We extend the singlet Majoron model of dark radiation by adding another singlet scalar of unit lepton charge. The spontaneous breaking of global $U(1{)}_L$ connects dark radiation with neutrino mass generation via the type-I seesaw mechanism. The model naturally has a stable scalar dark matter field. It also predicts the existence of a light scalar of mass less than 1 GeV that mixes with the Standard Model Higgs boson. We perform a numerical analysis of the parameters of the model by imposing constraints from giving correct relic abundance and satisfying bounds from direct dark matter detection, rare decays of the $B$ meson, and invisible width of the Higgs boson. The viability of the model in accommodating the gamma rays from the Galactic center is discussed as well. The model gives rise to new rare Higgs boson decays such as four-muon final states with displaced vertices. Another unique signal is two muons and missing energy recoil against the muon pair. Our result also shows that such a bridge between dark radiation and the seesaw mechanism will put the seesaw scale in the range of 1–100 TeV.

The radar experiment connects the geometry of spacetime with an observers measurement of spatial length. We investigate the radar experiment on Finsler spacetimes which leads to a general definition of radar orthogonality and radar length. The directions radar orthogonal to an observer form the spatial equal time surface an observer experiences and the radar length is the physical length the observer associates to spatial objects. We demonstrate these concepts on a forth order polynomial Finsler spacetime geometry which may emerge from area metric or premetric linear electrodynamics or in quantum gravity phenomenology. In an explicit generalization of Minkowski spacetime geometry we derive the deviation from the Euclidean spatial length measure in an observers rest frame explicitly.

We propose a nonlinear massive gravitational theory which includes $F(R)$ modifications. This construction inherits the benefits of the de Rham-Gabadadze-Tolley model and is free of the Boulware-Deser ghost due to the existence of a Hamiltonian constraint accompanied by a nontrivial secondary one. The scalar perturbations in a cosmological background can be stabilized at the linear level for a wide class of the $F(R)$ models. The linear scalar mode arisen from the $F(R)$ sector can absorb the nonlinear longitudinal graviton, and hence, our scenario demonstrates the possibility of a gravitational Goldstone theorem. Finally, due to the combined contribution of the $F(R)$ and graviton-mass sectors, the proposed theory allows for a large class of cosmological evolutions, such as the simultaneous and unified description of inflation and late-time acceleration.

The cosmological consequences of $f(R)$ gravity are reviewed in the framework of thermal leptogenesis. In $f(R)$ cosmology the expansion laws of the Universe are modified with respect to the standard cosmology, which also changes the thermal history of particles. In these cosmological scenarios it turns out that the condition for the out-of-equilibrium decay of the lightest heavy neutrino gives rise to a modulated upper bound on the lightest light neutrino mass, i.e. ${\tilde{m}}_1\lesssim {10}^{-3}A(T=M_1)\mathrm{eV}$, where $A(T)$ is the ratio between the expansion rates of the Universe evaluated in $f(R)$ cosmology and in standard cosmology, and $M_1$ is the lightest heavy neutrino mass. This factor can be parametrized in terms of the temperature $T$ as $A(T)=(T/T_{*}{)}^p$, where $T_{*}$ is the transition temperature at which the expansion law in $f(R)$ cosmology deviates from the standard one, and $p$ is related to the parameters characterizing the $f(R)$ model under consideration. Results imply that if $A\gg 1$ then the thermal leptogenesis scenario can accommodate the case of a degenerate mass spectrum of the light neutrinos (for a low enough transition temperature), which is otherwise impossible with standard cosmology. In our analysis we consider $f(R)$ models of the form $f(R)=R+\alpha R^n$.

