Neutrino flavor conversion studies based on astrophysical environments usually implement neutrino mixings, neutrino interactions with matter, and neutrino self-interactions. In anisotropic media, the most general mean-field treatment includes neutrino mass contributions as well, which introduce a coupling between neutrinos and antineutrinos termed helicity or spin coherence. We discuss resonance conditions for helicity coherence for Dirac and Majorana neutrinos. We explore the role of these mean-field contributions on flavor evolution in the context of a binary neutron star merger remnant. We find that resonance conditions can be satisfied in neutron star merger scenarios while adiabaticity is not sufficient for efficient flavor conversion. We analyze our numerical findings by discussing general conditions to have multiple Mikheyev-Smirnov-Wolfenstein-like resonances, in the presence of nonlinear feedback, in astrophysical environments.

We analyze the contribution of $2n$ scalars to the operator product expansion series for Maximum Helicity Violating (MHV) gluon scattering amplitudes/polygonal Wilson loops in planar $\mathcal{N}=4$ supersymmetric Yang-Mills (SYM). Hence, we sum up on $2n$ for large coupling $\lambda$: the logarithm of the amplitude is proportional to $\sqrt{\lambda }$, thus competing, unexpectedly, with the famous classical contribution. We also give explicit expressions for the first terms at large $\lambda$. For this analysis, we find an explicit computation of the $2n$-scalar term at any coupling by means of Young tableaux, similar to Nekrasov-Okounkov expressions in $\mathcal{N}=2$ SYM.

The magnetic moments of the recently observed resonance $X_b(5568)$ by D0 Collaboration and its partner with charm quark are calculated in the framework of the light cone QCD sum rules, by assuming that these resonances are represented as tetraquark states with quantum numbers $J^{PC}=1^{+\pm }$. The magnetic moment can play a critical role in the determination of the quantum numbers, as well as give useful information about the inner structure of these mesons.

We study the behavior of the complex potential between a heavy quark and its antiquark, which are in relative motion with respect to a hot and dense medium. The heavy quark-antiquark complex potential is obtained by correcting both the Coulombic and the linear terms in the Cornell potential through a dielectric function estimated within the real-time formalism using the hard thermal loop approximation. We show the variation of both the real and the imaginary parts of the potential for different values of velocities when the bound state ($Q\overline{Q}$ pair) is aligned in the direction parallel as well as perpendicular to the relative velocity of the $Q\overline{Q}$ pair with the thermal medium. With an increase of the relative velocity the screening of the real part of the potential becomes weaker at short distances and stronger at large distances for the parallel case. However, for the perpendicular case the potential decreases with an increase of the velocity at all distances, which results in the larger screening of the potential. In addition, the inclusion of the string term makes the screening of the potential weaker as compared to the Coulombic term alone for both cases. Therefore, by combining all these effects we expect a stronger binding of a $Q\overline{Q}$ pair in a moving medium in the presence of the string term as compared to the Coulombic term alone. The imaginary part decreases (in magnitude) with an increase of the relative velocity, leading to a decrease of the width of the quarkonium state at higher velocities. The inclusion of the string term increases the magnitude of the imaginary part, which results in an increase of the width of the quarkonium states. All of these effects lead to the modification in the dissolution of quarkonium states.

We consider a concise dark matter (DM) scenario in the context of a nonexotic U(1) extension of the Standard Model (SM), where a new ${\mathrm{U}(1)}_X$ gauge symmetry is introduced along with three generations of right-handed neutrinos (RHNs) and a SM gauge singlet Higgs field. The model is a generalization of the minimal gauged $\mathrm{U}(1{)}_{B-L}$ (baryon number minus lepton number) extension of the SM, in which the extra ${\mathrm{U}(1)}_X$ gauge symmetry is expressed as a linear combination of the SM ${\mathrm{U}(1)}_Y$ and $\mathrm{U}(1{)}_{B-L}$ gauge symmetries. We introduce a $Z_2$-parity and assign an odd-parity only for one RHN among all particles, so that this $Z_2$-odd RHN plays the role of DM. The so-called minimal seesaw mechanism is implemented in this model with only two $Z_2$-even RHNs. In this context, we investigate the physics of RHN DM, focusing on the case where this DM particle communicates with the SM particles through the ${\mathrm{U}(1)}_X$ gauge boson ($Z^{\prime }$ boson). This “$Z^{\prime }$-portal RHN DM” scenario is controlled by only three free parameters: the ${\mathrm{U}(1)}_X$ gauge coupling (${\alpha }_X$), the $Z^{\prime }$ boson mass ($m_{Z^{\prime }}$), and the ${\mathrm{U}(1)}_X$ charge of the SM Higgs doublet ($x_H$). We consider various phenomenological constraints to identify a phenomenologically viable parameter space. The most important constraints are the observed DM relic abundance and the latest LHC Run-2 results on the search for a narrow resonance with the dilepton final state. We find that these are complementary with each other and narrow the allowed parameter region, leading to the lower mass bound of $m_{Z^{\prime }}\gtrsim 2.7\mathrm{TeV}$.

