Proton
description
Transcript of Proton
Small-x and Diffraction in DIS at HERAII
Henri KowalskiDESY
12th CTEQ Summer School Madison - Wisconsin
June 2004
Proton
b – impact p.
Dipole Saturation Models
T(b) - proton shape 1)( 2
0
bdbT
GlauberMueller
))(),()(
32exp(12
),( 2222
2bTxxgr
bd
rxds
GBW
KT
6.520
202
2
)1(1
),( xx
Axxg
r
C
g
g
BGBK
DGLAP
IIM Model with BFKL & CG evolution
Derivation of the GM dipole cross section
probability that a dipole at b does not suffer an inelastic interaction passing through one slice of a proton1),(
),(),()(1)(
2
2222
zbbdzd
dzzbxxgrN
bP sC
),()(
)(),()(exp)( 2222
2
zbdzbT
bTxxgrN
bS sC
))(),()(32
exp(12
))(Re1(2
2222
2
2
bTxxgrbd
d
bSbd
d
sqq
S2 -probability that a dipole does not suffer an inelastic interaction passing through the entire proton
<= Landau-Lifschitz
Uncorrelated scatterings
NOTE: the assumption of uncorrelated scatterings isnot valid for BK and JIMWLK equations
Correlations from evolution IIM Dipole fitGM Dipole + DGLAP mimics full evolution
Parameters fitted to HERA DIS data: 2 /N ~ 1 0 = 23 mb = 0.29 x0 = 0.0003
Data precision is essential to the progress of understanding
GBW GBW
GBW
))((22
)/1(~),( reffxxxg
Smaller dipoles steeper rise Large spread of eff characteristic for Impact Parameter Dipole Models (KT)
)()(2 22*
)/1(~)(~ QQp tottot xW
----- universal rate of rise of all hadronic cross-sections
GBW=0.29
)()(2 22*
)/1(~)(~ QQp tottot xW
BGBK
KT
In IP Saturation Model (KT) change of with Q2 is mainly due to evolution effects
GBW
In GBW Model change of with Q2 is due to saturation effects
In BGBK Model change of with Q2 is due to saturation and evolution effects
Analysis of data within Dipole Models
Theory (RV): evolution leads to saturation - Balitzki- Kovchegov and JIMWLK
GBW=0.29
GBW - - - - - - - - - - - - - - - - - - - - -
BGBK ___________________________________
- numerical evaluation
x = 10-6
x = 10-2
x = 10-4
x = 10-2
Evolution increases gluon density => smaller dipoles scatter stronger, gluons move to higher virtualities
Fouriertransform
In Color-Glass gluons occupy higher momentum states
A glimpse into nuclei
Naïve assumption for T(b): Wood-Saxon like, homogeneous, distribution of nuclear matter
)2/exp(~)(
)exp(~
2 BbbT
tBdt
d diff
))(),(
32exp(1
2
),( 222
2bATxxgr
Abd
rxdWSs
Aqq
Smooth Gluon Cloud
Q2 (GeV2) C 0.74 1.20 1.70 Ca 0.60 0.94 1.40
AqqWS
Aqq rxbT
Abd
rxd)/2),()(1(1
2
),(2
Lumpy Gluon Cloud
Q2 (GeV2) C 0.74 1.20 1.70 Ca 0.60 0.94 1.40
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
Saturation Scale at RHIC
HERASRHICS QQ )()( 22
Diffractive production of a qq pair_
Diffractive production of a qqg system
Inclusive Diffraction
Non-Diffraction Diffraction
Select diffractive events by requirement of no forward energy deposition called max cut
Q: what is the probability that a non-diff event has no forward energy deposition?
e => <=p
p p
Y
log W2 detector detector
log MX 2
MX Method
Non-Diffractive Event Diffractive Event
*p-CMS *p-CMS
Y
non-diff events are characterized by uniform, uncorrelated particle emission along the whole rapidity axis => probability to see a gap Y is ~ exp(-Y) – Gap Suppression Coefficient
since Y ~ log(W2/M2X) – 0
dN/dlogM 2X ~exp( log(M 2
X))
diff events are characterized by exponentially non-suppressed rapidity gap Y
dN/ dM 2X ~ 1/ M 2
X => dN/dlogM2
X ~ const
Y Y
Non-diff
diff
MX Method
Non-diff
Non-diff
diffdiff
Non-DiffractiondN/dM 2
X ~exp( log(M 2X))
Gap suppression coefficient independent of Q2 and W2
for Q2 > 4 GeV2
Diffraction dN/dlog M 2
X ~ const
Gap Suppression in Non-Diff MC---- Generator Level CDM---- Detector Level CDM
dN/dM 2X ~exp( log(M 2
X))
In MC independent of Q2 and W2
~ 2 in MC in data
Detector effects cancel in
Gap Suppression !
