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CHINESE JOURNAL OF PHYSICS AUGUST 1997 VOL. 35, NO. 4 The Structure of the Proton Ling-Fong Li Department of Physics, Carnegie Mellon University, Pittsburgh, Pennsylvania 15213, U.S.A. (Received April 30, 1997) Recent development on the understanding the structure of the proton is briefly discussed. It is noted that the chiral quark model, where quarks interact with Goldstone bosons, seems to be able to explain many of the results which are hard to understand in the simple quark model. PACS. 12.39.Fe - Chiral Lagrangians. PACS. 13.60.Hb - Total and inclusive cross sections. PACS. 13.88.+e - Polarization in interactions and scattering. I. Introduction The proton is probably the first hadron ever discovered and has been around f o r more than eighty years. It also has been studied more extensively than any other hadron in the laboratories because it is the only stable hadron besides the nuclei. It is fair to say that we are still far from a complete understanding of the structure of the proton. The reason for this is our inability to solve the strong interaction dynamics. Nevertheless, lots of progresses have been made over the years and there are several interesting features and surprises having been uncovered in recent years. The starting point for the discussion of the property of the proton is the evidence that proton has a finite size. This information comes from the elastic electron proton scattering experiments in the fifties [l]. In this elastic scattering the structure of proton can be parameterized in terms of form factors F(q2) which is essentially the Fourier transform of the charge distribution, where p(rJ is the charge density. Thus the form factor, which is measured in the elastic scattering, gives information about the charge distribution inside the proton and the experimental data indicates that F(q2) has the form, fYq2) = (q2 ‘,2,2 ’ with a2w -.i’l Gev2. This is usually called the dipole form factor and corresponds to charge distribution of the form, 436 @ 1997 THE PHYSICAL SOCIETY OF THE REPUBLIC OF CHINA VOL. 35 p(r) = emaT LING-FONG LI 437 (3) This charge distribution, which falls off sharply for r N l/a, implies that the charge radius of the proton is about .86 fm, [2] which is probably closely related to the real size of the proton. Note that for a point particle we have p(r) N” J3(r) and the form factor has the form F(q2) = 1. Thus proton is not a point particle and is a composite object made out of smaller constituents. But the elastic scattering can not yield information about what are the constituents inside the proton. In addition, this dipole form factor falls off very rapidly as q2 becomes large and will make the cross section very small for large enough q2. This just reflects the fact that due to its finite size it becomes harder and harder for the proton to stay as proton without breaking apart when given a very large momentum transfer. In the early sixties, the symmetry pattern emerging from the study of large number of hadrons led to the formulation of the quark model [3], in which hadrons of are made out of fundamental building blocks, called quarks. It is quite remarkable that only three different types of quark, up-, down-, and strange quarks, are needed to explain the observed quantum numbers of all the hadrons which were known at that time. For example, 2 u-quarks and 1 d-quark can account for the quantum numbers of proton such as isospin, strangeness and baryon number, IP >N IUZld > . (4) Thus quantum numbers of the constituents inside the proton are revealed. This deals with the symmetry properties of the proton and its constituent but not the dynamics which governs how these quarks bind together to form hadrons. In the late sixties, the deep inelastic electron proton scattering experiments [7] revealed that there are point-like constituents inside the proton, called partons [8]. It is tempting to identify these partons as the quarks of the quark model. However, structure functions measured in the deep inelastic scattering seem to require infinite number of partons rather than three quarks as in the quark model. Since partons carry the quark quantum numbers and interact with electroweak currents in a simple way, they are usually called current quarks and appear directly in the fundamental Lagrangian for the strong interaction, Quantum Chromodynamics(QCD). In distinction, the quarks used in the simple quark model are referred to as constituent quarks. For example, the proton is made out of three constituent quarks but contains infinite number of current quarks. The understanding of the precise relations between current and constituent quarks will go a long way toward unraveling the strong interaction dynamics. This goal so far has been elusive and is worth of attacks on all possible fronts. In the following we will give a brief discussion about the important properties of these two very different yet very closely related quarks. II. Quark model The quark model [3] was proposed in early 60’s to explain the patterns