A complete calculation of the $\mathcal{O}({\alpha }_s^4)$ perturbative quantum chromodynamics (pQCD) corrections to the hadronic decay width of the $Z$ boson has recently been performed by Baikov et al. [Phys. Rev. Lett. 108, 222003 (2012)]. In their analysis, Baikov et al. relied on the conventional practice of simply guessing the renormalization scale and taking an arbitrary range to estimate the pQCD uncertainties. This procedure inevitably introduces an arbitrary, scheme-dependent theoretical systematic error in the predictions. In this paper, we show that the renormalization scale uncertainties for hadronic $Z$ decays can be greatly reduced by applying the principle of maximum conformality (PMC), a rigorous extension of the Brodsky-Lepage-Mackenzie method. The PMC prediction is independent of the choice of renormalization scheme; i.e., it respects renormalization group invariance, and thus it provides an optimal and theoretically rigorous method for setting the renormalization scale. We show that the convergence of the pQCD prediction for the $Z$ hadronic width is greatly improved using the PMC since the divergent renormalon series does not appear. The magnitude of the high-order corrections quickly approach a steady point. The PMC predictions also have the property that any residual dependence on the choice of initial scale is highly suppressed, even for low-order predictions. Thus, one obtains optimal fixed-order predictions for the $Z$-boson hadronic decay rates thus enabling high precision tests of the Standard Model.

The gauge parameter dependence of the effective potential is determined by partial differential equations involving also the Higgs boson field expectation value. Solving these equations by the method of characteristics leads to elimination of the gauge parameter dependence of the effective potential. The construction is carried out in the case of the standard model of electroweak unification for the renormalization group improved effective potential up to the next-leading logarithmic order.

The first measurement that relates semileptonic and hadronic decay rates of the $B_c^{+}$ meson is performed using proton-proton collision data corresponding to $1.0{\mathrm{fb}}^{-1}$ of integrated luminosity collected with the LHCb detector. The measured value of the ratio of branching fractions, $\mathcal{B}(B_c^{+}\to J/\psi {\pi }^{+})/\mathcal{B}(B_c^{+}\to J/\psi {\mu }^{+}{\nu }_{\mu })=0.0469\pm 0.0028(\text{stat})\pm 0.0046(\text{syst})$, is at the lower end of available theoretical predictions.

Regular black strings solutions associated to a dynamical Friedmann-Robertson-Walker braneworld are obtained as a particular case of a bulk metric in the context of a variable tension braneworld. By analyzing the 5D Kretschmann invariants, we show that the variable brane tension is capable of attenuating the bulk physical singularities along some eras of the evolution of the Universe. nIn particular, the black string is analyzed for the McVittie metric on an Eötvös fluid braneworld, wherein the fluid dynamical brane tension depends on the brane temperature. The whole bulk is shown to be regular for a universe dominated by nonrelativistic matter or by relativistic matter/radiation, as the cosmological time elapses. In a particular case, the black strings are shown to have finite extension along the extra dimension, which prominently modify the higher-dimensional soft physical singularities. For a universe dominated by matter or radiation, we show that the bulk is regular as the cosmological time elapses, as an effect of the variable brane tension.

Using the $\mathrm{AdS}/\mathrm{CFT}$ correspondence, we compute analytically the late-time behavior of two-point functions, Wilson loops and entanglement entropy in a strongly coupled $\mathcal{N}=4$ super-Yang-Mills plasma undergoing a boost-invariant expansion. We take into account the effects of first order dissipative hydrodynamics and investigate the effects of the (time-dependent) shear viscosity on the various observables. The two-point functions decay exponentially at late times and are unaffected by the viscosity if the points are separated along the transverse directions. For longitudinal separation we find a much richer structure. In this case the exponential is modulated by a nonmonotonic function of the rapidities and a dimensionless combination of the shear viscosity and proper time. We show that this peculiar behavior constrains the regime of validity of the hydrodynamical expansion. In addition, similar results are found for certain Wilson loops and entanglement entropies.

We calculate the graviton’s $\beta$ function in the AdS string-theoretic sigma model, perturbed by vertex operators for Vasiliev’s higher spin gauge fields in ${\mathrm{AdS}}_5$. The result is given by ${\beta }_{mn}=R_{mn}+4T_{mn}(g,u)$ (with the AdS radius set to 1 and the graviton polarized along the ${\mathrm{AdS}}_5$ boundary), with the matter stress-energy tensor given by that of conformal holographic fluid in $d=4$, evaluated at the temperature given by $T=\frac{1}{\pi }$. The stress-energy tensor is given by $T_{mn}=g_{mn}+4u_m{u}_n+\sum _N{T}_{mn}^{(N)}$ where $u$ is the vector excitation satisfying $u^2=-1$ and $N$ is the order of the gradient expansion in the dissipative part of the tensor. We calculate the contributions up to $N=2$. The higher spin excitations contribute to the $\beta$ function, ensuring the overall Weyl covariance of the matter stress tensor. We conjecture that the structure of gradient expansion in $d=4$ conformal hydrodynamics at higher orders is controlled by the higher spin operator algebra in ${\mathrm{AdS}}_5$.

