TeV-scale seesaw mechanisms are interesting due to their potential testability at existing collider experiments. Herein we propose an ${\mathrm{E}}_6$-inspired model allowing a TeV-scale pseudo-Dirac singlet neutrino seesaw mechanism with naturally sizeable Yukawa couplings of $\mathcal{O}({10}^{-2})$. The model also contains new U(1) gauge interactions (and associated $Z^{\prime }$ bosons with which the singlet neutrinos can be produced at colliders), typically long-lived color triplet fermions, SU(2) doublet fermions, and a complex scalar—potentially all at the TeV scale. Additionally we identify three possible explanations for the 750 GeV diphoton excess.

We provide a classification of generalized $CP$ symmetries preserved by the neutrino mass matrix according to the number of zero entries in the associated transformation matrix. We determine the corresponding constrained form of the lepton mixing matrix, characterized by correlations between the mixing angles and the $CP$ violating phases. We compare with the corresponding restrictions from current neutrino oscillation global fits and show that, in some cases, the Dirac $CP$ phase characterizing oscillations is highly constrained. Implications for current and upcoming long baseline neutrino oscillation experiments T2K, $\mathrm{NO}\nu \mathrm{A}$, and DUNE, as well as neutrinoless double beta decay experiments are discussed. We also study the cosmological implications of such schemes for leptogenesis.

We present an analysis of the decay $D^{+}\to K^{-}{\pi }^{+}{e}^{+}{\nu }_e$ based on data collected by the BESIII experiment at the $\psi (3770)$ resonance. Using a nearly background-free sample of 18262 events, we measure the branching fraction $\mathcal{B}(D^{+}\to K^{-}{\pi }^{+}{e}^{+}{\nu }_e)=(3.77\pm 0.03\pm 0.08)\%$. For $0.8<m_{K\pi }<1.0\mathrm{GeV}/c^2$, the partial branching fraction is $\mathcal{B}(D^{+}\to K^{-}{\pi }^{+}{e}^{+}{\nu }_e{)}_{[0.8,1.0]}=(3.39\pm 0.03\pm 0.08)\%$. A partial wave analysis shows that the dominant ${\overline{K}}^{*}(892{)}^0$ component is accompanied by an $S$-wave contribution accounting for $(6.05\pm 0.22\pm 0.18)\%$ of the total rate and that other components are negligible. The parameters of the ${\overline{K}}^{*}(892{)}^0$ resonance and of the form factors based on the spectroscopic pole dominance predictions are also measured. We also present a measurement of the ${\overline{K}}^{*}(892{)}^0$ helicity basis form factors in a model-independent way.

The pattern of quark and lepton mass matrices is unexplained in the standard model of particle interactions. I propose the novel idea of a progressive gauge $U(1)$ symmetry where it is a reflection of the regressive electroweak symmetry breaking pattern, caused by an extended Higgs scalar sector. Phenomenological implications of this new hypothesis are discussed.

In arXiv [K. Narayan, arXiv:1501.03019.], the areas of certain complex extremal surfaces in de Sitter space were found to have resemblance with entanglement entropy in appropriate dual Euclidean nonunitary CFTs, with the area being real and negative in ${\mathrm{dS}}_4$. In this paper, we study some toy models of 2-dim ghost conformal field theories with negative central charge with a view to exploring this further from the CFT point of view. In particular we consider $bc$-ghost systems with central charge $c=-2$ and study the replica formulation for entanglement entropy for a single interval, and associated issues arising in this case, notably pertaining to (i) the $SL(2)$ vacuum coinciding with the ghost ground state, and (ii) the background charge inherent in these systems which leads to particular forms for the norms of states (involving zero modes). This eventually gives rise to negative entanglement entropy. We also discuss a (logarithmic) CFT of anticommuting scalars, with similarities in some features. Finally we discuss a simple toy model of two “ghost-spins” which mimics some of these features.

