We show that at tree level, on-shell gauge invariance can be used to fully determine the first subleading soft-gluon behavior and the first two subleading soft-graviton behaviors. Our proofs of the behaviors for $n$-gluon and $n$-graviton tree amplitudes are valid in $D$ dimensions and are similar to Low’s proof of universality of the first subleading behavior of photons. In contrast to photons coupling to massive particles, in four dimensions the soft behaviors of gluons and gravitons are corrected by loop effects. We comment on how such corrections arise from this perspective. We also show that loop corrections in graviton amplitudes arising from scalar loops appear only at the second soft subleading order. This case is particularly transparent because it is not entangled with graviton infrared singularities. Our result suggests that if we set aside the issue of infrared singularities, soft-graviton Ward identities of extended Bondi, van der Burg, Metzner and Sachs symmetry are not anomalous through the first subleading order.

We derive the equations of motion of extended deformable bodies in metric-affine gravity. The conservation laws which follow from the invariance of the action under the general coordinate transformations are used as a starting point for the discussion of the dynamics of extended deformable test bodies. By means of a covariant approach, based on Synge’s world function, we obtain the master equation of motion for an arbitrary system of coupled conserved currents. This unified framework is then applied to metric-affine gravity. We confirm and extend earlier findings; in particular, we once again demonstrate that it is only possible to detect the post-Riemannian spacetime geometry by ordinary (nonmicrostructured) test bodies if gravity is nonminimally coupled to matter.

We demonstrate that elastic scattering between dark matter (DM) and baryons can affect the thermal evolution of the intergalactic medium at early epochs and discuss the observational consequences. We show that, due to the interaction between DM and baryons, the baryon temperature is cooled after decoupling from the CMB temperature. We illustrate our findings by calculating the 21 cm power spectrum in coexistence with a velocity-dependent DM elastic scattering cross section. For instance, for a DM mass of 10 GeV, the 21 cm brightness temperature angular power spectrum can be suppressed by a factor of 2 within the currently allowed DM-baryon cross section bounded by the CMB and large-scale structure data. This scale-independent suppression of the angular power spectrum can be even larger for a smaller DM mass with a common cross section (for instance, as large as a factor of 10 for $m_d\sim 1\mathrm{GeV}$), and such an effect would be of great interest for probing the nature of DM in view of forthcoming cosmological surveys.

We forecast future constraints on local-type primordial non-Gaussianity parameter $f_{\mathrm{NL}}$ with a photometric galaxy survey by Euclid, a continuum galaxy survey by Square Kilometre Array (SKA), and their combination. We derive a general expression for the covariance matrix of the power spectrum estimates of multiple tracers to show how the so-called multitracer technique improves constraints on $f_{\mathrm{NL}}$. In particular we clarify the role of the overlap fraction of multiple tracers and the division method of the tracers. Our Fisher matrix analysis indicates that stringent constraints of $\sigma (f_{\mathrm{NL}})\lesssim 1$ can be obtained even with a single survey, assuming five mass bins. When Euclid and SKA phase 1 (2) are combined, constraints on $f_{\mathrm{NL}}$ are improved to $\sigma (f_{\mathrm{NL}})=0.61(0.50)$.

