We explore the origin and Yukawa interactions of the scalars with peculiar $CP$ properties which were recently found in a multi-Higgs model based on an order-4 $CP$ symmetry. We relate the existence of such scalars to the enhanced freedom of defining $CP$, even beyond the well-known generalized $CP$ symmetries, which arises in models with several zero-charge scalar fields. We also show that despite possessing exotic $CP$ quantum numbers, these scalars do not have to be inert: they can have $CP$-conserving Yukawa interactions provided the $CP$ acts on fermions by also mixing generations. This paper focuses on formal aspects—exposed in a pedagogical manner—and includes a brief discussion of possible phenomenological consequences.

We present the derivation of second-order relativistic viscous hydrodynamics from an effective Boltzmann equation for a system consisting of quasiparticles of a single species. We consider temperature-dependent masses of the quasiparticles and devise a thermodynamically consistent framework to formulate second-order evolution equations for shear and bulk viscous pressure corrections. The main advantage of this formulation is that one can consistently implement a realistic equation of state of the medium within the framework of kinetic theory. Specializing to the case of a one-dimensional purely longitudinal boost-invariant expansion, we study the effect of this new formulation on the viscous hydrodynamic evolution of strongly interacting matter formed in relativistic heavy-ion collisions.

We demonstrate that four top-quark production is a powerful tool to constrain the top Yukawa coupling. The constraint is robust in the sense that it does not rely on the Higgs boson decay. Taking into account the projection of the $t\overline{t}H$ production by the ATLAS Collaboration, we obtained a bound on the Higgs boson width, ${\mathrm{\Gamma }}_H\le 2.57{\mathrm{\Gamma }}_H^{\mathrm{SM}}$, at the 14 TeV Large Hadron Collider with an integrated luminosity of $300{\mathrm{fb}}^{-1}$.

We study the universal contributions to the entanglement entropy (EE) of $2+1$-dimensional and $3+1$-dimensional holographic conformal field theories (CFTs) on topologically nontrivial manifolds, focusing on tori. The holographic bulk corresponds to anti–de Sitter-soliton geometries. We characterize the properties of these regulator-independent EE terms as a function of both the size of the cylindrical entangling region, and the shape of the torus. In $2+1$ dimensions, in the simple limit where the torus becomes a thin one-dimensional ring, the EE reduces to a shape-independent constant $2\gamma$. This is twice the EE obtained by bipartitioning an infinite cylinder into equal halves. We study the renormalization group flow of $\gamma$ by defining a renormalized EE that (1) is applicable to general QFTs, (2) resolves the failure of the area law subtraction, and (3) is inspired by the F-theorem. We find that the renormalized $\gamma$ decreases monotonically at small coupling when the holographic CFT is deformed by a relevant operator for all allowed scaling dimensions. We also discuss the question of nonuniqueness of such renormalized EEs both in $2+1$ dimensions and $3+1$ dimensions.

In this paper we examine gauge coupling unification of the non-SUSY SO(10) grand unified theory proposed by Babu and Mohapatra [Phys. Lett. B 715, 328 (2012)] at the two loop level. This theory breaks down to the standard model in a single step and has the distinguishing feature of TeV nonstandard model scalars. This leads to a plethora of interesting new physics at the TeV scale and the discovery of new particles at the LHC. This model gives rise to testable proton decay, neutron-antineutron oscillations, provides a mechanism for baryogenesis, and contains potential dark matter candidates. In this paper, we compute the two loop beta function and show that this model unifies to two loop order around $10^{15}\mathrm{GeV}$. We then compute the proton lifetime, taking into account threshold effects and show that these effects place it above the Super-Kamiokande limit [K. Abe et al. (Super-Kamiokande Collaboration), Phys. Rev. D 95, 012004 (2017).].

