Download The Structure of the Proton more than eighty years. It also has been

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. Hofstadter and R. W. McAllister, Phy. Rev. 98, 217 (1955).
[ 2 ] G. G. Simon et al., Nucl. Phys. A333, 381 (1980).
e I ann, Phys. Lett. 8, 214 (1964); G. Zweig, CERN report no. 8182/TH 401.
[ 3 ] M. G 11-M
[ 4 ] M. Gell-M ann, California Institute of Technology Synchrotron Laboratory Report No. CTSL20 (1961) (Reprinted in Gell-Mann and Ne’eman “The Eightfold Way”); S. Okubo, Prog.
Theo. Phys. 27, 949 (1962).
[ 51 0. W. Greenberg Phys. Rev. Lett.13, 598 (1964). M. H an and Y. Nambu, Phys. Rev. 139B
1006 (1965). Y. Nambu, In Preludes in Theoretical Physics, ed. de. DeShalit (North Holland,
Amsterdam, 1966).
[ 6 ] Particle Data Group, Phys. Rev. D54, 1 (1996).
[7] J. T. F’ried man, and H. W. Kendall, Ann. Rev. Nucl. Sci 22, 203 (1972); R. E. Taylor,
Proceedings of International Symposium on Lepton and Photon Interaction at High Energies,
ed. W. T. Kirk (Stanford, 1975), p. 679.
[ 8 ] R. P. Feynman, Phys. Rev. Lett. 23, 1415 (1969); J. D. Bjorken, and E. A. Paschos, Phys.
Rev. 185, 1975 (1969).
[ 91 D. Gross and F. Wilczek, Phys. Rev. Lett. 30, 1343 (1972); S. Weinberg, Phys. Rev. Lett.
29, 1698 (1972); H. Fritzsch, M. Gell-M arm, and H. Leutwyler, Phys. Lett. 47B, 365 (1973).
[lo] D. Gross and F. Wilczek, Phys. Rev. Lett. 30, 1343 (1972) H. D. Politzer, Phys. RevI. Lett.
30, 1346 (1972).
[ll] New Muon Collaboration, P. Amaudruz, et al. Phys. Rev. Lett. 66, 2712 (19911); M.
Arneodo et al., Phys. Rev. D50, l(l994).
[12] European Muon Collaboration, J. Ashman, et al., Phys Lett. B206, 364 (1988); Nucl P h y s .
B328, 1 (1990).
[13] A. Manohar, and H. Georgi, Nucl Phys, B234, 189 (1984); S. Weinberg, Physica (Amstxdam)
96A, 327 (1979).
[14] T. P. Ch en g and Ling-Fong Li, Phys. Rev. Lett. 74, 2872 (1995).
[15] K. Gottfried, Phys. Rev. Lett. 18, 1174 (1967).
[16] Spin Muon Collaboration, B. Adeva et al., Phys. Lett. B369, 93 (1996).