In this work corrections to the usual flavor SU(2) Nambu-Jona-Lasinio (NJL) coupling due to a weak external magnetic field are calculated by considering quark polarization in a (dressed) gluon exchange mechanism for quark interactions. The quark field is split into two components: one that condenses and another one that is a background field for interacting quarks, the former being integrated out. The resulting determinant is expanded for relatively large quark mass and small magnetic field $(e{B}_0/{M^{*}}^2)<1$ by resolving magnetic-field-dependent low energy quark effective interactions. Besides the corrections for the NJL and vector NJL effective couplings, different $B_0$-dependent effective couplings that break isospin and chiral symmetry emerge.

We study the gauge-independent observables associated with two interesting stationary configurations of the Standard Model Higgs potential (extrapolated to high energy according to the present state of the art, namely the next-to-next-to-leading order): i) the value of the top mass ensuring the stability of the SM electroweak minimum and ii) the value of the Higgs potential at a rising inflection point. We examine in detail and reappraise the experimental and theoretical uncertainties which plague their determination, finding that i) the stability of the SM is compatible with the present data at the $1.5\sigma$ level and ii) despite the large theoretical error plaguing the value of the Higgs potential at a rising inflection point, the application of such a configuration to models of primordial inflation displays a $3\sigma$ tension with the recent bounds on the tensor-to-scalar ratio of cosmological perturbations.

We study the large-$N$ scaling behavior of the $\theta$ dependence of the ground-state energy density $E(\theta )$ of four-dimensional (4D) $SU(N)$ gauge theories and two-dimensional (2D) $C{P}^{N-1}$ models, where $\theta$ is the parameter associated with the Lagrangian topological term. We consider its $\theta$ expansion around $\theta =0$, $E(\theta )-E(0)=\frac{1}{2}\chi {\theta }^2(1+b_2{\theta }^2+b_4{\theta }^4+\dots )$, where $\chi$ is the topological susceptibility and $b_{2n}$ are dimensionless coefficients. We focus on the first few coefficients $b_{2n}$, which parametrize the deviation from a simple Gaussian distribution of the topological charge at $\theta =0$. We present a numerical analysis of Monte Carlo simulations of 4D $SU(N)$ lattice gauge theories for $N=3$, 4, 6 in the presence of an imaginary $\theta$ term. The results provide a robust evidence of the large-$N$ behavior predicted by standard large-$N$ scaling arguments, i.e. $b_{2n}=O(N^{-2n})$. In particular, we obtain $b_2={\overline{b}}_2/N^2+O(1/N^4)$ with ${\overline{b}}_2=-0.23(3)$. We also show that the large-$N$ scaling scenario applies to 2D $C{P}^{N-1}$ models as well, by an analytical computation of the leading large-$N$ $\theta$ dependence around $\theta =0$.

We compute the jet quenching parameter $\widehat{q}$ of a quark-gluon plasma in the presence of a strong magnetic field using perturbative QCD (pQCD) in the weakly coupled regime, and $\mathrm{AdS}/\mathrm{CFT}$ correspondence in the strongly coupled regime of $\mathcal{N}=4$ super Yang-Mills. In the weakly coupled regime, we compute $\widehat{q}$ in pQCD at complete leading order (that is, leading log as well as the constant under the log) in the QCD coupling constant ${\alpha }_s$, assuming the hierarchy of scales ${\alpha }_{s}eB\ll T^2\ll eB$. We consider two cases of jet orientations with respect to the magnetic field: 1) the case of a jet moving parallel to the magnetic field; 2) the case of a jet moving perpendicular to the magnetic field. In the former case, we find $\widehat{q}\sim {\alpha }_s^2(eB)T\log (1/{\alpha }_s)$, while in the latter we have $\widehat{q}\sim {\alpha }_s^2(eB)T\log (T^2/{\alpha }_{s}eB)$. In both cases, this leading-order result arises from the scatterings with thermally populated lowest-Landau-level quarks. In the strongly coupled regime described by the $\mathrm{AdS}/\mathrm{CFT}$ correspondence, we find $\widehat{q}\sim \sqrt{\lambda }(eB)T$ or $\widehat{q}\sim \sqrt{\lambda }\sqrt{eB}{T}^2$ in the same hierarchy of $T^2\ll eB$ depending on whether the jet is moving parallel or perpendicular to the magnetic field, respectively, which indicates a universal dependence of $\widehat{q}$ on $(eB)T$ in both regimes for the parallel case, the origin of which should be the transverse density of lowest-Landau-level states proportional to $eB$. Finally, the asymmetric transverse momentum diffusion in the case of a jet moving perpendicular to the magnetic field may give an interesting azimuthal asymmetry of the gluon bremsstrahlung spectrum in the Baier-Dokshitzer-Mueller-Peigne-Schiff and Zakharov (BDMPS-Z) formalism.

