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<jats:title>Abstract</jats:title> <jats:p>We investigate current-current correlation functions, or the so-called response functions of a two-flavor Nambu-Jona-Lasino model at finite temperature and density. The linear response is investigated introducing the conjugated gauge fields as external sources within the functional path integral approach. The response functions can be obtained by expanding the generational functional in powers of the external sources. We derive the response functions parallel to two well-established approximations for equilibrium thermodynamics, namely mean-field theory and a beyond-mean-field theory, taking into account mesonic contributions. Response functions based on the mean-field theory recover the so-called quasiparticle random phase approximation. We calculate the dynamical structure factors for the density responses in various channels within the random phase approximation, showing that the dynamical structure factors in the baryon axial vector and isospin axial vector channels can be used to reveal the quark mass gap and the Mott dissociation of mesons, respectively. Noting that the mesonic contributions are not taken into account in the random phase approximation, we also derive the response functions parallel to the beyond-mean-field theory. We show that the mesonic fluctuations naturally give rise to three kinds of famous diagrammatic contributions: the Aslamazov-Lakin contribution, the self-energy or density-of-state contribution, and the Maki-Thompson contribution. Unlike the equilibrium case, in evaluating the fluctuation contributions, we need to carefully treat the linear terms in external sources and the induced perturbations. In the chiral symmetry breaking phase, we find an additional chiral order parameter induced contribution, which ensures that the temporal component of the response functions in the static and long-wavelength limit recovers the correct charge susceptibility defined using the equilibrium thermodynamic quantities. These contributions from mesonic fluctuations are expected to have significant effects on the transport properties of hot and dense matter around the chiral phase transition or crossover, where the mesonic degrees of freedom are still important.</jats:p>

<jats:title>Abstract</jats:title> <jats:p>This study presents the systematics of energy staggering for magnetic rotational bands with <jats:inline-formula> <jats:tex-math><?CDATA $ M1 $?></jats:tex-math> <jats:inline-graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="cpc_43_9_094104_M1.jpg" xlink:type="simple" /> </jats:inline-formula> and <jats:inline-formula> <jats:tex-math><?CDATA $ E2 $?></jats:tex-math> <jats:inline-graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="cpc_43_9_094104_M2.jpg" xlink:type="simple" /> </jats:inline-formula> transition properties, which are strictly consistent with the features of good candidates of magnetic rotational bands in the <jats:inline-formula> <jats:tex-math><?CDATA $ A\sim80 $?></jats:tex-math> <jats:inline-graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="cpc_43_9_094104_M3.jpg" xlink:type="simple" /> </jats:inline-formula>, 110, 130, and 190 mass regions. The regularities exhibited by these bands with respect to the staggering parameter, which increases with increasing spin, are in agreement with the semiclassical description of shears mechanism. Moreover, the abnormal behaviour in the backbend regions or close to band termination has also been discussed. Taking the magnetic dipole bands with same configuration in three <jats:inline-formula> <jats:tex-math><?CDATA $ N = 58 $?></jats:tex-math> <jats:inline-graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="cpc_43_9_094104_M4.jpg" xlink:type="simple" /> </jats:inline-formula> isotones, i.e., <jats:inline-formula> <jats:tex-math><?CDATA $ ^{103} {\rm Rh}$?></jats:tex-math> <jats:inline-graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="cpc_43_9_094104_M5.jpg" xlink:type="simple" /> </jats:inline-formula>, <jats:inline-formula> <jats:tex-math><?CDATA $ ^{105} {\rm Ag}$?></jats:tex-math> <jats:inline-graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="cpc_43_9_094104_M6.jpg" xlink:type="simple" /> </jats:inline-formula>, and <jats:inline-formula> <jats:tex-math><?CDATA $ ^{107} {\rm In}$?></jats:tex-math> <jats:inline-graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="cpc_43_9_094104_M7.jpg" xlink:type="simple" /> </jats:inline-formula>, as examples, the transition from chiral to magnetic rotation with the proton number approaching <jats:inline-formula> <jats:tex-math><?CDATA $ Z = 50 $?></jats:tex-math> <jats:inline-graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="cpc_43_9_094104_M8.jpg" xlink:type="simple" /> </jats:inline-formula> is presented. Moreover, the self-consistent tilted axis and principle axis cranking relativistic mean-field theories are applied to investigate the rotational mechanism in the dipole band of <jats:inline-formula> <jats:tex-math><?CDATA $ ^{105} {\rm Ag}$?></jats:tex-math> <jats:inline-graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="cpc_43_9_094104_M9.jpg" xlink:type="simple" /> </jats:inline-formula>. </jats:p>