Modified gravity theories with geometry-matter coupling, in which the action is an arbitrary function of the Ricci scalar and the matter Lagrangian [$f(R,L_m)$ gravity], and of the Ricci scalar and of the trace of the matter energy-momentum tensor [$f(R,T)$ gravity], respectively, have the intriguing property that the divergence of the matter energy-momentum tensor is nonzero. In the present paper, by using the formalism of open thermodynamic systems, we interpret the generalized conservation equations in these gravitational theories from a thermodynamic point of view as describing irreversible matter creation processes, which could be validated by fundamental particle physics. Thus particle creation corresponds to an irreversible energy flow from the gravitational field to the created matter constituents, with the second law of thermodynamics requiring that space-time transforms into matter. The equivalent particle number creation rates, the creation pressure and the entropy production rates are obtained for both $f(R,L_m)$ and $f(R,T)$ gravity theories. The temperature evolution laws of the newly created particles are also obtained. In the case of the $f(R,T)$ gravity theory the open irreversible thermodynamic interpretation of a simple cosmological model is presented in detail. It is also shown that due to the geometry-matter coupling, during the cosmological evolution a large amount of comoving entropy could be produced.

We derive a stationary and axisymmetric black hole solution in Einstein-Dilaton-Gauss-Bonnet gravity to quadratic order in the ratio of the spin angular momentum to the black hole mass squared. This solution introduces new corrections to previously found nonspinning and linear-in-spin solutions. The location of the event horizon and the ergosphere are modified, as well as the quadrupole moment. The new solution is of Petrov type I, although lower order in spin solutions are of Petrov type D. There are no closed timelike curves or spacetime regions that violate causality outside of the event horizon in the new solution. We calculate the modifications to the binding energy, Kepler’s third law, and properties of the innermost stable circular orbit. These modifications are important for determining how the electromagnetic properties of accretion disks around supermassive black holes are changed from those expected in general relativity.

The relation between Gribov ambiguity and degeneracies in the symplectic structure of physical systems is analyzed. It is shown that, in finite-dimensional systems, the presence of Gribov ambiguities in regular constrained systems (those where the constraints are functionally independent) always leads to a degenerate symplectic structure upon Dirac reduction. The implications for the Gribov-Zwanziger approach to QCD are discussed.

We examine a simple example of gravitational wave memory due to the decay of a point particle into two point particles. In the case where one of the decay products is null, there are two types of memory: a null memory due to the null particle and an ordinary memory due to the recoiling timelike particle. In the case where both decay products are timelike, there is only ordinary memory. However, this ordinary memory can mimic the null memory in the limit where one of the decay products has a large velocity.

We discuss the implications for gamma ray burst studies of a dark unbroken $U(1{)}_D$ sector that couples predominantly through gravity to the visible sector. The dominant dark matter component remains neutral under $U(1{)}_D$. The collapsar model is assumed to explain the origin of long gamma ray bursts. The main idea is that, by measuring the change in stellar black hole spin during the duration of the gamma ray burst, one can make inferences about the existence of a dark matter accretion disk. This could potentially provide evidence for the existence of a $U(1{)}_D$ sector.

We examine the evolution of cosmological perturbations in a nonthermal inflationary history with a late-time matter domination period prior to big bang nucleosynthesis. Such a cosmology could arise naturally in the well-motivated moduli scenario in the context of supersymmetry (SUSY)—in particular in models of split SUSY. Subhorizon dark matter perturbations grow linearly during the matter dominated phase before reheating and can lead to an enhancement in the growth of substructure on small scales, even in the presence of dark matter annihilations. This suggests that a new scale (the horizon size at reheating) could be important for determining the primordial matter power spectrum. However, we find that in many nonthermal models free-streaming effects or kinetic decoupling after reheating can completely erase the enhancement leading to small-scale structures. In particular, in the moduli scenario with wino or Higgsino dark matter we find that the dark matter particles produced from moduli decays would thermalize with radiation and kinetically decouple below the reheating temperature. Thus, the growth of dark matter perturbations is not sustained, and the predictions for the matter power spectrum are similar to a standard thermal history. We comment on possible exceptions, but these appear difficult to realize within standard moduli scenarios. We conclude that although enhanced structure does not provide a new probe for investigating the cosmic dark ages within these models, it does suggest that nonthermal histories offer a robust alternative to a strictly thermal post inflationary history.

