Small-x and Diffraction at HERA and LHC Henri Kowalski DESY EDS Château de Blois 2005
description
Transcript of Small-x and Diffraction at HERA and LHC Henri Kowalski DESY EDS Château de Blois 2005
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Small-x and Diffraction at HERA and LHC
Henri KowalskiDESY
EDS Château de Blois 2005
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ZEUS H1
Q2 - virtuality of the incoming photonW - CMS energy of the incoming photon-proton system
x - Fraction of the proton momentum carried by the struck quark x ~ Q2/W2
Liquid Argon Calorimeter Uranium-Scintillator Calorimeter
e 27 GeV
p920GeV
HERA – ep Collider
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2
2L
223
224
2em
2
eP2
y)(11Y
)]Q(x,Fy)Q(x,xFY )Q(x,F[Y xQ
απ 2
dxdQ
σd
y – inelasticityQ2 = sxy
Infinite momentum frame
Proton looks like a cloud of non-interacting quarks and gluons
F2 measures parton density in theproton at a scale Q2
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Gluon density
Gluon density dominates F2 for x < 0.01
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Diffractive Scattering
Non-Diffractive Event ZEUS detector
Diffractive Event
MX - invariant mass of all particles seen in the central detector t - momentum transfer to the diffractively scattered proton t - conjugate variable to the impact parameter
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222
20
22222
2
20
221
22222
2
)1(
)}()1(4{2
3
)}()(])1({[2
3
q
qemf
L
qqemf
T
mQzz
rKzzQe
rKmrKzze
Dipole description of DISequivalent to Parton Picture in perturbative region
),(ˆ 2*1
0
2*
rxdzrd qqp
tot ),(
16
1| 22*
1
0
20
*
rxdzrddt
dqqt
pdiff
)))/,(3
exp(1(),( 20
222
0
2
0 rCxxgrrx sqq
GBW – first Dipole Model only rudimentary evolution
BGBK – DM with DGLAP
Iancu, Itakura, Mounier (IIM) - CGC motivated ansatz Forshaw, Shaw (FS) - Regge type ansatz with saturation, CGC-inspired
Mueller, Nikolaev, Zakharov
GBW
x
x
GeVR
R
rrxqq
02
202
0
2
0
1 ));exp(1(),(
r Q2~1/r2Optical T
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Comparison with DataComparison with Data
FS model with/without saturation and IIM CGC model hep-ph/0411337.
Fit F2 and predictxIPF2
D(3)
F2
F2
FS(nosat)
x
CGC
FS(sat)
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Diffractive contribution of the total cross sectionDiffractive contribution of the total cross section
tot
pγ
M
M Xdiff
GeV 2.3MXN,pγXdiff tot σ
/dMdσdMr
b
a N
For larger MX, diff has the similar W and Q2 dependences as tot.
• For the highest W bin (200<W<245 GeV), diff (0.28<MX<35 GeV, MN<2.3 GeV) /tot 22
1.21.0 GeV 4Qat %15.8
22
0.70.7 GeV 27Qat %9.6
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Proton
b – impact parameter
Impact Parameter Dipole Saturation Model
T(b) - proton shape
Glauber-Mueller, Levin, Capella, Kaidalov…
))(),()(
32exp(12
),( 2222
2bTxxgr
bd
rxds
)2/exp(~)()exp(~ 2 BbbTtBdt
d diff
KowalskiTeaney
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x < 10-2
universal rate of rise of all hadronic cross-sections
tottot xWp )/1(~)(~ 2*
Total *p cross-section
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Dipole cross section determined by fit to F2
Simultaneous description of many reactions
Gluon density test? Teubner
*p -> J/ p
*p -> J/ p
IP-Dipole Model
F2 C
IP-Dipole Model
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)]4
exp(1[ ),(20
2
0 R
rrxqq
GBW Model
))()/,(32
exp(12 ),( 2
022
2
2bTQrCxxgr
bd
rxds
IP Dipole Model
less saturation (due to IP and charm)
strong saturation
02
20
1)(
x
x
GeVxR
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Saturation scale
HERA RHIC
22
22
22
GeV 1
fm 7 1000
1
1
4
S
C
CsS
Q
Rdy
dN
dy
dN
RN
NQ
qSqSF
CgS QQ
C
NQ )(
4
9)()( 222
QSRHIC ~ QS
HERA
22 2
SS r
Q
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Saturated state is partially perturbative
p cross-section exhibits the universal rate of growth
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Absorptive correction to F2
....4/))2/exp(1(2 22
bd
d
Example in Dipole Model
F2 ~ -
Single inclusive pure DGLAP
Diffraction
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2-Pomeron exchange in QCD Final States(naïve picture)
0-cut
1-cut
2-cut
p*p-CMS
Y
detector
p*p-CMS
p*p-CMS
detector
<n>
<2n>
Diffraction
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0-cut
1-cut
2-cut
3-cut
Feynman diagrams QCD amplitudes J. Bartels A. Sabio-Vera H. K.
