We reexamine lepton mixing in gauge models by considering two theories within the type I seesaw mechanism, the extended Standard Model, i.e. $SU(2{)}_L\times U(1{)}_Y$ with singlet right-handed heavy neutrinos, and the left-right model, $SU(2{)}_L\times SU(2{)}_R\times U(1{)}_{B-L}$. The former is often used as a simple heuristic approach to masses and mixing of light neutrinos and to leptogenesis, while we consider the latter as an introduction to other left-right symmetric gauge theories like $SO(10)$. We compare lepton mixing in both theories for general parameter space and discuss also some particular cases. In the electroweak broken phase, we study in parallel both models in the current basis (diagonal gauge interactions) and in the mass basis (diagonal mass matrices and mixing in the interaction), and perform the counting of $CP$-conserving and $CP$-violating parameters in both bases. We extend the analysis to the Pati-Salam model $SU(4{)}_C\times SU(2{)}_L\times SU(2{)}_R$ and to $SO(10)$. Although specifying the Higgs sector increases the predictive power, in the most general case one has the same parameter structure in the lepton sector for all the left-right symmetric gauge models. We make explicit the differences between the extended Standard Model and the left-right models, in particular $CP$-violating and lepton-number-violating new terms involving the $W_R$ gauge bosons. As expected, at low energy, the differences in the light neutrino spectrum and mixing appear only beyond leading order in the ratio of the Dirac mass to the right-handed Majorana mass.

The abundance of massive galaxy clusters is a powerful probe of departures from general relativity (GR) on cosmic scales. Despite current stringent constraints placed by stellar and galactic tests, on larger scales alternative theories of gravity such as $f(R)$ can still work as effective theories. Here we present constraints on two popular models of $f(R)$, Hu-Sawicki and “designer,” derived from a fully self-consistent analysis of current samples of x-ray selected clusters and accounting for all the covariances between cosmological and astrophysical parameters. Using cluster number counts in combination with recent data from the cosmic microwave background (CMB) and the CMB lensing potential generated by large scale structures, as well as with other cosmological constraints on the background expansion history and its mean matter density, we obtain the upper bounds ${\log }_{10}|f_{R0}|<4.79$ and ${\log }_{10}{B}_0<3.75$ at the 95.4% confidence level, for the Hu-Sawicki (with $n=1$) and designer models, respectively. The robustness of our results derives from high-quality cluster growth data for the most massive clusters known out to redshifts $z\sim 0.5$, a tight control of systematic uncertainties including an accurate and precise mass calibration from weak gravitational lensing data, and the use of the full shape of the halo mass function over the mass range of our data.

Using the spectral energy distribution of M87, a nearby radio galaxy in the Virgo cluster, and assuming a supermassive black hole induced spike in the dark matter halo profile, we exclude any dark matter candidate with a velocity-independent (s-wave) annihilation cross-section of the order of $⟨\sigma v⟩\sim {10}^{-26}{\mathrm{cm}}^3{\mathrm{s}}^{-1}$ and a mass up to $O(100)\mathrm{TeV}$. These limits supersede all previous constraints on thermal, s-wave, annihilating dark matter candidates by orders of magnitude, and rule out the entire canonical mass range. We remark in addition that, under the assumption of a spike, dark matter particles with a mass of a few TeV and an annihilation cross-section of $\sim {10}^{-27}{\mathrm{cm}}^3{\mathrm{s}}^{-1}$ could explain the TeV $\gamma$-ray emission observed in M87. A central dark matter spike is plausibly present around the supermassive black hole at the center of M87, for various, although not all, formation scenarios, and would have profound implications for our understanding of the dark matter microphysics.

We discuss the detection of gravitational-wave backgrounds in the context of Bayesian inference and suggest a practical definition of what it means for a signal to be considered stochastic—namely, that the Bayesian evidence favors a stochastic signal model over a deterministic signal model. A signal can further be classified as Gaussian-stochastic if a Gaussian signal model is favored. In our analysis we use Bayesian model selection to choose between several signal and noise models for simulated data consisting of uncorrelated Gaussian detector noise plus a superposition of sinusoidal signals from an astrophysical population of gravitational-wave sources. For simplicity, we consider colocated and coaligned detectors with white detector noise, but the method can be extended to more realistic detector configurations and power spectra. The general trend we observe is that a deterministic model is favored for small source numbers, a non-Gaussian stochastic model is preferred for intermediate source numbers, and a Gaussian stochastic model is preferred for large source numbers. However, there is very large variation between individual signal realizations, leading to fuzzy boundaries between the three regimes. We find that a hybrid, transdimensional model comprised of a deterministic signal model for individual bright sources and a Gaussian-stochastic signal model for the remaining confusion background outperforms all other models in most instances.

