International Journal of Modern Physics A

Our SLq(2) extension of the standard model is constructed by replacing the elementary field operators, $\mathrm{\Psi }(x)$, of the standard model by ${\widehat{\mathrm{\Psi }}}_{m{m}^{\prime }}^j(x)D_{m{m}^{\prime }}^j$ where $D_{m{m}^{\prime }}^j$ is an element of the $(2j+1)$-dimensional representation of the SLq(2) algebra, which is also the knot algebra. The allowed quantum states $(j,m,m^{\prime })$ are restricted by the topological conditions

This paper reviews the concept of Lorentz invariant relative velocity that is often misunderstood or unknown in high energy physics literature. The properties of the relative velocity allow to formulate the invariant flux and cross-section without recurring to nonphysical velocities or any assumption about the reference frame. Applications such as the luminosity of a collider, the use as kinematic variable, and the statistical theory of collisions in a relativistic classical gas are reviewed. It is emphasized how the hyperbolic properties of the velocity space explain the peculiarities of relativistic scattering.

We explicitly show that the Bern–Carrasco–Johansson color-kinematic duality holds at tree level through at least eight points in Aharony–Bergman–Jafferis–Maldacena theory with gauge group $SU(N)\times SU(N)$. At six points we give the explicit form of numerators in terms of amplitudes, displaying the generalized gauge freedom that leads to amplitude relations. However, at eight points no amplitude relations follow from the duality, so the diagram numerators are fixed unique functions of partial amplitudes. We provide the explicit amplitude-numerator decomposition and the numerator relations for eight-point amplitudes.

By using the renormalization group (RG) equation it has proved possible to sum logarithmic corrections to quantities that arise due to quantum effects in field theories. In particular, the effective potential $V$ in the Standard Model in the limit that there are no massive parameters in the classical action (the “conformal limit”) has been subject to this analysis, as has the effective potential in a scalar theory with a quartic self-coupling and in massless scalar electrodynamics. Having multiple coupling constants and/or mass parameters in the initial action complicates this analysis, as then several mass scales arise. We show how to address this problem by considering the effective potential in a Yukawa model when the scalar field has a tree-level mass term. In addition to summing logarithmic corrections by using the RG equation, we also consider the consequences of the condition $V^{\prime }(v)=0$ where $v$ is the vacuum expectation value of the scalar. If $V$ is expanded in powers of logarithms that arise, then it proves possible to show that either $v$ is zero or that $V$ is independent of the scalar. (That is, either there is no spontaneous symmetry breaking or the vacuum expectation value is not determined by minimizing $V$ as $V$ is “flat”.)

It has long been known that two-point functions of conformal field theory (CFT) are nothing but the integral kernels of intertwining operators for two equivalent representations of conformal algebra. Such intertwining operators are known to fulfill some operator identities — the intertwining relations — in the representation space of conformal algebra. Meanwhile, it has been known that the S-matrix operator in scattering theory is nothing but the intertwining operator between the Hilbert spaces of in- and out-particles. Inspired by this algebraic resemblance, in this paper, we develop a simple Lie-algebraic approach to momentum-space two-point functions of thermal CFT living on the hyperbolic space–time ${ℍ}^1\times {ℍ}^{d-1}$ by exploiting the idea of Kerimov’s intertwining operator approach to exact S-matrix. We show that in thermal CFT on ${ℍ}^1\times {ℍ}^{d-1}$, the intertwining relations reduce to certain linear recurrence relations for two-point functions in the complex momentum space. By solving these recurrence relations, we obtain the momentum-space representations of advanced and retarded two-point functions as well as positive- and negative-frequency two-point Wightman functions for a scalar primary operator in arbitrary space–time dimension $d\ge 3$.

A method to simulate anomalous fermion–boson interactions in Wtb vertex is presented with a minimal set of simulated samples of single top quark events at the LHC energies. In the proposed method, additional subsidiary vector fields corresponding to the Standard Model gauge fields are implemented for each type of the anomalous vertex structure. The method allows to simulate a manifestation of anomalous gauge couplings in two approaches used in experimental analyses either keeping only the linear order contributions in the anomalous couplings or keeping all contributions in numerators and denominators as appeared in matrix elements. For the processes with several anomalous couplings contributing simultaneously to the production and to the decay as well as to various interference terms the method allows to model correctly the dependence of kinematic distributions on anomalous couplings. The method shows how to generate a minimum set of event samples needed for a concrete analysis. All the single top quark production mechanisms, t-, s- and associative tW-channels, are considered. The correctness of the proposed method is demonstrated.

In this paper, we examine the (2+1)-dimensional Dirac equation in a homogeneous magnetic field under the nonrelativistic anti-Snyder model which is relevant to doubly/deformed special relativity (DSR) since it exhibits an intrinsic upper bound of the momentum of free particles. After setting up the formalism, exact eigensolutions are derived in momentum space representation and they are expressed in terms of finite orthogonal Romanovski polynomials. There is a finite maximum number of allowable bound states $n_{\mathrm{\text{max}}}$ due to the orthogonality of the polynomials and the maximum energy is truncated at $n_{\mathrm{\text{max}}}$. Similar to the minimal length case, the degeneracy of the Dirac–Landau levels in anti-Snyder model are modified and there are states that do not exist in the ordinary quantum mechanics limit $\beta \to 0$. By taking $m\to 0$, we explore the motion of effective massless charged fermions in graphene-like material and obtained a maximum bound of deformed parameter ${\beta }_{\mathrm{\text{max}}}$. Furthermore, we consider the modified energy dispersion relations and its application in describing the behavior of neutrinos oscillation under modified commutation relations.

