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H. Jung, QCD & Collider Physics, Lecture 13 WS 05/06 1
QCD and Collider Physics: Diffraction II (and high density systems)
Resume from last lectureDiffraction
brief historical surveyrapidity gapsIngelman Schlein Model
Hard Diffractioncollinear factorisation in diffractive DIS2gluon exchange
http://wwwh1.desy.de/~jung/qcd_collider_physics_2005
H. Jung, QCD & Collider Physics, Lecture 13 WS 05/06 2
Rapidity and all that
Definition:
rewrite with mass terms:
for massless case define pseudo rapidity:
for
y =1
2log
E + pzE ¡ pz
=1
2log
p+
p¡
y =1
2log
E + pzE ¡ pz
=1
2log
(E + pz)2
m2 + p2t
´ = yjm=0 = logE + pzpt
= ¡ logµtan
µ
2
¶
ep! e0Xp0
t =¡x2IPm2 ¡ p2t1¡ xIP
xIP = 1¡p0+
p+
ykin = log2xIPEpm
H. Jung, QCD & Collider Physics, Lecture 13 WS 05/06 3
Rapidity and x define:
➔ with
➔
➔ problem for virtual particles:
➔ define:
k = (k+; k¡; kt)
= (x+p+; x¡p¡; kt)
k2 = 2k+k¡ ¡ k2t
k+k¡ < 0
y = logk+
kt
= logx+p+
kt= log x+ + log
p+
kty » log x+
y =1
2log
k+
k¡
=1
2log
2k+k+
k2 + k2?
4H. Jung, QCD & Collider Physics, Lecture 13 WS 05/06
Rapidity Gaps during Hadronizationassume a statistical distribution of particles, uniform in rapidity:
all correlations between particles are local in rapidity
➔ probability of rapidity gap of size is:
➔ coming from Poisson distribution ➔ Hadronization produces
exponentially suppressed rapgap distributions
¢´
P » e¡¢´
dN
d´» c
5H. Jung, QCD & Collider Physics, Lecture 13 WS 05/06
Rapidity Gap Events: measurementsdesy 94133
6H. Jung, QCD & Collider Physics, Lecture 13 WS 05/06
Diffraction: brief historical survey1960's
➔ slow energy increase of total xsection➔ shrinkage of the forward peak: increasing slope with energy➔ Pomeranchuk 1956/57
1970's➔ diffraction lost ground due to increasing interest in DIS and birth of QCD➔ moved from soft to hard pQCD processes
1980's➔ Donnachie/Landshoff parameterization of high energy xsections➔ pQCD picture of pomeron by 2gluon model of F.E.Low, S. Nussinov
(1975,1976) and BFKL et al➔ Ingelman/Schlein picture for jet production in diff. events
1990's➔ Diffractive physics at HERA and TeVatron➔ J.D. Bjorken pointed out rapidity gap events as a signature for diffraction➔ approaches beyond qualitative understanding of pomeron➔ development of color dipole approach➔ calculations in 2gluon approach➔ proof of factorization by J. Collins
Barone, Predazzi, high energy diffraction
7H. Jung, QCD & Collider Physics, Lecture 13 WS 05/06
Diffraction: brief historical survey1960's
➔ slow energy increase of total xsection
➔ shrinkage of the forward peak: increasing slope with energy
➔ Pomeranchuk 1956/57parametrisation of xsection (DonnachieLandshoff 1990 ff)
with
S. Eidelman et al., Phys. Lett. B592,1 (2004)
¾ » Xs² + Y s¡´
² » 0:095´ » 0:34
8H. Jung, QCD & Collider Physics, Lecture 13 WS 05/06
Diffraction: brief historical survey1960's
➔ slow energy increase of total xsection➔ shrinkage of the forward peak: increasing slope with energy➔ Pomeranchuk 1956/57
1970's➔ diffraction lost ground due to increasing interest in DIS and birth of QCD➔ moved from soft to hard pQCD processes➔ In a discussion session about on large Q2 and hadron structure at the
ECFA workshop (Proc. of the study of an ep facility for europe DESY 79/48) J. Ellis suggested:
“The most boring remark which I can think of is that in addition to doing scattering off a pion you can also do scattering off a pomeron, if anybody remembers, what the pomeron was” !!!!!
Barone, Predazzi, high energy diffraction
9H. Jung, QCD & Collider Physics, Lecture 13 WS 05/06
Why Diffraction ?Optics:
diffraction pattern: large forward (diffractive) peak and series of symmetric maxima and minima
with
elastic protonproton scattering:
I(µ)
I(µ = 0)=[2J1(x)]2
x2' 1¡ R20
4(kµ)2
x = kR0 sin µ ' kR0 µ
M. Arneodo, M. Diehl hepph/0511047 HERALHC proceedings
d¾dt (t)
d¾dt (t = 0)
' e¡bjtj ' 1¡ b (Pµ)2
10H. Jung, QCD & Collider Physics, Lecture 13 WS 05/06
Diffraction: brief historical survey1980's
➔ Donnachie/Landshoff parameterization of high energy xsections
➔ pQCD picture of pomeron by 2gluon model of F.E.Low, S. Nussinov (1975,1976) and BFKL et al
➔ Ingelman/Schlein picture for jet production in diffractive
events (Phys.Lett.B152:256,1985)
➔ Hard Processes in Diffraction !
