Diffractive PDFs
Paul Laycock
University of Liverpool
BLOIS 2007
Overview
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Diffractive DIS at Hera
–
●
Comparison of Experimental Techniques
–
●
●
Rapidity gap, MX and leading proton techniques
Factorisation, NLO QCD Fits and Diffractive PDFs
–
MY, t and xIP dependences factorise from Q2 and β dependences
–
QCD and the unconstrained high z gluon
Diffractive dijets
–
●
Kinematics and Observables
Factorisation holds in diffractive DIS
Combined fit and Diffractive PDFs
–
Diffractive PDFs with more constraints on the gluon
Paul Laycock
Diffractive PDFs
BLOIS 2007
Page 2
Diffractive DIS Kinematics and Observables
Large Gap in Rapidity
`
Cross section:
Paul Laycock
Diffractive PDFs
BLOIS 2007
Page 3
Experimentally
selecting
Forward Proton
Spectrometer
ep  eXp
Large Rapidity Gap in H1
Large
z  64, z  80m Rapidity Gap
e
p
Measure Leading Proton (FPS)
No proton dissociation
X
Require Large Rapidity Gap (LRG)
spanning at least 3.3 < η < ~7.5
Measure the t dependence
Kinematics measured from X system,
integrate |t| < 1.0 GeV2, MY < 1.6 GeV
Low detector acceptance
High detector acceptance → precision
Paul Laycock
Diffractive PDFs
BLOIS 2007
Page 4
Latest Zeus results – MX and LRG
Zeus and H1 both comparing
LRG and MX methods
Shown here – Zeus LRG
(blue) and Zeus MX (red)
Reasonable agreement but
ongoing work to understand
the differences
Paul Laycock
Diffractive PDFs
BLOIS 2007
A wealth of precision data to
Page 5
add to future diffractive PDFs
Two Levels of Factorisation
QCD hard scattering collinear factorisation (Collins) at fixed xIP and t
Applied after integration over measured MY and t ranges
`Proton vertex’ factorisation of β and Q2 from xIP, t, and MY dependences
Paul Laycock
Diffractive PDFs
BLOIS 2007
Page 6
H1 Inclusive
Data Overview
LRG: MY < 1.6 GeV
  Q2  GeV2
FPS: Y=p
2.7  Q2  24 GeV2
Paul Laycock
Diffractive PDFs
BLOIS 2007
Page 7
Detailed Comparison LRG v FPS
• LRG measurement
also done with FPS bins
• Form ratio of
measurements as a function
of xIP, β and Q2
 ( M Y  1.6 GeV)
 1.23  0.03 (stat.)
 (Y  p)
0.16 (syst.)
MY dependence factorises from xIP, β and
Q2 within 10% (non-normalisation) errors
Paul Laycock
Diffractive PDFs
BLOIS 2007
Page 8
Effective Pomeron Intercept Independent of β and Q2
From fits to LRG and MX
data, with current
experimental precision:
• Data compatible with no
dependence of aIP(0)
on Q2 (Zeus and H1) or β (H1)
• The xIP dependence also
factorises from Q2 and b
• xIP, t and MY dependences factorise
from the Q2 and β dependences
within errors
→ Data support Proton Vertex Factorisation
Paul Laycock
Diffractive PDFs
BLOIS 2007
Page 9
 r D(3) (b , Q2 , xIP ) at xIP  0.01
Study β and Q2 dependences at fixed xIP
Analogous to making an inclusive F2
measurement at each value of xIP
Paul Laycock
Diffractive PDFs
BLOIS 2007
Page 10
Q2 Dependence in More Detail
Fit data at fixed x, xIP to
 rD  A  B ln Q2
such that
d D
r
B
d ln Q 2
Divide results by f IP / p ( xIP )
to compare different xIP values
Different xIP measurements agree
Derivatives large and positive… suggests large gluon
Paul Laycock
Diffractive PDFs
BLOIS 2007
Page 11
H1 2006 DPDF Fit - Overview
DPDF
aIP(0)
IP component:
• Fit aIP(0) (xIP dependence).
• Simultaneously, fit 5 parameters of
DPDFs (β and Q2 dependences) using
NLO QCD.
Paul Laycock
IR component:
• Fit nIR one parameter for normalisation.
• All flux parameters taken from previous H1
data. PDFs taken from Owens-p.
Diffractive PDFs
BLOIS 2007
Page 12
H1 2006 DPDF Fit - Details
• Fit is stable with variations of, e.g. bmax – the
maximum value of β allowed in the fit.
• Fit stable for Q2min > 8.5 GeV2.
Q2  8.5 GeV2 (and M X  2 GeV, b  0.8)
• Fit all data with:
Q2  8.5 GeV2 (and M X  2 GeV, b  0.8)
DPDF
• Parameterise quark singlet zS(z,Q02) and
gluon zg(z,Q02) densities, where z is parton
momentum fraction (= b for QPM).
aIP(0)
IP component:
• Fit aIP(0) (xIP dependence).
• Simultaneously, fit 5 parameters of
DPDFs (β and Q2 dependences) using
NLO QCD.
