Diffraction:An Experimental Perspective

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DiffractionAn Experimental Perspective

• Andrew Brandt
• University of Texas, Arlington

CTEQ Summer School June 3,4 2002 Madision, WI
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Proton remnant
spectator partons
p
?
?
Jet
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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

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40 years of Diffraction
60s First evidence for hadronic diffraction, S
matrix Regge theory, Pomeron
70s DIS, High pT processes. Parton model,
QCD, c, t, b, gluon
80s Ingelman-Schlein, BFKL
90s Hard Diffraction (UA8), Rapidity Gaps
(Bjorken), HERA (diffraction in ep), Tevatron
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Outline

• Diffraction
• Regge Theory
• Ingelman-Schlein Model
• Hard Diffraction (UA8)
• BFKL Theory
• HERA
• Color Evaporation
• Tevatron
• Future

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Elastic 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
A
P
B
B
B
f
A
h
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Add ristos elastic scattering here
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Soft Single Diffraction

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

A
A
P
X
B
Rapidity Gap
f
A
h
Experimentally, can tag outgoing beam particle or
rapidity gap as signature of diffraction
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Mandelstam Variables

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

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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 aR(t) is the Reggeon trajectory and
  has experimental form
• The trajectories correspond to particles

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Regge Theory II (pre QCD)

• 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 aR(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

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Here are 4 slides from cox Need I-s reference
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Ingelman-Schlein Model

• G. 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, x 1 pA/pA , the
  momentum fraction of hadron A taken by the
  Pomeron (diffraction dominates for x lt 0.05) and
  t, the standard momentum transfer. MX for the
  resultant system is given by

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Ingelman-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 b) in the
  Pomeron so measurements of the cross section
  allow us to probe this structure function

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Ingelman-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

A
A
P
J2
X
J1
B
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Ingelman-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

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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 x
  M2
• with proton tagger measure
• without, just measure s

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7 UA8 slides go here
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BFKL 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

A
A
X
B
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BFKL 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)

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BFKL 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

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Hera slides go here
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Color 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

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Color Evaporation II

• Examples

f
h
f
h
f
h
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Color 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 1.2
• Theory predicts 2.5 0.5
• CDF measured 2.0 0.9
• Theory predicts 2.0 0.4

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EVENT TOPOLOGIES
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Hard 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/y or
  massive quarks)

A
A
X
P
P
J2
B
X
X
J1
f
A
h
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Hard Double Pomeron

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

A
A
P
X
J2
P
X
X
J1
B
B
B
f
A
h
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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, F2D
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 x dependence)
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Ingelman-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 as of 0.1