<jats:title>Abstract</jats:title> <jats:p>We consider a simple model for the diffusion of heavy quarks in a hot bath, modeling the latter by an ensemble of oscillators distributed according to either a thermal distribution or to an out-of-equilibrium distribution with a saturation scale. In this model it is easy to introduce memory effects by changing the distribution of oscillators: we model them by introducing a Gaussian distribution, <jats:inline-formula> <jats:tex-math><?CDATA $ {\rm d}N/{\rm d}\omega $?></jats:tex-math> <jats:inline-graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="cpc_43_9_094105_M1.jpg" xlink:type="simple" /> </jats:inline-formula>, which can be deformed continuously from a <jats:inline-formula> <jats:tex-math><?CDATA $ \delta- $?></jats:tex-math> <jats:inline-graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="cpc_43_9_094105_M2.jpg" xlink:type="simple" /> </jats:inline-formula>function, giving a Markov dissipation, to a broad kernel with memory. Deriving the equation of motion of the heavy quark in the bath, we remark how dissipation comes out naturally as an effect of the back-reaction of the oscillators on the bath. Moreover, the exact solution of this equation allows to define the thermalization time as the time necessary to remove any memory of the initial conditions. We find that the broadening of the dissipative kernel, while keeping the coupling fixed, lowers the thermalization time. We also derive the fluctuation-dissipation theorem for the bath, and use it to estimate the kinematic regime in which momentum diffusion of the heavy quark dominates over drift. We find that diffusion is more important as long as <jats:inline-formula> <jats:tex-math><?CDATA $ K_0/{\cal E} $?></jats:tex-math> <jats:inline-graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="cpc_43_9_094105_M3.jpg" xlink:type="simple" /> </jats:inline-formula> is small, where <jats:inline-formula> <jats:tex-math><?CDATA $ K_0 $?></jats:tex-math> <jats:inline-graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="cpc_43_9_094105_M4.jpg" xlink:type="simple" /> </jats:inline-formula> and <jats:inline-formula> <jats:tex-math><?CDATA $ {\cal E} $?></jats:tex-math> <jats:inline-graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="cpc_43_9_094105_M5.jpg" xlink:type="simple" /> </jats:inline-formula> denote the initial energy of the heavy quark and the average energy of the bath, respectively. </jats:p>

<jats:title>Abstract</jats:title> <jats:p>We investigate a 6D generalized Randall-Sundrum brane world scenario with a bulk cosmological constant. Each stress-energy tensor <jats:inline-formula> <jats:tex-math><?CDATA $ T_{ab}^{i} $?></jats:tex-math> <jats:inline-graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="cpc_43_9_095101_M1.jpg" xlink:type="simple" /> </jats:inline-formula> on the brane is shown to be similar to a constant vacuum energy. This is consistent with the Randall-Sundrum model, in which each 3-brane Lagrangian yielded a constant vacuum energy. By adopting an anisotropic metric ansatz, we obtain the 5D Friedmann-Robertson-Walker field equations. In a slightly later period, the expansion of the universe is proportional to the square root of time, <jats:inline-formula> <jats:tex-math><?CDATA $ t^{\frac{1}{2}} $?></jats:tex-math> <jats:inline-graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="cpc_43_9_095101_M2.jpg" xlink:type="simple" /> </jats:inline-formula>, which is similar to the period of the radiation-dominated regime. Moreover, we investigate the case with two <jats:inline-formula> <jats:tex-math><?CDATA $ a(t) $?></jats:tex-math> <jats:inline-graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="cpc_43_9_095101_M3.jpg" xlink:type="simple" /> </jats:inline-formula> and two <jats:inline-formula> <jats:tex-math><?CDATA $ b(t) $?></jats:tex-math> <jats:inline-graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="cpc_43_9_095101_M4.jpg" xlink:type="simple" /> </jats:inline-formula>. In a large range of <jats:inline-formula> <jats:tex-math><?CDATA $ t $?></jats:tex-math> <jats:inline-graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="cpc_43_9_095101_M5.jpg" xlink:type="simple" /> </jats:inline-formula>, we obtain the 3D effective cosmological constant <jats:inline-formula> <jats:tex-math><?CDATA $ \Lambda_{\rm eff} = -2\Omega/3 \gt 0 $?></jats:tex-math> <jats:inline-graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="cpc_43_9_095101_M6.jpg" xlink:type="simple" /> </jats:inline-formula>, which is independent of the integral constant. Here, the scale factor is an exponential expansion, which is consistent with our present observation of the universe. Our results demonstrate that it is possible to construct a model that solves the dark energy problem, while guaranteeing a positive brane tension. </jats:p>

