NN Scattering and Nucleon Quark Core

ScienceAsia 27 (2001) : 251-259 NN Scattering and Nucleon Quark Core Y Yana, * and R Tegenb a School of Physics, Suranaree University of Technology, Nakhon Ratchasima 30000, Thailand. b Permanent address: Nuclear and Particle Theory Group, Physics Department, University of the Witwatersrand, P.O. WITS, Johannesburg 2050, South Africa. e-mail: tegen@physnet,phys, wits.ac.za * Corresponding author, E-mail: [email protected] Received 8 Feb 2000 Accepted 25 May 2001 ABSTRACT We review here nucleon-nucleon elastic and charge exchange scattering with special emphasis on the quark hard core inside the nucleon. It is found that total cross sections are sensitive only to the total hadronic size of the proton, which has two components, the quark core and the surrounding meson cloud. At higher energies differential cross sections are found to reveal, for larger -t, a hard core size of order ~ 0.3 fm. We present model calculations for unpolarized cross sections and find that a meson exchange model with QCD vertex functions reflecting the quark/antiquark structure of the nucleon is well capable of reproducing existing data. A quark core size of order 0.3 fm is found in our model and ω ρ ƒ a preference for certain meson exchanges. As expected the pion exchange supplemented with , , 0, ƒ π ρ 2, a2 dominates the t-dependence of the elastic cross sections while isovector exchanges , , a2 with a background field dominate the charge exchange n-p reaction. KEYWORDS: Quark core of nucleon, meson cloud, nucleon-nucleon scattering, meson exchange. INTRODUCTION explanation in the mass hierarchy of the electron, pion and nucleon and in the hierarchy of the funda- Up until the early 1920s the investigation of all mental coupling constants of the electromagnetic matter revealed atoms as the only building blocks of interactions (represented by the fine structure matter. Soon afterwards the supposedly point-like constant α ~ 1/137) and of the strong interactions atoms turned out to be composed of a positively (represented by the pion-nucleon coupling constant ≈ charged nucleus in its center and a negatively charged gπNN 13). Experiments done by Rutherford and, electron cloud surrounding it. While the electron later, Hofstädter allowed to extract from the has so far revealed no internal structurea the nucleus differential cross sections electromagnetic radii has turned out to be a rather complex particle, <>r 2 , magnetic moments and more electro- consisting of strongly interacting sub-particles, called EM,, pn “hadrons” (proton, neutron, pion, and their flavour magnetic properties (embedded in the so-called 1 Gqpn, ()2 excitations, comprising some 250 known particles). electromagnetic form factors EM, ). Those All these hadrons have a finite size, of order 1 fm = electromagnetic radii were typically 0.8 fm (the case 10-15 m, much smaller than the size of the atoms of the electric form factor of the neutral partner of which is of order 1 Ao = 10-10 m = 105 fm. This implies the proton, the slightly heavier neutron, is to be that the space occupied by atoms is almost treated differently, see discussion in Ref 3, 4). It completely devoid of matter.2 We will deal here with turned out, however, that the size of any object (here the lightest atom, the hydrogen atom H. The nucleus the proton) depends on the nature of the (point- of the hydrogen atom H is known as the proton p like) probe which is used in the scattering process. (≡ H+) which is ≈ 2000 times heavier than the Electromagnetic radii are extracted by using an electron e orbiting around the proton. The sum of electron beam which interacts with the proton via -21 their charges is exactly zero, |qp + qe|/e<1.0 x 10 . the exchange of a photon γ (quantum of electro- The electrical neutrality of the hydrogen atom H is magnetic radiation). Axial radii result from neutrino one of the experimentally best-known cosmological beams which interact via the exchange of a W± gauge parameters.1 We have recently pointed out2 that the boson (a heavy “partner” of the γ in the electro-weak vastly different size of atoms and nuclei finds an gauge theory, see discussion in Ref 5). One finds a For upper limits on the electron size, see Ref 1. 