## Diffractive Deep-Inelastic Scattering with a Leading Proton at HERA |

The above paper presents a measurement of the
diffractive deep-inelastic scattering (DIS) cross section with the H1
detector at HERA. The process *ep→eXp *is studied by tagging
the leading final state proton. The Forward Proton Spectrometer (FPS)
is used to detect and measure the four-momentum of the outgoing
proton. Forward protons scattered through small angles are
deflected by the proton beam-line magnets into a system
of detectors placed within the proton beam pipe inside movable
stations known as Roman Pots. This detection method has the
advantages that the proton unambiguously scatters elastically and
that the squared four-momentum transfer at the proton vertex *t*
can be reconstructed. However, the available statistics are limited
by the FPS acceptance.

The
FPS data provide a means of studying inclusive diffraction as a
function of all relevant kinematic variables. In addition to *t *and
the usual DIS variables *x* and *Q*^{2}, the
measurements are made as a function of the fractional proton
longitudinal momentum loss *x*_{IP} and of
*β*=x/x_{IP},
which corresponds to the fraction of the exchanged momentum which
is carried by the quark coupling to the virtual photon. The
diffractive DIS data have been interpreted in a combined
framework, which applies the QCD factorization theorem to *x*
and *Q*^{2} dependences and uses a Regge
inspired approach to express the dependences on *t* and
*x*_{IP}. The
dependences on *x*_{IP }and *t *can then be
expressed in terms of an 'effective flux' of colorless exchange,
whilst the *β* and *Q*^{2} dependences can be
interpreted in terms of diffractive parton distribution functions
(DPDFs), which describe the partonic structure of that exchange.
Within Regge phenomenology, diffractive cross sections
are described by the exchange of a leading pomeron (*IP*)
trajectory *α*_{IP}(t)=α_{IP}(0)+α'_{IP}t with an
intercept *α*_{IP}(0)>1. In
order to describe the data at larger *x*_{IP}, it is
necessary to include a sub-leading exchange trajectory (*IR*) with
an
intercept *α*_{IP}(0)~0.5.

The*t*
dependence of diffractive cross sections are commonly parameterized
with an exponential, *dσ/dt**~e*^{Bt}.
The values of *B *resulting from such fits are shown as a
function of *x*_{IP }in the figure.

The

Atlow *x*_{IP} , the data are compatible
with a constant
slope parameter, *B* ≈ 6 GeV^{2}. In a Regge approach
with a
single linear exchanged pomeron trajectory the slope parameter B
decreases with increasing *x*_{IP} if *α'*_{IP}>0
('shrinkage' of the
diffractive cone). The low *x*_{IP }data thus favor a
small value of *α'*_{IP}≈
0.06 GeV^{-2 },
which is lower than *α'*_{IP}≈
0.25 obtained from
soft hadronic interactions. Further analysis in which the slope *B*
is allowed to vary with *β* and *Q*^{2 }shows no
significant dependences, confirming factorization of the
*t* dependence in the proton vertex for the present data.

The results of the FPS method are compared in detail
with the measurement of diffractive processes selected on the basis
of a large rapidity gap (LRG)
in the distribution of the final state hadrons. The measured LRG
process is *ep→eXY *where *Y *corresponds to proton
dissociation state with mass *M _{Y}*<1.6 GeV. The
ratio of the LRG to FPS cross sections is found to be independent on
variables

In this paper diffractive reduced cross section *σ*_{r}^{D(4)}(β*,Q*^{2}*,x*_{IP}*,t)
*is measured at *|t|*=0.25 GeV^{2}. The *x*_{IP}
dependence is described using a model which is
motivated by Regge phenomenology, in which a leading pomeron and a
sub-leading exchange contribute. The effective pomeron intercept
describing the data is *α*_{IP}(0)~1.11,
which is consistent within the errors with the value *α*_{IP}(0)~1.08
obtained from the energy dependence of
the total cross section. The data are also analyzed in terms of the
diffractive reduced cross section *σ*_{r}^{D(3)
}obtained by integrating *σ*_{r}^{D(4)}
over *t*. At fixed *x*_{IP},
a relatively flat *β*
dependence is observed over most of the kinematic range. The *Q*^{2
}dependence displays positive scaling violations, except at
the highest *β~*0.7.
The *β*
and *Q*^{2 }behavior of the reduced cross section
*σ*_{r}^{D(3)
}is well described using DPDFs
extracted from a next-to-leading QCD fit to LRG
data.

In general, The FPS and
LRG data exhibit a remarkable consistency with 'proton vertex'
factorization, whereby the dependences on variables *x _{IP },
t* and