We calculate the $\beta$-functions for $SO(N)$ and $SU(N)$ gauge theories coupled to adjoint and fundamental scalar representations, correcting longstanding, previous results. We explore the constraints on $N$ resulting from requiring asymptotic freedom for all couplings. When we take into account the actual allowed behavior of the gauge coupling, the minimum value of $N$ in both cases turns out to be larger than realized in earlier treatments. We also show that in the large $N$ limit, both models have large regions of parameter space corresponding to total asymptotic freedom.

We explore the possibility that scale symmetry is a quantum symmetry that is broken only spontaneously and apply this idea to the standard model. We compute the quantum corrections to the potential of the Higgs field ($\varphi$) in the classically scale-invariant version of the standard model ($m_{\varphi }=0$ at tree level) extended by the dilaton ($\sigma$). The tree-level potential of $\varphi$ and $\sigma$, dictated by scale invariance, may contain nonpolynomial effective operators, e.g., ${\varphi }^6/{\sigma }^2$, ${\varphi }^8/{\sigma }^4$, ${\varphi }^{10}/{\sigma }^6$, etc. The one-loop scalar potential is scale invariant, since the loop calculations manifestly preserve the scale symmetry, with the dimensional regularization subtraction scale $\mu$ generated spontaneously by the dilaton vacuum expectation value $\mu \sim ⟨\sigma ⟩$. The Callan-Symanzik equation of the potential is verified in the presence of the gauge, Yukawa, and the nonpolynomial operators. The couplings of the nonpolynomial operators have nonzero beta functions that we can actually compute from the quantum potential. At the quantum level, the Higgs mass is protected by spontaneously broken scale symmetry, even though the theory is nonrenormalizable. We compare the one-loop potential to its counterpart computed in the “traditional” dimensional regularization scheme that breaks scale symmetry explicitly ($\mu =\text{constant}$) in the presence at the tree level of the nonpolynomial operators.

Chiral representations are the key to obtaining light fermions from some ultraviolet completed theories. The well-known chiral example is one family set of 15 chiral fields in the standard model. We find a new chiral theory ${\mathrm{SU}(2)}_{\mathrm{dark}}\times \mathrm{U}(1{)}_Q$ with 16 chiral fields, which does not have any gauge and gravitational anomalies. The group ${\mathrm{SU}(2)}_{\mathrm{dark}}\times \mathrm{U}(1{)}_Q$ may belong to the dark sector, and we present a derivation of the spectrum from the ${\mathrm{E}}_8\times {\mathrm{E}}_8^{\prime }$ heterotic string. Necessarily, there appear two degrees at low energy: two dark-$Z^{\prime }$’s, or a dark-$Z^{\prime }$ plus a dark photon. Being chiral, there is a chance to probe this theory at TeV accelerators. Since the model belongs to the dark sector, the way to probe it is through the kinetic mixing.

While the presence of a light stop is increasingly disfavored by the experimental limits set on R-parity conserving scenarios, the naturalness of supersymmetry could still be safely concealed in the more challenging final states predicted by the existence of non-null R-parity violating couplings. Although R-parity violating signatures are extensively looked for at the Large Hadron Collider, these searches mostly assume 100% branching ratios for the direct decays of supersymmetric particles into Standard Model ones. In this paper we scrutinize the implications of relaxing this assumption by focusing on one motivated scenario where the lightest stop is heavier than a chargino and a neutralino. Considering a class of R-parity baryon number violating couplings, we show on general grounds that while the direct decay of the stop into Standard Model particles is dominant for large values of these couplings, smaller values give rise, instead, to the dominance of a plethora of longer decay chains and richer final states that have been so far barely analyzed at the LHC, thus weakening the impact of the present experimental stop mass limits. We characterize the case for R-parity baryon number violating couplings in the ${10}^{-7}-{10}^{-1}$ range, in two different benchmark points scenarios within the model-independent setting of the low-energy phenomenological Minimal Supersymmetric Standard Model. We identify the different relevant experimental signatures from stop pair production and decays, estimate the corresponding proton–proton cross sections at $\sqrt{s}=14\mathrm{TeV}$ and discuss signal versus background issues.