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Note: AGK rules underestimate the amount of diffraction in DIS
)exp(!2
kbd
d kk )(),()( 222
2
bTxxgrN s
C
AGK rules in theDipole Model
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)2
exp(12 2bd
d qq)exp(
!2
kbd
d kk
)(),()( 2222
bTxxgrN s
C
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HERA Result
Unintegrated Gluon Density
)2/exp()( ),,0,()(),,,( 11 BttbQtxftQtxf tgtg
)],(),([ln
)(),( 22
2tt
tg QxxgQT
Qtxf
2
2
)/(
02
22
)(2
)(exp),(
t
tt
Q
kk
ggt
ttSt dzzzP
k
dkkQT
Dipole Model
Example from dipole model
- BGBK
Another approach (KMR)
Active field of study at HERA:
UGD in heavy quark production, new result expected from high luminosity running in 2005, 2006, 2007
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Exclusive Double Diffractive Reactions at LHC
2
22114
2
2
22
2
),,,',(),,,',()1(
ˆ
tgtgt
t
c
exclusive
Diff
QtxxfQtxxfQ
dQ
bNO
OSMy
LM
L Diff = hard X-section × Gluon Luminosity
factorization !!!
fg – unintegrated gluon
densities
HiggsHiggs
T
s
Edt
d
ˆ
4
9ˆ4
2
gg Jet+Jet
gg Higgs
low x QCD reactions: pp => pp + gJet gJet ~ 1 nb for ET > 20 GeV , M(jj) ~ 50 GeV ~ 0.5 pb for ET > 60 GeV , M(jj) ~ 200 GeV JET| < 2 KMR Eur. Phys J. C23, p 311
xIP = p/p, pT xIP ~ 0.2-1.5%
pp => pp + Higgs 3) fb SM ~ O(100) fb MSSM
1 event/sec
xIP = p/p, pT xIP ~ 0.2-1.5%
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t – distributions at HERA
|)|4exp(~ tdt
d diffhard
t – distributions at LHC
with the cross-sections of the O(1) nb and L ~ 1 nb-1 s-1 => O(107) events/year are expected.
For hard diffraction this allows to follow the t – distribution to tmax ~ 4 GeV2 For soft diffraction tmax ~ 2 GeV2
Saturated gluons
Non-Saturated gluons
t-distribution of hard processesshould be sensitive to the evolution and/or saturation effects
see: Al Mueller dipole evolution, BK equation, and the impact parameter saturation model for HERA data
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Dipole form double eikonal single eikonal
KhozeMartinRyskin
t – distributions at LHC
Effects of soft proton absorption modulate the hard t – distributions
t-measurement will allow to disentangle the effects of soft absorption from hard behavior
Survival Probability S2
Soft Elastic Opacity
bdbsM
bdebsMS
bs
22
2),(2
2
),(
),(
),(/
)()(),( 21
220
222
21
2
21 tttt ppSbS
ttppF
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2
22114
2
2),,,',(),,,',(
)1(
tgtg
t
t
c
exclusive QtxxfQtxxfQ
dQ
bNO
L. Motyka, HKpreliminary
Gluon Luminosity
QT2 (GeV2)
Dipole Model
F2
Exclusive Double Diffraction
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Conclusions
We are developing a very good understanding of inclusive and diffractive g*p interactions: F2 , F2
D(3) , F2c , Vector Mesons (J/Psi)….
Observation of diffraction indicates multi-gluon interaction effects at HERA HERA measurements suggests presence of Saturation phenomena Saturation scale determined at HERA agrees with RHIC
HERA determined properties of the Gluon Cloud
Diffractive LHC ~ pure Gluon Collider => investigations of properties of the gluon cloud in the new region Gluon Cloud is a fundamental QCD object - SOLVE QCD!!!!
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))((22
)/1(~),( reffxxxg
Smaller dipoles steeper rise Large spread of eff characteristic for IP Dipole Models
)()(2 22*
)/1(~)(~ QQp tottot xW
universal rate of rise of all hadronic cross-sections
The behavior of the rise with Q2
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)]4
exp(1[ ),(20
2
0 R
rrxqq
GBW Model
))()/,(32
exp(12 ),( 2
022
2
2bTQrCxxgr
bd
rxds
KT-IP Dipole Model
less saturation (due to charm)
strong saturation
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Unintegrated Gluon Densities
Exclusive Double Diffraction
)2/exp()( ),,0,',()(),,,',( 1111 BttbQtxxftQtxxf tgtg
)],(),([ln
)(),,,',( 22 ttt
gtg QxxgQTQ
RtQtxxf
2
2
)/(
02
22
)(2
)(exp),(
t
tt
Q
kk
ggt
ttSt dzzzP
k
dkkQT
Note: xg(x,.) and Pgg drive the rise of F2 at HERA and Gluon Luminosity decrease at LHC
Dipole Model
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Saturation Model Predictions for Diffraction
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Absorptive correction to F2
....4/))2/exp(1(2 22
bd
d
Example in Dipole Model
F2 ~ -
Single inclusive pure DGLAP
Diffraction
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Fit to diffractive data using MRST Structure Functions A. Martin M. Ryskin G. Watt
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A. Martin M. Ryskin G. Watt
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AGK Rules
)(
)!(!
