We develop a powerful analytical formalism for calculating the energy density of the stochastic gravitational wave background, including a full description of its anisotropies. This is completely general, and can be applied to any astrophysical or cosmological source. As an example, we apply these tools to the case of a network of Nambu-Goto cosmic strings. We find that the angular spectrum of the anisotropies is relatively insensitive to the choice of model for the string network, but very sensitive to the value of the string tension $G\mu$.

Current cosmological constraints on the scalar spectral index of primordial fluctuations $n_{\mathrm{s}}$ in the $\mathrm{\Lambda }$Vcold dark matter ($\mathrm{\Lambda }\mathrm{CDM}$) model have excluded the minimal scale-invariant Harrison-Zel’dovich model ($n_{\mathrm{s}}=1$; hereafter HZ) at high significance, providing support for inflation. In recent years, however, some tensions have emerged between different cosmological data sets that, if not due to systematics, could indicate the presence of new physics beyond the $\mathrm{\Lambda }\mathrm{CDM}$ model. In light of these developments, we evaluate the Bayesian evidence against HZ in different data combinations and model extensions. Considering only the Planck temperature data, we find inconclusive evidence against HZ when including variations in the neutrino number $N_{\mathrm{eff}}$ and/or the helium abundance $Y_{\text{He}}$. Adding the Planck polarization data, on the other hand, yields strong evidence against HZ in the extensions we considered. Perhaps most interestingly, Planck temperature data combined with local measurements of the Hubble parameter [A. G. Riess et al., Astrophys. J. 826, 56 (2016); A. G. Riess et al. Astrophys. J. 861, 126 (2018)] give as the most probable model a HZ spectrum, with additional neutrinos. However, with the inclusion of polarization, standard $\mathrm{\Lambda }\mathrm{CDM}$ is once again preferred, but the HZ model with extra neutrinos is not strongly disfavored. The possibility of fully ruling out the HZ spectrum is therefore ultimately connected with the solution to current tensions between cosmological data sets. If these tensions are confirmed by future data, then new physical mechanisms could be at work and a HZ spectrum could still offer a valid alternative.

We consider the total nonlocal energy associated with a particle at rest in the Hubble flow, i.e., the relational energy between this particle and all connected particles within the causal horizon. The particle, even while at rest, partakes in relative recessional and peculiar motion of connected particles in three dimensions. A geometrical argument due to Berkeley suggests that the nonlocal mass of recessional energy associated with the particle is 3 times its Newtonian mass. It follows that nonlocal recessional and peculiar energy of the Universe are equal, and match Misner-Sharp energy within the apparent horizon. Contributions of recessional and peculiar nonlocal energy are thus shown to generate a 6 times higher level of matter energy than expected from the Newtonian mass. Accordingly, the nonlocal energy density of baryons is expected to be 6 times the standard local energy density of baryons, i.e., ${\mathrm{\Omega }}_{\mathrm{b},\mathrm{eff}}=6{\mathrm{\Omega }}_{\mathrm{b}}$. At ${\mathrm{\Omega }}_{\mathrm{b}}\sim 0.0484\pm 0.0017$ [P. A. R. Ade et al. (Planck Collaboration), Astron. Astrophys. 594, A13 (2016) ] this predicts a nonlocal baryon energy density ${\mathrm{\Omega }}_{\mathrm{b},\mathrm{eff}}\sim 0.290\pm 0.010$, in agreement with observed matter density ${\mathrm{\Omega }}_{\mathrm{m}}\sim 0.308\pm 0.012$. The effect of nonlocal mass on solar system and galactic scales is considered.

