Geodesics are used in a wide array of applications in cosmology and astrophysics. However, it is not a trivial task to efficiently calculate exact geodesic distances in an arbitrary spacetime. We show that in spatially flat ($3+1$)-dimensional Friedmann-Lemaître-Robertson-Walker (FLRW) spacetimes, it is possible to integrate the second-order geodesic differential equations, and derive a general method for finding both timelike and spacelike distances given initial-value or boundary-value constraints. In flat spacetimes with either dark energy or matter, whether dust, radiation, or a stiff fluid, we find an exact closed-form solution for geodesic distances. In spacetimes with a mixture of dark energy and matter, including spacetimes used to model our physical universe, there exists no closed-form solution, but we provide a fast numerical method to compute geodesics. A general method is also described for determining the geodesic connectedness of an FLRW manifold, provided only its scale factor.

In the context of the interaction between the electromagnetic field and a dielectric dispersive lossless medium, we present a nonlinear version of the relativistically covariant Hopfield model, which is suitable for the description of a dielectric Kerr perturbation propagating in a dielectric medium. The nonlinearity is introduced in the Lagrangian through a self-interacting term proportional to the fourth power of the polarization field. We find an exact solution for the nonlinear equations describing a propagating perturbation in the dielectric medium. Furthermore, the presence of an analogue Hawking effect, as well as the thermal properties of the model, are discussed, confirming and improving the results achieved in the scalar case.

Significant polarization of $\mathrm{\Lambda }$-hyperons produced in heavy ion collisions has been recently observed. It is believed to be a manifestation of the original rotation of the quark-gluon plasma as a whole. In a search for a microscopic mechanism for this phenomenon, we turn to the toy model of pionic superfluidity induced by chemical potentials. We argue that, in this case, the rotation is transferred to polarization of baryons. Quantitatively, the chiral vortical effect, or flow of axial current along the axis of rotation, is realized as a nonvanishing spin density of baryons. The role of vortices is crucial, and baryons emerge as $a$ related ultraviolet cutoff.

QCD-like theories can be engineered to remain in a confined phase when compactified on an arbitrarily small circle, where their features may be studied quantitatively in a controlled fashion. Previous work has elucidated the generation of a nonperturbative mass gap and the spontaneous breaking of chiral symmetry in this regime. Here, we study the rich spectrum of hadronic states, including glueball, meson, and baryon resonances. We find an exponentially growing Hagedorn density of states, as well as the emergence of nonperturbative energy scales given by iterated exponentials of the inverse Yang-Mills coupling $g^2$.

The Georgi-Machacek model is used to motivate and interpret LHC searches for doubly- and singly-charged Higgs bosons decaying into vector boson pairs. In this paper we study the constraints on and phenomenology of the “H5plane” benchmark scenario in the Georgi-Machacek model, which has been proposed for use in these searches. We show that the entire H5plane benchmark is compatible with the LHC measurements of the 125 GeV Higgs boson couplings. We also point out that, over much of the H5plane benchmark, the line shapes of the two $CP$-even neutral heavy Higgs bosons $H$ and $H_5^0$ will overlap and interfere when produced in vector boson fusion with decays to $W^{+}{W}^{-}$ or $ZZ$. Finally we compute the decay branching ratios of the additional heavy Higgs bosons within the H5plane benchmark to facilitate the development of search strategies for these additional particles.

The cosmological phase transition with Q-balls production mechanism can explain the baryogenesis and dark matter simultaneously, where constraints on dark matter masses and reverse dilution are significantly relaxed. We study how to probe this scenario by collider signals at QCD next-to-leading order and gravitational wave signals.

