We explore the consequences of the neutrino mass matrix having a hidden ${\mathcal{Z}}_2$ symmetry and one zero eigenvalue. When implemented, these two conditions give relations among the mixing angles. In addition, fitting these relations to the existing oscillation data allows limits to be placed on the parameter of the symmetry.

Conformal low-spin anomalous currents and shadow fields in flat space-time of dimensions greater than or equal to four are studied. The gauge invariant formulation for such currents and shadow fields is developed. Gauge symmetries are realized by involving Stueckelberg and auxiliary fields. The gauge invariant differential constraints for anomalous currents and shadow fields and the realization of global conformal symmetries are obtained. Gauge invariant two-point vertices for anomalous shadow fields are also obtained. In the Stueckelberg gauge frame, these gauge invariant vertices become the standard two-point vertices of conformal field theory. Light-cone gauge two-point vertices of the anomalous shadow fields are derived. The AdS/CFT correspondence for anomalous currents and shadow fields and the respective normalizable and non-normalizable solutions of massive low-spin anti–de Sitter fields is studied. The bulk fields are considered in a modified de Donder gauge that leads to decoupled equations of motion. We demonstrate that leftover on-shell gauge symmetries of bulk massive fields correspond to gauge symmetries of boundary anomalous currents and shadow fields, while the modified (Lorentz) de Donder gauge conditions for bulk massive fields correspond to differential constraints for boundary anomalous currents and shadow fields.

We compute the QCD phase diagram in the plane of the chiral chemical potential and temperature using the linear sigma model coupled to quarks and to the Polyakov loop. The chiral chemical potential accounts for effects of imbalanced chirality due to QCD sphaleron transitions which may emerge in heavy-ion collisions. We found three effects caused by the chiral chemical potential: the imbalanced chirality (i) tightens the link between deconfinement and chiral phase transitions; (ii) lowers the common critical temperature; (iii) strengthens the order of the phase transition by converting the crossover into the strong first order phase transition passing via the second order end point. Since the fermionic determinant with the chiral chemical potential has no sign problem, the chirally imbalanced QCD matter can be studied in numerical lattice simulations.

We investigate the linearized form of metric $f(R)$-gravity, assuming that $f(R)$ is analytic about $R=0$ so it may be expanded as $f(R)=R+a_2{R}^2/2+\dots$. Gravitational radiation is modified, admitting an extra mode of oscillation, that of the Ricci scalar. We derive an effective energy-momentum tensor for the radiation. We also present weak-field metrics for simple sources. These are distinct from the equivalent Kerr (or Schwarzschild) forms. We apply the metrics to tests that could constrain $f(R)$. We show that light deflection experiments cannot distinguish $f(R)$-gravity from general relativity as both have an effective post-Newtonian parameter $\gamma =1$. We find that planetary precession rates are enhanced relative to general relativity; from the orbit of Mercury we derive the bound $|a_2|\lesssim 1.2\times {10}^{18}{\mathrm{m}}^2$. Gravitational-wave astronomy may be more useful: considering the phase of a gravitational waveform we estimate deviations from general relativity could be measurable for an extreme-mass-ratio inspiral about a ${10}^6{M}_{\odot }$ black hole if $|a_2|\gtrsim {10}^{17}{\mathrm{m}}^2$, assuming that the weak-field metric of the black hole coincides with that of a point mass. However Eöt-Wash experiments provide the strictest bound $|a_2|\lesssim 2\times {10}^{-9}{\mathrm{m}}^2$. Although the astronomical bounds are weaker, they are still of interest in the case that the effective form of $f(R)$ is modified in different regions, perhaps through the chameleon mechanism. Assuming the laboratory bound is universal, we conclude that the propagating Ricci scalar mode cannot be excited by astrophysical sources.

For a large class of space and time-dependent warped geometries we find the general solution of the six-dimensional Einstein-Gauss-Bonnet equations in the presence of $p$-form matter fields. This is done under two conditions on the matter sector which we show impose the integrability of the full system. Solutions are classified and known black hole limits are found. It is shown that Lovelock gravity restricts drastically the possible horizon geometries and allowed matter sources. In fact, we show that if we allow only for solutions of asymptotically flat falloff behavior, then the only permissible black hole is that of Boulware-Deser with electromagnetic charge. The situation of six-dimensional Lovelock gravity is therefore almost identical to four-dimensional General Relativity. The gravitational horizon constraints lead us to find static solutions involving 3-form matter fields in anti de Sitter space which are also new to General Relativity along with other cosmological and black string type of solutions.