We report on salient features of a mixed lattice QCD action using valence Möbius domain-wall fermions solved on the dynamical $N_f=2+1+1$ highly improved staggered quark sea-quark ensembles generated by the MILC Collaboration. The approximate chiral symmetry properties of the valence fermions are shown to be significantly improved by utilizing the gradient-flow scheme to first smear the highly improved staggered quark configurations. The greater numerical cost of the Möbius domain-wall inversions is mitigated by the highly efficient QUDA library optimized for NVIDIA GPU accelerated compute nodes. We have created an interface to this optimized QUDA solver in Chroma. We provide tuned parameters of the action and performance of QUDA using ensembles with the lattice spacings $a\simeq \{0.15,0.12,0.09\}\mathrm{fm}$ and pion masses $m_{\pi }\simeq \{310,220,130\}\mathrm{MeV}$. We have additionally generated two new ensembles with $a\sim 0.12\mathrm{fm}$ and $m_{\pi }\sim \{400,350\}\mathrm{MeV}$. With a fixed flow time of $t_{gf}=1$ in lattice units, the residual chiral symmetry breaking of the valence fermions is kept below 10% of the light quark mass on all ensembles, $m_{\text{res}}\lesssim 0.1\times m_l$, with moderate values of the fifth dimension $L_5$ and a domain-wall height $M_5\le 1.3$. As a benchmark calculation, we perform a continuum, infinite volume, physical pion and kaon mass extrapolation of $F_{K^{\pm }}/F_{{\pi }^{\pm }}$ and demonstrate our results are independent of flow time and consistent with the FLAG determination of this quantity at the level of less than one standard deviation.

We calculate the electromagnetic Pauli form factor of quark induced by the nontrivial topological fluctuations of QCD vacuum called instantons. It is shown that such a contribution is significant. We discuss the possible implications of our result in the photon-hadron reactions and in the dynamics of quark-photon interactions in the dense/hot quark matter.

The thermodynamics of $SU(2)$ Yang-Mills theory in the covariant variational approach is studied by relating the free action density in the background of a nontrivial Polyakov loop to the pressure of the gluon plasma. The Poisson resummed expression for the pressure can be evaluated analytically in limiting cases, and shows the correct Stefan-Boltzmann limit at $T\to \infty$, while the limit $T\to 0$ is afflicted by artifacts due to massless modes in the confined phase. Several remedies to remove these artifacts are discussed. Using the numerical $T=0$ solutions for the ghost and gluon propagators in the covariant variational approach as input, the pressure, energy density and interaction strength are calculated and compared to lattice data.

We present a calculation of the strong decays of the exotic states $Z_b(10610)$ and $Z_b^{\prime }(10650)$ using a covariant quark model. We use a molecular-type four-quark current for the coupling of the $Z_b(10610)$ and $Z_b^{\prime }(10650)$ to the constituent heavy and light quarks.

Experimental data from hadronic $\tau$ decays allow for a precision determination of the slope of the $I=1$ vacuum polarization at zero momentum. We use this information to provide a value for the next-to-next-to-leading order (NNLO) low-energy constant $C_{93}$ in chiral perturbation theory. The largest systematic error in this determination results from the neglect of terms NNNLO (and higher) in the effective chiral Lagrangian, whose presence in the data will, in general, make the effective $C_{93}$ determined in an NNLO analysis mass dependent. We estimate the size of this effect by using strange hadronic $\tau$-decay data to perform an alternate $C_{93}$ determination based on the slope of the strange vector polarization at zero momentum, which differs from that of the $I=1$ vector channel only through $SU(3)$ flavor-breaking effects. We also comment on the impact of such higher order effects on ChPT-based estimates for the hadronic vacuum polarization contribution to the muon anomalous magnetic moment.

We unify two widely different approaches to understanding the infrared behavior of quantum chromodynamics (QCD), one essentially phenomenological, based on data, and the other computational, realized via quantum field equations in the continuum theory. Using the latter, we explain and calculate a process-independent running coupling for QCD, a new type of effective charge that is an analogue of the Gell-Mann–Low effective coupling in quantum electrodynamics. The result is almost identical to the process-dependent effective charge defined via the Bjorken sum rule, which provides one of the most basic constraints on our knowledge of nucleon spin structure. This reveals the Bjorken sum to be a near direct means by which to gain empirical insight into QCD’s Gell-Mann–Low effective charge.

The problem of the existence of a stable vacuum field in pure QCD is revised. Our approach is based on using classical stationary nonlinear wave type solutions with an intrinsic mass scale parameter. Such solutions can be treated as quantum-mechanical wave functions describing massive spinless states in quantum theory. We verify whether nonlinear wave type solutions can form a stable vacuum field background within the framework of the effective action formalism. We demonstrate that there is a special class of stationary generalized Wu-Yang monopole solutions that are stable against quantum gluon fluctuations.