The flavor problem, neutrino physics, and the fermion mass hierarchy are important motivations to extend the Standard Model to the TeV scale. A new family nonuniversal extension is presented with three Higgs doublets, one Higgs singlet, and one scalar dark matter candidate. Exotic fermions are included in order to cancel chiral anomalies and to allow family nonuniversal ${\mathrm{U}(1)}_X$ charges. By implementing an additional ${\mathbb{Z}}_2$ symmetry, the Yukawa coupling terms are suited in such a way that the fermion mass hierarchy is obtained without fine-tuning. The neutrino sector includes Majorana fermions to implement the inverse seesaw mechanism. The effective mass matrix for Standard Model neutrinos is fitted to current neutrino oscillation data to check the consistency of the model with experimental evidence, obtaining that the normal-ordering scheme is preferred over the inverse ones, and the values of the neutrino Yukawa coupling constants are shown. Finally, the $h\to \tau \mu$ lepton-flavor-violation process is addressed with the rotation matrices of the $CP$-even scalars, left- and right-handed charged leptons, yielding definite regions where the model is consistent with CMS reports of $\mathrm{BR}(h\to \tau \mu )$.

The current work focuses on the process of vacuum Cherenkov radiation for Lorentz-violating fermions that are described by the minimal standard-model extension (SME). To date, most considerations of this important hypothetical process have been restricted to Lorentz-violating photons, as the necessary theoretical tools for the SME fermion sector have not been available. With their development in a very recent paper, we are now in a position to compute the decay rates based on a modified Dirac theory. Two realizations of the Cherenkov process are studied. In the first scenario, the spin projection of the incoming fermion is assumed to be conserved, and in the second, the spin projection is allowed to flip. The first type of process is shown to be still forbidden for the dimensionful $a$ and $b$ coefficients where there are strong indications that it is energetically disallowed for the $H$ coefficients, as well. However, it is rendered possible for the dimensionless $c$, $d$, $e$, $f$, and $g$ coefficients. For large initial fermion energies, the decay rates for the $c$ and $d$ coefficients were found to grow linearly with momentum and to be linearly suppressed by the smallness of the Lorentz-violating coefficient where for the $e$, $f$, and $g$ coefficients this suppression is even quadratic. The decay rates vanish in the vicinity of the threshold, as expected. The decay including a fermion spin-flip plays a role for the spin-nondegenerate operators and it was found to occur for the dimensionful $b$ and $H$ coefficients as well as for the dimensionless $d$ and $g$. The characteristics of this process differ much from the properties of the spin-conserving one, e.g., there is no threshold. Based on experimental data of ultra-high-energy cosmic rays, new constraints on Lorentz violation in the quark sector are obtained from the thresholds. However, it does not seem to be possible to derive bounds from the spin-flip decays. This work reveals the usefulness of the quantum field theoretic methods recently developed to study the phenomenology of high-energy fermions within the framework of the SME.

A generalization of the Wilson loop area-law criterion, which is applicable to gauge theories with matter in the fundamental representation of the gauge group, is proposed. This new criterion, like the area law, is stronger than the statement that asymptotic particle states are massive color singlets, which holds even for theories described by the Brout-Englert-Higgs mechanism.

The isovector bottomoniumlike exotic resonances $Z_b(10610)$ and $Z_b(10650)$ are very close to the thresholds of heavy meson pairs $B{\overline{B}}^{*}(\overline{B}{B}^{*})$ and $B^{*}{\overline{B}}^{*}$, and are naturally understood as “molecular” states made of the corresponding meson-antimeson pairs. The picture with a full separation of the two channels cannot be exact and a cross-feed between the states necessarily takes place. A simple model is considered here describing the mixing between the channels in terms of one parameter. The model reasonably describes the current data on the decays of the $Z_b$ resonances to bottomonium plus a pion and predicts the rate and a distinctive interference pattern for the decay $Z_b(10650)\to B{\overline{B}}^{*}(\overline{B}{B}^{*})$ as well as excess of the mass splitting between the resonances over the mass difference between $B^{*}$ and $B$ mesons.

Within the framework of QCD sum rules, we have investigated the tetraquark states with three heavy quarks. We systematically construct the interpolating currents for the possible $cc\overline{c}\overline{q}$, $cc\overline{b}\overline{q}$, $bc\overline{b}\overline{q}$, $bb\overline{b}\overline{q}$ tetraquark states with quantum numbers $J^P=0^{+}$ and $J^P=1^{+}$. Using these interpolating currents, we have calculated the two-point correlation functions and extracted the mass spectra for the above tetraquark states. We also discuss the decay patterns of these tetraquarks, and notice that the $cc\overline{c}\overline{q}$, $cc\overline{b}\overline{q}$, $bc\overline{b}\overline{q}$ may decay quickly with a narrow width due to their mass spectra. The $bb\overline{b}\overline{q}$ tetraquarks are expected to be very narrow resonances since their OZI (Okubo-Zweig-Iizuka)-allowed decay modes are kinematically forbidden. These states may be searched for in the final states with a $B$ meson plus a light meson or photon.