We explore cosmology in the decoupling limit of a nonlinear covariant extension of Fierz-Pauli massive gravity obtained recently in arXiv:1007.0443. In this limit the theory is a scalar-tensor model of a unique form defined by symmetries. We find that it admits a self-accelerated solution, with the Hubble parameter set by the graviton mass. The negative pressure causing the acceleration is due to a condensate of the helicity-0 component of the massive graviton, and the background evolution, in the approximation used, is indistinguishable from the $\Lambda \mathrm{CDM}$ model. Fluctuations about the self-accelerated background are stable for a certain range of parameters involved. Most surprisingly, the fluctuation of the helicity-0 field above its background decouples from an arbitrary source in the linearized theory. We also show how massive gravity can remarkably screen an arbitrarily large cosmological constant in the decoupling limit, while evading issues with ghosts. The obtained static solution is stable against small perturbations, suggesting that the degravitation of the vacuum energy is possible in the full theory. Interestingly, however, this mechanism postpones the Vainshtein effect to shorter distance scales. Hence, fifth force measurements severely constrain the value of the cosmological constant that can be neutralized, making this scheme phenomenologically not viable for solving the old cosmological constant problem. We briefly speculate on a possible way out of this issue.

We study the numerical effects of several renormalization schemes of the Cabibbo-Kobayashi-Maskawa (CKM) quark mixing matrix on the top-quark decay widths. We then employ these results to infer the relative shifts in the CKM parameters $|V_{tq}{|}^2$ due to the quark mixing renormalization corrections, assuming that they are determined directly from the top-quark partial decay widths, without imposing unitarity constraints. We also discuss the implications of these effects on the ratio $\mathcal{R}=\Gamma (t\to Wb)/{\Gamma }_t$ and the determination of $|V_{tb}{|}^2$.

It is shown that the study of correlations in the associative production of $B_c$ and $\overline{D}$ mesons at LHC allows one to obtain essential information about the $B_c$ production mechanism.

We calculate the pion-pion elastic scattering phase shifts for pion masses from the chiral limit to values of interest for lattice studies. At low energies, we use the standard Chiral Perturbation Theory expressions to one and two loops. In addition, we study the phase shifts’ mass dependence in the resonance region by means of dispersion theory in the form of unitarized Chiral Perturbation Theory and the inverse amplitude method. We pay particular attention to the case when resonances are close to threshold, illustrating the different behavior between scalar and vector resonances. We also provide the estimation of uncertainties, which are dominated by those of the $O(p^6)$ chiral parameters.

We study the anomalous electromagnetic pion form factor $F_{{\pi }^0{\gamma }^{*}{\gamma }^{*}}$ with a set of holographic models. By comparing with the measured value of the linear slope, some of these models can be ruled out. From the remaining models, we obtain predictions for the low-energy quadratic slope parameters of $F_{{\pi }^0{\gamma }^{*}{\gamma }^{*}}$, currently out of experimental reach but testable in the near future. We find it particularly useful to encode this low-energy information in a form factor able to satisfy also QCD short-distance constraints. We choose the form factor introduced by D’Ambrosio, Isidori, and Portoles in kaon decays, which has the right short distance for a particular value of the quadratic slope, which is later shown to be compatible with our holographic predictions. We then turn to a determination of the (dominant) pion exchange diagram in the hadronic light by light scattering contribution to the muon anomalous magnetic moment. We quantify the theoretical uncertainty in $(g-2{)}_{\mu }$ coming from the different input we use: QCD short distances, experimental input, and low-energy holographic predictions. We also test the pion-pole approximation. Our final result is $a_{\mu }^{{\pi }^0}=6.54(25)\times {10}^{-10}$, where the error is driven by the linear slope of $F_{{\pi }^0{\gamma }^{*}{\gamma }^{*}}$, soon to be measured with precision at KLOE-2. Our numerical analysis also indicates that large values of the magnetic susceptibility ${\chi }_0$ are disfavored, therefore pointing at a mild effect from the pion off-shellness. However, in the absence of stronger bounds on ${\chi }_0$, an additional $(10–15)\%$ systematic uncertainty on the previous value for $a_{\mu }^{{\pi }^0}$ cannot be excluded.