If the Universe’s energy density was dominated by a fast-rolling scalar field while the radiation bath was hot enough to thermally produce dark matter, then dark matter with larger-than-canonical annihilation cross sections can generate the observed dark matter relic abundance. To further constrain these scenarios, we investigate the evolution of small-scale density perturbations during such a period of kination. We determine that once a perturbation mode enters the horizon during kination, the gravitational potential drops sharply and begins to oscillate and decay. Nevertheless, dark matter density perturbations that enter the horizon during an era of kination grow linearly with the scale factor prior to the onset of radiation domination. Consequently, kination leaves a distinctive imprint on the matter power spectrum: scales that enter the horizon during kination have enhanced inhomogeneity. We also consider how matter density perturbations evolve when the dominant component of the Universe has a generic equation-of-state parameter $w$. We find that matter density perturbations do not grow if they enter the horizon when $0<w<1/3$. If matter density perturbations enter the horizon when $w>1/3$, their growth is faster than the logarithmic growth experienced during radiation domination. The resulting boost to the small-scale matter power spectrum leads to the formation of enhanced substructure, which effectively increases the dark matter annihilation rate and could make thermal dark matter production during an era of kination incompatible with observations.

We discuss diffractive photon production of vector mesons in holographic QCD. At large $\sqrt{s}$, the QCD scattering amplitudes are reduced to the scattering of pairs of dipoles exchanging a closed string or a pomeron. We use the holographic construction in a 5-dimensional anti-deSitter space (${\mathrm{Ad}\mathrm{S}}_5$) to describe both the intrinsic dipole distribution in each hadron, and the pomeron exchange. Our results for the heavy meson photon production are made explicit and compared to some existing experiments.

We study the chiral expansion of meson masses and decay constants using a chiral Lagrangian that was constructed previously based on the hadrogenesis conjecture. The one-loop self-energies of the Goldstone bosons and vector mesons are evaluated. It is illustrated that a order-by-order renormalizable effective field theory arises once specific conditions on the low-energy constants are imposed. For the case where the hadrogenesis mass gap scale ${\mathrm{\Lambda }}_{\mathrm{HG}}$ is substantially larger than the chiral symmetry breaking scale ${\mathrm{\Lambda }}_{\chi }$ a partial summation scheme is required. All terms proportional to $(M/{\mathrm{\Lambda }}_{\chi }{)}^n$ can be summed by a suitable renormalization, where $M$ is the chiral and large-$N_c$ limit of the vector meson masses in QCD. The size of loop effects from vector meson degrees of freedom is illustrated for physical quark masses. Naturally sized effects are observed that have significant impact on the chiral structure of low-energy QCD with three light flavors.

In a large-momentum nucleon state, the matrix element of a gauge-invariant Euclidean Wilson line operator accessible from lattice QCD can be related to the standard light-cone parton distribution function through the large-momentum effective theory (LaMET) expansion. This relation is given by a factorization formula with a nontrivial matching coefficient. Using the operator product expansion we derive the large-momentum factorization of the quasiparton distribution function in LaMET, and show that the more recently discussed pseudoparton distribution approach also obeys an equivalent factorization formula. Explicit results for the coefficients are obtained and compared at one loop. We also prove that the matching coefficients in the $\overline{\mathrm{MS}}$ scheme depend on the large partonic momentum rather than the nucleon momentum.

We investigate the possible detection of the hypercharge axion (HCA) in colliders. The HCA is a hypothetical pseudoscalar that couples to weak hypercharge topological density and could potentially explain the dominance of matter over antimatter in the observable universe. If the HCA exists, it can be produced in colliders via vector boson fusion or in association with a photon or with a $Z$ boson, and detected by looking for its decay into photons or $Z$ bosons. We find that for certain values of the HCA mass and coupling scales, both of the order of a TeV, existing data from the Large Hadron Collider (LHC) can already put interesting constraints, and in future colliders, such as the High Luminosity LHC, the accessible detection range is increased significantly.

We discuss the possibility of finding an upper bound on the seesaw scale using the cosmological bound on the cold dark matter relic density. We investigate a simple relation between the origin of neutrino masses and the properties of a dark matter candidate in a simple theory where the new symmetry breaking scale defines the seesaw scale. Imposing the cosmological bounds, we find an upper bound of order multi-TeV on the lepton number violation scale. We investigate the predictions for direct and indirect detection dark matter experiments and the possible signatures at the Large Hadron Collider.

