[en] We provide an explicit Lagrangian construction for the massless infinite spin $N=1$ supermultiplet in four dimensional Minkowski space. Such a supermultiplet contains a pair of massless bosonic and a pair of massless fermionic infinite spin fields with properly adjusted dimensionful parameters. We begin with the gauge invariant Lagrangians for such massless infinite spin bosonic and fermionic fields and derive the supertransformations which leave the sum of their Lagrangians invariant. It is shown that the algebra of these supertransformations is closed on-shell.

[en] Choosing how gauge $U{(1)}_{\chi }$ breaks in the context of $SO(10)\to SU(5)\times U{(1)}_{\chi }$, $Z_4$ lepton number may be obtained which maintains neutrinos as Dirac fermions. Choosing $\mathrm{\Delta }(27)$ as the family symmetry of leptons, tree-level Dirac neutrino masses may be forbidden. Choosing a specific set of self-interacting dark-matter particles, Dirac neutrino masses and mixing may then be generated in two loops. This framework allows the realization of cobimaximal neutrino mixing, i.e. ${\theta }_{13}\ne 0$, ${\theta }_{23}=\pi /4$, ${\delta }_{CP}=\pm \pi /2$, as well as the desirable feature that the light scalar mediator of dark-matter interactions decays only to neutrinos, thereby not disrupting the cosmic microwave background (CMB).

[en] The mass and leptonic decay constants of recently observed two new excited $B_c$ states at LHC are studied within the QCD sum rules. Considering the contributions of the ground and radially excited states, the mass and residues of the excited states of pseudoscalar and vector mesons are calculated in the framework of two different approaches of the QCD sum rules, namely, linear combinations of the corresponding sum rules and its derivatives as well as QCD sum rules with the incorporation of the least square fitting method. The obtained results on mass $m_{B_c^{+}}(2S)=6.88\pm 0.03\text{GeV}$ and $m_{B_c^{⁎+}}(2S)=6.94\pm 0.03\text{GeV}$ are in good agreement with the experimental data. Our predictions for the decay constants of these states are: $f_{B_c^{+}}(2S)=0.42\pm 0.02\mathrm{GeV}$ and $f_{B_c^{⁎+}}(2S)=0.46\pm 0.01\mathrm{GeV}$, which can be checked at future experiments to be conducted at the LHC. Comparison of our results with the predictions of the other approaches on mass and residues is also presented.

[en] We study anomalous couplings among neutral gauge bosons in ZZ production at the LHC for $\sqrt{s}=13$ TeV in 4-lepton final state. We use the cross section and polarization asymmetries of the Z boson to estimate simultaneous limits on anomalous coupling using Markov-chain–Monte-Carlo (MCMC) method for luminosities 35.9 fb⁻¹, 150 fb⁻¹, 300 fb⁻¹ and 1000 fb⁻¹. The CP-even polarization asymmetry $A_{x^2-y^2}$ is sensitive mainly to the CP-odd couplings $f_4^{Z/\gamma }$ (quadratically) providing a probe to identify CP-odd nature of interaction at the LHC. We find that the polarization asymmetries significantly improve the estimation of anomalous couplings should a deviation from the Standard Model (SM) be observed.

[en] We show that a choice of Pauli-Villars regulators allows the cancellation of all the conformal and chiral anomalies in an effective field theory from ${\mathbb{Z}}_3$ compactification of the heterotic string with two Wilson lines and an anomalous $U(1)$.

[en] We study features of the resonances $X(2100)$ and $X(2239)$ by treating them as the axial-vector and vector tetraquarks with the quark content $ss\bar{s}\bar{s}$, respectively. The spectroscopic parameters of these exotic mesons are calculated in the framework of the QCD two-point sum rule method. Obtained prediction for the mass $m=(2067\pm 84)\text{MeV}$ of the axial-vector state is in excellent agreement with the mass of the structure $X(2100)$ recently observed by the BESIII Collaboration in the decay $J/\psi \to \varphi \eta {\eta }^{\prime }$ as the resonance in the $\varphi {\eta }^{\prime }$ mass spectrum. We also explore the decays $X(2100)\to \varphi {\eta }^{\prime }$ and $X(2100)\to \varphi \eta$ using QCD light-cone sum rule approach and technical methods of the soft-meson approximation. The width of the axial-vector tetraquark, $\mathrm{\Gamma }=(130.2\pm 30.1)\text{MeV}$, saturated by these two processes is comparable with the measured full width of the resonance $X(2100)$. Our prediction for the vector $ss\bar{s}\bar{s}$ tetraquark's mass $\tilde{m}=(2283\pm 114)\text{MeV}$ is consistent with the experimental result $(2239.2\pm 7.1\pm 11.3)\text{MeV}$ of the BESIII Collaboration for the mass of the resonance $X(2239)$.