Quintessential dark energy with pressure $p$ and density $\rho$ is related by equation of state $p=\omega \rho$ with the state parameter $-1<\omega <-1/3$. The cosmological dark energy influence on black hole spacetime is interesting and important. In this paper, we study the Kerr-Newman-AdS solutions of the Einstein-Maxwell equation in quintessence field around a black hole by Newman-Janis algorithm and complex computations. From the horizon structure equation, we obtain the expression between quintessence parameter $\alpha$ and cosmological constant $\mathrm{\Lambda }$ if the black hole exists two cosmological horizon $r_q$ and $r_c$ when $\omega =-2/3$, the result is different from rotational black hole in quintessence matter situation. Through analysis we find that the black hole charge cannot change the value of $\alpha$. But the black hole spin and cosmological constant are opposite. The black hole spin and cosmological constant make the maximum value of $\alpha$ small. The existence of four horizon leads seven types of extremal black holes to constrain the parameter $\alpha$. With the state parameter $\omega$ ranging from $-1$ to $-1/3$, the maximum value of $\alpha$ changes from $\mathrm{\Lambda }$ to 1. When $\omega \to -1$, the quintessential dark energy likes cosmological constant. The singularity of the black holes is the same with that of Kerr black hole. We also discuss the rotation velocity of the black holes on the equatorial plane for $\omega =-2/3$, $-1/2$ and $-1/3$. For small value of $\alpha$, the rotation velocity on the equatorial plane is asymptotically flat and it can explain the rotation curves in spiral galaxies.

A supermassive black hole moving through a field of stars will gravitationally scatter the stars, inducing a backreaction force on the black hole known as dynamical friction. In Newtonian gravity, the axisymmetry of the system about the black hole’s velocity $\mathbf{v}$ implies that the dynamical friction must be antiparallel to $\mathbf{v}$. However, in general relativity the black hole’s spin $\mathbf{S}$ need not be parallel to $\mathbf{v}$, breaking the axisymmetry of the system and generating a new component of dynamical friction similar to the Lorentz force $\mathbf{F}=q\mathbf{v}\times \mathbf{B}$ experienced by a particle with charge $q$ moving in a magnetic field $\mathbf{B}$. We call this new force gravitomagnetic dynamical friction and calculate its magnitude for a spinning black hole moving through a field of stars with Maxwellian velocity dispersion $\sigma$, assuming that both $v$ and $\sigma$ are much less than the speed of light $c$. We use post-Newtonian equations of motion accurate to $\mathcal{O}(v^3/c^3)$ needed to capture the effect of spin-orbit coupling and also include direct stellar capture by the black hole’s event horizon. Gravitomagnetic dynamical friction will cause a black hole with uniform speed to spiral about the direction of its spin, similar to a charged particle spiraling about a magnetic field line, and will exert a torque on a supermassive black hole orbiting a galactic center, causing the angular momentum of this orbit to slowly precess about the black hole spin. As this effect is suppressed by a factor $(\sigma /c{)}^2$ in nonrelativistic systems, we expect it to be negligible in most astrophysical contexts but provide this calculation for its theoretical interest and potential application to relativistic systems.

Theories of gravity in the beyond Horndeski class encompass a wide range of scalar-tensor theories that will be tested on cosmological scales over the coming decade. In this work, we investigate the possibility of testing them in the strong field regime by looking at the properties of compact objects—neutron, hyperon, and quark stars—embedded in an asymptotically de Sitter space-time, for a specific subclass of theories. We extend previous works to include slow rotation and find a relation between the dimensionless moment of inertia ($\overline{I}=I{c}^2/G_{\mathrm{N}}{M}^3$) and the compactness $\mathcal{C}=G_{\mathrm{N}}M/R{c}^2$ (an $\overline{I}-\mathcal{C}$ relation), independent of the equation of state, that is reminiscent of but distinct from the general relativity prediction. Several of our equations of state contain hyperons and free quarks, allowing us to revisit the hyperon puzzle. We find that the maximum mass of hyperon stars can be larger than $2M_{\odot }$ for small values of the beyond Horndeski parameter, thus providing a resolution of the hyperon puzzle based on modified gravity. Moreover, stable quark stars exist when hyperonic stars are unstable, which means that the phase transition from hyperon to quark stars is predicted just as in general relativity (GR), albeit with larger quark star masses. Two important and potentially observable consequences of some of the theories we consider are the existence of neutron stars in a range of masses significantly higher than in GR and $\overline{I}-\mathcal{C}$ relations that differ from their GR counterparts. In the former case, we find objects that, if observed, could not be accounted for in GR because they violate the usual GR causality condition. We end by discussing several difficult technical issues that remain to be addressed in order to reach more realistic predictions that may be tested using gravitational wave searches or neutron star observations.