The primordial lithium abundance inferred from spectroscopic observations of metal-poor stars is $\sim 3$ times smaller than the theoretical prediction in the standard big bang nucleosynthesis (BBN) model. We assume a simple model composed of standard model particles and a sterile neutrino ${\nu }_{\mathrm{H}}$ with mass of $\mathcal{O}(10)\mathrm{MeV}$ which decays long after BBN. We then investigate cosmological effects of a sterile neutrino decay, and check if a sterile neutrino can reduce the primordial lithium abundance. We formulate the injection spectrum of nonthermal photon induced by the ${\nu }_{\mathrm{H}}$ decay. We take into account the generation of electrons and positrons, $e^{\pm }$’s, and active neutrinos at the ${\nu }_{\mathrm{H}}$ decay, the primary photon production via the inverse Compton scattering of cosmic background radiation (CBR) by energetic $e^{\pm }$, and electromagnetic cascade showers induced by the primary photons. The steady state injection spectrum is then derived as a function of the ${\nu }_{\mathrm{H}}$ mass and the photon temperature. The ${\nu }_{\mathrm{H}}$ decay produces energetic active neutrinos which are not thermalized, and $e^{\pm }$’s which are thermalized. We then derive formulas relevant to the ${\nu }_{\mathrm{H}}$ decay rates and formulas for the baryon-to-photon ratio $\eta$ and effective neutrino number $N_{\text{eff}}$. The initial abundance, mass, and lifetime of ${\nu }_{\mathrm{H}}$ are taken as free parameters. We then consistently solve (1) the cosmic thermal history, (2) nonthermal nucleosynthesis induced by the nonthermal photons, (3) the $\eta$ value, and (4) the $N_{\text{eff}}$ value. We find that an effective ${}^7\mathrm{Be}$ destruction can occur only if the sterile neutrino decays at photon temperature $T=\mathcal{O}(1)\mathrm{keV}$. Amounts of energy injection at the ${\nu }_{\mathrm{H}}$ decay are constrained from limits on primordial D and ${}^7\mathrm{Li}$ abundances, the $N_{\text{eff}}$ value, and the CBR energy spectrum. We find that ${}^7\mathrm{Be}$ is photodisintegrated and the Li problem is partially solved for the lifetime ${10}^4–{10}^5\mathrm{s}$ and the mass $\gtrsim 14\mathrm{MeV}$. ${}^7\mathrm{Be}$ destruction by more than a factor of 3 is not possible because of an associated D overdestruction. In the parameter region, the $\eta$ value is decreased slightly, while the $N_{\text{eff}}$ value is increased by a factor of $\mathrm{\Delta }{N}_{\text{eff}}\lesssim 1$. In this study, errors in photodisintegration cross sections of ${}^7\mathrm{Be}(\gamma ,\alpha ){}^3\mathrm{He}$ and ${}^7\mathrm{Li}(\gamma ,\alpha ){}^3\mathrm{H}$ that have propagated through the literature are corrected, and new functions are derived based on recent nuclear experiments. It is found that the new photodisintegration rates are 2.3 to 2.5 times smaller than the old rates. The correct cross sections thus indicate significantly smaller efficiencies of ${}^7\mathrm{Be}$ and ${}^7\mathrm{Li}$ photodisintegration. Abundances of sterile neutrino necessary for the ${}^7\mathrm{Li}$ reduction are much smaller than thermal freeze-out abundances. The relic sterile neutrino, therefore, must be diluted between the freeze-out and BBN epochs by some mechanism.

A general framework for effective theories propagating two tensor and one scalar degrees of freedom is investigated. Geometrically, it describes dynamical foliation of spacelike hypersurfaces coupled to a general background, in which the scalar mode encodes the fluctuation of the hypersurfaces. Within this framework, various models in the literature—including $k$-essence, Horndeski theory, the effective field theory of inflation, ghost condensate as well as the Hořava gravity—get unified. Our framework generalizes the Horndeski theory in the sense that, it propagates the correct number of degrees of freedom, although the equations of motion are generally higher order. We also identify new operators beyond the Horndeski theory, which yield second order equations of motion for linear perturbations around a Friedmann-Robertson-Walker background.

In this work the $B{\overline{B}}^{*}/D{\overline{D}}^{*}$ system is studied in the Bethe-Salpeter approach with quasipotential approximation. In our calculation both direct and cross diagrams are included in the one-boson-exchange potential. The numerical results indicate the existence of an isoscalar bound state $D{\overline{D}}^{*}$ with $J^{PC}=1^{++}$, which may be related to the $X(3872)$. In the isovector sector, no bound state is produced from the interactions of $D{\overline{D}}^{*}$ and $B{\overline{B}}^{*}$, which suggests the molecular state explanations for $Z_b(10610)$ and $Z_c(3900)$ are excluded.

