arXiv subjects

D. Binosi

Publications and source records attributed to D. Binosi.

At least 37 records · Page 2Linked to original sources

arXiv2015

A new method for determining the quark-gluon vertex

We present a novel nonperturbative approach for calculating the form factors of the quark-gluon vertex, in a general covariant gauge. The key ingredient of this method is the exact all-order relation connecting the conventional quark-gluon vertex with the corresponding vertex of the background field method, which is Abelian-like. When this latter relation is combined with the standard gauge technique, supplemented by a crucial set of transverse Ward identities, it allows the approximate determination of the nonperturbative behavior of all twelve form factors comprising the quark-gluon vertex, for arbitrary values of the momenta. The actual implementation of this procedure is carried out in the Landau gauge, in order to make contact with the results of lattice simulations performed in this particular gauge. The most demanding technical aspect involves the calculation of certain (fully-dressed) auxiliary three-point functions, using lattice data as input for the gluon propagators appearing in their diagrammatic expansion. The numerical evaluation of the relevant form factors in three special kinematical configurations (soft gluon and quark symmetric limit, zero quark momentum) is carried out in detail, finding rather good agreement with the available lattice data. Most notably, a concrete mechanism is proposed for explaining the puzzling divergence of one of these form factors observed in lattice simulations.

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arXiv2015

Yang-Mills two-point functions in linear covariant gauges

In this work we use two different but complementary approaches in order to study the ghost propagator of a pure SU(3) Yang-Mills theory quantized in the linear covariant gauges, focusing on its dependence on the gauge-fixing parameter $ξ$ in the deep infrared. In particular, we first solve the Schwinger-Dyson equation that governs the dynamics of the ghost propagator, using a set of simplifying approximations, and under the crucial assumption that the gluon propagators for $ξ>0$ are infrared finite, as is the case in the Landau gauge $(ξ=0)$. Then we appeal to the Nielsen identities, and express the derivative of the ghost propagator with respect to $ξ$ in terms of certain auxiliary Green's functions, which are subsequently computed under the same assumptions as before. Within both formalisms we find that for $ξ>0$ the ghost dressing function approaches zero in the deep infrared, in sharp contrast to what happens in the Landau gauge, where it known to saturate at a finite (non-vanishing) value. The Nielsen identities are then extended to the case of the gluon propagator, and the $ξ$-dependence of the corresponding gluon masses is derived using as input the results obtained in the previous steps. The result turns out to be logarithmically divergent in the deep infrared; the compatibility of this behavior with the basic assumption of a finite gluon propagator is discussed, and a specific Ansatz is put forth, which readily reconciles both features.

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arXiv2014

Nonperturbative study of the four gluon vertex

In this paper we study the nonperturbative structure of the SU(3) four-gluon vertex in the Landau gauge, concentrating on contributions quadratic in the metric. We employ an approximation scheme where "one-loop" diagrams are computed using fully dressed gluon and ghost propagators, and tree-level vertices. When a suitable kinematical configuration depending on a single momentum scale $p$ is chosen, only two structures emerge: the tree-level four-gluon vertex, and a tensor orthogonal to it. A detailed numerical analysis reveals that the form factor associated with this latter tensor displays a change of sign (zero-crossing) in the deep infrared, and finally diverges logarithmically. The origin of this characteristic behavior is proven to be entirely due to the masslessness of the ghost propagators forming the corresponding ghost-loop diagram, in close analogy to a similar effect established for the three-gluon vertex. However, in the case at hand, and under the approximations employed, this particular divergence does not affect the form factor proportional to the tree-level tensor, which remains finite in the entire range of momenta, and deviates moderately from its naive tree-level value. It turns out that the kinematic configuration chosen is ideal for carrying out lattice simulations, because it eliminates from the connected Green's function all one-particle reducible contributions, projecting out the genuine one-particle irreducible vertex. Motivated by this possibility, we discuss in detail how a hypothetical lattice measurement of this quantity would compare to the results presented here, and the potential interference from an additional tensorial structure, allowed by Bose symmetry, but not encountered within our scheme.

