A Study of Diffractive Dijets with a Leading Antiproton at sqrt{s}=1800 GeV
Contact persons:
Kerstin Borras1,
Konstantin Goulianos1,
Kenichi Hatakeyama1,
Hosai Nakada2
1 Rockefeller University, New York, New York, 10021
2 University of Tsukuba, Tsukuba, Ibaraki 315, Japan
Diffractive dijets with a leading antiproton in pbar-p collisions
at sqrt{s}=1800 GeV
T. Affolder et al., The CDF Collaboration
FERMILAB-PUB-00/055-E.
Submitted to Phys. Rev. Lett. March 7, 2000.
Measurement of the Diffractive Structure Function of the Antiproton
(model independent)
Blessed: 17 December 1999 and 11 February 2000
CDF Note Number(s):
4920
Studies with Monte Carlo Simulations based on Regge Phenomenology
(model dependent)
Blessed: 13 August 1998
CDF Note Number(s):
4524
Measurement of the Diffractive Structure Function of the
Antiproton
This page summarizes results from a study of events with a leading
antiproton of beam momentum fraction 0.905< xF < 0.965 and
4-momentum transfer squared | t | < 3 GeV2
produced in
pbar-p collisions at sqrt{s}=1800 GeV at the Fermilab Tevatron
collider.
Approximately 2% of the events contain two jets of transverse energy
ETjet > 7 GeV. Using the dijet
events, we evaluate the diffractive structure function of the antiproton
and compare it with expectations based on results obtained in deep
inelastic scattering experiments at the DESY ep
collider HERA.
Introduction
We have studied diffractive dijet events produced in pbar-p
collisions at sqrt{s}=1800 GeV, which are characterized
by two jets with high transverse energy and a leading (anti)proton
accompanied by a rapidity gap. The rapidity gap, defined as a region
of pseudorapidity devoid of particles, is associated with the
exchange of a Pomeron (IP) which is a color-singlet
entity with vacuum quantum numbers. In this framework, diffractive
dijet events produced in pbar-p collisions can be expressed
as, pbar + p -> [pbar' + IP] + p -> pbar' + Jet1 + Jet2 + X
(in case the antiproton is diffracted).
The central issue of this study is whether hard diffraction
processes obey QCD
factorization, i.e. can be described in terms of parton level cross
sections convoluted with a universal "diffractive" (anti)proton
structure function.
In this analysis, the diffractive structure function is measured
using events with two jets and a leading antiproton produced in
pbar-p collisions at sqrt{s}=1800 GeV,
and the factorization is examined by comparing with expectations
based on the diffractive proton structure function determined
by deep inelastic scattering experiments.
[Introduction]
[Physics Motivation]
Data
During the Tevatron collider run of 1995-96 (Run 1C), a forward "Roman Pot"
spectrometer (RPS) was added to CDF, to collect an inclusive sample
of single diffractive (SD) events by triggering on a leading antiproton.
From the inclusive sample of events collected with RPS, we
selected a dijet subsample of events containing two jets with
ET > 7 GeV.
Similarly, a non-diffractive (ND) dijet sample
is extracted from events collected with a minimum bias (MB) trigger
which requires a coincidence between beam-beam counter (BBC) arrays.
[Roman Pot Location]
[Roman Pot Arrangement]
Comparison of soft and hard diffractive interactions
- Soft_Hard_xi_t.ps
[Slide]
Distributions versus xi and t:
(a) Roman Pot acceptance;
(b) inclusive diffractive event sample
(c) ratio of dijet to inclusive events versus xi and
(d) versus t,
where xi is the fractional momentum loss of the antiproton and
t is the four momentum transfer squared.
The fraction of dijet events in the inclusive diffractive sample
increases as a function of xi, since the available center
of mass energy is larger and jets are more central in the detector
in events with higher xi values.
However, no significant t dependence is observed.
Comparison of diffractive and non-diffractive dijet events
- SD_ND_kinematics.ps
[Slide]
Comparison of diffractive to non-diffractive dijet
(a) mean ET and
(b) mean eta distributions.
The diffractive mean-ET distribution is somewhat
steeper than the non-diffractive, and the diffractive mean-eta
distribution boosted toward the proton direction (positive eta).
