We study the decay of a Z' boson into two Z bosons by extending the Landau-Yang theorem to a parent particle decaying into two Z bosons. For a spin-1 parent the theorem predicts: 1) there are only two possible couplings and 2) the normalized differential cross-section depends on kinematics only through a phase shift in the azimuthal angle between the two decay planes of the Z boson. When the parent is a Z' the two possible couplings are anomaly-induced and CP-violating, respectively. At the Large Hadron Collider (LHC) effects of the two couplings could be disentangled when both Z bosons decay leptonically.
The Landau-Yang theorem, forbidding transition amplitudes between a massive spin-1 particle and two photons, is widely assumed to apply to other massless spin-1 particles. We show that this is not true in Standard-Model QCD, so that for instance antisymmetric colour-octet spin-1 quarkonia can be formed by two on-shell gluons in second-order perturbative QCD.
We summarise results for the running coupling from the four-gluon vertex in Landau gauge, SU($N_c$) Yang-Mills theory as given by a combination of dressing functions of the vertex and the gluon propagator. These functions have been determined numerically from the corresponding set of Dyson-Schwinger equations. In the infrared we obtain a nontrivial infrared fixed point which is three orders of magnitude smaller than the corresponding one in the coupling of the ghost-gluon vertex.
${\cal N}=4$ Super Yang-Mills theory is a highly constrained theory, and therefore a valuable tool to test the understanding of less constrained Yang-Mills theories. Our aim is to use it to test our understanding of both the Landau gauge beyond perturbation theory as well as truncations of Dyson-Schwinger equations in ordinary Yang-Mills theories. We derive the corresponding equations within the usual one-loop truncation for the propagators after imposing the Landau gauge. We find a conformal solution in this approximation, which surprisingly resembles many aspects of ordinary Yang-Mills theor…
Landau-Yang theorem is sometimes formulated as a selection rule forbidding two real (that is, non-virtual) photons with zero total momentum to be in the state of the total angular momentum J=1. In this paper we discuss whether the theorem itself and this particular formulation can be extended to a pair of two {\em twisted} photons, which carry orbital angular momentum with respect to their propagation direction. We point out possible sources of confusion, which may arise both from the unusual features of twisted photons and from the fact that usual proofs of the Landau-Yang theorem operate in …
Recently it has been argued that infrared singularities of the quark-gluon vertex of Landau gauge QCD can confine static quarks via a linear potential. It is demonstrated that the same mechanism also may confine fundamental scalar fields. This opens the possibility that within functional approaches static confinement is an universal property of the gauge sector even though it is formally represented in the functional equations of the matter sector. The colour structure of Dyson-Schwinger equations for fundamental and adjoint scalar fields is determined for the gauge groups SU(N) and G(2) exhib…
Correlation functions of Yang-Mills theory in the Landau gauge are calculated from their equations of motion. The employed setup is completely parameter free and leads, within errors, to good quantitative agreement with corresponding lattice results for the ghost and gluon propagators as well as the ghost-gluon and three-gluon vertices. Also the four-gluon vertex is calculated. The present setup allows for the first time for a unique subtraction of quadratic divergences in the gluon propagator Dyson-Schwinger equation. Thus, there are no ambiguities which can arise due to the use of models or …
Solutions for the three-gluon and quark-gluon vertices from Dyson-Schwinger equations and the three-particle irreducible formalism are discussed. Dynamical quarks (``unquenching'') change the three-gluon vertex via the quark-triangle diagrams which themselves include fully dressed quark-gluon vertex functions. On the other hand, the quark-swordfish diagram is, at least with the model used for the two-quark-two-gluon vertex employed here, of minor importance. For the leading tensor structure of the three-gluon vertex the "unquenching" effect can be summarized for the nonperturbative part as a s…
Correlation functions of Landau gauge Yang-Mills theory are calculated from their equations of motion. Solutions for the three- and four-gluon vertices and the role of two-loop diagrams in the gluon propagator equation are discussed.
Two-loop corrections to the pole mass of the vector boson and the pole masses and the magnetic moments of fermions are calculated in the framework of an effective field theory of massive Yang-Mills fields interacting with fermions. It is shown that the limit of vanishing vector boson mass is finite for all these quantities. Implications of the obtained results are discussed.
