DESY–96–260 hep-ph/9612415

Production of Charm Quark Jets in

DIS Diffractive Dissociation

H. Lotter

II. Institut f. Theoretische Physik, Universität Hamburg,

Luruper Chaussee 149,
D-22761 Hamburg
^{1}^{1}1Supported by
Bundesministerium für Forschung und
Technologie, Bonn, Germany under Contract 05 6HH93P(5) and
EEC Program ”Human Capital and Mobility” through Network
”Physics at High Energy Colliders” under Contract
CHRX-CT93-0357 (DG12 COMA).

We present a calculation of open charm quark production in diffractive deep inelastic electron-proton scattering in a perturbative QCD framework. The cross section is proportional to the square of the gluon density and explicitly displays breaking of Regge factorization. Jet cross sections as well as the charm contribution to the diffractive structure function are calculated. As a consequence of the steep rise of the gluon density at small the charm contribution to rises with decreasing .

1.)
In the context of the discussion of rapidity gap events
in deep inelastic electron-proton scattering
observed at HERA a subclass
of diffractive events in which a large mass scale appears in the diffractively
produced hadronic final state has created particular interest.
Representatives of this type of events are the
diffractive production of heavy
vector mesons [1], diffractive jet production
[2, 3, 4, 5, 6]
and diffractive production of
open charm [7, 8].
Due to the presence of the large mass scale these processes offer the
possibility to apply and test perturbative QCD in
the setting of diffractive scattering.
The common feature of the above cited processes is the
dependence of the cross section on the square of the gluon density of the
proton. Because of this strong sensitivity these events have been
considered as a possible probe of the gluon density.

In the above list the process of diffractive open charm production
is particularly promising. Compared to heavy vector meson production
it does not depend on a meson wave function which is poorly determined
from the theoretical side. Compared to jet production
charm production does not require
a large transverse momentum which in turn leads to a strongly
suppressed event rate.

In this letter we generalize our preceding calculations
on jet production [2, 3] in DIS diffractive
dissociation to finite quark mass. This allows, in particular, the
investigation of open charm production.
Our calculation is based on an analytical expression for the
unintegrated gluon structure function which enables us to take into account
a subset of subleading corrections which turn out to be numerically
important [2].
As the new contribution of the present work
we calculate jet cross sections for charm
quarks and compare with massless flavours.
In addition we compare the magnitude of the jet cross section
calculated in our model with the predictions of a model which is based
on nonperturbative two-gluon exchange [4].
Furthermore our formulae for the elecron-proton cross section include
the dependence of the cross section on the angle of the jet plane relative
to the electron plane.
For the case of the large charm
mass we can extend our expressions to low transverse momenta and can
even integrate the transverse momentum to obtain the charm contribution
of the diffractive structure function.
We discuss the and dependence of the
charm contribution to .
In this part of our analysis we obtain results similar to the ones
presented in [7] and [8].

2.)
The kinematics of the process is well-known and we only give the
key ingredients.
To calculate first the hadronic tensor consider
the photon-proton subprocess
.
We define the momenta of the particles as indicated in
figure 1.

The calculation is performed for zero momentum transfer . For the momenta and we use a Sudakov decomposition w. r. t. the light cone momenta and ()

(1) | |||||

(2) |

Using the mass shell conditions for the outgoing particles one can show that we have . Assuming and hence neglecting and we can cast the phase space in the form

(3) |

with the charm quark mass and being the invariant mass of the pair which is related to the light cone momentum fraction through the relation

(4) |

Energy-momentum conservation then leads to the phase space restriction . Furthermore the longitudinal momentum fraction transferred from the proton to the pair is fixed as

(5) |

is the cms-energy of the photon-proton system. Another often used variable is defined as

(6) |

from which follows .

Now we have to specify the coupling of the pair to the proton.
As the simplest model for an interaction in which no color is transferred
from the proton to the pair we take two-gluon exchange.
Since the charm quark is sufficiently heavy we treat both gluons
perturbatively. We then make use of high-energy factorization [9]
to express the amplitude of the photon-proton subprocess
in terms of the unintegrated gluon density of the proton
(fig. 2)

(7) |

This factorization is valid in the leading-log() approximation in which the imaginary part of the diagrams in fig. 2 contributes. In this approximation the difference of the longitudinal momenta of the two gluons is neglected. It is therefore legitimate to use the same diagonal gluon density which appears in inclusive DIS.