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<jats:title>Abstract</jats:title> <jats:p>We study light rays in the static and spherically symmetric gravitational field of the null aether theory (NAT). To this end, we employ the Gauss-Bonnet theorem to compute the deflection angle formed by a NAT black hole in the weak limit approximation. Using the optical metrics of the NAT black hole, we first obtain the Gaussian curvature and then calculate the leading terms of the deflection angle. Our calculations indicate how gravitational lensing is affected by the NAT field. We also illustrate that the bending of light stems from global and topological effects.</jats:p>

<jats:title>Abstract</jats:title> <jats:p>We investigated the tendency in the variations of CFT<jats:sub>2</jats:sub> when a rotating AdS<jats:sub>3</jats:sub> black hole changes because of the fluxes transferred by the scattering of a massive scalar field according to the anti-de Sitter (AdS)/conformal field theory (CFT) correspondence. The conserved quantities of the black hole are definitely constrained by the extremal condition. Moreover, the laws of thermodynamics provide a direction for the changes in the conserved quantities. Therefore, the black hole cannot be extremal under the scattering; this is naturally preferred. According to the relationship between the rotating AdS<jats:sub>3</jats:sub> black hole and dual CFT<jats:sub>2</jats:sub>, we find that such changes in the black hole constrain the<jats:bold />variations in the eigenstates of dual CFT<jats:sub>2</jats:sub>. Furthermore, the tendency in the variations is closely related to the laws of thermodynamics. </jats:p>

<jats:title>Abstract</jats:title> <jats:p>We revisit the hyperon weak radiative decays in the framework of the non-relativistic constituent quark model. This study confirms the nonlocal feature of the hyperon weak radiative transition operators, which are dominated by the pole terms, and an overall self-consistent description of the available experimental data for the Cabibbo-favored hyperon weak radiative decays is presented. It provides a natural mechanism for evading the Hara theorem, where sizeable parity-violating contributions can come from the intermediate orbital excitations. Cancellations between pole terms also explain the significant <jats:italic>SU</jats:italic>(3) flavor symmetry breaking manifested by the experimental data. We also discuss several interesting selection rules arising from either the electromagnetic or the weak interaction vertices. These features suggest nontrivial relations among various hyperon decays. </jats:p>

<jats:title>Abstract</jats:title> <jats:p>We consider a class of models with extra complex scalars that are charged under both the Standard Model and a hidden strongly coupled <jats:inline-formula> <jats:tex-math><?CDATA $SU(N)_H$?></jats:tex-math> <jats:inline-graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="cpc_45_1_013102_M1.jpg" xlink:type="simple" /> </jats:inline-formula> gauge sector and discuss the scenarios in which the new scalars are identified as the messenger fields that mediate the spontaneously broken supersymmetries from the hidden sector to the visible sector. The new scalars are embedded into 5-plets and 10-plets of an <jats:inline-formula> <jats:tex-math><?CDATA $SU(5)_V$?></jats:tex-math> <jats:inline-graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="cpc_45_1_013102_M2.jpg" xlink:type="simple" /> </jats:inline-formula> gauge group that potentially unifies the Standard Model gauge groups. The Higgs bosons remain as elementary particles. In the supersymmetrized version of this class of models, vector-like fermions whose left-handed components are superpartners of the new scalars are introduced. Owing to the hidden strong force, the new low-energy scalars hadronize before decaying and thus evade the common direct searches of the supersymmetric squarks. This can be seen as a gauge mediation scenario with the scalar messenger fields forming low-energy bound states. We also discuss the possibility that in the tower of bound states formed under hidden strong dynamics (of at least the TeV scale), there exist a dark matter candidate and the collider signatures (e.g. diphoton, diboson, or dijet) of models that may show up in the near future. </jats:p>

