In this work we revisit the zero textures in low energy Majorana neutrino mass matrix when the active neutrino sector is extended by a light sterile neutrino in the eV scale, i.e., the $3+1$ scheme. In $3+1$ scenario, the low energy neutrino mass matrix ($m_{\nu }$) has ten independent elements. Thus in principle one can have minimum one-zero texture to maximum ten-zero texture. We summarize the previous results of one, two, three, and four-zero textures which already exist in the literature and present our new results on five-zero textures. In our analysis we find that among six possible five-zero textures, only one is allowed by the present data. We discuss possible theoretical model which can explain the origin of the allowed five-zero texture and discuss other possible implications of such a scenario. Our results also concludes that in $3+1$ scheme, one cannot have more than five-zeros in $m_{\nu }$.

We study the vector and axial-vector current correlators in perturbative and nonperturbative regimes of QCD. The correlators in Euclidean coordinate space are calculated on the lattice using the Möbius domain-wall fermion formulation at three lattice spacings covering 0.044–0.080 fm. The dynamical quark effects of $2+1$ light flavors are included. The sum $V+A$ and the difference $V-A$ of the vector ($V$) and axial-vector ($A$) current correlators calculated on the lattice after extrapolating to the physical point agree with those converted from the ALEPH experimental data of hadronic $\tau$ decays. The level of the agreement in the $V+A$ channel is about $1.3\sigma$ or smaller in the region of $|x|\ge 0.4\mathrm{fm}$, while that in the $V-A$ channel is about $1.8\sigma$ at $|x|=0.74\mathrm{fm}$ and smaller at other distances. We also extract the chiral condensate from the short-distance correlators on the lattice using the partially conserved axial current relation. Its result extrapolated to the chiral and continuum limit is compatible with other estimates at low energies.

We present a fully differential and high-precision calculation of top-quark pair-production and decay at the LHC, providing predictions for observables constructed from top-quark leptonic and $b$-flavored jet final states. The calculation is implemented in a parton-level Monte Carlo and includes an approximation to the next-to-next-to-leading-order (NNLO) corrections to the production and, for the first time, the exact NNLO corrections to the decay subprocesses. The corrections beyond NLO are sizable, and including them is crucial for an accurate description of the cross section constrained by experimental phase-space restrictions. We compare our predictions to published ATLAS and CMS measurements at the LHC, finding improved agreement compared with lower orders in the perturbative expansion.

We analyze tree-level string amplitudes in a linear dilaton background, motivated by its use as a gauge-invariant tracer of string interactions in scattering experiments and its genericity among simple perturbative string theory limits. A simple case is given by a lightlike dependence for the dilaton. The zero mode of the embedding coordinate in the direction of dilaton variation requires special care. Employing Gaussian wave packets and a well-defined modification of the dilaton profile far from the dominant interaction region, we obtain finite results which explicitly reproduce the interaction time scales expected from joining and splitting interactions involving oscillating strings in simple string scattering processes. There is an interesting interplay between the effects of the linear dilaton and the $i\epsilon$ prescription. In more general circumstances this provides a method for tracing the degree of nonlocality in string interactions, and it gives a basis for further studies of perturbative supercritical string theory at higher loop order.

We investigate the validity of the equivalence principle near horizons in string theory, analyzing the breakdown of effective field theory caused by longitudinal string spreading effects. An experiment is set up where a detector is thrown into a black hole a long time after an early infalling string. Light cone gauge calculations, taken at face value, indicate a detectable level of root-mean-square longitudinal spreading of the initial string as measured by the late infaller. This results from the large relative boost between the string and detector in the near-horizon region, which develops automatically despite their modest initial energies outside the black hole and the weak curvature in the geometry. We subject this scenario to basic consistency checks, using these to obtain a relatively conservative criterion for its detectability. In a companion paper, we exhibit longitudinal nonlocality in well-defined gauge-invariant S-matrix calculations, obtaining results consistent with the predicted spreading albeit not in a direct analog of the black hole process. We discuss applications of this effect to the firewall paradox, and estimate the time and distance scales it predicts for new physics near black hole and cosmological horizons.

