Direct-Channel Resonance Model of Deep-Inelastic Electron Scattering. I. Scattering on Unpolarized Targets

Abstract

that pemZ"O is about one third of pemr-I. However, if, as has been discussed by Pais and Treiman,20 the soft-pion techniques are valid a t q2--MW2, then we can extract the isovector contribution p,,r-1(q2) directly from ex-~eriments. The Dresence of an isoscalar contribution can easily be incorporated into our results.A sizable branching ratjo makes possible the search for the IVB through its hadronic decay modes. Our estimates imply that about half of the W events will decay into hadrons. The background from inelastic neutrino-nucleon scattering, discussed by Cline, Mann, and Rubbia." is still manageable. because a com~leteWe construct a resonance model of deep-inelastic electron scattering. Using semiempirical rules for the form of the nucleon spectrum and a universality hypothesis for the transition form factors, we obtain explicit expressions for the structure functions W1 and W2 in the Bjorken limit. The ratio of the longitudinal to transverse photoabsorption cross sections vanishes for large momentum transfers, and vWz becomes scale invariant. A one-parameter fit is obtained to VWZ (proton), and a zero-parameter prediction is made of vW2 (proton)-vWz (neutron). There is good agreement between the theory and experiment in the region where scale invariance is well established.' J. D. Bjorken, Phys. Rev. 179, 1547 (1969. 2 J. D. Bjorken and E. A. Paschos, Phys. Rev. 185, 1975 (1969). the data is scale i~zvariance, i.e., that the structure func- R, P. Feynman, Phys, Rev, Letters 23, 1415 (1969). tions essentially depend on the ratio v/q2 only, where v S. D. Drell, D. J. Levy, and T. M. Yan, Phys. Rev. Letters is the energy loss of the electron, and q2 is the invariant 22, 744 6 J. J. Sakurai, Phys. Rev. Letters 22, 981 (1969). momentum transfer squared. 6 H. Harari, Phys. Rev. Letters 22, 1978 (1969).

Semi-inclusive charged-pion electroproduction off protons and deuterons: Cross sections, ratios, and access to the quark-parton model at low energies

“…(5). Theoretically, such a factorized description is only valid at leading order in α s , and after integration over the transverse momentum P t and the azimuthal angle φ.…”

“…The level of 5 corrections applied to the experimental data and related systematic uncertainties are listed in Table X. For absolute cross sections we have added all systematic uncertainties in quadrature. Note, that in practice the range of applied corrections and related systematic errors are slightly different for π + and π − .…”

“…Initial interpretations of this duality naturally used the theoretical tools available at the time, finite-energy sum rules or consistency relations between hadronic amplitudes inspired by the developments in Regge theory that occurred in the 1960s [2,3]. With the advent of QCD, De Rújula, Georgi, and Politzer offered a qualitative explanation of BloomGilman duality [4] in terms of either small or on-averagecanceling higher-twist contributions, but a quantitative understanding of the origin of the duality phenomenon in QCD remains elusive, although some insight has been obtained through phenomenological model calculations [5].…”

Quark–hadron duality: resonances and the onset of scaling

“…Similar models have also been considered in Refs. 13,14 . Although clearly too simple to provide a realistic description of data, a model with these features nevertheless allows one to study the critical questions of when and why duality holds.…”

“…In fact, the correct density of states is crucial to compensate for the falling off with q 2 of each individual form factor, F 0N ∼ q N exp(− q 2 /4 β 2 ), where β is related to the relativistic string constant 12 . Had the spacing between the excited states not been Regge-like 13 , E N ∼ √ N , but linear as in a nonrelativistic solution, the density of states would not have been sufficient to produce duality. While it remains an interesting exercise to see whether potentials other than a harmonic oscillator give rise to similar behavior, this simple example illustrates that Bloom-Gilman duality appears as a natural consequence of even the most elementary quantum mechanical systems, with the only requirements being confinement and a correct treatment of kinematics 12 .…”