[en] We study a classically accidental scale-invariant extension of the Standard Model (SM) containing three additional fields, a vector leptoquark ($V_{\mu }$), a real scalar (ϕ), and a neutral Majorana fermion (χ) as a dark matter (DM) candidate. The scalar ϕ (scalon) and Majorana fermion χ are both singlets under the SM gauge group, while $V_{\mu }$ has (3, 1, 2/3) quantum numbers under the $SU{(3)}_c\times SU{(2)}_L\times U{(1)}_Y$. The Majorana DM couples to the SM sector via both Higgs and leptoquark portals. We perform a scan over the independent parameters to determine the viable parameter space consistent with the Planck data for DM relic density, and with the PandaX-II and LUX direct detection limits for the spin-independent (SI) and spin-dependent (SD) DM-nucleon cross section. The model generally evades indirect detection constraints while being consistent with collider data.

[en] We consider the conformal group of a space of $\dim n=p+q$, with $SO(p,q)$ metric. The quotient of this group by its homogeneous Weyl subgroup gives a principal fiber bundle with 2n-dim base manifold and Weyl fibers. The Cartan generalization to a curved 2n-dim geometry admits an action functional linear in the curvatures. Because symmetry is maintained between the translations and the special conformal transformations in the construction, these spaces are called biconformal; this same symmetry gives biconformal spaces overlapping structures with double field theories, including manifest T-duality. We establish that biconformal geometry is a form of double field theory, showing how general relativity with integrable local scale invariance arises from its field equations. While we discuss the relationship between biconformal geometries and the double field theories of T-dual string theories, our principal interest is the study of the gravity theory. We show that vanishing torsion and vanishing co-torsion solutions to the field equations overconstrain the system, implying a trivial biconformal space. With co-torsion unconstrained, we show that (1) the torsion-free solutions are foliated by copies of an n-dim Lie group, (2) torsion-free solutions generically describe locally scale-covariant general relativity with symmetric, divergence-free sources on either the co-tangent bundle of n-dim $(p,q)$-spacetime or the torus of double field theory, and (3) torsion-free solutions admit a subclass of spacetimes with n-dim non-abelian Lie symmetry. These latter cases include the possibility of a gravity-electroweak unification. It is notable that the field equations reduce all curvature components to dependence only on the solder form of an n-dim Lagrangian submanifold, despite the increased number of curvature components and doubled number of initial independent variables.

[en] Kerov functions provide an infinite-parametric deformation of the set of Schur functions, which is a far-going generalization of the 2-parametric Macdonald deformation. In this paper, we concentrate on a particular subject: on Kerov functions labeled by the Young diagrams associated with the conjugate and, more generally, composite representations. Our description highlights peculiarities of the Macdonald locus (ideal) in the space of the Kerov parameters, where some formulas and relations get drastically simplified. However, even in this case, they substantially deviate from the Schur case, which illustrates the problems encountered in the theory of link hyperpolynomials. An important additional feature of the Macdonald case is uniformization, a possibility of capturing the dependence on N for symmetric polynomials of N variables into a single variable $A=t^N$, while in the generic Kerov case the N-dependence looks considerably more involved.

[en] Inflationary cosmology represents a well-studied framework to describe the expansion of space in the early universe, as it explains the origin of the large-scale structure of the cosmos and the isotropy of the cosmic microwave background radiation. The recent detection of the Higgs boson renewed research activities based on the assumption that the inflaton could be identified with the Higgs field. At the same time, the question whether the inflationary potential can be extended to the electroweak scale and whether it should be necessarily chosen ad hoc in order to be physically acceptable are at the center of an intense debate. Here, we propose and perform the slow-roll analysis of the so-called Massive Natural Inflation (MNI) model which has three adjustable parameters, the explicit mass term, a Fourier amplitude u, and a frequency parameter β, in addition to a constant term of the potential. This theory has the advantage to present a structure of infinite non-degenerate minima and is amenable to an easy integration of high-energy modes. We show that, using PLANCK data, one can fix, in the large β-region, the parameters of the model in a unique way. We also demonstrate that the value for the parameters chosen at the cosmological scale does not influence the results at the electroweak scale. We argue that other models can have similar properties both at cosmological and electroweak scales, but with the MNI model one can complete the theory towards low energies and easily perform the integration of modes up to the electroweak scale, producing the correct order-of-magnitude for the Higgs mass.