Modern Physics Letters A

In this review, we discuss why, in the determination of ${\alpha }_s(m_{\tau }^2)$ from hadronic $\tau$ decays, two important assumptions made in most of previous analyses, namely the neglect of higher-dimension condensates and of duality violations (DVs), have introduced uncontrolled systematic errors into this determination. Although the use of pinched weights is usually offered as a justification of these assumptions, we explain why it is not possible to simultaneously suppress these two contributions; particularly since the Operator Product Expansion (OPE) is expected to be an asymptotic, rather than a convergent expansion. There is not only experimental and theoretical evidence for DVs but they also affect the extraction of ${\alpha }_s(m_{\tau }^2)$.

Using the most recent release of the ALEPH $\tau$ decay data, we present a very detailed phenomenological update of the ${\alpha }_s(m_{\tau }^2)$ determination. We have exploited the sensitivity to the strong coupling in many different ways, exploring several complementary methodologies. All determinations turn out to be in excellent agreement, allowing us to extract a very reliable value of the strong coupling. We find ${\alpha }_s^{(n_f=3)}(m_{\tau }^2)=0.328\pm 0.012$ which implies ${\alpha }_s^{(n_f=5)}(M_Z^2)=0.1197\pm 0.0014$. We critically revise previous work, and point out the problems flawing some recent analyses which claim slightly smaller values.

We present a determination of the strong coupling constant from lattice quantum chromodynamics (QCD) using the moments of pseudo-scalar charmonium correlators calculated using highly improved staggered quark action. We obtain a value ${\alpha }_s(\mu =m_c)=0.3397(56)$, which is the lowest energy determination of the strong coupling constant so far.

A general quantum-mechanical setting is proposed for the field–antifield formalism as a unique hyper-gauge theory in the field–antifield space. We formulate a Schrödinger-type equation to describe the quantum evolution in a “current time” purely formal in its nature. The corresponding Hamiltonian is defined in the form of a supercommutator of the delta-operator with a hyper-gauge fermion. The initial wave function is restricted to be annihilated with the delta-operator. The Schrödinger’s equation is resolved in a closed form of the path integral, whose action contains the symmetric Weyl’s symbol of the Hamiltonian. We take the path integral explicitly in the case of a hyper-gauge fermion being an arbitrary function rather than an operator.

We investigate the Newton law in the unimodular F(R) gravity. In the standard F(R) gravity, due to the extra scalar mode, there often appear the large corrections to the Newton law and such models are excluded by the experiments and/or the observations. In the unimodular F(R) gravity, however, the extra scalar mode become not to be dynamical due to the unimodular constraint and there is not any correction to the Newton law. Even in the unimodular Einstein gravity, the Newton law is reproduced but the mechanism is a little bit different from that in the unimodular F(R) gravity. We also investigate the unimodular F(R) gravity in the covariant formulation. In the covariant formulation, we include the three-form field. We show that the three-form field could not have any unwanted property, like ghost nor correction to the Newton law. In the covariant formulation, however, the above extra scalar mode becomes dynamical and could give a correction to the Newton law. We also show that there are no difference in the Friedmann–Robertson–Walker (FRW) dynamics in the non-covariant and covariant formulation.

A recent search for the lepton flavor violating (LFV) decays of the Higgs boson, performed by CMS collaboration, reports an interesting deviation from the Standard Model (SM). The search conducted in the channel $H\to \mu {\tau }_e$ and $H\to \mu {\tau }_{\mathrm{\text{had}}}$ shows an excess of 2.4$\sigma$ signal events with 19.6 fb${}^{-1}$ data at a center-of-mass energy $\sqrt{s}$ = 8 TeV. On the other hand, a search performed by CMS collaboration for the SM Higgs boson produced in association with a top quark pair $(t\bar{t}H)$ also showed an excess in the same-sign dimuon final state. In this work, we try to find out if these two seemingly uncorrelated excesses are related or not. Our analysis reveals that a LFV Higgs decay $(H\to \mu \tau )$ can partially explain the excess in the same-sign dimuon final state in the $t\bar{t}H$ search, infact brings down the excess well within 2$\sigma$ error of the SM expectation. Probing such non-standard Higgs boson decay is of interest and might contain hints of new physics at the electroweak scale.

This paper is devoted to study evolution of the isotropic universe models in the framework of $F(T,T_G)$ gravity ($T$ represents torsion scalar and $T_G$ is the teleparallel equivalent of the Gauss–Bonnet (GB) term). We construct $F(T,T_G)$ models by taking different eras of the universe like non-relativistic and relativistic matter eras, dark energy (DE) dominated era and their combinations. It is found that the reconstructed models indicate decreasing behavior for DE dominated era and its combination with other eras. We also discuss stability of each reconstructed model. Finally, we evaluate equation of state (EoS) parameter by considering two models and study its behavior graphically.