The observed acceleration of the Universe can be explained by modifying general relativity. One such attempt is the nonlocal model of Deser and Woodard. Here we fix the background cosmology using results from the Planck satellite and examine the predictions of nonlocal gravity for the evolution of structure in the Universe, confronting the model with three tests: gravitational lensing, redshift space distortions, and an estimator of gravity $E_G$ that combines spectroscopic information with lensing. Current data favor general relativity (GR) over nonlocal gravity: fixing primordial cosmology with the best fit parameters from Planck leads to weak lensing results favoring GR by 6.8 sigma; redshift space distortions measurements of the growth rate preferring GR by 7.8 sigma; and the single measurement of $E_G$ favoring GR, but by less than 1 sigma. The significance holds up even after the parameters are allowed to vary within Planck limits. The larger lesson is that a successful modified gravity model will likely have to suppress the growth of structure compared to general relativity.

We investigate the axion dark matter scenario (ADM), in which axions account for all of the dark matter in the Universe, in light of the most recent cosmological data. In particular, we use the Planck temperature data, complemented by WMAP E-polarization measurements, as well as the recent BICEP2 observations of B-modes. Baryon acoustic oscillation data, including those from the baryon oscillation spectroscopic survey, are also considered in the numerical analyses. We find that, in the minimal ADM scenario and for ${\mathrm{\Lambda }}_{\mathrm{QCD}}=200\mathrm{MeV}$, the full data set implies that the axion mass $m_{\mathrm{a}}=82.2\pm 1.1\mu \mathrm{eV}$ [corresponding to the Peccei-Quinn symmetry being broken at a scale $f_{\mathrm{a}}=(7.54\pm 0.10)\times 10^{10}\mathrm{GeV}$], or $m_{\mathrm{a}}=76.6\pm 2.6\mu \mathrm{eV}$ [$f_{\mathrm{a}}=(8.08\pm 0.27)\times 10^{10}\mathrm{GeV}$] when we allow for a nonstandard effective number of relativistic species $N_{\mathrm{eff}}$. We also find a $2\sigma$ preference for $N_{\mathrm{eff}}>3.046$. The limit on the sum of neutrino masses is $\sum m_{\nu }<0.25\mathrm{eV}$ at 95% C.L. for $N_{\mathrm{eff}}=3.046$, or $\sum m_{\nu }<0.47\mathrm{eV}$ when $N_{\mathrm{eff}}$ is a free parameter. Considering extended scenarios where either the dark energy equation-of-state parameter $w$, the tensor spectral index $n_t$, or the running of the scalar index $d{n}_s/d\ln k$ is allowed to vary does not change significantly the axion mass-energy density constraints. However, in the case of the full data set exploited here, there is a preference for a nonzero tensor index or scalar running, driven by the different tensor amplitudes implied by the Planck and BICEP2 observations. We also study the effect on our estimates of theoretical uncertainties, in particular the imprecise knowledge of the QCD scale ${\mathrm{\Lambda }}_{\mathrm{QCD}}$, in the calculation of the temperature-dependent axion mass. We find that in the simplest ADM scenario the $\mathrm{Planck}+\mathrm{WP}$ data set implies that the axion mass $m_{\mathrm{a}}=63.7\pm 1.2\mu \mathrm{eV}$ for ${\mathrm{\Lambda }}_{\mathrm{QCD}}=400\mathrm{MeV}$. We also comment on the possibility that axions do not make up for all the dark matter, or that the contribution of string-produced axions has been grossly underestimated; in that case, the values that we find for the mass can conservatively be considered as lower limits. Dark matter axions with mass in the $60–80\mu \mathrm{eV}$ (corresponding to an axion-photon coupling $G_{\mathrm{a}\gamma \gamma }\sim 10^{-14}{\mathrm{GeV}}^{-1}$) range can, in principle, be detected by looking for axion-to-photon conversion occurring inside a tunable microwave cavity permeated by a high-intensity magnetic field, and operating at a frequency $\nu \simeq 15–20\mathrm{GHz}$. This is out of the reach of current experiments like the axion dark matter experiment (limited to a maximum frequency of a few GHzs), but is, on the other hand, within the reach of the upcoming axion dark matter experiment-high frequency experiment that will explore the 4–40 GHz frequency range and then be sensitive to axion masses up to $\sim 160\mu \mathrm{eV}$.

