A complete numerical calculation of the temperature anisotropies and polarization of the cosmic microwave background in the presence of a stochastic helical magnetic field is presented which includes the contributions due to scalar, vector and tensor modes. The correlation functions of the magnetic field contributions are calculated numerically including a Gaussian window function to effectively cut off the magnetic field spectrum due to damping. Apart from parity-even correlations the helical nature of the magnetic field induces parity-odd correlations between the $E$ and $B$ mode of polarization as well as between temperature ($T$) and the polarization $B$ mode.

Asymptotically safe theories of gravitation have received great attention in recent times. In this framework an effective action embodying the basic features of the renormalized flow around the non-Gaussian fixed-point is derived and its implications for the early universe are discussed. In particular, a landscape of a countably infinite number of cosmological inflationary solutions characterized by an unstable de Sitter phase lasting for a large enough number of e-folds is found.

We derive bounds on the dark matter annihilation cross-section for low-mass (5–20 GeV) dark matter annihilating primarily to up or down quarks, using the Fermi-LAT bound on gamma-rays from Milky Way satellites. For models in which dark matter-Standard Model interactions are mediated by particular contact operators, we show that these bounds can be directly translated into bounds on the dark matter-proton scattering cross section. For isospin-violating dark matter, these constraints are tight enough to begin to constrain the parameter-space consistent with experimental signals of low-mass dark matter. We discuss possible models that can evade these bounds.

Direct detection strategies are proposed for dark matter particles with MeV to GeV mass. In this largely unexplored mass range, dark matter scattering with electrons can cause single-electron ionization signals, which are detectable with current technology. Ultraviolet photons, individual ions, and heat are interesting alternative signals. Focusing on ionization, we calculate the expected dark matter scattering rates and estimate the sensitivity of possible experiments. Backgrounds that may be relevant are discussed. Theoretically interesting models may be within reach using existing data and ongoing direct detection experiments. Significant improvements in sensitivity should be possible with dedicated experiments, opening up a window to new regions in dark matter parameter space.

Within the QCD factorization formalism, we study the possible impacts of the nonuniversal $Z^{\prime }$ model, which provides a flavor-changing neutral current at the tree level, on rare decays $B\to K_0^{*}(1430)\pi$. Under two different scenarios, Scenerio-1 (S1) and Scenerio-2 (S2), for identifying the scalar meson $K_0^{*}(1430)$, the branching ratios, $CP$ asymmetries, and isospin asymmetries are calculated in both the standard model and the family nonuniversal $Z^{\prime }$ model. We find that the branching ratios and $CP$ asymmetries are sensitive to weak annihilation. In the standard model, with ${\rho }_A=1$ and ${\varphi }_A\in [-30°,30°]$, the branching ratios of S1 (S2) are smaller (larger) than the experimental data. Adding the contribution of the $Z^{\prime }$ boson in two different cases (Case I and Case II), for S1, the branching ratios are still far away from experiment. For S2, in Case II, the branching ratios become smaller and can accommodate the data; in Case I, although the center values are enhanced, they can also explain the data with large uncertainties. Similar conclusions are also reached for $CP$ asymmetries. Our results indicate that S2 is more favored than S1, even after considering new physics effects. Moreover, if there exists a nonuniversal $Z^{\prime }$ boson, Case II is preferred. All results can be tested in the LHC-b experiment and forthcoming super-$B$ factory.

The unitarity condition unambiguously requires the Orear region to appear in between the diffraction cone at low transferred momenta and the hard parton scattering regime at high transferred momenta in hadron elastic scattering. It originates from rescattering of the diffraction cone processes. It is shown that such a region has been observed in the differential cross-section of the elastic $pp$-scattering at $\sqrt{s}=7\mathrm{TeV}$. The Orear region is described by exponential decrease with the scattering angle, and imposed on it damped oscillations. They explain the steepening at the end of the diffraction cone as well as the dip and the subsequent maximum observed in TOTEM data. The failure of several models to describe the data in this region can be understood as an improper account of the unitarity condition. It is shown that the real part of the amplitude can be as large as the imaginary part in this region. The overlap function is calculated and shown to be small outside the diffraction peak. Its negative sign there indicates the important role of phases in the amplitudes of inelastic processes.

