Diffraction:An Diffraction:An Experimental Perspective PerspectiveDiffraction:An Diffraction:An Experimental Perspective Perspective

Andrew BrandtUniversity of Texas, Arlington

CTEQ Summer SchoolJune 3,4 2002Madision, WI

Jet

Protonremnant

p

p

spectator partons

What Is Diffraction?What Is Diffraction?

• Diffraction in high energy hadron physics encompasses those phenomena in which no quantum numbers are exchanged between interacting particles– Diffused particles have same quantum numbers as

incident particles

• Exchanging quanta of the vacuum is synonymous with the exchanging of a Pomeron – Named after Russian physicist I.Y. Pomeranchuk

– Virtual (pseudo) particle carries no charge, isospin, baryon number or color

– Couples through internal structure

• Can be studied in occur in p-p, p-p, and e-p collisions

60’s: First evidence for hadronic diffraction, S matrix

Regge theory, Pomeron

70’s: DIS, High pT processes. Parton model, QCD,

c, τ, b, gluon

80’s: Ingelman-Schlein, BFKL

90’s: Hard Diffraction (UA8), Rapidity Gaps (Bjorken), HERA (diffraction in ep), Tevatron

40 years of Diffraction40 years of Diffraction

OutlineOutlineOutlineOutline

• Diffraction

• Regge Theory

• Ingelman-Schlein Model

• Hard Diffraction (UA8)

• BFKL Theory

• HERA

• Color Evaporation

• Tevatron

• Future

Elastic ScatteringElastic Scattering

• The particles after diffraction are the same as the incident particles

• The cross section can be written as:

• This has the same form as light diffracting from a small absorbing disk, hence the name diffractive phenomena

A

B*

P

B

B*

A*

** BABA

2

0

)(1

pbe

dtd

dtd bt

t

A*

Add risto’s elastic scattering here

Soft Single DiffractionSoft Single Diffraction

• One particle continues intact while the other becomes excited and breaks apart

AA*

P

B

A*

X

XABA *

Rapidity Gap

Experimentally, can tag outgoing beam particle or rapidity gap as signature of diffraction

Mandelstam VariablesMandelstam Variables

• For we can use two scalar variables to describe the reaction, k (CM momentum) and (CM scattering angle),or

• This describes an s-channel reaction where s is the squared total CM energy and t is minus the squared momentum transfer

• Applying relativistic invariance and crossing (Pomeranchuk theorem) we can consider an incoming particle of momentum p as an outgoing antiparticle of momentum –p and vice versa to give:

2

22*

22*

222

4

)cos1(2)(

)cos1(2)(

)(4)(

muts

kppu

kppt

mkpps

BA

AA

BA

)(*)(*)()( ** BABA pBpApBpA

channel)-u (crossed )(*)()(*)(

channel)- t(crossed )(*)()(*)(

**

**

ABBA

BBAA

pApBpBpA

pBpBpApA

Regge Theory (pre QCD)Regge Theory (pre QCD)• A Reggeon is a pole in the partial wave in the t-

channel of the scattering process in the complex angular momentum plane. The amplitude can be written as:

• The theory hypothesizes that fl(t) has a pole of the form

• The function R(t) is the Reggeon trajectory and has experimental form

• The trajectories correspond to “particles” :

0

)(cos)12)(()(l

lll Pltftf

)(1

)()()( 21

t

tgtgtf

Rl

tt RRR )0(')0()(

(Pion) 9.0)(

(Reggeon) 5.0)(

(Pomeron) )('1)(

tt

tt

ttt

R

PP

• At high energy, the asymptotic scattering amplitude becomes

• This has the important property that at t = mR2

where mR is the mass of resonance with spin j

(j = R(t = mR2)) this formula describes the

exchange of the resonance, namely

• The theory predicts (after applying the optical theorem) a cross section of the form

• Where X corresponds to Pomeron exchange and Y corresponds to other Hadron exchange and are found through fits to the data. At high energy, the Pomeron dominates

)(sin

)(),(

)()(

21 t

ssggtsA

R

tt

R

RR

tm

sggmtsA

R

j

RR

2212 ),(

45.08.01)0(1)0( YsXsYsXs RPTOT

Regge Theory II (pre QCD)Regge Theory II (pre QCD)

Here are 4 slides from coxNeed I-s reference

Ingelman-Schlein ModelIngelman-Schlein ModelG. Ingelman and P. Schlein, Phys. Lett. B 152, 256 (1985)

• This model is an attempt to blend Regge phenomenology with QCD

• Applying perturbative QCD tools, propose the cross section for diffractive hard scattering can be factorized as:

• The first term is the flux factor or the structure function of the Pomeron in particle A while the second is the cross section of the Pomeron interacting with particle B to give X

• The important variables are, = 1 – pA/pA* , the momentum fraction of hadron A taken by the Pomeron (diffraction dominates for < 0.05) and t, the standard momentum transfer. MX for the resultant system is given by

)(),()(

/

2

XPBtFdtd

AXABdAP

s

Ingelman-Schlein IIIngelman-Schlein II

• The flux factor term has been found by Donnachie and Landshoff after comparison to global data to be

• The remaining cross-section can be found from standard factorization processes to be

• The only unknown is the structure function of parton a (with momentum fraction ) in the Pomeron so measurements of the cross section allow us to probe this structure function

t..α(t)

ttm

tmtF

o

topP

250081

Coupling)Quark -(Pomeron GeV 5.3

71.014

8.24

4

9),(

2-2

2

22

2)(21

2

2

/

)(ˆ)(

)()(

/

/

Xabxf

fdxdXPB

bBb

abPab

Ingelman-Schlein IIIIngelman-Schlein III

• The factorization allows us to look at the diffractive reaction as a two step process. Hadron A emits a Pomeron then partons in the Pomeron interact with hadron B.