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arXiv2014

Renormalization Group Equation for Weakly Power Counting Renormalizable Theories

We study the renormalization group flow in weak power counting (WPC) renormalizable theories. The latter are theories which, after being formulated in terms of certain variables, display only a finite number of independent divergent amplitudes order by order in the loop expansion. Using as a toolbox the well-known SU(2) non linear sigma model, we prove that for such theories a renormalization group equation holds that does not violate the WPC condition: that is, the sliding of the scale $μ$ for physical amplitudes can be reabsorbed by a suitable set of finite counterterms arising at the loop order prescribed by the WPC itself. We explore in some detail the consequences of this result; in particular, we prove that it holds in the framework of a recently introduced beyond the Standard Model scenario in which one considers non-linear Stückelberg-like symmetry breaking contributions to the fermion and gauge boson mass generation mechanism.

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arXiv2014

Slavnov-Taylor Identity for the Effective Field Theory of the Color Glass Condensate

We show that a powerful Slavnov-Taylor (ST) identity exists for the Effective Field Theory (EFT) of the Color Glass Condensate (CGC), allowing to control by purely algebraic means the full dependence on the background fields of the fast gluon modes, as well as the correlators of the quantum fluctuations of the classical gluon source. We use this formalism to study the change of the background fast modes (in the Coulomb gauge), induced by the quantum corrections of the semi-fast gluons. We establish the evolution equation for the EFT of the CGC, which points towards an algebraic derivation of the JIMWLK equation. Being based on symmetry-arguments only, the approach can be used to extend the analysis to arbitrary gauges and to higher orders in the perturbation expansion of the EFT.

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arXiv2014

High-energy QCD evolution from BRST symmetry

We show that the (gauge fixed) classical action of the Color Glass Condensate is invariant under a suitable Becchi-Rouet-Stora-Tyutin symmetry, that holds after the gluon modes are split into their fast, semi-fast and soft components, according to the longitudinal momenta they carry. This entails the existence of a corresponding Slavnov-Taylor identity which in turn strongly constrains the effective field theory arising when integrating out the semi-fast modes. Specifically, we prove that this identity guarantees the gauge invariance of the resulting effective theory. In addition, we use it to demonstrate that the integration over the semi-fast modes does not deform the classical Yang-Mills equations of motion, thus validating a key assumption in the usual procedure adopted when deriving the renormalization group equation governing the evolution with energy of the effective theory. As far as the latter are concerned, we finally prove that its functional form is common, and it is determined by symmetries arguments alone. The formal properties of these equations valid in different regimes and/or approximations (e.g., the JIMWLK equation and its BFKL limit) can be therefore derived in a unified setting within this algebraic approach.

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arXiv2014

Renormalization group analysis of the gluon mass equation

In the present work we carry out a systematic study of the renormalization properties of the integral equation that determines the momentum evolution of the effective gluon mass. A detailed, all-order analysis of the complete kernel appearing in this particular equation reveals that the renormalization procedure may be accomplished through the sole use of ingredients known from the standard perturbative treatment of the theory, with no additional assumptions. However, the subtle interplay of terms operating at the level of the exact equation gets distorted by the approximations usually employed when evaluating the aforementioned kernel. This fact is reflected in the form of the obtained solutions, whose deviations from the correct behavior are best quantified by resorting to appropriately defined renormalization-group invariant quantities. This analysis, in turn, provides a solid guiding principle for improving the form of the kernel, and furnishes a well-defined criterion for discriminating between various possibilities. Certain renormalization-group inspired Ansätze for the kernel are then proposed, and their numerical implications are explored in detail. One of the solutions obtained fulfills the theoretical expectations to a high degree of accuracy, yielding a gluon mass that is positive-definite throughout the entire range of physical momenta, and displays in the ultraviolet the so-called "power-law" running, in agreement with standard arguments based on the operator product expansion. Some of the technical difficulties thwarting a more rigorous determination of the kernel are discussed, and possible future directions are briefly mentioned.

