Yang-Mills theory is studied at finite temperature within the Hamiltonian approach in Coulomb gauge by means of the variational principle using a Gaussian-type Ansatz for the vacuum wave functional. Temperature is introduced by compactifying one spatial dimension. As a consequence the finite-temperature behavior is encoded in the vacuum wave functional calculated on the spatial manifold ${\mathbb{R}}^2\times {\mathrm{S}}^1(L)$ where $L^{-1}$ is the temperature. The finite-temperature equations of motion are obtained by minimizing the vacuum energy density to two-loop order. We show analytically that these equations yield the correct zero-temperature limit while at infinite temperature they reduce to the equations of the $2+1$-dimensional theory in accordance with dimensional reduction. The resulting propagators are compared to those obtained from the grand canonical ensemble where an additional Ansatz for the density matrix is required.

We study the quantization of geometry in the presence of a cosmological constant, using a discretization with constant-curvature simplices. Phase space turns out to be compact and the Hilbert space finite dimensional for each link. Not only the intrinsic, but also the extrinsic geometry turns out to be discrete, pointing to the discreteness of time, in addition to space. We work in $2+1$ dimensions, but these results may be relevant also for the physical $3+1$ case.

The integrability conditions for the existence of Killing-Yano tensors or, equivalently, covariantly closed conformal Killing-Yano tensors, in the presence of torsion are worked out. As an application, all metrics and torsions compatible with the existence of a Killing-Yano tensor of order $n-1$ are obtained. Finally, the issue of defining a maximally symmetric space with respect to connections with torsion is addressed.

Loop quantum cosmology tries to capture the main ideas of loop quantum gravity and to apply them to the Universe as a whole. Two main approaches within this framework have been considered to date for the study of cosmological perturbations: the dressed metric approach and the deformed algebra approach. They both have advantages and drawbacks. In this article, we accurately compare their predictions. In particular, we compute the associated primordial tensor power spectra. We show—numerically and analytically—that the large scale behavior is similar for both approaches and compatible with the usual prediction of general relativity. The small scale behavior is, the other way round, drastically different. Most importantly, we show that in a range of wave numbers explicitly calculated, both approaches do agree on predictions that, in addition, differ from standard general relativity and do not depend on unknown parameters. These features of the power spectrum at intermediate scales might constitute a universal loop quantum cosmology prediction that can hopefully lead to observational tests and constraints. We also present a complete analytical study of the background evolution for the bouncing universe that can be used for other purposes.

We develop an exact analytical formulation of neutrino oscillations in matter within the framework of the standard neutrino model assuming three Dirac neutrinos. Our Hamiltonian formulation, which includes $CP$ violation, leads to expressions for the partial oscillation probabilities that are linear combinations of spherical Bessel functions in the eigenvalue differences. The coefficients of these Bessel functions are polynomials in the neutrino CKM matrix elements, the neutrino mass differences squared, the strength of the neutrino interaction with matter, and the neutrino mass eigenvalues in matter. We give exact closed-form expressions for all partial oscillation probabilities in terms of these basic quantities. Adopting the standard neutrino model, we then examine how the exact expressions for the partial oscillation probabilities might simplify by expanding in one of the small parameters $\alpha$ and $\sin {\theta }_{13}$ of this model. We show explicitly that for small $\alpha$ and $\sin {\theta }_{13}$, there are branch points in the analytic structure of the eigenvalues that lead to singular behavior of expansions near the solar and atmospheric resonances. We present numerical calculations that indicate how to use the small-parameter expansions in practice.

Within the QCD factorization approach, we calculate the branching fractions and $CP$ asymmetry parameters of 12 $B\to K_0^{*}(1430)K^{(*)}$ decay modes under the assumption that the scalar meson $K_0^{*}(1430)$ is the first excited state or the lowest-lying ground state in the quark model. We find that the decay modes with the scalar meson emitted have large branching fractions due to the enhancement of the large chiral factor $r_{\chi }^{K_0^{*}}$. The branching fractions of decays with the vector meson emitted become much smaller owing to the smaller factor $r_{\chi }^{K^{*}}$. Moreover, the annihilation-type diagram will induce large uncertainties because of the extra free parameters dealing with the end-point singularity. For the pure annihilation-type decays, our predictions are smaller than those from the perturbative QCD approach by 2–3 orders of magnitude. These results will be tested by the ongoing LHCb experiment, forthcoming Belle-II experiment and the proposing circular electron-positron collider.

