Download t - H1

Exclusive Diffraction
at HERA
Henri Kowalski
DESY
Ringberg
October 2005
γp
σ tot

1
ImAel (W 2 , t  0)
2
W
Q2
γ* P
2
F2 (x, Q ) 

σ
tot (W, Q )
2
4 π αem
2
Q2
x 2
W
F2 is dominated by single ladder exchange
ladder symbolizes the QCD evol. process
( DGLAP or others )
Gluon density
Gluon density dominates F2 for x < 0.01
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
Diffractive Signature
diff
Nondiff
~ DY= log(W2/M2X)
Non-Diffraction
Diffraction
- Rapidity
uniform, uncorrelated particle emission
along the rapidity axis =>
probability to see a gap DY is
~ exp(-<n>DY)
<n> - average multipl. per unit of Y
dN/dM2X ~ 1/M2X =>
dN/dlog M2X ~ const
Observation of diffraction indicates that single ladder may not be sufficient
(partons produced from a single chain produce exponentially suppressed rap. gaps)
Diffractive Structure Function
Dipole Model
______________
Initial Diff. SF
Q20 ~ 4 GeV2
Study of exclusive diffractive states
may clarify which pattern is right
Only few final states present in DiMo:
qq, qqg (aligned and as jets)
VM
Dipole description of DIS
equivalent to Parton Picture in the perturbative region
momentum space
configuration space
dipole preserves
its size during
interaction.
qq ~ r2xg(x,m)
for small r
Optical T
Tf
2
Lf
2
3 em 2 2
eq {[ z  (1  z ) 2 ] 2 K12 (r )  mq2 K 02 (r )}
2
2
3
 em2 eq2 {4Q 2 z 2 (1  z ) 2 K 02 (r )}
2
 2  z (1  z )Q 2  mq2
r<<1

Q2~1/r2
Mueller, Nikolaev, Zakharov
 tot
*p
1

  d rˆ  dz* qq ( x, r 2 )
2
0
 p



d VM
1
*
|t 0 
|  d 2 r  dzVM
(Q 2 , z, r )  qq ( x, r 2 )(Q 2 , z, r ) |2
dt
16
0
*
1
 p
d diff
*
dt
1
|t  0 
16
1

*
2
2
d
r
  dz  qq ( x, r )
2
0
Dipole description of DIS
GBW – first Dipole Saturation Mode (rudimentary evolution)
Golec-Biernat, Wuesthoff
r2
 qq ( x, r )   0 (1  exp(  2 ));
R0
1  x
 
R 
GeV 2  x0 
GBW
2
0
BGBK – DSM with DGLAP
Bartels, Golec-Biernat, Kowalski
2 2
 qq ( x, r )   0 (1  exp( 
r  s xg( x, m 2  C / r 2  m02 )))
3 0
Iancu, Itakura, Munier
-
BFKL-CGC motivated ansatz
Forshaw and Shaw
-
Regge ansatz with saturation
Impact Parameter Dipole Saturation Model
Kowalski
Teaney
b – impact parameter
Glauber-Mueller,
d qq ( x, r )
d 2b
Levin, Capella, Kaidalov…


