We consider a symmetric scalar theory with quartic coupling in four dimensions. We show that the four-loop 2PI calculation can be done using a renormalization group method. The calculation involves one bare coupling constant which is introduced at the level of the Lagrangian and is therefore conceptually simpler than a standard 2PI calculation, which requires multiple counterterms. We explain how our method can be used to do the corresponding calculation at the 4PI level, which cannot be done using any known method by introducing counterterms.

We present a quantum algorithm for the calculation of scattering amplitudes of massive charged scalar particles in scalar quantum electrodynamics. Our algorithm is based on continuous-variable quantum computing architecture resulting in exponential speedup over classical methods. We derive a simple form of the Hamiltonian including interactions and a straightforward implementation of the constraint due to gauge invariance.

We compute the mass function of bound states of asymmetric dark matter—nuggets—synthesized in the early Universe. We apply our results for the nugget density and binding energy computed from a nuclear model to obtain analytic estimates of the typical nugget size exiting synthesis. We numerically solve the Boltzmann equation for synthesis including two-to-two fusion reactions, estimating the impact of bottlenecks on the mass function exiting synthesis. These results provide the basis for studying the late Universe cosmology of nuggets in a future companion paper.

The one-loop renormalization of the action for a set of Dirac fermions and a set of scalars spanning an arbitrary manifold coupled via Yukawa-like and gauge interactions is presented. The computation is performed with functional methods and in a geometric formulation that preserves at all stages the symmetries of the action. The result is then applied to Higgs effective field theory to obtain the renormalization group evolution. In the standard model limit of this effective field theory the renormalization group evolution equations collapse into a smaller linearly independent set; this allows to probe the dynamics of the scalar discovered at LHC via de-correlations in the running of couplings.

We study the complementarity between accelerator and reactor coherent elastic neutrino-nucleus elastic scattering ($\mathrm{CE}\nu \mathrm{NS}$) experiments for constraining new physics in the form of nonstandard neutrino interactions (NSI). First, considering just data from the recent observation by the Coherent experiment, we explore interpretive degeneracies that emerge when activating either two or four unknown NSI parameters. Next, we demonstrate that simultaneous treatment of reactor and accelerator experiments, each employing at least two distinct target materials, can break a degeneracy between up and down flavor-diagonal NSI terms that survives analysis of neutrino oscillation experiments. Considering four flavor-diagonal ($ee/\mu \mu$) up- and down-type NSI parameters, we find that all terms can be measured with high local precision (to a width as small as $\sim 5\%$ in Fermi units) by next-generation experiments, although discrete reflection ambiguities persist.

We investigate the quark content of the low-lying states in the $I(J^P)=1(0^{+})$ sector, which are the quantum numbers of the $a_0(980)$ meson, using lattice QCD. To this end, we consider correlation functions of six different two- and four-quark interpolating fields. We evaluate all diagrams, including diagrams, where quarks propagate within a time slice, e.g. with closed quark loops. We demonstrate that diagrams containing such closed quark loops have a drastic effect on the final results and, thus, may not be neglected. Our analysis, which is carried out at unphysically heavy $u$ and $d$ quark mass corresponding to $m_{\pi }=296(3)\mathrm{MeV}$ and in a single spatial volume of extent 2.9 fm, shows that in addition to the expected spectrum of two-meson scattering states there is an additional energy level around the two-particle thresholds of $K+\overline{K}$ and $\eta +\pi$. This additional state, which is a candidate for the $a_0(980)$ meson, couples to a quark-antiquark as well as to a diquark-antidiquark interpolating field, indicating that it is a superposition of an ordinary $\overline{q}q$ and a tetraquark structure. The analysis is performed using AMIAS, a novel statistical method based on the sampling of all possible spectral decompositions of the considered correlation functions, as well as solving standard generalized eigenvalue problems.

We determine the light meson spectrum in QCD in the presence of background magnetic fields using quenched Wilson fermions. Our continuum extrapolated results indicate a monotonous reduction of the connected neutral pion mass as the magnetic field grows. The vector meson mass is found to remain nonzero, a finding relevant for the conjectured $\rho$-meson condensation at strong magnetic fields. The continuum extrapolation was facilitated by adding a novel magnetic field–dependent improvement term to the additive quark mass renormalization. Without this term, sizable lattice artifacts that would deceptively indicate an unphysical rise of the connected neutral pion mass for strong magnetic fields are present. We also investigate the impact of these lattice artifacts on further observables like magnetic polarizabilities and discuss the magnetic field–induced mixing between $\rho$-mesons and pions. We also derive Ward-Takashi identities for $\mathrm{QCD}+\mathrm{QED}$ both in the continuum formulation and for (order $a$–improved) Wilson fermions.