The exceptional supersymmetric standard model is a low energy alternative to the minimal supersymmetric standard model (MSSM) with an extra $U(1)$ gauge symmetry and three generations of matter filling complete 27-plet representations of $E_6$. This provides both new D and F term contributions that raise the Higgs mass at tree level, and a compelling solution to the $\mu$-problem of the MSSM by forbidding such a term with the extra $U(1)$ symmetry. Instead, an effective $\mu$-term is generated from the vacuum expectation value of an SM singlet which breaks the extra $U(1)$ symmetry at low energies, giving rise to a massive $Z^{\prime }$. We explore the phenomenology of the constrained version of this model in substantially more detail than has been carried out previously, performing a ten dimensional scan that reveals a large volume of viable parameter space. We classify the different mechanisms for generating the measured relic density of dark matter found in the scan, including the identification of a new mechanism involving mixed bino/inert-Higgsino dark matter. We show which mechanisms can evade the latest direct detection limits from the LUX 2016 experiment. Finally we present benchmarks consistent with all the experimental constraints and which could be discovered with the XENON1T experiment.

We introduce a factorization of the fermion determinant in lattice QCD with Wilson-type fermions that leads to a bosonic action which is local in the block fields. The interaction among gauge fields on distant blocks is mediated by multiboson fields located on the boundaries of the blocks. The resultant multiboson domain-decomposed hybrid Monte Carlo passes extensive numerical tests carried out by measuring standard gluonic observables. The combination of the determinant factorization and of the one of the propagator, that we put forward recently, paves the way for multilevel Monte Carlo integration in the presence of fermions. We test this possibility by computing the disconnected correlator of two flavor-diagonal pseudoscalar densities, and we observe a significant increase of the signal-to-noise ratio due to a two-level integration.

We recalculate the branching ratio and $CP$ asymmetry for ${\overline{B}}^0(B^0)\to {\pi }^0{\pi }^0$ decays in the perturbative QCD approach. In this approach, we consider all the possible diagrams including nonfactorizable contributions and annihilation contributions. We obtain $\mathrm{Br}({\overline{B}}^0(B^0)\to {\pi }^0{\pi }^0)=(1.17_{-0.12}^{+0.11})\times {10}^{-6}$. Our result is in agreement with the latest measured branching ratio of $B^0\to {\pi }^0{\pi }^0$ by the Belle and HFAG collaborations. We also predict large direct $CP$ asymmetry and mixing $CP$ asymmetry in $B^0\to {\pi }^0{\pi }^0$ decays, which can be tested by the coming Belle-II experiments.