In this paper we study a ($1+1$)-dimensional version of the famous Nambu–Jona-Lasinio model of quantum chromodynamics (QCD2) both at zero and at finite baryon density. We use nonperturbative techniques (non-Abelian bosonization and the truncated conformal spectrum approach). When the baryon chemical potential, $\mu$, is zero, we describe the formation of fermion three-quark (nucleons and $\mathrm{\Delta }$ baryons) and boson (two-quark mesons, six-quark deuterons) bound states. We also study at $\mu =0$ the formation of a topologically nontrivial phase. When the chemical potential exceeds the critical value and a finite baryon density appears, the model has a rich phase diagram which includes phases with a density wave and superfluid quasi-long-range (QLR) order, as well as a phase of a baryon Tomonaga-Luttinger liquid (strange metal). The QLR order results in either a condensation of scalar mesons (the density wave) or six-quark bound states (deuterons).

We present a generalized theoretical framework for dealing with the important issue of dynamical mass generation in Yang-Mills theories, and, in particular, with the infrared finiteness of the gluon propagators, observed in a multitude of recent lattice simulations. Our analysis is manifestly gauge invariant, in the sense that it preserves the transversality of the gluon self-energy, and gauge independent, given that the conclusions do not depend on the choice of the gauge-fixing parameter within the linear covariant gauges. The central construction relies crucially on the subtle interplay between the Abelian Ward identities satisfied by the nonperturbative vertices and a special integral identity that enforces a vast number of “seagull cancellations” among the one- and two-loop dressed diagrams of the gluon Schwinger-Dyson equation. The key result of these considerations is that the gluon propagator remains rigorously massless, provided that the vertices do not contain (dynamical) massless poles. When such poles are incorporated into the vertices, under the pivotal requirement of respecting the gauge symmetry of the theory, the terms comprising the Ward identities conspire in such a way as to still enforce the total annihilation of all quadratic divergences, inducing, at the same time, residual contributions that account for the saturation of gluon propagators in the deep infrared.

We propose a solution to the quantum measurement problem in inflation. Our model treats Fourier modes of cosmological perturbations as analogous to particles in a weakly interacting Bose gas. We generalize the idea of a macroscopic wave function to cosmological fields, and construct a self-interaction Hamiltonian that focuses that wave function. By appropriately setting the coupling between modes, we obtain the standard adiabatic, scale-invariant power spectrum. Because of central limit theorem, we recover a Gaussian random field, consistent with observations.

Two triplet vectorlike quarks (VLQs) with hypercharges of $Y=2/3$, $-1/3$ and one singlet scalar boson are embedded in the standard model to resolve the 750 GeV diphoton excess. The constraints on the tree-level Higgs- and $Z$-mediated flavor-changing neutral currents are discussed in detail. Besides the resolution of excess, it is found that the signal strength of diphoton Higgs decay can have a 10% deviation from the SM prediction and that the upper limits of the branching ratios for rare top-quark decays are $\mathrm{BR}(t\to c(h,Z))<(6.8,0.48)\times {10}^{-5}$. We find that the production cross section of a single VLQ by electroweak processes is larger than that of a VLQ pair by QCD processes. To explore the signals of the heavy VLQs at the LHC, we thoroughly analyze the production of single $X_{\pm 5/3}$ and $Y_{\mp 4/3}$ via $q_i{q}_j^{\prime }$ annihilations in $pp$ collisions at $\sqrt{s}=13\mathrm{TeV}$. It is found that the electroweak production cross sections for $d{X}_{5/3}$, $u{Y}_{-4/3}$, and $d{Y}_{4/3}$ channels with $m_X=m_Y=1\mathrm{TeV}$ can be 84.3, 72.3, and 157.8 fb, respectively, and the dominant decay modes are $X_{5/3}\to (c,t)W^{+}$ and $Y_{-4/3}\to (s,b)W^{-}$. With adopting kinematic cuts, the significance for the $pp\to d{W}^{+}t$ channel can be over $5\sigma$.

