In Ref. [1] we have presented the results of an exploratory lattice QCD computation of the long-distance contribution to the $K^{+}\to {\pi }^{+}\nu \overline{\nu }$ decay amplitude. In the present paper we describe the details of this calculation, which includes the implementation of a number of novel techniques. The $K^{+}\to {\pi }^{+}\nu \overline{\nu }$ decay amplitude is dominated by short-distance contributions which can be computed in perturbation theory with the only required nonperturbative input being the relatively well-known form factors of semileptonic kaon decays. The long-distance contributions, which are the target of this work, are expected to be of $O(5\%)$ in the branching ratio. Our study demonstrates the feasibility of lattice QCD computations of the $K^{+}\to {\pi }^{+}\nu \overline{\nu }$ decay amplitude, and in particular of the long-distance component. Though this calculation is performed on a small lattice ($16^3\times 32$) and at unphysical pion, kaon and charm quark masses, $m_{\pi }=420\mathrm{MeV}$, $m_K=563\mathrm{MeV}$ and $m_c^{\overline{\mathrm{MS}}}(2\mathrm{GeV})=863\mathrm{MeV}$, the techniques presented in this work can readily be applied to a future realistic calculation.

We study the density of states method as well as reweighting to explore the low temperature phase diagram of QCD at finite baryon chemical potential. We use four flavors of staggered quarks, a tree-level Symanzik-improved gauge action, and four stout smearing steps on lattices with $N_s=4$, 6, 8 and $N_t=6–16$. We compare our results to that of the phase quenched ensemble and also determine the pion and nucleon masses. In the density of states approach, we apply pion condensate or gauge action density fixing. We find that the density of states method performs similarly to reweighting. At $T\approx 100\mathrm{MeV}$, we find an indication of the onset of the quark number density at around $\mu /m_N\sim 0.16–0.18$ on $6^4$ lattices at $\beta =2.9$.

We investigate the dynamic properties of systems at thermal first-order transitions (FOT), when boundary conditions favor one of the two phases. In particular, we study the dynamic scaling properties arising from a slow heating of systems with disordered boundary conditions, starting in the ordered phase and moving across the FOT. As a theoretical laboratory we consider the two-dimensional Potts model. We show that a power-law dynamic scaling emerges, associated with a mixed regime where the two phases are spatially separated. We argue that these features generally apply to systems at FOTs, when boundary conditions favor one of the two phases. In particular, they should be relevant for the experimental search of FOTs of the quark-gluon plasma in heavy-ion collisions.

Various classical solutions to lower dimensional Ishibashi-Kawai-Kitazawa-Tsuchiya–like Lorentzian matrix models are examined in their commutative limit. Poisson manifolds emerge in this limit, and their associated induced and effective metrics are computed. Signature change is found to be a common feature of these manifolds when quadratic and cubic terms are included in the bosonic action. In fact, a single manifold may exhibit multiple signature changes. Regions with a Lorentzian signature may serve as toy models for cosmological spacetimes, complete with cosmological singularities, occurring at the signature change. The singularities are resolved away from the commutative limit. Toy models of open and closed cosmological spacetimes are given in two and four dimensions. The four-dimensional cosmologies are constructed from noncommutative complex projective spaces, and they are found to display a rapid expansion near the initial singularity.

We consider a noncommutative field theory in three space-time dimensions, with space-time star commutators reproducing a solvable Lie algebra. The $\star$-product can be derived from a twist operator and it is shown to be invariant under twisted Poincaré transformations. In momentum space the noncommutativity manifests itself as a noncommutative $\star$-deformed sum for the momenta, which allows for an equivalent definition of the $\star$-product in terms of twisted convolution of plane waves. As an application, we analyze the $\lambda {\varphi }^4$ field theory at one loop and discuss its UV/IR behavior. We also analyze the kinematics of particle decay for two different situations: the first one corresponds to a splitting of space-time where only space is deformed, whereas the second one entails a nontrivial $\star$-multiplication for the time variable, while one of the three spatial coordinates stays commutative.

We calculate the entropy and the temperature dependent part of the free energy for a free standing plane plasma sheet and for the a free standing plane slab of finite thickness with dispersion described by the plasma model. In case the plasma sheet describes a charged fluid, the entropy is positive. In case it describes a polarizable dipole sheet, the entropy takes negative values in a certain parameter region. Negative entropy is also observed for the slab, however with the reservation that the contribution from the surface plasmons was not accounted for.

