arXiv subjects
Publications and source records attributed to A. A. Natale.
We briefly discuss some results obtained recently about dynamical gluon mass generation. We comment that this mass provides a natural QCD infrared cutoff and also implies an infrared finite coupling constant. We also discuss the phenomenological applications of these results and how they can be treated in the context of the so-called Dynamical Perturbation Theory.
We investigate the two-gluon-exchange model of the Pomeron using nonperturbative gluon propagators characterized by a dynamical mass scale. We present the results for an analysis of the available $pp$ differential cross section data at TeV energies which accounts for dynamical gluon masses obtained from a non-linear version of the Schwinger-Dyson equations. We show that our two-gluon exchange model gives a very good description of the LHC data, provided we demand the Reggeization of the scattering amplitude and make a suitable choice for the convolution of proton wave functions.
We perform a Bethe-Salpeter equation (BSE) evaluation of composite scalar boson masses in order to verify how these masses can be smaller than the composition scale. The calculation is developed with a constituent self-energy dependent on its mass anomalous dimension ($γ$), and we obtain a relation showing how the scalar mass decreases as $γ$ is increased. We also discuss how fermionic corrections to the BSE kernel shall decrease the scalar mass, whose effect can be as important as the one of a large $γ$. An estimate of the top quark loop effect that must appear in the BSE calculation gives a lower bound on the composite scalar mass.
The trilinear self-coupling of the Higgs boson, in a theory in which this boson is composite, is compared to the experimental bound of this quantity obtained by the CMS experiment. In the case of a model where technicolor (TC) is coupled to QCD, we find that the experimental result already constrain the dynamics of the theory, which is represented by an expression of the technifermion self-energy ($Σ_{tc}$) typical of technicolor coupled models, and function of the dynamically generated technifermion mass and two other parameters that describe the technifermion dynamical mass momentum dependence. The limits imposed on this dynamics allow us to make a simple determination of pseudo-Goldstone boson masses that appear in these theories, indicating that these bosons may be expected to be quite massive.
When technicolor (TC), QCD, extended technicolor (ETC) and other interactions become coupled through their different Schwinger-Dyson equations, the solution of these equations are modified compared to those of the isolated equations. The change in the self-energies is similar to that obtained in the presence of four-fermion interactions, but without their ad hoc inclusion in the theory. In this case the TC and QCD self-energies decrease logarithmically with the momenta, which allows us to build models where ETC boson masses can be pushed to very high energies, and do not lead to undesirable flavor changing interactions. Viable TC models may be built along this line including a necessary horizontal symmetry. The different fermionic mass scales are dictated by the different strong interactions. Pseudo-Goldstone bosons acquire large masses in this class of models.
We discuss fermion mass generation in unified models where QCD and technicolor (or any two strongly interacting theories) have their Schwinger-Dyson equations coupled. In this case the technicolor (TC) and QCD self-energies are modified in comparison with the behavior observed in the isolated theories. In these models the pseudo-Goldstone boson masses are much higher than the ones obtained in different contexts, and phenomenological signals, except from a light scalar composite boson, will be quite difficult to be observed at present collider energies. The most noticeable fact of these models is how the mass splitting between the different ordinary fermions is generated. We discuss how a necessary horizontal (or family) symmetry can be implemented in order to generate the mass splitting between fermions of different generations; how the fermionic mass spectrum may be modified due to GUT interactions, as well as how the mass splitting within the same fermionic generation are generated due to electroweak and GUT interactions.
Considering, as a limit case, an approximately flat pion distribution amplitude, which is determined from the hardest, in momentum space, solution of the Bethe-Salpeter equation for the pion wave function, we compute the pion transition form factor $F_{πγγ^{*}}(Q^{2})$ and the pion form factor $F_π(Q^2)$, taking into account the LO as well as NLO form of the hard coefficient function entering the leading-twist factorization formula. We also compute the exclusive photoproduction of pions pairs at high energies, $γγ\to π^{+}π^{-}$, where perturbative QCD can be used to compute the hard scattering matrix elements. We verify that the existent data for exclusive pion production can be reasonably described as a function of such flat distribution amplitude.
When Technicolor (TC), QCD, Extended Technicolor (ETC) and other interactions become coupled through their different Schwinger-Dyson equations, the solution of these equations are modified in comparison with the ones of the isolated equations. The change in the self-energies is similar to the one obtained in the presence of four-fermion interactions, but without their \textsl{ad hoc} inclusion in the theory. In this case TC and QCD self-energies decrease logarithmically with the momenta, what allow us to build models where ETC boson masses can be pushed to very high energies, and their effects will barely appear at present energies. Here we present a detailed discussion of this class of TC models. We first review the Schwinger-Dyson TC and QCD coupled equations, explaining the origin of the asymptotic self-energies. We develop the basic ideas of how viable TC models may be built along this line, where ordinary lepton masses appear naturally lighter than quark masses. One specific unified TC model associated with a necessary horizontal (or family) symmetry is described. The values of scalar and pseudo-Goldstone boson masses in this class of models are also discussed, as well as the value of the trilinear scalar coupling, and the consistency of the models with the experimental constraints.