We study the dipion transitions $\mathrm{\Upsilon }(4S)\to \mathrm{\Upsilon }(nS){\pi }^{+}{\pi }^{-}(n=1,2)$. In particular, we consider the effects of the two intermediate bottomoniumlike exotic states $Z_b(10610)$ and $Z_b(10650)$ as well as bottom meson loops. The strong pion-pion final-state interactions, especially including channel coupling to $K\overline{K}$ in the $S$ wave, are taken into account model independently by using dispersion theory. Based on a nonrelativistic effective field theory we find that the contribution from the bottom meson loops is comparable to those from the chiral contact terms and the $Z_b$-exchange terms. For the $\mathrm{\Upsilon }(4S)\to \mathrm{\Upsilon }(2S){\pi }^{+}{\pi }^{-}$ decay, the result shows that including the effects of the $Z_b$ exchange and the bottom meson loops can naturally reproduce the two-hump behavior of the $\pi \pi$ mass spectra. Future angular distribution data are decisive for the identification of different production mechanisms. For the $\mathrm{\Upsilon }(4S)\to \mathrm{\Upsilon }(1S){\pi }^{+}{\pi }^{-}$ decay, we show that there is a narrow dip around 1 GeV in the $\pi \pi$ invariant mass distribution, caused by the final-state interactions. The distribution is clearly different from that in similar transitions from lower $\mathrm{\Upsilon }$ states, and needs to be verified by future data with high statistics. Also we predict the decay width and the dikaon mass distribution of the $\mathrm{\Upsilon }(4S)\to \mathrm{\Upsilon }(1S)K^{+}{K}^{-}$ process.

A search for the decays $B_c^{+}\to J/\psi D^{(*)0}{K}^{+}$ and $B_c^{+}\to J/\psi D^{(*)+}{K}^{*0}$ is performed with data collected at the LHCb experiment corresponding to an integrated luminosity of $3{\mathrm{fb}}^{-1}$. The decays $B_c^{+}\to J/\psi D^0{K}^{+}$ and $B_c^{+}\to J/\psi D^{*0}{K}^{+}$ are observed for the first time, while first evidence is reported for the $B_c^{+}\to J/\psi D^{*+}{K}^{*0}$ and $B_c^{+}\to J/\psi D^{+}{K}^{*0}$ decays. The branching fractions of these decays are determined relative to the $B_c^{+}\to J/\psi {\pi }^{+}$ decay. The $B_c^{+}$ mass is measured, using the $J/\psi D^0{K}^{+}$ final state, to be $6274.28\pm 1.40(\text{stat})\pm 0.32(\text{syst})\mathrm{MeV}/c^2$. This is the most precise single measurement of the $B_c^{+}$ mass to date.

A spacetime interpretation of deformed relativity symmetry groups was recently proposed by resorting to Finslerian geometries, seen as the outcome of a continuous limit endowed with first-order corrections from the quantum gravity regime. In this work, we further investigate such connections between deformed algebras and Finslerian geometries by showing that the Finsler geometries associated with the generalization of the Poincaré group (the so-called $\kappa$-Poincaré Hopf algebra) are maximally symmetric spacetimes which are also of the Berwald type: Finslerian spacetimes for which the connections are substantially Riemannian, belonging to the unique class for which the weak equivalence principle still holds. We also extend this analysis by considering a generalization of the de Sitter group (the so-called $q$–de Sitter group) and showing that its associated Finslerian geometry reproduces locally the one from the $\kappa$-Poincaré group, and that it itself can be recast in a Berwald form in an appropriate limit.

In this paper, we consider the one-dimensional semirelativistic Schrödinger equation for a particle interacting with $N$ Dirac delta potentials. Using the heat kernel techniques, we establish a resolvent formula in terms of an $N\times N$ matrix, called the principal matrix. This matrix essentially includes all the information about the spectrum of the problem. We study the bound state spectrum by working out the eigenvalues of the principal matrix. With the help of the Feynman-Hellmann theorem, we analyze how the bound state energies change with respect to the parameters in the model. We also prove that there are at most $N$ bound states and explicitly derive the bound state wave function. The bound state problem for the two-center case is particularly investigated. We show that the ground state energy is bounded below, and there exists a self-adjoint Hamiltonian associated with the resolvent formula. Moreover, we prove that the ground state is nondegenerate. The scattering problem for $N$ centers is analyzed by exactly solving the semirelativistic Lippmann-Schwinger equation. The reflection and the transmission coefficients are numerically and asymptotically computed for the two-center case. We observe the so-called threshold anomaly for two symmetrically located centers. The semirelativistic version of the Kronig-Penney model is shortly discussed, and the band gap structure of the spectrum is illustrated. The bound state and scattering problems in the massless case are also discussed. Furthermore, the reflection and the transmission coefficients for the two delta potentials in this particular case are analytically found. Finally, we solve the renormalization group equations and compute the beta function nonperturbatively.

