QCD vacuum tensor susceptibility and properties of transversely polarized mesons

We re-estimate the tensor susceptibility of the QCD vacuum, , and to this end, we re-estimate the tensor coupling constants for the transversely polarized -, - and -mesons. The origin of the susceptibility is analyzed using (anti-)duality between the - and - channels in the 2-point correlator of the tensor currents. We conclude that the origin of the differences in - and -meson masses and tensor couplings is the (anti-)duality breakdown in QCD due to the 4-quark condensate. We confirm the results of Govaerts et al. for the 2-point correlator of the tensor currents and disagree with Belyaev and Oganesyan on both the OPE expansion and the value of the QCD vacuum tensor susceptibility. Using our value for the latter we determine new estimations of the nucleon tensor charges related to the first moment of the transverse structure function of a nucleon. Received: 17 May 2000 / Published online: 9 August 2000     

A new gravitational energy tensor

The Bel-Robinson tensor is the most used gravitational energy tensor; however, it has the dimensions of energy squared. How to construct tensors with the dimensions of energy by using Lancoz tensors is shown here. The resulting tensors have a large number of arbitrary parameters, frequently have spacelike currents, and frequently do not reduce to familiar pseudo-energy tensors in the weak field limit. Two particular examples of interest are one with well-behaved currents and one which reduces to an energy pseudo-tensor in the weak field limit.     

Corrections to the single-particle M1 and Gamow-Teller matrix elements

Consideration of second-order core-polarisation, isobar-current and meson-exchange-current processes gives a satisfactory understanding of the ground-state magnetic moments and mirror β-decay transition probabilities in closed-shell-plus- (or minus) one nuclei, A = 3, 15, 17, 39 and 41. Perturbation contributions from high-lying excited states (tensor correlations) from one-body and two-body meson-exchange operators cancel strongly in diagonal matrix elements, but in off-diagonal matrix elements between spin-orbit partners the cancellation is less. Similarly, with isobar currents, there is a strong cancellation between direct and exchange contributions in diagonal matrix elements, while the exchange term is suppressed in off-diagonal cases. Of the two contributions, tensor correlations are found to be as important as, if not more important than, isobar currents. The calculated lowest-order meson-exchange-current contributions to magnetic moments are close to the soft-pion limit predictions.     

Two-Point Fermionic Correlators in External Constant Uniform Magnetic Field

The results of calculation of two-point correlation functions of fermionic currents in a constant uniform magnetic field are presented. The off-diagonal correlation functions including the tensor current (namely, the scalar-tensor and pseudoscalar-tensor) are calculated in addition to the correlators of scalar, pseudoscalar, vector, and axial-vector fermionic currents. The tensor fermionic current is a part of the Pauli term in the Lagrangian, which is responsible for the electromagnetic interaction of the fermion through an anomalous magnetic moment. In particular, if we take this interaction into account, we modify the frequency of axion-photon oscillations. In the future, it is planned to investigate this feature in details.     

Magnetic moments of light nuclei

Magnetic moments of the nuclei ¹⁵N, ¹⁵O, ¹⁷O, ¹⁷F and ¹⁹F are investigated. The importance ; of configuration mixing as well as meson-exchange currents is discussed in detail. Meson-exchange currents are treated in the one-boson exchange limit. Short-range N-N correlations are obtained from solutions of the Bethe-Goldstone equation for doubly closed shell nuclei by the use of realistic N-N potentials which ensure a correct treatment of tensor correlations.     

Locally conserved currents linearly dependent on the energy-momentum tensor and the polynomial in the position variables

In this note we are considering a symmetrical locally conserved energy-momentum tensor, whose trace vanishes. We show that there are no other combinations of the position variables x and the energy-momentum tensor, whose divergence vanishes except the well-known currents of translations, four-dimensional Lorentz rotations as well as con- formal and dilatational transformations.     

Poincaré gauge theory from self-coupling

Poincaré gauge theory is derived from a linear theory by the method suggested by Gupta for deriving Einstein’s general relativity from the linear theory of a spin-2 field. Non-linearity is introduced by requiring that a set of tensor fields be coupled to the Noether currents of the Poincaré group (energy-momentum and spin).     

Heavy quark induced effective action for gauge fields in the SU(N_c)\otimes U(1) model and the low-energy structure of heavy quark current correlators

We calculate the low-energy limit of heavy quark current correlators within an expansion in the inverse heavy quark mass. The induced low-energy currents built from the gluon fields corresponding to the initial heavy quark currents are obtained from an effective action for gauge fields in the one-loop approximation at the leading order of the expansion. Explicit formulae for the low-energy spectra of electromagnetic and tensor heavy quark current correlators are given. Consequences of the appearance of a nonvanishing spectral density below the two-particle threshold for high precision phenomenology of heavy quarks are discussed quantitatively. Received: 21 April 2001 / Revised version: 18 May 2001 / Published online: 29 June 2001     

The origin of the electromagnetic interaction in Einstein's unified field theory with sources

Einstein's unified field theory is extended by the addition of matter terms in the form of a symmetric energy tensor and of two conserved currents. From the field equations and from the conservation identities emerges the picture of a gravoelectrodynamics in a dynamically polarizable Riemannian continuum. Through an approximate calculation exploiting this dynamical polarizability it is argued that ordinary electromagnetism may be contained in the theory.     

