In this paper we study the structure of the phase space in noncommutative geometry in the presence of a nontrivial frame. Our basic assumptions are that the underlying space is a symplectic and parallelizable manifold. Furthermore, we assume the validity of the Leibniz rule and the Jacobi identities. We consider noncommutative spaces due to the quantization of the symplectic structure and determine the momentum operators that guarantee a set of canonical commutation relations, appropriately extended to include the nontrivial frame. We stress the important role of left vs right acting operators and of symplectic duality. This enables us to write down the form of the full phase space algebra on these noncommutative spaces, both in the noncompact and in the compact case. We test our results against the class of four-dimensional and six-dimensional symplectic nilmanifolds, thus presenting a large set of nontrivial examples that realizes the general formalism.

Motivated by issues on inflation, a generalized modified gravity model is investigated, where the model Lagrangian is described by a smooth function $f(R,K,\varphi )$ of the Ricci scalar $R$, the kinetic term $K$ of a scalar field $\varphi$. In particular, the one-loop effective action in the de Sitter background is examined on shell as well as off shell in the Landau gauge. In addition, the on-shell quantum equivalence of $f(R)$ gravity in the Jordan and Einstein frames is explicitly demonstrated. Furthermore, we present applications related to the stability of the de Sitter solutions and the one-loop quantum correction to inflation in quantum-corrected $R^2$ gravity. It is shown that, for a certain range of parameters, the spectral index of the curvature perturbations can be consistent with the Planck analysis, but the tensor-to-scalar ratio is smaller than the minimum value within the $1\sigma$ error range of the BICEP2 result.

This is a continuation of the paper published in Phys. Rev. D 89, 023520 (2014). Here we investigate how the luminosity distance–redshift relation $D_L(z)$ of the $\mathrm{\Lambda }$CDM model is duplicated in the Lemaître-Tolman (L-T) model with $\mathrm{\Lambda }=0$, constant bang-time function $t_B$ and the energy function $E(r)$ mimicking accelerated expansion on the observer’s past light cone ($r$ is a uniquely defined comoving radial coordinate). Numerical experiments show that $E>0$ necessarily. The functions $z(r)$ and $E(r)$ are numerically calculated from the initial point at the observer’s position, then backward from the initial point at the apparent horizon (AH). Reconciling the results of the two calculations allows one to determine the values of $E/r^2$ at $r=0$ and at the AH. The problems connected with continuing the calculation through the AH are discussed in detail and solved. Then $z(r)$ and $E(r)$ are continued beyond the AH, up to the numerical crash that signals the contact of the light cone with the big bang. Similarly, the light cone of the L-T model is calculated by proceeding from the two initial points, and compared with the $\mathrm{\Lambda }\mathrm{CDM}$ light cone. The model constructed here contains shell crossings, but they can be removed by matching the L-T region to a Friedmann background, without causing any conflict with the type Ia supernovae observations. The mechanism of imitating the accelerated expansion by the $E(r)$ function is explained in a descriptive way.

We study the spin-independent neutralino dark matter scattering off heavy nuclei in the minimal supersymmetric Standard Model. We identify analytically the blind spots in direct detection for intermediate values of $m_A$. In the region where $\mu$ and $M_{1,2}$ have opposite signs, there is not only a reduction of the lightest $CP$-even Higgs coupling to neutralinos, but also a destructive interference between the neutralino scattering through the exchange of the lightest $CP$-even Higgs and that through the exchange of the heaviest $CP$-even Higgs. At critical values of $m_A$, the tree-level contribution from the light Higgs exchange cancels the contribution from the heavy Higgs, so the scattering cross section vanishes. We denote these configurations as blind spots, since they provide a generalization of the ones previously discussed in the literature, which occur at very large values of $m_A$. We show that the generalized blind spots may occur in regions of parameter space that are consistent with the obtention of the proper neutralino relic density and can be tested by nonstandard Higgs boson searches and EWino searches at the LHC and future linear colliders.