We set up a tree-level six-point scattering process in which two strings are separated longitudinally such that they could only interact directly via a nonlocal spreading effect such as that predicted by light-cone gauge calculations and the Gross-Mende saddle point. One string, the “detector,” is produced at a finite time with energy $E$ by an auxiliary $2\to 2$ subprocess, with kinematics such that it has sufficient resolution to detect the longitudinal spreading of an additional incoming string, the “source.” We test this hypothesis in a gauge-invariant S-matrix calculation convolved with an appropriate wavepacket peaked at a separation $X$ between the central trajectories of the source and produced detector. The amplitude exhibits support for scattering at the predicted longitudinal separation $X\sim {\alpha }^{\prime }E$, in sharp contrast to the analogous quantum field theory amplitude (whose support manifestly traces out a tail of the position-space wavefunction). The effect arises in a regime in which the string amplitude is not obtained as a convergent sum of such QFT amplitudes, and has larger amplitude than similar QFT models (with the same auxiliary four-point amplitude). In a linear dilaton background, the amplitude depends on the string coupling as expected if the scattering is not simply occurring on the wavepacket tail in string theory. This manifests the scale of longitudinal spreading in a gauge-invariant S-matrix amplitude, in a calculable process with significant amplitude. It simulates a key feature of the dynamics of time-translated horizon infallers.

We study (nonperturbatively) the interactions of delta-coupled detectors with coherent states of a scalar field. We show that the time-evolved density matrix spectra of (i) a single detector, (ii) two detectors, and (iii) the partial transpose of the latter, are all independent of which coherent state the field was in. Furthermore, we find that the eigenvalues in (iii) are non-negative, implying that a delta-coupled detector pair cannot harvest entanglement from the vacuum, or any other coherent field state.

In this paper we derive new static phantom traversable wormholes by assuming a shape function with a quadratic dependence on the radial coordinate $r$. We mainly focus our study on wormholes sustained by exotic matter with positive energy density (as seen by any static observer) and a variable equation of state $p_r/\rho <-1$, dubbed “phantom matter.” Among phantom wormhole spacetimes extending to infinity, we show that a quadratic shape function allows us to construct static spacetimes of finite size, composed of a phantom wormhole connected to an anisotropic spherically symmetric distribution of dark energy. The wormhole part of the full spacetime does not fulfill the dominant energy condition, while the dark energy part does.

We compute the (center-of-mass frame) scattering angle $\chi$ of hyperboliclike encounters of two spinning black holes, at the fourth post-Newtonian approximation level for orbital effects, and at the next-to-next-to-leading order for spin-dependent effects. We find it convenient to compute the gauge-invariant scattering angle (expressed as a function of energy, orbital angular momentum and spins) by using the effective-one-body formalism. The contribution to scattering associated with nonlocal, tail effects is computed by generalizing to the case of unbound motions the method of time localization of the action introduced in the case of (small-eccentricity) bound motions by Damour et al. [Phys. Rev. D 91, 084024 (2015)].

We consider a dark matter model offering a very natural explanation of the observed relation, ${\mathrm{\Omega }}_{\mathrm{dark}}\sim {\mathrm{\Omega }}_{\text{visible}}$. This generic consequence of the model is a result of the common origin of both types of matter (dark and visible) which are formed during the same QCD transition. The masses of both types of matter in this framework are proportional to one and the same dimensional parameter of the system, ${\mathrm{\Lambda }}_{\mathrm{QCD}}$. The focus of the present work is the detailed study of the dynamics of the $\mathcal{C}\mathcal{P}$-odd coherent axion field $a(x)$ just before the QCD transition. We argue that the baryon charge separation effect on the largest possible scales inevitably occurs as a result of merely the existence of the coherent axion field in the early Universe. It leads to preferential formation of one species of nuggets on the scales of the visible Universe where the axion field $a(x)$ is coherent. A natural outcome of this preferential evolution is that only one type of the visible baryons remains in the system after the nuggets complete their formation. This represents a specific mechanism of how the baryon charge separation mechanism (when the Universe is neutral, but the visible part of matter consists of the baryons only) replaces the conventional “baryogenesis” scenario.

The accelerated expansion of the Universe can be interpreted as a tendency to satisfy holographic equipartition. It can be expressed by a simple law, $\mathrm{\Delta }V=\mathrm{\Delta }t(N_{\mathrm{surf}}-\epsilon N_{\text{bulk}})$, where $V$ is the Hubble volume in Planck units, $t$ is the cosmic time in Planck units, and $N_{\mathrm{surf}/\text{bulk}}$ is the number of degrees of freedom on the horizon/bulk of the Universe. We show that this holographic equipartition law effectively implies the maximization of entropy. In the cosmological context, a system that obeys the holographic equipartition law behaves as an ordinary macroscopic system that proceeds to an equilibrium state of maximum entropy. We consider the standard $\mathrm{\Lambda }\mathrm{CDM}$ model of the Universe and show that it is consistent with the holographic equipartition law. Analyzing the entropy evolution, we find that it also proceeds to an equilibrium state of maximum entropy.