A short history of nuclear magnetic moments and GT transitions

We summarize the history and our present understanding of nuclear magnetic moments and Gamow-Teller transitions.The roles of configuration mixing,meson exchange currents and relativistic effects are examined.Experimental evidence for the importance of tensor correlations is also discussed.     

Conformal invariant two and three-point functions for fields with arbitrary spin

The conformal invariant two and three-point functions for any “fundamental” fields with an arbitrary spin and scale dimensions are found in the Minkowsky x-space. The two-point functions for Dirac, symmetric and antisymmetric tensor fields are given. The three-point functions for two Dirac fields and one symmetrical tensor field, as well as any other field for which this function is nonvanishing, are given. In the case of conserved currents the Ward identities are considered.     

Supersymmetry and tensor coupling in

We study a possible explanation of the tensor currents in the weak radiative decay which was suggested recently by Bolotov et al. [Phys. Lett. B 243 (1990) 308] and Poblaguev [Phys. Lett. B 238 (1990) 108]. It can be shown that the supersymmetric particles can produce a tensor coupling at order (10⁻⁴−10⁻⁵)G_F which is 2–3 orders of magnitude smaller than the estimates extracted from the experimental data. A reliable calculation of the hadronic matrix element is done. The importance of a precision measurement of the tensor coupling in this decay is discussed as well as the possible relevance of the technicolour models.     

Mirror transitions and second class currents

Theoretical implications of observed mirror asymmetry in nuclear beta decay are examined, taking into account CP violation and internal symmetries. The second class induced tensor current is shown not to be responsible for the observed asymmetry, which must be the result of multinucleon or meson exchange effects. The result is general and holds for all values of momentum transfer. Possible two nucleon transitions are discussed. Mirror asymmetry in the Σ−Λ decay cannot be produced by SU(3) octet currents or single quark currents in the quark model even if such second class currents exist.     

RI′/SMOM scheme amplitudes for quark currents at two loops

We determine the two loop corrections to the Green’s function of a quark current inserted in a quark 2-point function at the symmetric subtraction point. The amplitudes for the scalar, vector and tensor currents are presented in both the [`(MS)]\overline {\mathrm {MS}} and RI′/SMOM renormalization schemes. The RI′/SMOM scheme two loop renormalization for the scalar and tensor cases agree with previous work. The vector current renormalization requires special treatment as it must be consistent with the Slavnov–Taylor identity which we demonstrate. We also discuss the possibility of an alternative definition of the RI′/SMOM scheme in the case of the tensor current.     

静电场和稳恒电流磁场诸定律的统一性浅探

从点电荷的场强公式出发，根据狭义相对论中场强张量的变换，推导出了静电场和稳恒电流磁场的诸定律，使学生对电场和磁场的统一性有了更为深刻的认识．     

Two-loop corrections to the correlation function for tensor currents in gluodynamics

The results of evaluating the leading-order a_s corrections to the correlation function for tensor currents in pure gluodynamics are presented. These corrections to the parton result for the correlation function are not large numerically, which allows one to use perturbation theory to analyze the resonance spectrum within the sum-rule method.     

Structure of weak nucleon currents and charge asymmetry in nuclear beta decay

Structure of weak nucleon currents is studied from the beta decays in the A=12 system. We have investigated the experimental data on the beta-ray angular distribution in the aligned ¹²B and ¹²N recently given by the Osaka group with our formulas to find a new limit for the induced tensor current. A possible difference of the ratio y of the axial charge to Gamow-Teller matrix elements between the beta decays of ¹²B and ¹²N is calculated theoretically in connection with the ft-value asymmetry, since it affects the evaluation of the strength of the induced tensor current.     

Emergent Newtonian dynamics and the geometric origin of mass

We consider a set of macroscopic (classical) degrees of freedom coupled to an arbitrary many-particle Hamiltonian system, quantum or classical. These degrees of freedom can represent positions of objects in space, their angles, shape distortions, magnetization, currents and so on. Expanding their dynamics near the adiabatic limit we find the emergent Newton’s second law (force is equal to the mass times acceleration) with an extra dissipative term. In systems with broken time reversal symmetry there is an additional Coriolis type force proportional to the Berry curvature. We give the microscopic definition of the mass tensor. The mass tensor is related to the non-equal time correlation functions in equilibrium and describes the dressing of the slow degree of freedom by virtual excitations in the system. In the classical (high-temperature) limit the mass tensor is given by the product of the inverse temperature and the Fubini–Study metric tensor determining the natural distance between the eigenstates of the Hamiltonian. For free particles this result reduces to the conventional definition of mass. This finding shows that any mass, at least in the classical limit, emerges from the distortions of the Hilbert space highlighting deep connections between any motion (not necessarily in space) and geometry. We illustrate our findings with four simple examples.     

Bestimmung des Abschirmtensors der magnetischen Kernresonanz und des Tensors der magnetischen Suszeptibilität durch numerische Berechnung der Stromdichte in der Ladungsverteilung diamagnetischer Moleküle

Determination of the NMR Shielding Tensor and of the Tensor of Magnetic Susceptibility by Numerical Calculation of the Current Density in the Chargedistribution of Diamagnetic Molecules In papers [1] and [2] a semiclassical approach for calculation of the NMR shielding tensor and of the tensor of magnetic susceptibility of diamagnetic molecules was represented by SCHMIEDEL. In this method the equation of continuity for the currents in the electronic cloud induced by an external magnetic field must be solved. In this paper a method of numerical solution of this partial differential equation is developed. The H₂-molecule serves as an example to present the possibilities of this method.