Tree-level Vertex Research Articles

Quark-gluon vertex from Nf=2 lattice QCD

We study the quark-gluon vertex in the limit of vanishing gluon momentum using lattice QCD with two flavors of $\mathcal{O}(a)$ improved Wilson fermions, for several lattice spacings and quark masses. We find that all three form factors in this kinematics have a significant infrared strength and that both the leading form factor ${\ensuremath{\lambda}}_{1}$, multiplying the tree-level vertex structure, and the scalar, chiral symmetry breaking form factor ${\ensuremath{\lambda}}_{3}$ are significantly enhanced in the infrared compared to the quenched (${N}_{f}=0$) case. These enhancements are orders of magnitude larger than predicted by one-loop perturbation theory. We find only a weak dependence on the lattice spacing and quark mass.

Nonperturbative Ball-Chiu construction of the three-gluon vertex

We present the detailed derivation of the longitudinal part of the three-gluon vertex from the Slavnov-Taylor identities that it satisfies, by means of a nonperturbative implementation of the Ball-Chiu construction; the latter, in its original form, involves the inverse gluon propagator, the ghost dressing function, and certain form factors of the ghost-gluon kernel. The main conceptual subtlety that renders this endeavor nontrivial is the infrared finiteness of the gluon propagator, and the resulting need to separate the vertex into two pieces, one that is intimately connected with the emergence of a gluonic mass scale, and one that satisfies the original set of Slavnov-Taylor identities, but with the inverse gluon propagator replaced by its "kinetic" term. The longitudinal form factors obtained by this construction are presented for arbitrary Euclidean momenta, as well as special kinematic configurations, parametrized by a single momentum. A particularly preeminent feature of the components comprising the tree-level vertex is their considerable suppression for momenta below 1 GeV, and the appearance of the characteristic "zero-crossing" in the vicinity of 100-200 MeV. Special combinations of the form factors derived with this method are compared with the results of recent large-volume lattice simulations as well as Schwinger-Dyson equations, and good overall agreement is found. A variety of issues related to the distribution of the pole terms responsible for the gluon mass generation are discussed in detail, and their impact on the structure of the transverse parts is elucidated. In addition, a brief account of several theoretical and phenomenological possibilities involving these newly acquired results is presented.

The quark-gluon vertex and the QCD infrared dynamics

The Dyson–Schwinger quark equation is solved for the quark-gluon vertex using the most recent lattice data available in the Landau gauge for the quark, gluon and ghost propagators, the full set of longitudinal tensor structures in the Ball-Chiu vertex, taking into account a recently derived normalisation for a quark-ghost kernel form factors and the gluon contribution for the tree level quark-gluon vertex identified on a recent study of the lattice soft gluon limit. A solution for the inverse problem is computed after the Tikhonov linear regularisation of the integral equation, that implies solving a modified Dyson–Schwinger equation. We get longitudinal form factors that are strongly enhanced at the infrared region, deviate significantly from the tree level results for quark and gluon momentum below 2 GeV and at higher momentum approach their perturbative values. The computed quark-gluon vertex favours kinematical configurations where the quark momentum p and the gluon momentum q are small and parallel. Further, the quark-gluon vertex is dominated by the form factors associated to the tree level vertex gamma _mu and to the operator 2 , p_mu + q_mu . The higher rank tensor structures provide small contributions to the vertex.

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.