We derive the relativistic chiral transport equation for massless fermions and antifermions by performing a semiclassical Foldy-Wouthuysen diagonalization of the quantum Dirac Hamiltonian. The Berry connection naturally emerges in the diagonalization process to modify the classical equations of motion of a fermion in an electromagnetic field. We also see that the fermion and antifermion dispersion relations are corrected at first order in the Planck constant by the Berry curvature, as previously derived by Son and Yamamoto for the particular case of vanishing temperature. Our approach does not require knowledge of the state of the system, and thus it can also be applied at high temperature. We provide support for our result by an alternative computation using an effective field theory for fermions and antifermions: the on-shell effective field theory. In this formalism, the off-shell fermionic modes are integrated out to generate an effective Lagrangian for the quasi-on-shell fermions/antifermions. The dispersion relation at leading order exactly matches the result from the semiclassical diagonalization. From the transport equation, we explicitly show how the axial and gauge anomalies are not modified at finite temperature and density despite the incorporation of the new dispersion relation into the distribution function.

We consider LHC searches for dilepton resonances in an intermediate mass range, $\sim 10–80\mathrm{GeV}$. We adopt a kinetically mixed $Z^{\prime }$ as an example of weakly coupled new physics that might have evaded detection at previous experiments but which could still be probed by LHC dilepton spectrum measurements in this mass range. Based on Monte Carlo simulations, we estimate that existing data from the 7 and 8 TeV LHC could be used to test values of the kinetic mixing parameter $\epsilon$ several times smaller than precision electroweak upper bounds, provided an appropriate analysis were carried out by one of the experimental collaborations.

We combine constraints from analyticity with experimental electron-proton scattering data to determine the proton magnetic radius without model-dependent assumptions on the shape of the form factor. We also study the impact of including electron-neutron scattering data, and $\pi \pi \to N\overline{N}$ data. Using representative data sets we find for a cut of $Q^2\le 0.5{\mathrm{GeV}}^2$, $r_M^p=0.91_{-0.06}^{+0.03}\pm 0.02\mathrm{fm}$ using just proton scattering data; $r_M^p=0.87_{-0.05}^{+0.04}\pm 0.01\mathrm{fm}$ adding neutron data; and $r_M^p=0.87_{-0.02}^{+0.02}\mathrm{fm}$ adding $\pi \pi$ data. We also extract the neutron magnetic radius from these data sets obtaining $r_M^n=0.89_{-0.03}^{+0.03}\mathrm{fm}$ from the combined proton, neutron, and $\pi \pi$ data.

We present a measurement of the cross section and transverse single-spin asymmetry ($A_N$) for $\eta$ mesons at large pseudorapidity from $\sqrt{s}=200\mathrm{GeV}$ $p^{\uparrow }+p$ collisions. The measured cross section for $0.5<p_T<5.0\mathrm{GeV}/c$ and $3.0<|\eta |<3.8$ is well described by a next-to-leading-order perturbative-quantum-chromodynamics calculation. The asymmetries $A_N$ have been measured as a function of Feynman-$x$ ($x_F$) from $0.2<|x_F|<0.7$, as well as transverse momentum ($p_T$) from $1.0<p_T<4.5\mathrm{GeV}/c$. The asymmetry averaged over positive $x_F$ is $⟨A_N⟩=0.061\pm 0.014$. The results are consistent with prior transverse single-spin measurements of forward $\eta$ and ${\pi }^0$ mesons at various energies in overlapping $x_F$ ranges. Comparison of different particle species can help to determine the origin of the large observed asymmetries in $p^{\uparrow }+p$ collisions.

The investigation of a cosmologically viable choice of a coupling function and scalar field potential is of great interest in scalar-tensor theories. The present work explores the form of the coupling function and scalar field potential using a Noether symmetry approach in a modified scalar-tensor gravity by including a nonminimal coupling of the scalar field with a torsion scalar. For this purpose, we consider locally rotational symmetric Bianchi I geometry in vacuum as well as nonvacuum cases and evaluate the corresponding conserved quantities for three different cases. By introducing cyclic variables, we find an exact solution of the corresponding field equations. We also discuss the expanding behavior of the resulting universe model through different cosmological parameters. Finally, we explore Noether gauge symmetry generators for Friedmann–Robertson–Walker and locally rotational symmetric Bianchi I universe models. It is concluded that in each case the symmetry generator as well as the conserved quantity exist, and the resulting solution is consistent with recent observations.