In this work, we explore the competition between magnetic catalysis effect and chiral rotation effect in a general parallel electromagnetic field within the effective Nambu–Jona-Lasinio model. For a given electric field $E$ at zero temperature, the mass gap shows three different features with respect to an increasing magnetic field $B$: increasing monotonically, decreasing after increasing, and decreasing monotonically. By making use of strong magnetic field approximation, we illuminate that this is due to the competition between catalysis effect and chiral rotation effect induced both by the magnetic field, and a critical electric field $\sqrt{e{E}_c}=86.4\mathrm{MeV}$ is found beyond which the mass gap will eventually decrease at large $B$. As only large magnetic field is relevant for the derivation, the critical electric field does not depend on the temperature $T$ or chemical potential $\mu$.

We perform real-time lattice simulations of nonequilibrium quark production in the longitudinally expanding QCD plasma. Starting from a highly occupied gluonic state with vacuum quark sector, we extract the time evolution of quark and gluon number densities per unit transverse area and rapidity. The total quark number shows after an initial rapid increase an almost linear growth with time. Remarkably, this growth rate appears to be consistent with a simple kinetic theory estimate involving only two-to-two scattering processes in small-angle approximation. This extends previous findings about the role of two-to-two scatterings for purely gluonic dynamics in accordance with the early stages of the bottom-up thermalization scenario.

We calculate the masses and sigma terms of the doubly charmed baryons up to next-to-next-to-next-to-leading order [i.e., $\mathcal{O}(p^4)$] in a covariant baryon chiral perturbation theory by using the extended-on-mass-shell renormalization scheme. Their expressions both in infinite and finite volumes are provided for chiral extrapolation in lattice QCD. As a first application, our chiral results of the masses are confronted with the existing lattice QCD data in the presence of finite-volume corrections. Up to $\mathcal{O}(p^3)$, all relevant low-energy constants can be well determined. As a consequence, we obtain the physical values for the masses of ${\mathrm{\Xi }}_{cc}$ and ${\mathrm{\Omega }}_{cc}$ baryons by extrapolating to the physical limit. Our determination of the ${\mathrm{\Xi }}_{cc}$ mass is consistent with the recent experimental value by LHCb Collaboration, however, larger than the one by SELEX Collaboration. In addition, we predict the pion-baryon and strangeness-baryon sigma terms, as well as the mass splitting between the ${\mathrm{\Xi }}_{cc}$ and ${\mathrm{\Omega }}_{cc}$ states. Their quark mass dependences are also discussed. The numerical procedure can be applied to the chiral results of $\mathcal{O}(p^4)$ order, where more unknown constants are involved, when more data are available for unphysical pion masses.

We propose a direct measurement of the Cabibbo-Kobayashi-Maskawa element $V_{td}$ at the LHC. Making use of the imbalance between $d$ and $\overline{d}$ quark content in the proton, we show that a nonzero $V_{td}$ induces a charge asymmetry in the $tW$ associated production. The main backgrounds to this process—$t\overline{t}$ production, and $tW$-associated production mediated by $V_{tb}$—give charge-symmetric contributions at leading order in QCD. Therefore, using specific kinematic features of the signal, we construct a charge asymmetry in the dilepton final state which—due also to a reduction of systematic uncertainties in the asymmetry—is potentially sensitive to $V_{td}$ suppressed effects. In particular, using signal and background simulations up to the detector level, we show that this new observable could already improve the current direct upper bound on $|V_{td}|$ with existing LHC data. We also project that $|V_{td}|$ values down to $\sim 10$ times the standard model prediction could be probed at the high-luminosity LHC.

Motivated by the large number of $B_c$ meson decay modes observed recently by several detectors at the LHC, we present a detailed analysis of the $B_c$ meson decaying to the $P$-wave charmonium states and a light pseudoscalar ($P$) or vector ($V$) meson within the framework of perturbative QCD factorization. The $P$-wave charmonium distribution amplitudes are extracted from the $n=2$, $l=1$ Schrödinger states for a Coulomb potential, which can be taken as the universal nonperturbative objects to analyze the hard exclusive processes with $P$-wave charmonium production. It is found that these decays have large branching ratios of the order of ${10}^{-5}\sim {10}^{-2}$, which seem to be in the reach of future experiments. We also provide predictions for the polarization fractions and relative phases of $B_c\to ({\chi }_{c1},{\chi }_{c2},h_c)V$ decays. It is expected that the longitudinal polarization amplitudes dominate the branching ratios according to the quark helicity analysis, and the magnitudes and phases of parallel polarization amplitude are approximately equal to the perpendicular ones. The obtained results are compared with available experimental data, our previous studies, and numbers from other approaches.