We argue that deep inelastic scattering (DIS) at small values of $Q^2$ is an essentially nonperturbative process and can be described, partially at least, by the vector meson dominance (VMD) model. We show this by the straightforward calculation that the VMD model alone can successfully explain data on structure functions of DIS in a broad interval of $x(5\times {10}^{-2}÷{10}^{-4})$ for the region $Q^2\le 1{\text{GeV}}^2$. For a description of data at larger $Q^2$ we use the two-component ($\mathrm{VMD}+\text{perturbative}\mathrm{QCD}$) approach. We show that these two components can be separated if VMD is used in the aligned jet version. We take into account, in calculations of the VMD component of structure functions, the excited states of the $\rho$-meson and nondiagonal transitions between different members of the $\rho$-meson family. Amplitudes of these transitions arre obtained using a formalism of the light-front Bethe-Salpeter equation and the method of diffraction-scattering eigenstates. The perturbative QCD component is calculated using a framework of the color dipole model with the dipole cross section having a Regge-type energy dependence. We present results of the detailed comparison of our predictions with experimental data for structure functions of the nucleon. We also obtain approximate predictions for the structure functions in the region of very small $x$, up to ${10}^{-8}÷{10}^{-9}$, and show that the nonperturbative component at such values of $x$ is still relatively large and must be taken into account if $Q^2$ is about a few ${\mathrm{GeV}}^2$ or less.

We discuss the connection between the origin of neutrino masses and their mixings, which arises in a class of scenarios with radiatively induced neutrino masses. In these scenarios, the neutrino mass matrix acquires textures with two entries close to zero in the basis where the charged-lepton mass matrix is diagonal. This results in specific constraints on the neutrino mixing parameters, which leads to the prediction of (i) a normal ordering of neutrino masses with the lightest neutrino mass in the $\sim \mathrm{meV}$ range and (ii) testable correlations among the various mixing angles, including a nonzero ${\theta }_{13}$ angle with its exact value correlated with the values of the atmospheric angle ${\theta }_{23}$ and the $CP$ phase $\delta$. We quantify the impact of deviations from exact zeroes in the mass matrix texture and connect it to the amount of hierarchy among Yukawa couplings. These scenarios of radiative neutrino mass generation also give rise to new short-range contributions to neutrinoless double beta decay, which dominate over the usual light-neutrino exchange contribution. As a result, this class of models can have a sizable neutrinoless double beta decay rate, in the range of upcoming experiments despite the normal mass ordering of neutrinos.

We derive nonrelativistic equations of motion for the formation of cosmological structure in a scalar field dark matter (SFDM) model corresponding to a complex scalar field endowed with a quadratic scalar potential. Starting with the equations of motion written in the Newtonian gauge of scalar perturbations, we separate out the involved fields into relativistic and nonrelativistic parts and find the equations of motion for the latter that can be used to build up the full solution. One important assumption will be that the SFDM field is in the regime of fast oscillations, under which its behavior in the homogeneous regime is exactly that of cold dark matter. The resultant equations are quite similar to the Schrödinger-Poisson system of Newtonian boson stars plus relativistic leftovers, and they can be used to study the formation of cosmological structure in SFDM models, and others alike, to ultimately prove their viability as complete dark matter models.

Astrophysical tests of the stability of dimensionless fundamental couplings, such as the fine-structure constant $\alpha$, are an area of much increased recent activity, following some indications of possible spacetime variations at the few parts per million level. Here we obtain updated constraints on the Bekenstein-Sandvik-Barrow-Magueijo model, which is arguably the simplest model allowing for $\alpha$ variations. Recent accurate spectroscopic measurements allow us to improve previous constraints by about an order of magnitude. We briefly comment on the dependence of the results on the data sample, as well as on the improvements expected from future facilities.

Anti-de Sitter plane wave backgrounds are dual to conformal field theory excited states with energy momentum density $T_{++}=Q$. Building on previous work on entanglement entropy in these and nonconformal brane plane wave backgrounds, we first describe a phenomenological scaling picture for entanglement in terms of “entangling partons.” We then study aspects of holographic mutual information in these backgrounds for two strip shaped subsystems, aligned parallel or orthogonal to the flux. We focus on the wide ($Q{l}^d\gg 1$) and narrow ($Q{l}^d\ll 1$) strip regimes. In the wide strip regime, mutual information exhibits growth with the individual strip sizes, and a disentangling transition as the separation between the strips increases, for which the behavior is distinct from the ground and thermal states. In the narrow strip case, our calculations have parallels with “entanglement thermodynamics” for these anti-de Sitter plane wave deformations. We also discuss some numerical analyses.

We compute the partition function and specific heat for a quantum-mechanical particle under the influence of a quartic double-well potential nonperturbatively, using the semiclassical method. Near the region of bounded motion in the inverted potential, the usual quadratic approximation fails due to the existence of multiple classical solutions and caustics. Using the tools of catastrophe theory, we identify the relevant classical solutions, showing that at most two have to be considered. This corresponds to the first step towards the study of spontaneous symmetry breaking and thermal phase transitions in the nonperturbative framework of the boundary effective theory.

