Transcript Small-x and Diffraction in DIS at HERA II 12 Henri Kowalski

Small-x and Diffraction in DIS at HERA
II
Henri Kowalski
DESY
12th CTEQ Summer School
Madison - Wisconsin
June 2004
Dipole Saturation Models
b – impact p.
Proton
GBW
2 
BGBK
C
  02
2
r
DGLAP
g
1
xg( x,  )  Ag   (1  x)5.6
 x
2
0
IIM Model with BFKL & CG evolution
d qq ( x, r )
d 2b


2 2
 2  1  exp( 
r  s (  2 ) xg( x,  2 )T (b)) 
23


KT

T(b) -
proton shape
 T (b)d
0
2
b 1
Glauber
Mueller
Derivation of the GM dipole cross section
P(b)  1 
d
2
2
NC
r 2 s (  2 ) xg( x,  2 )  (b, z )dz
bdz (b, z )  1
probability that a dipole at b
does not suffer an inelastic
interaction passing through
one slice of a proton
Uncorrelated scatterings
S (b)
2
 2 2

 exp  
r  s (  2 ) xg( x,  2 )T (b) 
 NC

T (b)   dz  (b, z )
d qq
d 2b

 2(1  Re S (b))
<= Landau-Lifschitz
S2 -probability that a dipole
does not suffer an inelastic
interaction passing through
the entire proton
NOTE: the assumption of
uncorrelated scatterings is
not valid for BK and JIMWLK
equations
Correlations from evolution


2 2
 2  1  exp( 
r  s (  2 ) xg( x,  2 )T (b))   IIM Dipole fit
2
d b
23

 GM Dipole + DGLAP mimics
full evolution
d qq
Data precision is essential to the progress of understanding
GBW
GBW
Parameters fitted to HERA DIS data: c2 /N ~ 1
0 = 23 mb  = 0.29 x0 = 0.0003
GBW
  p ~ (W 2 )
*
tot ( Q
2
)
~ (1 / x)tot (Q
2
)
xg( x,  ) ~ (1 / x)
2
eff (  2 ( r ))
GBW=0.29
----- universal rate of rise of all
hadronic cross-sections
Smaller dipoles  steeper rise
Large spread of eff characteristic for
Impact Parameter Dipole Models (KT)
Analysis of data within Dipole Models

 *p
2 tot ( Q2 )
~ (W )
~ (1 / x)
tot (Q 2 )
BGBK
GBW=0.29
KT
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
Theory (RV):
In IP Saturation Model (KT) change
of  with Q2 is mainly due to
evolution effects
evolution leads to saturation - Balitzki- Kovchegov and
JIMWLK
GBW - - - - - - - - - - - - - - - - - - - - -
x = 10-6
BGBK
___________________________________
x = 10-2
Evolution increases gluon density =>
smaller dipoles scatter stronger,
gluons move to higher virtualities
Fourier
transform
x = 10-4
-
numerical evaluation
In Color-Glass gluons occupy higher
momentum states
x = 10-2
A glimpse into nuclei
d diff
~ exp( B  t )
dt


T (b) ~ exp( b 2 / 2 B )
Naïve assumption for T(b):
Wood-Saxon like, homogeneous, distribution of nuclear matter
A
d qq
( x, r )
d 2b

2 
2 2
  1  exp( 
r  s xg( x,  2 ) ATW S (b)) 
A 
23

Smooth Gluon Cloud
Q2 (GeV2)
C
0.74
Ca
0.60
1.20
0.94
1.70
1.40
A
d qq
( x, r )
d 2b

2
 1  (1  TW S (b) qq ( x, r )/2) A 
A
Lumpy Gluon Cloud
Q2 (GeV2)
C
0.74
Ca
0.60
1.20
0.94
1.70
1.40
(QS2 ) g 
NC 2
9
(QS ) q  (QS2 ) q
CF
4
Saturation Scale at RHIC
4 2 s N C 1 dN
Q 
N C2  1 R 2 dy
2
S
dN
 1000
dy
R  7 fm
QS2  1
(QS2 ) RHIC  (QS2 ) HERA
_
Diffractive production of a qq pair
Diffractive production of a qqg system
Inclusive Diffraction
Non-Diffraction
Diffraction
<=p
e =>
Select diffractive events by requirement of
no forward energy deposition
called hmax cut
Q: what is the probability that a non-diff event
has no forward energy deposition?
MX Method
Non-Diffractive Event
Diffractive Event
detector
detector
log W2
Y
p
log MX 2
DY
*p-CMS
DY
Y
*
non-diff events are characterized by
uniform, uncorrelated particle emission
along the whole rapidity axis =>
probability to see a gap DY is
p
*p-CMS
diff events are characterized by
exponentially non-suppressed
rapidity gap DY
~ exp(-DY)
 – Gap Suppression Coefficient
since DY ~ log(W2/M2X) – h0
dN/dlogM 2X ~exp(  log(M 2X))
*
dN/ dM 2X ~ 1/ M 2X =>
dN/dlogM2X ~ const
MX Method
diff
Nondiff
diff
Non-Diffraction
dN/dM 2X ~exp(  log(M 2X))
Gap suppression coefficient 
independent of Q2 and W2
for Q2 > 4 GeV2
Nondiff
diff
Nondiff
Diffraction
dN/dlog M 2X ~ const
Gap Suppression in Non-Diff MC
---- Generator Level CDM
---- Detector Level CDM
Detector effects
cancel in
Gap Suppression !
dN/dM 2X ~exp(  log(M 2X))
In MC  independent of Q2 and W2
~ 2 in MC
~ 1.7 in data
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
exp(- DY ) = exp(-log(W2/M2X)= (W2/M2X)
from Regge point of view ~ (W2)2(1)
  2 for the exchange of pion q.n. (0)
 1 for the exchange of rho q.n. (1/2)
 0 for the exchange of pomeron q.n. (1)
 is well measurable provided good calorimeter coverage
SR = SATRAP: MC based on the Saturated Dipole Saturation Model
~ H1 approach
A. Martin M. Ryskin G. Watt
A. Martin M. Ryskin G. Watt
 BEKW
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
Example in Dipole Model
d
2