2 2
 2  1  exp( 
r  s ( m 2 ) xg( x, m 2 )T (b)) 
23


T(b) -
proton shape
 p


d VM
1
2
2
ib D
*

|  d r  d be  dzVM
(Q 2 , z, r )
dt
16
0
*
1



2 2
r  s xg( x, m 2 )T (b))(Q 2 , z, r ) |2
1  exp( 
23



d diff
~ exp( B  t )  T (b) ~ exp( b 2 / 2 B)
dt
Total *p cross-section

*p
~ (W 2 )tot ~ (1/ x)tot
universal rate of rise
of all hadronic cross-sections
x < 10-2
m2 
C
 m 02
2
r
g
1
xg( x, m )  Ag   (1  x)5.6
 x
2
0
Ratio of tot to diff
from fit to tot predict diff
GBW, BGBK …
diff is
not a square of
tot !
_
Diffractive production of a qq pair
~ probability to find a Pomeron(2g) in p
~ probability for a Pomeron(2g)
to couple to a quark
spin 1/2
spin 1
 ~ s1
=>
dN/dlog M2X ~ const
Diffractive production of a qqg state
Inclusive Diffraction
LPS
— BGBK Dipole
Comparison with Data
FS model with/without saturation and IIM CGC model
hep-ph/0411337.
Fit F2 and predict
xIPF2D(3)
FS(nosat)
F2
CGC
FS(sat)
F2
x
Dipole cross section determined
by fit to F2
Simultaneous description of many
reactions
F2 C
Gluon density test?
IP-Dipole
Model
Teubner
*p -> J/y p
*p -> J/y p
IP-Dipole Model
 VM ~ W 
 VM ~ W 
Exclusive r production
d diff
~ exp( BD  t )
dt
Modification by Bartels,
Golec-Biernat, Peters,
(first proposed by
Nikolaev, Zakharov)
e
 p


d VM
1
2
2
ib D
*

|  d r  d be  dzVM
(Q 2 , z, r )
dt
16
0
*
1
 
ib D
e

 
i ( b  (1 z ) r )D


 2
2 2
2
2
1

exp(

r

xg
(
x
,
m
)
T
(
b
))

(Q , z, r ) |
s
23


H. Kowalski, L. Motyka, G. Watt
preliminary
Diffractive Di-jets
Q2 > 5 GeV2
-RapGap
Satrap
Diffractive Di-jets
Q2 > 5 GeV2
Diffractive Di-jets
Q2 > 5 GeV2
Diffractive Di-jets at the Tevatron
Dijet cross section factor 3-10 lower than expected
using HERA Diffractive Structure Functions
suppression due to secondary interactions ?
H1 and ZEUS:
NLO overestimates data
by factor 1.6.
Kaidalov et al.:
resolved part needs
to be rescaled by 0.34
scaled by factor 0.34
Survival Probability S2
S2 
Soft Elastic Opacity
t – distributions
at LHC
2
  ( s ,b ) 2
M
(
s
,
b
)
e
d b

2
2
M
(
s
,
b
)
d
b

 
 2 (t1 )  2 (t2 ) 2  
F ( p1t , p2t ) 
S ( p1t , p2t )
2
2
2
< S   / b0
Khoze
Martin
Ryskin
Effects of soft proton
absorption modulate the
hard t – distributions
t-measurement will allow
to disentangle the effects
of soft absorption from
hard behavior
Dipole form
double eikonal
single eikonal
ZEUS-LPS
H1 VFPS at HERA
Conclusions
Inclusive diffraction, exclusive diffractive VM
and jet production can be successfully derived
from the measured F2
(Dipole Model with u. gluon densities obtained from F2 )
Detailed VM-data from HERA should allow to pin down
VM wave functions
Diffractive Structure Function analysis describes well
the inclusive diffractive processes and
the exclusive diffractive jet production
although it has some tendency to amplify small
differences of the input distributions
Exclusive diffractive processes give detailed
insight into DIS dynamics
Press Release: The 2005 Nobel Prize in Physics
4 October 2005
The Royal Swedish Academy of Sciences has decided to award the Nobel Prize
in Physics for 2005 with one half to
Roy J. Glauber
Harvard University, Cambridge, MA, USA
"for
his contribution to the quantum theory of optical coherence"
Glauber wrote his formula for heavy nuclei and for deuteron. He was the
first who realized that his formula in the case of deuteron describes
both the elastic cross section and the diffractive dissociation of the
deuteron.
Genya Levin
Roy Glauber’s Harvard Webpage
Roy Glauber's
recent research has dealt with problems in a number
of areas of quantum optics, a field which, broadly speaking, studies the
quantum electrodynamical interactions of light and matter. He is also
continuing work on several topics in high- energy collision theory,
including the analysis of hadron collisions, and the statistical correlation
of particles produced in high-energy reactions.
Specific topics of his current research include: the quantum mechanical
behavior of trapped wave packets; interactions of light with trapped
ions; atom counting-the statistical properties of free atom beams and
their measurement; algebraic methods for dealing with fermion
statistics; coherence and correlations of bosonic atoms near the BoseEinstein condensation; the theory of continuously monitored photon
counting-and its reaction on quantum sources; the fundamental nature of
“quantum jumps”; resonant transport of particles produced multiply in
high-energy collisions; the multiple diffraction model of proton-proton
and proton-antiproton scattering
Saturation and Absorptive corrections
F2
~
Single inclusive
linear QCD evolution
-
Diffraction
Example in Dipole Model
d
2