Using a data sample collected with the BESIII detector operating at the BEPCII storage ring at a center-of-mass energy of $\sqrt{s}=4.600\mathrm{GeV}$, we search for the production of $e^{+}{e}^{-}\to \varphi {\chi }_{c0,1,2}$. A search is also performed for the charmonium-like state $X(4140)$ in the radiative transition $e^{+}{e}^{-}\to \gamma X(4140)$ with $X(4140)$ subsequently decaying into $\varphi J/\psi$. The processes $e^{+}{e}^{-}\to \varphi {\chi }_{c1}$ and $\varphi {\chi }_{c2}$ are observed for the first time, each with a statistical significance of more than $10\sigma$, and the Born cross sections are measured to be ($4.2_{-1.0}^{+1.7}\pm 0.3$) and $(6.7_{-1.7}^{+3.4}\pm 0.5)\mathrm{pb}$, respectively, where the first uncertainties are statistical and the second systematic. No significant signals are observed for $e^{+}{e}^{-}\to \varphi {\chi }_{c0}$ and $e^{+}{e}^{-}\to \gamma X(4140)$ and upper limits on the Born cross sections at 90% C.L. are provided at $\sqrt{s}=4.600\mathrm{GeV}$.

We study a class of eight-supercharge little string theories (LSTs) on the world volume of $N$ M5-branes with transverse space ${\mathbb{S}}^1\times ({\mathbb{C}}^2/{\mathbb{Z}}_M)$. These M-brane configurations compactified on a circle are dual to $M$ D5-branes intersecting $N$ NS5-branes on ${\mathbb{T}}^2\times {\mathbb{R}}^{7,1}$ as well as to F-theory compactified on a toric Calabi-Yau threefold $X_{N,M}$. We argue that the Kähler cone of $X_{N,M}$ admits three regions associated with weakly coupled quiver gauge theories of gauge groups $[U(N){]}^M,[U(M){]}^N$, and $[U(\frac{NM}{k}){]}^k$ where $k=\gcd (N,M)$. These provide low-energy descriptions of different LSTs. The duality between the first two gauge theories is well known and is a consequence of the S-duality between D5- and NS5-branes or the T-duality of the LSTs. The triality involving the third gauge theory is new, and we demonstrate it using several examples. We also discuss implications of this triality for the W-algebras associated with the Alday-Gaiotto-Tachikawa dual theories.

Owing to the extreme smallness of any noncommutative scale that may exist in nature, both in the spatial and momentum sector of the quantum phase space, a credible possibility of their detection lies in the gravitational wave (GW) detection scenario, where one effectively probes the relative length-scale variations $\sim \mathcal{O}[{10}^{-20}-{10}^{-23}]$. With this motivation, we have theoretically constructed how a free particle and a harmonic oscillator will respond to linearly and circularly polarized gravitational waves if their quantum mechanical phase space has a noncommutative structure. We critically analyze the formal solutions which show resonance behavior in the responses of both free particle and HO systems to GW with both kind of polarizations. We discuss the possible implications of these solutions in detecting noncommutativity in a GW detection experiment. We use the currently available upper-bound estimates on various noncommutative parameters to anticipate the relative importance of various terms in the solutions. We also argue how the quantum harmonic oscillator system we considered here can be very relevant in the context of the resonant bar detectors of GW which are already operational.

We consider a recently proposed generalization of unimodular gravity, where the lapse function is constrained to be equal to a function of the determinant of the spatial metric $f(h)$, as a potential origin of a dark fluid with a generally $h$-dependent equation of state parameter. We establish the Hamiltonian analysis and the canonical path integral for the theory. All the special cases that do not match unimodular gravity involve the violation of general covariance, and consequently the physical content of the theory is changed significantly. Particularly, the case of a constant function $f$ is shown to contain an extra physical degree of freedom in each point of space. Physical consequences of the extra degree of freedom are studied in a linearized theory, where the extra mode is carried by the trace of the metric perturbation. The trace mode does not propagate as a wave, since it satisfies an elliptic partial differential equation in spacetime. Consequently, the trace perturbation is shown to grow exponentially with time, which implies instability. The case of a general $f(h)$ involves additional second-class constraints, which implies the presence of an extra global degree of freedom that depends only on time (instead of the extra local degree of freedom in the case of a constant $f$).