The Diffractive Structure Function
In leading order QCD, the ratio of the SD to ND dijet event
rates as a function of x, R(x), is equal to the
ratio of the antiproton SD to ND structure functions,
where x is the momentum fraction of the parton in
the antiproton participating in the dijet production.
Thus, the diffractive structure function may be obtained by multiplying the
known ND structure function by R(x).
We denote the associated structure functions by
Fjj=x [g(x)+4/9 q(x)], where g(x) is the
gluon and q(x) the quark density.
We evaluate x with:
x = \sum{i=1,n}
(ETiexp(-etai) / sqrt{s})
where the sum is carried over the leading two jets plus the next highest
ET jet, if there is one with ET > 5 GeV.
Below, the results are shown for 0.035 < xi < 0.095,
| t | < 1 GeV2.
In the R(x) distribution, detector effects are canceled
out since jets at the same x have similar eta
and ET.
An estimated 20% normalization uncertainty of the diffractive data
added in quadrature with the uncertainty due to the underlying event
energy subtraction from SD and ND jets
yields an systematic uncertainty of +\- 25%
in the normalization of the distributions shown below.
- Rsdnd_xbj_3.ps
[Slide]
x distribution for (top left) SD dijet
events and overlap background, and (top right) ND dijet events.
(bottom left) Shape comparison between the SD and ND distributions.
(bottom right) The ratio of SD to ND rates as a function of
x.
The line through the data points is a fit of the form
R(x)=R0(x/0.0065)-r.
- Rsdnd_xbj_2.ps
[Slide]
Ratio of SD to ND rates as a function of x
(momentum fraction of the
parton in the antiproton participating in the dijet production).
The line through the data points is a fit of the form
R(x)=R0(x/0.0065)-r
in the region 0.001 < x < 0.5 ximin.
The lower x limit is imposed to minimize the influence of detector
end-effects.
- Rsdnd_xbj_1.ps
[Slide]
Ratio of SD to ND dijet event rates as a function of x
(momentum fraction of parton in antiproton) in six xi intervals of
width Delta_xi=0.01 in the range 0.035< xi <0.095.
The lines are fits to the form
R(x)=R0(x/0.0065)-r.
The shape of the R(x) distribution shows no significant
xi dependence.
The diffractive structure function of the antiproton is obtained from
the equation :
FDjj(beta) = R(x=beta xi)
FNDjj(x -> beta xi)
We use
GRV98LO parton densities
for FNDjj(x).
Comparisons are made with expectations based on the diffractive structure
functions determined in diffractive deep inelastic ep scattering
by the H1 Collaboration
(Z. Phys. C 76, 613(1997)).
- FDjj_beta_2.ps
[Slide]
FDjj(beta) distributions integrated
over xi from 0.035 to 0.095.
The line through the data points is a fit with
B(beta/0.1)-n in the region
0.001 / xi < beta < 0.5,
which corresponds to the region 0.001 < x < 0.5 ximin.
- FDjj_beta_1.ps
[Slide]
FDjj(beta) distributions for six xi
regions of width Delta_xi=0.01 in the range
0.035 < xi < 0.095. The lines are fits to the form
B(beta/0.1)-n.
The shape of the FDjj(beta) distribution
exhibits no significant xi dependence.
- FDjj_beta_5.ps
[Slide]
(top) The exponent n from fits with
B(beta/0.1)-n to the
FDjj(beta,xi) as a function of xi.
(bottom) Values of B from fits with
B(beta/0.1)-n to the
FDjj(beta,xi) distributions for six xi
regions (circles), and 1/NincldN/dxi distribution
(triangles).
The curve is a fit to the form C xi-m.
The exponent n is approximately the same in the 6 xi bins.
The FDjj(beta=0.1,xi) distribution is
falling with increasing xi as expected for the Pomeron
exchange in the framework of Regge phenomenology.
- FDjj_beta_9.ps
[Slide]
The exponent m from fits with C xi-m to the
FDjj(beta,xi) in the xi region
0.035 < xi < 0.095, as a function of beta.
The power m is approximately constant in beta<0.4,
and exhibits a rise at the high beta region.
- FDjj_beta_8.ps
FDjj(beta) distribution (points) compared with
expectations from the parton densities of the proton (lines) extracted from
diffractive deep inelastic scattering by the H1 Collaboration.
