Wesley Smith, U. Wisconsin SLAC Summer School, August, 1996
Outline: Outline:• Introduction
• HERA & ep scattering• Structure Functions
• Parton Model & Scaling Violation
• F2: Gluons, charm, total γ*P σ
• High Q2 NC & CC
• Jets• Deep Inelastic Scattering (DIS): αs
• Photoproduction
• resolved vs. direct• Diffraction
• Deep Inelastic Scattering
• structure of diffractive exchange• Photoproduction
• σ's & jets
• Vector mesons• Photoproduction & DIS
• Conclusions
QCD Studies in ep CollisionsWesley Smith, U. Wisconsin
Wesley Smith, U. Wisconsin SLAC Summer School, August, 1996
Acknowledgements
Appreciation for the help of many people from H1 and ZEUS:
(Advice, slides, etc.)
E. Barberis, V. Boudry, J. Bulmahn,A. Caldwell, R. Cross, J. Dainton, S. Dasu,
R. Eichler, L. Feld, C. Foudas, E. Gallo,G. Grindhammer,G. Iacobucci, S. Magill,
A. Mehta, S. Mattingly, S. Nam, P. Newman, A. Quadt, D. Reeder,
J. Repond, S. Ritz, R. Sacchi,F. Sciulli, B. Surrow, S. Tapprogge,
T. Trefzger, and many others.
Wesley Smith, U. Wisconsin SLAC Summer School, August, 1996
Collider:• √s= 300 GeV
• Equivalent to 47 TeV fixed target
Experiments:• 2 general purpose detectors (discussed):
• H1 & Zeus
• Dedicated Fixed Target (not discussed):• HERMES:
• Polarized electrons on polarized H target
• HERA-B• Proton Halo on wire target
H1
ZEUS
p
e
North Hall
South Hall
EastHall
HERMESHERA-B
WestHall
820 GeV p x 27 GeV e±
HERA
Wesley Smith, U. Wisconsin SLAC Summer School, August, 1996
Deep Inelastic Scattering
x = the fraction of the proton's momentum carried by the struck parton
y = the fraction of the electron's energy lost in the proton rest frame
s = (k + P)2 = center of mass energy
Q2 = -q2 = -(k-k')2 = (momentum transferred)2
Q2 = sxyy = P•qP•kx = Q2
2P•q
e±(k')e±(k)
(q)xP
p(P)
The DIS process
Measuring DIS at HERA:
electron (27 GeV) proton (820 GeV)
electron
jet
proton remnant
Forward Rear
beampipe
SLAC Summer School, August, 1996Wesley Smith, U. Wisconsin
electronDIS event Q2 = 1600 GeV2
Jet
Wesley Smith, U. Wisconsin SLAC Summer School, August, 1996
Photoproduction
photon remnant
Proton Remnant
Jet
Jet
electron goes down the
beampipe (low Q2)
photon remnant
q
q
q
q
Q2 < 4 GeV2
Almost real photon
θ > 170°
Jet
Jet
Proton RemnantProton Remnant
Direct: Resolved:
(Jet)
(Jet)
(Jet)
(Jet)(Jet)
γ γ
gg
(down beampipe)
(towards rear)
Background for DIS
SLAC Summer School, August, 1996Wesley Smith, U. Wisconsin
Photoproduction event
Calorimeter transverse
energy
Jet
Jet
Jet
φη
Wesley Smith, U. Wisconsin SLAC Summer School, August, 1996
Major background is beam-gas interactions:Background rejection
Incoming proton
Rear CALorimeterForward
CAL.Mimics electron
Mimics current jet
reject beam gas*vertex cut*timing σt ~ 1 ns
← Cal. timing
(E - Pz) is conservedInitially:EP - PP + Ee -(-Pe) = 2Eeremains same if no energydown rear beam pipe.