<jats:title>Abstract</jats:title> <jats:p>In this paper, we investigate whether it is possible to determine the neutrino mass hierarchy via a high-statistics and real-time observation of supernova neutrinos with short-time characteristics. The essential idea is to utilize distinct times-of-flight for different neutrino mass eigenstates from a core-collapse supernova to the Earth, which may significantly change the time distribution of neutrino events in the future huge water-Cherenkov and liquid-scintillator detectors. For illustration, we consider two different scenarios. The first case is the neutronization burst of <jats:inline-formula> <jats:tex-math><?CDATA $ \nu^{}_e$?></jats:tex-math> <jats:inline-graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="cpc_43_9_095102_M1.jpg" xlink:type="simple" /> </jats:inline-formula> emitted in the first tens of milliseconds of a core-collapse supernova, while the second case is the black hole formation during the accretion phase for which neutrino signals are expected to be abruptly terminated. In the latter scenario, it turns out only when the supernova is at a distance of a few Mpc and the fiducial mass of the detector is at the level of gigaton, might we be able to discriminate between normal and inverted neutrino mass hierarchies. In the former scenario, the probability for such a discrimination is even less due to a poor statistics. </jats:p>

<jats:title>Abstract</jats:title> <jats:p> <jats:italic>f</jats:italic> (Ricci) gravity is a special kind of higher curvature gravity whose bulk Lagrangian density is the trace of a matrix-valued function of the Ricci tensor. It is shown that under some mild constraints, <jats:italic>f</jats:italic> (Ricci) gravity admits Einstein manifolds as exact vacuum solutions, and can be ghost-free and tachyon-free around maximally symmetric Einstein vacua. It is also shown that the entropy for spherically symmetric black holes in <jats:italic>f</jats:italic> (Ricci) gravity calculated via the Wald method and the boundary Noether charge approach are in good agreement. </jats:p>

<jats:title>Abstract</jats:title> <jats:p>In a previous publication, we claimed that a black hole can be considered as a topological insulator. A direct consequence of this claim is that their symmetries should be related. In this paper, we give a representation of the near-horizon symmetry algebra of the BTZ black hole using the <jats:italic>W</jats:italic> <jats:sub>1+∞</jats:sub> symmetry algebra of the topological insulator in three-dimensional spacetime. Based on the <jats:italic>W</jats:italic> <jats:sub>1+∞</jats:sub> algebra, we count the number of the microstates of the BTZ black holes and obtain the Bekenstein-Hawking entropy. </jats:p>

<jats:title>Abstract</jats:title> <jats:p>We study the sensitivity of constraining the model independent <jats:italic>H</jats:italic> <jats:italic>ZZ</jats:italic> coupling based on the effective theory up to dimension-6 operators at a future Higgs factory. Using the current conceptual design parameters of the Circular Electron Positron Collider, we give the experimental limits for the model independent operators given by the total Higgsstrahlung cross-section and the angular distribution of <jats:italic>Z</jats:italic> boson decays. In particular, we give the very small sensitivity limit for the CP violation parameter <jats:inline-formula> <jats:tex-math><?CDATA $ \tilde g$?></jats:tex-math> <jats:inline-graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="cpc_43_10_103001_M1.jpg" xlink:type="simple" /> </jats:inline-formula>, which will be a clear window to test the Standard Model and look for new physics signals. </jats:p>

<jats:title>Abstract</jats:title> <jats:p>Using symmetry properties, we determine the mixing pattern of a class of nonlocal quark bilinear operators containing a straight Wilson line along a spatial direction. We confirm the previous study that mixing among the lowest dimensional operators, which have a mass dimension equal to three, can occur if chiral symmetry is broken in the lattice action. For higher dimensional operators, we find that the dimension-three operators will always mix with dimension-four operators, even if chiral symmetry is preserved. Also, the number of dimension-four operators involved in the mixing is large, and hence it is impractical to remove the mixing by the improvement procedure. Our result is important for determining the Bjorken-<jats:italic>x</jats:italic> dependence of the parton distribution functions using the quasi-distribution method on a Euclidean lattice. The requirement of using large hadron momentum in this approach makes the control of errors from dimension-four operators even more important. </jats:p>

<jats:title>Abstract</jats:title> <jats:p>We study the phenomenology of a model that addresses the neutrino mass, dark matter, and generation of the electroweak scale in a single framework. Electroweak symmetry breaking is realized via the Coleman-Weinberg mechanism in a classically scale invariant theory, while the neutrino mass is generated radiatively through interactions with dark matter in a typically scotogenic manner. The model introduces a scalar triplet and singlet and a vector-like fermion doublet that carry an odd parity of <jats:inline-formula> <jats:tex-math><?CDATA $ Z_2 $?></jats:tex-math> <jats:inline-graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="cpc_43_10_103102_JY01.jpg" xlink:type="simple" /> </jats:inline-formula>, and an even parity scalar singlet that helps preserve classical scale invariance. We sample over the parameter space by taking into account various experimental constraints from the dark matter relic density and direct detection, direct scalar searches, neutrino mass, and charged lepton flavor violating decays. We then examine by detailed simulations possible signatures at the LHC to find some benchmark points of the free parameters. We find that the future high-luminosity LHC will have a significant potential in detecting new physics signals in the dilepton channel. </jats:p>