Modern Physics Letters A

In this paper, we give a brief review of recent theoretical studies of double prompt $J/\psi$ production at the FNAL Tevatron and the CERN LHC, to which both single- and double-parton-scattering processes contribute. In single parton scattering, we mainly present the results computed within the framework of non-relativistic quantum chromodynamics factorization combined with one of the two approaches to describe the parton inside the (anti)proton, the collinear parton model and the parton Reggeization approach. The contributions from double parton scattering calculated with different values of ${\sigma }_{\mathrm{\text{eff}}}$ are also discussed. We conclude that, in double prompt $J/\psi$ hadroproduction, there remain some differences between theoretical predictions and experimental measurements.

We construct a non-renormalizable $B-L$ model based on $\mathrm{\Sigma }(18)$ symmetry, whereby, neutrino mass ordering and the tiny neutrino masses are explained at tree level via type I seesaw mechanism. The model can reproduce the recent observed neutrino oscillation data in which neutrino oscillation parameters including three mixing angles ${𝜃}_{12,23,13}$, Dirac CP phase plus neutrino squared-mass splittings $\mathrm{\Delta }{m}_{21,32}$ get the best-fit values for both Normal ordering (NO) and Inverted ordering (IO). The Majorana phases are predicted to be $\alpha =0$ for NO, $\alpha =\pi$ for IO and $\beta =0.86\pi$ for both NH and IO. The sum of neutrino mass and the effective neutrino mass are, respectively, predicted to be $\sum m_{\nu }=0.059\mathrm{\text{eV}}$ for NO while $\sum m_{\nu }=0.1002\mathrm{\text{eV}}$ for IO and $〈m_{ee}〉=1.51\mathrm{\text{meV}}$ for NO while $〈m_{ee}〉=48.8\mathrm{\text{meV}}$ for IO which are well compatible with the most recent experimental constraints.

We compute the string susceptibility ${\gamma }_{\mathrm{\text{str}}}$ for the regularized Nambu–Goto string in $d$ dimensions and obtain ${\gamma }_{\mathrm{\text{str}}}=1/2$ in $2<d<26$. This agrees with previous results obtained for lattice strings.

One of the most important mathematical tools necessary for Quantum Field Theory calculations is the field propagator. Applications are always done in terms of plane waves and although this has furnished many magnificent results, one may still be allowed to wonder what is the form of the most general propagator that can be written. In this paper, by exploiting what is called polar form, we find the most general propagator in the case of spinors, whether regular or singular, and we give a general discussion in the case of vectors.

Based on the Pomeranchuk theorem, one constructs the $\delta (s)$ parameter to measure the difference between experimental data for the particle–particle and particle–antiparticle total cross-section at same energy. The experimental data for the proton–proton and proton–antiproton total cross-section were used to show that, at the same energy, this parameter tends to zero as the collision energy grows. Furthermore, one assumes a classical description for the total cross-section, dividing it into a finite number of non-interacting disjoint cells, each one containing a quark–antiquark pair subject to the confinement potential. Near the minimum of the total cross-section, one associates $\delta (s)$ with the entropy generated by these cells, analogously to the $XY$-model. Using both the Quigg–Rosner and Cornell confinement potentials and neglecting other energy contributions, one can calculate the internal energy of the hadron. One obtains that both the entropy and internal energy possess the same logarithmic dependence on the spatial separation between the pairs in the cell. The Helmholtz free energy is used to estimate the transition temperature, which is far from the temperature widely related to the Quark–Gluon Plasma.

In this paper, we investigate the relationship between quadratic gravity and a restricted Weyl symmetry where a gauge parameter $\mathrm{\Omega }(x)$ of Weyl transformation satisfies a constraint $\square \mathrm{\Omega }=0$ in a curved spacetime. First, we briefly review a model with a restricted gauge symmetry on the basis of QED, where a $U(1)$ gauge parameter $𝜃(x)$ obeys a similar constraint $\square 𝜃=0$ in a flat Minkowski spacetime, and explain that the restricted gauge symmetry removes one on-shell mode of gauge field, which together with the Feynman gauge leaves only two transverse polarizations as physical states. Next, it is shown that the restricted Weyl symmetry also eliminates one component of a dipole field in quadratic gravity around a flat Minkowski background, leaving only a single scalar state. Finally, we show that the restricted Weyl symmetry cannot remove any dynamical degrees of freedom in static background metrics by using the zero-energy theorem of quadratic gravity. This fact also holds for the Euclidean background metrics without imposing the static condition.

In the first part of this note, we observe that a non-Riemannian piece in the affine connection (a “dark connection”) leads to an algebraically determined, conserved, symmetric 2-tensor in the Einstein field equations that is a natural dark matter candidate. The only other effect it has, is through its coupling to standard model fermions via covariant derivatives. If the local dark matter density is the result of a background classical dark connection, these Yukawa-like mass corrections are minuscule ($\sim 10^{-31}\mathrm{\text{eV}}$ for terrestrial fermions) and none of the tests of general relativity or the equivalence principle are affected. In the second part of the note, we give dynamics to the dark connection and show how it can be re-interpreted in terms of conventional dark matter particles. The simplest way to do this is to treat it as a composite field involving scalars or vectors. The (pseudo-)scalar model naturally has a perturbative shift-symmetry and leads to versions of the Fuzzy Dark Matter (FDM) scenario that has recently become popular (e.g. arXiv:1610.08297) as an alternative to WIMPs. A vector model with a ${{𝒵}}_2$-parity falls into the Planckian Interacting Dark Matter (PIDM) paradigm, introduced in arXiv:1511.03278. It is possible to construct versions of these theories that yield the correct relic density, fit with inflation and are falsifiable in the next round of CMB experiments. Our work is an explicit demonstration that the meaningful distinction is not between gravity modification and dark matter, but between theories with extra fields and those without.

Thomas–Fermi model is considered here to make it cogent to capture the Planck-scale effect with the use of a generalization of uncertainty relation. Here generalization contains both linear and quadratic terms of momentum. We first reformulate the Thomas–Fermi model for the non-relativistic case. We have shown that it can also be reformulated for taking into account the relativistic effect. We study the dialectic screening for both the non-relativistic and relativistic cases and find out the Fermi length for both the cases explicitly.

Experimental evidences of a first-order phase transition from a superfluid to a non-interacting Fermi gas system are studied for ${}^{97,98}$Mo isotopes. The experimental observations are compared with the semi-empirical macroscopic model and superfluid formalism. We have shown that the entropy excess ratio introduced in our previous publications within the superfluid model can describe the first-order phase transition due to pair-breaking in atomic nuclei.