Thermal fluctuations and correlations between the light and heavy-light mesons are explored within a chiral effective theory implementing heavy quark symmetry. We show that various heavy-light flavor correlations indicate a remnant of the chiral criticality in a narrow range of temperature in which the chiral susceptibility exhibits a peak structure. The onset of the chiral crossover, in the heavy-light flavor correlations, is therefore independent from the light flavors. This indicates that the fluctuations carried by strange charmed mesons can also be used to identify the chiral crossover, which is dominated by the nonstrange light quark dynamics.

Neutralino pair production via photon-photon collision is analyzed in the context of the minimal supersymmetric standard model at a future linear collider. Since the photon does not have self- coupling, this process is only possible at next-to-leading order (NLO), and all the possible diagrams are calculated for the photon-photon interaction, including box, triangle, and quartic coupling diagrams. Numerical analysis of the production rates for ${\tilde{\chi }}_1^0{\tilde{\chi }}_1^0$, ${\tilde{\chi }}_1^0{\tilde{\chi }}_2^0$ and ${\tilde{\chi }}_2^0{\tilde{\chi }}_2^0$ are presented for four new distinct benchmark models which are presented in the light of LHC8. Angular dependence of each neutralino pair for the benchmark points is also analyzed. Total integrated photonic cross section goes up to 1.43 fb for the ${\tilde{\chi }}_2^0{\tilde{\chi }}_2^0$ pairs at $\sqrt{s}=1\mathrm{TeV}$ for the radiatively driven natural supersymmetric benchmark point.

There is considerable controversy about the size and importance of nonperturbative contributions to the evolution of transverse-momentum-dependent (TMD) parton distribution functions. Standard fits to relatively high-energy Drell–Yan data give evolution that when taken to lower $Q$ is too rapid to be consistent with recent data in semi-inclusive deeply inelastic scattering. Some authors provide very different forms for TMD evolution, even arguing that nonperturbative contributions at large transverse distance $b_{\mathrm{T}}$ are not needed or are irrelevant. Here, we systematically analyze the issues, both perturbative and nonperturbative. We make a motivated proposal for the parametrization of the nonperturbative part of the TMD evolution kernel that could give consistency: with the variety of apparently conflicting data, with theoretical perturbative calculations where they are applicable, and with general theoretical nonperturbative constraints on correlation functions at large distances. We propose and use a scheme- and scale-independent function $A(b_{\mathrm{T}})$ that gives a tool to compare and diagnose different proposals for TMD evolution. We also advocate for phenomenological studies of $A(b_{\mathrm{T}})$ as a probe of TMD evolution. The results are important generally for applications of TMD factorization. In particular, they are important to making predictions for proposed polarized Drell–Yan experiments to measure the Sivers function.

N-particle irreducible effective actions (nPIEA) are a powerful tool for extracting nonperturbative and nonequilibrium physics from quantum field theories. Unfortunately, practical truncations of nPIEA can unphysically violate symmetries. Pilaftsis and Teresi (PT) addressed this by introducing a “symmetry improvement” scheme in the context of the 2PIEA for an O (2) scalar theory, ensuring that the Goldstone boson is massless in the broken symmetry phase [A. Pilaftsis and D. Teresi, Nucl. Phys. B874, 594 (2013)]. We extend this idea by introducing a symmetry improved 3PIEA for $\mathrm{O}(N)$ theories, for which the basic variables are the one-, two- and three-point correlation functions. This requires the imposition of a Ward identity involving the three-point function. We find that the method leads to an infinity of physically distinct schemes, though a field theoretic analogue of d’Alembert’s principle is used to single out a unique scheme. The standard equivalence hierarchy of nPIEA no longer holds with symmetry improvement, and we investigate the difference between the symmetry improved 3PIEA and 2PIEA. We present renormalized equations of motion and counterterms for two- and three-loop truncations of the effective action, though we leave their numerical solution to future work. We solve the Hartree-Fock approximation and find that our method achieves a middle ground between the unimproved 2PIEA and PT methods. The phase transition predicted by our method is weakly first order and the Goldstone theorem is satisfied, while the PT method correctly predicts a second-order phase transition. In contrast, the unimproved 2PIEA predicts a strong first-order transition with large violations of the Goldstone theorem. We also show that, in contrast to PT, the two-loop truncation of the symmetry improved 3PIEA does not predict the correct Higgs decay rate, although the three-loop truncation does, at least to leading order. These results suggest that symmetry improvement should not be applied to $n$PIEA truncated to $<n$ loops. We also show that symmetry improvement schemes are compatible with the Coleman-Mermin-Wagner theorem, giving a check on the consistency of the formalism.