The semiclassical approximation of the worldline path integral is a powerful tool to study nonperturbative electron-positron pair creation in spacetime-dependent background fields. Finding solutions of the classical equations of motion, i.e., worldline instantons, is possible analytically only in special cases, and a numerical treatment is nontrivial as well. We introduce a completely general numerical approach based on an approximate evaluation of the discretized path integral that easily and robustly gives the full semiclassical pair production rate in nontrivial multidimensional fields, and apply it to some example cases.

For gauge groups $\mathrm{SO}(n+1)$, $\mathrm{SU}(m+1)$, and $\mathrm{Sp}(\ell +1)$, we construct equivariant Yang-Mills solutions on de Sitter space in $n+1$, $2(m+1)$, and $4(\ell +1)$ spacetime dimensions. The latter is conformally mapped to a finite cylinder over a coset space realizing an appropriate unit sphere. The equivariance condition reduces the Yang-Mills system to an analog Newtonian particle in one or two dimensions subject to a time-dependent friction and a particular potential. We analyze some properties of the solutions such as their action and energy and display all analytic ones. Beyond ${\mathrm{dS}}_4$, all such configurations have finite energy but infinite action.

The Brans-Dicke-like field of scalar-tensor gravity can be described as an imperfect fluid in an approach in which the field equations are regarded as effective Einstein equations. After completing this approach, we recover, as a special case, the known effective fluid for a scalar coupled nonminimally to the Ricci curvature, and we describe the imperfect fluid equivalent of $f(R)$ gravity. A symmetry of electrovacuum Brans-Dicke gravity is translated into a symmetry of the corresponding effective fluid. The discussion is valid for any spacetime geometry.

Binary-black-hole dynamics cannot be related to the resulting gravitational-wave signal by a constant retarded time. This is due to the nontrivial dynamical spacetime curvature between the source and the signal. In a numerical-relativity simulation there is also some ambiguity in the black-hole dynamics, which depend on the gauge (coordinate) choices used in the numerical solution of Einstein’s equations. It has been shown previously that a good approximation to the direction of the binary’s time-dependent orbital angular momentum $\widehat{\mathbf{L}}(t)$ can be calculated from the gravitational-wave signal. This is done by calculating the direction that maximizes the quadrupolar ($\ell =2$, $|m|=2$) emission. The direction depends on whether we use the Weyl scalar ${\psi }_4$ or the gravitational-wave strain $h$, but these directions are nonetheless invariant for a given binary configuration. We treat the ${\psi }_4$-based direction as a proxy to $\widehat{\mathbf{L}}(t)$. We investigate how well the binary’s orbital phase, ${\varphi }_{\mathrm{orb}}(t)$, can also be estimated from the signal. For this purpose we define a quantity $\mathrm{\Phi }(t)$ that agrees well with ${\varphi }_{\mathrm{orb}}(t)$. One application is to studies that involve injections of numerical-relativity waveforms into gravitational-wave detector data.

We explore possible non-Gaussian features of primordial gravitational waves by constructing model-independent templates for nonlinearity parameters of the tensor bispectrum. Our analysis is based on effective field theory of inflation that relies on no particular model as such, and thus the results are quite generic. The analysis further reveals that chances of detecting the squeezed limit tensor bispectrum are fairly high compared to the equilateral limit. We also discuss the prospects of detectability in upcoming CMB missions.

We consider a scenario in which the inflaton $\varphi$ is a pseudoscalar field nonminimally coupled to gravity through a term of the form $\mathcal{X}R{\varphi }^2$. The pseudoscalar is also coupled to a $U(1)$ gauge field (or an ensemble of $\mathcal{N}$ gauge fields) through an axial coupling of the form $\varphi F\tilde{F}$. After [M. M. Anber and L. Sorbo, Phys. Rev. D 81, 043534 (2010)], it is well known that this axial coupling leads to a production of gauge particles which acts as a friction term in the dynamics of the inflaton, producing a slow-roll regime even in presence of a steep potential. A remarkable result in this scenario is that the spectrum of the chiral gravitational waves sourced by the scalar-gauge field interplay can be enhanced due to the nonminimal coupling with gravity, leading to measurable signatures, while maintaining agreement with current observational constraints on $n_s$ and $r$. The inclusion of nonminimal coupling could be helpful to alleviate tensions with non-Gaussianity bounds in models including axial couplings.