Whether the kinematics includes the hard transverse photon momenta or not makes a dramatic difference in computing deeply virtual Compton scattering in terms of the widely used reduced operators that define generalized parton distributions. Our tree-level complete deeply virtual Compton scattering amplitude including the lepton current plays the role of spin filter to analyze such kinematic dependence on the contribution of longitudinally polarized virtual photon as well as the conservation of angular momentum.

Recent pulsar timing observations by the Parkers Pulsar Timing Array (PPTA) and European Pulsar Timing Array (EPTA) teams obtained the constraint on the relic gravitational waves at the frequency $f_{*}=1/\mathrm{yr}$, which provides the opportunity to constrain $H_{*}$, the Hubble parameter, when these waves crossed the horizon during inflation. In this paper, we investigate this constraint by considering the general scenario for the early Universe: we assume that the effective (average) equation-of-state $w$ before the big bang nucleosynthesis stage is a free parameter. In the standard hot big-bang scenario with $w=1/3$, we find that the current PPTA result follows a bound $H_{*}\le 1.15\times {10}^{-1}{m}_{\mathrm{Pl}}$, and the EPTA result follows $H_{*}\le 6.92\times {10}^{-2}{m}_{\mathrm{Pl}}$. We also find that these bounds become much tighter in the nonstandard scenarios with $w>1/3$. When $w=1$, the bounds become $H_{*}\le 5.89\times {10}^{-3}{m}_{\mathrm{Pl}}$ for the current PPTA and $H_{*}\le 3.39\times {10}^{-3}{m}_{\mathrm{Pl}}$ for the current EPTA. In contrast, in the nonstandard scenario with $w=0$, the bound becomes $H_{*}\le 7.76m_{\mathrm{Pl}}$ for the current PPTA.

The suggestion that we occupy a privileged position near the center of a large, nonlinear, and nearly spherical void has recently attracted much attention as an alternative to dark energy. Putting aside the philosophical problems with this scenario, we perform the most complete and up-to-date comparison with cosmological data. We use supernovae and the full cosmic microwave background spectrum as the basis of our analysis. We also include constraints from radial baryonic acoustic oscillations, the local Hubble rate, age, big bang nucleosynthesis, the Compton $y$ distortion, and for the first time include the local amplitude of matter fluctuations, ${\sigma }_8$. These all paint a consistent picture in which voids are in severe tension with the data. In particular, void models predict a very low local Hubble rate, suffer from an “old age problem,” and predict much less local structure than is observed.

Underground searches for dark matter involve a complicated interplay of particle physics, nuclear physics, atomic physics, and astrophysics. We attempt to remove the uncertainties associated with astrophysics by developing the means to map the observed signal in one experiment directly into a predicted rate at another. We argue that it is possible to make experimental comparisons that are completely free of astrophysical uncertainties by focusing on integral quantities, such as $g(v_{\min })={\int }_{v_{\min }}dvf(v)/v$ and ${\int }_{v_{\mathrm{thresh}}}dvvg(v)$. Direct comparisons are possible when the $v_{\min }$ space probed by different experiments overlap. As examples, we consider the possible dark matter signals at CoGeNT, DAMA, and CRESST-Oxygen. We find that the expected rate from CoGeNT in the XENON10 experiment is higher than observed, unless scintillation light output is low. Moreover, we determine that S2-only analyses are constraining, unless the charge yields $Q_y<2.4\mathrm{electrons}/\mathrm{keV}$. For DAMA to be consistent with XENON10, we find for $q_{\mathrm{Na}}=0.3$ that the modulation rate must be extremely high ($\gtrsim 70\%$ for $m_{\chi }=7\mathrm{GeV}$), while for higher quenching factors, it makes an explicit prediction ($0.8–0.9\mathrm{cpd}/\mathrm{kg}$) for the modulation to be observed at CoGeNT. Finally, we find CDMS-Si, even with a 10 keV threshold, as well as XENON10, even with low scintillation, would have seen significant rates if the excess events at CRESST arise from elastic WIMP scattering, making it very unlikely to be the explanation of this anomaly.