<jats:title>Abstract</jats:title> <jats:p>The minimal <jats:inline-formula> <jats:tex-math><?CDATA ${U}(1)_{\rm{{B-L}}}$?></jats:tex-math> <jats:inline-graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="cpc_45_1_013103_M3.jpg" xlink:type="simple" /> </jats:inline-formula> extension of the Standard Model (B-L-SM) offers an explanation for neutrino mass generation via a seesaw mechanism; it also offers two new physics states, namely an extra Higgs boson and a new <jats:inline-formula> <jats:tex-math><?CDATA $ Z' $?></jats:tex-math> <jats:inline-graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="cpc_45_1_013103_M4.jpg" xlink:type="simple" /> </jats:inline-formula> gauge boson. The emergence of a second Higgs particle as well as a new <jats:inline-formula> <jats:tex-math><?CDATA $ Z^\prime $?></jats:tex-math> <jats:inline-graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="cpc_45_1_013103_M5.jpg" xlink:type="simple" /> </jats:inline-formula> gauge boson, both linked to the breaking of a local <jats:inline-formula> <jats:tex-math><?CDATA ${U}(1)_{\rm{{B-L}}}$?></jats:tex-math> <jats:inline-graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="cpc_45_1_013103_M6.jpg" xlink:type="simple" /> </jats:inline-formula> symmetry, makes the B-L-SM rather constrained by direct searches in Large Hadron Collider (LHC) experiments. We investigate the phenomenological status of the B-L-SM by confronting the new physics predictions with the LHC and electroweak precision data. Taking into account the current bounds from direct LHC searches, we demonstrate that the prediction for the muon <jats:inline-formula> <jats:tex-math><?CDATA $ \left(g-2\right)_\mu $?></jats:tex-math> <jats:inline-graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="cpc_45_1_013103_M7.jpg" xlink:type="simple" /> </jats:inline-formula> anomaly in the B-L-SM yields at most a contribution of approximately <jats:inline-formula> <jats:tex-math><?CDATA $ 8.9 \times 10^{-12} $?></jats:tex-math> <jats:inline-graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="cpc_45_1_013103_M8.jpg" xlink:type="simple" /> </jats:inline-formula> , which represents a tension of <jats:inline-formula> <jats:tex-math><?CDATA $ 3.28 $?></jats:tex-math> <jats:inline-graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="cpc_45_1_013103_M9.jpg" xlink:type="simple" /> </jats:inline-formula> standard deviations, with the current <jats:inline-formula> <jats:tex-math><?CDATA $ 1\sigma $?></jats:tex-math> <jats:inline-graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="cpc_45_1_013103_M10.jpg" xlink:type="simple" /> </jats:inline-formula> uncertainty, by means of a <jats:inline-formula> <jats:tex-math><?CDATA $ Z^\prime $?></jats:tex-math> <jats:inline-graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="cpc_45_1_013103_M11.jpg" xlink:type="simple" /> </jats:inline-formula> boson if its mass is in the range of <jats:inline-formula> <jats:tex-math><?CDATA $ 6.3 $?></jats:tex-math> <jats:inline-graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="cpc_45_1_013103_M12.jpg" xlink:type="simple" /> </jats:inline-formula> to <jats:inline-formula> <jats:tex-math><?CDATA $ 6.5\; {\rm{TeV}} $?></jats:tex-math> <jats:inline-graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="cpc_45_1_013103_M13.jpg" xlink:type="simple" /> </jats:inline-formula>, within the reach of future LHC runs. This means that the B-L-SM, with heavy yet allowed <jats:inline-formula> <jats:tex-math><?CDATA $ Z^\prime $?></jats:tex-math> <jats:inline-graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="cpc_45_1_013103_M14.jpg" xlink:type="simple" /> </jats:inline-formula> boson mass range, in practice, does not resolve the tension between the observed anomaly in the muon <jats:inline-formula> <jats:tex-math><?CDATA $ \left(g-2\right)_\mu $?></jats:tex-math> <jats:inline-graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="cpc_45_1_013103_M15.jpg" xlink:type="simple" /> </jats:inline-formula> and the theoretical prediction in the Standard Model. Such a heavy <jats:inline-formula> <jats:tex-math><?CDATA $ Z^\prime $?></jats:tex-math> <jats:inline-graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="cpc_45_1_013103_M16.jpg" xlink:type="simple" /> </jats:inline-formula> boson also implies that the minimal value for the new Higgs mass is of the order of 400 GeV. </jats:p>

<jats:title>Abstract</jats:title> <jats:p>The heavy quark effective theory vastly reduces the weak-decay form factors of hadrons containing one heavy quark. Many works attempt to directly apply this theory to hadrons with multiple heavy quarks. In this paper, we examine this confusing application by the instantaneous Bethe-Salpeter method from a phenomenological perspective, and give the numerical results for <jats:inline-formula> <jats:tex-math><?CDATA $B_c$?></jats:tex-math> <jats:inline-graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="cpc_45_1_013104_M2.jpg" xlink:type="simple" /> </jats:inline-formula> decays to charmonium where the final states include <jats:inline-formula> <jats:tex-math><?CDATA $1S$?></jats:tex-math> <jats:inline-graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="cpc_45_1_013104_M3.jpg" xlink:type="simple" /> </jats:inline-formula>, <jats:inline-formula> <jats:tex-math><?CDATA $1P$?></jats:tex-math> <jats:inline-graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="cpc_45_1_013104_M4.jpg" xlink:type="simple" /> </jats:inline-formula>, <jats:inline-formula> <jats:tex-math><?CDATA $2S$?></jats:tex-math> <jats:inline-graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="cpc_45_1_013104_M5.jpg" xlink:type="simple" /> </jats:inline-formula>, and <jats:inline-formula> <jats:tex-math><?CDATA $2P$?></jats:tex-math> <jats:inline-graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="cpc_45_1_013104_M6.jpg" xlink:type="simple" /> </jats:inline-formula>. Our results indicate that the form factors parameterized by a single Isgur-Wise function deviate substantially from the full ones, especially when excited states are involved. The relativistic corrections ( <jats:inline-formula> <jats:tex-math><?CDATA $1/m_Q$?></jats:tex-math> <jats:inline-graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="cpc_45_1_013104_M7.jpg" xlink:type="simple" /> </jats:inline-formula> corrections) require the introduction of more non-perturbative universal functions, similar to the Isgur-Wise function, which are the overlapping integrals of the wave functions with the relative momentum between the quark and antiquark. </jats:p>

