Diffraction:An Perspective Diffraction:An Experimental Perspective Andrew Brandt University of...
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Transcript of Diffraction:An Perspective Diffraction:An Experimental Perspective Andrew Brandt University of...
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
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*
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)
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
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
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 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
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