There exists some tension on large scales between the Planck data and the $\mathrm{\Lambda }\mathrm{CDM}$ concordance model of the Universe, which has been amplified by the recently claimed discovery of nonzero tensor-to-scalar ratio $r$. At the same time, the current best-fit value of $r$ suggests large field inflation $\mathrm{\Delta }{\varphi }_{\inf }>M_p$, which requires a UV complete description of inflation. A very promising working example that predicts large tensor modes and can be UV completed is axion monodromy inflation. This realization of inflation naturally produces oscillating features, as consequence of a broken shift symmetry. We analyze a combination of Planck, ACT, SPT, WMAP low $\ell$ polarization, and BICEP2 data and show a long wavelength feature from a periodic potential can alleviate the tension at low multipoles with an improvement $\mathrm{\Delta }{\chi }^2\simeq 2.5-4$ per degree of freedom, depending on the level of foreground subtraction. As with an introduction of running, one expects that any scale dependence should lead to a worsened fit at high multipoles. We show that the logarithmic nature of the axion feature in combination with a tilt $n_s\sim 1$ allows the fit to be identical to a no-feature model at the 2% level on scales $100\le \ell \le 3500$ and quite remarkably actually slightly improves the fit at scales $\ell >2000$. We also consider possible unremoved dust foregrounds and show that including these hardly changes the best-fit parameters. Corrected for potential foregrounds and fixing the frequency to the best fit value, we find an amplitude of the feature $\delta n_s=0.095_{-0.05}^{+0.03}$, a spectral index $n_s=1.0_{-0.04}^{+0.03}$, the overall amplitude $\log 10^{10}{A}_s=3.06\pm 0.04$, and a phase $\varphi =0.85_{-1.6}^{+0.9}$. These parameters suggest an axion decay constant of $f/M_p\sim \mathcal{O}(.01)$. We discuss how Planck measurements of the temperature-Emode polarization (TE) and Emode polarization-Emode polarization (EE) spectra can further constrain axion monodromy inflation with such a large feature. A measurement of the large scale structure power spectrum is even more promising, as the effect is much bigger since the tensor modes do not affect the large scales. At the same time, a feature could also lead to a lower ${\sigma }_8$, lifting the tension between cosmic microwave background and Sunyaev-Zel’dovich (SZ) constraints on ${\sigma }_8$.

We study the thermodynamics of the SU(3) gauge theory using the fixed-scale approach with shifted boundary conditions. The fixed-scale approach can reduce the numerical cost of the zero-temperature part in the equation of state calculations, while the number of possible temperatures is limited by the integer $N_t$, which represents the temporal lattice extent. The shifted boundary conditions can overcome such a limitation while retaining the advantages of the fixed-scale approach. Therefore, our approach enables the investigation of not only the equation of state in detail but also the calculation of the critical temperature with increased precision even with the fixed-scale approach. We also observe numerically that the boundary conditions suppress the lattice artifact of the equation of state, which has been observed in the noninteracting limit.

We formulate the lattice QCD simulation with background classical gravitational fields. This formulation enables us to study nonperturbative aspects of quantum phenomena in curved spacetimes from the first principles. As the first application, we perform the simulation with the Friedmann-Lemaítre-Robertson-Walker metric and analyze particle production in the expanding universe.

We investigate the low-temperature phase of QCD and the crossover region with two light flavors of quarks. The chiral expansion around the point $(T,m=0)$ in the temperature vs quark-mass plane indicates that a sharp real-time excitation exists with the quantum numbers of the pion. An exact sum rule is derived for the thermal modification of the spectral function associated with the axial charge density; the (dominant) pion pole contribution obeys the sum rule. We determine the two parameters of the pion dispersion relation using lattice QCD simulations and test the applicability of the chiral expansion. The time-dependent correlators are also analyzed using the maximum entropy method, yielding consistent results. Finally, we test the predictions of the chiral expansion around the point $(T=0,m=0)$ for the temperature dependence of static observables.