We suggest a description of the beam asymmetry in $p\overline{p}$ and $\mathrm{\Lambda }\overline{\mathrm{\Lambda }}$ photoproduction off the proton $\overrightarrow{\gamma }+p\to p\overline{p}+p$ and $\overrightarrow{\gamma }+p\to \mathrm{\Lambda }\overline{\mathrm{\Lambda }}+p$, which takes into account the contribution of the scalar mesons $f_0(1370)$, $f_0(1500)$, and $f_0(1710)$. These scalars are considered as mixed states of a glueball and nonstrange and strange quarkonia in the framework based on the use of effective hadronic Lagrangians. Present results can be used to guide the possible search for this reaction by the GlueX Collaboration at JLab. Also, we did an estimate of contribution of heavier scalar meson states $f_0(2020)$, $f_0(2100)$, and $f_0(2200)$.

We evaluate the $s$-wave interaction of pseudoscalar and vector mesons with both charm and beauty to investigate the possible existence of molecular $BD$, $B^{*}D$, $B{D}^{*}$, $B^{*}{D}^{*}$, $B\overline{D}$, $B^{*}\overline{D}$, $B{\overline{D}}^{*}$, or $B^{*}{\overline{D}}^{*}$ meson states. The scattering amplitude is obtained implementing unitarity starting from a tree level potential accounting for the dominant vector meson exchange. The diagrams are evaluated using suitable extensions to the heavy flavor sector of the hidden gauge symmetry Lagrangians involving vector and pseudoscalar mesons, respecting heavy quark spin symmetry. We obtain bound states at energies above 7 GeV for $BD$ ($J^P=0^{+}$), $B^{*}D$ ($1^{+}$), $B{D}^{*}$ ($1^{+}$), and $B^{*}{D}^{*}$ ($0^{+}$, $1^{+}$, $2^{+}$), all in isospin 0. For $B\overline{D}$ ($0^{+}$), $B^{*}\overline{D}$ ($1^{+}$), $B{\overline{D}}^{*}$ ($1^{+}$), and $B^{*}{\overline{D}}^{*}$ ($0^{+}$, $1^{+}$, $2^{+}$) we also find similar bound states in $I=0$, but much less bound, which would correspond to exotic meson states with $\overline{b}$ and $\overline{c}$ quarks, and for the $I=1$ we find a repulsive interaction. We also evaluate the scattering lengths in all cases, which can be tested in current investigations of lattice QCD.

Using a data sample of $448\times {10}^6\psi (3686)$ events collected with the BESIII detector operating at the BEPCII storage ring, the decays $\psi (3686)\to \gamma \eta$ and $\psi (3686)\to \gamma {\pi }^0$ are observed with a statistical significance of $7.3\sigma$ and $6.7\sigma$, respectively. The branching fractions are measured to be $\mathcal{B}(\psi (3686)\to \gamma \eta )=(0.85\pm 0.18\pm 0.05)\times {10}^{-6}$ and $\mathcal{B}(\psi (3686)\to \gamma {\pi }^0)=(0.95\pm 0.16\pm 0.05)\times {10}^{-6}$. In addition, we measure the branching fraction of $\psi (3686)\to \gamma {\eta }^{\prime }$ to be $\mathcal{B}(\psi (3686)\to \gamma {\eta }^{\prime })=(125.1\pm 2.2\pm 6.2)\times {10}^{-6}$, which represents an improvement of precision over previous results.

In the context of loop quantum gravity (LQG), we study the fate of Thiemann complexifier in homogeneous and isotropic Friedmann-Lemaitre-Roberston-Walker (FLRW) cosmology. The complexifier is the dilatation operator acting on the canonical phase space for gravity and generates the canonical transformations shifting the Barbero-Immirzi parameter. We focus on the closed algebra consisting in the complexifier, the 3d volume and the Hamiltonian constraint, which we call the CVH algebra (for Complexier-Volume-Hamiltonian constraint algebra). In standard cosmology, for gravity coupled to a scalar field, the CVH algebra is identified as a $\mathfrak{su}(1,1)$ Lie algebra, with the Hamiltonian as a null generator, the complexifier as a boost and the $\mathfrak{su}(1,1)$ Casimir given by the matter density. The loop gravity cosmology approach introduces a regularization length scale $\lambda$ and regularizes the gravitational Hamiltonian in terms of SU(2) holonomies. We show that this regularization is compatible with the CVH algebra, if we suitably regularize the complexifier and inverse volume factor. The regularized complexifier generates a generalized version of the Barbero’s canonical transformation which reduces to the classical one when $\lambda \to 0$. This structure allows for the exact integration of the actions of the Hamiltonian constraints and the complexifier. This straightforwardly extends to the quantum level: the cosmological evolution is described in terms of SU(1, 1) coherent states and the regularized complexifier generates unitary transformations. The Barbero-Immirzi parameter is to be distinguished from the regularization scale $\lambda$, it can be rescaled unitarily and the Immirzi ambiguity ultimately disappears from the physical predictions of the theory. Finally, we show that the complexifier becomes the effective Hamiltonian when deparametrizing the dynamics using the scalar field as a clock, thus underlining the deep relation between cosmological evolution and scale transformations.

