International Journal of Modern Physics A

In this paper, we investigate the exact time-dependent black hole solution on a warped five-dimensional Randall–Sundrum space–time in conformal dilaton gravity. The zeroes of the model are described by a meromorphic quintic polynomial, which has no essential singularities. The quintic equation can be reduced to the Brioschi form by means of the Weierstrass elliptic curve over $\mathbb{Q}$. The model fits the antipodal boundary condition, i.e. antipodal points in the projected space are identified using the embedding of a Klein surface in ${ℂ}^2$, using the ${\mathbb{Z}}_2$ symmetry on the two sides of the brane. If one writes ${}^{(5)}{g}_{\mu \nu }={\omega }^{4∕3}{}^{(5)}{\tilde{g}}_{\mu \nu },{}^{(5)}{\tilde{g}}_{\mu \nu }={}^{(4)}{\tilde{g}}_{\mu \nu }+n_{\mu }{n}_{\nu }$, ${}^{(4)}{\tilde{g}}_{\mu \nu }={\bar{\omega }}^2{}^{(4)}{ḡ}_{\mu \nu }$, with $n_{\mu }$ the normal to the brane and $\omega$ the dilaton field, then ${}^{(4)}{ḡ}_{\mu \nu }$ is conformally flat. It is the contribution from the bulk which determines the real pole on the effective four-dimensional space–time. There is no objection applying ’t Hooft’s back reaction method in constructing the unitary S-matrix for the Hawking radiation. Again, there is no “inside” of the black hole. The zeroes can also be analyzed by the icosahedron equation and by the Hopf-fibration of the Klein surface.

For the interacting Feynman propagator ${\mathrm{\Delta }}_{F,\mathrm{\text{int}}}(x,y)$ of scalar electrodynamics, we show that the sign property, $\mathrm{\text{Re}}{i\mathrm{\Delta }}_{F,\mathrm{\text{int}}}\ge 0$, may hinge on the reversibility of time evolution. In contrast, $\mathrm{\text{Im}}{i\mathrm{\Delta }}_{F,\mathrm{\text{int}}}$ is indeterminate. When we switch to reduced dynamics under the weak coupling approximation, the positive semidefinite sign of $\mathrm{\text{Re}}{i\mathrm{\Delta }}_{F,\mathrm{\text{int}}}$ is generally lost, unless we impose severe restrictions on the Kraus operators that govern time evolution. With another approximation, the rotating wave approximation, we may recover the sign by restricting the test functions to exponentials under certain conditions.

The purpose of this paper is to examine the model dependence of the stringent constraints on the gluino mass obtained from the Large Hadron Collider (LHC) experiments by analyzing the Run II data using specific simplified models based on several ad hoc sparticle spectra which cannot be realized even in the fairly generic pMSSM models. We first revisit the bounds on the gluino mass placed by the ATLAS collaboration using the $1l+\mathrm{\text{jets}}+{∕E}_T$ data. We show that the exclusion region in the $M_{\tilde{g}}-M_{{\tilde{\chi }}_1^0}$ plane in the pMSSM scenario sensitively depends on the mass hierarchy between the left and right squarks and composition of the lighter electroweakinos and to a lesser extent, other parameters. Most importantly, for higgsino-type lighter electroweakinos (except for the LSP), the bound on the gluino mass from this channel practically disappears. However, if such models are confronted by the ATLAS $\mathrm{\text{jets}}+{∕E}_T$ data, fairly strong limits are regained. Thus, in the pMSSM, an analysis involving a small number of channels may provide more reliable mass limits. We have also performed detailed analyses on neutralino Dark Matter (DM) constraints in the models we have studied and have found that for a significant range of LSP masses, the relic density constraints from the WMAP/PLANCK data are satisfied and LSP-gluino coannihilation plays an important role in relic density production. We have also checked the simultaneous compatibility of the models studied here with the direct DM detection, and the LHC constraints.

The main idea behind this paper is to study $f({𝒢},\phi )$ theory of gravity, where ${𝒢}$ is Gauss–Bonnet (GB) term and $\phi$ is the scalar field. Scalar field has been introduced to explore gravitational interaction between geometry and scalar field. Field equations in Friedmann–Robertson–Walker (FRW) cosmology are constructed and found to be coherent with the existing literature. Exponential solutions are reconstructed. The coupling of the scalar field to the GB term leads to viable results. Further, we probe the oscillating universe in the said gravity model using linear trace term. Energy conditions are explored and graphically analyzed in detail to substantiate our work. Behavior of the Hubble and deceleration parameter is also examined. It is evident from the results that our model provides us with acceptable bouncing solutions for chosen parameters.

