Modern Physics Letters A

The discovery of the Higgs particle at 125 GeV is demanding a detailed knowledge of the properties of this fundamental component of the Standard Model. To that aim various proposals of electron and muon colliders have been put forward for precision studies of the partial widths of the various decay channels. It is shown that in the case of a Higgs factory through a muon collider, sizeable radiative effects — of order of 50% — must be carefully taken into account for a precise measurement of the leptonic and total widths of the Higgs particle. Similar effects do not apply in the case of Higgs production in electron–positron colliders.

We obtain the elementary modes of a system of parity-time reversal (PT)-symmetric coupled oscillators with balanced loss and gain. These modes are used to give a physical picture of the phase transition recently reported [C. M. Bender, M. Gianfreda, B. Peng, S. K. Özdemir and L. Yang, Phys. Rev. A 88, 062111 (2013); L. Yang, S. K. Özdemir and B. Peng, 12th Int. Workshop and Conf. Pseudo-Hermitian Hamiltonians in Quantum Physics, Istanbul, Turkey, July 2013; B. Peng, S. K. Özdemir, F. Lei, F. Monifi, M. Gianfreda, G. L. Long, S. Fan, F. Nori, C. M. Bender and L. Yang, Nat. Phys. 10, 394 (2014)] in experiments with whispering-gallery microresonators.

Using the functional analysis method, we present the exact solutions of the double ring-shaped oscillator (DRSO) potential with certain parity in the cylindrical coordinates. Such a quantum system is separated to two differential equations, i.e. a one-dimensional harmonic oscillator plus an inverse square term and a two-dimensional harmonic oscillator plus an inverse square term. The key point is how to find the adapted symmetrical solutions of the one-dimensional harmonic oscillator plus an inverse square term at the singular point $z=0$. The obtained results are compared with those in the spherical coordinates. We also explore intimate connections $E_T(i\rho )=-E_T(\rho )$ and $E_z(iz)=-E_z(z)$ by substituting $\rho \to i\rho$ and $z\to iz$.

Since the conformal transformations of metric do not change its causal structure, we use these transformations to embed the Lemaître metrics into the FRW background. In our approach, conformal transformation is in agreement with the universe expansion regimes. Indeed, we use the Lemaître metrics because the horizon singularity is eliminated in these metrics. Moreover, some physical and mathematical properties of the introduced metrics have been addressed. We show that the resultant metrics include event horizons while their physical radii are increasing as a function of the universe expansion which may provide suitable metrics for investigating the effects of the universe expansion on the black holes.

It is known that Nambu–Goto extended objects present some pathological structures, such as cusps and kinks, during their evolution. In this paper, we propose a model through the generalized Raychaudhuri (Rh) equation for membranes to determine if there are cusps and kinks in the worldsheet. We extend the generalized Rh equation for membranes to allow the study of the effect of higher order curvature terms in the action on the issue of cusps and kinks, using it as a tool for determining when a Nambu–Goto string generates cusps or kinks in its evolution. Furthermore, we present three examples where we test graphically this approach.

We consider a generalization of non-relativistic Schrödinger–Higgs Lagrangian by introducing a nonstandard kinetic term. We show that this model is Galilean invariant, we construct the conserved charges associated to the symmetries and realize the algebra of the Galilean group. In addition, we study the model in the presence of a gauge field. We also show that the gauged model is Galilean invariant. Finally, we explore relations between the twin models and their solutions.

One of the less well-understood ambiguities of quantization is emphasized to result from the presence of higher-order time derivatives in the Lagrangians resulting in multiple-valued Hamiltonians. We explore certain classes of branched Hamiltonians in the context of nonlinear autonomous differential equation of Liénard type. Two eligible elementary nonlinear models that emerge are shown to admit a feasible quantization along these lines.

Our investigation of high energy $pp$ and $\bar{p}p$ elastic scattering over the last ten years has led us to consider that the proton has three regions: (i) an outer region consisting of a quark–antiquark $(q\bar{q})$ condensate ground state (also described as quark–antiquark outer cloud), (ii) an inner shell of topological (geometrical) baryonic charge of size $\sim$ 0.44 fm, and (iii) a core of size $\sim$ 0.2 fm, where the three valence quarks of a proton with baryonic charges are confined. The proton structure that has emerged leads to four main elastic scattering processes in $pp$ scattering. The first process (which gives rise to diffraction scattering) is described by a profile function. The second process involves multiple $\omega$-exchanges. The third process in $pp$ scattering is quark–quark scattering via gluon–gluon interaction. The fourth process — which appears for the first time in our investigation of $pp$ scattering — is a glancing collision at the boundary of a proton with that of the other proton. To describe quantitatively the four processes, their parameters have to be determined. For this purpose, we investigate: (i) $pp$ 7 TeV $d\sigma /dt$ measured by the TOTEM Collaboration and (ii) $\bar{p}p$ 1.96 TeV $d\sigma /dt$ measured by the D0 Collaboration.

Once the parameters are satisfactorily obtained, we calculate $pp$ $d\sigma /dt$ at 7 TeV and compare with the TOTEM data. We also calculate $\bar{p}p$ $d\sigma /dt$ at 1.96 TeV and compare with the D0 data. We then predict $pp$ elastic $d\sigma /dt$ at 13 TeV which will soon be measured at LHC by the TOTEM Collaboration. This measurement will establish how well we have predicted the 13 TeV $d\sigma /dt$ and determined the structure of the proton.