e p = 920 gev, e e = 27.5 gev, # bunches = 189 i p = 110 ma, i e = 40 ma
DESCRIPTION
Small-x and Diffraction in DIS at HERA I Henri Kowalski DESY 12 th CTEQ Summer School Madison - Wisconsin June 2004. H1 detector. ZEUS detector. E p = 920 GeV, E e = 27.5 GeV, # bunches = 189 I p = 110 mA, I e = 40 mA L inst = 2 x 10 31 cm -2 s - 1. ZEUS detector. - PowerPoint PPT PresentationTRANSCRIPT
Small-x and Diffraction in DIS at HERAI
Henri KowalskiDESY
12th CTEQ Summer School Madison - Wisconsin
June 2004
Ep = 920 GeV, Ee = 27.5 GeV, # bunches = 189Ip = 110 mA, Ie = 40 mALinst= 2 x 1031 cm-2 s-1
ZEUS detector
H1 detector
Q2 ~ 2 –100 GeV2
Q2 ~ 0.05-0.6 GeV2
Q2 - virtuality of the incoming photonW - CMS energy of the incoming photon-proton system
ZEUS detector
x - Fraction of the proton momentum carried by struck quark x ~ Q2/W2
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 noninteracting quarks and gluons
F2 measures parton density in proton at scale Q2
F2 = f e2f x q(x,Q2)
there is a change of slope at small-x, near Q2 = 1 GeV2
Gluon density
Gluon density dominates F2 for x < 0.01
Gluon density known with good precision at larger Q2. For Q2 ~1 GeV2 gluons tends to go negative.
NLO, so not impossible
BUT – cross sections such as L also negative !
MX - invariant mass of all particles seen in the central detector t - momentum transfer to the diffractively scattered proton
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
Non-diff
diff
Y ~ log(W2 / M 2X)
fm 10001011
xmE p
Slow Proton Frame
Transverse size of the quark-antiquark cloudis 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
Radiation process
),()3
( 202
1
21
121
21
1 Qydyk
dkdy
k
dkdyC nn
tn
tnn
t
tn
n
sptot
emission of gluons is ordered in rapidities
)/1ln()/ln(0 22121 xQWyyyy nn
QCD Toy Model:integrals over transverse momenta are independent of each other
)(
2
222max
20
3 Qk
Qit
its
k
kd
n
n
ny
n
x yn
n
ptot x
nCdydydyC
n
))/1(ln(!
11
0
)/1ln(
0 0
21
)(~)/1())/1ln(exp( 2WxCxCptot
Rise of ptot with W is a measure of radiation intensity
Dipole description of DIS
),,(),(),,(ˆ 22*21
0
2*
rzQrxrzQdzrd qqp
tot
2222*1
0
20 |),,(),(),,(|
16
1|
*
rzQrxrzQdzrddt
dqqVMt
pVM
)section cross (dipolproton on pair qq
of scatteringfor section cross ),(
function waveQCD qq ),(2rx
rz
),,(),(),,(16
1| 2222*
1
0
20
*
rzQrxrzQdzrddt
dqqt
pdiff
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)
)]4
exp(1[ ),(20
2
0 R
rrxqq
GBW ModelK. Golec-Biernat, M. Wuesthoff
02
20
1)(
x
x
GeVxR
Parameters fitted to DIS F2 data:0 = 23 mb = 0.29 x0 = 0.0003
Scaling in
20
2 / Rr
Geometrical Scaling A. Stasto & Golec-Biernat J. Kwiecinski
Parameters fitted to HERA DIS data: 2 /N ~ 1 0 = 23 mb = 0.29 x0 = 0.0003
Saturation Model Predictions for Diffraction
)(20
2 xRQ
Geometrical Scaling A. Stasto & Golec-Biernat J. Kwiecinski
02
20
1)(
x
x
GeVxR
GBW model, in spite of its compelling success has some obvious shortcomings:
The treatment of QCD evolution is only rudimentary remedy => incorporate DGLAP into dipole cross-section J. Bartels, K. Golec-Biernat, H. Kowalski
The dipole cross section is integrated over the transverse coordinatealthough the gluon density is expected to be a strongly varying functionof the impact parameter.
)))/,(3
exp(1(),(
1 ));exp(1(),(
20
222
0
2
0
02
202
0
2
0
rCxxgrrx
x
x
GeVR
R
rrx
sqq
GBW
Recently: BFKL motivated Ansatz proposed by Iancu, Itakura, Munier
Proton
b – impact parameter
Impact Parameter Dipole Saturation Model
T(b) - proton shape 1)( 2
0
bdbT
well motivated:
GlauberMueller LevinCapellaKaidalov
))(),()(
32exp(12
),( 2222
2bTxxgr
bd
rxds
H. Kowalski D. Teaney hep-ph/0304189
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
d)-(2 parameter impact - d)-(2 momentum transv.- 2 bt
t-dependence of the diffractive cross sections determines the b distribution
22222
2*1
0
22 |),,())(),(32
exp(1),,(|16
1*
rzQbTxxgrrzQdzebdrddt
dsVM
bip
VM
)2/exp(~)(
)exp(~
2 BbbT
tBdt
d diff
)/()2/)(exp()(
GeV 25.4 )2/exp()(
022
-22
EGGY
GGG
wbKwbbbdbT
wwbbT
Q2 > 0.25 GeV2
mu = 0.05 GeV mc = 1.30 GeV
Fit parameters g= -0.12 C= 4.0 Q0
2 = 0.8 GeV2
2/N = 0.8
x < 10-2
6.520
202
2
)1(1
),( xx
Axxg
r
C
g
g
),,())(),(32
exp(1),,( 2222
2*1
0
22*
rzQbTxxgrrzQdzbdrd ff
sfp
)]4
exp(1[ ),(20
2
0 R
rrxqq
GBW Model
))()/,(32
exp(12 ),( 2
022
2
2bTQrCxxgr
bd
rxds
IP Saturation Model
))((22
)/1(~),( reffxxxg
Smaller dipoles steeper rise Large spread of eff characteristic for Impact Parameter Dipole Models
)()(2 22*
)/1(~)(~ QQp tottot xW
----- universal rate of rise of all hadronic cross-sections
Saturation region-------------------------------------------------------------------------------------------------------
))(),(
32exp(12
),( 222
2bTxxgr
bd
rxds
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
Gluon density Charm structure function
Photo-production of Vector Mesons
Absolute values of cross sections are strongly dependent on mc
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
Fit to diffractive data using MRST Structure Functions A. Martin M. Ryskin G. Watt
A. Martin M. Ryskin G. Watt
)())(,())((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
Saturated state = = high interaction probability S2 => 0
rS - dipole size for which proton consists of one int. length
12 eS
S2 -probability that a dipole does not suffer an inelastic interaction passing through the entire proton
Saturation scale = Density profile at the saturation radius rS 22 2
SS r
Q 2SQ
S = 0.15
S = 0.25
Saturation in the un-integrated gluon distribution
kT factorisation formula
dipole formula
GBW - - - - - - - - - - - - - - - - - - - - -
BGBK ___________________________________
GBW - - - - - - - - - - - - - - - - - - - - -
BGBK ___________________________________
- numerical evaluation
x = 10-6
x = 10-2
x = 10-4
x = 10-2
Diffractive production of a qq pair_
Inclusive Diffraction LPS - Method
END of Part I