The probability of creating an electron-positron pair out of the quantum vacuum by a strong electric field can be enhanced tremendously via an additional weaker time-dependent field. This dynamically assisted Sauter-Schwinger effect has already been studied in several works. It has been found that the enhancement mechanism depends on the shape of the weaker field. For example, a Sauter pulse $1/\cosh (\omega t{)}^2$ and a Gaussian profile $\exp (-{\omega }^2{t}^2)$ exhibit significant, qualitative differences. However, so far most of the analytical studies were focused on the exponent entering the pair-creation probability. Here, we study the subleading prefactor in front of the exponential using the worldline instanton method. We find that the main features of the dynamically assisted Sauter-Schwinger effect, including the dependence on the shape of the weaker field, are basically unaffected by the prefactor. To test the validity of the instanton approximation, we compare the number of produced pairs to a numerical integration of the full Riccati equation.

We treat quantum creation of gravitons by small scale factor oscillations around the average of an expanding universe. Such oscillations can arise in standard general relativity due to oscillations of a homogeneous, minimally coupled scalar field. They can also arise in modified gravity theories with a term proportional to the square of the Ricci scalar in the gravitational action. The graviton wave equation is different in the two cases, leading to somewhat different creation rates. Both cases are treated using a perturbative method due to Birrell and Davies, involving an expansion in a conformal coupling parameter to calculate the number density and energy density of the created gravitons. Cosmological constraints on the present graviton energy density and the dimensionless amplitude of the oscillations are discussed. We also discuss decoherence of quantum systems produced by the spacetime geometry fluctuations due to such a graviton bath.

Combining information from weak sources, such as known pulsars, for gravitational wave detection, is an attractive approach to improve detection efficiency. We propose an optimal statistic for a general ensemble of signals and apply it to an ensemble of known pulsars. Our method combines $\mathcal{F}$-statistic values from individual pulsars using weights proportional to each pulsar’s expected optimal signal-to-noise ratio to improve the detection efficiency. We also point out that to detect at least one pulsar within an ensemble, different thresholds should be designed for each source based on the expected signal strength. The performance of our proposed detection statistic is demonstrated using simulated sources, with the assumption that all pulsar ellipticities belong to a common (yet unknown) distribution. Comparing with an equal-weight strategy and with individual source approaches, we show that the weighted combination of all known pulsars, where weights are assigned based on the pulsars’ known information, such as sky location, frequency and distance, as well as the detector sensitivity, always provides a more sensitive detection statistic.

To take full advantage of the unprecedented power of upcoming weak lensing surveys, understanding the noise, such as cosmic variance and geometry/mask effects, is as important as understanding the signal itself. Accurately quantifying the noise requires a large number of statistically independent mocks for a variety of cosmologies. This is impractical for weak lensing simulations, which are costly for simultaneous requirements of large box size (to cover a significant fraction of the past light cone) and high resolution (to robustly probe the small scale where most lensing signal resides). Therefore, fast mock generation methods are desired and are under intensive investigation. We propose a new fast weak lensing map generation method, named the inverse-Gaussianization method, based on the finding that a lensing convergence field can be Gaussianized to excellent accuracy by a local transformation [Y. Yu, P. Zhang, W. Lin, W. Cui, and J. N. Fry, Phys. Rev. D 84, 023523 (2011).]. Given a simulation, it enables us to produce as many as infinite statistically independent lensing maps as fast as producing the simulation initial conditions. The proposed method is tested against simulations for each tomography bin centered at lens redshift $z\sim 0.5$, 1, and 2, with various statistics. We find that the lensing maps generated by our method have reasonably accurate power spectra, bispectra, and power spectrum covariance matrix. Therefore, it will be useful for weak lensing surveys to generate realistic mocks. As an example of application, we measure the probability distribution function of the lensing power spectrum, from 16384 lensing maps produced by the inverse-Gaussianization method.