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arXiv2013

Effects of divergent ghost loops on the Green's functions of QCD

In the present work we discuss certain characteristic features encoded in some of the fundamental QCD Green's functions, whose origin can be traced back to the nonperturbative masslessness of the ghost field, in the Landau gauge. Specifically, the ghost loops that contribute to these Green's functions display infrared divergences, akin to those encountered in the perturbative treatment, in contradistinction to the gluonic loops, whose perturbative divergences are tamed by the dynamical generation of an effective gluon mass. In d=4, the aforementioned divergences are logarithmic, thus causing a relatively mild impact, whereas in d=3 they are linear, giving rise to enhanced effects. In the case of the gluon propagator, these effects do not interfere with its finiteness, but make its first derivative diverge at the origin, and introduce a maximum in the region of infrared momenta. The three-gluon vertex is also affected, and the induced divergent behavior is clearly exposed in certain special kinematic configurations, usually considered in lattice simulations; the sign of the corresponding divergence is unambiguously determined. The main underlying concepts are developed in the context of a simple toy model, which demonstrates clearly the interconnected nature of the various effects. The picture that emerges is subsequently corroborated by a detailed nonperturbative analysis, combining lattice results with the dynamical integral equations governing the relevant ingredients, such as the nonperturbative ghost loop and the momentum-dependent gluon mass.

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arXiv2013

Gluon mass generation in the presence of dynamical quarks

We study in detail the impact of dynamical quarks on the gluon mass generation mechanism, in the Landau gauge, for the case of a small number of quark families. As in earlier considerations, we assume that the main bulk of the unquenching corrections to the gluon propagator originates from the fully dressed quark-loop diagram. The nonperturbative evaluation of this diagram provides the key relation that expresses the unquenched gluon propagator as a deviation from its quenched counterpart. This relation is subsequently coupled to the integral equation that controls the momentum evolution of the effective gluon mass, which contains a single adjustable parameter; this constitutes a major improvement compared to the analysis presented in Phys. Rev. D86 (2012) 014032, where the behaviour of the gluon propagator in the deep infrared was estimated through numerical extrapolation. The resulting nonlinear system is then treated numerically, yielding unique solutions for the modified gluon mass and the quenched gluon propagator, which fully confirm the picture put forth recently in several continuum and lattice studies. In particular, an infrared finite gluon propagator emerges, whose saturation point is considerably suppressed, due to a corresponding increase in the value of the gluon mass. This characteristic feature becomes more pronounced as the number of active quark families increases, and can be deduced from the infrared structure of the kernel entering in the gluon mass equation.

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arXiv2013

Nonlinearly Realized Gauge Theories for LHC Physics

We consider a minimal nonlinearly realized electroweak theory where mass generation happens à la Stueckelberg. Deformation of the nonlinearly realized gauge symmetry is controlled by functional methods. The Weak Power Counting allows to select uniquely the Hopf algebra of the theory and gives definite predictions on the Beyond-the-Standard Model (BSM) sector of the theory: the latter includes one CP-odd and two charged physical scalars (in addition to the Higgs-like CP-even resonance). The model interpolates between a purely Stueckelberg and a Higgs scenario. It can be used in order to check whether the presence of a Stueckelberg mass component can already be excluded on the basis of the existing LHC7-8 data.

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arXiv2013

AntiBRST symmetry and Background Field Method

We show that the requirement that a SU(N) Yang-Mills action (gauge fixed in a linear covariant gauge) is invariant under both the Becchi-Rouet-Stora-Tyutin (BRST) symmetry as well as the corresponding antiBRST symmetry, automatically implies that the theory is quantized in the (linear covariant) background field method (BFM) gauge. Thus, the BFM and its associated background Ward identity naturally emerge from antiBRST invariance of the theory and need not be introduced as an ad hoc gauge fixing procedure. Treating ghosts and antighosts on an equal footing, as required by a BRST-antiBRST invariant formulation of the theory, gives also rise to a local antighost equation that together with the local ghost equation completely resolve the algebraic structure of the ghost sector for any value of the gauge fixing parameter. We finally prove that the background fields are stationary points of the background effective action obtained when the quantum fields are integrated out.

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arXiv2013

Scalar Resonances in the Non-linearly Realized Electroweak Theory

We introduce a physical scalar sector in a SU(2)xU(1) electroweak theory in which the gauge group is realized non linearly. By invoking theoretical as well as experimental constraints, we build a phenomenologically viable model in which a minimum of four scalar resonances appear, and the mass of the CP even scalar is controlled by a vacuum expectation value; however, the masses of all other particles (both matter as well as vector boson fields) are unrelated to spontaneous symmetry breaking and generated by the Stückelberg mechanism. We evaluate in this model the CP-even scalar decay rate to two photons and use this amplitude to perform a preliminary comparison with the recent LHC measurements. As a result, we find that the model exhibits a preference for a negative Yukawa coupling between the top quark and the CP-even resonance.