Exploring the universal extra dimension at the LHC

Besides supersymmetry, the other prime candidate of physics beyond the Standard Model (SM), crying out for verification at the CERN Large Hadron Collider (LHC), is extra-dimension. To hunt for effects of Kaluza–Klein (KK) excitations of known fermions and bosons is very much in the agenda of the LHC. These KK states arise when the SM particles penetrate in the extra space-like dimension(s). In this paper, we consider a 5d scenario, called ‘Universal Extra Dimension’, where the extra space coordinate, compactified on an orbifold S 1 / Z 2 , is accessed by all the particles. The KK number ( n) is conserved at all tree level vertices. This entails the production of KK states in pairs and renders the lightest KK particle stable, which leaves the detector carrying away missing energy. The splitting between different KK flavors is controlled by the zero mode masses and the bulk- and brane-induced one-loop radiative corrections. We concentrate on the production of an n = 1 KK electroweak gauge boson in association with an n = 1 KK quark. This leads to a signal consisting of only one jet, one or more leptons and missing p T . For definiteness we usually choose the inverse radius of compactification to be R − 1 = 500 GeV , which sets the scale of the lowest lying KK states. We show on a case-by-case basis (depending on the number of leptons in the final state) that with 10 fb −1 integrated luminosity at the LHC with s = 14 TeV this signal can be detected over the SM background by imposing appropriate kinematic cuts. We record some of the expectations for a possible intermediate LHC run at s = 10 TeV and also exhibit the integrated luminosity required to obtain a 5 σ signal as a function of R −1 .

Precise predictions for [formula omitted] decays in the complex MSSM

Complete one-loop results for the decay widths of neutral Higgs bosons (ha) into lighter neutral Higgs bosons (hb,hc) are presented for the MSSM with complex parameters. The results are obtained in the Feynman-diagrammatic approach, taking into account the full dependence on the spectrum of supersymmetric particles and all complex phases of the supersymmetric parameters. The genuine triple-Higgs vertex contributions are supplemented with two-loop propagator-type corrections, yielding the currently most precise prediction for this class of processes. The genuine vertex corrections turn out to be very important, yielding a large increase of the decay width compared to a prediction based on the tree-level vertex. The new results are used to analyse the impact of the experimental limits from the LEP Higgs searches on the parameter space with a very light MSSM Higgs boson. It is found that a significant part of the parameter space of the CPX benchmark scenario exists where channels involving the decay h2→h1h1 have the highest search sensitivity, and the existence of an unexcluded region with Mh1≈45 GeV is confirmed.

Magnetic Color-Flavor Locking Phase in High-Density QCD

We investigate the effects of an external magnetic field in the gap structure of a color superconductor with three massless quark flavors. Using an effective theory with four-fermion interactions, inspired by one-gluon exchange, we show that the long-range component B of the external magnetic field that penetrates the color-flavor locked phase modifies its gap structure, producing a new phase of lower symmetry. A main outcome of our study is that the B field tends to strengthen the gaps formed by Q-charged and Q-neutral quarks that coupled among themselves through tree-level vertices. These gaps are enhanced by the field-dependent density of states of the Q-charged quarks on the Fermi surface. Our considerations are relevant for the study of highly magnetized compact stars.

Virtual black holes in generalized dilaton theories

The virtual black hole phenomenon, which has been observed previously in specific models, is established for generic 2D dilaton gravity theories with scalar matter. The ensuing effective line element can become asymptotically flat only for two classes of models, among them spherically reduced theories and the string inspired dilaton black hole (CGHS model). We present simple expressions for the lowest order scalar field vertices of the effective theory which one obtains after integrating out geometry exactly. Treating the boundary in a natural and simple way asymptotic states, tree-level vertices and tree-level S-matrix are conformally invariant. Examples are provided pinpointing the physical consequences of virtual black holes on the (CPT-invariant) S-matrix for gravitational scattering of scalar particles. For minimally coupled scalars the evaluation of the S-matrix in closed form is straightforward. For a class of theories including the CGHS model all tree-graph vertices vanish, which explains the particular simplicity of that model and at the same time shows yet another essential difference to the Schwarzschild case.

Graviton-Scalar Interaction in the pp-Wave Background

We compute the graviton two scalar off-shell interaction vertex at tree level in Type IIB superstring theory on the pp-wave background using the light-cone string field theory formalism. We then show that the tree level vertex vanishes when all particles are on-shell and conservation of p+ and p- are imposed. We reinforce our claim by calculating the same vertex starting from the corresponding SUGRA action expanded around the pp-wave background in the light-cone gauge.