identified with the complex pole positions and the wave-function renormalization (WFR) matrices are adjusted in compliance with the Lehmann-Symanzik-Zimmermann reduction formalism. We present closed analytic all-order expressions and their expansions through two loops for the renormalization constants in terms of the scalar, pseudoscalar, vector, and pseudovector parts of the unrenormali…
It is known that Noncommutative QED (NCQED) exhibits Gribov ambiguities in the Landau gauge. These ambiguities are related to zero modes of the Faddeev-Popov operator and arise in the ghost propagator when it has a pole. In this work, we establish a positive Faddeev-Popov operator for NCQED and the condition for the ghost propagator not to have poles, the so-called Gribov no-pole condition. This condition is implemented in the path integral, and allows for the calculation of the photon propagator in momentum space, which is dependent on the squared non-commutativity parameter. In the commutati…
We study the properties of the poles of the resummed graviton propagator obtained by resumming bubble matter diagrams which correct the classical graviton propagator. These poles have been previously interpreted as black holes precursors. Here, we show using the Horizon Wave-Function formalism that these poles indeed have properties which make them compatible with being black hole precursors. In particular, when modeled with a Breit-Wigner distribution, they have a well defined gravitational radius. The probability that the resonance is inside its own gravitational radius, and thus that it is …
We present a generalized theoretical framework for dealing with the important issue of dynamical mass generation in Yang-Mills theories, and, in particular, with the infrared finiteness of the gluon propagators, observed in a multitude of recent lattice simulations. Our analysis is manifestly gauge-invariant, in the sense that it preserves the transversality of the gluon self-energy, and gauge-independent, given that the conclusions do not depend on the choice of the gauge-fixing parameter within the linear covariant gauges. The central construction relies crucially on the subtle interplay bet…
We perform lattice simulations in pure-SU(2) Yang-Mills theory to investigate how the infrared behavior of electric and magnetic gluon propagators in Landau gauge is affected by temperature. We consider the largest lattices to date, in an attempt to keep systematic errors under control. Electric and magnetic screening masses are calculated through an Ansatz from the zero-temperature case, based on complex-conjugate poles for the momentum-space propagators. As recently reported in [1], we find good fits to the proposed form at all temperatures considered, with different ratios of real to imagin…
We determine the gluon and ghost spectral functions along with the analytic structure of the associated propagators from numerical data describing gauge correlators at space-like momenta obtained by either solving the Dyson-Schwinger equations or through lattice simulations. Our novel reconstruction technique shows the expected branch cut for the gluon and the ghost propagator, which, in the gluon case, is supplemented with a pair of complex conjugate poles. Possible implications of the existence of these poles are briefly addressed.
Generalized dispersion relations are discussed for unphysical particles, e.g. confined degrees of freedom that are not present in the physical spectra but can give rise to observable bound states. While in general the propagator of the unphysical particles can have complex poles and cannot be reconstructed from the knowledge of the imaginary part, under reasonable assumptions the missing piece of information is shown to be in the rational function that contains the poles and must be added to the integral representation. For pure Yang-Mills theory, the rational part and the spectral term are id…
We study a toy model for an interacting scalar field theory in which the fundamental excitations are confined in the sense of having unphysical, positivity-violating propagators, a fact tracing back to a decomposition of these in propagators with complex conjugate mass poles (the so-called $i$-particles). Similar two-point functions show up in certain approaches to gluon or quark propagators in Yang-Mills gauge theories. We investigate the spectrum of our model and show that suitable composite operators may be constructed having a well-defined Källén-Lehmann spectral representation, thus allow…
In this paper we study perturbatively an extension of the Stelle higher derivative gravity involving an infinite number of derivative terms. We know that the usual quadratic action is renormalizable but is not unitary because of the presence of a ghost in the theory (pole with negative residue in the propagator). The new theory is instead ghost-free since an entire function (or form factor) is introduced in the model without involving new poles in the propagator. The local high derivative theory is recovered expanding the entire functions to the lowest order in the mass scale of the theory. An…
Explicit analytical expressions are derived for the gluon propagator in a generic linear covariant $R_ξ$ gauge, by a screened massive expansion for the exact Faddeev-Popov Lagrangian of pure Yang-Mills theory. At one-loop, if the gauge invariance of the pole structure is enforced, the gluon dressing function is entirely and uniquely determined, without any free parameter or external input. The gluon propagator is found finite in the IR for any $ξ$, with a slight decrease of its limit value when going from the Landau gauge ($ξ=0$) towards the Feynman gauge ($ξ=1$). An excellent agreement is fou…
In this work we study a modified theory of gravity that contains up to fourth order spatial derivatives as a model for the Horava-Lifshitz gravity. The propagator is evaluated and, as a result, it is obtained one extra pole corresponding to a spin two nonrelativistic massless particle, an extra term which jeopardizes renormalizability, besides the unexpected general relativity unmodified propagator. Then, unitarity is proved at the tree-level, where the general relativity pole has shown to have no dynamics, remaining only the two degrees of freedom of the new pole. Next, the nonrelativistic ef…
The symmetries of a scalar field theory in multifractional spacetimes are analyzed. The free theory realizes the Poincaré algebra, and the associated symmetries are modifications of ordinary translations and Lorentz transformations. In the interacting case, the Poincaré algebra is broken by interaction terms. The Feynman propagator of the scalar field is computed and found to possess the usual mass poles. As a consequence of these findings, the mass of a particle is a well-defined concept at all scales, and a perturbative quantum theory can be constructed.
In this work analyze the physical consistency of a nonbirefringent Lorentz-violating planar model via the analysis of the pole structure of its Feynman propagators. The nonbirefringent planar model, obtained from the dimensional reduction of the CPT-even gauge sector of the standard model extension, is composed of a gauge and a scalar fields, being affected by Lorentz-violating (LIV) coefficients encoded in the symmetric tensor $κ_{μν}$. The propagator of the gauge field is explicitly evaluated and expressed in terms of linear independent symmetric tensors, presenting only one physical mode. T…
In this work we study the behaviour of Yang--Mills--Chern--Simons theory coupled to a Higgs field in the fundamental representation by taking into account the effects of the presence of the Gribov horizon. By analyzing the infrared structure of the gauge field propagator, both confined and de-confined regions can be detected. The confined region corresponds to the appearance of complex poles in the propagators, while the de-confined one to the presence of real poles. One can move from one region to another by changing the parameters of the theory.
A longstanding question in QCD is the origin of the mass gap in the Yang-Mills sector of QCD, i.e., QCD without quarks. In Landau gauge QCD this mass gap, and hence confinement, is encoded in a mass gap of the gluon propagator, which is found both in lattice simulations and with functional approaches. While functional methods are well suited to unravel the mechanism behind the generation of the mass gap, a fully satisfactory answer has not yet been found. In this work we solve the coupled Dyson-Schwinger equations for the ghost propagator, gluon propagator and three-gluon vertex. We corroborat…
