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Marta Ruspa, "Inclusive diffraction", DIS 2004 1
Inclusive diffractive DIS
Diffractive cross section and diffractive structure function
Comparison with colour dipole models
NLO QCD fit
Marta Ruspa Univ. of Eastern Piedmont-Novara and INFN-Torino (Italy)
XII International Workshop on Deep Inelastic Scattering
Strbske Pleso, High Tatras, Slovakia April 14-18, 2004
on behalf of
Marta Ruspa, "Inclusive diffraction", DIS 2004 2
IP
Q2
W MX
e’
p’
*e
p
Q2 = virtuality of photon = = (4-momentum exchanged at e vertex)2
t = (4-momentum exchanged at p vertex)2
typically: |t|<1 GeV2
W = invariant mass of photon-proton system
MX = invariant mass of photon-Pomeron system
xIP = fraction of proton’s momentum taken by Pomeron
ß = Bjorken’s variable for the Pomeron = fraction of Pomeron’s momentum carried by struck quark = x/xIP
xIP
t
Inclusive diffraction γ*p Xp
Exchange of an object with the vacuum q. n.
Proton almost intact after the collision
Marta Ruspa, "Inclusive diffraction", DIS 2004 3
(Breit frame)
Diffractive DIS in the Breit frame
Diffractive Deep Inelastic Scattering probes the diffractive PDFs of the proton relevant when the vacuum quantum numbers are exchanged
)ˆ 2iγIP
2pi
* Q(z,σt),x,Q(z,f~Xp)pσ(γ *
fi/pD(z,Q2,xIP,t): probability to find in a proton, with a probe of
resolution Q2, parton i with momentum fraction z, under the condition that the proton remains intact and emerges with small energy loss, xIP, and momentum transfer,t
HARD SCATTERING FACTORISATION
DIS of a pointlike virtual photon off the exchanged object
PDFs
Marta Ruspa, "Inclusive diffraction", DIS 2004 4
Diffractive DIS in the colour dipole picture
We can learn more about the structure of the proton by studying DDIS in a frame in which the virtual photon is faster than the proton
(γ* much faster than p)
• Lifetime of dipoles very long due to large γ boost (E γ ~ W2 ~ 1/x 50TeV ! ) it is the dipole that interacts with the proton !
• Transverse size of dipoles proportional to can be so small
that the strong interaction with proton can be treated perturbatively !
)M(Q1/_qq
22
2 gluon exchange: LO QCD realisation of vacuum q.n.
Marta Ruspa, "Inclusive diffraction", DIS 2004 5
Diffractive DIS in the colour dipole picture
BEKW model : at medium β; at small β
saturation model : : as Q2 0,
growth tamed by requiring saturation
22
qq1/Qrσ _ _
qqσ
β)β(1~FTqq
γT
gqqβ)(1~F _
We can learn more about the structure of the proton by studying DDIS in a frame in which the virtual photon is faster than the proton
(γ* much faster than p)
2 gluon exchange: LO QCD realisation of vacuum q.n.
Marta Ruspa, "Inclusive diffraction", DIS 2004 6
e pExchange ofcolor singletproducing a
GAPin the
particle flow
Inclusive diffraction γ*p Xp
No activity in the forward direction
Proton suffers only a small energy loss
MX method
Marta Ruspa, "Inclusive diffraction", DIS 2004 7
Diffr. Non-diffr.
c, b from fit n.d. events subtracted
contamination from reaction epeXN
Selection of events γ*p Xp with Mx method
Properties of Mx
distribution:
- exponentially falling for decreasing Mx for non-diffractive events
- flat vs ln Mx2 for
diffractive events
Forward Plug Calorimeter (FPC):
CAL acceptance extended by 1 unit in pseudorapidity from η=4 to η=5
higher Mx and lower W
if MN > 2.3 GeV deposits EFPC > 1 GeV recognized and rejected!
Diffr. Non-diffr.
