Jan Stern

Relativistic dynamics on a null plane

Abstract In view of possible applications to the quark model and to hadron spectroscopy, we investigate relativistic Hamiltonian quantum theories of finitely many degrees of freedom. We make use of the fact that if null planes are used as initial surfaces, the structure of the theory closely resembles nonrelativistic quantum mechanics: the inner variables that describe the structure of the system uncouple from the motion of the system as a whole. The dynamical content of such a theory resides in the operators M, j of mass and spin that act in the space carrying the inner degrees of freedom. Relativistic invariance is equivalent to the requirement that M and j generate a unitary representation of U(2). In contrast to this requirement, the condition that the wavefunctions of the system transform covariantly strongly restricts the dynamics. It is proven that for systems containing two constituents, covariance is equivalent to an algebraic relation that involves M and j — the angular condition. A class of solutions of the angular condition is provided by a particular type of local manifestly covariant wave equations. One nontrivial solution of this class, a relativistic oscillator is given in detail. Confinement models of this type represent an interesting alternative to the solutions of the angular condition that result from the perturbation expansion of a local field theory through the three-dimensional quasipotential versions of the Bethe-Salpeter equation.

Singularities of current commutators on the light cone

Abstract We consider the forward proton matrix element of the electromagnetic current commutator and express its singularities on the light cone in terms of the scaling functions. This relation between the light cone and the deep inelastic region implies a family of sum rules for the electroproduction structure functions and connects the equal time commutators with the scaling functions. In particular the operator part of the Schwinger term and the related divergences of the electromagnetic mass of the proton are expressed in terms of measurable quantities.

Finite energy chiral sum rules and tau spectral functions

A combination of finite energy sum rule techniques and Chiral Perturbation Theory (ChPT) is used in order to exploit recent ALEPH data on the non-strange tau vector (V) and axial-vector (A) spectral functions with respect to an experimental determination of the ChPT quantity L_{10}. A constrained fit of R_{\tau,V-A}^(k,l) inverse moments (l =0) adjusts simultaneously L_{10} and the nonperturbative power terms of the Operator Product Expansion. We give explicit formulae for the first k=0,1 and l=-1,-2 strange and non-strange inverse moment chiral sum rules to one-loop order generalized ChPT. Our final result reads L^r_{10}(M_\rho)=-(5.13 +/- 0.19)x10^{-3}, where the error includes experimental and theoretical uncertainties.

Paramagnetic effect of light quark loops on chiral symmetry breaking

Wearguethatlight quark loopsproduceaparamagnetic suppression of infrared-sensitive order parameters such ashqqi,asthenumberNfof light fermions increases. The possibly strong dependence ofhqqionNf is related to the observed Zweig rule violationin the scalar channel. Presuming the existence of a chiral phase transitionfornottoolargeNf,wediscussthephenomenologicalpossibilitiesofsepa- ratelydeterminingthetwo-flavourandthree-flavourcondensatesandthequarkmass ratior=2ms=(mu+md). The issue is closely related to the interpretation of new forthcoming precisedata at low energy.

Kμ3L decay: A stringent test of right-handed quark currents

Abstract Clean tests of a small admixture of right-handed quark currents directly coupled to the standard W are still lacking. We show that such non-standard couplings can be significantly constrained measuring the value of the scalar Kπ form factor at the Callan–Treiman point to a few percent. A realistic prospect of such a measurement in K μ 3 L decay based on an accurate dispersive representation of the scalar form factor is presented. The inadequacy of the currently used linear parametrization is explained and illustrated using recent KTeV data. We briefly comment on the charged kaon mode.

Dispersive representation and shape of the Kl3 form factors: robustness

An accurate low-energy dispersive parametrization of the scalar

New dispersion sum rules for inelastic e - p scattering

K\ensuremath{\pi}

Vacuum fluctuations of and values of low-energy constants

form factor was constructed some time ago in terms of a single parameter guided by the Callan-Treiman low-energy theorem. A similar twice-subtracted dispersive parametrization for the vector

What can we learn from sum rules for vertex functions in QCD

K\ensuremath{\pi}

Dispersive analysis of KLμ3 and KLe3 scalar and vector form factors using KTeV data

form factor will be investigated here. The robustness of the parametrization of these two form factors will be studied in great detail. In particular the cutoff dependence, the isospin breaking effects, and the possible, though not highly probable, presence of zeros in the form factors will be discussed. Interesting constraints in the latter case will be obtained from the soft-kaon analog of the Callan-Treiman theorem and a comparison with the recent