True for DISFalse for photoproduction
Wesley Smith, U. Wisconsin SLAC Summer School, August, 1996
DIS cross section
DIS differential cross section:
γ* is longitudinally or transversely polarized
F2(x,Q2) = Structure function = interaction btw. transversely polarized photons & spin 1/2 partons = charge weighted sum of the quark distributions.
FL(x,Q2) = Structure function = cross section due to longitudinally polarized photons that interact with the proton. The partons that interact have transverse momentum. (Important at high y).
F3(x,Q2) = Parity-violating structure function from Z0 exchange. (Important at high Q2).
e±(k')e±(k)
p(P)
α
α
γ∗(q)
JetJet
Y± = 1± (1− y)2
dσ NC (e± p)dxdQ2 = 2πα 2
xQ4 Y+ F2 − y2
Y+FL m
Y−
Y+xF3
Wesley Smith, U. Wisconsin SLAC Summer School, August, 1996
Kinematic Reconstruction
2 kinematic variables• x,Q2
4 measured quantities• Ee’,θe’,Eh,γh
Any 2 measured variables can be used to reconstruct x,Q2
• Reconstruction may not be optimal.
PT method
• Best performance for full kinematic range
• Uses (Ee’,θe’,Eh,γh ), E-Pz conservation, and PT balance between the electron and current jet
E’e,θ’e
Eh,γh
Wesley Smith, U. Wisconsin SLAC Summer School, August, 1996
Experiments - High Q2
←pe→
H1:
ZEUS:
e→ ←p
Wesley Smith, U. Wisconsin SLAC Summer School, August, 1996
Experiments - Low Q2
+e
BPC
Zeus Beampipe Calorimeter:
H1 & Zeus Shifted Vertex:
H1 & Zeus Initial State Radiation
Wesley Smith, U. Wisconsin SLAC Summer School, August, 1996
Experimental Kinematic Range
Wesley Smith, U. Wisconsin SLAC Summer School, August, 1996
Proton is made up of non-interacting partons.
Bjorken scaling, i.e., Q2 independence of structure functions holds. SLAC-MIT experiments obseved approximate scaling in data.
Structure function is given by the charge weighted sum of parton momentum densities
For spin-half partons
For spin-zero partons
The parton densities fi(x) are not calculable in the model and are to be derived from experiment.
Deep inelastic scattering provides a good laboratory for parton density extraction because the electromagnetic probe is well understood.
F2 (x) = ei2xf i (x)
i∑
FL = 0
FL = F2
Parton model
Wesley Smith, U. Wisconsin SLAC Summer School, August, 1996
α
α
αs
QCD Compton
γ∗
αsα
αγ∗
Boson-Gluon Fusion
electron
gluon
gluon
q
Quark transverse momentum from quark-gluon in-teractions causes scaling violation: F2(x) →F2(x,Q2).
Splitting functions, probablities for these interac-tions, are calculated in 2nd order perturbative QCD.
These interactions drive F2(x) to grow with decreasing x:
Scaling violations
electron
10-4
10-3
10-2
10-1
1
1
2
MRSD-
MRSD0
Q 2 = 25 GeV 2Q 2 = 25 GeV 2Q 2 = 25 GeV 2
ZEUS 1993
NMC
x
F2
P
small x
Wesley Smith, U. Wisconsin SLAC Summer School, August, 1996
Perturbative QCD
Dokshitzer-Gribov-Lipatov-Altarelli-Parisi equations describe evolution of parton densities to higher Q2
Next-to-leading order splitting functions, P, are now available.