Marta Ruspa, "Inclusive diffraction", DIS 2004 8
e pExchange ofcolor singletproducing a
GAPin the
particle flow
Inclusive diffraction γ*p Xp
No activity in the forward direction
Proton suffers only a small energy loss
LPS method
MX method
Marta Ruspa, "Inclusive diffraction", DIS 2004 9
Free of p-diss background
Low acceptance
low statistics
z
zIP p
p'x1
Selection of events γ*p Xp with LPS
Diffractive peak
IPx1
Marta Ruspa, "Inclusive diffraction", DIS 2004 10
97 LPS sample
0.03 < Q2 < 100 GeV2
25 < W < 280 GeV
1.5 < Mx < 70 GeV
xIP < 0.1
Higher xIP region
99-00 FPC sample(Mx method)
22 < Q2 < 80 GeV2
37 < W < 245 GeV
Mx < 35 GeV
MN < 2.3 GeV
Higher β region
Data samples
Marta Ruspa, "Inclusive diffraction", DIS 2004 11
diffractive γ*p cross section
dWdMdQ
σd
)y)(α(
WπQ
dM
dσ
X
De'Xp'ep
X
Dpγ*
2
3
2
2
11
diffractive structure function
(assumes ) 0)3( DLF
IP
XpeepD
IPD
dxdQd
d
yy
QxQF
2
''
22
42)3(
2)2/1(4
),,(
Cross section and structure function
Marta Ruspa, "Inclusive diffraction", DIS 2004 12
xIP dep. of F2
D(3) equivalent to W dep. of dσ/dMx (1/xIP ~ W2)
F2D(3) xIP
dependence
Data agree with Regge factorisation assumption in the region of the fit
)(02.0)(02.016.1)0( sysstatIP
(LPS)
Regge fit (xIP<0.01):
),()( 22
)3(2 QFxfF IP
IPIPD
dtx
exf
tIP
t
IP
tb
IPIP
1)(2)( with
tt IPIPIP ')0()(
Marta Ruspa, "Inclusive diffraction", DIS 2004 13
p-dissociation events with MN<2.3 GeV included
MX< 2 GeV: weak W dep.
MX> 2 GeV: d/dMX rises with W
Cross section W dependence (Mx method)
power-like fit
Marta Ruspa, "Inclusive diffraction", DIS 2004 14
fit to total cross section data:
fit to diffractive cross section data:
Evidence of a rise of IPdiff with
Q2 mild Regge factorisation violation .
αIP from diffractive and total γ*p scattering
IPdiff higher than soft Pomeron
Similar W dep. of diffractive and total cross section
(Mx method)
(0)αtotIP
(0)αdiffIP
Marta Ruspa, "Inclusive diffraction", DIS 2004 15
low MX : strong decrease of
diff/tot with increasing Q2
high MX : no Q2 dependence !
Regge expectation:
19.01)0(2
222
*
*
)(
)(/W
W
WdMdIP
IP
totp
XD
p
σdiff/ σtot W and Q2 dependence(Mx method)
[hep-ph 0203258]
Explained by saturation model
BUT ratio ~ flat in W
Marta Ruspa, "Inclusive diffraction", DIS 2004 16
Main features of the data described by BEKW parametrization (xIP<0.01)
Cross section Q2 dependence
Transition to a constant cross section as Q20(similar to total cross section )
qqg fluctuations dominant at low Q2
(Bartels, Ellis, Kowalski and Wüsthoff)
medium β
small β
)1(~ Tqq
F
)1(~ Tqgq
F
tot
p*
(LPS)
Marta Ruspa, "Inclusive diffraction", DIS 2004 17
F2D(3) Q2 dependence(LPS)
Data well described by BGK saturation model (xIP<0.01)
Positive scaling violation at all values of β QCD fit
(prel.)