We consider the possibility that the Universe, viewed as a three-brane, originated in a region of strong external field strength due to a four-form gauge field in the bulk. It is shown that in a scenario of this kind inflation is generic for a wide range of initial conditions. This is true even for small field inflation with a simple quadratic inflaton potential, as well as for Higgs potentials with the initial field well away from the local maximum, not necessarily starting from rest. The power spectrum, spectral index, and $r$ parameter help to constrain parameters in this scenario, and $r<0.1$ favors Higgs potentials.

This paper studies the cosmology of a homogeneous and isotropic spacetime endorsed with a conformally coupled massless scalar field. We find six different solutions of the Friedmann equation that represent six different types of universes, and all of them are periodically distributed along the complex time axis. From a classical point of view, they are then isolated, separated by Euclidean regions that represent quantum mechanical barriers. Quantum mechanically, however, there is a nonzero probability for the state of the universes to tunnel out through a Euclidean instanton and suffer a sudden transition to another state of the spacetime. We compute the probability of transition for this and other nonlocal processes like the creation of universes in entangled pairs and, generally speaking, in multipartite entangled states. We obtain the quantum state of a single universe within the formalism of the Wheeler-DeWitt equation and give the semiclassical state of the universes that describes the quantum mechanics of a scalar field propagating in a de Sitter background spacetime. We show that the superposition principle of the quantum mechanics of matter fields alone is an emergent feature of the semiclassical description of the universe that is not valid, for instance, in the spacetime foam. We use the third quantization formalism to describe the creation of an entangled pair of universes with opposite signs of the momentum conjugated to the scale factor. Each universe of the entangled pair represents an expanding spacetime in terms of the Wentzel-Kramers-Brillouin (WKB) time experienced by internal observers in their particle physics experiments. We compute the effective value of the Friedmann equation of the background spacetime of the two entangled universes, and thus, the effect that the entanglement would have in their expansion rates. We analyze as well the effects of the interuniversal entanglement in the properties of the scalar fields that propagate in each spacetime of the entangled pair. We find that the largest modes of the scalar field are unaware of the entanglement between the universes, but the effects can be significant for the lowest modes, allowing us to compute, in principle, detailed observational imprints of the multiverse in the properties of a single universe like ours.

Gravitational lensing of the cosmic microwave background (CMB) is a valuable cosmological signal that correlates to tracers of large-scale structure and acts as a important source of confusion for primordial $B$-mode polarization. State-of-the-art lensing reconstruction analyses use quadratic estimators, which are easily applicable to data. However, these estimators are known to be suboptimal, in particular for polarization, and large improvements are expected to be possible for high signal-to-noise polarization experiments. We develop a method and numerical code, lensit, that is able to find efficiently the most probable lensing map, introducing no significant approximations to the lensed CMB likelihood, and applicable to beamed and masked data with inhomogeneous noise. It works by iteratively reconstructing the primordial unlensed CMB using a deflection estimate and its inverse, and removing residual lensing from these maps with quadratic estimator techniques. Roughly linear computational cost is maintained due to fast convergence of iterative searches, combined with the local nature of lensing. The method achieves the maximal improvement in signal to noise expected from analytical considerations on the unmasked parts of the sky. Delensing with this optimal map leads to forecast tensor-to-scalar ratio parameter errors improved by a factor $\simeq 2$ compared to the quadratic estimator in a CMB stage IV configuration.

We demonstrate the applicability of the EPR entanglement squeezing scheme for enhancing the shot-noise-limited sensitivity of detuned dual-recycled Michelson interferometers. In particular, this scheme is applied to the GEO600 interferometer. The effect of losses throughout the interferometer, arm length asymmetries, and imperfect separation of the signal and idler beams is considered.

We present holographic descriptions of dynamical electroweak symmetry breaking models that incorporate the top mass generation mechanism. The models allow computation of the spectrum in the presence of large anomalous dimensions due to walking and strong Nambu–Jona-Lasinio interactions. Technicolor and QCD dynamics are described by the bottom-up Dynamic AdS/QCD model for arbitrary gauge groups and numbers of quark flavors. An assumption about the running of the anomalous dimension of the quark bilinear operator is input, and the model then predicts the spectrum and decay constants for the mesons. We add Nambu–Jona-Lasinio interactions responsible for flavor physics from extended technicolor, top-color, etc., using Witten’s multitrace prescription. We show the key behaviors of a top condensation model can be reproduced. We study generation of the top mass in (walking) one doublet and one family technicolor models and with strong extended technicolor interactions. The models clearly reveal the tensions between the large top mass and precision data for $\delta \rho$. The necessary tunings needed to generate a model compatible with precision constraints are simply demonstrated.