We perform a high-precision calculation of the phase shifts for $\pi \text{−}\pi$ scattering in the $I=1$, $J=1$ channel in the elastic region using elongated lattices with two mass-degenerate quark flavors ($N_f=2$). We extract the $\rho$ resonance parameters using a Breit-Wigner fit at two different quark masses, corresponding to $m_{\pi }=226\mathrm{MeV}$ and $m_{\pi }=315\mathrm{MeV}$, and perform an extrapolation to the physical point. The extrapolation is based on a unitarized chiral perturbation theory model that describes well the phase shifts around the resonance for both quark masses. We find that the extrapolated value, $m_{\rho }=720(1)(15)\mathrm{MeV}$, is significantly lower that the physical rho mass and we argue that this shift could be due to the absence of the strange quark in our calculation.

In order to describe the hadronization of polarized quarks, we discuss an extension of the quark-jet model to transverse momentum dependent fragmentation functions. The description is based on a product ansatz, where each factor in the product represents one of the transverse momentum dependent splitting functions, which can be calculated by using effective quark theories. The resulting integral equations and sum rules are discussed in detail for the case of inclusive pion production. In particular, we demonstrate that the three-dimensional momentum sum rules are satisfied naturally in this transverse momentum dependent quark-jet model. Our results are well suited for numerical calculations in effective quark theories and can be implemented in Monte Carlo simulations of polarized quark hadronization processes.

We present the systematic results for three-dimensional fragmentation functions of spin-1 hadrons defined via the quark-quark correlator. There are totally 72 such fragmentation functions, among them 18 are twist-2, 36 are twist-3 and 18 are twist-4. We also present the relationships between the twist-3 parts and those defined via the quark-gluon-quark correlator obtained from the QCD equation of motion. We show that the two particle semi-inclusive hadron production process $e^{+}{e}^{-}\to V\pi X$ at high energies is one of the best places to study the three-dimensional tensor polarization dependent fragmentation functions. We present the general kinematic analysis of this process and show that the cross section should be expressed in terms of 81 independent structure functions. After that we present parton model results for the hadronic tensor, the structure functions, and the azimuthal and spin asymmetries in terms of these gauge invariant fragmentation functions at the leading order perturbative quantum chromodynamics up to twist-3.

We extend the scalar-tensor reconstruction techniques for classical cosmology frameworks, in the context of loop quantum cosmology. After presenting in some detail how the equations are generalized in the loop quantum cosmology case, we discuss which new features and limitations the quantum framework introduces, and we use various illustrative examples in order to demonstrate how the method works. As we show, the energy density has two different classes of solutions, and one of these yields the correct classical limit, while the second captures the quantum phenomena. We study in detail the scalar tensor reconstruction method for both of these solutions. We also discuss some scenarios for which the Hubble rate becomes unbounded at finite time, which corresponds for example to the case in which the big rip occurs. As we show, this issue is nontrivial and we discuss how this case should be treated in a consistent way. Finally, we investigate how the classical stability conditions for the scalar-tensor solutions are generalized in the loop quantum framework.

The effective average action (EAA) is a scale-dependent effective action where a scale $k$ is introduced via an infrared regulator. The $k$ dependence of the EAA is governed by an exact flow equation to which one associates a boundary condition at a scale $\mu$. We show that the $\mu$ dependence of the EAA is controlled by an equation fully analogous to the Callan-Symanzik equation which allows one to define scaling quantities straightforwardly. Particular attention is paid to composite operators which are introduced along with new sources. We discuss some simple solutions to the flow equation for composite operators and comment on their implications in the case of a local potential approximation.

A new alternative volume operator is constructed for loop quantum gravity by using the so-called cotriad operators as building blocks. It is shown that the new volume operator shares the same qualitative properties with the standard volume operator. Moreover, a new alternative inverse volume operator is also constructed in the light of the construction of the alternative volume operator, which is possessed of the same qualitative properties as those of the alternative volume operator. The new inverse volume operator can be employed to construct the Hamiltonian operator of matter fields, which may lead to an anomaly-free on-shell quantum constraint algebra without any special restriction on the regularization procedure for gravity coupled to matter fields.