We improve the accuracy of the effective-one-body (EOB) waveforms that were employed during the first observing run of Advanced LIGO for binaries of spinning, nonprecessing black holes by calibrating them to a set of 141 numerical-relativity (NR) waveforms. The NR simulations expand the domain of calibration toward larger mass ratios and spins, as compared to the previous EOBNR model. Merger-ringdown waveforms computed in black-hole perturbation theory for Kerr spins close to extremal provide additional inputs to the calibration. For the inspiral-plunge phase, we use a Markov-chain Monte Carlo algorithm to efficiently explore the calibration space. For the merger-ringdown phase, we fit the NR signals with phenomenological formulae. After extrapolation of the calibrated model to arbitrary mass ratios and spins, the (dominant-mode) EOBNR waveforms have faithfulness—at design Advanced-LIGO sensitivity—above 99% against all the NR waveforms, including 16 additional waveforms used for validation, when maximizing only on initial phase and time. This implies a negligible loss in event rate due to modeling for these binary configurations. We find that future NR simulations at mass ratios $\gtrsim 4$ and double spin $\gtrsim 0.8$ will be crucial to resolving discrepancies between different ways of extrapolating waveform models. We also find that some of the NR simulations that already exist in such region of parameter space are too short to constrain the low-frequency portion of the models. Finally, we build a reduced-order version of the EOBNR model to speed up waveform generation by orders of magnitude, thus enabling intensive data-analysis applications during the upcoming observation runs of Advanced LIGO.

The Einstein-Proca system is studied in the case of a complex vector field self-interacting through an appropriate potential with a global $U(1)$ symmetry. The corresponding equations for a static, cylindrically symmetric metric and matter fields are then constructed and solved. In the probe limit (no gravity), it is shown that the equations admit at least two classes of regular solutions distinguished by the asymptotic behavior of the matter fields. One of these classes corresponds to lumps of vector fields localized in a cylindrical region; we naturally call these solutions “Proca $Q$ tubes”. They constitute the cylindrical counterparts of spherical Proca $Q$ balls constructed recently; they can be characterized by finite mass and charge per unit length of the tube. The domain of existence of these Proca $Q$ tubes with respect to the coupling constants determining the potential is studied in detail. Finally, the gravitating Proca $Q$ tubes are constructed and studied.

In this paper, we revisit and complete our preceding work on the Fokker Lagrangian describing the dynamics of compact binary systems at the fourth post-Newtonian (4PN) order in harmonic coordinates. We clarify the impact of the nonlocal character of the Fokker Lagrangian or the associated Hamiltonian on both the conserved energy and the relativistic periastron precession for circular orbits. We show that the nonlocality of the action, due to the presence of the tail effect at the 4PN order, gives rise to an extra contribution to the conserved integral of energy with respect to the Hamiltonian computed on shell, which was not taken into account in our previous work. We also provide a direct derivation of the periastron advance by taking carefully into account this nonlocality. We then argue that the infrared (IR) divergences in the calculation of the gravitational part of the action are problematic, which motivates us to introduce a second ambiguity parameter, in addition to the one already assumed previously. After fixing these two ambiguity parameters by requiring that the conserved energy and the relativistic periastron precession for circular orbits be in agreement with numerical and analytical gravitational self-force calculations, valid in the limiting case of small mass ratio, we find that our resulting Lagrangian is physically equivalent to the one obtained in the ADM Hamiltonian approach.

We show that an effective particle Lagrangian yields the Mathisson-Papapetrou-Dixon (MPD) equations. The spin of the effective particle is defined without any reference to a fixed body frame or angular velocity variable. We then demonstrate that a continuous body, defined by a congruence of world lines and described by a general action, can be rewritten as an effective particle. We analyze the gauge freedom of the body and show that a natural center of mass condition is related to a spin supplementary condition.