We calculate the polarization of prompt $J/\psi$ and $\mathrm{\Upsilon }(1\mathrm{S})$ production using the color evaporation model at leading order. We present the polarization parameter ${\lambda }_{\vartheta }$ as a function of center-of-mass energy and rapidity in $p+p$ collisions. We also compare the $x_F$ dependence to experimental results in $p+\mathrm{Cu}$ and $\pi +\mathrm{W}$ collisions and predict the $x_F$ dependence in $p+\mathrm{Pb}$ collisions at fixed-target energies. At energies far above the $Q\overline{Q}$ production threshold, we find the prompt $J/\psi$ and $\mathrm{\Upsilon }(1\mathrm{S})$ production to be longitudinally polarized with ${\lambda }_{\vartheta }^{J/\psi }=-0.51_{-0.16}^{+0.05}$ and ${\lambda }_{\vartheta }^{\mathrm{\Upsilon }(1\mathrm{S})}=-0.69_{-0.02}^{+0.03}$. Both prompt $J/\psi$ and prompt $\mathrm{\Upsilon }(1\mathrm{S})$ are also longitudinally polarized at central rapidity, becoming transversely polarized at the most forward rapidities.

Recent LHCb data for time-dependent $CP$ violation in $B^0\to {\pi }^{+}{\pi }^{-}$ and $B_s^0\to K^{+}{K}^{-}$ show deviations from theoretical predictions. Besides their central values for ${\mathcal{C}}_{K^{+}{K}^{-}}$, ${\mathcal{S}}_{K^{+}{K}^{-}}$ and ${\mathcal{A}}_{K^{+}{K}^{-}}^{\mathrm{\Delta }\mathrm{\Gamma }}$ violate quantum mechanic $CPT$ invariant sum rule ($CPT$ sum rule) prediction of $|{\mathcal{C}}_{K^{+}{K}^{-}}{|}^2+|{\mathcal{S}}_{K^{+}{K}^{-}}{|}^2+|{\mathcal{A}}_{K^{+}{K}^{-}}^{\mathrm{\Delta }\mathrm{\Gamma }}{|}^2=1$ (LHCb data imply the sum to be $0.67\pm 0.20$.), their values for ${\mathcal{C}}_{K^{+}{K}^{-}}=0.24\pm 0.06\pm 0.02$ and ${\mathcal{C}}_{{\pi }^{+}{\pi }^{-}}=-0.24\pm 0.07\pm 0.01$ also show large violation of SU(3) or its U-spin sub-group symmetry ($\mathrm{SU}(3)/\mathrm{U}$) relation ${\mathcal{C}}_{K^{+}{K}^{-}}/{\mathcal{C}}_{{\pi }^{-}{\pi }^{+}}=-\overline{\mathcal{B}}(B^0\to {\pi }^{-}{\pi }^{+}){\tau }_{B_s^0}/\overline{\mathcal{B}}(B_s^0\to K^{+}{K}^{-}){\tau }_{B^0}$ (LHCb data imply the ratio of left-side to right-side to be $4.67\pm 1.88$.). The LHCb results need to be further confirmed to be taken seriously. We suggest to use time-dependent $CP$ violation in $B_s\to K^0{\overline{K}}^0,{\pi }^{+}{\pi }^{-},{\pi }^0{\pi }^0$ to further test the $CPT$ sum rule. Assuming that the sum rule holds, we propose that violation of the $\mathrm{SU}(3)/\mathrm{U}$ relation may indicate a large FSI phase difference in the ${\pi }^{+}{\pi }^{-}$ and $K^{+}{K}^{-}$ rescattering. We suggest several other U-spin pairs of $B\to PP$ decays to further test $\mathrm{SU}(3)/\mathrm{U}$ relations.

Compactifications of six-dimensional (6D) superconformal field theories (SCFTs) on four- manifolds generate a large class of novel two-dimensional (2D) quantum field theories. We consider in detail the case of the rank-one simple non-Higgsable cluster 6D SCFTs. On the tensor branch of these theories, the gauge group is simple and there are no matter fields. For compactifications on suitably chosen Kähler surfaces, we present evidence that this provides a method to realize 2D SCFTs with $\mathcal{N}=(0,2)$ supersymmetry. In particular, we find that reduction on the tensor branch of the 6D SCFT yields a description of the same 2D fixed point that is described in the UV by a gauged linear sigma model (GLSM) in which the parameters are promoted to dynamical fields, that is, a “dynamic GLSM” (DGLSM). Consistency of the model requires the DGLSM to be coupled to additional non-Lagrangian sectors obtained from reduction of the antichiral two-form of the 6D theory. These extra sectors include both chiral and antichiral currents, as well as spacetime filling noncritical strings of the 6D theory. For each candidate 2D SCFT, we also extract the left- and right-moving central charges in terms of data of the 6D SCFT and the compactification manifold.