A small Higgs mass parameter $m_{h_u}^2$ can be insensitive to various trial heavy stop masses, if a universal soft squared mass is assumed for the chiral superpartners and the Higgs boson at the grand unification (GUT) scale, and a focus point (FP) of $m_{h_u}^2$ appears around the stop mass scale. The challenges in the FP scenario are (1) a too heavy stop mass ($\approx 5\mathrm{TeV}$) needed for the 126 GeV Higgs mass and (2) the too high gluino mass bound ($\gtrsim 1.4\mathrm{TeV}$). For a successful FP scenario, we consider (1) a superheavy right-hand (RH) neutrino and (2) the first and second generations of hierarchically heavier chiral superpartners. The RH neutrino can move a FP in the higher energy direction in the space of $(Q,m_{h_u}^2(Q))$, where $Q$ denotes the renormalization scale. On the other hand, the hierarchically heavier chiral superpartners can lift up a FP in that space through two-loop gauge interactions. Precise focusing of $m_{h_u}^2(Q)$ is achieved with the RH neutrino mass of $\sim 10^{14}\mathrm{GeV}$ together with an order one (0.9–1.2) Yukawa coupling to the Higgs boson, and the hierarchically heavy masses of 15–20 TeV for the heavier generations of superpartners, when the $\mathrm{U}(1{)}_R$ breaking soft parameters $m_{1/2}$ and $A_0$ are set to be 1 TeV at the GUT scale. Those values can naturally explain the small neutrino mass through the seesaw mechanism, and suppress the flavor violating processes in supersymmetric models.

The chiral Lagrangian describing the low-energy behavior of $N_f=2+1+1$ twisted mass lattice QCD is constructed through $\mathrm{O}(a^2)$. In contrast to existing results the effects of a heavy charm quark are consistently removed. This Lagrangian is used to compute the pion and kaon masses to one loop in a regime where the pion mass splitting is large and taken as a leading order effect. In comparison with continuum chiral perturbation theory additional chiral logarithms are present in the results. In particular, chiral logarithms involving the neutral pion mass appear. These predict rather large finite volume corrections in the kaon mass which roughly account for the finite volume effects observed in lattice data.

We explore the breaking of rotational symmetry on the lattice for bound state energies and practical methods for suppressing this breaking. We demonstrate the general problems associated with lattice discretization errors and finite-volume errors using an $\alpha$ cluster model for ${}^8\mathrm{Be}$ and ${}^{12}\mathrm{C}$. We consider the two and three $\alpha$-particle systems and focus on the lowest states with nonzero angular momentum which split into multiplets corresponding to different irreducible representations of the cubic group. We examine the dependence of such splittings on the lattice spacing and box size. We find that lattice spacing errors are closely related to the commensurability of the lattice with the intrinsic length scales of the system. We also show that rotational symmetry breaking effects can be significantly reduced by using improved lattice actions, and that the physical energy levels are accurately reproduced by the weighted averages of the spin multiplets.

In this work, we adopt the spin rearrangement scheme in the heavy quark limit and extensively investigate three classes of the radiative decays: $\mathfrak{M}\to (b\overline{b})+\gamma$, $(b\overline{b})\to \mathfrak{M}+\gamma$, $\mathfrak{M}\to {\mathfrak{M}}^{\prime }+\gamma$ corresponding to the electromagnetic transitions between one molecular (resonant) state and bottomonium, one bottomonium and molecular (resonant) state, and two molecular (resonant) states, respectively. We also extend the same formalism to study the radiative decays of the molecular (resonant) states with hidden charm. We derive some model-independent ratios when the initial or final states belong to the same spin-flavor multiplet. Future experimental measurement of these ratios will test the molecular picture and explore the underlying structures of the $XYZ$ states.

We perform the first systematic study of the nonlinear electromagnetic currents induced by the external electromagnetic field in quark-gluon plasma, in cases where the inhomogeneity of the electromagnetic field is small (large) so that the collision effect is important (negligible). In the former case, we list and classify possible components of the currents in a systematic way and make an order estimate of each component by using the Boltzmann equation in the relaxation time approximation. In the latter case, we explicitly calculate the quadratic current by using the Vlasov equation, and we find that the current generated by the chiral magnetic effect and the quadratic current can have the same order of magnitude by using the Kadanoff-Baym equation. We also demonstrate this property by using a possible configuration of the electromagnetic field realized in a heavy ion collision.

The decays ${\mathrm{\Xi }}_b\to {\mathrm{\Lambda }}_b\pi$ are strangeness changing weak transitions involving only the light diquark in the baryon. Thus these decays can test the properties of such diquarks, in particular the suggestions existing in the literature of enhanced correlations in $J^P=0^{+}$ light diquarks. We revisit the estimates of the rates of these decays and point out that with the enhanced correlation their branching fraction can reach a few percent and may become visible in the measurements of differences of the lifetimes of $b$ baryons.