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%% section 6 The Physics of LightCone Fock States [slacpub7056006 in slacpub7056006: slacpub7056007]
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\section{\usemenu{slacpub7056::context::slacpub7056006}{ The Physics of LightCone Fock States }}\label{section::slacpub7056006}
The lightcone formalism provides the theoretical framework which
allows for a hadron to exist in various Fock configurations. For
example, quarkonium states not only have valence $Q \overline Q$
components but they also contain $Q\overline Q g$ and $Q \overline Q
g g$ states in which the quark pair is in a coloroctet
configuration. Similarly, nuclear LC wave functions contain
components in which the quarks are not in colorsinglet nucleon
subclusters. In some processes, such as large momentum transfer
exclusive reactions, only the valence colorsinglet Fock state of
the scattering hadrons with small interquark impact separation
$b_\perp = {\cal O} (1/Q)$ can couple to the hard scattering
amplitude. In reactions in which large numbers of particles are
produced, the higher Fock components of the LC wavefunction will be
emphasized. The higher particle number Fock states of a hadron
containing heavy quarks can be diffractively excited, leading to
heavy hadron production in the high momentum fragmentation region of
the projectile. In some cases the projectile's valence quarks can
coalesce with quarks produced in the collision, producing unusual
leadingparticle correlations. Thus the multiparticle nature of
the LC wavefunction can manifest itself in a number of novel ways.
For example:
\vskip.1in
\noindent\underbar{{\it Color Transparency}}
QCD predicts that the Fock components of a hadron with a small color
dipole moment can pass through nuclear matter without interactions
\cite{60,61}. Thus in the case of large momentum transfer
reactions, where only smallsize valence Fock state configurations
enter the hard scattering amplitude, both the initial and final
state interactions of the hadron states become negligible. There is
now evidence for QCD ``color transparency" in exclusive virtual
photon $\rho$ production for both nuclear coherent and incoherent
reactions in the E665 experiment at Fermilab \cite{66}, as well
as the original measurement at BNL in quasielastic $p p$ scattering
in nuclei \cite{67}. In contrast to color transparency,
Fock states with largescale color configurations interact strongly
and with high particle number production \cite{68}.
\vskip.1in
\noindent\underbar{{\it Hidden Color}}
The deuteron form factor at high $Q^2$ is sensitive to wavefunction
configurations where all six quarks overlap within an impact
separation $b_{\perp i} < {\cal O} (1/Q);$ the leading powerlaw
falloff predicted by QCD is $F_d(Q^2) = f(\alpha_s(Q^2))/(Q^2)^5$,
where, asymptotically, $f(\alpha_s(Q^2))\propto
\alpha_s(Q^2)^{5+2\gamma}$ \cite{69}. The derivation of the
evolution equation for the deuteron distribution amplitude and its
leading anomalous dimension $\gamma$ is given in Ref. \cite{70}.
In general, the sixquark wavefunction of a deuteron is a mixture of
five different colorsinglet states. The dominant color
configuration at large distances corresponds to the usual
protonneutron bound state. However at small impact space
separation, all five Fock colorsinglet components eventually
acquire equal weight, i.e., the deuteron wavefunction evolves to
80\%\ ``hidden color.'' The relatively large normalization of the
deuteron form factor observed at large $Q^2$ points to sizable
hidden color contributions \cite{71}.
\vskip.1in
\noindent\underbar{{\it SpinSpin Correlations in NucleonNucleon
Scattering and the Charm Threshold}}
One of the most striking anomalies in elastic protonproton
scattering is the large spin correlation $A_{NN}$ observed at large
angles \cite{72}. At $\sqrt s \simeq 5 $ GeV, the rate for
scattering with incident proton spins parallel and normal to the
scattering plane is four times larger than that for scattering with
antiparallel polarization. This strong polarization correlation can
be attributed to the onset of charm production in the intermediate
state at this energy \cite{73}. The intermediate state $\vert u
u d u u d c \bar c \rangle$ has odd intrinsic parity and couples to
the $J=S=1$ initial state, thus strongly enhancing scattering when
the incident projectile and target protons have their spins parallel
and normal to the scattering plane. The charm threshold can also
explain the anomalous change in color transparency observed at the
same energy in quasielastic $ p p$ scattering. A crucial test is
the observation of open charm production near threshold with a cross
section of order of $1 \mu$b.