Fluctuations of conserved quantum numbers are associated with the corresponding susceptibilities because of the symmetry of the system. The underlying fact is that these fluctuations as defined through the static correlators become identical to the direct calculation of these susceptibilities defined through the thermodynamic derivatives, due to the fluctuation-dissipation theorem. Through a rigorous exercise we explicitly show that a diagrammatic calculation of the static correlators associated with the conserved quark number fluctuations and the corresponding susceptibilities are possible in the case of mean field theories, if the implicit dependence of the mean fields on the quark chemical potential are taken into account appropriately. As an aside we also give an analytical prescription for obtaining the implicit dependence of the mean fields on the quark chemical potential.

Beam and jet functions in soft-collinear effective theory describe collinear initial- and final-state radiation (jets), and enter in factorization theorems for $N$-jet production, the Higgs $p_T$ spectrum, etc. We show that they may directly be calculated as phase-space integrals of QCD splitting functions. At next-to-leading order (NLO) all computations are trivial, as we demonstrate explicitly for the beam function, the transverse-momentum-dependent beam function, the jet function, and the fragmenting jet function. This approach also highlights the role of crossing symmetry in these calculations. At next-to-next-to leading order (NNLO) we reproduce the quark jet function and calculate the fragmenting quark jet function for the first time. Here we use two methods: a direct phase-space integration and a reduction to master integrals that are computed using differential equations.

We point out that the recent excess observed in searches for a right-handed gauge boson $W_R$ at CMS can be explained in a left-right symmetric model with $D$-parity violation. In a class of SO(10) models, in which $D$ parity is broken at a high scale, the left-right gauge symmetry breaking scale is naturally small, and at a few TeV the gauge coupling constants satisfy $g_R\approx 0.6g_L$. Such models therefore predict a right-handed charged gauge boson $W_R$ in the TeV range with a suppressed gauge coupling as compared to the usually assumed manifest left-right symmetry case $g_R=g_L$. The recent CMS data show excess events which are consistent with the cross section predicted in the $D$-parity breaking model for $1.9\mathrm{TeV}<M_{W_R}<2.4\mathrm{TeV}$. If the excess is confirmed, it would in general be a direct signal of new physics beyond the Standard Model at the LHC. A TeV scale $W_R$ would for example not only rule out SU(5) grand unified theory models. It would also imply $B-L$ violation at the TeV scale, which would be the first evidence for baryon or lepton number violation in nature, and it has strong implications on the generation of neutrino masses and the baryon asymmetry in the Universe.

A measurement of the decay time-dependent $CP$-violating asymmetry in $B_s^0\to \varphi \varphi$ decays is presented, along with measurements of the $T$-odd triple-product asymmetries. In this decay channel, the $CP$-violating weak phase arises from the interference between $B_s^0\text{−}{\overline{B}}_s^0$ mixing and the loop-induced decay amplitude. Using a sample of proton-proton collision data corresponding to an integrated luminosity of $3.0{\mathrm{fb}}^{-1}$ collected with the LHCb detector, a signal yield of approximately 4000 $B_s^0\to \varphi \varphi$ decays is obtained. The $CP$-violating phase is measured to be ${\varphi }_s=-0.17\pm 0.15(\text{stat})\pm 0.03(\text{syst})\mathrm{rad}$. The triple-product asymmetries are measured to be $A_U=-0.003\pm 0.017(\text{stat})\pm 0.006(\text{syst})$ and $A_V=-0.017\pm 0.017(\text{stat})\pm 0.006(\text{syst})$. Results are consistent with the hypothesis of $CP$ conservation.