2
(
1

exp(


/
2
))




/ 4  ....
2
d b
High density limit —> Color Glass Condensate
coherent gluon state
McLerran
Venogopulan
2-Pomeron exchange
in QCD
0-cut
Final States
(naïve picture)
Diffraction
1-cut
<n>
2-cut
<2n>
QCD diagrams
d qq
 


2

1

exp(

)

2
d b
2 

d k  k

exp( )
2
d b k!
2 2

r  s ( m 2 ) xg( x, m 2 )T (b)
NC
AGK rules in the
Dipole Model
d k  k

exp( )
2
d b
k!
2 2

r  s ( m 2 ) xg( x, m 2 )T (b)
NC
Note: AGK rules underestimate the amount of diffraction in DIS
GBW Model
IP Dipole Model
r2
 qq ( x, r )   0 [1  exp( 
)]
4 R02
1
R ( x) 
GeV 2
2
0
 x 

x 

 0

strong saturation
d qq ( x, r )
d 2b


2 2
 2  1  exp( 
r  s xg( x, C / r 2  Q02 )T (b)) 
23


less saturation
(due to IP and charm)
Saturation scale
(a measure of gluon density)
2
HERA
QS2 
rS2
N
9
(Q )  C (QS2 ) q  (QS2 ) q
CF
4
2
S g
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 GeV 2
QSRHIC ~ QSHERA
Geometrical Scaling
A. Stasto & Golec-Biernat
J. Kwiecinski
1  x
 
R02 ( x) 
2 
GeV  x0 
  Q 2 R02 ( x)

Dipole X-section
——
----
BGBK
GBW
Geometrical Scaling can be derived from
traveling wave solutions of
non-linear QCD evolution equations
Velocity of the wave front gives the
energy dependence of the saturation
scale
Munier, Peschanski
L. McLerran +…
Al Mueller + ..
Question:
Is GS an intrinsic (GBW) or effective
(KT) property of HERA data?
2-Pomeron exchange
in QCD
0-cut
Final States
(naïve picture)
Diffraction
1-cut
<n>
2-cut
<2n>
AGK rules in the
Dipole Model
d k  k

exp( )
2
d b
k!
2 2

r  s ( m 2 ) xg( x, m 2 )T (b)
NC
Note: AGK rules underestimate the amount of diffraction in DIS
d qq
 


2

1

exp(

)

2
d b
2 

d k  k

exp( )
2
d b k!
2 2

r  s ( m 2 ) xg( x, m 2 )T (b)
NC
HERA Result
Unintegrated Gluon Density
Dipole Model
Example from dipole model
- BGBK
Another approach (KMR)

f g ( x, m 2 )   (t ) 
[ T (Qt , m )  xg( x, Qt2 )]
2
 ln Qt
 m 2  S (kt2 ) dkt2 kt /(m  kt )