!2)1( mm
km
kmk F
kmk
m
The cross-section for k-cut pomerons:Abramovski, Gribov, KancheliSov. ,J., Nucl. Phys. 18, p308 (1974)
1-cut
1-cut
2-cut
QCD Pomeron
F (m) – amplitude for the exchange of m Pomerons
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2-Pomeron exchange in QCD Final States(naïve picture)
0-cut
1-cut
2-cut
p*p-CMS
Y
detector
p*p-CMS
p*p-CMS
detector
<n>
<2n>
Diffraction
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0-cut
1-cut
2-cut
3-cut
Feynman diagrams QCD amplitudes J. Bartels A. Sabio-Vera H. K.
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),,()exp(!
),,(
),,()2
exp(12),,(
22*1
0
22
22*1
0
22
*
*
rzQk
rzQdzbdrd
rzQrzQdzbdrd
ff
k
fp
k
ff
fp
Probability of k-cut in HERA data
DipoleModel
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Problem of DGLAP QCD fits to F2
CTEQ, MRST, …., IP-Dipole Model
0 ,~),( 20 xxxg at small x
valence like gluon structure function ?
Remedy: Absorptive corrections? MRW Different evolution? BFKL, CCSS, ABFT
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),(),(ln
),( 221
2
2
z
xgzP
z
dz
d
xdg
x
gg
Cs N
gg xxP
2ln41
~
BFKL ------
from Gavin Salam - Paris2004
As
gg CxP 22
)(~
2
LO DGLAP ---
at low x
Next to leading logs NLLx -----
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from Gavin Salam - Paris 2004
Ciafalloni, Colferai, Salam, Stasto
Similar results byAltarelli, BallForte, Thorn
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)())(,())((3
2 222
bTrxxgrD s Density profile
2exp
22 r
DS
grows with diminishing x and r
approaches a constant value Saturated State - Color Glass Condensate
multiple scattering
S – Matrix => interaction probability Saturated state = high interaction probability S2 => 0
rS - dipole size for which proton consists of one int. length
12 eS
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Saturation scale = Density profile at the saturation radius rS 22 2
SS r
Q 2SQ
S = 0.15
S = 0.25
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Saturated state is partially perturbative
cross-sectiom exhibits the universal rate of growth
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qSqSF
CgS QQ
C
NQ )(
4
9)()( 222
1
fm 7 1000
1
1
4
2
22
22
S
C
CsS
Q
Rdy
dN
dy
dN
RN
NQ
RHIC
HERASRHICS QQ )()( 22
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Conclusions
We are developing a very good understanding of inclusive and diffractive *p interactions: F2 , F2
D(3) , F2c , Vector Mesons (J/Psi)….
Observation of diffraction indicates multi-gluon interaction effects at HERA Open problems: valence-like gluon density? absorptive corrections low-x QCD-evolution HERA measurements suggests presence of Saturation phenomena Saturation scale determined at HERA agrees with the RHIC one
HERA+NMC data => Saturation effects are considerably increased in nuclei
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Diffractive Scattering
Non-Diffractive Event ZEUS detector
Diffractive Event
MX - invariant mass of all particles seen in the central detector t - momentum transfer to the diffractively scattered proton t - conjugate variable to the impact parameter
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Non-Diffraction Diffraction
- Rapidity
uniform, uncorrelated particle emission along the rapidity axis => probability to see a gap Y is ~ exp(-<n>Y) <n> - average multiplicity per unit of rapidity
Diffractive Signature
dN/ dM 2X ~ 1/ M 2
X => dN/dlog M 2
X ~ const note : Y ~ log(W2 / M 2
X)
Non-diff
diff
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fm 10001011
xmE p
Slow Proton Frame
Transverse size of the quark-antiquark cloud
is determined by r ~ 1/Q ~ 2 10-14cm/ Q (GeV)
Diffraction is similar to the elastic scattering: replace the outgoing photon by the diffractive final state , J/ or X = two quarks
incoming virtual photon fluctuates into a quark-antiquark pair which in turn emits a cascade-like cloud of gluons
0)t,(WImAW
1σ 2
el2γptot )Q(x, F
Q
α π4 )Q(W,σ 2
2 2em
22Pγ
tot
*
Rise of ptot with W is a measure of radiation intensity