We report a measurement of the ${\nu }_{\mu }$ inclusive charged current cross sections on iron and hydrocarbon in the Tokai-to-Kamioka (T2K) on-axis neutrino beam. The measured inclusive charged current cross sections on iron and hydrocarbon averaged over the T2K on-axis flux with a mean neutrino energy of 1.51 GeV are $(1.444\pm 0.002(\text{stat}{)}_{-0.157}^{+0.189}(\text{syst}))\times 10^{-38}{\mathrm{cm}}^2/\text{nucleon}$ and $(1.379\pm 0.009(\text{stat}{)}_{-0.147}^{+0.178}(\text{syst}))\times 10^{-38}{\mathrm{cm}}^2/\text{nucleon}$, respectively, and their cross-section ratio is $1.047\pm 0.007(\text{stat})\pm 0.035(\text{syst})$. These results agree well with the predictions of the neutrino interaction model, and thus we checked the correct treatment of the nuclear effect for iron and hydrocarbon targets in the model within the measurement precisions.

We suggest that the vacuum field equation in Finsler spacetime is equivalent to the vanishing of the Ricci scalar. The Schwarzschild metric can be deduced from a solution of our field equation if the spacetime preserves spherical symmetry. Supposing that the spacetime preserves the symmetry of the “Finslerian sphere,” we find a non-Riemannian exact solution of the Finslerian vacuum field equation. The solution is similar to the Schwarzschild metric. It reduces to the Schwarzschild metric as the Finslerian parameter $\epsilon$ vanishes. It is proven that the Finslerian covariant derivative of the geometrical part of the gravitational field equation is conserved. The interior solution is also given. We get solutions of the geodesic equation in such a Schwarzschild-like spacetime, and show that the geodesic equation returns to its counterpart in Newtonian gravity in the weak-field approximation. Celestial observations give a constraint on the Finslerian parameter $\epsilon <10^{-4}$, and the recent Michelson-Morley experiment requires $\epsilon <10^{-16}$. A counterpart of Birkhoff’s theorem exists in the Finslerian vacuum. This shows that the Finslerian gravitational field with the symmetry of the “Finslerian sphere” in vacuum must be static.

The theory of nonlinear massive gravity can be extended into the $F(R)$ form as developed by Cai et al. [Phys. Rev. D 90, 064051 (2014)]. Being free of the Boulware-Deser ghost, such a construction has the additional advantage of exhibiting no linear instabilities around a cosmological background. We investigate various cosmological evolutions of a universe governed by this generalized massive gravitational theory. Specifically, under the Starobinsky Ansatz, this model provides a unified description of the cosmological history, from early-time inflation to late-time self-acceleration. Moreover, under viable $F(R)$ forms, the scenario leads to a very interesting dark energy phenomenology, including the realization of the quintom scenario without any pathology. Finally, we provide a detailed analysis of the cosmological perturbations at linear order, as well as the Hamiltonian constraint analysis, in order to examine the physical degrees of freedom.

We study slow-roll inflation with a Gauss-Bonnet term that is coupled to an inflaton field nonminimally. We investigate the inflationary solutions for a specific type of the nonminimal coupling to the Gauss-Bonnet term and inflaton potential both analytically and numerically. We also calculate the observable quantities such as the power spectra of the scalar and tensor modes, the spectral indices, the tensor-to-scalar ratio, and the running spectral indices. Finally, we constrain our result with the observational data by Planck and BICEP2 experiment.

Motivated by dark-photon $\overline{\gamma }$ scenarios extensively considered in the literature, we explore experimentally allowed models where the Higgs boson coupling to photon and dark photon $H\gamma \overline{\gamma }$ can be enhanced. Correspondingly, large rates for the $H\to \gamma \overline{\gamma }$ decay become plausible, giving rise to one monochromatic photon with $E^{\gamma }\simeq m_H/2$ (i.e., more than twice the photon energy in the rare standard-model decay $H\to \gamma Z\to \gamma \overline{\nu }\nu$), and a similar amount of missing energy. We perform a model-independent study of this exotic resonant monophoton signature at the LHC, featuring a distinctive $E_T^{\gamma }$ peak around 60 GeV, and $\gamma +{\cancel{E}}_T$ transverse invariant mass ruled by $m_H$. At parton level, we find a $5\sigma$ sensitivity of the present LHC data set for a $H\to \gamma \overline{\gamma }$ branching fraction of 0.5%. Such large branching fractions can be naturally obtained in dark $U(1{)}_F$ models explaining the origin and hierarchy of the standard model Yukawa couplings. We urge the LHC experiments to search for this new exotic resonance in the present data set and in future LHC runs.

