arXiv subjects
Publications and source records attributed to R. L. Jaffe.
I review the ways that have been proposed to measure the quark transversity distribution in the nucleon. I then explain a proposal, developed by Xuemin Jin, Jian Tang and myself, to measure transversity through the final state interaction between two mesons ($ππ$, $K \bar K$, or $πK$) produced in the current fragmentation region in deep inelastic scattering on a transversely polarized nucleon.
We consider the interplay of a quark state and a hadronic threshold in the framework of the P-matrix formalism, which is reviewed and extended for use together with conventional methods of computing quark-gluon dynamics. We provide a quantitative dynamical interpretation of the reduced R or K matrices and their poles that suggests a natural classification of threshold phenomena. At a threshold with a quark state close to it up to three S-matrix poles can be found. The scattering amplitudes for the corresponding cases are discussed. Our analysis is applied to make an outlook for experimental observation of the doubly strange H-dibaryon if it is not stable to strong decays.
We study the kinematics and cross section of the scattering process $e p \rightarrow e Σ^+$. The cross section is expressed in terms of complex form factors characterizing the hadron vertices. We estimate the cross section for small momentum transfer using known experimental information. To first order in the momentum transfer, we obtain a model independent result for the photon-exchange part of the cross section, which is completely determined by the decay width $Γ(Σ^+ \rightarrow pγ)$. For the kinematics of the parity violation experiment at MAMI, this first order result gives rise to a ratio of $(dσ/dΩ)_{ep\rightarrow eΣ^+}$ $/(dσ/dΩ)_{ep\rightarrow ep} \simeq 4.0\times 10^{-15}$. The $Z^0$-exchange and interference parts give much smaller contributions due to the suppression of the flavor changing weak neutral current in the standard model. Feasibility of the experimental measurement is briefly discussed.
We reduce the problem of many-channel hadron scattering at nonrelativistic energies to calculations on the scale of a few fermis. Having thus disentangled kinematics from interior quark dynamics, we study their interplay when a quark state occurs near a hadronic threshold. Characteristic parameters, such as the observed peak width, the decay width, and the shape of a cross-section itself are highly affected by the threshold. A general pole-form expression for the S-matrix in an arbitrary background is given, and the pole structure of S is examined. We show that at a hadronic threshold two poles in S are generally important. We also classify the S-matrix pole structure considering an example where nonsingular coupled channels are closed at the threshold. The framework of our paper is the P-matrix formalism, which is reviewed and extended for use together with conventional methods of computing quark-gluon dynamics. Results and applications are illustrated for the doubly strange two-baryon system, the detailed analysis of which we postpone till our forthcoming paper.
Data on the nucleon spin structure suggests that the $u$ (and $d$) quark distributions in the $Λ$ hyperon may be polarized. If this correlation carries over into fragmentation, then the study of polarized $Λ$'s in the current fragmentation region of deep inelastic lepton scattering will be a sensitive probe of nucleon spin structure. $Λ$ production by polarized electrons from unpolarized targets can search for this correlation. If it is signficant, $Λ$ production by unpolarized electrons from longitudinally and transversely polarized targets can probe the $u$-quark helicity and transversity distributions in the nucleon. We review what is known about quark polarization in the $Λ$, summarize electroproduction of polarized $Λ$s, and estimate the sensitivity to quark polarizations in the nucleon. We also describe polarization phenomena associated with vector meson electroproduction that can be observed in the same experimental regime.
Plans are underway to measure spin asymmetries at large momentum transfer in hadron hadron collisions at RHIC and elsewhere. Proposals have focused on measuring quark transversity and quark and gluon helicity distributions in the nucleon. These experiments will also provide a strong and simple test of perturbative QCD, namely that ${\cal A}_{TT}/{\cal A}_{LL}\ll 1$ in $pp\rightarrow 2\, {\rm jets} +X$ and several related processes, whereas ${\cal A}_{TT}/{\cal A}_{LL}\sim 1$ in Drell-Yan production of muon pairs. The prediction tests the helicity, twist and chirality selection rules of perturbative QCD that form the foundation for the analysis of spin dependent hard processes. We estimate the ratio ${\cal A}_{TT}/{\cal A}_{LL}$ numerically for polarized protons at RHIC.
Opening talk presented at the Adriatico Research Conference -- Trends in Collider Spin Physics and at the RIKEN Symposium -- Spin Structure of the Nucleon. We present an overview of the opportunities to explore QCD at a very high energy polarized hadron collider. We review connections to low energy flavor physics, transverse spin in QCD and higher twist. It is clear that polarized colliders will provide a wealth of new information about the behavior of quarks and gluons inside hadrons complementing that available from lepton scattering and other more familiar probes of hadron structure.