252 ScienceAsia 27 (2001) 1 pattern for the hadronic size of those elementary <>r 2 2 ~.05 fm much smaller than any of the A particles is strikingly similar to the one obtained electromagnetic radii. In an analogous fashion a from electromagnetic probes and in some cases is scalar radius of the nucleon can be defined, although the only empirical information on the hadron’s size. not directly accessible to experiment.3 A typical Summarizing one can say that the analysis of total 1 result is <>r 2 2 ~.12 fm. A careful theoretical hadron-proton cross sections gives at a qualitative s level the systematics of hadron radii and, by intro- analysis of those data has revealed that, in principle, ducing “effective radii”, allows for a quasi-geometrical two “components” of the nucleon contribute to its picture.7 Here we want to push such an approach size: the 3-quark core and the meson cloud even further in order to probe even deeper into the surrounding it. In the electromagnetic radii both interior of the proton. We will refer here to high- components are present while the axial radius is energy nucleon-nucleon (elastic pp→ pp and 3,6 dominated by the 3-quark core. The size of this → charge exchange (CEX) np pn) scattering, both quark core is expected to be smaller than 0.5 fm. polarised and unpolarised. Our aim is to demonstrate The relatively large experimental uncertainty in in this communication that pp elastic scattering <>2 rA (due to a weak interaction process with a becomes relatively simple at high energies and participating almost invisible neutrino)6 does not (including spin effects) is sensitive for large 4- allow to pin down the size of that quark core. Some momentum transfers to the above mentioned intrinsic theoretical models favour a large quark core, others 3-quark core size of the proton. This provides for a a small one. But how small could it really be? long-awaited alternative to the scarce axial form Topological soliton models of the nucleon represent factor data from neutrino experiments. one of the extremes. They build a nucleon out of an infinitely complex meson cloud without any quarks. The original MIT bag model treated the meson cloud as a perturbation thus favouring a large quark core. In order to decide this important question one can try to experimentally push for better neutrino scattering experiments or (and this is at first sight rather surprising) look at a more complicated scattering process under restrictive kinematical conditions. The latter approach was pursued, for different reasons, by the “high-energy” community and their results went unnoticed for a long time by the medium-energy physics community [which is interested in the low-energy (ie non-perturbative) properties of the nucleon]. From Fig 1 it is obvious that scattering of point-like particles (here the electron) off the extended hadron (here the proton) leads to a simpler sub-process because the known electron-photon vertex (accurately described by the well-tested gauge theory Quantum Electrodynamics, Fig 1. Feynman diagrams depicting electron-proton elastic QED) can be separated off. This is not so for the scattering as compared to proton-proton elastic scattering. proton-proton scattering process where (i) more than Also shown are the fundamental quark line diagrams corresponding with those processes. QED is the relativistic, a photon can be exchanged and (ii) any exchanged quantized version of classical electrodynamics; QCD refers photon etc can be exchanged between any of the 3 to the relativistic, quantized version of the nuclear (or quarks in either of the two protons. In view of this strong) force. obvious complication it came as a surprise when b Povh and Hüfner7 were able to extract hadronic sizes cms stands for center-of-mass system; in this system the vectorial sum of the two incoming 3-momenta is zero -- a for many particles, p,,K,,J,,,,pπ φ ψΛΣΞ from head-on collision, in other words. known hadron-proton scattering data at cmsb c This energy scale 1 GeV = 109 eV is to be compared with the energies beyond 15 GeVc using the eikonal ap- energy equivalent of the hydrogen atoms rest mass which is ~ 940 MeV = 0.94109 eV and could perhaps also be compared proximation which leads to a geometric factorisation with the electrons binding energy, -13.6 eV, in the hydrogen of hadron-proton total cross sections. The emerging atom. ScienceAsia 27 (2001) 253 PROTON-PROTON SCATTERING AT HIGH inelastic channels (ie those reactions where at least ENERGIES one more particle appears in the final state) open up only beyond Pbeam = 1 GeV/c. The optical theorem pp→ pp The elastic reaction is an important relates the total cross-section to the imaginary part d → part of the total pp X reacation. In order to of the forward scattering amplitude → understand the physics behind pp X better it is → π instructive to compare it with the reactions pp X σ = 4 tot Imfk ( ,0 ) (1) +− k and ee → X . In Fig 2 we display total and elastic cross sections for pp and pp. In theoretical models This relation lead to the formulation of “optical” or of these reactions one obtains the real part of the pp “diffraction” models in which inelastic processes potentials by a symmetry transformation from the dominate. For example the differential cross section pp potentials (which latter are well-tested in various for the elastic scattering of hadrons 1 and 2 is given phase shift analyses of the nuclear potential, with at high energies ase low energy properties of nuclear physics, like nuclear matter density, deuteron properties, etc, as input).

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