Barone, Predazzi, high energy diffraction
UA8 Measurement, Phys.Lett.B211:239,1988
11H. Jung, QCD & Collider Physics, Lecture 13 WS 05/06
Single dissociation in pp
pp xsection:
extract pom flux:
d¾SD
dM 2dt
¯̄¯̄t=0
» 1
(M2)®IP (0)
Goulianos, Montanha hepph/9805496
f(xIP ; t) » x1¡2®IP (t)IP e¡B0jtj
12H. Jung, QCD & Collider Physics, Lecture 13 WS 05/06
Applying IS to diffractive DIS
Ingelman Schlein (IS) model for diffractive DIS
use hard processes as in nondiffractive DISuse diffractive PDFs (example pomeron flux and F2
pom)additional variables:
xIP¯ = xBj =Q2
2p:q
13H. Jung, QCD & Collider Physics, Lecture 13 WS 05/06
Rapidity Gap Events
Observation of Diffraction in DIS !
H1 Collaboration, desy 94133
14H. Jung, QCD & Collider Physics, Lecture 13 WS 05/06
In the early days....
from one of the early papers ...
it was not yet common folklore...
H1 Collaboration, desy 94133
15H. Jung, QCD & Collider Physics, Lecture 13 WS 05/06
Diffractive DIS
inclusive DIS cross section:
inclusive diffractive DIS cros section:
Ingelman Schlein ansatz:
FD(4)2 (¯;Q2; xIP ; t) = fp IP (xIP ; t)F
IP2 (¯;Q
2)
d4¾(ep! e0Xp0)dy dQ2 dxIP dt
=4¼®2
yQ4
µµ1¡ y + y2
2
¶FD(4)2 (x;Q2; xIP ; t)
¡y2
2FD(4)L (x;Q2;xIP ; t)
¶
d¾(ep! e0X)dy dQ2
=4¼®2
yQ4
µµ1¡ y + y2
2
¶F p2 (x;Q
2) ¡ y2
2F pL(x;Q
2)
¶
16H. Jung, QCD & Collider Physics, Lecture 13 WS 05/06
Frist Rapidity Gap Results
Investigate ratio of diffractive to nondiffractive DIS xsection Diffraction up to very large Q2
NOT a soft nonperturbatuive effect
H1 Collaboration, desy 94133
17H. Jung, QCD & Collider Physics, Lecture 13 WS 05/06
Measurement of diffractive structure function
observe diffractive behaviorextract parton densities
H1 Collaboration, desy 95036
18H. Jung, QCD & Collider Physics, Lecture 13 WS 05/06
Diffraction: brief historical survey1960's
➔ slow energy increase of total xsection➔ shrinkage of the forward peak: increasing slope with energy➔ Pomeranchuk 1956/57
1970's➔ diffraction lost ground due to increasing interest in DIS and birth of QCD➔ moved from soft to hard pQCD processes
1980's➔ Donnachie/Landshoff parameterization of high energy xsections➔ pQCD picture of pomeron by 2gluon model of F.E.Low, S. Nussinov
(1975,1976) and BFKL et al➔ Ingelman/Schlein picture for jet production in diff. events
1990's➔ Diffractive physics at HERA and TeVatron➔ J.D. Bjorken pointed out rapidity gap events as a signature for diffraction➔ approaches beyond qualitative understanding of pomeron➔ development of color dipole approach➔ proof of factorization by J. Collins➔ calculation in 2gluon approach
Barone, Predazzi, high energy diffraction
19H. Jung, QCD & Collider Physics, Lecture 13 WS 05/06
Factorization of Hard Diffraction
Factorization in hard diffraction (J. Collins Phys.Rev.D57:30513056,1998, Erratum
ibid.D61:019902,2000):
diffractive pdfs behave similar to usual pdfsno assumptions on Regge factorization
collinear factorizationDGLAP evolutionfor Q2 sufficently large, while are fixeduse full machinery of NLO DGLAP evolution...
d¾ =X
i
Zd»f
(D)i (»; xIP ; t;¹)d¾̂i+non¡ leading power of Q
xBj ; xIP ; t
20H. Jung, QCD & Collider Physics, Lecture 13 WS 05/06
Inclusive diffractive cross section
different measurementsdescribe it with DGLAP fit
Ingelman/Schlein ansatz stays in initial condition of diffractive pdfQ2 evolution starts from there....
d3¾
dxIP dx dQ2=4¼®2
xQ4
µ1¡ y + y2
2
¶¾D(3)r (xIP ; x;Q
2)
21H. Jung, QCD & Collider Physics, Lecture 13 WS 05/06
Comparison of F2D and F2
d¾ep!eXp
d¯ dQ2 dxIP dt=4¼®2em¯Q4
·³1¡ y + y2
2
´FD(4)2 (¯;Q2; xIP ; t)¡
y2
2FD(4)L (¯;Q2; xIP ; t)
¸;
22H. Jung, QCD & Collider Physics, Lecture 13 WS 05/06
Q2 dependence of F2D
Ratio of F2D/F2
no Q2 dependencenot suppressed with larger Q2
leading effect (leading twist)
desy 94133
23H. Jung, QCD & Collider Physics, Lecture 13 WS 05/06
Scaling violations in F2D
Observation of strong positive scaling violation ...Signature for hard pQCD process
24H. Jung, QCD & Collider Physics, Lecture 13 WS 05/06
Diffractive PDFs
FD(4)2 (¯;Q2; xIP ; t) =
X
i
Z 1
¯
dz
zCi³¯z
´fDi (z; xIP ; t;Q
2);
25H. Jung, QCD & Collider Physics, Lecture 13 WS 05/06
Diffractive Factorisation is broken
use diffractive pdf also for photo production dijetspredicted cross section ~ factor 2 too largesimilar effect seen in protonproton collisions
➔ factorization is broken