In order to explore nonlinear effects on the distribution of matter during collisions within the Bose-Einstein condensate (BEC) dark matter model driven by the Schrödinger-Poisson system of equations, we study the head-on collision of structures and focus on the interference pattern formation in the density of matter during the collision process. We explore the possibility that the collision of two structures of fluid matter modeled with an ideal gas equation of state also forms interference patterns and found a negative result. Given that a fluid is the most common flavor of dark matter models, we conclude that one fingerprint of the BEC dark matter model is the pattern formation in the density during a collision of structures.

The supermassive objects at the center of many galaxies are commonly thought to be black holes. In 4-dimensional general relativity, a black hole is completely specified by its mass $M$ and by its spin angular momentum $J$. All the higher multipole moments of the gravitational field depend in a very specific way on these two parameters. For instance, the mass quadrupole moment is $Q=-J^2/M$. If we can estimate $M$, $J$, and $Q$ for the supermassive objects in galactic nuclei, we overconstrain the theory and we can test the black hole hypothesis. While there are many works studying how this can be done with future observations, in this paper a constraint on the quadrupole moment of these objects is obtained by using the current estimate of the mean radiative efficiency of AGN. In terms of the anomalous quadrupole moment $q$, the bound is $-2.01<q<0.14$.

A large bulk flow, which is in tension with the Lambda cold dark matter ($\Lambda \mathrm{CDM}$) cosmological model, has been observed. In this paper, we provide a physically plausible explanation of this bulk flow, based on the assumption that some fraction of the observed dipole in the cosmic microwave background is due to an intrinsic fluctuation, so that the subtraction of the observed dipole leads to a mismatch between the cosmic microwave background defined rest frame and the matter rest frame. We investigate a model that takes into account the relative velocity (hereafter the tilted velocity) between the two frames, and develop a Bayesian statistic to explore the likelihood of this tilted velocity. By studying various independent peculiar velocity catalogs, we find that (1) the magnitude of the tilted velocity $u$ is around $400\mathrm{km}/\mathrm{s}$, and its direction is close to what is found from previous bulk flow analyses; for most catalogs analyzed, $u=0$ is excluded at about the $2.5\sigma$ level; (2) constraints on the magnitude of the tilted velocity can result in constraints on the duration of inflation, due to the fact that inflation can neither be too long (no dipole effect) nor too short (very large dipole effect); (3) under the assumption of a superhorizon isocurvature fluctuation, the constraints on the tilted velocity require that inflation lasts at least 6 e-folds longer (at the 95% confidence interval) than that required to solve the horizon problem. This opens a new window for testing inflation and models of the early universe from observations of large scale structure.

We explore the unification of gauge couplings and fermion masses in two different types of supersymmetric left-right models, one with Higgs triplets and the other with both Higgs triplets as well as bitriplets. The minimal versions of these models do not give rise to the desired unification and some extra fields have to be added. After such a modification, it is possible in one model to get gauged $B-L$ symmetry to be unbroken down to the TeV scale. We also identify the parameter space at the electroweak scale which gives rise to fermion mass unification at a high scale $M_G$. The Type I seesaw emerges as the natural explanation of the small neutrino masses in both the models.

A fermiophobic Higgs boson can arise in models with an extended Higgs sector, such as models with scalars in an isospin triplet representation. In a specific model with a scalar triplet and spontaneous violation of lepton number induced by a scalar singlet field, we show that fermiophobia is not a fine-tuned situation, unlike in two higgs doublet models. We study distinctive signals of fermiophobia which can be probed at the LHC. For the case of a small Higgs mass, a characteristic signal would be a moderate $B(H\to \gamma \gamma )$ accompanied by a large $B(H\to JJ)$ (where $J$ is a Majoron), the latter being an invisible decay. For the case of a large Higgs mass there is the possibility of dominant $H\to ZZ$, $WW$ and suppressed $H\to JJ$ decay modes. In this situation, $B(H\to ZZ)$ is larger than $B(H\to WW)$, which differs from the SM prediction.

In this work we present a calculation of both $t$-channel and $s$-channel single-top production at next-to-leading order in QCD for the Tevatron and for the LHC at a center-of-mass energy of 7 TeV. All the cross sections and kinematical distributions presented include leading nonfactorizable corrections arising from interferences of the production and decay subprocesses, extending previous results beyond the narrow-width approximation. The new off shell effects are found to be generally small, but can be sizeable close to kinematical endpoints and for specific distributions.