Paul Laycock
• Parameterisation used is zS( z, Q02 )  Aq z Bq (1  z )Cq
and zg ( z, Q02 )  A (1  z)Cg (gluon insensitive to Bg)
g
• Results reproducible with Chebyshev
polynomials.
Diffractive PDFs
BLOIS 2007
Page 13
DPDFs from inclusive data
• Fit A
Q02 = 1.75 GeV2
c2 ~158 / 183 d.o.f.
• Fit B
Drop Cg - gluon is
parameterised as a constant at
the starting scale!
c2 ~164 / 184 d.o.f.
Q02 = 2.5 GeV2
• Quarks very stable
• Gluon similar at low z
• No sensitivity to gluon at
high z
Paul Laycock
Diffractive PDFs
BLOIS 2007
Page 14
A Closer Look at the High z Region
We have only singlet
quarks, so DGLAP
evolution equation for F2D ….
dF D
a
2
 s  Pqg  g + Pqq  S 
2
d ln Q 2
+
At high b, relative error on derivative grows, q  qg contribution
to evolution becomes important … sensitivity to gluon is lost
Paul Laycock
Diffractive PDFs
BLOIS 2007
Page 15
Compare to diffractive dijets in DIS
We can compare the predictions of Fit A
and Fit B with the experimental
measurement of diffractive dijets in DIS
This process is particularly sensitive to
the gluon
Paul Laycock
Diffractive PDFs
BLOIS 2007
Page 16
Compare to diffractive dijets
in DIS
At low zIP (< 0.3) Fit A and Fit B are similar
The data are in good agreement with the predictions, consistent
with factorisation (more on factorisation in A. Bonato’s talk)
At high zIP the diffractive dijet data clearly prefer Fit B
Paul Laycock
Diffractive PDFs
BLOIS 2007
Page 17
Combined fit of dijet and inclusive data
• The diffractive dijet data can be used as an additional constraint in a NLO QCD fit procedure
• Details similar to the inclusive case but can now consrtain 3 parameters for the gluon
• Very good simultaneous fit of both inclusive and dijet data achieved
Diffractive PDFs
Paul Laycock
BLOIS 2007
Page 18
Combined fit DPDFs from H1
The singlet and gluon
are constrained with
similar precision across
the kinematic range
To be published very
soon!
Paul Laycock
Diffractive PDFs
BLOIS 2007
Page 19
Summary
●
●
●
●
A wealth of inclusive data from H1 and Zeus using LPS, MX and
LRG methods (I didn’t have time to show it all!)
Proton vertex factorisation holds: MY, t and xIP dependences factorise
from β and Q2
DPDFs from NLO QCD fits to b, Q2 dependences
(H1 2006 DPDF Fits A+B)
–
Quark singlet very well constrained (~5%)
–
Gluon constrained to ~15%, but poorly known at high z
Combined fit to inclusive and dijet data finally constrains both the
quark and the gluon to similar precision
H1 2007 Jets DPDF to appear soon – use it!
Paul Laycock
Diffractive PDFs
BLOIS 2007
Page 20
BACK-UP SLIDES FOLLOW
Paul Laycock
Diffractive PDFs
BLOIS 2007
Page 21
Effective Pomeron Intercept Independent of β and Q2
From fit to LRG data: a ( 0  1.118  0.008 ( exp.
IP
+0.029
- 0.010
( theory
• No dependence of aIP(0)
on Q2 or β
• The xIP dependence also
factorises from Q2 and b
• xIP, t and MY dependences
factorise from the Q2 and β
dependences within errors
→ Data support Proton Vertex Factorisation
Paul Laycock
Diffractive PDFs
BLOIS 2007
Page 22
t Slope Dependence on β or Q2?
B measured double differentially in (b or Q2) at fixed xIP
• t dependence does not change with b or Q2 at fixed xIP
Paul Laycock
Diffractive PDFs
BLOIS 2007
Page 23
t dependence from FPS
measurements
B(xIP) from fit to
• Fitting low xIP data to
B  BIP  2a 'IP ln(1/ xIP )
yields:
-2
2,0
-2
a 'IP  0.060.19
GeV
B

5.5
GeV
0.06
IP
0.7
• B(xIP) data constrain IP, IR flux factors in proton
vertex factorisation model
Paul Laycock
Diffractive PDFs
BLOIS 2007
Page 24
Comparison of H1 LRG, H1 FPS, ZEUS LPS
Data
• ZEUS (LPS) and H1 (FPS)
Leading Proton Data agree very well
(they agree to 8% cf. 10%
normalisation uncertainities)
• ZEUS LPS and H1 FPS
scaled by global factor of 1.23 to
compare with LRG MY < 1.6 GeV
• Very good agreement between
Leading Proton and LRG methods
after accounting for proton diss’n
• Both experimental techniques
measure the same cross section
Paul Laycock
Diffractive PDFs
BLOIS 2007
Page 25
Paul Laycock
Diffractive PDFs
BLOIS 2007
Page 26
Q2 derivative and gluon/quark
ratios
If
then
Diffractive
0.7
Inclusive
0.3
At low x, gluon:quark ratio ~ 70%/30%, common to diffractive and incl
Paul Laycock
Diffractive PDFs
BLOIS 2007
Page 27