We study the solutions to the wave equation in a two-dimensional tube of unit width comprised of two straight regions connected by a region of constant curvature. We introduce a numerical method which permits high accuracy at high curvature. We determine the bound state energies as well as the transmission and reflection matrices, ${\cal T}$ and ${\cal R}$ and focus on the nature of the resonances which occur in the vicinity of channel thresholds. We explore the dependence of these solutions on the curvature of the tube and angle of the bend and discuss several limiting cases where our numerical results confirm analytic predictions.
We study the operator description of the gluon spin contribution ($Γ$) to the nucleon's spin as it is measured in deep inelastic processes. $Γ$ can be related to the forward matrix element of a local gluon operator in $A^+=0$ gauge. In quark models the nucleon contains ambient color electric and magnetic fields. The latter are thought to be responsible for spin splittings among the light baryons. We show that these fields give rise to a significant {\it negative\/} contribution to $Γ$ at the quark model renormalization scale, $μ_0^2$. The non-Abelian character of QCD is responsible for the sign of $Γ$. In a generic non-relativistic quark model $Γ_{NQM}=-{8\over 9}{α_{NQM}\over m_q}\langle{1\over r}\rangle$, in the bag model $Γ_{bag}=-.1α_{bag}$. These correspond to $Γ_{NQM}\approx -0.7$ and $Γ_{bag}\approx -0.4$ at $α_{QCD}\approx 1.0$.
Various issues surrounding a recently proposed inequality among twist-two quark distributions in the nucleon are discussed. We provide a rigorous derivation of the inequality in QCD, including radiative corrections and scale dependence. We also give a more heuristic, but more physical derivation, from which we show that a similar inequality does not exist among twist-three quark distributions. We demonstrate that the inequality does not constrain the nucleon's tensor charge. Finally we explore physical mechanisms for saturating the inequality, arguing it is unlikely to occur in Nature.
We study the measurement of the quark fragmentation functions for spin-1/2 baryon production ($Λ$ and $\bar Λ$, in particular) in unpolarized $e^+e^-$ annihilation. The spin-dependent fragmentation functions $\hat g_1(z)$ and $\hat h_1(z)$ can be probed in the process as a result of quark-antiquark spin correlation and the weak decay of the baryons. The relevant cross section is expressed as a product of the two-jet cross-section, the fragmentation functions, and the differential width of the hyperon decay.
We define twist-two and twist-three quark fragmentation functions in Quantum Chromodynamics (QCD) and study their physical implications. Using this formalism we show how the nucleon's transversity distribution can be measured in single pion inclusive electroproduction.
We present a QCD based interpretation of heavy quark fragmentation which utilizes the heavy quark mass expansion. By distinguishing between perturbative and non-perturbative QCD effects, we show how to reliably extract mass independent parameters characterizing the fragmentation function. Because these parameters are quark mass independent, this procedure should permit tests of heavy quark symmetry. Furthermore, we show that heavy quark mass corrections vanish at order $m^2/Q^2$ in QCD. There also exist higher twist corrections of order $Λm/Q^2$ and ${α_{QCD}\overπ} {m^2\over Q^2} \ln (Q^2/m^2)$ which we relate to the leading twist fragmentation function.
We study the stability of small strangelets by employing a simple model of strange matter as a gas of non-interacting fermions confined in a bag. We solve the Dirac equation and populate the energy levels of the bag one quark at a time. Our results show that for system parameters such that strange matter is unbound in bulk, there may still exist strangelets with $A<100$ that are stable and/or metastable. The lifetime of these strangelets may be too small to detect in current accelerator experiments, however.
Measurement of the helicity asymmetric cross section for semi-inclusive production of $Λ$-hyperons in $e^+e^-$ annihilation near the $Z^0$ resonance allows a complete determination of the spin-dependent fragmentation functions for the different quark flavors into the $Λ$. The parity violating, self analyzing, decay of the final state $Λ$ makes the experimental analysis of the helicity asymmetry possible. This experiment should be practical with present day technology at the LEP collider at CERN or at SLC at SLAC.
I review the spin dependent structure functions which control dominant (twist-2) and sub-dominant (twist-3) phenomena in hard processes. Novel effects associated with chirally odd parton distributions and with transverse polarization are emphasized.