Physical meaning of the Gap Suppression Coefficient
Uncorrelated Particle Emission (Longitudinal Phase Space Model) – particle multiplicity per unit of rapidity
Feynman (~1970): depends on the quantum numbers carried by the gap
2 for the exchange of pion q.n. for the exchange of rho q.nfor the exchange of pomeron
q.n
is well measurable provided good calorimeter coverage
exp(- Y ) = exp(-log(W2/M2X)= (W2/M2
X)
from Regge point of view ~ (W2)
SR = SATRAP: MC based on the Saturated Dipole Saturation Model
~ H1 approach
A. Martin M. Ryskin G. Watt
BEKW
A. Martin M. Ryskin G. Watt
Fit to diffractive data using MRST Structure Functions A. Martin M. Ryskin G. Watt
Fit to diffractive data using MRST Structure Functions A. Martin M. Ryskin G. Watt
Absorptive correction to F2
from AGK rules
....4/))2/exp(1(2 22
bd
d Example in Dipole Model
F2 ~ -
Single inclusive pure DGLAP
Diffraction
)(),()( 2222
bTxxgrN s
C
A. Martin M. RyskinG. Watt
A. Martin M. Ryskin G. Watt
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
Color singlet dominates over octet in the 2-gluon exchange amplitude at high energies
3-gluon exchange amplitude is suppressed at high energies
2-gluon pairs in color singlet (Pomerons) dominate the multi-gluon QCD amplitudes at high energies
Pomeron in QCD t-channel picture
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
0-cut
1-cut
2-cut
3-cut
AGK Rules in the Dipole Model
)(
1
1)1(2 m
m
mtot F
!
1
2)1(2))2/exp(1(2
1
12 mbd
dm
m
m
Total cross section Mueller-Salam (NP B475, 293)
Dipole cross section
)(),()( !
1
2222
2)( bTxxgr
NmF s
C
mm
Amplitude for the exchange of m pomerons in the dipole model
KT model
)(2 )!(!
!2)1( mm
km
kmk Fkmk
m
bd
d
AGK rules
Dipole model
)!()1(
!!
1
2)!(!
!2)1(
2 kmkmkmk
m
bd
d km
km
kmkm
m
km
kmk
)exp(!2
kbd
d kk
Diffraction from AGK rules
2
1222
))2/exp(1()exp()2/exp(21
))exp(1())2/exp(1(2
k
kqqdiff
bd
d
bd
d
bd
d very simple but not quite right
)2
exp(12 2bd
d qq)exp(
!2
kbd
d kk
)(),()( 2222
bTxxgrN s
C
22220
22222
22
20
221
22222
22
22,
1
00
22,
)1( )}()1(4{2
3),,(
)}()(])1({[2
3),,(
),(),,(),(*
qqemf
L
qqemf
T
qqf
fLT
PLT
mQzzrKzzQeQzr
rKmrKzzeQzr
rxQzrdzrdQx
Q2~1/r2
1for /1)(1 rrrK
1for ) exp(2/)(1 rrxrK
exp(-mq r)
All quarks Charmed quark
GeV 3.1 MeV 100
),(),,(2
,,
22,
1
0
csdu
qqf
fLT
mm
rxQzrdzr
GeV 3.1
),,(),(2 22,
1
0
c
cLTqq
m
Qzrrxdzr
),,()exp(!
),,(
),,()2
exp(12),,(
22*1
0
22
22*1
0
22
*
*
rzQk
rzQdzbdrd
rzQrzQdzbdrd
ff
k
fp
k
ff
fp
Note: AGK rules underestimate the amount of diffraction in DIS
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-pomeron interaction effects at HERA HERA measurements suggests presence of Saturation phenomena Saturation scale determined at HERA agrees with the RHIC one
Saturation effects in ep are considerably increased in nuclei
Thoughts after CTEQ School
George Sterman: Parton Model Picture (in Infinite Momentum Frame) is in essence probabilistic, non-QM. It is summing probabilities and not amplitudes
F2 = f e2f x q(x,Q2)
Parton Model Picture is extremely successful, it easily carries information from process to process, e.g. we get jet cross-sections in pp from parton densities detemined in ep
Dipole Models (Proton rest Frame) are very successful carrying information from process to process within ep. They are in essence QM, main objects are amplitudes:
0)t,(WImAW
1σ 2
el2γptot
In DM Picture diffraction is a shadow of F2 . Many other multi-pomeron effects should be present
Several attempts are underway to build a bridge over the gap between Infinite Momentum Frame and Proton Rest Frame Pictures
Jochen Bartels, Lipatov & Co: Feynman diagrams for multi-pomeron processes…
Raju Venogopulan & Co, Diffraction from Wilson loops, fluctuations from JIMWLK… ……………………………………..
A new detector to study strong interaction physics
e
p
HadronicCalorimeter
EM CalorimeterSi tracking stations
Compact – fits in dipole magnet with inner radius of 80 cm.Long - |z|5 m
e 27 GeV
p920GeV
ForwardDetector
Increase of kinematic range by over 4 order of magnitude in x at moderate Q2 and 6 order of magnitude in Q2
HERA InteractionsCollisions of e+ (e-) of 27.5 GeV with p of 920 GeV