Gravitational wave data from ground-based detectors is dominated by instrument noise. Signals will be comparatively weak, and our understanding of the noise will influence detection confidence and signal characterization. Mismodeled noise can produce large systematic biases in both model selection and parameter estimation. Here we introduce a multicomponent, variable dimension, parametrized model to describe the Gaussian-noise power spectrum for data from ground-based gravitational wave interferometers. Called BayesLine, the algorithm models the noise power spectral density using cubic splines for smoothly varying broadband noise and Lorentzians for narrow-band line features in the spectrum. We describe the algorithm and demonstrate its performance on data from the fifth and sixth LIGO science runs. Once fully integrated into LIGO/Virgo data analysis software, BayesLine will produce accurate spectral estimation and provide a means for marginalizing inferences drawn from the data over all plausible noise spectra.

In the framework of a general scalar-tensor theory, we investigate the equivalence between two different parametrizations of fields that are commonly used in cosmology—the so-called Jordan frame and Einstein frame. While it is clear that both parametrizations are mathematically equivalent at the level of the classical action, the question about their mathematical equivalence at the quantum level as well as their physical equivalence is still a matter of debate in cosmology. We analyze whether the mathematical equivalence still holds when the first quantum corrections are taken into account. We explicitly calculate the one-loop divergences in both parametrizations by using the generalized Schwinger-DeWitt algorithm and compare both results. We find that the quantum corrections do not coincide off shell and hence induce an off-shell dependence on the parametrization. According to the equivalence theorem, the one-loop divergences should however coincide on shell. For a cosmological background, we show explicitly that the on-shell equivalence is indeed realized by a nontrivial cancellation.

We study the vacuum-subtracted von Neumann entropy of a segment on a null plane. We argue that for interacting quantum field theories in more than two dimensions, this entropy has a simple expression in terms of the expectation value of the null components of the stress tensor on the null interval. More explicitly, $\mathrm{\Delta }S=2\pi \int d^{d-2}y{\int }_0^{1}d{x}^{+}g(x^{+})⟨T_{++}⟩$, where $g(x^{+})$ is a theory-dependent function. This function is constrained by general properties of quantum relative entropy. These constraints are enough to extend our recent free field proof of the quantum Bousso bound to the interacting case. This unusual expression for the entropy as the expectation value of an operator implies that the entropy is equal to the modular energy, $\mathrm{\Delta }S=⟨\mathrm{\Delta }K⟩$, where $K$ is the modular Hamiltonian. We explain how this equality is compatible with nonvanishing $\mathrm{\Delta }S$. Finally, we explicitly compute the function $g(x^{+})$ for theories that have a gravity dual.

We improve predictions of the cosmic microwave background (CMB) power spectrum induced by cosmic strings by using source terms obtained from Nambu–Goto network simulations in an expanding universe. We use three high-resolution cosmic string simulations that cover the entire period from recombination until late-time $\mathrm{\Lambda }$ domination to calculate unequal time correlators (UETCs) for scalar, vector, and tensor components of the cosmic string energy-momentum tensor. We calculate the CMB angular power spectrum from strings in two ways. First, to aid comparison with previous work, we fit our simulated UETCs to those obtained from different parameter combinations from the unconnected segment model and then calculate the CMB power spectra using these parameters to represent the string network. Second and more accurately, we decompose the UETCs into their corresponding eigenvalues and eigenvectors and input them directly into an Einstein–Boltzmann solver to calculate the power spectrum for each of the three simulation time periods. We combine the three simulations together, using each of them in its relevant redshift range, and we obtain overall power spectra in temperature and polarization channels. Finally, we use the power spectra obtained with the latest Planck and BICEP2 likelihoods to obtain constraints on the cosmic string tension.