In the so-called Yukawaon model, the (effective) Yukawa coupling constants $Y_f^{\text{eff}}$ are given by vacuum expectation values (VEVs) of scalars $Y_f$ (Yukawaons) with $3\times 3$ components. In the present model, all of the VEV matrices $⟨Y_f⟩$ are given by a bilinear form of VEVs of flavons ${\mathrm{\Phi }}_f$, ${{⟨Y_f⟩}_i}^j=k_f⟨{\mathrm{\Phi }}_f{⟩}_{ik}⟨{\overline{\mathrm{\Phi }}}_f{⟩}^{kj}$, where ${\mathrm{\Phi }}_f$ is assigned to $\mathbf{6}$ of U(3) family symmetry. As input parameters with family number–dependent values, we use only charged lepton mass values. Under this formulation, we can give reasonable values of quark and lepton masses and their mixings. A $CP$-violating phase ${\delta }_{CP}^{\ell }=\pm 26°$ in the lepton sector is predicted. The effective Majorana neutrino mass is also predicted.

Particle-number-violating interactions wash out the primordial asymmetry of the particle number density generated by some interaction satisfying Sakharov conditions for baryogenesis. In this paper, we study how the primordial asymmetry evolves in time under the presence of particle-number-violating interactions and in the environment of an expanding universe. We introduce a complex scalar model with particle-number-violating mass terms and calculate the time evolution of the particle number density with nonequilibrium quantum field theory. We show how the time evolution of the number density depends on parameters, including the chemical potential related to the particle number, temperature, the size of the particle-number-violating mass terms, and the expansion rate of the universe. The number density behaves differently depending upon whether the chemical potential is larger or smaller than the rest mass of the scalar particle. When the chemical potential is smaller than the mass, the interference among the contribution of oscillators with various momenta reduces the number density in addition to the dilution due to the expansion of the universe. In the opposite case, the oscillation of the particle number density lasts for a long time and the cancellation due to the interference does not occur.

We present the inclusive transverse momentum distribution for Higgs bosons produced in bottom quark annihilation at the LHC. The results are obtained in the five-flavor scheme. The soft and collinear terms at small $p_T$ are resummed through NNLL accuracy and matched to the NNLO transverse momentum distribution at large $p_T$. We find that the theoretical uncertainty, derived from a variation of the unphysical scales entering the calculation, is significantly reduced with respect to lower orders.

We will explore the consequences on the electroweak breaking condition, the mass of supersymmetric partners and the scale at which supersymmetry breaking is transmitted, for arbitrary values of the supersymmetric parameters $\tan \beta$ and the stop mixing $X_t$, which follow from the Higgs discovery with a mass $m_H\simeq 126\mathrm{GeV}$ at the LHC. Within the present uncertainty on the top quark mass we deduce that radiative breaking requires $\tan \beta \gtrsim 8$ for maximal mixing $X_t\simeq \sqrt{6}$, and $\tan \beta \gtrsim 20$ for small mixing $X_t\lesssim 1.8$. The scale at which supersymmetry breaking is transmitted $\mathcal{M}$ can be of order the unification or Planck scale only for large values of $\tan \beta$ and negligible mixing $X_t\simeq 0$. On the other hand for maximal mixing and large values of $\tan \beta$ supersymmetry should break at scales as low as $\mathcal{M}\simeq {10}^5\mathrm{GeV}$. The uncertainty in those predictions stemming from the uncertainty in the top quark mass, i.e. the top Yukawa coupling, is small (large) for large (small) values of $\tan \beta$. In fact for $\tan \beta =1$ the uncertainty on the value of $\mathcal{M}$ is several orders of magnitude.

We have been studying QCD with two flavors of color-sextet quarks as a candidate walking-technicolor theory using lattice-QCD simulations. The evolution of the coupling constant with lattice spacing is measured at the finite-temperature chiral transition to determine if this theory is asymptotically free and hence QCD-like. The lattice spacing is varied by changing the number of lattice sites, $N_t$, in the Euclidean time direction. QCD with three flavors is studied for comparison. Since this theory is expected to be conformal, with an infrared fixed point, the coupling constant at the chiral transition should approach a nonzero value as $N_t$ becomes large. Our earlier simulations on lattices with $N_t=4$ and $N_t=6$ exhibited a significant decrease in coupling at the chiral transition as $N_t$ was increased. We have now extended these simulations to $N_t=8$, and performed additional simulations at $N_t=6$ to measure the coupling constant at the chiral transition more precisely. These indicate that while there is an appreciable decrease in coupling between $N_t=6$ and $N_t=8$, this is much smaller than that between $N_t=4$ and $N_t=6$. Thus we are hopeful that we are approaching the large-$N_t$ limit. However, further simulations at larger $N_t(\mathrm{s})$ are needed.