Two kinds of Yang-Mills fields are found upon the concepts of mass eigenstate and nonmass eigenstate. The Yang-Mills fields of the first kind were proposed by Yang and Mills, which couple to the mass eigenstates with the same rest mass, whose gauge bosons are massless. I find that there are second kind of Yang-Mills fields, which are constructed on a five-dimensional manifold. Only the nonmass eigenstates couple to the Yang-Mills fields of the second kind, which are the nonmass eigenstates as well and composed of mass eigenstates of gauge bosons. The mass eigenstates of the Yang-Mills fields o…
Examples of normalizable zero modes of the Faddeev-Popov operator in SU(2) Euclidean Yang-Mills theories in the Landau gauge are constructed in d=2,3,4 dimensions.
Using elementary considerations of Lorentz invariance, Bose symmetry and BRST invariance, we argue why the decay of a massive color-octet vector state into a pair of on-shell massless gluons is possible in a non-Abelian SU(N) Yang-Mills theory, we constrain the form of the amplitude of the process and offer a simple understanding of these results in terms of effective-action operators.
Vertices describe the interactions between the fundamental degrees of freedom, and are therefore of vital importance in many ab-initio descriptions of field theory, especially using functional methods. To this end, we present the first lattice study of the thermal behavior of (minimal) Landau-gauge SU(2) Yang--Mills three-point functions, i.e. three-gluon and ghost-gluon vertices. Focusing on the chromomagnetic sector, we find that the phase transition mainly affects the three-gluon vertex, while the ghost-gluon vertex is relatively inert.
We show that contrary to naive expectations the recently observed diphoton excess can be explained by a vector resonance, which decays to a photon and a light scalar $s$, followed by a decay of the scalar into two photons: $Z' \rightarrow γs \rightarrow 3 γ$. As the two photons from the scalar decay are highly boosted, the experimental signature is an apparent diphoton final state. In fact all the necessary ingredients are naturally present in $Z'$ models: Additional fermions with electroweak quantum numbers are required in order to render the theory anomaly free and naturally induce the requi…
The issue of the Gribov copies is discussed in Euclidean N=4 Super Yang-Mills theory quantized in the Landau gauge. As a consequence of the absence of a renormalization group invariant scale, it turns out that it is not possible to attach a dynamical meaning to the Gribov parameter. This implies that, in N=4 Super Yang-Mills, there is no need for the restriction of the domain of integration in the functional integral to the Gribov region, and no non-perturbative dynamical scale is generated. This result is in agreement with the absence of a confining phase observed from the Coulomb behaviour o…
We prove that the Faddeev-Popov ghost dressing function in the Yang-Mills theory is non-zero and finite in the limit of vanishing momenta and hence the ghost propagator behaves like free in the deep infrared regime, within the Gribov-Zwanziger framework of the $D$-dimensional SU(N) Yang-Mills theory in the Landau gauge for any $D>2$. This result implies that the Kugo-Ojima color confinement criterion is not satisfied in its original form. We point out that the result crucially depends on the explicit form of the non-local horizon term adopted. The original Gribov prediction in the Landau gauge…
We discuss the properties of ghost and gluon propagators in the deep infrared momentum region of Landau gauge Yang-Mills theory. Within the framework of Dyson-Schwinger equations and the functional renormalization group we demonstrate that it is only a matter of infrared boundary conditions whether infrared scaling or decoupling occurs. We argue that the second possibility is at odds with global BRST symmetry in the confining phase. For this purpose we improve upon existing truncation schemes in particular with respect to transversality and renormalization.
We investigate Landau gauge $SU(3)$ Yang-Mills theory in a systematic vertex expansion scheme for the effective action with the functional renormalisation group. Particular focus is put on the dynamical creation of the gluon mass gap at non-perturbative momenta and the consistent treatment of quadratic divergences. The non-perturbative ghost and transverse gluon propagators as well as the momentum-dependent ghost-gluon, three-gluon and four-gluon vertices are calculated self-consistently with the classical action as only input. The apparent convergence of the expansion scheme is discussed and …
We calculate the dressed gluon and ghost propagators of Landau gauge Yang-Mills theory in the complex momentum plane from their Dyson-Schwinger equations. To this end, we develop techniques for a direct calculation such that no mathematically ill-posed inverse problem needs to be solved. We provide a detailed account of the employed ray technique and discuss a range of tools to monitor the stability of the numerical calculation. Within a truncation employing model ansaetze for the three-point vertices and neglecting effects due to four-point functions, we find a singularity in the gluon propag…
Analytic solutions for the three-gluon and ghost-gluon vertices in Landau gauge Yang-Mills theory at low momenta are presented in terms of hypergeometric series. They do not only show the expected scaling behavior but also additional kinematic divergences when only one momentum goes to zero. These singularities, which have also been proposed previously, induce a strong dependence on the kinematics in many dressing functions. The results are generalized to two and three dimensions and a range of values for the ghost propagator's infrared exponent kappa.