Taking into account the mass splittings between three active neutrinos, we investigate the impacts of dark energy on constraining the total neutrino mass $\sum m_{\nu }$ by using recent cosmological observations. We consider two typical dark energy models, namely, the $w\mathrm{CDM}$ model and the holographic dark energy (HDE) model, which both have an additional free parameter compared with the $\mathrm{\Lambda }\mathrm{CDM}$ model. We employ the Planck 2015 data of CMB temperature and polarization anisotropies, combined with low-redshift measurements on BAO distance scales, type Ia supernovae, the Hubble constant, and Planck lensing. Compared to the $\mathrm{\Lambda }\mathrm{CDM}$ model, our study shows that the upper limit on $\sum m_{\nu }$ becomes much looser in the $w\mathrm{CDM}$ model but much tighter in the HDE model. In the HDE model, we obtain the 95% confidence level upper limit $\sum m_{\nu }<0.105\mathrm{eV}$ for three degenerate neutrinos. This might be the most stringent constraint on $\sum m_{\nu }$ by far, and it is on the verge of diagnosing the neutrino mass hierarchies in the HDE model. However, the difference of ${\chi }^2$ is still not significant enough to distinguish the neutrino mass hierarchies, even though the minimal ${\chi }^2$ of the normal hierarchy is slightly smaller than that of the inverted hierarchy.

We study the nonlinear gravitational dynamics of a universe filled with a pressureless fluid and a cosmological constant $\mathrm{\Lambda }$ in the context of Newtonian gravity, and in the relativistic post-Friedmann approach proposed in paper I [I. Milillo et al., Phys. Rev. D 92, 023519 (2015)]. The post-Friedmann approximation scheme is based on the $1/c$ expansion of the space-time metric and the energy-momentum tensor, and includes nonlinear Newtonian cosmology. Here we establish the nonlinear post-Friedmann framework in the Lagrangian-coordinates approach for structure formation. For this we first identify a Lagrangian gauge which is suitable for incorporating nonzero vorticity. We analyze our results in two limits: at the leading order we recover the fully nonlinear Newtonian cosmological equations in the Lagrangian formulation, and we provide a space-time metric consistent from the perspective of general relativity. We then linearize our expressions and recover the relativistic results at first order in cosmological perturbation theory. Therefore, the introduced approximation scheme provides a unified treatment for the two leading-order regimes, from the small scales described by Newtonian gravity to the large linear scale, where first-order relativistic cosmological perturbation theory gives a very good description of structure formation.

We study the collapse of a self-gravitating Bose-Einstein condensate with attractive self-interaction. Equilibrium states in which the gravitational attraction and the attraction due to the self-interaction are counterbalanced by the quantum pressure (Heisenberg’s uncertainty principle) exist only below a maximum mass $M_{\max }=1.012\hslash /\sqrt{Gm|a_s|}$ where $a_s<0$ is the scattering length of the bosons and $m$ is their mass [P. H. Chavanis, Phys. Rev. D 84, 043531 (2011)]. For $M>M_{\max }$ the system is expected to collapse and form a black hole. We study the collapse dynamics by making a Gaussian ansatz for the wave function and reducing the problem to the study of the motion of a particle in an effective potential. We find that the collapse time scales as $(M/M_{\max }-1{)}^{-1/4}$ for $M\to M_{\max }^{+}$ and as $M^{-1/2}$ for $M\gg M_{\max }$. Other analytical results are given above and below the critical point corresponding to a saddle-node bifurcation. We apply our results to QCD axions with mass $m={10}^{-4}\mathrm{eV}/c^2$ and scattering length $a_s=-5.8\times {10}^{-53}\mathrm{m}$ for which $M_{\max }=6.5\times {10}^{-14}{M}_{\odot }$ and $R=3.3\times {10}^{-4}{R}_{\odot }$. We confirm our previous claim that bosons with attractive self-interaction, such as QCD axions, may form low mass stars (axion stars or dark matter stars) but cannot form dark matter halos of relevant mass and size. These mini axion stars could be the constituents of dark matter. They can collapse into mini black holes of mass $\sim {10}^{-14}{M}_{\odot }$ in a few hours. In that case, dark matter halos would be made of mini black holes. We also apply our results to ultralight axions with mass $m=1.93\times {10}^{-20}\mathrm{eV}/c^2$ and scattering length $a_s=-8.29\times {10}^{-60}\mathrm{fm}$ for which $M_{\max }=0.39\times 10^6{M}_{\odot }$ and $R=33\mathrm{pc}$. These ultralight axions could cluster into dark matter halos. Axionic dark matter halos with attractive self-interaction can collapse into supermassive black holes of mass $\sim 10^6{M}_{\odot }$ (similar to those reported at the center of galaxies) in about one million years. We point out the limitations of the Gaussian ansatz to describe the late stages of the collapse dynamics. We also mention the possibility that, instead of forming a black hole, the collapse may be accompanied by a burst or relativistic axions (bosenova) leading to a cycle of collapses and explosions as observed for nongravitational Bose-Einstein condensates with attractive self-interaction.