The full solution of technicolor (TC) Schwinger-Dyson equations should include radiative corrections induced by extended technicolor (ETC) (or other) interactions. We verify that when TC is embedded into a larger theory including also QCD, these radiative corrections couple the different strongly interacting Schwinger-Dyson equations, providing a tiny mass to technifermions and changing the ultraviolet behavior of the gap equation solution. We argue about the origin of the different quark masses without appealing for different ETC boson masses, in one scenario where most of the new physics will appear in interactions with the third fermion generation and with a TC scalar boson possibly lighter than the TC characteristic scale ($Λ_{\tt{TC}}$)
The technicolor (TC) Schwinger-Dyson equations (SDE) should include radiative corrections induced by extended technicolor (ETC) interactions when TC is embedded into a larger theory including also QCD. These radiative corrections couple the different strongly interacting Dyson equations. We discuss how the boundary conditions of the coupled SDE system are modified by these corrections, and verify that the ultraviolet behavior of the self-energies are described by a function that decreases logarithmically with momentum.
Theories with large mass anomalous dimensions ($γ_m$) have been extensively studied because of their deep consequences for models where the scalar bosons are composite. Large $γ_m$ values may appear when a non-Abelian gauge theory has a large number of fermions or is affected by four-fermion interactions. In this note we provide a simple explanation how $γ_m$ can be directly read out from the IR and UV boundary conditions derived from the gap equation, and verify that moderate $γ_m$ values appear when the theory possess a large number of fermions, but large $γ_m$ values are obtained only when four-fermion interactions are added to the theory. We also verify how the critical line separating the different chiral phases emerge from these conditions.
Fixed points in QCD can appear when the number of quark flavors ($N_f$) is increased above a certain critical value as proposed by Banks and Zaks (BZ). There is also the possibility that QCD possess an effective charge indicating an infrared frozen coupling constant. In particular, an infrared frozen coupling associated to dynamical gluon mass generation (DGM) does lead to a fixed point even for a small number of quarks. We compare the BZ and DGM mechanisms, their $β$ functions and fixed points, and within the approximations of this work, which rely basically on extrapolations of the dynamical gluon masses at large $N_f$, we verify that near the so called QCD conformal window both cases exhibit fixed points at similar coupling constant values ($g^*$). We argue that the states of minimum vacuum energy, as a function of the coupling constant up to $g^*$ and for several $N_f$ values, are related to the dynamical gluon mass generation mechanism.
Models of strongly interacting theories with a large mass anomalous dimension ($γ_m$) provide an interesting possibility for the dynamical origin of the electroweak symmetry breaking. A laboratory for these models is QCD with many flavors, which may present a non-trivial fixed point associated to a conformal region. Studies based on conformal field theories and on Schwinger-Dyson equations have suggested the existence of bounds on the mass anomalous dimension at the fixed points of these models. In this note we discuss $γ_m$ values of multi-flavor QCD exhibiting a non-trivial fixed point and affected by relevant four-fermion interactions.
We discuss the possibility of generating a light composite scalar boson, in a scenario that we may generically call Technicolor, or in any variation of a strongly interacting theory, where by light we mean a scalar composite mass about one order of magnitude below the characteristic scale of the strong theory. Instead of most of the studies about a composite Higgs boson, which are based on effective Lagrangians, we consider this problem in the framework of non-perturbative solutions of the fermionic Schwinger-Dyson and Bethe-Salpeter equations. We study a range of mechanisms proposed during the recent years to form such light composite boson, and verify that such possibility seems to be necessarily associated to a fermionic self-energy that decreases slowly with the momentum.
We consider the electron-positron annihilation process into hadrons $R_{e^+e^-}$ up to $\mathcal{O}(α_{s}^{3})$ and we adopt the smearing method suggest by Poggio, Quinn and Weinberg to confront the experimental data with theory. As a theoretical model we use a QCD coupling constant frozen in the low energy regime, where this coupling can be parameterised in terms of an effective dynamical gluon mass ($m_g$) which is determined through Schwinger-Dyson equations. In order to find the best fit between experimental data and theory we perform a $χ^2$ study, that, within the uncertainties of the approach, has a minimum value when $m_g/Λ_{QCD}$ is in the range $1.2 \, - \, 1.4$. These values are in agreement with other phenomenological determinations of this ratio and lead to an infrared effective charge $α_s(0) \approx 0.7$. We comment how this effective charge may affect the global duality mass scale that indicates the frontier between perturbative and non-perturbative physics.
We consider the possibility of a light composite scalar boson arising from mass mixing between a relatively light and heavy scalar singlets in a see-saw mechanism expected to occur in two-scale Technicolor (TC) models. A light composite scalar boson can be generated when the TC theory features two technifermions species in different representations, $R_1$ and $R_2$, under a single technicolor gauge group, with characteristic scales $Λ_1$ and $Λ_2$. We determine the final composite scalar fields, $Φ_1$ and $Φ_2$, effective theory using the effective potential for composite operators approach. To generate a light composite scalar it is enough to have a walking (or quasi-conformal) behavior just for one of the technifermions representations.
We compute the Standard Model scalar coupling ($λ$) evolution in a particular QCD resummation scheme, where the QCD coupling becomes infrared finite due to the presence of a dynamically generated gluon mass, leading to the existence of a non-perturbative infrared fixed point. We discuss how this scheme can be fixed taking recourse to phenomenological considerations in the infrared region. The QCD $β$ function associated to this non-perturbative coupling when introduced into the SM renormalization group equations increases the $λ$ values at high energies.
Considering a QCD chiral symmetry breaking model where the gap equation contains an effective confining propagator and a dressed gluon propagator with a dynamically generated mass, we verify that the chiral symmetry is restored for a large number of quarks $n_{f}\approx 7-13$. We discuss the uncertainty in the results, that is related to the determination of the string tension ($K_{F}$), appearing in the confining propagator, and the effective gluon mass ($m_{g}$) at large $n_{f}$.