As a sequel to our preceding work [Y. Jia et al. J. High Energy Phys. 11 (2017) 151], we carry out a comprehensive comparative study between the quasiparton distribution functions (PDFs), distribution amplitudes (DAs), and their light-cone counterparts for various flavor-neutral mesons in the context of the ’t Hooft model, that is, the two-dimensional QCD in the large-$N$ limit. In contrast to the original derivation via diagrammatic techniques exemplified by Dyson-Schwinger and Bethe-Salpeter equations, here we employ the Hamiltonian operator approach to reconstruct the celebrated ’t Hooft equation in light-front quantization, and Bars-Green equations in equal-time quantization. The novelty of our derivation is to employ the soft momentum cutoff as the IR regulator. As a virtue of this operator approach, the functional form of the quasidistributions can be transparently built out of the Bars-Green wave functions and the Bogoliubov angle with the aid of bosonization technique. Equipped with various bound-state wave functions numerically inferred by Jia et al. [J. High Energy Phys. 11 (2017) 151], we then investigate how rapidly the quasidistributions approach their light-cone counterparts with the increasing meson momentum. We observe that the light mesons’ quasidistributions approach the light-cone distributions at a slower pace than the heavy quarkonia. Curiously, lattice simulations of quasidistributions in four-dimensional QCD also discover this feature. Furthermore, we also compute the partonic light-cone PDF and quasi-PDF to one-loop order in perturbation theory, again employing the momentum cutoff as the IR regulator. We explicitly verify one of the backbones underlying the large momentum effective field theory (LaMET), namely, both quasi-PDFs and light-cone PDFs in ${\mathrm{QCD}}_2$ indeed possess the same IR behavior at leading order in $1/P^z$.

Recently the Belle collaboration has discovered a narrow $S=-3$ baryon, the $\mathrm{\Omega }(2012)$. We explore the possibility that the $\mathrm{\Omega }(2012)$ is a $\mathrm{\Xi }(1530)\overline{K}$ molecule, where the binding mechanism is the coupled channel dynamics with the $\mathrm{\Omega }\eta$ channel. The characteristic signature of a molecular $\mathrm{\Omega }(2012)$ will be its decay into the three body channel $\mathrm{\Xi }\pi \overline{K}$, for which we expect a partial decay width of 2–3 MeV. The partial decay width into the $\mathrm{\Xi }\overline{K}$ channel should lie in the range of 1–11 MeV, a figure compatible with experiment and which we have deduced from the assumption that the coupling involved in this decay is of natural size. For comparison purposes the decay of a purely compact $\mathrm{\Omega }(2012)$ into the $\mathrm{\Xi }\overline{K}$ and $\mathrm{\Xi }\pi \overline{K}$ channels is of the same order of magnitude as and one order of magnitude smaller than in the molecular scenario, respectively. This comparison indicates that the current experimental information is insufficient to distinguish between a compact and a molecular $\mathrm{\Omega }(2012)$ and further experiments will be required to determine its nature. A molecular $\mathrm{\Omega }(2012)$ will also imply the existence of two- and three-body molecular partners. The two-body partners comprise two $\mathrm{\Lambda }$ hyperons located at 1740 and 1950 MeV respectively, the first of which might correspond to the $\mathrm{\Lambda }(1800)$ while the second to the $\mathrm{\Lambda }(2000)$ or the $\mathrm{\Lambda }(2050)$. The three-body partners include a $\mathrm{\Xi }(1530)K\overline{K}$ and a $\mathrm{\Xi }(1530)\eta \overline{K}$ molecule, with masses of $M=2385–2445\mathrm{MeV}$ and $M=2434–2503\mathrm{MeV}$ respectively. We might be tempted to identify the first with the $\mathrm{\Xi }(2370)$ and the latter with the $\mathrm{\Omega }(2470)$ listed in the PDG.

