International Journal of Modern Physics A

This paper presents the current status of the theory of electron anomalous magnetic moment a_e ≡(g-2)/2, including a complete evaluation of 12,672 Feynman diagrams in the tenth-order perturbation theory. To solve this problem, we developed a code-generator which converts Feynman diagrams automatically into fully renormalized Feynman-parametric integrals. They are evaluated numerically by an integration routine VEGAS. The preliminary result obtained thus far is 9.16 (58) (α/π)⁵, where (58) denotes the uncertainty in the last two digits. This leads to a_e(theory) = 1.159 652 181 78 (77) ×10^-3, which is in agreement with the latest measurement a_e (exp:2008) = 1.159 652 180 73 (28) ×10^-3. It shows that the Feynman–Dyson method of perturbative QED works up to the precision of 10^-12.

The effects originated in dispersion with time on spreading of wave packets for the time-integrated two-flavor neutrino oscillation probabilities in vacuum are studied in the context of a field theory treatment. The neutrino flavor states are written as superpositions of neutrino mass eigenstates which are described by localized wave packets. This study is performed for the limit of nearly degenerate masses and considering an expansion of the energy until third-order in the momentum. We obtain that the time-integrated neutrino oscillation probabilities are suppressed by a factor 1/L² for the transversal and longitudinal dispersion regimes, where L is the distance between the neutrino source and the detector.

In order to understand the self-consistent theory of dyons, we have undertaken the study of octonion analysis of generalized Dirac–Maxwell's (GDM) equations of dyons in isotropic medium and chiral medium. Consequently, we have developed the octonion forms of potential, field and current equation of dyons in simple and compact manner in homogeneous or isotropic medium. It is emphasized that the corresponding quantum equations are invariant under Lorentz and duality transformations. Furthermore, the generalized electrodynamics of dyons in chiral medium has also been discussed in terms of simple, compact and consistent octonion analysis. It is shown that in the absence of chiral parameter the theory of dyons reduces to that for homogeneous (isotropic) medium. The generalized theory of dyons in chiral medium thus reproduces the field equation of moving charge particle-like electron (monopole) in the absence of monopole (electron) in vacuum if we consider neither chiral nor isotropic medium parameters therein.

We explicitly solve the classical equations of motion for strings in backgrounds obtained as non-Abelian T-duals of a homogeneous isotropic plane-parallel wave. To construct the dual backgrounds, semi-Abelian Drinfeld doubles are used which contain the isometry group of the homogeneous plane wave metric. The dual solutions are then found by the Poisson–Lie transformation of the explicit solution of the original homogeneous plane wave background. Investigating their Killing vectors, we have found that the dual backgrounds can be transformed to the form of more general plane-parallel waves.

We consider extensions of the standard model with fourth generation fermions (SM4) in which extra symmetries are introduced such that the transitions between the fourth generation fermions and the ones in the first three generations are forbidden. In these models, the stringent lower bounds on the masses of fourth generation quarks from direct searches can be relaxed, and the lightest fourth neutrino is allowed to be stable and light enough to trigger the Higgs boson invisible decay. In addition, the fourth Majorana neutrino can be a subdominant but highly detectable dark matter component. We perform a global analysis of the current Large Hadron Collider (LHC) data on the Higgs production and decay in this type of SM4. The results show that the mass of the lightest fourth Majorana neutrino is confined in the range ~41–59 GeV. Within the allowed parameter space, the predicted effective cross-section for spin-independent DM–nucleon scattering is ~3×10^-48–6×10^-46cm², which is close to the current XENON100 upper limit and is within the reach of the XENON1T experiment in the near future. The predicted spin-dependent cross sections can also reach ~8×10^-40cm².

A quantum scalar field theory with spacetime-dependent coupling is studied. Surprisingly, while translation invariance is explicitly broken in the classical theory, momentum conservation is recovered at the quantum level for some specific choice of the coupling's profile for any finite-order perturbative expansion. For one of these cases, some tree and one-loop diagrams are calculated. This is an example of a theory where violation of Lorentz symmetry is not enhanced at the quantum level. We draw some consequences for the renormalization properties of certain classes of fractional field theories.

We re-examine d = 4 hidden-variables model for a system of two spin-1/2 particles in view of the concrete model of Hardy, who analyzed the criterion of entanglement without referring to inequality. The basis of our analysis is the linearity of the probability measure related to the Born probability interpretation, which excludes noncontextual hidden-variables model in d≥3. To be specific, we note the inconsistency of the noncontextual hidden-variables model in d = 4 with the linearity of the quantum mechanical probability measure in the sense 〈ψ|a⋅σ ⊗b ⋅σ|ψ〉+ 〈ψ|a ⋅σ ⊗b′ ⋅σ|ψ〉 = 〈ψ|a⋅σ⊗(b + b′)⋅σ|ψ〉 for noncollinear b and b′. It is then shown that Hardy's model in d = 4 does not lead to a unique mathematical expression in the demonstration of the discrepancy of local realism (hidden-variables model) with entanglement and thus his proof is incomplete. We identify the origin of this nonuniqueness with the nonuniqueness of translating quantum mechanical expressions into expressions in hidden-variables model, which results from the failure of the above linearity of the probability measure. In contrast, if the linearity of the probability measure is strictly imposed, which tantamounts to asking that the noncontextual hidden-variables model in d = 4 gives the Clauser–Horne–Shimony–Holt (CHSH) inequality |〈B〉|≤2 uniquely, it is shown that the hidden-variables model can describe only separable quantum mechanical states; this conclusion is in perfect agreement with the so-called Gisin's theorem which states that |〈B〉|≤2 implies separable states.

The Bialas–Bzdak model of elastic proton–proton scattering is generalized to the case when the real part of the parton–parton level forward scattering amplitude is nonvanishing. Such a generalization enables the model to describe well the dip region of the differential cross-section of elastic scattering at the intersecting storage rings (ISR) energies, and improves significantly the ability of the model to describe also the recent TOTEM data at LHC energy. Within this framework, both the increase of the total cross-section, as well as the decrease of the location of the dip with increasing colliding energies, is related to the increase of the quark–diquark distance and to the increase of the "fragility" of the protons with increasing energies. In addition, we present and test the validity of two new phenomenological relations: one of them relates the total p+p cross-section to an effective, model-independent proton radius, while the other relates the position of the dip in the differential elastic cross-section to the measured value of the total cross-section.

The capabilities of some approaches to the relativistic description of hadronic states with any rest spin are analysed. The key feature in the Wigner's construction of irreducible representations of the Poincaré group, which makes this construction fruitless in particle physics, is picked out. A realization of unitary irreducible representations of the Poincaré group of the standard type, which has not yet been considered, is discussed. The viability of the description of hadrons by the Poincaré group representations of the standard type in the space of the infinite-component ISFIR-class fields is pointed out.