We investigate the constraint ability of the gravitational wave (GW) as the standard siren on the cosmological parameters by using the third-generation gravitational wave detector: the Einstein Telescope. The binary merger of a neutron with either a neutron or black hole is hypothesized to be the progenitor of a short and intense burst of $\gamma$ rays; some fraction of those binary mergers could be detected both through electromagnetic radiation and gravitational waves. Thus we can determine both the luminosity distance and redshift of the source separately. We simulate the luminosity distances and redshift measurements from 100 to 1000 GW events. We use two different algorithms to constrain the cosmological parameters. For the Hubble constant $H_0$ and dark matter density parameter ${\mathrm{\Omega }}_m$, we adopt the Markov chain Monte Carlo approach. We find that with about 500–600 GW events we can constrain the Hubble constant with an accuracy comparable to Planck temperature data and Planck lensing combined results, while for the dark matter density, GWs alone seem not able to provide the constraints as good as for the Hubble constant; the sensitivity of 1000 GW events is a little lower than that of Planck data. It should require more than 1000 events to match the Planck sensitivity. Yet, for analyzing the more complex dynamical property of dark energy, i.e., the equation of state $w$, we adopt a new powerful nonparametric method: the Gaussian process. We can reconstruct $w$ directly from the observational luminosity distance at every redshift. In the low redshift region, we find that about 700 GW events can give the constraints of $w(z)$ comparable to the constraints of a constant $w$ by Planck data with type-Ia supernovae. Those results show that GWs as the standard sirens to probe the cosmological parameters can provide an independent and complementary alternative to current experiments.

It was recently revealed that a rotating compact body responds dynamically when it is subjected to a gravitomagnetic tidal field, even when this field is idealized as time independent. The dynamical response is characterized by time-changing internal currents, and it was suspected to originate from zero-frequency $g$-modes and $r$-modes driven by the tidal forces. In this paper, we provide additional insights into the phenomenon by examining the tidal response of a rotating body within the framework of post-Newtonian gravity. This approach allows us to develop an intuitive picture for the phenomenon, which relies on the close analogy between post-Newtonian gravity and Maxwell’s theory of electromagnetism. In this picture, the coupling between the gravitomagnetic tidal field and the body’s rotational velocity is naturally expected to produce an unbalanced Lorentz-like force within the body, and it is this force that is responsible for the tidal currents. The simplicity of the fluid equations in the post-Newtonian setting allows us to provide a complete description of the zero-frequency modes and demonstrate their precise role in the establishment of the tidal currents. We estimate the amplitude of these currents, and find that for neutron-star binaries of relevance to LIGO, the scale of the velocity perturbation is measured in kilometers per second when the rotation period is comparable to 100 milliseconds. This estimate indicates that the tidal currents may have a significant impact on the physics of neutron stars near merger.

We investigate scalar-tensor theories where matter couples to the scalar field via a kinetically dependent conformal coupling. These models can be seen as the low-energy description of invariant field theories under a global Abelian symmetry. The scalar field is then identified with the Goldstone mode of the broken symmetry. It turns out that the properties of these models are very similar to the ones of ultralocal theories where the scalar-field value is directly determined by the local matter density. This leads to a complete screening of the fifth force in the Solar System and between compact objects, through the ultralocal screening mechanism. On the other hand, the fifth force can have large effects in extended structures with large-scale density gradients, such as galactic halos. Interestingly, it can either amplify or damp Newtonian gravity, depending on the model parameters. We also study the background cosmology and the linear cosmological perturbations. The background cosmology is hardly different from its $\mathrm{\Lambda }\text{−}\mathrm{CDM}$ counterpart while cosmological perturbations crucially depend on whether the coupling function is convex or concave. For concave functions, growth is hindered by the repulsiveness of the fifth force while it is enhanced in the convex case. In both cases, the departures from the $\mathrm{\Lambda }\text{−}\mathrm{CDM}$ cosmology increase on smaller scales and peak for galactic structures. For concave functions, the formation of structure is largely altered below some characteristic mass, as smaller structures are delayed and would form later through fragmentation, as in some warm dark matter scenarios. For convex models, small structures form more easily than in the $\mathrm{\Lambda }\text{−}\mathrm{CDM}$ scenario. This could lead to an over-abundance of small clumps. We use a thermodynamic analysis and show that although convex models have a phase transition between homogeneous and inhomogeneous phases, on cosmological scales the system does not enter the inhomogeneous phase. On the other hand, for galactic halos, the coexistence of small and large substructures in their outer regions could lead to observational signatures of these models.