International Journal of Modern Physics A

We review the main recent progresses in noncommutative space–time phenomenology in underground experiments. A popular model of noncommutative space–time is $𝜃$-Poincaré model, based on the Groenewold–Moyal plane algebra. This model predicts a violation of the spin-statistic theorem, in turn implying an energy and angular dependent violation of the Pauli exclusion principle. Pauli exclusion principle violating transitions in nuclear and atomic systems can be tested with very high accuracy in underground laboratory experiments such as DAMA/LIBRA and VIP(2). In this paper we derive that the $𝜃$-Poincaré model can be already ruled-out until the Planck scale, from nuclear transitions tests by DAMA/LIBRA experiment.

We review on further new developments of Generalized Uncertainty Principle (GUP) and implications for the cosmological vacuum energy. First, we introduce basic aspects of GUP as well as several possible different and viable formulation of it. Second, we move on discussing two recent new types of higher D-dimensional nonperturbative GUP models; which we dub D-Type-I and D-Type-II GUPs. The D-Type-I and D-Type-II GUPs are both related to the existence of a critical conspiracy between a minimal uncertainty length and a maximal observable momentum. Finally, we show direct implications of D-Type-I and D-Type-II on the cosmological vacuum energy obtained in quantum mechanical systems such as the typical quantum harmonic oscillator. Such a computation goes through investigations of the density of states for D-dimensional coordinate systems in the momentum space. We will also comment on several possible connections with fundamental issues of quantum gravity such as black hole physics and gravitational radiative aspects.

Motivated by the recent interest in underground experiments phenomenology (see Refs. 1–3), we review the main aspects of one specific noncommutative space–time model, based on the Groenewold–Moyal plane algebra, the $𝜃$-Poincaré space–time. In the $𝜃$-Poincaré scenario, the Lorentz co-algebra is deformed introducing a noncommutativity of space–time coordinates. In such a theory, a new quantum field theory in noncommutative space–time can be reformulated. Tackling on several conceptual misunderstanding and technical mistakes in the literature, we will focus on several issues such: (i) the construction of fields theories in $𝜃$-Poincaré; (ii) the unitarity of the S-matrix; (iii) the violation of locality, (iv) the violation of the spin-statistic theorem and the Pauli principle; (v) the observables for underground experiments.

The framework of the relativistic quantum mechanics on spatially flat FLRW space–times is considered for deriving the analytical solutions of the Dirac equation in different local charts of these manifolds. Systems of commuting conserved operators are used for determining the fundamental solutions as common eigenspinors giving thus physical meaning to the integration constants related to the eigenvalues of these operators. Since these systems, in general, are incomplete on the FLRW space–times there are integration constants that must be fixed by setting the vacuum either as the traditional adiabatic one or as the rest frame vacuum we proposed recently. All the known solutions of the Dirac equation on these manifolds are discussed in all details and a new type of spherical waves of given energy in the de Sitter expanding universe is reported here for the first time.

In a previous paper, hereafter referred to as I, we have analyzed the 7 TeV LHC data on $W+\mathrm{\text{jets}}$ events from the standpoint of IR-improved DGLAP parton shower effects, using the IR-improved Herwiri1.031 parton shower MC in comparison with the Herwig6.5 parton shower MC in the context of the exact $O({\alpha }_s)$ matrix element matched parton shower framework provided by MG5_aMC@NLO. In this paper, we extend this analysis to the LHC 8 and 13 TeV data to investigate the energy dependence of the results obtained in I. Specifically, $W+\mathrm{\text{jet}}$ events are generated in the MADGRAPH5_aMC@NLO framework and showered by HERWIG6.521 and HERWIRI1.031 with $PTRMS=2.2$ and 0 GeV, respectively. The differential cross sections are reported as functions of jet multiplicity, transverse linear momenta $(P_T)$, the jet pseudorapidity $(\eta )$ and the scalar sum of jet transverse momenta $(H_T)$ for different jet multiplicities 1–3. The dijet cross sections as functions of transverse linear momenta, invariant mass of the dijet and the jet separation are shown as well. Distributions of angular correlations between the jets and the muon are examined as well and the corresponding cross sections are presented. The respective measured cross sections are compared with the exact next-to-leading-order (NLO) matrix element matched parton shower theoretical predictions provided by MADGRAPH5_aMC@NLO/HERWIRI1.031 $(PTRMS=0)$ and MADGRAPH5_aMC@NLO/HERWIG6.521 $(PTRMS=2.2\mathrm{\text{GeV}})$ and the phenomenological consequences are discussed with an eye toward their energy dependence.