A new covariant generalization of Einstein’s general relativity is developed which allows the existence of a term proportional to $T_{\alpha \beta }{T}^{\alpha \beta }$ in the action functional of the theory ($T_{\alpha \beta }$ is the energy-momentum tensor). Consequently, the relevant field equations are different from general relativity only in the presence of matter sources. In the case of a charged black hole, we find exact solutions for the field equations. Applying this theory to a homogeneous and isotropic spacetime, we find that there is a maximum energy density ${\rho }_{\max }$, and correspondingly a minimum length $a_{\min }$, at the early Universe. This means that there is a bounce at early times, and this theory avoids the existence of an early-time singularity. Moreover, we show that this theory possesses a true sequence of cosmological eras. We also argue that, although in the context of the standard cosmological model the cosmological constant $\mathrm{\Lambda }$ does not play any important role in the early times and becomes important only after the matter-dominated era, in this theory the “repulsive” nature of the cosmological constant plays a crucial role at early times in resolving the singularity.

We propose a new form of the rotating C-metric with cosmological constant, which generalizes the form found by Hong and Teo for the Ricci-flat case. This solution describes the entire class of spherical black holes undergoing rotation and acceleration in dS or AdS space-time. The new form allows us to identify the complete ranges of coordinates and parameters of this solution. We perform a systematic study of its geometrical and physical properties, and of the various limiting cases that arise from it.

An important observable signature of a detectable nontrivial spatial topology of the Universe is the presence in the cosmic microwave background sky of pairs of matching circles with the same distributions of temperature fluctuations—the so-called circles in the sky. Most of the recent attempts to find these circles, including the ones undertaken by the Planck Collaboration, were restricted to antipodal or nearly antipodal circles with radii $\lambda \ge 15°$. In the most general search, pairs of circles with deviation from antipodality angles $0°\le \theta \le 169°$ and radii $10°\le \lambda \le 90°$ were investigated. No statistically significant pairs of matching circles were found in the searches so far undertaken. Assuming that the negative result of general search can be confirmed through analysis made with data from Planck and future cosmic microwave background experiments, we examine the question as to whether there are nearly flat universes with compact topology, satisfying Planck constraints on cosmological parameters, that would give rise to circles in the sky whose observable parameters $\lambda$ and $\theta$ fall outside the parameter ranges covered by this general search. We derive the expressions for the deviation from antipodality and for the radius of the circles associated to a pair of elements ($\gamma$, ${\gamma }^{-1}$) of the holonomy group $\mathrm{\Gamma }$ which define the spatial section of any positively curved universe with a nontrivial compact topology. We show that there is a critical position that maximizes the deviation from antipodality and prove that, no matter how nearly flat the Universe is, it can always have a nontrivial spatial topology that gives rise to circles whose deviation from antipodality $\theta$ is larger than 169° and whose radii of the circles $\lambda$ are smaller than 10° for some observers’s positions. This makes it apparent that slightly positively curved nearly flat universes with cosmological parameters within Planck bounds can be endowed with a nontrivial spatial topology with values of the observable parameters $\lambda$ and $\theta$ outside the ranges covered by the searches for circles carried out so far with either WMAP or Planck data. Thus, these circles-in-the-sky searches carried out so far are not sufficient to exclude the possibility of a universe with a detectable nontrivial cosmic topology. We present concrete examples of lens spaces universes whose associated circles have both, or at least one, value of the observable parameters ($\lambda$, $\theta$) outside the ranges covered by these searches. We also present a brief discussion of the implications of our results in view of unavoidable practical limits of the circles-in-the-sky method.

A resonancelike structure, the $P_c(4450)$, has recently been observed in the $J/\psi p$ spectrum by the LHCb Collaboration. We discuss the feasibility of detecting this structure in $J/\psi$ photoproduction in the CLAS12 experiment at JLab. We present a first estimate of the upper limit for the branching ratio of the $P_c(4450)$ to $J/\psi p$. Our estimates, which take into account the experimental resolution effects, predict that it will be possible to observe a sizable cross section close to the $J/\psi$ production threshold and shed light on the $P_c(4450)$ resonance in the future photoproduction measurements.