of the hadron mass spectrum, in a way very similar to the explanation of the periodic table. In this model, additive quantum numbers, like electric charges, isospin, strangeness and baryon number, of all baryons and mesons can be accounted for very simply in terms of that of the smaller VOL. THESTRUCTUREOFTHEPROTON 438 35 constituents, quarks. More specifically, baryons consist of three quarks and mesons are made of quark and anti-quark pair. This includes all the spin l/2, spin 3/2 baryons, spin 0 pseudoscalar mesons, spin 1 vector mesons and spin 2 tensor mesons. There are three different types of (light)quarks, which give rise to an approximate SU(3) symmetry. The quantum numbers of these quarks are given below: flavor isospin charge strangeness baryon number U l/2 213 0 l/3 d -l/2 -l/3 -l/3 0 -1 l/3 I/3 S 0 The symmetry transformations among these quarks form the SU(3) symmetry group. It turns out that all the mesons are in the octet representation of SU(3) and all the baryons are in the octet or decuplet representation of SU(3). Of course, this SU(3) is not an exact symmetry and is believed to be broken mainly by the differences in quark masses. If we assume that the isospin mass difference is negligible, i.e. m, z md, the mass difference for the mesons and baryons in the same SU(3) multiplets can be described in terms of m, and m,. These mass relations, usually referred to as Gell-Mann-Okubo mass formula [4], work quite well experimentally with accuracy of order of 10% or so. For example, in the ground state baryon octet, the mass relation has the form, which is satisfied to about few percent accuracy. In addition to the quantum numbers and mass relations of the hadrons, quark model is also very successful in giving a simple description of the magnetic moments of the bayrons. Here one combines the SU(3) symmetry with the SU(2) symmetry of the spin to construct the SU(6) wavefunctions of the baryons in terms of spins and flavors of the quarks. For example, the proton spin wavefunction is of the form, IP 1‘>= &s 111 t d I> -_Iu r d r u 1> -Id T ‘u. t u I>] (6) which gives the polarization of the quarks as, Since the magnetic moment is proportional to the spin, the proton magnetic moment is then given by, (8) LING-FONG LI VOL. 35 439 where pU, and pd, are the intrinsic magnetic moment of u-quark and d-quark respectively. It is easy to see that all the baryon magnetic moments can be expressed in terms of quark magnetic moments, pU, pd, and /& and fit to the experimental data gives [6] & = 1.852pN, /&j = -0.972pN, PL, = -.613pjv (9) where PN is the nuclear magneton. If we assume for simplicity that these quarks are elementary Dirac particles, for which we have pe = $, with q the charge of the quark, we . can get the quark masses, m, = 338Mev, md = 322ibfev, m, = 510Mev. These are usually referred to as constituent quark masses. The most striking features of these quarks is that they carry fractional electric charges, 2/3 or -l/3 while all the particles that have been observed so far all carry integral charges. This implies from the charge conservation that one of these quarks is absolutely stable and makes it easier to search for it experimentally. Such searches have been carried out very extensively in the 60’s and early 70’s with many ingenuity and creativity. The failure to find these fractionally charged quarks, stable or unstable, leads to the idea that for some unknown dynamical reasons quarks are permanently confined inside the hadrons and can never be observed in isolation. This is usually called quark confinement. Even though the quark confinement has not been derived rigorously from the present theory of strong interaction, &CD, it seems that it is the only phenomenologically viable solution. Another difficulty in the original quark model is that the baryon wavefunctions are totally symmetric under the interchange of the quarks which are spin l/2 fermions, in violation of Fermi-Dirac statistics. Later the color quantum numbers [5] are introduced so that the anti-symmetry of the baryon wavefunctions is accounted for by the color degrees of freedom. Each quark can have three colors so that the color wavefunctions for the baryons, which are made out three quarks are totally antisymmetric under the interchange of the quarks. It turns out that this totally antisymmetric color wavefunciton is a singlet under the color SU(3) transformations while the quarks themselves are color triplets. This transforms the confinement postulate into the statement that only SU(3) color singlets are physically observables and color non-singlets like quarks are not observables. This of course does not solve the problem of quark confinement. But it does give a more precise formulation for the quark confinement hypothesis. Another support for this hypothesis comes from the fact that we have not observed any qq bound states which, if exist, will have masses below that of baryons which are made out of qqq. The absence of such states can be explained by the SU(3) group theory that qq can not form a color singlet state and hence