Primordial magnetic fields (PMFs) can source gravitational wave background (GWB). In this paper, we investigate the possible constraints on small-scale PMF considering the ongoing and forthcoming direct detection observations of GWB. In contrast to the conventional cosmological probes, e.g., cosmic microwave background anisotropies, which are useful to investigate large-scale PMFs ($>1\mathrm{Mpc}$), the direct detection experiments of GWB can explore small-scale PMFs whose scales correspond to the observed frequencies of GWB. We show that future ground-based or space-based interferometric gravitational wave detectors give a strong constraint of about $10^2\mathrm{nG}$ on much smaller scales of about $k\approx {10}^{12}{\mathrm{Mpc}}^{-1}$. We also demonstrate that pulsar timing arrays have a potential to strongly constrain PMFs. The current limits on GWB from pulsar timing arrays can put the tight constraint on the amplitude of the PMFs of about 30 nG whose coherent length is about $k\approx {10}^6{\mathrm{Mpc}}^{-1}$. The future experiments for the direct detection of GWB by the Square Kilometre Array could give much tighter constraints on the amplitude of PMFs of about 5 nG on $k\approx {10}^6{\mathrm{Mpc}}^{-1}$, on which scales it is difficult to reach by using the cosmological observations.

Cannibals are dark matter particles with a scattering process that allows three particles to annihilate to two. This exothermic process keeps the gas of the remaining particles warm long after they become nonrelativistic. A cannibalizing dark sector which is decoupled from the standard model naturally arises from a pure-glue confining hidden sector. It has an effective field theory description with a single massive interacting real scalar field, the lightest glueball. Since warm dark matter strongly suppresses the growth of structure, cannibals cannot be all of the dark matter. Thus, we propose a scenario where most dark matter is noninteracting and cold but about 1 percent is cannibalistic. We review the cannibals’ unusual scaling of the temperature and energy and number densities with redshift and generalize the equations for the growth of matter density perturbations to the case of cannibals. We solve the equations numerically to predict the scaling of the Hubble parameter and the characteristic shape of the linear matter power spectrum as a function of model parameters. Our results may have implications for the ${\sigma }_8$ and $H_0$ problems.

The HAWC Collaboration has recently reported the detection of bright and spatially extended multi-TeV gamma-ray emission from Geminga, Monogem, and a handful of other nearby, middle-aged pulsars. The angular profile of the emission observed from these pulsars is surprising, in that it implies that cosmic-ray diffusion is significantly inhibited within $\sim 25\mathrm{pc}$ of these objects, compared to the expectations of standard Galactic diffusion models. This raises the important question of whether the diffusion coefficient in the local interstellar medium is also low, or whether it is instead better fit by the mean Galactic value. Here, we utilize recent observations of the cosmic-ray electron spectrum (extending up to $\sim 20\mathrm{TeV}$) by the H.E.S.S. Collaboration to show that the local diffusion coefficient cannot be as low as it is in the regions surrounding Geminga and Monogem. Instead, we conclude that cosmic rays efficiently diffuse through the bulk of the local interstellar medium. Among other implications, this further supports the conclusion that pulsars significantly contribute to the observed positron excess and provides strong evidence for spatially varying diffusion coefficients throughout the Milky Way.

The electroweak fine-tuning measure ${\mathrm{\Delta }}_{\mathrm{EW}}$ allows for correlated supersymmetry (SUSY) soft terms as are expected in any ultraviolet complete theory. Requiring no less than 3% electroweak fine-tuning implies upper bounds of about 360 GeV on all Higgsinos, while top squarks are lighter than $\sim 3\mathrm{TeV}$ and gluinos are bounded by $\sim 6–9\mathrm{TeV}$. We examine the reach for SUSY of the planned high luminosity (HL: $3{\mathrm{ab}}^{-1}$ at 14 TeV) and the proposed high energy (HE: $15{\mathrm{ab}}^{-1}$ at 27 TeV) upgrades of the LHC via four LHC collider search channels relevant for natural SUSY: 1. gluino pair production followed by gluino decay to third generation (s)quarks, 2. top squark pair production followed by decay to third generation quarks and light Higgsinos, 3. neutral Higgsino pair production with QCD jet radiation (resulting in monojet events with soft dileptons), and 4. wino pair production followed by decay to light Higgsinos leading to same-sign diboson production. We confront our reach results with upper limits on superpartner masses in four natural SUSY models: natural gravity mediation via the 1. two- and 2. three-extra-parameter nonuniversal Higgs models, 3. natural minilandscape models with generalized mirage mediation and 4. natural anomaly mediation We find that while the HL-LHC can probe considerable portions of natural SUSY parameter space in all these models, the HE-LHC will decisively cover the entire natural SUSY parameter space with better than 3% fine-tuning.