\vskip.1in
\noindent\underbar{{\it Anomalous Decays of the $J/\psi$}}
The dominant twobody hadronic decay channel of the $J/\psi$ is
$J/\psi \rightarrow \rho \pi$, even though such vectorpseudoscalar
final states are forbidden in leading order by helicity conservation
in perturbative QCD \cite{74}. The $\psi^\prime$, on the other
hand, appears to respect PQCD. The $J/\psi$ anomaly may signal
mixing with vector gluonia or other exotica \cite{74}.
\vskip.1in
\noindent\underbar{{\it The QCD Van Der Waals Potential and
Nuclear Bound Quarkonium}}
The simplest manifestation of the nuclear force is the interaction
between two heavy quarkonium states, such as the $\Upsilon (b \bar
b)$ and the $J/\psi(c \bar c)$. Since there are no valence quarks in
common, the dominant colorsinglet interaction arises simply from
the exchange of two or more gluons. In principle, one could measure
the interactions of such systems by producing pairs of quarkonia in
high energy hadron collisions. The same fundamental QCD van der
Waals potential also dominates the interactions of heavy quarkonia
with ordinary hadrons and nuclei. As shown in Ref. \cite{75},
the small size of the $Q \overline Q$ bound state relative to the
much larger hadron allows a systematic expansion of the gluonic
potential using the operator product expansion. The coupling of the
scalar part of the interaction to largesize hadrons is rigorously
normalized to the mass of the state via the trace anomaly. This
scalar attractive potential dominates the interactions at low
relative velocity. In this way one establishes that the nuclear
force between heavy quarkonia and ordinary nuclei is attractive and
sufficiently strong to produce nuclearbound quarkonium
\cite{75,76}.
\vskip.1in
\noindent\underbar{{\it Anomalous Quarkonium Production at the
Tevatron}}
Strong discrepancies between conventional QCD predictions and
experiment of a factor of 30 or more have recently been observed for
$\psi$, $\psi^\prime$, and $\Upsilon$ production at large $p_T$ in
high energy $p \overline p$ collisions at the Tevatron \cite{77}.
Braaten and Fleming \cite{78} have suggested that the surplus of
charmonium production is due to the enhanced fragmentation of gluon
jets coupling to the octet $c\overline c$ components in higher Fock
states $\vert c\overline{c}gg\rangle$ of the charmonium
wavefunction. Such Fock states are required for a consistent
treatment of the radiative corrections to the hadronic decay of
$P$waves in QCD \cite{79}.