The structure function F2 is given by,
Calculation of DIS cross section requires FL:
Parameterization of gluon density can be deter-mined by fitting QCD evolution to DIS data.
dqi (x,Q2 )
d lnQ2 = αs (Q2 )2π
dwwx
1∫ qi (w,Q2 )Pqq
xw
+ g(w,Q2 )Pqg
xw
dg(x,Q2 )d lnQ2 = αs (Q2 )
2πdwwx
1∫ qi (w,Q2 )
i∑ Pgq
xw
+ g(w,Q2 )Pgg
xw
F2 (x,Q2 ) = ei2xqi (x,Q2 )
i∑
FL (x,Q2 ) = αs (Q2 )π
dww
xw
2
x
1∫
43
F2 (w,Q2 ) + 2 ei2
i∑ 1− x
w
wg(w,Q2 )
Given an empirical parameterization for parton densities at Q2=Q0
2 ,e.g.:
xg(x) = Agxδg (1− x)
ηg (1+ γ gx)
Wesley Smith, U. Wisconsin SLAC Summer School, August, 1996
Expected low-x behavior of F2• Regge Approach
• Donnachie-Landshoff (DL)
• Martin-Roberts-Stirling (MRS)
• Assume g(x,Q02) ~ xγ1 & F2(x,Q0
2) ~ xγ2
• Evolve in Q2 according to QCD• Gluck-Reya-Vogt (GRV)
• Use "valence-like" distributions at low Q2
• Evolve in Q2 according to QCD
• Empically produces γ << -0.08
• Balitsky-Fadin-Kuraev-Lipatov (BFKL)• Summation of many QCD graphs in
powers of ln(1/x)
since :
but at
and at low
Therefore : lim
Q2
FQ
p
Q p C W
x WQ
xp C Q X
F x Q f Q x
2
2
2
2 2 0 08
22
2 0 08
02
2 2 0 08
4
0
=
= =
= → = ′
=
−
−
→
−
πασ γ
σ γ
σ γ
( * )
: ( * ) ( )
: ( * ) ( )
( , ) ( )
.
.
.
g x Q x s( , ) ~ln( )
~ .02 12 2
0 5γ γπ
α and = − −
Wesley Smith, U. Wisconsin SLAC Summer School, August, 1996
F2 Results Extraction:
• Bin data in x, Q2
• Subtract background
• Cross section multiplied by QCD FL
calculation using parameterizations of q(x,Q2) and G(x,Q2)
• Acceptance estimated from Monte Carlo
• F2 unfolded iteratively until MC matches data
• Estimate Systematic Error Issues:
• Does rise at low x continue?• Over what kinematic range is rise
observed?• Agreement with fixed target
experiments?
DGLAP describes down to x ~ 10-4, Q2 ~ 1.5 GeV2
No need to resum ln(1/x) terms (BFKL)
Scaling violations → Gluons
Overlap with FT: good agreement
Wesley Smith, U. Wisconsin SLAC Summer School, August, 1996
Scaling Violation - Gluon sensitivity
0.6
0.8
1
1.2
1.4
1.6
10 102
Q2
F2
ZEUS 1994, x = 0.0016
ZEUS 1993, x = 0.0016
0.6
0.8
1
1.2
1.4
1.6
10 102
Q2
F2
ZEUS 1994, x = 0.0025
ZEUS 1993, x = 0.0027
0.8
1
1.2
1.4
1.6
1.8
6 7 8 9 10 20Q2
F2
ZEUS 1994, x = 0.0004
ZEUS 1993, x = 0.00042
0.6
0.8
1
1.2
1.4
1.6
10 102
Q2
F2
ZEUS 1994, x = 0.004
ZEUS 1993, x = 0.0047
Sensitivity to the gluon distribution is in the slope of F2 versus logQ2 plots. 1994 and 1993 ZEUS F2 data is shown above. It is seen that 94 data constrains dF2/dlogQ2 with high precision.
Wesley Smith, U. Wisconsin SLAC Summer School, August, 1996
Example: fit to ZEUS 1994 F2 data:
• Used NMC data to constrain fit at larger values of x.
• Assumed momentum sum rule to constrain gluon density.
• Assumed quark and gluon density functional forms.
• Assumed (SLAC/BCDMS) αs(MZ2)=0.113
and evolved to higher Q2.• Evolved the distributions using GLAP
eq'ns to measured Q2 bins to calculate F2.• In computation of χ2 for agreement with
the fit only the statistical errors were included.