Non-Abelian gauge theories with fermions transforming in the adjoint representation of the gauge group (AdjQCD) are a fundamental ingredient of many models that describe the physics beyond the Standard Model. Two relevant examples are N=1 Supersymmetric Yang-Mills (SYM) theory and Minimal Walking Technicolor, which are gauge theories coupled to one adjoint Majorana and two adjoint Dirac fermions, respectively. While confinement is a property of N=1 SYM, Minimal Walking Technicolor is expected to be infrared conformal. We study the propagators of ghost and gluon fields in the Landau gauge to co…
The propagators of the elementary degrees of freedom of (minimal-)Landau-gauge Yang-Mills theory have been a useful tool in various investigations. However, in lattice calculations they show severe dependencies on lattice artifacts. This problem has been addressed for various subsets of lattice artifacts and various subsets of propagators over the time. Here, an extended study of all propagators in momentum space, and for the gluon also in position space, as well as derived quantities like the running coupling, is provided simultaneously for two, three, and four dimensions over one or more ord…
Recently it has been shown that infrared singularities of Landau gauge QCD can confine static quarks via a linearly rising potential. We show that the same mechanism can also provide a confining interaction between charged scalar fields in the fundamental representation. This confirms that within this scenario static confinement is a universal property of the gauge sector even though it is formally represented in the functional equations of the matter sector. The simplifications compared to the fermionic case make the scalar system an ideal laboratory for a detailed analysis of the confinement…
We solve the Dyson-Schwinger equations of the ghost and gluon propagators of Landau gauge Yang-Mills theory together with that of the ghost-gluon vertex. The latter plays a central role in many truncation schemes for functional equations. By including it dynamically we can determine its influence on the propagators. We also suggest a new model for the three-gluon vertex motivated by lattice data which plays a crucial role to obtain stable solutions when the ghost-gluon vertex is included. We find that both vertices have a sizable quantitative impact on the mid-momentum regime and contribute to…
Yang-Mills theory can be formulated for any semi-simple Lie algebra, and thus any semi-simple Lie group. In principle, the dynamics could be different for each one. However, functional studies predict that the propagators in Landau gauge depend only quantitatively on the gauge algebra. In particular, genuine non-perturbative effects should be present even in the large N-limit for su(N) gauge algebras. Lattice gauge theory is used to investigate this in detail. The propagators are determined for the gauge groups SU(2), SU(3), SU(4), SU(5), SU(6) and G2, in two and three dimensions. In accordanc…
We present a more detailed picture of the infrared regime of Landau gauge Yang-Mills theory. This is done within a novel framework that allows one to take into account the influence of finite scales within an infrared power counting analysis. We find that there are two qualitatively different infrared fixed points of the full system of Dyson-Schwinger equations. The first extends the known scaling solution, where the ghost dynamics is dominant and gluon propagation is strongly suppressed. It features in addition to the strong divergences of gluonic vertex functions in the previously considered…
We show that the low-momentum behavior of the lattice Landau-gauge gluon and ghost propagators is sensitive to the lowest non-trivial eigenvalue (λ_1) of the Faddeev-Popov operator. If the gauge fixing favors Gribov copies with small λ_1 the ghost dressing function rises more rapidly towards zero momentum than on copies with large λ_1. This effect is seen for momenta below 1 GeV, and interestingly also for the gluon propagator at momenta below 0.2 GeV: For large λ_1 the gluon propagator levels out to a lower value at zero momentum than for small λ_1. For momenta above 1 GeV no dependence on Gr…
Yang-Mills-Higgs theory offers a rich set of physics. In particular, in some region of its parameter space it has QCD-like behavior, while in some other range it is Higgs-like. Furthermore, for the choice of the gauge group SU(2) and an SU(2) Higgs flavor symmetry it is the Higgs sector of the standard model. Therefore, it is possible to study a plethora of phenomena within a single theory. Here the standard-model version is studied using lattice gauge theory. Choosing non-aligned minimal Landau gauge, its propagators and three-point vertices will be determined in both the QCD-like and Higgs-l…
The BCFW recursion relation allows to calculate tree-level scattering amplitudes in generalized Yang-Mills theory and, in particular, four-particle amplitudes for the production rate of non-Abelian tensor gauge bosons of arbitrary high spin in the fusion of two gluons. The consistency of the calculations in different kinematical channels is fulfilled when all dimensionless cubic coupling constants between vector bosons (gluons) and high spin non-Abelian tensor gauge bosons are equal to the Yang-Mills coupling constant. There are no high derivative cubic vertices in the generalized Yang-Mills t…