T (Qt , m )  exp    2
zP
(
z
)
dz
gg
2 0
Qt
2

k
t


f g ( x1 , t , Qt , m )   (t ) f g ( x1 , t  0, Qt , m )
b(t )  exp( Bt / 2)
Active field of study at HERA:
UGD in heavy quark production, new result
expected from high luminosity running in 2005,
2006, 2007
Exclusive Double Diffractive Reactions at LHC
xIP = Dp/p, pT
xIP ~ 0.2-1.5%
xIP = Dp/p, pT
xIP ~ 0.2-1.5%
1 event/sec
High momentum
measurement
precision
 Diff  ˆ  L
L
 S 2O
2
yM
2


dQt2

exclusive
O
  2
f g ( x1 , Qt ) f g ( x2 , Qt ) 
4

(
N

1
)
b
Q
t
 c

M2
low x QCD reactions:
pp => pp + gJet gJet
pp => pp + Higgs
 ~ 1 nb for M(jj) ~ 50 GeV
 ~ 0.5 pb for M(jj) ~ 200 GeV
hJET| < 1
  O(3) fb SM
 O(100) fb MSSM
t – distributions at LHC
t – distributions at HERA
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
diff
d hard
~ exp( 4 | t |)
dt
Non-Saturated
gluons
t-distribution of hard processes
should 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
Saturated
gluons
Survival Probability S2
S2 
Soft Elastic Opacity
t – distributions
at LHC
2
  ( s ,b ) 2
M
(
s
,
b
)
e
d b

2
2
M
(
s
,
b
)
d
b

 
 2 (t1 )  2 (t2 ) 2  
F ( p1t , p2t ) 
S ( p1t , p2t )
2
2
2
< S   / b0
Khoze
Martin
Ryskin
Effects of soft proton
absorption modulate the
hard t – distributions
t-measurement will allow
to disentangle the effects
of soft absorption from
hard behavior
Dipole form
double eikonal
single eikonal
F2
Dipole Model
Gluon Luminosity
Exclusive Double Diffraction
L. Motyka, HK
preliminary
 Diff  ˆ  L
M2
L
 S 2O
2
yM
QT2 (GeV2)


dQt2

exclusive

O
  2
f
(
x
,
x
'
,
t
,
Q
,
m
)
f
(
x
,
x
'
,
t
,
Q
,
m
)
g
1
1
t
g
2
2
t
4

(
N

1
)
b
Q
t
 c

fg – unintegrated gluon densities
2
Conclusions
We are developing a very good understanding of inclusive and
diffractive g*p interactions:
F2 ,
F2D(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!!!!
Precise
measurement
of the Higgs
Mass
J. Ellis,
HERA-LHC
Workshop
Higher symmetries (e.g. Supersymmetry) lead to existence of several scalar,
neutral, Higgs states, H, h, A . . . . Higgs Hunter Guide, Gunnion, Haber, Kane, Dawson
1990
In MSSM Higgs x-section are likely to be much enhanced as
compared to Standard Model
(tan large because MHiggs > 115 GeV)
CP violation is highly probable in MSSM
similar masses ~120 GeV
all three neutral Higgs bosons have
can ONLY be RESOLVED in DIFFRACTION
Ellis, Lee, Pilaftisis Phys Rev D, 70, 075010, (2004) , hep-ph/0502251
Correlation between transverse momenta of the tagged protons give a handle on the
CP-violation in the Higgs sector
Khoze, Martin, Ryskin, hep-ph 040178
Gluon density
Gluon density dominates F2 for x < 0.01
The behavior of the rise with Q2
  p ~ (W 2 )
*
tot ( Q
2
)
~ (1 / x)tot (Q
2
)
xg( x, m ) ~ (1 / x)
2
eff ( m 2 ( r ))
universal rate of rise
of all hadronic cross-sections
Smaller dipoles  steeper rise
Large spread of eff characteristic
for IP Dipole Models
GBW Model
r2
 qq ( x, r )   0 [1  exp( 
)]
4 R02
strong saturation
KT-IP Dipole Model
d qq ( x, r )
d 2b


2 2
 2  1  exp( 
r  s xg( x, C / r 2  Q02 )T (b)) 
23


less saturation
(due to charm)
Unintegrated Gluon Densities
Dipole Model
Exclusive Double Diffraction
f g ( x, x' , t , Qt , m )   (t )  Rg 