The predictability of hierarchical quark mass matrices with symmetrically placed texture zeros is explored in light of current precision measurements on quark masses and mixing data and interesting phenomenological relations among the quark mass ratios and flavor mixing angles along with $CP$ asymmetry angle $\beta$ are deduced for different predictive textures within the framework of the Standard Model. It is shown that a single nontrivial phase in these mass matrices is sufficient enough to account for the observed $CP$-violation in the quark sector. In particular, it is observed that the Cabibbo angle is predominantly determined by the ratio $\sqrt{m_d/m_s}$ and corrections may also result from $\sqrt{m_u/m_c}$. Furthermore, $V_{cb}\cong \sqrt{m_d/m_b}$ or $V_{cb}\cong \sqrt{m_c/2m_t}$ along with $V_{ub}\simeq \sqrt{m_u/m_t}$ provide excellent agreements with the current mixing data and $\beta =-\mathrm{Arg}\{V_{td}\}$ may provide a rigorous test at the B-factories for some of these texture zero structures.

Environmental decoherence of oscillating neutrinos of strength $\mathrm{\Gamma }=(2.3\pm 1.1)\times {10}^{-23}\mathrm{GeV}$ can explain how maximal ${\theta }_{23}$ mixing observed at 295 km by T2K appears to be nonmaximal at longer baselines. As shown recently by R. Oliveira, the Mikheyev-Smirnov-Wolfenstein matter effect for neutrinos is altered by decoherence: in normal (inverted) mass hierarchy, a resonant enhancement of ${\nu }_{\mu }({\overline{\nu }}_{\mu })\to {\nu }_e({\overline{\nu }}_e)$ occurs for $6<E_{\nu }<20\mathrm{GeV}$. Thus decoherence at the rated strength may be detectable as an excess of charged-current ${\nu }_e$ events in the full ${\nu }_{\mu }$ exposures of $\mathrm{MINOS}+$ and OPERA.

We investigate the relative importance of initial and final state effects on azimuthal correlations of gluons in low and high multiplicity $p+\mathrm{Pb}$ collisions. To achieve this, we couple Yang-Mills dynamics of pre-equilibrium gluon fields (IP-GLASMA) to a perturbative QCD based parton cascade for the final state evolution (BAMPS) on an event-by-event basis. We find that signatures of both the initial state correlations and final state interactions are seen in azimuthal correlation observables, such as $v_2\{2PC\}(p_T)$, their strength depending on the event multiplicity and transverse momentum. Initial state correlations dominate $v_2\{2PC\}(p_T)$ in low multiplicity events for transverse momenta $p_T>2\mathrm{GeV}$. While final state interactions are dominant in high multiplicity events, initial state correlations affect $v_2\{2PC\}(p_T)$ for $p_T>2\mathrm{GeV}$ as well as the pT integrated $v_2\{2PC\}$.

We present the results of a search for the rare decays $B\to h\nu \overline{\nu }$, where $h$ stands for $K^{+},K_{\mathrm{S}}^0,{K^{*}}^{+},{K^{*}}^0,{\pi }^{+},{\pi }^0,{\rho }^{+}$ and ${\rho }^0$. The results are obtained with $772\times {10}^{6}B\overline{B}$ pairs collected with the Belle detector at the KEKB $e^{+}{e}^{-}$ collider. We reconstruct one $B$ meson in a semileptonic decay and require a single $h$ meson but nothing else on the signal side. We observe no significant signal and set upper limits on the branching fractions. The limits set on the $B^0\to K_{\mathrm{S}}^0\nu \overline{\nu }$, $B^0\to {K^{*}}^0\nu \overline{\nu }$, $B^{+}\to {\pi }^{+}\nu \overline{\nu }$, $B^0\to {\pi }^0\nu \overline{\nu }$, $B^{+}\to {\rho }^{+}\nu \overline{\nu }$, and $B^0\to {\rho }^0\nu \overline{\nu }$ channels are the world’s most stringent.