• The Pomeron to leading order is proposed to have a minimal structure of two gluons or two quarks of flavors similar to the proton in order to have quantum numbers of the vacuum

AA*

BJ1

J2

P

X

Ingelman-Schlein IVIngelman-Schlein IVIngelman-Schlein IVIngelman-Schlein IV

• The partonic structure of the Pomeron can be probed through hard diffractive reactions and a structure function can be proposed similar to that for a proton.– Inititially considered two possible gluon structure

functions:

– The momentum sum rule is used for normalization:

– Later extended to include other structures such as:

(quark) )1(4

6)(

gluon) hard-(super )1()(

/

g/P

Pqf

f

1

0

1)( df

gluon)(soft )1(6)(

gluon) (hard )1(6)(

/

/

Pg

Pg

f

f

Learning about the Pomeron Learning about the Pomeron

• QCD is theory of strong interactions, but 40% of total cross section is attributable to Pomeron exchange -- not calculable and poorly understood

• Does it have partonic structure? Soft? Hard? Quark? Gluon? Is it universal -- same in ep and ? Is it the same with and without jet production?

• Answer questions in HEP tradition -- collide it with something that you understand to learn its structure

• Note: variables of diffraction are t and ~ M2

with proton tagger measure

without, just measure

dtd

d 2

pp

7 UA8 slides go here

BFKL TheoryBFKL TheoryBFKL TheoryBFKL Theory

• Named after Balitsky, Fadin, Kuraev and Lipatov

• Proposes a more involved gluon structure of the Pomeron (higher order that Ingelman-Schlein)

• Basic Ingelman-Schlein proposes a two-quark structure which could be drawn as

AA*

BX

BFKL IIBFKL II

• Starting with the two reggeized gluons we can add perturbative corrections of real ladder gluons and virtual radiative gluons to get a gluon ladder

• Mathematically, each successive order of correction adds a power of log s to the perturbative expansion and at sufficient energies will “break” the perturbation

• BFKL Proposes to fix this by isolating in each order the contribution with the highest power of log s and resumming these leading terms (leading logarithmic approximation)

BFKL IIIBFKL IIIBFKL IIIBFKL III

• The ladders are resummed using an integral equation known as the BFKL equation. In the diffractive regime we can write by introducing a dependence on kT

• The resummed amplitude has a cut in the complex angular momentum plane which is called the perturbative or BFKL Pomeron

• The kT dependence causes a different jet topology than the Ingelman-Schlein model proposes which could in theory be probed in a collider.

• Due to infrared-safety considerations, current detectors may not be sensitive enough to see the small corrections predicted by BFKL theory

1s

Hera slides go here

Color EvaporationColor EvaporationColor EvaporationColor Evaporation

• This theory attempts to account for rapidity gaps in diffractive events without resorting to the use of a Pomeron

• Model has been successfully applied to onium production (charmonium, J/psi)

• Proposes that allowing soft color interactions can change the hadronization process such that color is bleached out and rapidity gaps appear

• This is a non-perturbative reaction

• The color topology of the event is changed

Color Evaporation IIColor Evaporation IIColor Evaporation IIColor Evaporation II

• Examples

Color Evaporation IIIColor Evaporation IIIColor Evaporation IIIColor Evaporation III

• This theory shows same exponential t-dependence as Ingelman-Schlein due to primordial kT of the partons

• Shows the same event characteristics as Ingelman-Schlein

• Suggests a formation rate of gaps in gluon-gluon sub processes which is less than or equal to the formation rate in quark-quark sub processes

• Gap fraction can be found through simple color counting and compared to data– D0 measured R = FGAP(630)/FGAP(1800) = 3.4

• Theory predicts 2.5 – CDF measured 2.0 0.9

• Theory predicts 2.0

EVENT TOPOLOGIES

Hard Single DiffractionHard Single DiffractionHard Single DiffractionHard Single Diffraction

• One particle continues intact while the other undergoes inelastic scattering with the Pomeron and breaks apart into a soft underlying event as well as some hard objects (jets, W/Z, J/or massive quarks)

AA*

P

B

A*

P

J1

J2

X

X

X

XJJABA 21*

Hard Double PomeronHard Double PomeronHard Double PomeronHard Double Pomeron

• Both particles continue intact while hard objects still appear in the detector (Pomeron undergoing inelastic scattering with another Pomeron)

AA*

P

B

A*

P

J1

J2

X

X

X

XJJBABA 21**

B*

B*

Pomeron Structure

1) UA8 shows partonic structure of pomeron (diffractive dijet production) consistent with hard structure (like gg or qq) and perhaps a super-hard component

2) HERA DIS with large gap shows a quark component in pomeron, F2

D shows pomeron dominantly gluonic

3) HERA diffractive jet and structure function analysis indicate dominantly hard gluonic structure

4) Observation of diffractive jets at 1800 (CDF, DØ) 630 (DØ) and diffractive W bosons (CDF) at ~ 1% level

Data samples are statistically limited, lack information on t dependence (and at Tevatron dependence)

Ingelman-Schlein VIngelman-Schlein VIngelman-Schlein VIngelman-Schlein V

• The different possible structure compositions can be probed through different hard diffractive interactions– Jet production probes the gluon structure

– W/Z production probes the quark structure (gluon coupling is suppressed on the order of the strong coupling constant)

• Experimental Probes of structure functions– UA8 (probes gluon content)

• Found ~57% hard, ~30% super-hard and ~13% soft

– HERA (probes quark content with virtual high-Q2 photons)

• Finds an effective structure function of the form:

• The first term is quark and the second is gluon using an s of 0.1

2/ )1(3)7/4(167/3 s

effpqf