Marta Ruspa, "Inclusive diffraction", DIS 2004 18
QCD fit describes data
fractional gluon momentum
is
at initial scale
NLO QCD fit on LPS+charm data
))%(9)(882( sysstat
)36/9.37/( 2 ndf
[F2D(3)cc from DESY-03-094, see N. Vlasov
talk]
• xIP <0.01
• QCDNUM
• Regge factorisation assumption possible for this small data set
• DL flux
• initial scale Q2=2 GeV2
• zf(z)=(a1+a2z+a3z2)(1-x)a4
• other PDFs parametrisation tried
• Thorne-Robert variable-flavour- number-scheme
(LPS)
Marta Ruspa, "Inclusive diffraction", DIS 2004 19
LPS QCD fit compared to Mx data
Main discrepancies at high β, where no LPS data available
NB: fits scaled by 0.69to account for p-dissbackground in Mx data
Mx method data described by the fit in the region of overlap LPS-Mx method
ZEUS (MX method)
Marta Ruspa, "Inclusive diffraction", DIS 2004 20
xIP.F2D(3)/F2
Q2 and xBJ dependences(LPS) (LPS)
Compare the proton structure function for events with a leading proton and without
Nearly the same Q2 dep. (except high β and low xIP)
Different behaviour vs x at low xIP
Marta Ruspa, "Inclusive diffraction", DIS 2004 21
Recent data from ZEUS with improved precision and extended kinematic range
Data described by colour dipole models (BEKW, saturation)
Data described by a NLO QCD fit lots of gluons
Possible indication that αIP increases with Q2 in diffraction
W dep. of diffractive and total cross section similar at high Q2
Summary
Marta Ruspa, "Inclusive diffraction", DIS 2004 22
RESERVE
Marta Ruspa, "Inclusive diffraction", DIS 2004 23
Diffractive DIS in the proton rest frame
We can learn more about the structure of the proton by studying DDIS in a frame in which the virtual photon is faster than the proton
(γ* much faster than p)
• Lifetime of dipoles very long due to large γ boost (E γ ~ W2 ~ 1/x 50TeV ! ) it is the dipole that interacts with the proton !
• Transverse size of dipoles proportional to can be so small
that the strong interaction with proton can be treated perturbatively !
)M(Q1/_qq
22
2 gluon exchange: LO QCD realisation of vacuum q.n.
saturation model : (colour transparency)
as Q2 0, growth tamed by saturating
22
qq1/Qrσ _
_qq
σ _qq
σ
β)β(1~FTqq
γT
gqqβ)(1~F _ BEKW model : at medium β; at small β
Marta Ruspa, "Inclusive diffraction", DIS 2004 24
IP
Q2
W MX
e’
p’
*e
p
Q2 = virtuality of photon = = (4-momentum exchanged at e vertex)2
t = (4-momentum exchanged at p vertex)2
typically: |t|<1 GeV2
W = invariant mass of photon-proton system
MX = invariant mass of photon-Pomeron system
xIP = fraction of proton’s momentum taken by Pomeron
ß = Bjorken’s variable for the Pomeron = fraction of Pomeron’s momentum carried by struck quark = x/xIP
xIP
t
Inclusive diffraction γ*p Xp
Exchange of an object with the vacuum q. n.