Repulsive gravity has been investigated in several scenarios near compact objects by using different intuitive approaches. Here, we propose an invariant method to characterize regions of repulsive gravity, associated to black holes and naked singularities. Our method is based upon the behavior of the curvature tensor eigenvalues, and leads to an invariant definition of a repulsion radius. The repulsion radius determines a physical region, which can be interpreted as a repulsion sphere, where the effects due to repulsive gravity naturally arise. Further, we show that the use of effective masses to characterize repulsion regions can lead to coordinate-dependent results whereas, in our approach, repulsion emerges as a consequence of the spacetime geometry in a completely invariant way. Our definition is tested in the spacetime of an electrically charged Kerr naked singularity and in all its limiting cases. We show that a positive mass can generate repulsive gravity if it is equipped with an electric charge or an angular momentum. We obtain reasonable results for the spacetime regions contained inside the repulsion sphere whose size and shape depend on the value of the mass, charge and angular momentum. Consequently, we define repulsive gravity as a classical relativistic effect by using the geometry of spacetime only.

We consider the self-force on a charged particle moving in a curved spacetime with a background electromagnetic field, extending previous studies to situations in which gravitational and electromagnetic perturbations are comparable. The formal expression $f_{\alpha }^{\text{ret}}$ for the self-force on a particle, written in terms of the retarded perturbed fields, is divergent, and a renormalization is needed to find the particle’s acceleration at linear order in its mass $m$ and charge $e$. We assume that, as in previous work in a Lorenz gauge, the renormalization for accelerated motion comprises an angle average and mass renormalization. Using the short distance expansion of the perturbed electromagnetic and gravitational fields, we show that the renormalization is equivalent to that obtained from a mode sum regularization in which one subtracts from the expression for the self-force in terms of the retarded fields a singular field comprising only the leading and subleading terms in the mode sum. The most striking part of our result, arising from a remarkable cancellation, is that the renormalization involves no mixing of electromagnetic and gravitational fields. In particular, although the Einstein-Maxwell system couples the perturbed electromagnetic and gravitational fields, the renormalized mass is obtained by subtracting (1) the purely electromagnetic contribution from a point charge moving along an accelerated trajectory and (2) the purely gravitational contribution from a point mass moving along the same trajectory. In a mode-sum regularization, the same cancellation implies that the required regularization parameters are sums of their purely electromagnetic and gravitational values.

The gravitational self-force has thus far been formulated in background spacetimes for which the metric is a solution to the Einstein field equations in vacuum. While this formulation is sufficient to describe the motion of a small object around a black hole, other applications require a more general formulation that allows for a nonvacuum background spacetime. We provide a foundation for such extensions, and carry out a concrete formulation of the gravitational self-force in two specific cases. In the first we consider a particle of mass $m$ and scalar charge $q$ moving in a background spacetime that contains a background scalar field. In the second we consider a particle of mass $m$ and electric charge $e$ moving in an electrovac spacetime. The self-force incorporates all couplings between the gravitational perturbations and those of the scalar or electromagnetic fields. It is expressed as a sum of local terms involving tensors defined in the background spacetime and evaluated at the current position of the particle, as well as tail integrals that depend on the past history of the particle. Because such an expression may not be a useful starting point for an explicit evaluation of the self-force, we also provide covariant expressions for the singular potentials, expressed as local expansions near the world line; these can be involved in the construction of effective extended sources for the regular potentials, or in the computation of regularization parameters when the self-force is computed as a sum over spherical-harmonic modes.