The straight lines are fits to the data of the form
B(beta/0.1)-n.
The lines for the expectations from the H1 Collaboration (fit 2 and fit 3)
are scaled down by a factor of 20 to ease the shape comparisons.
- FDjj_beta_10.ps
[Slide1|
Slide2]
FDjj(beta) distribution (points) compared with
expectations from the parton densities of the proton extracted from
diffractive deep inelastic scattering by the H1 Collaboration.
The straight line is a fit to the data of the form
B(beta/0.1)-n.
The lower (upper) boundary of the filled band represents the data
distribution obtained by using only the two leading jets (up to four jets of
ET > 5 GeV) in evaluating beta.
The dashed (dotted) lines are expectations from the H1 fit 2 (fit 3).
The measured and expected structure functions disagree both in normalization
and shape.
The discrepancy in normalization, defined as the ratio of the integral over
beta of data to expectation, is
D=0.06 +\- 0.02 (0.05 +\- 0.02) for fit 2 (fit 3).
The observed discrepancy represents a breakdown of factorization.
A similar breakdown was found in comparing diffractive
W-boson
and dijet
production rates at the Tevatron
with expectations based on ZEUS results obtained from
diffractive DIS and
dijet photoproduction at HERA.
Conclusion
We have studied the characteristics of diffractive events containing
two jets of ETjet>7 GeV produced
in pbar-p collisions at sqrt{s}=1800 GeV,
and determined the diffractive structure function of the antiproton,
FDjj(beta), as a function of
beta = x / xi.
The ratio of dijet to inclusive diffractive events shows no significant
t-dependence.
For 0.001 / xi < beta < 0.5 and 0.035 < xi < 0.095,
FDjj(beta,xi) varies as
~ 1/beta 1/xi.
In the comparison of FDjj(beta) with
expectations based on the diffractive parton densities extracted from
diffractive DIS at HERA, a discrepancy is observed both in
normalization and shape which indicates a breakdown of factorization.
[Conclusion]
Studies with Monte Carlo Simulations based on Regge Phenomenology
(model dependent)
During the Tevatron collider run of 1995-96 (Run 1C), data were taken by
triggering on a leading antiproton in a forward Roman Pot spectrometer.
The events containing dijets in the hadronic final state were analyzed
to study the structure of the pomeron using the observable
beta=(E_T^1 exp(-eta_1)+E_T^2 exp(-eta_2))/(2 xi p_beam), with
xi=momentum fraction of the beam particle taken by the pomeron,
as a measure for the momentum fraction of the parton in the pomeron
participating in the hard subprocess.
The raw data beta distribution is modulated by the detector acceptance,
which can be unfolded by dividing the data
by simulations using a flat gluon parton density in the pomeron and the
standard form of the pomeron flux. The ratio of the cross sections in
the data to those predicted by the flat gluon simulations as a
function of beta shows a flat behavior at beta>=0.2
and a rising behavior for
smaller beta values. The level of the flat region reveals a discrepancy
between the data and the standard flux prediction of about a factor of six,
which is in agreement with the discrepancy factor of
D = 0.18 +\- 0.04 measured by CDF in
diffractive W and
dijet
productions.
These conclusions remain the same after subtracting physics background from
additional meson exchanges and
double diffractive dissociation events.
The data, with all backgrounds subtracted, are further compared to simulations
assuming pomeron parton densities and a pomeron flux parameterization as
measured by the H1 Collaboration, as well as to a flat gluon distribution and
the renormalized pomeron flux. In both cases, shape agreement is found for
beta>=0.2, whereas for lower beta values the enhancement
is decreased,
but still remains significant.
The ratio of data to simulations using the H1 model shows
in the flat region a similar discrepancy of cross sections,
in agreement with the previous CDF result.
In the ratio of data to simulations using a flat gluon pomeron and the
renormalized flux no discrepancy is found and the level of the flat
region is in agreement with expectations assuming a pomeron with a
gluon fraction of 0.7, as suggested by the previous CDF result of
f_g = 0.7 +\- 0.2.
Comparisons of the dijet kinematics for events with beta>0.2
and beta<0.2
show no difference in the characteristic variables, which can not be
attributed to pure kinematics.
