qcd and collider physicsh. jung, qcd & collider physics, lecture 13 ws 05/06 8 diffraction:...

$: QCD and Collider PhysicsH. Jung, QCD & Collider Physics, Lecture 13 WS 05/06 8 Diffraction: brief historical survey 1960's slow energy increase of total x section shrinkage of the$
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


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


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


Rapidity Gap Events: measurementsdesy 94133


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



➔ 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




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” !!!!!



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



➔ 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 !


UA8 Measurement, Phys.Lett.B211:239,1988


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


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


Rapidity Gap Events

Observation of Diffraction in DIS !

H1 Collaboration, desy 94133


In the early days....

from one of the early papers ...

it was not yet common folklore...



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)

¶


Frist Rapidity Gap Results

Investigate ratio of diffractive to nondiffractive DIS xsection Diffraction up to very large Q2

NOT a soft nonperturbatuive effect



Measurement of diffractive structure function

observe diffractive behaviorextract parton densities





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



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


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)


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)

¸;


Q2 dependence of F2D

Ratio of F2D/F2

no Q2 dependencenot suppressed with larger Q2

leading effect (leading twist)

desy 94133


Scaling violations in F2D

Observation of strong positive scaling violation ...Signature for hard pQCD process


Diffractive PDFs

FD(4)2 (¯;Q2; xIP ; t) =

X

i

Z 1

¯

dz

zCi³¯z

´fDi (z; xIP ; t;Q

2);


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

qcd and collider physicsh. jung, qcd & collider physics, lecture 13 ws 05/06 8 diffraction:...

Documents