arXiv subjects
Publications and source records attributed to Philip G. Ratcliffe.
A pedagogical introduction to single-spin asymmetries (SSA's) and transversity is presented. Discussion in some detail is made of certain aspects of (SSA's) in lepton-nucleon and in hadron-hadron scattering and the role of pQCD and evolution in the context of transversity.
A matrix-based approach to numerical integration of the DGLAP evolution equations is presented. The method arises naturally on discretisation of the Bjorken x variable, a necessary procedure for numerical integration. Owing to peculiar properties of the matrices involved, the resulting equations take on a particularly simple form and may be solved in closed analytical form in the variable t=ln(alpha_0/alpha). Such an approach affords parametrisation via data x bins, rather than fixed functional forms. Thus, with the aid of the full correlation matrix, appraisal of the behaviour in different x regions is rendered more transparent and free of pollution from unphysical cross-correlations inherent to functional parametrisations. Computationally, the entire programme results in greater speed and stability; the matrix representation developed is extremely compact. Moreover, since the parameter dependence is linear, fitting is very stable and may be performed analytically in a single pass over the data values.
The analysis of hyperon semi-leptonic decay data is addressed with reference to SU(3) breaking and isospin mixing between Lambda^O and Sigma^O. Various approaches to SU(3) breaking are discussed and compared. The phenomenological implications of Lambda^0-Sigma^0 mixing are not to be underestimated: it can induce vector couplings in decays otherwise purely axial and may also modify rates. In regard of the KTeV data on Xi^0O -> Sigma^+ e antineutrino, predictions are presented and the impact of present a future data on the extraction of F and D is also examined. In addition, the implications of the new data for the use of octet baryon beta decays in determining V_us are considered.
We examine the behaviour of the polarised structure function data for g_1(x) in the region of small x (~0.01 to 0.1) for the various available targets (proton, neutron and deuteron) with the aim of clarifying what may be safely deduced with regard to the relation of the currently attained small-x region and the asymptotic behaviour as x -> 0. We find that fits using a single power-like term are susceptible to the isospin combination used. Double-power fits are more stable and also provide some evidence for an underlying SU(2) symmetry of the structure functions.
A summary is presented of the more theoretical aspects of the presentations made at Hyperon~99. In addition, some material is covered which was not presented at the symposium but which I feel is pertinent to the main theme of hyperons and/or, more in particular, to discussions conducted during the symposium.
Within the framework of a simple model, we study single-spin asymmetries for pion production in hadron-hadron collisions at high-energies with one hadron polarised. The asymmetries are generated via a mechanism of final (initial) state interactions. For peripheral kinematics, when the pion belongs to the fragmentation region of the polarised proton, we find non-zero asymmetries in the high-energy limit. Numerical results and comparision with existing experimental data are presented. We also discuss the relationship with odderon exchange phenomenology.
I discuss the present situation with regard to a variety of theoretical topics in hadronic spin physics: (a) global analysis of the g1 data---positivity at leading and next-to-leading order, renormalisation-scheme dependence, parametrisation, and hyperon beta-decays; (b) items from the realm of transverse spin---twist-three effects, single-spin asymmetries, and transversity; and finally (c) recent developments in understanding the Q^2 evolution of orbital angular momentum.
We analyse the twist-three amplitudes that can give rise to single-spin asymmetries in hadron-hadron scattering; in so doing we bring to light a novel factorisation property. As already known, the requirement of an imaginary part leads to consideration of twist-three contributions that are also related to transverse spin in deep-inelastic scattering. In particular, when an external line becomes soft in contributions arising from three-parton correlators, the imaginary part of an internal propagator may be exposed. As shown here, it is precisely this kinematical configuration that permits the factorisation. An important feature is the resulting simplification: the calculation of tens of Feynman diagrams normally contributing to such processes is reduced to the evaluation of products of the simple factors derived here and known two-body helicity amplitudes. We thus find clarifying relations between the spin-dependent and spin-averaged cross-sections and formulate a series of selection rules. In addition, the kinematical dependence of such asymmetries, is rendered more transparent.
SU(3) breaking in hyperon semi-leptonic decays is discussed. The SU(3) parameters $F$ and $D$, relevant to the ``proton-spin puzzle'', are extracted and a prediction is presented for the decay Xi0 -> Sigma+ e anti-neutrino, currently under study by the KTeV collaboration. The values found are g1/f1 = 1.16+/-0.03+/-0.01 and Gamma = (0.80+/-0.03+/-0.01) x 10^6 s^-1.