\vskip.1in
\noindent\underbar{{\it Intrinsic Heavy Quark Contributions in
Hadron Wavefunctions}}
As we have emphasized, the QCD wavefunction of a hadron can be
represented as a superposition of quark and gluon lightcone Fock
states: $\vert\Psi_{\pi^}\rangle = \sum_n \psi_{n/\pi^}
(x_i,k_{\perp i},\lambda_i)\vert n \rangle$, where the colorsinglet
states $\vert n \rangle$ represent the Fock components $\vert
\overline u d \rangle$, $\vert \overline u d g \rangle$, $\vert
\overline u d Q \overline Q \rangle$, etc. Microscopically, the
intrinsic heavyquark Fock component in the $\pi^$ wavefunction, $
\vert \overline u d Q \overline Q \rangle$, is generated by virtual
interactions such as $g g \rightarrow Q \overline Q$ where the
gluons couple to two or more projectile valence quarks. The
probability for $Q \overline Q$ fluctuations to exist in a light
hadron thus scales as $\alpha_s^2(m_Q^2)/m_Q^2$ relative to
leadingtwist production \cite{80}. This contribution is
therefore higher twist, and powerlaw suppressed compared to sea
quark contributions generated by gluon splitting. When the
projectile scatters in the target, the coherence of the Fock
components is broken and its fluctuations can hadronize, forming new
hadronic systems from the fluctuations \cite{16}. For example,
intrinsic $c \overline c$ fluctuations can be liberated provided the
system is probed during the characteristic time $\Delta t = 2p_{\rm
lab}/M^2_{c \overline c}$ that such fluctuations exist. For soft
interactions at momentum scale $\mu$, the intrinsic heavy quark
cross section is suppressed by an additional resolving factor
$\propto \mu^2/m^2_Q$ \cite{81}. The nuclear dependence arising
from the manifestation of intrinsic charm is expected to be
$\sigma_A\approx \sigma_N A^{2/3}$, characteristic of soft
interactions.
In general, the dominant Fock state configurations are not far off
shell and thus have minimal invariant mass ${\cal M}^2 = \sum_i
m_{T, i}^2/ x_i$ where $m_{T, i}$ is the transverse mass of the
$i^{\rm th}$ particle in the configuration. Intrinsic $Q \overline
Q$ Fock components with minimum invariant mass correspond to
configurations with equalrapidity constituents. Thus, unlike sea
quarks generated from a single parton, intrinsic heavy quarks tend
to carry a larger fraction of the parent momentum than do the light
quarks \cite{82}. In fact, if the intrinsic $Q \overline Q$
pair coalesces into a quarkonium state, the momentum of the two
heavy quarks is combined so that the quarkonium state will carry a
significant fraction of the projectile momentum.
There is substantial evidence for the existence of intrinsic $c
\overline c$ fluctuations in the wavefunctions of light hadrons. For
example, the charm structure function of the proton measured by EMC
is significantly larger than that predicted by photongluon fusion
at large $x_{Bj}$ \cite{83}. Leading charm production in $\pi
N$ and hyperon$N$ collisions also requires a charm source beyond
leading twist \cite{80,84}. The NA3 experiment has also shown
that the single $J/\psi$ cross section at large $x_F$ is greater
than expected from $gg$ and $q \overline q$ production \cite{85}.
The nuclear dependence of this forward component is
diffractivelike, as expected from the BHMT mechanism. In addition,
intrinsic charm may account for the anomalous longitudinal
polarization of the $J/\psi$ at large $x_F$ seen in $\pi N
\rightarrow J/\psi X$ interactions \cite{86}.
Further theoretical work is needed to establish that the data on
direct $J/\psi$ and $\chi_1$ production can indeed be described
using a highertwist intrinsic charm mechanism, as discussed in Ref.
\cite{16}. Experimentally, it is important to check whether the
$J/\psi$'s produced indirectly via $\chi_2$ decay are transversely
polarized. This would show that $\chi_2$ production is dominantly
leading twist. Better data on real or virtual photoproduction of the
individual charmonium states would also add important information.