<jats:title>Abstract</jats:title> <jats:p>The spectroscopic parameters and decay channels of the axial-vector tetraquark <jats:inline-formula> <jats:tex-math><?CDATA $ T_{bb;\overline{u}\overline{s}}^{-} $?></jats:tex-math> <jats:inline-graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="cpc_45_1_013105_M2.jpg" xlink:type="simple" /> </jats:inline-formula> (in what follows, <jats:inline-formula> <jats:tex-math><?CDATA $ T_{b:\overline{s}}^{\mathrm{AV}} $?></jats:tex-math> <jats:inline-graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="cpc_45_1_013105_M3.jpg" xlink:type="simple" /> </jats:inline-formula>) are explored using the quantum chromodynamics (QCD) sum rule method. The mass and coupling of this state are calculated using two-point sum rules by taking into account various vacuum condensates, up to 10 dimensions. Our prediction for the mass of this state <jats:inline-formula> <jats:tex-math><?CDATA $ m = (10215\pm 250)\; \mathrm{MeV} $?></jats:tex-math> <jats:inline-graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="cpc_45_1_013105_M4.jpg" xlink:type="simple" /> </jats:inline-formula> confirms that it is stable with respect to strong and electromagnetic decays and can dissociate to conventional mesons only via weak transformations. We investigate the dominant semileptonic <jats:inline-formula> <jats:tex-math><?CDATA $ T_{b:\overline{s}}^{\mathrm{AV}} \to {\cal{Z}}_{b:\overline{s}}^{0}l\overline{\nu}_l $?></jats:tex-math> <jats:inline-graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="cpc_45_1_013105_M5.jpg" xlink:type="simple" /> </jats:inline-formula> and nonleptonic <jats:inline-formula> <jats:tex-math><?CDATA $ T_{b:\overline{s}}^{\mathrm{AV}} \to {\cal{Z}}_{b:\overline{s}}^{0}M $?></jats:tex-math> <jats:inline-graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="cpc_45_1_013105_M6.jpg" xlink:type="simple" /> </jats:inline-formula> decays of <jats:inline-formula> <jats:tex-math><?CDATA $ T_{b:\overline{s}}^{\mathrm{AV}} $?></jats:tex-math> <jats:inline-graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="cpc_45_1_013105_M7.jpg" xlink:type="simple" /> </jats:inline-formula>. In these processes, <jats:inline-formula> <jats:tex-math><?CDATA $ {\cal{Z}}_{b:\overline{s}}^{0} $?></jats:tex-math> <jats:inline-graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="cpc_45_1_013105_M8.jpg" xlink:type="simple" /> </jats:inline-formula> is a scalar tetraquark <jats:inline-formula> <jats:tex-math><?CDATA $ [bc][\overline{u}\overline{s}] $?></jats:tex-math> <jats:inline-graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="cpc_45_1_013105_M9.jpg" xlink:type="simple" /> </jats:inline-formula> built of a color-triplet diquark and an antidiquark, whereas <jats:italic>M</jats:italic> is one of the vector mesons <jats:inline-formula> <jats:tex-math><?CDATA $ \rho ^{-} $?></jats:tex-math> <jats:inline-graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="cpc_45_1_013105_M11.jpg" xlink:type="simple" /> </jats:inline-formula>, <jats:inline-formula> <jats:tex-math><?CDATA $ K^{\ast}(892) $?></jats:tex-math> <jats:inline-graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="cpc_45_1_013105_M12.jpg" xlink:type="simple" /> </jats:inline-formula>, <jats:inline-formula> <jats:tex-math><?CDATA $ D^{\ast }(2010)^{-} $?></jats:tex-math> <jats:inline-graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="cpc_45_1_013105_M13.jpg" xlink:type="simple" /> </jats:inline-formula>, and <jats:inline-formula> <jats:tex-math><?CDATA $ D_{s}^{\ast -} $?></jats:tex-math> <jats:inline-graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="cpc_45_1_013105_M14.jpg" xlink:type="simple" /> </jats:inline-formula>. To calculate the partial widths of these decays, we use the QCD three-point sum rule approach and evaluate the weak transition form factors <jats:inline-formula> <jats:tex-math><?CDATA $ G_{i} $?></jats:tex-math> <jats:inline-graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="cpc_45_1_013105_M15.jpg" xlink:type="simple" /> </jats:inline-formula>( <jats:inline-formula> <jats:tex-math><?CDATA $ i = 0,1,2,3 $?></jats:tex-math> <jats:inline-graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="cpc_45_1_013105_M16.jpg" xlink:type="simple" /> </jats:inline-formula>), which govern these processes. The full width <jats:inline-formula> <jats:tex-math><?CDATA $ \Gamma _{\mathrm{full}} = (12.9\pm 2.1)\times 10^{-8}\; \mathrm{MeV} $?></jats:tex-math> <jats:inline-graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="cpc_45_1_013105_M17.jpg" xlink:type="simple" /> </jats:inline-formula> and the mean lifetime <jats:inline-formula> <jats:tex-math><?CDATA $ \tau = 5.1_{-0.71}^{+0.99}\; \mathrm{fs} $?></jats:tex-math> <jats:inline-graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="cpc_45_1_013105_M18.jpg" xlink:type="simple" /> </jats:inline-formula> of the tetraquark <jats:inline-formula> <jats:tex-math><?CDATA $ T_{b:\overline{s}}^{\mathrm{AV}} $?></jats:tex-math> <jats:inline-graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="cpc_45_1_013105_M19.jpg" xlink:type="simple" /> </jats:inline-formula> are computed using the aforementioned weak decays. The obtained information about the parameters of <jats:inline-formula> <jats:tex-math><?CDATA $ T_{b:\overline{s}}^{\mathrm{AV}} $?></jats:tex-math> <jats:inline-graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="cpc_45_1_013105_M20.jpg" xlink:type="simple" /> </jats:inline-formula> and <jats:inline-formula> <jats:tex-math><?CDATA $ {\cal{Z}}_{b:\overline{s}}^{0} $?></jats:tex-math> <jats:inline-graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="cpc_45_1_013105_M21.jpg" xlink:type="simple" /> </jats:inline-formula> is useful for experimental investigations of these double-heavy exotic mesons. </jats:p>