Proton almost intact after the collision
Marta Ruspa, "Inclusive diffraction", DIS 2004 25
(Breit frame)
Diffractive DIS in the Breit frame
Diffractive Deep Inelastic Scattering probes the diffractive PDFs of the proton relevant when the vacuum quantum numbers are exchanged
)ˆ 2iγIP
2pi
* Q(z,σt),x,Q(z,f~Xp)pσ(γ *
fi/pD(z,Q2,xIP,t): probability to find in a proton, with a probe of resolution
Q2 parton i with momentum fraction z, under the condition that proton remains intact and emerges with small energy loss, xIP, and momentum transfer, t diffractive PDFs are a feature of the proton
HARD SCATTERING FACTORISATION
Marta Ruspa, "Inclusive diffraction", DIS 2004 26
e p
Exchange ofcolor singletproducing a
GAPin the
particle flow
Inclusive diffraction γ*p Xp
diffractive γ*p cross section
dWdMdQ
d
y
WQ
dM
d
X
DXpeep
X
D
p
2
''3
2
2
))1(1(
*
diffractive structure function
(assumes ) 0)3( DLF
IP
XpeepD
IPD
dxdQd
d
yy
QtxQF
2
''
22
42)3(
2 )2/1(4),,,(
No activity in the forward direction
Proton almost intact after the collision
Marta Ruspa, "Inclusive diffraction", DIS 2004 27
diffractive γ*p cross section
dWdMdQ
σd
)y)(α(
WπQ
dM
dσ
X
De'Xp'ep
X
Dpγ*
2
3
2
2
11
diffractive structure function
(assumes ) 0)3( DLF
IP
XpeepD
IPD
dxdQd
d
yy
QxQF
2
''
22
42)3(
2)2/1(4
),,(
Cross section and structure function
xIP dependence of F2D(3)
and
W dependence of dσ/dMX
- extraction of αIP
- Regge factorisation
Q2 dependence of F2D(3)
and dσ/dMX
-sensitivity to diffractive
PDFs
comparison to BEKW model
and to saturation model
Marta Ruspa, "Inclusive diffraction", DIS 2004 28
F2D(3) β dependence
Different β dep. at
low and high xIP
Data well described by
BGK saturation model (xIP<0.01)
(LPS)
Marta Ruspa, "Inclusive diffraction", DIS 2004 29
For high β F2D(2) decrease with
rising Q2
F2D(3) at fixed xIP
As β 0 F2D(2) rises. The rise
becomes stronger as Q2 increases
Maximum near β=0.5 consistent with a β(1- β) behaviour suggesting main contribution from a quark-antiquark state
(Mx method)
Evidence for pQCD evolution
Marta Ruspa, "Inclusive diffraction", DIS 2004 30
MICHELE
Marta Ruspa, "Inclusive diffraction", DIS 2004 31
• pQCD: qq r 1/Q2
(colour transparency)
• As Q2 0, qq violation of unitarity
• Growth tamed by qq saturating at qq (p)
Part III: saturation (how dense is the proton at low x ???)
• Saturation occurs at “saturation scale” Qs
2(x) xg(x)] xx) with x010-4, 0.3 (proton denser at small x)
r
Saturation
npQCD
pQC
D
*r
cf talks by S. Munier, D. Kharzeev, C. Marquet
• Connection to high-density QCD, saturation of parton densities, Colour Glass Condensate, geometric scaling, physics of RHIC
~1/Qs
large x small x
Marta Ruspa, "Inclusive diffraction", DIS 2004 32
Saturation vs data
Q2
x IPF
2D
( 3)
F2
Inclusive diffraction:
Inclusive DIS:
Golec-Biernat,Wuesthoff,Bartels, Golec-Biernat, Kowalski
Diffraction more sensitive to saturationthan inclusive: mainly probe intermediate dipole sizes, close to saturation
Also good description of VM, DVCS...