The evolution of inflationary fluctuations can be recast as an inverse scattering problem. In this context, we employ the Gel’fand-Levitan method from inverse-scattering theory to reconstruct the evolution of both the inflaton field freeze-out horizon and the Hubble parameter during inflation. We demonstrate this reconstruction procedure numerically for a scenario of slow-roll inflation, as well as for a scenario which temporarily departs from slow-roll. The field freeze-out horizon is reconstructed from the accessible primordial scalar power spectrum alone, while the reconstruction of the Hubble parameter requires additional information from the tensor power spectrum. We briefly discuss the application of this technique to more realistic cases incorporating estimates of the primordial power spectra over limited ranges of scales and with specified uncertainties.

We construct a piecewise model that gives a physical viable realization of finite-time future singularity for a spatially flat Friedmann-Robertson-Walker universe within the interacting dark matter–dark energy framework, with the latter in the form of a variable vacuum energy. The scale factor solutions provided by the model are accommodated in several branches defined in four regions delimited by the scale factor and the effective energy density. A branch starts from a big bang singularity and describes an expanding matter-dominated universe until the sudden future singularity occurs. Then, an expanding branch emerges from a past singularity, reaches a maximum, reverses its expansion, and possibly collapses into itself while another expanding branch emerges from the latter singularity and has a de Sitter phase which is intrinsically stable. We obtain a different piecewise scale factor which describes a contracting de Sitter universe in the distant past until the finite-time future singularity happens. It emerges and continues in a contracting phase, bounces at the minimum, reverses, and enters into a stable de Sitter phase without a dramatic final. Also, we explore the aforesaid cosmic scenarios by focusing on the leading contributions of some physical quantities near the sudden future singularity and applying the geometric Tipler and Królak criteria in order to inspect the behavior of timelike geodesic curves around such singularity.

We present a detailed discussion of the lepton flavor and number violating conversion of bound muons into positrons. This process is a viable alternative to neutrinoless double beta decay, and, given that experiments on ordinary ${\mu }^{-}–e^{-}$ conversion are expected to improve their sensitivities by several orders of magnitude in the coming years, we can also assume the limit on ${\mu }^{-}–e^{+}$ conversion to improve by roughly the same factor. We discuss how new physics at a high scale can lead to short-range contributions to this conversion process, and we present one explicit case in great detail (the single one for which the corresponding nuclear matrix element is presently known). The main goal of our discussion is to make the respective computation accessible to the particle physics community, so that promising models can be investigated while the nuclear physics community can simultaneously advance the computation of nuclear matrix elements. Given the progress to be expected on the experimental side, it may even be possible that lepton number violation in the $e\mu$-sector is discovered by ${\mu }^{-}–e^{+}$ conversion before neutrinoless double beta decay can show its existence in the $ee$-sector.

A new renormalization scheme is defined for fermion bilinears in QCD at nonvanishing quark masses. This new scheme, denoted RI/mSMOM, preserves the benefits of the nonexceptional momenta introduced in the RI/SMOM scheme and allows a definition of renormalized composite fields away from the chiral limit. Some properties of the scheme are investigated by performing explicit one-loop computation in dimensional regularization.

We study the $\eta$ and ${\eta }^{\prime }$ distribution amplitudes (DAs) in the context of a nonlocal ${\mathrm{SU}(3)}_L\otimes {\mathrm{SU}(3)}_R$ chiral quark model. The corresponding Lagrangian allows us to reproduce the phenomenological values of pseudoscalar meson masses and decay constants, as well as the momentum dependence of the quark propagator arising from lattice calculations. It is found that the obtained DAs have two symmetric maxima, which arise from new contributions generated by the nonlocal character of the interactions. These DAs are then applied to the calculation of the $\eta \text{−}\gamma$ and ${\eta }^{\prime }\text{−}\gamma$ transition form factors. Implications of our results regarding higher twist corrections and/or contributions to the transition form factors originated by gluon-gluon components in the $\eta$ and ${\eta }^{\prime }$ mesons are discussed.