is not physically observable. Of course, to go beyond the simple quark model one needs to understand how these quarks are bounded together to form hadrons and how they are confined inside the hadrons. At the present time we do not have the answer to these questions. It seems to be clear that the dynamics governing the interaction between quarks is very complicate and does not resemble anything we have seen before. Presently, a large number of people are trying to study this problem in the context of lattice formulation of QCD by using large computers or built dedicated machines for this purpose. The calculation here is very 440 THESTRUCTUREOFTHEPROTON VOL.35 complicate and somewhat indirect. It is not so easy to penetrate to get some insight about the dynamics of the strong interaction. It is not clear how far one can go in this approach to get a much better understanding of strong interaction dynamics. III. Parton m o d e l In the late 60’s, the experiments on deep inelastic electron proton scattering, where electron gives a very large momentum transfer to the proton, yielded the results that the cross section is much larger than expected. This is kind of surprise because we have learned from the elastic electron proton scattering that the cross sections decrease very rapidly as the momentum transfer increases due to the finite size of the proton. Thus one expects that the deep inelastic cross sections to be very small at very large momentum transfer if the inelastic scattering is similar to the elastic one since other hadrons also have finite size. These unexpectedly large cross sections in the deep inelastic scattering have provided the essential ingredient for the formulation of Quantum Chromodynamics (QCD) [9] which is now an integral part of the Standard Model. This is the first time that we have a real theory for the strong interaction. The simple interpretation for these experiments is that in the region of very large momentum transfer, there are smaller constituents, called partons by Feymann, inside the proton which behave like point particles when probed by the photons, in contrast to the usual hadrons which have structures. It is the pointlike property that can explain the large deep inelastic cross sections. Since photons see the electric charges of the point particles, the experimental results show that the charges carried by the partons are the same as that of the quarks, 2/3 or --l/3 etc. Further experiments, including deep inelastic neutrino nucleon scattering and electron-positron annihilations, reveal that other quantum numbers of the partons, like spin, isospin . . . . are also the same as that of the quarks. But the data also indicates that there are infinite numbers of partons inside the proton. Thus these partons can not be identified with the quarks of the quark model. The point like behavior of these partons leads to the formulation of &CD, based on gluons interacting with the color degrees of freedom of the quarks and has the property of exhibiting the point-like behavior in the deep inelastic region, the asymptotic freedom [lo]. In other words it is a local gauge theory based on the color SU(3) symmetry. This is very similar to the quantum electrodynamics(QED) whic his a local gauge theory based on the U(1) symmetry. Since these partons carry the quark quantum numbers and have simple interaction with the electroweak currents, they are referred to as the “current quarks” in contrast to the “constituent quarks” of the quark model. Thus we have the situation that at low energies, the static properties of hadrons can be simply described by the constituent quarks while in the high energy deep inelastic region, the structure of hadrons are simple in terms of partons, or current quarks. It is not clear at all how these two different types of quarks which are important degrees of freedom in different energies regimes are related to each other. It is going to be a big theoretical challenge to comprehend the precise relation between these different types of quarks. Presumably this will involve understanding the strong interaction dynamics at low energies where the coupling constant is very strong that perturbation theory is not very useful. VOL. 35 LING-FONG LI 443 V. Discussion One of the challenging problem in the strong interaction dynamics is to understand the relation between the constituent quarks and the current quarks. At the moment it is not clear at all in what form these relations will take. It is probably useful to explore those phenomenologically successful models to get more understanding of the dynamics of the hadrons. The chiral quark model seems to be able to give simple explanations to many of the recent results which are difficult to understand in terms of the simple quark model. It is not clear at all why this simple model works so well. Maybe there is a deeper reason for and it has yet to be discovered. For now we can treat it a phenomenological model which summarized the data in a simple way. References [ 1 ] R. 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