Ideas of four-fermion operators in hadron physics

Nuclear Physics B, 1996

The next-to-leading-order (NLO) cross section for the production of heavy quarks at large transverse momenta (p±) in 3,3/collisions is calculated with perturbative fragmentation functions (PFFs). This approach allows for a resummation of terms cx as ln(p~/m 2) which arise in NLO from colfinear emission of gluons by heavy quarks at large p± or from almost collinear branching of photons or gluons into heavy-quark pairs. We present single-inclusive distributions in p± and rapidity including direct and resolved photons for yy production of heavy quarks at e+e -colliders and at high-energy yy colliders. The results are compared with the fixed-order calculation for m finite including QCD radiative corrections. The two approaches differ in the definitions and relative contributions of the direct and resolved terms, but essentially agree in their sum. The resummation of the as ln(p2/m e) terms in the PFF approach leads to a softer p± distribution and to a reduced sensitivity to the choice of the renormalization and factorization scales.

Physical Review D, 1999

We introduce and study the properties of the "color-straight" four-quark operators containing heavy and light quark fields. They are of the form (bΓ b b)(qΓ q q) where both brackets are color singlets. Their expectation values include the bulk of the nonfactorizable contributions to the nonleptonic decay widths of heavy hadrons. The expectation values of the color-straight operators in the heavy hadrons are related to the momentum integrals of the elastic light-quark formfactors of the respective heavy hadron. We calculate the asymptotic behavior of the light-current formfactors of heavy hadrons and show that the actual decrease is 1/(q 2) 3 2 rather than 1/q 4. The two-loop hybrid anomalous dimensions of the four-quark operators and their mixing (absent in the first loop) are obtained. Using plausible models for the elastic formfactors, we estimate the expectation values of the color-straight operators in the heavy mesons and baryons. Improved estimates will be possible in the future with new data on the radiative decays of heavy hadrons. We give the Wilson coefficients of the four-fermion operators in the 1/m b expansion of the inclusive widths and discuss the numerical predictions. Estimates of the nonfactorizable expectation values are given.

Il Nuovo Cimento A, 1980

Few-Body Systems

By the analysis of the world data base of elastic electron scattering on the proton and the neutron (for the latter, in fact, on 2 H and 3 He) important experimental insights have recently been gained into the flavor compositions of nucleon electromagnetic form factors. We report on testing the Graz Goldstone-bosonexchange relativistic constituent-quark model in comparison to the flavor contents in low-energy nucleons, as revealed from electron-scattering phenomenology. It is found that a satisfactory agreement is achieved between theory and experiment for momentum transfers up to Q 2 ∼ 4 GeV 2 , relying on three-quark configurations only. Analogous studies have been extended to the and the hyperon electromagnetic form factors. For them we here show only some sample results in comparison to data from lattice quantum chromodynamics. Evidently, electromagnetic (e.m.) form factors provide stringent tests on any model for hadrons. The Goldstoneboson-exchange (GBE) relativistic constituent-quark model (RCQM) for baryons constructed by the Graz group [1] had been tested with respect to covariant predictions for the elastic e.m. N form factors long ago [2,3]. An unprecedented overall agreement with experimental data up to momentum transfers of Q 2 ∼ 4 GeV 2 had then been achieved in a calculation along point-form relativistic quantum mechanics. After the appearance of phenomenological flavor analyses of elastic e.m. N form factors [4-6] it appeared more than interesting to check the performance of the GBE RCQM also in these respects. Recently we have performed such studies. Below we show pertinent results of selective quantities for the N and from extensions of this kind of investigations to the and to the hyperons with various u, d, and s quark contents. The theory and the calculations are exactly the same as explained for the point-form approach in our previous papers [2,3,7,8]. The predictions for the elastic e.m. form factors fulfill Poincaré invariance as well as time-reversal invariance and current conservation [7,8]. Accurate three-quark baryon wave functions were obtained solving a relativistically invariant mass operator along the stochastic variational method exploiting all possible symmetries in configuration, spin, and flavor spaces. For the rest frames they are depicted in Ref. [9] for singlet, octet and decuplet baryon states. In the calculation of the e.m. form factors the necessary Lorentz boosts can be executed rigorously when evaluating the matrix elements of the e.m. current operator in the framework of the point form. This article belongs to the Topical Collection "The 23rd European Conference on Few-Body Problems in Physics".

As a continuation of the preceding section, we shortly review a series of novel ideas on the physics of hadrons. In the present paper, emphasis is given on some di erent approaches to the hadron physics, which may be called as ’programs’ in the sense of Lakatos. For clarity, we only discuss geometrization program, symmetries/ unification program, and phenomenology of inter-quark potential program.