2
(
1

exp(


/
2
))




/ 4  ....
2
d b
F2
~
-
Single inclusive
pure DGLAP
Diffraction
2 2

r  s (  2 ) xg( x,  2 )T (b)
NC
A. Martin
M. Ryskin
G. Watt
A. Martin M. Ryskin
G. Watt
AGK Rules
QCD
Pomeron
The cross-section for k-cut pomerons:
Abramovski, Gribov, Kancheli
Sov. ,J., Nucl. Phys. 18, p308 (1974)

 k   (1)
mk
mk
m!
2
F (m)
k!(m  k )!
1-cut
m
F (m) – amplitude for the exchange of
m Pomerons
1-cut
2-cut
Pomeron in QCD
t-channel picture
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
2-Pomeron exchange in QCD
Final States
(naïve picture)
detector
0-cut
Diffraction
p
DY
*
*p-CMS
<n>
1-cut
*
p
*p-CMS
detector
<2n>
2-cut
p
*
*p-CMS
0-cut
1-cut
2-cut
3-cut
AGK Rules in the Dipole Model
Total cross section
Mueller-Salam (NP B475, 293)

 tot  2 (1) m 1 F ( m )
m 1
Dipole cross section

d
1
m 1   

2
(
1

exp(


/
2
))

2
(

1
)



d 2b
 2  m!
m 1
m
Amplitude for the exchange of m pomerons in the dipole model
 1
 
 2  m!
m
F
( m)
2 2

r  s ( 2 ) xg( x,  2 )T (b)
NC
KT model
AGK rules

d k
m!
mk m
(m)

(

1
)
2
F

d 2b m  k
k!(m  k )!
Dipole model
k

d k
m!
  1  
mk m
  (1) 2
   
2
d b mk
k!(m  k )!  2   m!  k!
m

 (1)
mk
mk
 mk
(m  k )!
d k  k

exp( )
2
d b
k!
Diffraction from AGK rules
d diff
2
d b

d qq
2
d b
d k
 2(1  exp(  / 2))  (1  exp( ))
2
d
b
k 1


 1  2 exp(  / 2)  exp( )  (1  exp(  / 2)) 2
very simple
but not quite
right
d qq
 


2

1

exp(

)

2
d b
2 

d k  k

exp( )
2
d b k!
2 2

r  s (  2 ) xg( x,  2 )T (b)
NC

1
2


 T , L ( x, Q )   d r  dz  Tf, L (r , z, Q 2 )  qq ( x, r )
 *P
2
2
0
0
f
2

3
Tf (r , z, Q 2 )  em2 eq2 {[ z 2  (1  z ) 2 ] 2 K12 (r )  mq2 K 02 (r )}
2
2

3
Lf (r , z, Q 2 )  em2 eq2 {4Q 2 z 2 (1  z ) 2 K 02 (r )}
 2  z (1  z )Q 2  mq2
2
K1 (r )  1/ r
for r  1
Q2~1/r2
K1 (r )   / 2 x exp( r )
for r  1
exp(-mq r)
All quarks
1
2

2r  dz   (r , z, Q 2 )  qq ( x, r )
f
T ,L
0
f
mu ,d , s  100 MeV
Charmed quark
1

2r  dz qq ( x, r )Tc, L (r , z, Q 2 ) 2
0
mc  1.3 GeV
mc  1.3 GeV

*p

*p
k

 

 
   d r  d 2b  dz *f (Q 2 , z , r ) 21  exp(  ) f (Q 2 , z , r )
2 

f
0
1
2
 2
 k

*
2
   d r  d b  dz f (Q , z , r )
exp( ) f (Q 2 , z , r )
k!
f
0
1
2
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 , F2D(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:
γp
σ tot

1
2
ImA
(W
, t  0)
el
2
W
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
p
Si tracking stations
Hadronic
Calorimeter
e
EM Calorimeter
Compact – fits in dipole
magnet with inner radius
of 80 cm.
Long - |z|5 m
Forward
Detector
e
27
GeV
p
920
GeV
HERA Interactions
Collisions of e+ (e-) of 27.5 GeV with p of 920 GeV
Increase of kinematic range by over 4 order of magnitude
in x at moderate Q2 and 6 order of magnitude in Q2