International Journal of Modern Physics A

Multiparticle production processes provide valuable information about the mechanism of the conversion of the initial energy of projectiles into a number of secondaries by measuring their multiplicity distributions and their distributions in phase space. They therefore serve as a reference point for more involved measurements. Distributions in phase space are usually investigated using the statistical approach, very successful in general but failing in cases of small colliding systems, small multiplicities, and at the edges of the allowed phase space, in which cases the underlying dynamical effects competing with the statistical distributions take over. We discuss an alternative approach, which applies to the whole phase space without detailed knowledge of dynamics. It is based on a modification of the usual statistics by generalizing it to a superstatistical form. We stress particularly the scaling and self-similar properties of such an approach manifesting themselves as the phenomena of the log-periodic oscillations and oscillations of temperature caused by sound waves in hadronic matter. Concerning the multiplicity distributions we discuss in detail the phenomenon of the oscillatory behavior of the modified combinants apparently observed in experimental data.

Correlations between the QCD coupling ${\alpha }_s$, the gluon condensate $〈{\alpha }_s{G}^2〉$ and the $c$, $b$-quark running masses ${\bar{m}}_{c,b}$ in the $\overline{\mathrm{\text{MS}}}$-scheme are explicitly studied (for the first time) from the (axial-)vector and (pseudo)scalar charmonium and bottomium ratios of Laplace sum rules (LSR) evaluated at the $\mu$-subtraction stability point where perturbative (PT) @N2LO, N3LO and $〈{\alpha }_s{G}^2〉$ @NLO corrections are included. Our results clarify the (apparent) discrepancies between different estimates of $〈{\alpha }_s{G}^2〉$ from $J/\psi$ sum rule and also show the sensitivity of the sum rules on the choice of the $\mu$-subtraction scale which does not permit a high-precision estimate of ${\bar{m}}_{c,b}$. We obtain from the (axial-)vector [respectively (pseudo)scalar] channels: $〈{\alpha }_s{G}^2〉=(7.4\pm 2.2)$ [respectively $(6.34\pm 0.39)]\times 10^{-2}$ GeV⁴, ${\bar{m}}_c({\bar{m}}_c)=1264(22)$ [respectively 1266(16)] MeV and ${\bar{m}}_b({\bar{m}}_b)=4192(15)$ MeV. Combined with our recent determinations from vector channel, one obtains the average: ${\bar{m}}_c({\bar{m}}_c){|}_{\mathrm{\text{average}}}=1264(10)$ MeV and ${\bar{m}}_b({\bar{m}}_b){|}_{\mathrm{\text{average}}}=4184(9)$ MeV. Adding the two above values of the gluon condensate to different previous estimates in Table 1, one obtains the 2018 sum rule average: $〈{\alpha }_s{G}^2〉{|}_{\mathrm{\text{average}}}=(6.35\pm 0.35)\times 10^{-2}$ GeV⁴. The mass-splittings $M_{{\chi }_{0c(0b)}}-M_{{\eta }_{c(b)}}$ give @N2LO: ${\alpha }_s(M_Z)=0.1182(15)(3)$ in good agreement with the world average.

In this paper, we analyze the classical geometric flow as a dynamical system. We obtain an action for this system, such that its equation of motion is the Raychaudhuri equation. This action will be used to quantize this system. As the Raychaudhuri equation is the basis for deriving the singularity theorems, we will be able to understand the effects and such a quantization will have on the classical singularity theorems. Thus, quantizing the geometric flow, we can demonstrate that a quantum space–time is complete (nonsingular). This is because the existence of a conjugate point is a necessary condition for the occurrence of singularities, and we will be able to demonstrate that such conjugate points cannot occur due to such quantum effects.

The near-zero modes of the Dirac operator are connected to spontaneous breaking of chiral symmetry in QCD (SBCS) via the Banks–Casher relation. At the same time, the distribution of the near-zero modes is well described by the Random Matrix Theory (RMT) with the Gaussian Unitary Ensemble (GUE). Then, it has become a standard lore that a randomness, as observed through distributions of the near-zero modes of the Dirac operator, is a consequence of SBCS. The higher-lying modes of the Dirac operator are not affected by SBCS and are sensitive to confinement physics and related $SU{(2)}_{\mathrm{\text{CS}}}$ and $SU(2N_F)$ symmetries. We study the distribution of the near-zero and higher-lying eigenmodes of the overlap Dirac operator within $N_F=2$ dynamical simulations. We find that both the distributions of the near-zero and higher-lying modes are perfectly described by GUE of RMT. This means that randomness, while consistent with SBCS, is not a consequence of SBCS and is linked to the confining chromo-electric field.