We show the existence of a family of four-dimensional vacuum spacetimes with asymptotically velocity-dominated singularities and without symmetries. The solutions are obtained using Fuchsian methods and are parametrized by several free functions of all space coordinates which control their asymptotic expansion.

The LHCb Collaboration has recently performed a first measurement of the angular production asymmetry in the distribution of beauty quarks and antiquarks at a hadron collider. We calculate the corresponding standard model prediction for this asymmetry at fixed order in perturbation theory. Our results show good agreement with the data, which are provided differentially for three bins in the invariant mass of the $b\overline{b}$ system. We also present similar predictions for both beauty-quark and charm-quark final states within the LHCb acceptance for a collision energy of $\sqrt{s}=13\mathrm{TeV}$. We finally point out that a measurement of the ratio of the $b\overline{b}$ and $c\overline{c}$ cross sections may be useful for experimentally validating charm-tagging efficiencies.

Recent developments showed that light-cone parton distributions can be studied by investigating the large momentum limit of the hadronic matrix elements of spacelike correlators, which are known as quasiparton distributions. Like a light-cone parton distribution, a quasiparton distribution also contains ultraviolet divergences and therefore needs renormalization. The renormalization of nonlocal operators in general is not well understood. However, in the case of quasi-quark distribution, the bilinear quark operator with a straight-line gauge link appears to be multiplicatively renormalizable by the quark wave function renormalization in the axial gauge. We first show that the renormalization of the self-energy correction to the quasi-quark distribution is equivalent to that of the heavy-light quark vector current in the heavy quark effective theory at one-loop order. Assuming this equivalence at two-loop order, we then show that the multiplicative renormalizability of the quasi-quark distribution is true at two-loop order.

The resonant substructures of $B^0\to {\overline{D}}^0{\pi }^{+}{\pi }^{-}$ decays are studied with the Dalitz plot technique. In this study a data sample corresponding to an integrated luminosity of $3.0{\mathrm{fb}}^{-1}$ of $pp$ collisions collected by the LHCb detector is used. The branching fraction of the $B^0\to {\overline{D}}^0{\pi }^{+}{\pi }^{-}$ decay in the region $m({\overline{D}}^0{\pi }^{\pm })>2.1\mathrm{GeV}/c^2$ is measured to be $(8.46\pm 0.14\pm 0.29\pm 0.40)\times {10}^{-4}$, where the first uncertainty is statistical, the second is systematic and the last arises from the normalization channel $B^0\to D^{*}(2010{)}^{-}{\pi }^{+}$. The ${\pi }^{+}{\pi }^{-}$ S-wave components are modeled with the isobar and K-matrix formalisms. Results of the Dalitz plot analyses using both models are presented. A resonant structure at $m({\overline{D}}^0{\pi }^{-})\approx 2.8\mathrm{GeV}/c^2$ is confirmed and its spin-parity is determined for the first time as $J^P=3^{-}$. The branching fraction, mass and width of this structure are determined together with those of the $D_0^{*}(2400{)}^{-}$ and $D_2^{*}(2460{)}^{-}$ resonances. The branching fractions of other $B^0\to {\overline{D}}^0{h}^0$ decay components with $h^0\to {\pi }^{+}{\pi }^{-}$ are also reported. Many of these branching fraction measurements are the most precise to date. The first observation of the decays $B^0\to {\overline{D}}^0{f}_0(500)$, $B^0\to {\overline{D}}^0{f}_0(980)$, $B^0\to {\overline{D}}^0\rho (1450)$, $B^0\to D_3^{*}(2760{)}^{-}{\pi }^{+}$ and the first evidence of $B^0\to {\overline{D}}^0{f}_0(2020)$ are presented.