We calculate the next-to-leading-order QCD corrections to the perturbative term in the operator product expansion of the spectral functions of light tetraquark currents. By using also configuration-space methods we keep the momentum-space four-loop calculation to a manageable level. We find that the next-to-leading-order corrections to the perturbative term are large and can amount to $O(100\%)$. The corrections to the corresponding Borel sum rules, however, are small since the nonperturbative condensate contributions dominate the Borel sum rules.

We consider extensions of the standard model based on open strings ending on D-branes, with gauge bosons due to strings attached to stacks of D-branes and chiral matter due to strings stretching between intersecting D-branes. Assuming that the fundamental string mass scale $M_s$ is in the TeV range and that the theory is weakly coupled, we discuss possible signals of string physics at the upcoming HL-LHC run (integrated $\mathrm{luminosity}=3000{\mathrm{fb}}^{-1}$) with a center-of-mass energy of $\sqrt{s}=14\mathrm{TeV}$ and at potential future $pp$ colliders, HE-LHC and VLHC, operating at $\sqrt{s}=33$ and 100 TeV, respectively (with the same integrated luminosity). In such D-brane constructions, the dominant contributions to full-fledged string amplitudes for all the common QCD parton subprocesses leading to dijets and $\gamma +\mathrm{jet}$ are completely independent of the details of compactification and can be evaluated in a parameter-free manner. We make use of these amplitudes evaluated near the first $(n=1)$ and second $(n=2)$ resonant poles to determine the discovery potential for Regge excitations of the quark, the gluon, and the color singlet living on the QCD stack. We show that for string scales as large as 7.1 TeV (6.1 TeV) lowest massive Regge excitations are open to discovery at the $\ge 5\sigma$ in dijet ($\gamma +\mathrm{jet}$) HL-LHC data. We also show that for $n=1$ the dijet discovery potential at HE-LHC and VLHC exceedingly improves: up to 15 TeV and 41 TeV, respectively. To compute the signal-to-noise ratio for $n=2$ resonances, we first carry out a complete calculation of all relevant decay widths of the second massive level string states (including decays into massless particles and a massive $n=1$ and a massless particle), where we rely on factorization and conformal field theory techniques. Helicity wave functions of arbitrary higher spin massive bosons are also constructed. We demonstrate that for string scales $M_s\lesssim 10.5\mathrm{TeV}$ ($M_s\lesssim 28\mathrm{TeV}$) detection of $n=2$ Regge recurrences at HE-LHC (VLHC) would become the smoking gun for D-brane string compactifications. Our calculations have been performed using a semianalytic parton model approach which is cross checked against an original software package. The string event generator interfaces with HERWIG and Pythia through BlackMax. The source code is publicly available in the hepforge repository.

Recently, a new interesting instability of a charged scalar field in the Reissner-Nordström-de Sitter background has been found [Z. Zhu et al. Phys. Rev. D 90, 044042 (2014)] through the time-domain integration of the perturbation equation. We investigate further properties of this instability, confirm its existence by concordant frequency-domain and time-domain calculations, and show that it occurs at however small value of the coupling $eQ$, where $e$ and $Q$ are charges of a scalar field and black hole, respectively. We also investigate the parametric region of instability and show that the critical values of $eQ$ at which the stabilization happens strongly depends on the value of cosmological constant $\mathrm{\Lambda }$ and softly on $Q$. We show that all the unstable modes are superradiant, but not all the superradiant modes are unstable. We analytically prove that superradiance is a necessary (but not sufficient) condition for the instability in this case and, thereby, demonstrate the superradiant origin of the instability.