A detection of B-mode polarization of the cosmic microwave background (CMB) anisotropies would confirm the presence of a primordial gravitational wave background (GWB). In the inflation paradigm, this would be an unprecedented probe of the energy scale of inflation as it is directly proportional to the power spectrum of the GWB. However, similar tensor perturbations can be produced by the matter fields present during inflation, breaking the simple relationship between energy scale and the tensor-to-scalar ratio $r$. It is therefore important to find ways of distinguishing between the generation mechanisms of the GWB. Without doing a full model selection, we analyze the detectability of a new axion-$SU(2)$ gauge field model by calculating the signal-to-noise ratio of future CMB and interferometer observations sensitive to the chirality of the tensor spectrum. We forecast the detectability of the resulting CMB temperature and B-mode (TB) or E-mode and B-mode (EB) cross-correlation by the LiteBIRD satellite, considering the effects of residual foregrounds, gravitational lensing, and assess the ability of such an experiment to jointly detect primordial TB and EB spectra and self-calibrate its polarimeter. We find that LiteBIRD will be able to detect the chiral signal for $r_{*}>0.03$, with $r_{*}$ denoting the tensor-to-scalar ratio at the peak scale, and that the maximum signal-to-noise ratio for $r_{*}<0.07$ is $\sim 2$. We go on to consider an advanced stage of a LISA-like mission, which is designed to be sensitive to the intensity and polarization of the GWB. We find that such experiments would complement CMB observations as they would be able to detect the chirality of the GWB with high significance on scales inaccessible to the CMB. We conclude that CMB two-point statistics are limited in their ability to distinguish this model from a conventional vacuum fluctuation model of GWB generation, due to the fundamental limits on their sensitivity to parity violation. In order to test the predictions of such a model as compared to vacuum fluctuations, it will be necessary to test deviations from the self-consistency relation or use higher order statistics to leverage the non-Gaussianity of the model. On the other hand, in the case of a spectrum peaked at very small scales inaccessible to the CMB, a highly significant detection could be made using space-based laser interferometers.

Neutron stars capture dark matter efficiently. The kinetic energy transferred during capture heats old neutron stars in the local galactic halo to temperatures detectable by upcoming infrared telescopes. We derive the sensitivity of this probe in the framework of effective operators. For dark matter heavier than a GeV, we find that neutron star heating can set limits on the effective operator cutoff that are orders of magnitude stronger than possible from terrestrial direct detection experiments in the case of spin-dependent and velocity-suppressed scattering.

By assuming the existence of extra-dimensional sterile neutrinos in the big bang nucleosynthesis (BBN) epoch, we investigate the sterile neutrino (${\nu }_{\mathrm{s}}$) effects on the BBN and constrain some parameters associated with the ${\nu }_{\mathrm{s}}$ properties. First, for the cosmic expansion rate, we take into account effects of a five-dimensional bulk and intrinsic tension of the brane embedded in the bulk and constrain a key parameter of the extra dimension by using the observational element abundances. Second, effects of the ${\nu }_{\mathrm{s}}$ traveling on or off the brane are considered. In this model, the effective mixing angle between a ${\nu }_{\mathrm{s}}$ and an active neutrino depends on energy, which may give rise to a resonance effect on the mixing angle. Consequently, the reaction rate of the ${\nu }_{\mathrm{s}}$ can be drastically changed during the cosmic evolution. We estimated abundances and temperature of the ${\nu }_{\mathrm{s}}$ by solving the rate equation as a function of temperature until the sterile neutrino decoupling. We then find that the relic abundance of the ${\nu }_{\mathrm{s}}$ is drastically enhanced by the extra dimension and maximized for a characteristic resonance energy $E_{\text{res}}\gtrsim 0.01\mathrm{GeV}$. Finally, some constraints related to the ${\nu }_{\mathrm{s}}$, i.e., mixing angle and mass difference, are discussed in detail with the comparison of our BBN calculations corrected by the extra-dimensional ${\nu }_{\mathrm{s}}$ to observational data on light element abundances.

Two recently found coupled Bogomol’nyi-Prasad-Sommerfield (BPS) submodels of the Skyrme model are further analyzed. First, we provide a geometrical formulation of the submodels in terms of the eigenvalues of the strain tensor. Second, we study their thermodynamical properties and show that the mean-field equations of state coincide at high pressure and read $p=\overline{\rho }/3$. We also provide evidence that matter described by the first BPS submodel has some similarity with a Bose-Einstein condensate. Moreover, we show that extending the second submodel to a non-BPS model by including certain additional terms of the full Skyrme model does not spoil the respective ansatz, leading to an ordinary differential equation for the profile of the Skymion, for any value of the topological charge. This allows for an almost analytical description of the properties of Skyrmions in this model. In particular, we analytically study the breaking and restoration of the BPS property. Finally, we provide an explanation of the success of the rational map ansatz.