We will study the splitting in the energy spectrum of the hydrogen atom subjected to an uniform electric field (Stark effect) with the Heisenberg algebra deformed leading to the minimum length. We will use the perturbation theory for cases not degenerate (n=1) and degenerate (n=2), along with known results of corrections in these levels caused by the minimum length applied purely to the hydrogen atom, so that we may find and estimate the corrections of minimum length applied to the Stark effect.

The aim of this work is to provide a phenomenological analysis of the contribution of $D^0$ meson to $f_0(980){\pi }^{+}{\pi }^{-}(f_0(980)\to {\pi }^{+}{\pi }^{-})$, $K^{+}{K}^{-}{\bar{K}}^{\ast }{(982)}^0({\bar{K}}^{\ast }{(982)}^0\to {\pi }^{+}{K}^{-})$ and $\varphi {({\pi }^{+}{\pi }^{-})}_{S\text{-wave}}(\varphi \to K^{+}{K}^{-})$ quasi-three-body decays. Such that the analysis of mentioned four-body decays is summarized into three-body decay and several channels are observed. Based on the factorization approach, hadronic three-body decays receive both resonant and nonresonant contributions. We compute both contributions of three-body decays. As, there are tree, penguin, emission, and emission annihilation diagrams for these decay modes. Our theoretical model for $D^0\to \varphi {(\pi \pi )}_{S\text{-wave}}$ decay is based on the QCD factorization to quasi-two body followed by $S$-wave. This model for this decay following experimental information which demonstrated two pion interaction in the $S$-wave is introduced by the scalar resonance. The theoretical values are $(1.82\pm 0.24)\times 10^{-4}$, $(4.46\pm 0.41)\times 10^{-5}$ and $(1.1\pm 0.18)\times 10^{-4}$, while the experimental results of them are $(1.8\pm 0.5)\times 10^{-4}$, $(4.4\pm 1.7)\times 10^{-5}$ and $(2.5\pm 0.33)\times 10^{-4}$, respectively. Comparing computation analysis values with experimental values show that our results are in agreement with them.

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 (DGM) generation does lead to a fixed point even for a small number of quarks. We compare the BZ and DGM mechanisms, their $\beta$ 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 between $N_f=8$ and $N_f=12$ both cases exhibit fixed points at similar coupling constant values $(g^{\ast })$. We argue that the states of minimum vacuum energy, as a function of the coupling constant up to $g^{\ast }$ and for several $N_f$ values, are related to the dynamical gluon mass generation mechanism.

We propose a supersymmetric explanation of the diphoton excess in the Minimal Supersymmetric Standard Model (MSSM) with the leptonic R-parity violation. In our model, sneutrino serves as the 750 GeV resonance and produced through quark–antiquark annihilation. With introducing appropriate trilinear soft parameters, we show that the diphoton branching ratio is significantly enhanced compared with the conventional MSSM. For current dijet and W-pair LHC constraints, we can successfully fit the observed diphoton signal rate in sizeable parameter regions, the resulting parameter space strongly favor the masses of light smuon and stau within the range from 375–500 GeV, which depends on the choice of electroweakino masses and soft trilinear terms. While after taking into account the compatibility of diphoton excess between the 8 TeV and 13 TeV LHC, only the coupling involved with the second generation quarks is survived. In this case, the corresponding parameter space favors a narrow mass range of smuon and stau with $m_{{\tilde{\mu }}_1,{\tilde{\tau }}_1}\in [375,390]\mathrm{\text{GeV}}$. Even if the 750 GeV diphoton excesses were not confirmed by the ATLAS and CMS experiments, we point out that our proposal can still be used to explain the current and future tentative diphoton excesses.

In this paper, we developed an algebraic formulation for the generalized thermal coherent states with a thermofield dynamics approach for multi-modes, based on coset space of Lie groups. In particular, we applied our construction on SU(2) and SU(1,1) symmetries and we obtain their thermal coherent states and density operator. We also calculate their thermal quantum Fidelity and thermal Wigner function.

The construction of a consistent measure for Yang–Mills is a precondition for an accurate formulation of nonperturbative approaches to QCD, both analytical and numerical. Using projective limits as subsets of Cartesian products of homomorphisms from a lattice to the structure group, a consistent interaction measure and an infinite-dimensional calculus have been constructed for a theory of non-Abelian generalized connections on a hypercubic lattice. Here, after reviewing and clarifying past work, new results are obtained for the mass gap when the structure group is compact.

Higgs boson couplings with gauge bosons are probed through $e^{-}{e}^{+}\to Z\gamma h$ in an effective Lagrangian framework. For this study, the beam polarization facility at the ILC along with the typical center-of-mass energy of 500 GeV is considered. The reach of the ILC with an integrated luminosity of 300 fb${}^{-1}$ in the determination of CP-conserving parameters is obtained. Sensitivity of the probe of each of these couplings in the presence of other couplings is investigated. The most influential coupling parameters are ${\bar{c}}_W=-{\bar{c}}_B$. Other parameters of significant effect are ${\bar{c}}_{HW}$ and ${\bar{c}}_{HB}$. A detailed study of the various kinematic distributions represents possibilities to disentangle the effect of some of these couplings.