<jats:title>Abstract</jats:title> <jats:p>The decay <jats:inline-formula> <jats:tex-math><?CDATA $t \to c V $?></jats:tex-math> <jats:inline-graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="cpc_45_1_013106_M2.jpg" xlink:type="simple" /> </jats:inline-formula> ( <jats:inline-formula> <jats:tex-math><?CDATA $V=\gamma,~Z,~g$?></jats:tex-math> <jats:inline-graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="cpc_45_1_013106_M3.jpg" xlink:type="simple" /> </jats:inline-formula>) processes in mirror twin Higgs models with colorless top partners are studied in this paper. We report that the branching ratios of these decays can strongly affect the standard model expectations in some parameter spaces and may be detectable according to the current precision electroweak measurements. Thus, constraints on the model parameters may be obtained from the branching fraction of the decay processes, which may serve as a robust detection tool for this new physics model. </jats:p>

<jats:title>Abstract</jats:title> <jats:p>We attempt to clarify several aspects concerning the recently presented four-dimensional Einstein-Gauss-Bonnet gravity. We argue that the limiting procedure outlined in [Phys. Rev. Lett. 124, 081301 (2020)] generally involves ill-defined terms in the four dimensional field equations. Potential ways to circumvent this issue are discussed, alongside remarks regarding specific solutions of the theory. We prove that, although linear perturbations are well behaved around maximally symmetric backgrounds, the equations for second-order perturbations are ill-defined even around a Minkowskian background. Additionally, we perform a detailed analysis of the spherically symmetric solutions and find that the central curvature singularity can be reached within a finite proper time.</jats:p>

<jats:title>Abstract</jats:title> <jats:p>The problem of the flat limits of the scalar and spinor fields on the de Sitter expanding universe is considered in the traditional adiabatic vacuum and in the new rest frame vacuum we proposed recently, in which the frequencies are separated in the rest frames as in special relativity. It is shown that only in the rest frame vacuum can the Minkowskian flat limit be reached naturally for any momentum, whereas in the adiabatic vacuum, this limit remains undefined in rest frames in which the momentum vanishes. An important role is played by the phases of the fundamental solutions in the rest frame vacuum, which must be regularized to obtain the desired Minkowskian flat limits. This procedure fixes the phases of the scalar mode functions and Dirac spinors, resulting in their definitive expressions derived here. The physical consequence is that, in the rest frame vacuum, the flat limits of the one-particle operators are simply the corresponding operators of special relativity.</jats:p>