On the basis of a previous analysis of hyperon semi-leptonic decay data, a prediction is presented for g_1/f_1 in the Xi^0 -> Sigma^+ e nu-bar beta-decay. The analysis takes into account SU(3) breaking in this sector via the inclusion of mass-driven corrections. A rather precise measurement of the above channel by the KTeV experiment at Fermilab will shortly be available. Since the dependence on the SU(3) parameters, F and D, is identical to that of the neutron beta-decay, such a measurement will provide a rather stringent test of SU(3) and the models used to describe its violation in these decays. The prediction given here for the above decay is g_1/f_1=1.17, which leads to a rate of 0.80 x 10^6 s^-1 and thus a branching fraction of 2.3 x 10^-4.
A new analysis of hyperon semi-leptonic decay data is presented, based on simple and general arguments for an SU(3)-breaking structure of the couplings involved. The results obtained are compatible with those of earlier investigations and highlight the uncertainties inherent in extraction of the V_us Cabibbo-Kobayashi-Maskawa matrix element from such data, and the need for complete analyses. For F and D, the results can be summarised by the ratio: F/D=0.57+/-0.01; while as far as the value of V_us is concerned, the only conclusion to be drawn is that, insofar as SU(3) breaking is still not totally under control, the value obtained is compatible but not competitive with that obtained from kaon semi-leptonic decays.
The plenary presentations of the conference are summarised, highlighting some aspects that were of particular interest and attempting to link a few of the topics covered. Particular emphasis is placed on the problem of deep-inelastic scattering and questions still to be answered with regard to the distribution functions, strange-quark and gluon contributions, and the possible rôle of orbital angular momentum. Passing reference is also made to some of the parallel session presentations.
The analysis of hyperon semi-leptonic decay data is re-examined in the light of a recent suggestion that SU(3) symmetry breaking effects may be taken into account by applying a correction to the $F/D$ ratio obtained via naive linear extrapolation in the hyperon masses. Comparison is made with the physically better motivated approach of applying so-called centre-of-mass corrections. This study (including all available data) reveals certain short-comings of the former of the above treatments, highlights some interesting aspects of this type of analysis and attempts to pinpoint the decay data that might usefully be improved. A tantalising result of the SU(3) breaking analysis performed here is that the magnitude of recoil correction required by the data corresponds closely to that required for the standard explanation of the reduction of $\gA$ from its SU(6) value of 5/3. We also comment on other recent suggestions for taking into account the effects of SU(3) breaking. Finally a few remarks are made on the relevance for predicting the flavour non-singlet contribution to the proton $g_1$ and the Ellis-Jaffe sum rule.
We examine the present status of the Bjorken sum rule in the light of recent data on the spin structure functions of the proton, neutron and deuteron obtained by the CERN and SLAC experimental groups. We also discuss the role of possible higher-twist contributions and higher-order PQCD corrections and comment on the extraction of the necessary parameters, D and F, obtained from hyperon semi-leptonic decays.
In the framework of Anisotropic Chromodynamics, a non-perturbative realization of QCD, we develop the Low-Nussinov picture of the Pomeron. In this approach all the usual problems of low pT perturbative calculations (infrared divergence) are naturally absent. Thus, we are able to perform an ab initio calculation of the hadron-hadron total cross section. The result is a cross section of the same magnitude as indicated experimentally and approximately energy-independent (with a log^2 s growth). We further discuss the pT dependence of the hadron-hadron elastic-scattering cross section, which displays all the experimentally observed features.
The status of the Bjorken sum rule is examined in the light of recent data on the spin structure functions of the deuteron and proton obtained by the SMC group, the neutron by the E142 group and the proton by the E143 group. Combining the new data with that already obtained for the proton by the EMC group and SLAC/YALE collaborations, we show that the Bjorken system of equations is violated at the 2-3 sigma level. We also discuss in detail the role of possible higher-twist contributions and higher-order PQCD corrections.
We discuss the present situation with regard to polarised nucleon structure function measurements. In particular we examine the status of the Bjorken sum rule in the light of the recent data on the spin structure functions of (i) the deuteron obtained by the SMC group at CERN and (ii) the neutron by the E142 group at SLAC. In order to fully exploit all the available data it is necessary to study the complete Bjorken system of equations, which may be done in any of several equivalent ways. Combining the new data with that already obtained for the proton by the EMC group and earlier SLAC/YALE collaborations, together with bounds obtained on the strange quark polarisation, we show that the Bjorken system of equations is violated at about the 2 sigma level. We also show, using unpolarised data, that arguments based on possible higher-twist contributions are unable to account for this discrepancy. In conclusion, a simple explanation in terms of a non-perturbative renormalisation of the relevant Wilson coefficients is presented.