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arXiv2013

QCD effective charge from the three-gluon vertex of the background-field method

In this article we study in detail the prospects of determining the infrared finite QCD effective charge from a special kinematic limit of the vertex function corresponding to three background gluons. This particular Green's function satisfies a QED-like Ward identity, relating it to the gluon propagator, with no reference to the ghost sector. Consequently, its longitudinal form factors may be expressed entirely in terms of the corresponding gluon wave function, whose inverse is proportional to the effective charge. After reviewing certain important theoretical properties, we consider a typical lattice quantity involving this vertex, and derive its exact dependence on the various form factors, for arbitrary momenta. We then focus on the particular momentum configuration that eliminates any dependence on the (unknown) transverse form factors, projecting out only the desired quantity. A preliminary numerical analysis indicates that the effective charge is relatively insensitive to the numerical uncertainties that may afflict future simulations of the aforementioned lattice quantity. The numerical difficulties associated with a parallel determination of the dynamical gluon mass are briefly discussed.

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arXiv2013

The all-order equation of the effective gluon mass

We present the general derivation of the full non-perturbative equation that governs the momentum evolution of the dynamically generated gluon mass, in the Landau gauge. The entire construction hinges crucially on the inclusion of longitudinally coupled vertices containing massless poles of non-perturbative origin, which preserve the form of the fundamental Slavnov-Taylor identities of the theory. The mass equation is obtained from a previously unexplored version of the Schwinger-Dyson equation for the gluon propagator, particular to the PT-BFM formalism, which involves a reduced number of "two-loop dressed" diagrams, thus simplifying the calculational task considerably. The two-loop contributions turn out to be of paramount importance, modifying the qualitative features of the full mass equation, and enabling the emergence of physically meaningful solutions. Specifically, the resulting homogeneous integral equation is solved numerically, subject to certain approximations, for the entire range of physical momenta, yielding positive-definite and monotonically decreasing gluon masses.

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arXiv2013

Nonperturbative results on the quark-gluon vertex

We present analytical and numerical results for the Dirac form factor of the quark-gluon vertex in the quark symmetric limit, where the incoming and outgoing quark momenta have the same magnitude but opposite sign. To accomplish this, we compute the relevant components of the quark-ghost scattering kernel at the one-loop dressed approximation, using as basic ingredients the full quark propagator, obtained as a solution of the quark gap equation, and the gluon propagator and ghost dressing function, obtained from large-volume lattice simulations.

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arXiv2013

Recent results in the infrared sector of QCD

We review the most recent results, derived within the combined framework of the pinch technique and the background field method, describing certain QCD nonperturbative properties.

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arXiv2013

Unquenching the infrared sector of QCD

We discuss the recent progress made in understanding how some fundamental results valid in the quenched infrared sector of non-Abelian Yang-Mills theories generalize to the unquenched case. In particular, we derive in the continuum an equation that allows to predict how the momentum dependence of the quenched gluon propagator is affected by the presence of a small number of dynamical quarks. In addition, we present the most recent lattice simulations of the (Landau gauge) gluon and ghost two-point sector obtained using gauge field configurations with two light and two light plus two heavy twisted-mass quark flavors. A comparison between the results obtained by these two complementary methods is then carried out.

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arXiv2012

Quark flavour effects on gluon and ghost propagators

We compute the full non-perturbative ghost and gluon two-point Green functions by using gauge field configurations with $\nf=2$ and $\nf=2+1+1$ twisted-mass quark flavours. We use simulations with several different light quark masses, heavy quark masses close to that of the strange and charm quarks, and lightest pseudoscalar masses ranging from 270 to 510 [MeV]. Quark flavour effects on both the gluon and the ghost propagators are then investigated in a wide range of momenta, bridging the deep infrared and intermediate momenta domain of QCD interactions in the presence of dynamical quarks. The ghost-gluon vertex is also indirectly probed through a consistency requirement among the lattice data for the gluon and ghost propagators and the ghost propagator Schwinger-Dyson equation. The effective full QCD coupling is finally constructed, and its dependence on the presence of dynamical fermions scrutinized.

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