In the paper, we construct eight color singlet–singlet-type five-quark currents with distinguished isospins to study the $\bar{D}{\mathrm{\Xi }}^{\prime }$, $\bar{D}{\mathrm{\Xi }}_c^{\ast }$, ${\bar{D}}^{\ast }{\mathrm{\Xi }}_c^{\prime }$ and ${\bar{D}}^{\ast }{\mathrm{\Xi }}_c^{\ast }$ molecular states with strangeness via the QCD sum rules. Numerical results show that the central values of the pentaquark masses with higher (lower) isospin are slightly above (below) the thresholds of the corresponding meson–baryon pairs, and support assigning the $P_{cs}(4459)$ as the $\bar{D}{\mathrm{\Xi }}_c^{\ast }$ molecular state with the quantum numbers $I{J}^P=0{\frac{3}{2}}^{-}$. The other predictions can be confronted to the experimental data in the future.

An approximate analytical solution of the Balitsky–Kovchegov (BK) equation using the homotopy perturbation method (HPM) is suggested in this work. We carried out our work in perturbative Quantum Chromodynamics (QCD) (pQCD) dipole picture of deep inelastic scattering (DIS). The BK equation in momentum space with some change of variables and truncation of the Balitsky–Fadin–Kuraev–Lipatov (BFKL) kernel can be reduced to Fisher–Kolmogorov–Petrovsky–Piscounov (FKPP) equation. The observed geometric scaling phenomena are similar to the travelling wave solution of the FKPP equation. We solved the BK equation using the HPM. The obtained solution in this work also suggests the travelling wave nature of the measured scattering amplitude $N(k,Y)$ plotted at various rapidities. We also extracted the saturation momentum, $Q_s^2(Y)$, from the obtained solution and plotted it against different rapidities. The result obtained in this work can be helpful for various phenomenological studies in high-density QCD.

We show a matrix decomposition of flavor mass matrix for Dirac neutrinos $M$ by sum as $M=M^{\prime }+M^0$ where $M^{\prime }$ obeys the feature of the magic square and $M^0$ is three-zero texture. The favorable three-zero textures in the context of magic square are explored. It turned out that the so-called normal ordering of neutrino masses is favored over the inverted ordering in the context of magic square.

The exact renormalization group (ERG) is formulated implementing the decimation of degrees of freedom by means of a particular momentum integration measure. The definition of this measure involves a distribution that links this decimation process with the dimensional regularization technique employed in field theory calculations. Taking the dimension $d=4-ϵ$, the one-loop solutions to the ERG equations for the scalar field theory in this scheme are shown to coincide with the dimensionally regularized perturbative field theory calculation in the limit $ϵ\to 0^{-}$, if a particular relation between the scale parameter $\mu$ and $ϵ$ is employed. In general, it is shown that in this scheme the solutions to the ERG equations for the proper functions coincide when $ϵ\to 0^{-}$ with the complete diagrammatic contributions appearing in field theory for these functions and this theory, provided that exact relations between $\mu$ and $ϵ$ hold. In addition, a nonperturbative approximation is considered. This approximation consists in a truncation of the ERG equations, which by means of a low-momentum expansion leads to reasonable results.

In this paper, we present the first interior solutions representing compact stars in $\kappa ({ℛ},{𝒯})$ gravity by solving the modified field equations in isotropic coordinates. Further, we have assumed the metric potentials in Schwarzschild’s form and a few parameters along with the isotropic condition of pressure. For solving, we use specific choice of the running gravitational constant as $\kappa ({ℛ},{𝒯})=8\pi -\lambda {𝒯}(G=\tilde{c}=1)$. Once arrived at the reduced field equations, we investigate two solutions with $c=1$ and $c\ne 1$, where $c$ denotes here another constant that should not be confused with the speed of light. Then, we investigate each solution by determining the thermodynamics variable viz pressure, density, speed of sound and adiabatic index. We found that these solutions satisfy the Bondi criterion, causality condition and energy conditions. We also found that the $M-R$ curves generated from these solutions satisfy the stringent constraints provided by the gravitational wave observations due to the neutron star merger GW 170817.