Marta Ruspa, "Inclusive diffraction", DIS 2004 33
Standard Deep Inelastic ScatteringFor Q2<< MZ
2:
),()],(1[2
14 2
22
2
4
2
2
2
QxFQxR
yy
xQdxdQ
d
In a frame in which the proton is very fast(Breit frame):
x = Bjorken’s variable= = fraction of proton’s momentum carried by struck quark Q2/W2
W = photon-proton centre of mass energy
y = W2/s
F2=i[ei2 x fi(x,Q2)]
R=LT
DIS probes the partonic structure of the proton
Q2
W
proton PDF
Marta Ruspa, "Inclusive diffraction", DIS 2004 34
Diffractive Deep Inelastic Scattering
xIP = fraction of proton’s momentum
taken by Pomeron
= inFermilab jargon
= Bjorken’s variable for the Pomeron = fraction of Pomeron’s momentum carried by struck quark = x/xIP
Flux of Pomerons
),,,()1(2
14 2)4(
2)4(
2
4
2
2
4
txQFR
yy
QdtdxdQd
dIP
DD
IP
“Pomeron structure function”
Naively, if IP were particle:
[Ingelman, Schlein]
xIP IP
Q2
t
*
e
e’
p p’
F2D(4) fIP (xIP,t) F2
IP (,Q2)
Marta Ruspa, "Inclusive diffraction", DIS 2004 35
IP
Q2
W MX
e’
p’
*e
p
Q2 = virtuality of photon = = (4-momentum exchanged at e vertex)2
t = (4-momentum exchanged at p vertex)2
typically: |t|<1 GeV2
W = invariant mass of photon-proton system
MX= invariant mass of photon-Pomeron system
xIP = fraction of proton’s momentum taken by Pomeron = in Fermilab jargon = Bjorken’s variable for the Pomeron = fraction of Pomeron’s momentum carried by struck quark = x/xIP
xIP
Previous talk: Diffractive Deep Inelastic Scatteringprobes the diffractive PDFs of the proton, relevant when the vacuum quantum numbers are exchanged
Diffractive DIS
t
N.B. will drop e, e’ from the diagrams in the rest of the talk
Marta Ruspa, "Inclusive diffraction", DIS 2004 36
(Diffractive) hard scattering factorisation
universal partonic cross section
fi/pD(z,Q2,xIP,t): probability to find, with probe of resolution Q2, in a
proton, parton i with momentum fraction z, under the condition that proton remains intact, and emerges with small energy loss, xIP, and momentum transfer t – diffractive PDFs are a feature of the proton
A new type of PDFs, with same dignity as standard PDFs. Applies
when vacuum quantum numbers are exchanged
Diffractive DIS, like inclusive DIS, is factorisable [Collins (1998);
Trentadue, Veneziano (1994); Berera, Soper (1996)…]:
diffractive parton distribution functions: evolve according to DGLAP
Rather than IP exchange: probe diffractive PDFs of proton
Marta Ruspa, "Inclusive diffraction", DIS 2004 37
Diffractive DIS in the proton rest frame
2-gluon exchange:LO realisation of vacuum quantum numbers in QCD
Cross section proportional to probability of finding 2 gluonsin the proton
Gluon density in the proton
!2g][x
X
pp
X
p
+p
X
p
*
IP
Marta Ruspa, "Inclusive diffraction", DIS 2004 38
Part I:The colour dipole approach
•The picture discussed in the previous talk emerges in a frame in which the proton is fast (the Breit frame)
•Can learn more about the structure of the proton by studying diffraction in a frame in which the virtual photon is faster than the proton. Find out that in exclusive processesdiffr [gluon density in proton]2
Example: exclusive vector meson production Calculable in QCD !
•Correlations in the proton: Generalised Parton Distributions (GPDs)
Marta Ruspa, "Inclusive diffraction", DIS 2004 39
•Lifetime of dipoles very long because of large boost (E 50TeV!)
it is the dipole that interacts with the proton
•Transverse size proportional to 1/ (Q2+ Mqq2)
(for longitudinally polarised photons)
•This is why can do diffraction in ep collisions !
Virtual photon fluctuates to qq, qqg states (colour dipoles)
Transverse size of incoming hadron beam can be reduced at will. Can be so small that strong interaction with proton becomes perturbative (colour transparency) !
The colour dipole picture
*
qqg
22
1
qqMQ
xWE 1~~ 2
*
Marta Ruspa, "Inclusive diffraction", DIS 2004 40
Factorization
Regge factorization - “resolved IP model” (IP with partonic structure):
1)(2/ ),( tIP
Bt
IPpIP xe
txf
(Breit frame)
QCD Hard Scattering factorization (by Collins; Trentadue, Veneziano; Berera, Soper…:)
),(ˆ),,,()( 22** QxQxtxpXpp
pIPpq
),(ˆ),(),()( 22** QQptxfXpp
ppqIPpIP
Regge motivated pomeron flux
At fixed xIP and t diffractive Parton Densities evolve according to DGLAP
Shape of diffractive pdfs independent of xIP and t