We consider the Aharonov-Bohm effect on entanglement entropy for one interval in ($1+1$) dimensional conformal field theory on a one dimensional ring. The magnetic field is confined inside the ring, i.e., there is a Wilson loop on the ring. The Aharonov-Bohm phase factor which is proportional to the Wilson loop is represented as insertion of twist operators. We compute exactly the Rényi entropy from a four point function of twist operators in a free charged scalar field.

The scalar-tensor theory of Damour and Esposito-Farèse recently gained some renewed interest because of its ability to suppress modifications to general relativity in the weak field, while introducing large corrections in the strong field of compact objects through a process called scalarization. A large sector of this theory that allows for scalarization, however, has been shown to be in conflict with Solar System observations when accounting for the cosmological evolution of the scalar field. We here study an extension of this theory by endowing the scalar field with a mass to determine whether this allows the theory to pass Solar System constraints upon cosmological evolution for a larger sector of coupling parameter space. We show that the cosmological scalar field goes first through a quiescent phase, similar to the behavior of a massless field, but then it enters an oscillatory phase, with an amplitude (and frequency) that decays (and grows) exponentially. We further show that after the field enters the oscillatory phase, its effective energy density and pressure are approximately those of dust, as expected from previous cosmological studies. Due to these oscillations, we show that the scalar field cannot be treated as static today on astrophysical scales, and so we use time-dependent perturbation theory to compute the scalar-field-induced modifications to Solar System observables. We find that these modifications are suppressed when the mass of the scalar field and the coupling parameter of the theory are in a wide range, allowing the theory to pass Solar System constraints, while in principle possibly still allowing for scalarization.

We consider the scalar perturbations of Eddington-inspired Born-Infeld braneworld models in this paper. The dynamical equation for the physical propagating degree of freedom $\xi (x^{\mu },y)$ is achieved by using the Arnowitt-Deser-Misner decomposition method: $F_1(y){\partial }_y^2\xi +F_2(y){\partial }_y\xi +{\partial }^{\mu }{\partial }_{\mu }\xi =0$. We conclude that the solution is tachyonic-free and stable under scalar perturbations for $F_1(y)>0$ but unstable for $F_1(y)<0$. The stability of a known analytic domain wall solution with the warp factor given by $a(y)={\mathrm{sech}}^{\frac{3}{4p}}(ky)$ is analyzed and it is shown that only the solution for $0<p<\sqrt{8/3}$ is stable.

The effects of highly relativistic spin-gravity coupling in the Schwarzschild–de Sitter background that follow from the Mathisson-Papapetrou equations are investigated. The dependence of gravitoelectric and gravitomagnetic components of gravitational field on the velocity of an observer that is moving in Schwarzschild–de Sitter’s background is estimated. The action of gravitomagnetic components on a fast moving spinning particle is considered. Different cases of the highly relativistic circular orbits of a spinning particle that essentially differ from the corresponding geodesic orbits are described.

Scalar-tensor theories of gravity modify general relativity by introducing a scalar field that couples nonminimally to the metric tensor, while satisfying the weak-equivalence principle. These theories are interesting because they have the potential to simultaneously suppress modifications to Einstein’s theory on Solar System scales, while introducing large deviations in the strong field of neutron stars. Scalar-tensor theories can be classified through the choice of conformal factor, a scalar that regulates the coupling between matter and the metric in the Einstein frame. The class defined by a Gaussian conformal factor with a negative exponent has been studied the most because it leads to spontaneous scalarization (i.e. the sudden activation of the scalar field in neutron stars), which consequently leads to large deviations from general relativity in the strong field. This class, however, has recently been shown to be in conflict with Solar System observations when accounting for the cosmological evolution of the scalar field. We here study whether this remains the case when the exponent of the conformal factor is positive, as well as in another class of theories defined by a hyperbolic conformal factor. We find that in both of these scalar-tensor theories, Solar System tests are passed only in a very small subset of coupling parameter space, for a large set of initial conditions compatible with big bang nucleosynthesis. However, while we find that it is possible for neutron stars to scalarize, one must carefully select the coupling parameter to do so, and even then, the scalar charge is typically 2 orders of magnitude smaller than in the negative-exponent case. Our study suggests that future work on scalar-tensor gravity, for example in the context of tests of general relativity with gravitational waves from neutron star binaries, should be carried out within the positive coupling parameter class.