A general method has been developed to solve the Schrödinger equation for an arbitrary derivative of the $\delta$-function potential in 1-d using cutoff regularization. The work treats both the relativistic and nonrelativistic cases. A distinction in the treatment has been made between the case when the derivative $n$ is an even number from the one when $n$ is an odd number. A general gap equation for each case has been derived. The case of ${\delta }^{(2)}$-function potential has been used as an example. The results from the relativistic case show that the ${\delta }^{(2)}$-function system behaves exactly like the $\delta$-function and the ${\delta }^{\prime }$-function potentials, which means it also shares the same features with quantum field theories, like being asymptotically free, in the massless limit, it undergoes dimensional transmutation and it possesses an infrared conformal fixed point. As a result, the evidence of universality of contact interactions has been extended further to include the ${\delta }^{(2)}$-function potential.

In this paper, we employed the quasi-particle (QP) Debye mass at finite baryonic chemical potential which can be used in the medium modified heavy quark potential to solve the $N$-dimensional Schrödinger equation. The bound state solution of the Schrödinger equation using Cornell potential been obtained by Super-Symmetry Quantum Mechanics (SUSYQM) method. The thermodynamical properties of quark matter are calculated by using baryonic chemical potential ($\mu$). We found that the binding energy of quarkonia dissociates more with QP Debye mass in comparison to nonperturbative and leading order Debye mass. The medium modified form of potential (real part) has been used to study the thermodynamical properties of quark matter with different equation of states (EoSs) (i.e. pressure, energy density and speed of sound) with $\mu$. The mass spectra of quarkonia have been also calculated in the $N$-dimensional space and compared with the experimental data at $N=3$. We have also calculated the dissociation temperature ($T_D$) for the ground states of quarkonium using the dissociation criteria of thermal width.

In this paper, a study of four different machine learning (ML) algorithms is performed to determine the most suitable ML technique to disentangle a hypothetical supersymmetry (SUSY) signal from its corresponding Standard Model (SM) backgrounds and to establish their impact on signal significance. The study focuses on the production of SUSY top squark pairs (stops), in the mass range of $500<m_{{\tilde{t}}_1}<800$GeV, from proton–proton collisions with a center of mass energy of 13TeV and an integrated luminosity of $140{\mathrm{\text{fb}}}^{-1}$, emulating the data-taking conditions of the run II Large Hadron Collider (LHC) accelerator. In particular, the semileptonic channel is analyzed, corresponding to final states with a single isolated lepton (electron or muon), missing transverse energy, and four jets, with at least one tagged as $b$-jet. The challenging compressed spectra region is targeted, where the stop decays mainly into a $W$ boson, a $b$-jet, and a neutralino (${\tilde{t}}_1\to W+b+{\tilde{\chi }}_1^0$), with a mass gap between the stop and the neutralino of about 150GeV. The ML algorithms are chosen to cover different mathematical implementations and features in ML. We compare the performance of a logistic regression (LR), a Random Forest (RF), an eXtreme Gradient Boosting, XGboost (XG) and a Neural Network (NN) algorithm. Our results indicate that XG and NN classifiers provide the highest improvements (over 17%) in signal significance, when compared to a standard analysis method based on sequential requirements of different kinematic variables. The improvement in signal significance provided by the NN increases up to 31% for the highest stop mass considered in this study (800GeV). The RF algorithm presents a smaller improvement that decreases with stop mass. On the other hand, the LR algorithm shows the worst performance in signal significance which even does not compete with the results obtained by an optimized cut and count method.

The second quantization of the quaternionic fermionic field is undertaken using the real Hilbert space approach to quaternionic quantum mechanics (${ℍ}$QM). The solution responds to an open problem of quaternionic quantum theory, and launches the basis to the development of the quaternionic interaction theory.

The long baseline (LBL) neutrino experiments use heavy nuclear targets for neutrino scattering in which nuclear effects give rise to complications in measuring the neutrino oscillation parameters up to high precision. These nuclear effects are not yet fully understood and therefore need to be quantified as they contribute to the systematic uncertainties. Precision reconstruction of neutrino energy is one of the main components in measuring the oscillation parameters, and it is required that the neutrino energy is reconstructed with very high precision. In this work, we investigate the effects of the resonance (RES) interaction process using two models for carbon target for ${\nu }_{\mu }\to {\nu }_{\mu }$ disappearance channel of the NO$\nu$A experiment, on neutrino-nucleus scattering cross-section, events, and neutrino oscillation parameter sensitivity. We also incorporate the realistic detector specifications of NO$\nu$A. To quantify the systematic uncertainties due to RES interactions, we compare the cross-sections, events, and sensitivity analysis for two models of RES processes—Rein–Sehgal (RS) and Berger–Sehgal (BS), and comment on which model produces more precision. We observe that RES processes contribute significantly, and should be included carefully in models while extracting neutrino oscillation parameters.