We study the Higgs boson ($h$) decay to two light jets at the 14 TeV High-Luminosity-LHC (HL-LHC), where a light jet ($j$) represents any nonflavor-tagged jet from the observational point of view. The decay mode $h\to gg$ is chosen as the benchmark since it is the dominant channel in the Standard Model, but the bound obtained is also applicable to the light quarks ($j=u$, $d$, $s$). We estimate the achievable bounds on the decay branching fractions through the associated production $Vh(V=W^{\pm },Z)$. Events of the Higgs boson decaying into heavy (tagged) or light (untagged) jets are correlatively analyzed. We find that with $3000{\mathrm{fb}}^{-1}$ data at the HL-LHC, we should expect approximately $1\sigma$ statistical significance on the SM $Vh(gg)$ signal in this channel. This corresponds to a reachable upper bound $\mathrm{BR}(h\to jj)\le 4$ ${\mathrm{BR}}^{\mathrm{SM}}(h\to gg)$ at 95% confidence level. A consistency fit also leads to an upper bound $\mathrm{BR}(h\to cc)<15$ ${\mathrm{BR}}^{\mathrm{SM}}(h\to cc)$ at 95% confidence level. The estimated bound may be further strengthened by adopting multiple variable analyses or adding other production channels.

Motivated by potential applications to ultracold matter, we perform a theoretical study of Majorana fermions confined to a finite volume, whose boundary conditions are characterized by self-adjoint extension parameters. While the boundary conditions for Dirac fermions in ($1+1$)-d are characterized by a 1-parameter family, $\lambda =-{\lambda }^{*}$, of self-adjoint extensions, for Majorana fermions $\lambda$ is restricted to $\pm i$. Based on this result, we compute the frequency spectrum of Majorana fermions confined to a 1-d interval. The boundary conditions for Dirac fermions confined to a 3-d region of space are characterized by a 4-parameter family of self-adjoint extensions, which is reduced to two distinct 1-parameter families for Majorana fermions. We also consider the problems related to the quantum mechanical interpretation of the Majorana equation as a single-particle equation. Furthermore, the equation is related to a relativistic Schrödinger equation that does not suffer from these problems. Here we restrict ourselves to theoretical considerations without yet focusing on concrete cold matter applications.

In this paper, we present a detailed study of the problem of classical stability of U(1) gauged Q-balls. In particular, we show that the standard methods that are suitable for establishing the classical stability criterion for ordinary (nongauged) one-field and two-field Q-balls are not effective in the case of U(1) gauged Q-balls, although all the technical steps of calculations can be performed in the same way as those for ordinary Q-balls. We also present the results of numerical simulations in models with different scalar field potentials, explicitly demonstrating that, in general, the regions of stability of U(1) gauged Q-balls are not defined in the same way as in the case of ordinary Q-balls. Consequently, the classical stability criterion for ordinary Q-balls cannot be applied to U(1) gauged Q-balls in the general case.

Since its introduction in 1962, the Newman-Penrose formalism has been widely used in analytical and numerical studies of Einstein’s equations, like for example for the Teukolsky master equation, or as a powerful wave extraction tool in numerical relativity. Despite the many applications, Einstein’s equations in the Newman-Penrose formalism appear complicated and not easily applicable to general studies of spacetimes, mainly because physical and gauge degrees of freedom are mixed in a nontrivial way. In this paper we approach the whole formalism with the goal of expressing the spin coefficients as functions of tetrad invariants once a particular tetrad is chosen. We show that it is possible to do so, and give for the first time a general recipe for the task, as well as an indication of the quantities and identities that are required.

It has been pointed out that nonsingular cosmological solutions in second-order scalar-tensor theories generically suffer from gradient instabilities. We extend this no-go result to second-order gravitational theories with an arbitrary number of interacting scalar fields. Our proof follows directly from the action of generalized multi-Galileons, and thus is different from and complementary to that based on the effective field theory approach. Several new terms for generalized multi-Galileons on a flat background were proposed recently. We find a covariant completion of them and confirm that they do not participate in the no-go argument.