We construct a new kinematical variable that is able to fully reconstruct the absolute value, and partially reconstruct the sign, of the angular distribution in the center of momentum system of a decaying particle in certain cases where the center of momentum system is only known up to a twofold ambiguity. After making contact with Drell-Yan production at the Large Hadron Collider, we apply this method to the pair production of dark matter in association with two charged leptons at the International Linear Collider and show that for a small intermediate width, perfect agreement is found with the true angular distribution in the absence of initial state radiation. In the presence of initial state radiation, we find that the modification to the angular distributions is small for most angles and that different spin combination classes should still be distinguishable. This enables us to determine the spin of the mother particle and the dark-matter particle in certain cases.

We calculate the Wigner functions for a quark target dressed with a gluon at one loop in perturbation theory. The Wigner distributions give the combined position and momentum space information of the quark distributions and are related to both generalized parton distributions and transverse momentum dependent parton distributions. We calculate and compare the different definitions of quark orbital angular momentum and the spin-orbit correlations in this perturbative model. We compare our results with other model calculations.

In CMS data at the CERN Large Hadron Collider, the ratio $\sigma (pp\to {\overline{\mathrm{\Lambda }}}_{b}X)/\sigma (pp\to {\mathrm{\Lambda }}_{b}X)$ appears to fall as the baryons become more forward. Mechanisms which could give rise to this effect are discussed. It is urged that the same physics be explored in data from the ATLAS and LHCb detectors at CERN and the Fermilab Tevatron proton-antiproton collider. In the latter, if such leading-baryon effects are present, one expects ${\mathrm{\Lambda }}_b$ to be preferentially produced in the direction of the proton and ${\overline{\mathrm{\Lambda }}}_b$ to be preferentially produced in the direction of the antiproton.

For the first time in the literature, we discuss the production of a four-jet final state in proton-proton collisions at the LHC through the mechanism of double-parton scattering (DPS), in the context of jets with large rapidity separation. This is the region where searches for a Balitsky-Fadin-Kuraev-Lipatov (BFKL) signal are planned and/or being performed. The DPS contributions are calculated within the so-called factorized ansatz, and each step of DPS is calculated in the leading order (LO) collinear approximation. The LO pQCD calculations are shown to give a reasonably good description of recent CMS and ATLAS data on inclusive jet production; therefore, this formalism can be used to estimate the DPS effects. We demonstrate that the relative contribution (with respect to single parton scattering dijets and to the BFKL Mueller-Navelet jets) of DPS is growing at large rapidity distance between jets. This is consistent with our experience from previous studies of DPS effects in the case of open and hidden charm production. The calculated differential cross sections, as a function of rapidity distance between the jets that are the most remote in rapidity, are compared with recent results of leading logarithm and next-to-leading logarithm BFKL calculations for the Mueller-Navelet jet production at $\sqrt{s}=7\mathrm{TeV}$. The DPS contribution to widely rapidity separated jet production is carefully studied for the present energy $\sqrt{s}=7\mathrm{TeV}$, and also at the nominal LHC energy $\sqrt{s}=14\mathrm{TeV}$ and in different ranges of jet transverse momenta. The differential cross section as a function of dijet transverse momenta as well as two-dimensional ($p_T(y_{\min })\times p_T(y_{\max })$)-plane correlations for DPS mechanism are also presented. Some ideas as to how the DPS effects could be studied in the case of four-jet production are suggested.

The axial-vector mesons $a_1(1260)$, $b_1(1235)$, $f_1(1285)$, $h_1(1170)$, $h_1(1380)$, and $K_1(1270)$ are dynamically generated in the unitized chiral perturbation theory. Such a picture has been tested extensively in the past few years. In this work, we calculate the interaction kernel up to $\mathcal{O}(p^2)$ and study the impact on the dynamically generated axial-vector states. In anticipation of future lattice QCD simulations, we calculate the scattering lengths and the pole positions as functions of the pion mass, with the light-quark mass dependence of the kaon, the eta, and the vector mesons determined by the $n_f=2+1$ lattice QCD simulations of the PACS-CS Collaboration.