In this work, we propose a possible experimental research topic on the $\mathrm{\Upsilon }(6S)\to \mathrm{\Upsilon }(nS){\eta }^{(\prime )}$ ($n=1$, 2, 3) transitions. Considering the hadronic loop effect from the intermediate $S$-wave $B_{(s)}$ and $B_{(s)}^{*}$ mesons, we estimate the partial decay widths and the corresponding branching ratios of the $\mathrm{\Upsilon }(6S)\to \mathrm{\Upsilon }(nS){\eta }^{(\prime )}$ hadronic decays, which become considerably large. With the running of the Belle II experiment, it becomes possible to explore these $\mathrm{\Upsilon }(6S)\to \mathrm{\Upsilon }(nS){\eta }^{(\prime )}$ transitions.

The origin of the apparent thermalization in high-energy collisions is investigated using the data of the ATLAS and CMS Collaborations at the LHC. For this purpose, we analyze the transverse momentum distributions in the following proton-proton collision processes, all at $\sqrt{s}=13\mathrm{TeV}$: (i) inclusive inelastic $pp$ collisions; (ii) single- and double-diffractive Drell-Yan production $pp\to {\mu }^{+}{\mu }^{-}X$; and (iii) Higgs boson production. We confirm the relation between the effective temperature and the hard scattering scale observed at lower energies, and find that it extends even to the Higgs boson production process. In addition we find that the thermal component disappears in diffractive events (even though many charged hadrons are still produced). We discuss the implications of our study for the mechanism of multiparticle production—in particular, we test the hypothesis about the link between quantum entanglement and thermalization in high-energy collisions.

We study how an external magnetic field modifies the chiral phase structure of QCD, in particular the phases characterized by inhomogeneous chiral condensates. The magnetic field can be systematically incorporated into a generalized Ginzburg-Landau framework, and it turns out to induce a model independent universal coupling between the magnetic field and the axial isospin current. The resulting effect is found to be drastic especially in the chiral limit; no matter how small the magnetic intensity is, the tricritical Lifshitz point is totally washed out, and the real kink crystal is replaced by a magnetically induced chiral spiral. The current quark mass, on the other hand, has an opposite effect, protecting the chiral critical point from the magnetically induced chiral spiral. But once the magnetic intensity exceeds a critical value, the critical point no longer exists. We draw a semiquantitative conclusion that the critical point disappears for $\sqrt{eB}\gtrsim 50\mathrm{MeV}$.

We compare the Standard Model (SM) predictions for the differential branching ratio of the rare $B\to K^{*}\nu \overline{\nu }$ decays using $B\to K^{*}$ form factors obtained from holographic light-front QCD (LFHQCD) and sum rules (SR) distribution amplitudes. For the total branching ratio, we predict $\mathcal{BR}(B\to K^{*}\nu \overline{\nu }{)}_{\text{LFHQCD}}=(6.36_{-0.74}^{+0.59})\times {10}^{-6}$ and $\mathcal{BR}(B\to K^{*}\nu \overline{\nu }{)}_{\mathrm{SR}}=(8.14_{-0.17}^{+0.16})\times {10}^{-6}$. More interestingly, we find that the two model predictions for the differential branching ratio are sufficiently different at low momentum transfer, so that future measurements at Belle II may be able to discriminate between them. We also confirm numerically that the $K^{*}$ longitudinal polarization fraction $F_L$ has little sensitivity to the nonperturbative form factors and is thus an excellent observable to probe new physics signals. We predict $F_L=0.40_{-0.01}^{+0.02}(0.41\pm 0.01)$ using LFHQCD (SR).