• Performed nonlinear minimization of χ2 to find fit parameters for assumed functional forms of quarks and gluons.
• Systematic uncertainty estimated separately by varying each of the 31 different systematic effects individually and performing a new fit.
Extraction of gluon density
Wesley Smith, U. Wisconsin SLAC Summer School, August, 1996
Gluon results
A significant improvement in the uncertainty and in the validity range in kinematic plane is seen in the gluon density extracted from the 1994 H1 and ZEUS DIS data. Agreement with 1993 extraction is remarkable.
H1 1994
ZEUS 1994 (preliminary)
H1 1993
ZEUS 1993
NMC
by A.Quadt
NLO QCD fit Q2 = 20 GeV2
x
x g(
x)
0
5
10
15
20
25
30
35
40
45
10-4
10-3
10-2
10-1
10
5
10
15
20
25
30
35
40
45
10-4
10-3
10-2
10-1
1
δg = 0.24 ± 0.02
Momentum sum @ Q2=7 GeV2
0.555 quarks + 0.445 gluons
Wesley Smith, U. Wisconsin SLAC Summer School, August, 1996
Impact of FL uncertainty (FL: 0 → F2) on F2 and dF2/dlnQ2
0
10
20
30
40
50
60
70
80
90
100
0 0.2 0.4 0.6 0.8 1y
(F2H
i - F 2Lo
) / F
2Lo (
%)
0
10
20
30
40
50
60
70
80
90
100
0 0.2 0.4 0.6 0.8 1y
|dF 2H
i - dF
2Lo| /
dF 2Lo
(%
)
Q2=5 GeV2
Q2=10
Q2=20
Q2=30
0
10
20
30
40
50
60
70
80
90
100
10-4
10-3
10-2
x
(F2H
i - F 2Lo
) / F
2Lo (
%)
Q2=5 GeV2
Q2=10
Q2=20
Q2=30
0
10
20
30
40
50
60
70
80
90
100
10-4
10-3
10-2
x
|dF 2H
i - dF
2Lo| /
dF 2Lo
(%
)
Q2=5 GeV2
Q2=10
Q2=20
Q2=30
Caveats on F2 & Gluons ZEUS F
2 extraction, as is true with most world F
2 data, involved
apriori assumptions for αs and quark-gluon parameterizations in
computing FL and F
3 corrections for DIS cross section.
The extracted F2 is sensitive to these assumptions, particularly
for high y kinematic range data, which is sensitive to the gluon. Therefore, an assumption independent analysis needs to be done by fitting directly to the cross section data.
The results of such analysis can yield consistent values for αs,
quark and gluon parameterizations.
Wesley Smith, U. Wisconsin SLAC Summer School, August, 1996
Analyze components of F2
• Identify Flavor in the final state• Justify NLO QCD assumptions• Further understand the rise in F2
Evolution of charm from the sea:• Boson Gluon Fusion:
• Small Contribution from framentation• Higher sensitivity to gluon density
than F2
Charm F2
-c
c
P
g
k
k'
γ
Wesley Smith, U. Wisconsin SLAC Summer School, August, 1996
Identifying open charm/D* signals
Mass(K,π)
D* → ( K π ) πS in DIS
0
10
20
30
40
50
60
1.4 1.6 1.8 2 2.2 2.4
GeV
Eve
nts
/ 20
MeV
Signal Region
Control Region
ZEUS 1994 Preliminary
Bck. Control Reg.
Bck. Side Band
Fit: Exp + Gauss
M(Do) = 1.859 ± 0.004 GeV
Delta M
0
20
40
60
80
100
135 140 145 150 155 160 165 170 175 180
MeV
Eve
nts
/ 1 M
eV Side BandsSignal Region Control Region
ZEUS 1994 Preliminary
Bck. Control Reg.
Fit: A ( x - mπ)B + Gauss
M(D*) - M(Do) = 145.57 ± 0.11 MeV
Wesley Smith, U. Wisconsin SLAC Summer School, August, 1996
H1 Result: