The naturalness problem may be studied on the complex two-dimensional plane with the technique of dimensional regularization. The renormalization group equation of the Higgs mass on the plane suggests the Higgs mass approaches zero at the ultraviolet scale; the scale can be Planck scale when the top quark pole mass $M_t=168\mathrm{GeV}$. The real issue of the naturalness problem in the sense of the Wilsonian renormalization group method is not about quadratic divergences but the rescaling effect. The Higgs mass can be considered to be one composed mass. All terms in the Lagrangian in this scenario are marginal terms and no relevant terms are left; thus, no rescaling effect exists to cause the naturalness problem. The renormalization group equation of the vacuum expectation value in the Landau gauge up to two-loop order is studied. Scale-dependent behavior of the composed Higgs mass shows that we can have one tiny Higgs mass at the high energy scale, even around the Planck scale, when $M_t\le 170.7\mathrm{GeV}$.

One of the simplest models of dark matter is where a scalar singlet field $S$ comprises some or all of the dark matter and interacts with the standard model through an $|H{|}^2{S}^2$ coupling to the Higgs boson. We update the present limits on the model from LHC searches for invisible Higgs decays, the thermal relic density of $S$, and dark matter searches via indirect and direct detection. We point out that the currently allowed parameter space is on the verge of being significantly reduced with the next generation of experiments. We discuss the impact of such constraints on possible applications of scalar singlet dark matter, including a strong electroweak phase transition, and the question of vacuum stability of the Higgs potential at high scales.

Much of the discussion regarding future measurements of the Higgs boson mass and self-coupling is focused on how well various collider options can do. In this article we ask a physics-based question of how well do we need colliders to measure these quantities to have an impact on discovery of new physics or an impact in how we understand the role of the Higgs boson in nature. We address the question within the framework of the Standard Model and various beyond the Standard Model scenarios, including supersymmetry and theories of composite Higgs bosons. We conclude that the LHC’s stated ability to measure the Higgs boson to better than 150 MeV will be as good as we will ever need to know the Higgs boson mass in the foreseeable future. On the other hand, we estimate that the self-coupling will likely need to be measured to better than 20% to see a deviation from the Standard Model expectation. This is a challenging target for future collider and upgrade scenarios.

We consider the interaction between two static sources in the color octet configuration and compute the potential to three loops. Special emphasis is put on the treatment of pinch contributions, and two methods are applied to reduce their evaluation to diagrams without pinches.

The phenomenology of the so-called $X$, $Y$ and $Z$ hadronic resonances is hard to reconcile with standard charmonium or bottomonium interpretations. It has been suggested that some of these new hadrons can possibly be described as tightly bound tetraquark states and/or as loosely bound two-meson molecules. In the present paper we focus on the hypothetical existence of flavored, doubly charmed tetraquarks. Such states might also carry double electric charge, and in this case, if discovered, they could univocally be interpreted in terms of compact tetraquarks. Flavored tetraquarks are also amenable to lattice studies, as their interpolating operators do not overlap with ordinary meson ones. We show that doubly charmed tetraquarks could significantly be produced at the LHC from $B_c$ or ${\Xi }_{bc}$ heavy baryons.

Using data samples of $89{\mathrm{fb}}^{-1}$, $703{\mathrm{fb}}^{-1}$, and $121{\mathrm{fb}}^{-1}$ collected with the Belle detector at the KEKB asymmetric-energy $e^{+}{e}^{-}$ collider at center-of-mass energies 10.52 GeV, 10.58 GeV, and 10.876 GeV, respectively, we study the exclusive reactions $e^{+}{e}^{-}\to \omega {\pi }^0$, $K^{*}(892)\overline{K}$, and $K_2^{*}(1430)\overline{K}$. (Charge-conjugate modes are included implicitly.) Significant signals of $\omega {\pi }^0$, $K^{*}(892{)}^0{\overline{K}}^0$, and $K_2^{*}(1430{)}^{-}{K}^{+}$ are observed for the first time at these energies, and the energy dependencies of the cross sections are presented. On the other hand, no significant excesses for $K^{*}(892{)}^{-}{K}^{+}$ and $K_2^{*}(1430{)}^0{\overline{K}}^0$ are found, and we set limits on the cross section ratios $R_{\mathrm{VP}}=\frac{{\sigma }_B(e^{+}{e}^{-}\to K^{*}(892{)}^0{\overline{K}}^0)}{{\sigma }_B(e^{+}{e}^{-}\to K^{*}(892{)}^{-}{K}^{+})}>4.3$, 20.0, and 5.4, and $R_{\mathrm{TP}}=\frac{{\sigma }_B(e^{+}{e}^{-}\to K_2^{*}(1430{)}^0{\overline{K}}^0)}{{\sigma }_B(e^{+}{e}^{-}\to K_2^{*}(1430{)}^{-}{K}^{+})}<1.1$, 0.4, and 0.6, for center-of-mass energies of 10.52 GeV, 10.58 GeV, and 10.876 GeV, respectively, at the 90% C.L.

We formulate a generic three-dimensional higher-derivative superfield theory for self-interacting scalar superfield action. We consider the cases of real and complex scalar superfields. For these theories, we explicitly calculate the one-loop effective potential.

A charged scalar field impinging upon a charged Reissner–Nordström black hole can be amplified as it scatters off the hole, a phenomenon known as super-radiant scattering. This scattering process in the super-radiant regime $\omega <qQ/r_{+}$ (here $\omega$, $q$, $Q$, and $r_{\pm }$ are the conserved frequency of the wave, the charge coupling constant of the field, the electric charge of the black hole, and the horizon radii of the black hole, respectively) results in the extraction of Coulomb energy and electric charge from the charged black hole. The black-hole-field system can be made unstable by placing a reflecting mirror around the black hole, which prevents the amplified field from escaping to infinity. This charged black-hole-mirror system is the spherically symmetric analog of the rotating black-hole-mirror bomb of Press and Teukolsky. In the present paper, we study analytically the charged black-hole-mirror bomb in the asymptotic regime $qQ\gg 1$ and for mirror radii $r_{\mathrm{m}}$ in the near-horizon region $x_{\mathrm{m}}\equiv (r_{\mathrm{m}}-r_{+})/r_{+}\ll \tau$, where $\tau \equiv (r_{+}-r_{-})/r_{+}$ is the dimensionless temperature of the black hole. In particular, we derive analytic expressions for the oscillation frequencies $\Re \omega$ and the instability growth time scales $1/\Im \omega$ of the super-radiant confined fields. Remarkably, we find a simple linear scaling $\Im \omega \propto qQ/r_{+}$ for the imaginary part of the resonances in the asymptotic $qQ\gg (\tau /x_{\mathrm{m}}{)}^2\gg 1$ regime, which implies that the instability time scale $1/\Im \omega$ of the system can be made arbitrarily short in the $qQ\to \infty$ limit. The short instability time scale found in the linear regime along with the spherical symmetry of the system make the charged bomb a convenient toy model for future numerical studies aimed to investigate the nonlinear end-state of super-radiant instabilities.

In this paper, we consider the structure of the ${\mathrm{AdS}}_3$ vacua in $R^3$ expansion of new massive gravity ($R^3$-NMG). We obtain the degeneracies of the ${\mathrm{AdS}}_3$ vacua at several points of the parametric space. Additionally, following a specific analysis we show that ${\mathrm{AdS}}_3$ wave solutions are present. Using these wave solutions, we single out two special points of the parametric space for which logarithmic terms appear in the solutions. The first one is a point at which the effective mass of the wave profile, which is interpreted as a scalar mode, completely saturates the Breitenlohner-Freedman bound of the ${\mathrm{AdS}}_3$ space in which the wave is propagating. The second special point is a point at which the central charge of the theory vanishes. Furthermore, we investigate the possibility of asymptotically Lifshitz black hole solutions to be present in the three-dimensional $R^3$-NMG. We derive analytically the Lifshitz vacua considering specific relations between the mass parameters of $R^3$-NMG. A certain polynomial equation arises at the first special point where solutions with logarithmic falloff in the ${\mathrm{AdS}}_3$ space appear. Solving this polynomial equation, we obtain the values of the dynamical exponent $z$ which correspond to possible asymptotically Lifshitz black hole solutions. However, it is shown that asymptotically Lifshitz black hole solutions do not exist in the three-dimensional $R^3$-NMG for a specific ansatz of the black hole metric.

Planck data has not found the “smoking gun” of non-Gaussianity that would have necessitated consideration of inflationary models beyond the simplest canonical single-field scenarios. This raises the important question of what these results do imply for more general models, and in particular, multifield inflation. In this paper we revisit four ways in which two-field scenarios can behave differently from single-field models; two-field slow-roll dynamics, curvaton-type behavior, inflation ending on an inhomogeneous hypersurface and modulated reheating. We study the constraints that Planck data puts on these classes of behavior, focusing on the latter two which are the least studied in the recent literature. We show that these latter classes are almost equivalent, and extend their previous analyses by accounting for arbitrary evolution of the isocurvature mode which, in particular, places important limits on the Gaussian curvature of the reheating hypersurface. In general, however, we find that Planck bispectrum results only constrain certain regions of parameter space, leading us to conclude that inflation sourced by more than one scalar field remains an important possibility.

In supersymmetric models with an unbroken $R$ symmetry (rather than only $R$ parity), the neutralinos are Dirac fermions rather than Majorana. In this article, we discuss the phenomenology of neutralino dark matter in such models, including the calculation of the thermal relic abundance, and constraints and prospects for direct and indirect searches. Because of the large elastic scattering cross sections with nuclei predicted in $R$-symmetric models, we are forced to consider a neutralino that is predominantly bino, with very little Higgsino mixing. We find a large region of parameter space in which binolike Dirac neutralinos with masses between 10 and 380 GeV can annihilate through slepton exchange to provide a thermal relic abundance in agreement with the observed cosmological density, without relying on coannihilations or resonant annihilations. The signatures for the indirect detection of Dirac neutralinos are very different than predicted in the Majorana case, with annihilations proceeding dominantly to ${\tau }^{+}{\tau }^{-}$, ${\mu }^{+}{\mu }^{-}$ and $e^{+}{e}^{-}$ final states, without the standard chirality suppression. And unlike Majorana dark matter candidates, Dirac neutralinos experience spin-independent scattering with nuclei through vector couplings (via $Z$ and squark exchange), leading to potentially large rates at direct detection experiments. These and other characteristics make Dirac neutralinos potentially interesting within the context of recent direct and indirect detection anomalies. We also discuss the case in which the introduction of a small Majorana mass term breaks the $R$ symmetry, splitting the Dirac neutralino into a pair of nearly degenerate Majorana states.

In the present mainstream cosmology, matter and space-time emerged from a singularity and evolved through four distinct periods: early inflation, radiation, dark matter, and late-time inflation (driven by dark energy). During the radiation and dark matter dominated stages, the universe is decelerating while the early and late-time inflations are accelerating stages. A possible connection between the accelerating periods remains unknown, and, even more intriguing, the best dark energy candidate powering the present accelerating stage ($\Lambda$-vacuum) is plagued with the cosmological constant and coincidence puzzles. Here we propose an alternative solution for such problems based on a large class of time-dependent vacuum energy density models in the form of power series of the Hubble rate, $\Lambda =\Lambda (H)$. The proposed class of $\Lambda (H)$-decaying vacuum model provides: (i) a new mechanism for inflation (different from the usual inflaton models), (ii) a natural mechanism for a graceful exit, which is universal for the whole class of models; (iii) the currently accelerated expansion of the universe, (iv) a mild dynamical dark energy at present; and (v) a final de Sitter stage. Remarkably, the late-time cosmic expansion history of our class of models is very close to the concordance $\Lambda \mathrm{CDM}$ model, but above all it furnishes the necessary smooth link between the initial and final de Sitter stages through the radiation- and matter-dominated epochs.

It is shown that by a simple extension of the fermion sector of flipped $SU(5)$ models and other flipped models, proton decay coming from dimension-six operators can be suppressed by fermion mixing angles by an arbitrary amount in a natural way.

We present a complete model whose low energy effective theory is the $R$-parity violating next-to-minimal supersymmetric standard model with a baryon number violating $\overline{u}\overline{d}\overline{d}$ vertex of the minimal flavor violation supersymmetry (MFV SUSY) form, leading to prompt lightest superpartner decay and evading the ever stronger LHC bounds on low-scale $R$-parity conserving supersymmetry. MFV flavor structure is enforced by gauging an SU(3) flavor symmetry at high energies. After the flavor group is spontaneously broken, mass mixing between the standard model fields and heavy vectorlike quarks and leptons induces hierarchical Yukawa couplings that depend on the mixing angles. The same mechanism generates the $\overline{u}\overline{d}\overline{d}$ coupling, explaining its shared structure. A discrete $R$-symmetry is imposed, which forbids all other dangerous lepton and baryon-number violating operators (including Planck-suppressed operators) and simultaneously solves the $\mu$ problem. While flavor constraints require the flavor gauge bosons to be outside of the reach of the LHC, the vectorlike top partners could lie below 1 TeV.