We study the properties of singular values of mixing matrices embedded within an experimentally determined interval matrix. We argue that any physically admissible mixing matrix needs to have the property of being a contraction. This condition constrains the interval matrix, by imposing correlations on its elements and leaving behind only physical mixings that may unveil signs of new physics in terms of extra neutrino species. We propose a description of the admissible three-dimensional mixing space as a convex hull over experimentally determined unitary mixing matrices parametrized by Euler angles, which allows us to select either unitary or nonunitary mixing matrices. The unitarity-breaking cases are found through singular values and we construct unitary extensions, yielding a complete theory of minimal dimensionality larger than 3 through the theory of unitary matrix dilations. We discuss further applications to the quark sector.

A search for the $b\overline{b}$ decay of the Standard Model Higgs boson produced through vector-boson fusion is presented. Three mutually exclusive channels are considered: two all-hadronic channels and a photon-associated channel. Results are reported from the analysis of up to $30.6{\mathrm{fb}}^{-1}$ of $pp$ data at $\sqrt{s}=13\mathrm{TeV}$ collected with the ATLAS detector at the LHC. The measured signal strength relative to the Standard Model prediction from the combined analysis is $2.5_{-1.3}^{+1.4}$ for inclusive Higgs boson production and $3.0_{-1.6}^{+1.7}$ for vector-boson fusion production only.

This paper presents several measurements of total production cross sections and total inelastic cross sections for the following reactions: ${\pi }^{+}+\mathrm{C}$, ${\pi }^{+}+\mathrm{Al}$, $K^{+}+\mathrm{C}$, $K^{+}+\mathrm{Al}$ at $60\mathrm{GeV}/c$, ${\pi }^{+}+\mathrm{C}$ and ${\pi }^{+}+\mathrm{Al}$ at $31\mathrm{GeV}/c$. The measurements were made using the NA61/SPS Heavy Ion and Neutrino Experiment spectrometer at the CERN Super Proton Synchrotron (SPS). Comparisons with previous measurements are given and good agreement is seen. These interaction cross sections measurements are a key ingredient for neutrino flux prediction from the reinteractions of secondary hadrons in current and future accelerator-based long-baseline neutrino experiments.

We study the behavior of a massless, quantized, scalar field on a two-dimensional cylinder spacetime as it responds to the time-dependent evolution of a Mamaev-Trunov potential of the form $V(x,t)=2\xi \delta (x)\theta (-t)$. We begin by constructing mode solutions to the classical Klein-Gordon-Fock equation with potential on the whole spacetime. For a given eigenmode solution of the IN region of the spacetime ($t<0$), we determine its evolution into the OUT region ($t>0$) through the use of a Fourier decomposition in terms of the OUT region eigenmodes. The classical system is then second quantized in the canonical quantization scheme. On the OUT region, there is a unitarily equivalent representation of the quantized field in terms of the OUT region eigenmodes, including zero-frequency modes which we also quantize in a manner which allows for their interpretation as particles in the typical sense. After determining the Bogolubov coefficients between the two representations, we study the production of quanta out of the vacuum when the potential turns off. We find that the number of “particles” created on the OUT region is finite for the standard modes, and with the usual ambiguity in the number of particles created in the zero-frequency modes. We then look at the renormalized expectation value of the stress-energy tensor on the IN and OUT regions for the IN vacuum state. We find that the resulting stress tensor can violate the null, weak, strong, and dominant energy conditions because the standard Casimir energy density of the cylinder spacetime is negative. Finally, we show that the same stress tensor satisfies a quantum inequality on the OUT region.

Within the framework of the two-Higgs-doublet model, we attempt to find some discrete, non-Abelian flavor symmetry that could provide an explanation for the masses and mixing matrix elements of leptons. Unlike the Standard Model, currently there is no need for the flavor symmetry to be broken. With the gap program we investigate all finite subgroups of the U3 group up to the order of 1025. Up to such an order there is no group for which it is possible to select free model parameters in order to match the masses of charged leptons, masses of neutrinos, and the Pontecorvo-Maki-Nakagawa-Sakata mixing matrix elements in a satisfactory manner.