Non-Gaussianity of the primordial density perturbations provides an important measure to constrain models of inflation. At cubic order the non-Gaussianity is captured by two parameters ${\tau }_{\mathrm{NL}}$ and $g_{\mathrm{NL}}$ that determine the amplitude of the density perturbation trispectrum. Here we report measurements of the kurtosis power spectra of the cosmic microwave background temperature as mapped by Planck by making use of correlations between square temperature-square temperature and cubic temperature-temperature anisotropies. In combination with noise simulations, we find the best joint estimates to be ${\tau }_{\mathrm{NL}}=0.4\pm 0.9\times {10}^4$ and $g_{\mathrm{NL}}=-1.2\pm 2.8\times {10}^5$. If ${\tau }_{\mathrm{NL}}=0$, we find $g_{\mathrm{NL}}=-1.4\pm 1.8\times {10}^5$.

When searching for deviations of statistical isotropy in the cosmic microwave background, a popular strategy is to write the two-point correlation function (2pcf) as the most general function of four spherical angles (i.e., two unit vectors) in the celestial sphere. Then, using a basis of bipolar spherical harmonics, statistical anisotropy will show up if and only if any coefficient of the expansion with nontrivial bipolar momentum is detected—although this detection will not in general elucidate the origin of the anisotropy. In this work we show that two new sets of four angles and basis functions exist which completely specify the 2pcf, while, at the same time, offering a possible geometrical interpretation of the mechanisms generating the signal. Since the coefficients of these expansions are zero if and only if isotropy holds, they act as a simple and geometrically motivated null test of statistical isotropy, with the advantage of allowing cosmic variance to be controlled in a systematic way. We report the results of the application of these null tests to the latest temperature data released by the Planck Collaboration.

The relationship between the cosmic microwave background radiation temperature and the redshift, i.e., the $T-z$ relation, is examined in a phenomenological dissipative model. The model contains two constant terms, as if a nonzero cosmological constant $\mathrm{\Lambda }$ and a dissipative process are operative in a homogeneous, isotropic, and spatially flat universe. The $T-z$ relation is derived from a general radiative temperature law, as appropriate for describing nonequilibrium states in a creation of cold dark matter model. Using this relation, the radiation temperature in the late Universe is calculated as a function of a dissipation rate ranging from $\tilde{\mu }=0$, corresponding to a nondissipative lambda cold dark matter model, to $\tilde{\mu }=1$, corresponding to a fully dissipative creation of cold dark matter model. The $T-z$ relation for $\tilde{\mu }=0$ is linear for standard cosmology and is consistent with observations. However, with increasing dissipation rate $\tilde{\mu }$, the radiation temperature gradually deviates from a linear law because the effective equation-of-state parameter varies with time. When the background evolution of the Universe agrees with a fine-tuned pure lambda cold dark matter model, the $T-z$ relation for low $\tilde{\mu }$ matches observations, whereas the $T-z$ relation for high $\tilde{\mu }$ does not. Previous work also found that a weakly dissipative model accords with measurements of a growth rate for clustering related to structure formations. These results imply that low dissipation is likely for the Universe. The weakly dissipative model should be further constrained by recent observations.

An epoch of Higgs relaxation may occur in the early universe during or immediately following postinflationary reheating. It has recently been pointed out that leptogenesis may occur in minimal extensions of the standard model during this epoch [A. Kusenko, L. Pearce, and L. Yang, Phys. Rev. Lett. 114, 061302 (2015)]. We analyze Higgs relaxation taking into account the effects of perturbative and nonperturbative decays of the Higgs condensate, and we present a detailed derivation of the relevant kinetic equations and of the relevant particle interaction cross sections. We identify the parameter space in which a sufficiently large asymmetry is generated.

We calculate the third-order moments of scalar curvature perturbations in configuration space for different inflationary models. We develop a robust numerical technique to compute the bispectrum for different models that have some features in the inflationary potential. From the bispectrum we evaluate moments analytically in the slow-roll regime while we devise a numerical mechanism to calculate these moments for non-slow-roll single-field inflationary models with a standard kinetic term that are minimally coupled to gravity. With the help of these third-order moments one can directly predict many non-Gaussian and geometrical measures of cosmic microwave background distributions in the configuration space. Thus, we devise a framework to calculate different third-order moments and geometrical measures, e.g. Minkowski functionals or the skeleton statistic, generated by different single-field models of inflation.