A correlated analysis of observables arising from loop induced effects from a vectorlike generation is given. The observables include flavor changing radiative decays $\mu \to e\gamma$, $\tau \to \mu \gamma$, $\tau \to e\gamma$, electric dipole moments of the charged leptons $e$, $\mu$, $\tau$, and corrections to magnetic dipole moments of $g_{\mu }-2$ and $g_e-2$. In this work we give a full analysis of the corrections to these observables by taking into account both the supersymmetry loops as well as the exchange of a vectorlike leptonic generation. Thus the fermion mass matrix involves a $5\times 5$ mixing matrix while the scalar sector involves a $10\times 10$ mixing matrix including the $CP$ violating phases from the vectorlike sector. The analysis is done under the constraint of the Higgs boson mass at the experimentally measured value. The loops considered include the exchange of $W$ and $Z$ bosons and of leptons and a mirror lepton, and the exchange of charginos and neutralinos, sleptons and mirror sleptons. The correction to the diphoton decay of the Higgs $h\to \gamma \gamma$ including the exchange of the vectorlike leptonic multiplet is also computed.

We analyze the prospects of reconstructing the mass of a heavy charged Higgs boson in the context of a type X two-Higgs-doublet model where a light pseudoscalar $A$ in the mass range 40–60 GeV is phenomenologically allowed, and is in fact favored if one wants to explain the muon anomalous magnetic moment. The associated production of charged Higgs bosons with the pseudoscalar $A$ and subsequent decay of the charged Higgs boson into a $W$ and $A$ is found to be our relevant channel. The branching ratio for $H^{+}\to W^{+}A$ with $M_{H^{+}}\sim 200\mathrm{GeV}$ is close to 50%. The hadronic decay of the $W$ boson, coupled with the leptonic decays of $A$ into a tau and muon pair, help in identifying the charged Higgs bosons. The neutral heavy Higgs boson, being degenerate with the charged Higgs boson for most of the allowed parameter space of the model, also contributes to similar final states. Thus, both the charged and neutral $CP$-even heavy Higgs bosons are reconstructed within a band of about 10 GeV.

We present the first nonperturbatively renormalized determination of the glue momentum fraction $⟨x{⟩}_g$ in the nucleon, based on lattice-QCD simulations at the physical pion mass using the cluster-decomposition error reduction technique. We provide the first practical strategy to renormalize the gauge energy-momentum tensor nonperturbatively in the regularization-independent momentum-subtraction (RI/MOM) scheme and convert the results to the $\overline{\mathrm{MS}}$ scheme with one-loop matching. The simulation results show that the cluster-decomposition error reduction technique can reduce the statistical uncertainty of its renormalization constant by a factor of $\mathcal{O}(300)$ in calculations using a typical state-of-the-art lattice volume, and the nonperturbatively renormalized $⟨x{⟩}_g$ is shown to be independent of the lattice definitions of the gauge energy-momentum tensor up to discretization errors. We determine the renormalized $⟨x{⟩}_g^{\overline{\mathrm{MS}}}(2\mathrm{GeV})$ to be 0.47(4)(11) at the physical pion mass, which is consistent with the experimentally determined value.

We have made a survey of heavy-to-heavy and heavy-to-light nonleptonic heavy baryon two-body decays and have identified those decays that proceed solely via $W$-boson emission, i.e., via the tree graph contribution. Some sample decays are ${\mathrm{\Omega }}_b^{-}\to {\mathrm{\Omega }}_c^{(*)0}{\rho }^{-}({\pi }^{-})$, ${\mathrm{\Omega }}_b^{-}\to {\mathrm{\Omega }}^{-}J/\psi ({\eta }_c)$, ${\mathrm{\Xi }}_b^{0,-}\to {\mathrm{\Xi }}^{0,-}J/\psi ({\eta }_c)$, ${\mathrm{\Lambda }}_b\to \mathrm{\Lambda }J/\psi ({\eta }_c)$, ${\mathrm{\Lambda }}_b\to {\mathrm{\Lambda }}_c{D}_s^{(*)}$, ${\mathrm{\Omega }}_c^0\to {\mathrm{\Omega }}^{-}{\rho }^{+}({\pi }^{+})$, and ${\mathrm{\Lambda }}_c\to p\varphi$. We make use of the covariant confined quark model previously developed by us to calculate the tree graph contributions to these decays. We calculate rates, branching fractions and, for some of these decays, decay asymmetry parameters. We compare our results to experimental findings and the results of other theoretical approaches when they are available. Our main focus is on decays to final states with a lepton pair because of their clean experimental signature. For these decays we discuss two-fold polar angle decay distributions such as in the cascade decay ${\mathrm{\Omega }}_b^{-}\to {\mathrm{\Omega }}^{-}(\to \mathrm{\Xi }\pi ,\mathrm{\Lambda }{K}^{-})+J/\psi (\to {\ell }^{+}{\ell }^{-})$. Lepton mass effects are always included in our analysis.