Grand unification groups (GUTs) are constructed from SO(32) heterotic string via $Z_{12-I}$ orbifold compactification. So far, most phenomenological studies from string compactification relied on $E_8\times E_8^{\prime }$ heterotic string, and this invites the SO(32) heterotic string very useful for future phenomenological studies. Here, spontaneous symmetry breaking is achieved by Higgsing of the antisymmetric tensor representations of SU$(N)$. The anti-SU$(N)$ presented in this paper is a completely different class from the flipped-SU$(N)$’s from the spinor representations of SO$(2N)$. Here, we realize chiral representations: $\overline{36}\oplus 5\cdot \bar{9}$ for a SU(9) GUT and $3\{{10}_L^{\prime }\oplus {\bar{5}}_L^{\prime }\}$ for a SU(5)${}^{\prime }$ GUT. In particular, we confirm that the non-Abelian anomalies of SU(9) gauge group vanish and hence our compactification scheme achieves the key requirement. We also present the Yukawa couplings, in particular for the heaviest fermion, $t$, and lightest fermions, neutrinos. In the supersymmetric version, we present a scenario how supersymmetry can be broken dynamically via the confining gauge group SU(9). Three families in the visible sector are interpreted as the chiral spectra of SU${(5)}^{\prime }$ GUT.

We present the result for the third and fourth moments of the nonsinglet four-loop anomalous dimension of Wilson twist-2 operators in QCD with full color and flavor structures. We also give general expressions for some contributions to the full four-loop anomalous dimension obtained by means of the method, based on LLL-algorithm, which was proposed by us earlier for the reconstruction of a general form of the anomalous dimension from the fixed values.

Many works, aiming to explain the origin of dark matter or dark energy, consider the existence of hidden (brane)worlds parallel to our own visible world — our usual Universe — in a multidimensional bulk. Hidden braneworlds allow for hidden copies of the Standard Model. For instance, atoms hidden in a hidden brane could exist as dark matter candidates. As a way to constrain such hypotheses, the possibility for neutron–hidden neutron swapping can be tested thanks to disappearance-reappearance experiments also known as passing-through-walls neutron experiments. The neutron-hidden neutron coupling $g$ can be constrained from those experiments. While $g$ could be arbitrarily small, previous works involving a $M_4\times R_1$ bulk, with DGP branes, show that $g$ then possesses a value which is reachable experimentally. It is of crucial interest to know if a reachable value for $g$ is universal or not and to estimate its magnitude. Indeed, it would allow, in a near future, to reject definitively — or not — the existence of hidden braneworlds from experiments. In the present paper, we explore this issue by calculating $g$ for DGP branes, for $M_4\times S_1/Z_2$, $M_4\times R_2$ and $M_4\times T^2$ bulks. As a major result, no disappearance-reappearance experiment would definitively universally rules out the existence of hidden worlds endowed with their own copy of Standard Model particles, except for specific scenarios with conditions reachable in future experiments.

The relation between certain Hamiltonians, known as dual, or partner Hamiltonians, under the transformation $x\to {\bar{x}}^{\bar{\alpha }}$ has long been used as a method of simplifying spectral problems in quantum mechanics. This paper seeks to examine this further by expressing such Hamiltonians in terms of the generators of sl(2) algebra, which provides another method of solving spectral problems. It appears that doing so greatly restricts the set of allowable potentials, with the only nontrivial potentials allowed being the Coulomb $\frac{1}{r}$ potential and the harmonic oscillator $r^2$ potential, for both of which the sl(2) expression is already known. It also appears that, by utilizing both the partner potential transformation and the formalism of the Lie-algebraic construction of quantum mechanics, it may be possible to construct part of a Hamiltonian’s spectrum from the quasi-solvability of its partner Hamiltonian.

Deep inelastic scattering is one of the best place to study hadron structures. In this paper we consider the target fragmentation region deep inelastic scattering process at leading twist. The calculations are carried out by applying the collinear expansion. In the collinear expansion formalism the multiple gluon scattering is taken into account and gauge links are obtained systematically and automatically. Quantum chromodynamics is a non-Abelian gauge theory of strong interactions in which parity symmetry can be violated by the nontrivial $𝜃$-vacuum tunneling effects. As a result, the axial vector current is induced. By defining and decomposing the parity-odd correlator we calculate both the parity-even and parity-odd contributions to the cross-section of the target fragmentation region deep inelastic scattering. We also present the positivity bounds for these fracture functions.