We express each Clebsch–Gordan (CG) coefficient of a discrete group as a product of a CG coefficient of its subgroup and a factor, which we call an embedding factor. With an appropriate definition, such factors are fixed up to phase ambiguities. Particularly, they are invariant under basis transformations of irreducible representations of both the group and its subgroup. We then impose on the embedding factors constraints, which relate them to their counterparts under complex conjugate and therefore restrict the phases of embedding factors. In some cases, the phase ambiguities are reduced to sign ambiguities. We describe the procedure of obtaining embedding factors and then calculate CG coefficients of the group ${{𝒫}{𝒮}{ℒ}}_2(7)$ in terms of embedding factors of its subgroups $S_4$ and ${{𝒯}}_7$.

Following earlier studies that provided a consistent theory of kinematics for tachyons (faster-than-light particles), we here embark on a study of tachyon dynamics, both in classical physics and in the quantum theory. Examining a general scattering process, we come to recognize that the labels given to “in” and “out” states are not Lorentz invariant for tachyons; and this lets us find a sensible interpretation of negative energy states. For statistical mechanics, as well as for scattering problems, we study what should be the proper expression for density of states for tachyons. We review the previous work on quantization of a Dirac field for tachyons and go on to expand earlier considerations of neutrinos as tachyons in the context of cosmology. We stumble into the realization that tachyon neutrinos would contribute to gravitation with the opposite sign compared to tachyon antineutrinos. This leads to the gobsmacking prediction that the Cosmic Neutrino Background, if they are indeed tachyons, might explain both phenomena of Dark Matter and Dark Energy. This theoretical study also makes contact with the anticipated results from the experiments KATRIN and PTOLEMY, which focus on beta decay and neutrino absorption by Tritium.

Fractal self-similarity of hadron interactions demonstrated by the $z$-scaling of inclusive spectra is studied. The scaling regularity reflects fractal structure of the colliding hadrons (or nuclei) and takes into account general features of fragmentation processes expressed by fractal dimensions. The self-similarity variable $z$ is a function of the momentum fractions $x_1$ and $x_2$ of the colliding objects carried by the interacting hadron constituents and depends on the momentum fractions $y_a$ and $y_b$ of the scattered and recoil constituents carried by the inclusive particle and its recoil counterpart, respectively. Based on entropy principle, new properties of the $z$-scaling concept are found. They are conservation of fractal cumulativity in hadron interactions and quantization of fractal dimensions characterizing hadron structure and fragmentation processes at a constituent level.

In the framework of the braneworld Randall–Sundrum type II model, we investigate an inflationary scalar model in the high-energy regime. In this regime, the slow-roll parameters and the perturbation spectrum of the model are derived. The corresponding results are dealt with according to the known observational data. Then the solutions to the equations of motion on the brane are given.

Scalar Quantum Electrodynamics is investigated in the Heisenberg picture via the Duffin-Kemmer-Petiau gauge theory. On this framework, a perturbative method is used to compute the vacuum polarization tensor and its corresponding induced current for the case of a charged scalar field in the presence of an external electromagnetic field. Charge renormalization is brought into discussion for the interpretation of the results for the vacuum polarization.

We study the signal rates of the second lightest CP-even Higgs boson, $h_2$, of the NMSSM produced in gluon fusion, in association with bottom quarks and in association with top quarks, which is not the SM-like Higgs boson, at the LHC. We evaluate the production rates of $h_2$ in the SM fermionic and bosonic final states in addition to $a_1{a}_1$, $h_1{h}_1$ and $Z{a}_1$ final states. It is observed that the size of the signal rates in some regions of the NMSSM parameter space is quite large and that could help extracting $h_2$ signals at the LHC through a variety of decay channels.