\vskip.1in
\noindent\underbar{{\it Double Quarkonium Hadroproduction}}
It is quite rare for two charmonium states to be produced in the
same hadronic collision. However, the NA3 collaboration has
measured a double $J/\psi$ production rate significantly above
background in multimuon events with $\pi^$ beams at laboratory
momentum 150 and 280 GeV/c and a 400 GeV/c proton beam
\cite{87}. The relative double to single rate, $\sigma_{\psi
\psi}/\sigma_\psi$, is $(3 \pm 1) \times 10^{4}$ for pioninduced
production, where $\sigma_\psi$ is the integrated single $\psi$
production cross section. A particularly surprising feature of the
NA3 $\pi^N\rightarrow\psi\psi X$ events is that the laboratory
fraction of the projectile momentum carried by the $\psi \psi$ pair
is always very large, $x_{\psi \psi} \geq 0.6$ at 150 GeV/c and
$x_{\psi \psi} \geq 0.4$ at 280 GeV/c. In some events, nearly all
of the projectile momentum is carried by the $\psi \psi$ system! In
contrast, perturbative $ g g$ and $q \overline q$ fusion processes
are expected to produce central $\psi \psi$ pairs, centered around
the mean value, $\langle x_{\psi\psi} \rangle \approx$ 0.40.5, in
the laboratory. There have been attempts to explain the NA3 data
within conventional leadingtwist QCD. Charmonium pairs can be
produced by a variety of QCD processes including $B \overline B$
production and decay, $B\overline B \rightarrow \psi \psi X$ and
${\cal O}(\alpha_s^4)$ $\psi \psi$ production via $gg$ fusion and $q
\overline q$ annihilation \cite{88,89}. Li and Liu have also
considered the possibility that a $2^{++} c\overline c c \overline
c$ resonance is produced, which then decays into correlated
$\psi\psi$ pairs \cite{90}. All of these models predict centrally
produced $\psi \psi$ pairs \cite{91,89}, in contradiction to
the $\pi^$ data.
Over a sufficiently short time, the pion can contain Fock states of
arbitrary complexity. For example, two intrinsic $c\overline c$
pairs may appear simultaneously in the quantum fluctuations of the
projectile wavefunction and then, freed in an energetic interaction,
coalesce to form a pair of $\psi$'s. In the simplest analysis, one
assumes the lightcone Fock state wavefunction is approximately
constant up to the energy denominator \cite{80}. The predicted
$\psi \psi$ pair distributions from the intrinsic charm model
provide a natural explanation of the strong forward production of
double $J/\psi$ hadroproduction, and thus gives strong
phenomenological support for the presence of intrinsic heavy quark
states in hadrons.
It is clearly important for the double $J/\psi$ measurements to be
repeated with higher statistics and at higher energies. The same
intrinsic Fock states will also lead to the production of
multicharmed baryons in the proton fragmentation region. The
intrinsic heavy quark model can also be used to predict the features
of heavier quarkonium hadroproduction, such as $\Upsilon \Upsilon$,
$\Upsilon \psi$, and $(c\bar b)$ $(\bar cb)$ pairs. It is also
interesting to study the correlations of the heavy quarkonium pairs
to search for possible new fourquark bound states and final state
interactions generated by multiple gluon exchange \cite{90}, since
the QCD Van der Waals interactions could be anomalously strong at
low relative rapidity \cite{75,76}.
\vskip.1in
\noindent\underbar{{\it Leading Particle Effect in Open Charm
Production}}
According to PQCD factorization, the fragmentation of a heavy quark
jet is independent of the production process. However, there are
strong correlations between the quantum numbers of $D$ mesons and
the charge of the incident pion beam in $\pi N \rightarrow D X$
reactions. This effect can be explained as being due to the
coalescence of the produced intrinsic charm quark with comoving
valence quarks. The same highertwist recombination effect can also
account for the suppression of $J/\psi$ and $\Upsilon$ production in
nuclear collisions in regions of phase space with high particle
density \cite{80}.
There are many ways in which the intrinsic heavy quark content of
light hadrons can be tested. More measurements of the charm and
bottom structure functions at large $x_F$ are needed to confirm the
EMC data \cite{83}. Charm production in the proton
fragmentation region in deep inelastic leptonproton scattering is
sensitive to the hidden charm in the proton wavefunction. The
presence of intrinsic heavy quarks in the hadron wavefunction also
enhances heavy flavor production in hadronic interactions near
threshold. More generally, the intrinsic heavy quark model leads to
enhanced open and hidden heavy quark production and leading particle
correlations at high $x_F$ in hadron collisions, with a distinctive
strongly shadowed nuclear dependence characteristic of soft hadronic
collisions.
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