We present an attempt of global analysis of semi-inclusive deep inelastic scattering $\ell p^{\uparrow }\to {\ell }^{\prime }\pi X$ data on single spin asymmetries and data on left-right asymmetry $A_N$ in $p^{\uparrow }p\to \pi X$ in order to simultaneously extract information on the Sivers function and the twist-three quark-gluon Efremov-Teryaev-Qiu-Sterman function. We explore different possibilities such as the node of the Sivers function in $x$ or $k_{\perp }$ in order to explain “sign mismatch” between these functions. We show that ${\pi }^{\pm }$ semi-inclusive deep inelastic scattering data and ${\pi }^0$ STAR data can be well described in a combined fit based on both the transverse momentum dependent and collinear twist-three factorization formalisms; however, ${\pi }^{\pm }$ BRAHMS data are not described in a satisfactory way. This leaves the question open of a solution to the “sign mismatch.” Possible explanations are then discussed.

We show that the more energetic superluminal neutrinos with quadratically dispersed superluminalities $\delta ={\beta }^2-1$, for $\beta =v/c$ where $v$ is the neutrino velocity, also lose significant energy to radiation to the $\nu +e^{-}+e^{+}$ final state in traveling from CERN to Gran Sasso as has been shown to occur for those with constant superluminality by Cohen and Glashow if indeed $\delta \simeq 5\times {10}^{-5}$. In addition, we clarify the dependence of such radiative processes on the size of the superluminality.

Unbroken continuous translational invariance is often taken as a basic assumption in discussions of spontaneous symmetry breaking (SSB), which singles out SSB of translational invariance itself as an exceptional case. We present a framework that allows us to treat translational invariance on the same footing as other symmetries. It is shown that existing theorems on SSB can be straightforwardly extended to this general case. As a concrete application, we analyze the Nambu-Goldstone modes in a (ferromagnetic) supersolid. We prove on the ground of the general theorems that the Bogoliubov mode stemming from a spontaneously broken internal U(1) symmetry and the longitudinal phonon due to a crystalline order are distinct physical modes.

We study the possibility of constructing Lorentz-violating supersymmetric quantum field theories under the assumption that these theories have to be described by Lagrangians which are renormalizable by weighted power counting. Our investigation starts from the observation that at high energies Lorentz-violation and the usual supersymmetry algebra are algebraically compatible. Demanding linearity of the supercharges, we see that the requirement of renormalizability drastically restricts the set of possible Lorentz-violating supersymmetric theories. In particular, in the case of supersymmetric gauge theories the weighted power counting has to coincide with the usual one and the only Lorentz-violating operators are introduced by some weighted constant $c$ that explicitly appears in the supersymmetry algebra. This parameter does not renormalize and has to be very close to the speed of light at low energies in order to satisfy the strict experimental bounds on Lorentz violation. The only possible models with nontrivial Lorentz-violating operators involve neutral chiral superfields and do not have a gauge invariant extension. We conclude that, under the assumption that high-energy physics can be described by a Lorentz-violating extension of the standard model which is renormalizable by weighted power counting, the Lorentz fine tuning problem does not seem solvable by the requirement of supersymmetry.

Rastall’s theory is based on the nonconservation of the energy-momentum tensor. We show that, in this theory, if we introduce a two-fluid model, one component representing vacuum energy whereas the other pressureless matter (e.g. baryons plus cold dark matter), the cosmological scenario is the same as for the $\Lambda \mathrm{CDM}$ model, both at background and linear perturbation levels, except for one aspect: now dark energy may cluster. We speculate that this can lead to a possibility of distinguishing the models at the nonlinear perturbation level.

Using the operator approach, we obtain quasinormal modes (QNMs) of the Bañados-Teitelboim-Zanelli black hole in spin-3 topologically massive gravity by solving the first-order equation of motion with the transverse-traceless condition. We find that these are different from those obtained when solving the second-order differential equation for the third-rank tensor of spin-3 field subject to suitable boundary conditions and having the sign ambiguity of mass. However, it is shown clearly that two approaches to the left-moving QNMs are identical, while the right-moving QNMs of solving the second-order equation are given by descendants of the operator approach.

In this paper, the dependency of $P_{ij}$’s on the dilepton invariant mass, $q^2$, and the model III two-Higgs-doublets model (2HDM) parameters for $B\to K_0^{*}(1430){\ell }^{+}{\ell }^{-}$ decay were investigated, and the results were compared to those of the standard model (SM) and Appelquist, Cheng and Dobrescu model. Also, for this decay, the effects of model III 2HDM parameters on the averages of double-lepton polarization asymmetries, $⟨P_{ij}⟩$’s, were studied, and by taking into account the corresponding theoretical and experimental errors in the SM, the results of the SM and 2HDM were compared to each other. In addition, by comparing the averages of double-lepton polarization asymmetries in 2HDM to those of SM4 and obtaining the required number of events for detecting each asymmetry at the LHC or the Super Large Hadron Collider, we present a comprehensive discussion regarding the lepton polarizations of $B\to K_0^{*}{\ell }^{+}{\ell }^{-}$ decay. We discovered that the study of the double-lepton polarization asymmetries and the corresponding averages in the $B\to K_0^{*}(1430){\ell }^{+}{\ell }^{-}$ decay can provide good signals for probing new physics beyond the SM in the future $B$-physics experiments.