We study one-dimensional chains of ghost-spins with nearest neighbor interactions amongst them, developing further the study of ghost-spins in previous work, defined as 2-state spin variables with indefinite norm. First we study finite ghost-spin chains with Ising-like nearest neighbor interactions: this helps organize and clarify the study of entanglement earlier, and we develop this further. Then we study a family of infinite ghost-spin chains with a different Hamiltonian containing nearest neighbor hopping-type interactions. By defining fermionic ghost-spin variables through a Jordan-Wigner transformation, we argue that these ghost-spin chains lead in the continuum limit to the $bc$-ghost conformal field theories.

We consider a real, massive scalar field in Bañados-Teitelboim-Zanelli spacetime, a $2+1$-dimensional black hole solution of Einstein’s field equations with a negative cosmological constant. First, we analyze the space of classical solutions in a mode decomposition, and we characterize the collection of all admissible boundary conditions of Robin type which can be imposed at infinity. Second, we investigate whether, for a given boundary condition, there exists a ground state by constructing explicitly its two-point function. We demonstrate that for a subclass of the boundary conditions it is possible to construct a ground state that locally satisfies the Hadamard property. In all other cases, we show that bound state mode solutions exist and, therefore, such construction is not possible.

We study properties of asymptotically free vectorial gauge theories with gauge groups $G=\mathrm{SO}(N_c)$ and $G=\mathrm{Sp}(N_c)$ and $N_f$ fermions in a representation $R$ of $G$, at an infrared (IR) zero of the beta function, ${\alpha }_{\mathrm{IR}}$, in the non-Abelian Coulomb phase. The fundamental, adjoint, and rank-2 symmetric and antisymmetric tensor fermion representations are considered. We present scheme-independent calculations of the anomalous dimensions of (gauge-invariant) fermion bilinear operators ${\gamma }_{\overline{\psi }\psi ,\mathrm{IR}}$ to $O({\mathrm{\Delta }}_f^4)$ and of the derivative of the beta function at ${\alpha }_{\mathrm{IR}}$, denoted ${\beta }_{\mathrm{IR}}^{\prime }$, to $O({\mathrm{\Delta }}_f^5)$, where ${\mathrm{\Delta }}_f$ is an $N_f$-dependent expansion variable. It is shown that all coefficients in the expansion of ${\gamma }_{\overline{\psi }\psi ,\mathrm{IR}}$ that we calculate are positive for all representations considered, so that to $O({\mathrm{\Delta }}_f^4)$, ${\gamma }_{\overline{\psi }\psi ,\mathrm{IR}}$ increases monotonically with decreasing $N_f$ in the non-Abelian Coulomb phase. Using this property, we give a new estimate of the lower end of this phase for some specific realizations of these theories.

The classical spinning particles are considered such that quantization of classical model leads to an irreducible massive representation of the Poincaré group. The class of gauge equivalent classical particle world lines is shown to form a $[(d+1)/2]$-dimensional world sheet in $d$-dimensional Minkowski space, irrespectively to any specifics of the classical model. For massive spinning particles in $d=3$, 4, the world sheets are shown to be circular cylinders. The radius of the cylinder is fixed by representation. In higher dimensions, the particle’s world sheet turns out to be a toroidal cylinder $\mathbb{R}\times {\mathbb{T}}^D$, $D=[(d-1)/2]$. Proceeding from the fact that the world lines of irreducible classical spinning particles are cylindrical curves, while all the lines are gauge equivalent on the same world sheet, we suggest a method to deduce the classical equations of motion for particles and also to find their gauge symmetries. In $d=3$ Minkowski space, the spinning particle path is defined by a single fourth-order differential equation having two zero-order gauge symmetries. The equation defines the particle’s path in Minkowski space, and it does not involve auxiliary variables. A special case is also considered of cylindric null curves, which are defined by a different system of equations. It is shown that the cylindric null curves also correspond to irreducible massive spinning particles. For the higher-derivative equation of motion of the irreducible massive spinning particle, we deduce the equivalent second-order formulation involving an auxiliary variable. The second-order formulation agrees with a previously known spinning particle model.