Diffractive Dijet Production and the Structure of the Pomeron
-
ddij1800_data_mb.ps--- Beta distributions for the Roman Pot
dijet data
and background from overlay events (non-diffractive dijet event plus soft
diffractive Roman Pot trigger) for dijets with a minimum E_T
of 7, 10 and 15 GeV.
The beta distributions are soft and get harder with
rising E_T threshold.
-
ddij1800_datamb_fg.ps--- Beta distributions for the data, after
subtracting the overlay background and unfolding the detector acceptance
by dividing by simulations using a flat gluon pomeron and a standard
pomeron flux. The shape shows a flat region for beta>=0.2 and a rising
behavior for lower beta values. The ratio in the flat region reveals a
discrepancy between the cross sections in the data to those predicted
by the standard flux,
in agreement with the previous CDF result of D = 0.18 +\- 0.04.
-
ddij1800_data07_pbg.ps--- Beta distribution for dijets with
E_T>=7 GeV for the data, the overlay
background and the backgrounds from additional meson exchanges and from double
diffractive dissociation as estimated by simulations. For demonstration
of the detector acceptance the results of a simulation using a flat gluon
pomeron and the standard flux are scaled to match the data point at
beta=0.45.
-
ddij1800_data10_pbg.ps--- Beta distribution for dijets with
E_T>=10 GeV for the data, the overlay
background and the backgrounds from additional meson exchanges and from double
diffractive dissociation as estimated by simulations. For demonstration
of the detector acceptance the results of a simulation using a flat gluon
pomeron and the standard flux are scaled to match the data point at
beta=0.45.
-
ddij1800_data15_pbg.ps--- Beta distribution for dijets with
E_T>=15 GeV for the data, the overlay
background and the backgrounds from additional meson exchanges and from double
diffractive dissociation as estimated by simulations. For demonstration
of the detector acceptance the results of a simulation using a flat gluon
pomeron and the standard flux are scaled to match the data point at
beta=0.45.
-
ddij1800_datacor_fg.ps--- Beta distributions for the data after
subtracting all backgrounds and unfolding the detector acceptance
by dividing by simulations using a flat gluon pomeron and the standard
pomeron flux. The shape shows again a flat region for beta>=0.2
and a rising
behavior for lower beta values. The ratio in the flat region reveals a
discrepancy between the cross sections in the data to those predicted by
the standard
flux, in agreement with the previous CDF result of
D = 0.18 +\- 0.04.
-
ddij1800_datacor_h1.ps--- Ratio of data, with all backgrounds
subtracted, to simulations using the H1 model of the pomeron.
The shape shows agreement for beta>=0.2 and an enhancement
for lower beta values. The ratio in the flat region reveals a
discrepancy between the cross sections in the data to those predicted by the
simulations with the H1 model, which is in agreement with the previous
CDF result of D = 0.18 +\- 0.04.
-
ddij1800_datacor_fgren.ps--- Ratio of data, with all backgrounds
subtracted, to simulations using a flat gluon structure and the renormalized
flux for the pomeron.
The shape shows agreement for beta>=0.2 and an enhancement
for lower beta values.
The ratio in the flat region shows no discrepancy
between the
data and the predicted cross sections and the level is in agreement with
the previous CDF result of a pomeron with a gluon fraction of
f_g = 0.7 +\- 0.2.
-
ddij1800_data07_lowbeta.ps--- Distributions of the mean dijet
eta, delta phi, xi, and t for
beta>0.2 and
beta<0.2 for dijet data with E_T>=7 GeV.
The observed differences can be reproduced by pure kinematics.
-
ddij1800_data10_lowbeta.ps---Distributions of the mean dijet eta,
delta phi, xi, and t for
beta>0.2 and beta<0.2 for dijet data with E_T>=10 GeV.
The observed differences can be reproduced by pure kinematics.
-
ddij1800_data15_lowbeta.ps---Distributions of the mean dijet eta,
delta phi, xi, and t for beta>0.2 and
beta<0.2 for dijet data with E_T>=15 GeV.
The observed differences can be reproduced by pure kinematics.
Last updated : March 31, 2000
For questions, please contact:
Kerstin Borras, Konstantin Goulianos, Kenichi Hatakeyama
The Rockefeller University
(
borras@physics.rockefeller.edu),
(
dino@physics.rockefeller.edu),
(
hatake@physics.rockefeller.edu)