We present a calculation of the leading-order hadronic contribution to the anomalous magnetic moment of the muon for a dynamical simulation of $2+1$ flavor QCD using domain wall fermions. The electromagnetic 2-point function is evaluated on the lattice gauge configurations and this is fitted to a continuous form motivated by models of vector dominance. We find broad agreement with previous lattice results for this quantity, while improvements in simulation and theory are clearly needed in order to produce satisfactorily precise results.

We introduce a two-flavor quark-meson-diquark model for two-color QCD and its extensions to include gauge-field dynamics as described by the Polyakov loop. Grand potential and phase structure are being studied both in mean-field approximation and with the functional renormalization group. The model provides an explicit example for the importance of baryonic degrees of freedom: When they are omitted, the phase diagram closely resembles that of the corresponding (Polyakov)-quark-meson models for QCD, in particular, including their critical endpoint. In order to reproduce the well-established main features based on the symmetries and breaking patterns of two-color QCD, however, they must be included and there is no critical endpoint. The competing dynamics of collective mesonic and baryonic fluctuations is well described by the functional renormalization group equation in lowest-order derivative expansion for the effective potential, which we solve numerically on a two-dimensional grid in field space.

Several proposals for studying neutrinos with large detectors are currently under discussion. We suggest that they could provide a precise measurement of the electroweak mixing angle as well as a probe for new physics, such as nonstandard neutrino interactions, and the electroweak gauge structure. We illustrate this explicitly for the case of the LENA proposal, either with an artificial radioactive source or by using the solar neutrino flux.

After imposing the Gauss law constraint as an initial condition upon the Hilbert space of the Nambu model, in all its generic realizations, we recover QED in the corresponding nonlinear gauge $A_{\mu }{A}^{\mu }=n^2{M}^2$. Our result is nonperturbative in the parameter $M$ for $n^2\ne 0$ and can be extended to the $n^2=0$ case. This shows that, in the Nambu model, spontaneous Lorentz symmetry breaking dynamically generates gauge invariance, provided the Gauss law is imposed as an initial condition. In this way, electrodynamics is recovered, with the photon being realized as the Nambu-Goldstone modes of the spontaneously broken symmetry, which finally turns out to be nonobservable.

An explicit and detailed investigation about the two-dimensional single axial-vector ($AVV$) triangle is performed. Such a perturbative amplitude is related to the anomalous axial-vector ($AV$) one through contractions with external momenta. Given this fact, before considering such a triangle we must give a clear point of view for the $AV$ amplitude. Such a point of view is constructed within the context of an alternative strategy to handle the divergences typical of perturbative solutions of quantum field theory. In this procedure all amplitudes in all theories, formulated in odd and even space-time dimensions, renormalizable or not, are treated in an absolutely identical way. The ambiguities are automatically eliminated and the symmetry relations preserved. The well-known divergent anomalous amplitudes are correctly described, in a predictive scenario. After performing, in a very detailed way, all the calculations involved we conclude that the same phenomenon occurring in the $AV$ amplitude is also present in the finite $AVV$ triangle. The conclusion gives support to the thesis that the phenomenon is present in all pseudoamplitudes in a chain where the divergent $AV$ one is only the most simple structure. The same must occur in all even space-time dimensions. In particular, the single and triple four-dimensional box amplitudes must exhibit anomalies too. A conclusive investigation is allowed due to the special features of the adopted procedure where regularization is completely avoided and an adequate systematization for the finite parts is introduced.

We studied different levels of resummations of the exactly solvable Bloch-Nordsieck model in order to be able to compare the approximations with an exact result. We studied one-loop perturbation theory, two-particle-irreducible resummation and Schwinger-Dyson equations truncated in a way to maintain Ward identities. At all levels we carefully performed renormalization. We found that although the two-particle-irreducible resummation does not exhibit infrared sensitivity at the mass shell, as the one-loop perturbation theory does, it is still far from the exact solution. The method of truncated renormalized Schwinger-Dyson equations, however, is exact in this model, so it provides a new way of solving the Bloch-Nordsieck model. This method may also be generalized to other, more complicated theories.