The abundance of massive dark matter halos hosting galaxy clusters provides an important test of the masses of relic neutrino species. The dominant effect of neutrino mass is to lower the typical amplitude of density perturbations that eventually form halos, but for neutrino masses $\gtrsim 0.4\mathrm{eV}$ the threshold for halo formation can be changed significantly as well. We study the spherical collapse model for halo formation in cosmologies with neutrino masses in the range $m_{\nu i}=0.05–1\mathrm{eV}$ and find that halo formation is differently sensitive to ${\mathrm{\Omega }}_{\nu }$ and $m_{\nu }$. That is, different neutrino hierarchies with a common ${\mathrm{\Omega }}_{\nu }$ are in principle distinguishable. The added sensitivity to $m_{\nu }$ is small but potentially important for scenarios with heavier sterile neutrinos. Massive neutrinos cause the evolution of density perturbations to be scale dependent at high redshift which complicates the usual mapping between the collapse threshold and halo abundance. We propose one way of handling this and compute the correction to the halo mass function within this framework. For $\sum m_{\nu i}\lesssim 0.3\mathrm{eV}$, our prescription for the halo abundance is only $\lesssim 15\%$ different than the standard calculation. However for larger neutrino masses the differences approach 50–100% which, if verified by simulations, could alter neutrino mass constraints from cluster abundance.

The mass composition of cosmic rays contains important clues about their origin. Accurate measurements are needed to resolve longstanding issues such as the transition from Galactic to extra-Galactic origin and the nature of the cutoff observed at the highest energies. Composition can be studied by measuring the atmospheric depth of the shower maximum $X_{\max }$ of air showers generated by high-energy cosmic rays hitting the Earth’s atmosphere. We present a new method to reconstruct $X_{\max }$ based on radio measurements. The radio emission mechanism of air showers is a complex process that creates an asymmetric intensity pattern on the ground. The shape of this pattern strongly depends on the longitudinal development of the shower. We reconstruct $X_{\max }$ by fitting two-dimensional intensity profiles, simulated with CoREAS, to data from the Low Frequency Array (LOFAR) radio telescope. In the dense LOFAR core, air showers are detected by hundreds of antennas simultaneously. The simulations fit the data very well, indicating that the radiation mechanism is now well understood. The typical uncertainty on the reconstruction of $X_{\max }$ for LOFAR showers is $17\mathrm{g}/{\mathrm{cm}}^2$.

We investigate the quark number fluctuations up to the fourth order in the matter composed of two light flavor quarks with isospin symmetry and at finite temperature and finite chemical potential using the Dyson-Schwinger equation approach of QCD. In order to solve the quark gap equation, we approximate the dressed quark-gluon vertex with the bare one and adopt both the Maris-Tandy model and the infrared constant (Qin-Chang) model for the dressed gluon propagator. Our results indicate that the second, third, and fourth order fluctuations of net quark number all diverge at the critical endpoint (CEP). Around the CEP, the second order fluctuation possesses obvious pump while the third and fourth order ones exhibit distinct wiggles between positive and negative. For the Maris-Tandy model and the Qin-Chang model, we give the pseudocritical temperature at zero quark chemical potential as $T_c=146\mathrm{MeV}$ and 150 MeV, and locate the CEP at $({\mu }_E^q,T_E)=(120,124)\mathrm{MeV}$ and (124,129) MeV, respectively. In addition, our results manifest that the fluctuations are insensitive to the details of the model, but the location of the CEP shifts to low chemical potential and high temperature as the confinement length scale increases.

We present lattice QCD calculations of nucleon electromagnetic form factors using pion masses $m_{\pi }=149$, 202, and 254 MeV and an action with clover-improved Wilson quarks coupled to smeared gauge fields, as used by the Budapest-Marseille-Wuppertal Collaboration. Particular attention is given to the removal of the effects of excited-state contamination by calculations at three source-sink separations and the use of the summation and generalized pencil-of-function methods. The combination of a calculation at the nearly physical mass $m_{\pi }=149\mathrm{MeV}$ in a large spatial volume ($m_{\pi }{L}_s=4.2$) and the removal of excited-state effects yields agreement with experiment for the electric and magnetic form factors $G_E(Q^2)$ and $G_M(Q^2)$ up to $Q^2=0.5{\mathrm{GeV}}^2$.