We investigate the effects of resonance-continuum interference on the diphoton spectrum in the presence of a new spin-0 or spin-2 state produced via gluons or quarks and decaying to pairs of photons. Interference effects can significantly influence the extraction of resonance masses and widths from the diphoton spectrum, particularly in the case of a spin-2 resonance produced via quarks. We illustrate these effects via a binned likelihood analysis of LHC diphoton data at both 8 and 13 TeV.

The LHC has recently reported a slight excess in the $h\to \tau \mu$ channel. If this lepton flavor violating (LFV) decay is confirmed, an extension of the standard model (SM) will be required to explain it. In this paper we investigate two different possibilities to accommodate such a LFV process: the first scenario is based on flavor off-diagonal $A$ terms in the minimal supersymmetric standard model, and the second is a model where the Higgs boson couples to new vectorlike fermions that couple to the SM leptons through a LFV four-fermion interaction. In the supersymmetric model, we find that the sizes of the $A$ terms needed to accommodate the $h\to \tau \mu$ excess are in conflict with charge- and color-breaking vacuum constraints. In the second model, the excess can be successfully explained while satisfying all other flavor constraints, with order-one couplings, vectorlike fermion masses as low as 15 TeV, and a UV scale higher than 35 TeV.

We study parton distributions for two partons, a quark and a gluon, in the light-front dressed quark model, with a focus on the correlations between the two partons. The model calculation leads to sizable spin-spin and spin-kinematic correlations of interest for studies of double parton scattering in high-energy collisions. In particular, we find that the transverse dependence of the double parton distributions (DPDs) does not factorize within the model. The results give insight into the strengths of the correlations in different kinematical regions, which can help in constructing input DPDs in cross-section calculations.

The variational approach to QCD in Coulomb gauge is revisited. By assuming the non-Abelian Coulomb potential to be given by the sum of its infrared and ultraviolet parts, i.e. by a linearly rising potential and an ordinary Coulomb potential, and by using a Slater determinant ansatz for the quark wave functional, which contains the coupling of the quarks and the gluons with two different Dirac structures, we obtain variational equations for the kernels of the fermionic vacuum wave functional, which are free of ultraviolet divergences. Thereby, a Gaussian-type wave functional is assumed for the gluonic part of the vacuum. By using the results of the pure Yang-Mills sector for the gluon propagator as input, we solve the equations for the fermionic kernels numerically and calculate the quark condensate and the effective quark mass in leading order. Assuming a value of ${\sigma }_{\mathrm{C}}=2.5\sigma$ for the Coulomb string tension (where $\sigma$ is the usual Wilsonian string tension) the phenomenological value of the quark condensate $⟨\overline{\psi }\psi ⟩\simeq (-235\mathrm{MeV}{)}^3$ is reproduced with a value of $g\simeq 2.1$ for the strong coupling constant of the quark-gluon vertex.

Properties of hot dense ultrarelativistic spinor matter in a slab of finite width, placed in a transverse uniform magnetic field, are studied. The admissible set of boundary conditions is determined by the requirement that spinor matter be confined inside the slab. In thermal equilibrium, the chiral separation effect in the slab is shown to depend on both temperature and chemical potential; this is distinct from the unrealistic case of the magnetic field filling the unbounded (infinite) medium, when the effect is temperature independent. In the realistic case of the slab, a stepwise behavior of the axial current density at zero temperature is smoothed out as temperature increases, turning into a linear behavior at infinitely large temperature. A choice of boundary conditions can facilitate either augmentation or attenuation of the chiral separation effect; in particular, the effect can persist even at zero chemical potential, if temperature is finite. Thus the boundary condition can serve as a source that is additional to the spinor matter density.

It is known that not all summation methods are linear and stable. Zeta function regularization is in general nonlinear. However, in some cases formal manipulations with zeta function regularization (assuming linearity of sums) lead to correct results. We consider several examples and show why this happens.

We study the impact of axion emission in simulations of massive star explosions, as an additional source of energy loss complementary to the standard neutrino emission. The inclusion of this channel shortens the cooling time of the nascent protoneutron star and hence the duration of the neutrino signal. We treat the axion-matter coupling strength as a free parameter to study its impact on the protoneutron star evolution as well as on the neutrino signal. We furthermore analyze the observability of the enhanced cooling in current and next-generation underground neutrino detectors, showing that values of the axion mass $m_a\gtrsim 8\times {10}^{-3}\mathrm{eV}$ can be probed. Therefore a galactic supernova neutrino observation would provide a valuable possibility to probe axion masses in a range within reach of the planned helioscope experiment, the International Axion Observatory.