[ T (Qt , m )  xg( x, Qt2 )]
2
 ln Qt
 m 2  S (kt2 ) dkt2 kt /(m  kt )


T (Qt , m )  exp    2
zP
(
z
)
dz
gg
2 0
Qt
2

k
t


f g ( x1 , x1 ' , t , Qt , m )   (t ) f g ( x1 , x1 ' , t  0, Qt , m )
b(t )  exp( Bt / 2)
Note: xg(x,.) and Pgg drive the rise of F2 at HERA
and Gluon Luminosity decrease at LHC
Saturation Model
Predictions for Diffraction
Absorptive correction to F2
Example in Dipole Model
d
 2(1  exp(  / 2))     2 / 4  ....
2
d b
F2
~
-
Single inclusive
pure DGLAP
Diffraction
Fit to diffractive data using MRST Structure Functions
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
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
Feynman diagrams QCD amplitudes
0-cut
1-cut
2-cut
3-cut
J. Bartels
A. Sabio-Vera
H. K.
Probability of k-cut in HERA data
Dipole
Model

*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
Problem of DGLAP QCD fits to F2
CTEQ, MRST, …., IP-Dipole Model
xg( x, m02 ) ~ x  ,
 0
at small x
valence like gluon structure function ?
Remedy:
Absorptive corrections?
MRW
Different evolution?
BFKL,
CCSS, ABFT
dg ( x, m 2 )
dz
x 2
2

P
(
z
,
m
)
g
(
,m )
x z gg
d ln m 2
z
1
from Gavin Salam
at low x
LO DGLAP ---
BFKL
------
 s (m 2 )
xPgg ~
2C A
2
1
xPgg ~  
 x
4 ln 2
 s NC

Next to leading logs NLLx -----
- Paris2004
Ciafalloni, Colferai, Salam, Stasto
Similar results
by
Altarelli, Ball
Forte, Thorn
from Gavin Salam
- Paris 2004
Density profile
2 2
D
 s ( m 2 (r )) xg( x, m 2 (r ))T (b)
3
grows with diminishing x and r
approaches a constant value
Saturated State
- Color Glass Condensate
S – Matrix => interaction probability
Saturated state = high interaction probability
S2 => 0
multiple scattering

r2 
S  exp   D  

2 

2
S 2  e 1
rS - dipole size for
which proton consists
of one int. length
QS2  Saturation scale
= Density profile at the saturation radius rS
S = 0.25
S = 0.15
QS2 
2
rS2
Saturated state
is partially perturbative
cross-sectiom
exhibits the universal rate of
growth
(QS2 ) g 
NC 2
9
(QS ) q  (QS2 ) q
CF
4
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
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-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
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
Diffractive Signature
diff
Non-Diffraction
Nondiff
Diffraction
- Rapidity
uniform, uncorrelated particle emission along the
rapidity axis =>
probability to see a gap DY is ~ exp(-<n>DY)
<n> - average multiplicity per unit of rapidity
dN/ dM 2X ~ 1/ M 2X =>
dN/dlog M 2X ~ const
note : DY ~ log(W2 / M
2
X)
Slow Proton Frame
incoming virtual photon fluctuates into a quark-antiquark
pair which in turn emits a cascade-like cloud of gluons
 qq 
1
1

 10  1000 fm
DE m p x
Transverse size of the quark-antiquark cloud
is determined by r ~ 1/Q ~ 2 10-14cm/ Q (GeV)
σ
γp
tot
1
 2 ImAel (W 2 , t  0)
W
σ
γ* P
tot
4 π 2 αem
(W, Q ) 
 F2 (x, Q 2 )
2
Q
2
Rise of ptot with W is a measure of radiation intensity
Diffraction is similar to the elastic scattering:
replace the outgoing photon by the diffractive final state
r , J/ or X = two quarks