Assuming that naturalness should be modified by ignoring quadratic divergences, we propose a simple extension of the standard model where the weak scale is dynamically generated together with an automatically stable vector. Identifying it as thermal dark matter, the model has one free parameter. It predicts one extra scalar, detectable at colliders, which triggers a first-order dark/electroweak cosmological phase transition with production of gravitational waves. Vacuum stability holds up to the Planck scale.

The spectrum of energy levels is computed for all available angular momentum and parity quantum numbers in the SU(2)-Higgs model, with parameters chosen to match experimental data from the Higgs-$W$ boson sector of the standard model. Several multiboson states are observed, with and without linear momentum, and all are consistent with weakly interacting Higgs and $W$ bosons. The creation operators used in this study are gauge-invariant so, for example, the Higgs operator is quadratic rather than linear in the Lagrangian’s scalar field.

We calculate, for the first time using unquenched lattice QCD, form factors for the rare decay $B\to K{\ell }^{+}{\ell }^{-}$ in and beyond the Standard Model. Our lattice QCD calculation utilizes a nonrelativistic QCD formulation for the $b$ valence quarks and the highly improved staggered quark formulation for the light valence quarks. We employ the MILC $2+1$ asqtad ensembles. The form factor results, based on the $z$ expansion, are valid over the full kinematic range of $q^2$. We construct the ratios $f_0/f_{+}$ and $f_T/f_{+}$, which are useful in constraining new physics and verifying effective theory form factor symmetry relations. We also discuss the calculation of Standard Model observables.

The next-to-leading order (NLO) QCD radiative corrections to $W^{+}{W}^{-}$ production at hadron colliders are well understood. We combine NLO perturbative QCD calculations with soft-gluon resummation of threshold logarithms to find a next-to-next-to-leading logarithmic (NNLL) prediction for the total cross section and the invariant mass distribution at the LHC. We also obtain approximate next-to-next-to-leading order (NNLO) results for the total $W^{+}{W}^{-}$ cross section at the LHC which includes all contributions from the scale dependent leading singular terms. Our result for the approximate NNLO total cross section is the most precise theoretical prediction available. Uncertainties due to scale variation are shown to be small when the threshold logarithms are included. NNLL threshold resummation increases the $W^{+}{W}^{-}$ invariant mass distribution by $\sim 3\%–4\%$ in the peak region for both $\sqrt{S}=8$ and 14 TeV. The NNLL threshold resummed and approximate NNLO cross sections increase the NLO cross section by 0.5%–3% for $\sqrt{S}=7$, 8, 13, and 14 TeV.

Transverse momentum dependent (TMD) parton correlators describing the partonic structure of hadrons contain gauge links, required by color gauge invariance. The required gauge links enter in the matrix elements that contain the parton fields and depend on the color flow in the hard process. The correlators are expanded in terms of transverse momentum dependent parton distribution functions, referred to as TMD PDFs, or in short TMDs. In this paper, we introduce gluon TMDs of definite rank, by making an expansion of the TMD gluon correlator with the help of irreducible tensors built from the transverse momenta. The process dependence is isolated in gauge-link-dependent gluonic pole factors multiplying the TMDs. It is important to account for the different possibilities in the color structure within the matrix elements, leading to multiple TMDs at a given rank. In this way we are able to write the leading tree-level result for a hard process in terms of process-dependent gluon correlators which are expressed in a finite set of universal TMDs. We tabulate the gluonic pole factors for various gauge links, among them those that are relevant for $2\to 2$ processes.

Based on the nonrelativistic QCD factorization scheme, we study the hadroproduction of the bottomonium states ${\rm Y}(5S)$ and ${\rm Y}(6S)$. We argue to search for them in the final states ${\rm Y}(1S,2S,3S){\pi }^{+}{\pi }^{-}$, which are found to have anomalously large production rates at ${\rm Y}(5S)$. The enhanced rates for the dipionic transitions in the ${\rm Y}(5S)$ energy region could, besides ${\rm Y}(5S)$, be ascribed to $Y_b(10890)$, a state reported by the Belle Collaboration, which may be interpreted as a tetraquark. The LHC/Tevatron measurements are capable of making a case in favor of or against the existence of $Y_b(10890)$, as demonstrated here. Dalitz analysis of the ${\rm Y}(1S,2S,3S){\pi }^{+}{\pi }^{-}$ states from the ${\rm Y}(5S)/Y_b(10890)$ decays also impacts directly on the interpretation of the charged bottomonium-like states, $Z_b(10600)$ and $Z_b(10650)$, discovered by Belle in these puzzling decays.