The Planck satellite has identified several patches of sky with low polarized dust emission, obvious targets for searches for the cosmic microwave background $B$-mode signal from inflationary gravitational waves. Still, given the Planck measurement uncertainties, the polarized dust foregrounds in these different candidate patches may differ by an order of magnitude or more. Here we show that a brief initial experiment to map these candidate patches more deeply at a single high frequency can efficiently zero in on the cleanest patch(es) and thus improve significantly the sensitivity of subsequent $B$-mode searches. A ground-based experiment with current detector technology operating at $\gtrsim 220\mathrm{GHz}$ for three months can efficiently identify a low-dust-amplitude patch and thus improve by up to a factor 2 or 3 on the sensitivity to cosmic $B$ modes of the subsequent lower-frequency deep integration. A balloon experiment with current detector sensitivities covering the set of patches and operating at $\sim 350\mathrm{GHz}$ can reach a similar result in less than two weeks. This strategy may prove crucial in accessing the smallest gravitational-wave signals possible in large-field inflation. The high-frequency data from this exploratory experiment should also provide valuable foreground templates to subsequent experiments that integrate on any of the candidate patches explored.

We examine dark matter production rates in supersymmetric (SUSY) axion models typified by the mass hierarchy $m_{3/2}\ll m(\text{neutralino})\ll m(\text{axino})$. In such models, one expects the dark matter to be composed of an axion/gravitino admixture. After presenting motivation for how such a mass hierarchy might arise, we examine dark matter production in the SUSY Kim-Shifman-Vainshtein-Zakharov (KSVZ) model, the SUSY Dine-Fischler-Srednicki-Zhitnitsky (DFSZ) model and a hybrid model containing contributions from both KSVZ and DFSZ. Gravitinos can be produced thermally and also nonthermally from axino, saxion or neutralino decay. We obtain upper bounds on $T_R$ due to overproduction of gravitinos including both the thermal and nonthermal processes. For $T_R$ near the upper bound, dark matter tends to be gravitino dominated, but for $T_R$ well below the upper bounds, axion domination is more typical although in many cases we find a comparable mixture of both axions and gravitinos. In this class of models, we ultimately expect detection of relic axions but no weakly interacting massive particle signal, although SUSY should ultimately be discovered at colliders.

Gaugino mediation is very attractive since it is free from the serious flavor problem in the supersymmetric standard model. We show that the observed Higgs boson mass at around 125 GeV and the anomaly of the muon $g-2$ can be easily explained in gaugino mediation models. It should be noted that no dangerous CP violating phases are generated in our framework. Furthermore, there are large parameter regions which can be tested not only at the planned International Linear Collider but also at the coming 13–14 TeV Large Hadron Collider.

We investigate the possibility of contributions from physics beyond the Standard Model (SM) to the Higgs couplings, in the light of the LHC data. The work is performed within an interim framework where the magnitude of the Higgs production and decay rates are rescaled through Higgs coupling scale factors. We perform Bayesian parameter inference on these scale factors, concluding that there is good compatibility with the SM. Furthermore, we carry out a Bayesian model comparison on all models where any combination of scale factors can differ from their SM values and find that typically models with fewer free couplings are strongly favored. We consider the evidence that each coupling individually equals the SM value, making the minimal assumptions on the other couplings. Finally, we make a comparison of the SM against a single “not-SM” model and find that there is moderate to strong evidence for the SM.

Isospin breaking effects in baryon octet (and decuplet) masses are due to a combination of up and down quark mass differences and electromagnetic effects and lead to small mass splittings. Between the Sigma and Lambda this mass splitting is much larger, this being mostly due to their different wave functions. However when isospin is broken, there is a mixing between these states. We describe the formalism necessary to determine the QCD mixing matrix and hence find the mixing angle and mass splitting between the Sigma and Lambda particles due to QCD effects.