The relativistic plasma jets from a misaligned black hole-accretion disk system will not be axially symmetric. Here we analyze nonaxisymmetric, stationary, translation invariant jets in the force-free approximation where the field energy dominates the particle energy. We derive a stream equation for these configurations involving the flux function $\psi$ for the transverse magnetic field, the linear velocity $v(\psi )$ of field lines along the jet, and the longitudinal magnetic field $B_z(\psi )$. The equations can be completely solved when $|v|=1$, and when $|v|<1$ the problem can be reduced to the pure magnetic case $v=0$ by a “field line dependent boost.” We also find a large class of nonaxisymmetric solutions with arbitrary dependence on the longitudinal retarded time. A subclass of these constitutes a novel type of jet that has vanishing electromagnetic pressure $\frac{1}{2}(B^2-E^2)$ and requires no external pressure for confinement. We prove that such self-confinement is impossible when $B^2>E^2$. Finally, we write down specific solutions approximating numerical results for the nonaxisymmetric jet produced by a spinning black hole in an external, misaligned magnetic field.

Interactions that manifest themselves as lepton number violating processes at low energies in combination with sphaleron transitions typically erase any preexisting baryon asymmetry of the Universe. In this article, we discuss the constraints obtained from an observation of neutrinoless double beta decay in this context. If a new physics mechanism of neutrinoless double beta decay other than the standard light neutrino exchange is observed, typical scenarios of high-scale baryogenesis will be excluded unless the baryon asymmetry is stabilized via some new mechanism. We also sketch how this conclusion can be extended beyond the first lepton generation by incorporating lepton flavor violating processes.

Diagonal and transition magnetic moments of the negative parity, spin-$1/2$ heavy baryons are studied in the framework of the light cone QCD sum rules. By constructing the sum rules for different Lorentz structures, the unwanted contributions coming from negative-to-positive (positive-to-negative) parity transitions are removed. It is obtained that the magnetic moments of all baryons, except ${\mathrm{\Lambda }}_b^0$, ${\mathrm{\Sigma }}_c^{+}$, and ${\mathrm{\Xi }}_c^{\prime +}$, are quite large. It is also found that the transition magnetic moments between neutral negative parity heavy ${\mathrm{\Xi }}_Q^{\prime 0}$ and ${\mathrm{\Xi }}_Q^0$ baryons are very small. Magnetic moments of the ${\mathrm{\Sigma }}_Q\to {\mathrm{\Lambda }}_Q$ and ${\mathrm{\Xi }}_Q^{\prime \pm }\to {\mathrm{\Xi }}_Q^{\pm }$ transitions are quite large and may be measured in further experiments.

We present a measurement of the top-quark mass in events containing two leptons (electrons or muons) with a large transverse momentum, two or more energetic jets, and a transverse-momentum imbalance. We use the full proton-antiproton collision data set collected by the CDF experiment during the Fermilab Tevatron Run II at center-of-mass energy $\sqrt{s}=1.96\mathrm{TeV}$, corresponding to an integrated luminosity of $9.1{\mathrm{fb}}^{-1}$. A special observable is exploited for an optimal reduction of the dominant systematic uncertainty, associated with the knowledge of the absolute energy of the hadronic jets. The distribution of this observable in the selected events is compared to simulated distributions of $t\overline{t}$ dilepton signal and background. We measure a value for the top-quark mass of $171.5\pm 1.9(\text{stat})\pm 2.5(\text{syst})\mathrm{GeV}/c^2$.

Interactions of different types of topological defects can play an important role in the aftermath of a phase transition. We study interactions of fundamental magnetic monopoles and stable domain walls in a grand unified theory in which $\mathrm{SU}(5)\times {\mathrm{Z}}_2$ symmetry is spontaneously broken to $\mathrm{SU}(3)\times \mathrm{SU}(2)\times \mathrm{U}(1)/{\mathrm{Z}}_6$. We find that there are only two distinct outcomes depending on the relative orientation of the monopole and the wall in internal space. In one case, the monopole passes through the wall, while in the other it unwinds on hitting the wall.

The extended Skyrme–Faddeev model possesses vortex solutions in a ($3+1$)-dimensional Minkowski space-time with target space $C{P}^N$. They have finite energy per unit of length and contain waves propagating along the vortices with the speed of light. We introduce various types of the potentials which correspond with holomorphic solutions of the integrable sector and also with several numerical solutions outside of this sector. The presented solutions constitute a strong indication that the current model contains a large class of solutions with a wide range of coupling constants, and the exact solution is just a particular case.