Deep Inelastic Scattering
José Repond
Argonne National Laboratory
CTEQ Summer School 2002, Madison, Wisconsin, June 2- 20, 2002
Introduction: What is Deep Inelastic Scattering?
Consider electron – proton scattering
Q2 = -q2 … mass of exchanged γ* squared
~ energy of photon in p rest mass
Probing the proton with a
wavelength or resolving power
γ*
λ = ħ/√Q2
e.g. Q2 = 10 5 GeV2: λ ~ 10-18 m or 10-3 ·Rp
Deep ≡ high resolving power ≡ high Q2
W2 = (P+q)2 … mass of scattering γ* and p
mass of hadronic final state X
Inelastic ≡ proton breaks up ≡ high W
June 2, 2002
J Repond - DIS
2
More variables…
s = (k + p)2 ~ 4EeEp …total center of mass energy squared
Consider elastic e – q scattering
with x the momentum fraction of the proton carried by the struck q
4- momentum of outgoing quark
mass of outgoing quark
xP+q
0 = (xP + q)2 ~ q2 + 2xP·q
x = Q2/2P·q … Bjorken x
y = P·q/P·k …Inelasticity
Fraction of k carried by the γ*
Related to scattering angle of e, q in their center of mass system
June 2, 2002
J Repond - DIS
3
Relations between variables…
e
Easy to show that…
e’(θ,E)
Q2 = sxy
W2 ≈ Q2(1-x)/x
At fixed center of mass energy s
only 2 independent
variables needed
Q2, x
x, y
W2, Q2
….
to describe inclusive deep inelastic scattering
June 2, 2002
J Repond - DIS
4
Introduction: History of Deep Inelastic Scattering
1911
1968
Rutherford
Elastic scattering of α – particles on atoms
Discovery of atomic nucleus
Size of nucleus 10-5 size of atom
SLAC-MIT
Deep inelastic scattering of e- of p, d
Observation of ~flat Q2 dependence of R= σinel/σMott
R can be interpreted as form factor
(describing form of scatterer)
R~const → pointlike scatterers inside proton
Partons later identified with quarks
June 2, 2002
J Repond - DIS
5
1973
Gargamelle (Bubble chamber at CERN)
Observation of ÷ö + N ! ÷ö + hadr ons
With no outgoing μ!!!
ν
ν
Z0
p
hadrons
Distance in detector
Discovery of neutral current interactions
(mediated by Z0 boson)
June 2, 2002
J Repond - DIS
6
1988
European Muon Collaboration
Scattering of
~!
ö
~+ N
at CERN
ö+ X
Study of spin asymmetries
R p
g1 (x)dx = 0:123 æ0:013 æ0:019
Integral of spin structure function g_1 related to
contributions of quarks to p spin
Î = É u + É d + É s = 0:12 æ0:16
(Expected Σ =1 from valence quarks)
Contribution of quarks to p spin small
June 2, 2002
J Repond - DIS
7
Introduction: The HERA Collider
First and only ep collider
√s = 318 GeV
e±
27.5 GeV
p
920 GeV
Equivalent to fixed target experiment with 50.6 TeV e±
Located in Hamburg (Germany)
June 2, 2002
J Repond - DIS
8
World’s most complicated collider
Two independent storage rings
H1 – ZEUS
H1
Colliding beam experiments
HERA-B
HERMES
Uses p beam on wire target
Goal: B - physics
HERA-B
HERMES
ZEUS
June 2, 2002
J Repond - DIS
Uses e± beam on gas jet target
Both lepton and target polarized
Measurement of polarized
structure functions
9
HERA Performance and Future
Commissioned in 1992
Ran almost continuously until 2000
Performance improved over years
Delivered
Total
R
Ldt = 27pb à 1(elect r ons)
R
L dt = 166pb à 1(posit r ons)
R
L dt = 193pb à 1
Shutdown in September 2000
Insertion of quadropoles close to IR
→ Increase of Luminosity by a factor of 5
Insertion of spin rotators around H1-ZEUS
→ Longitudinally polarized e±
June 2, 2002
J Repond - DIS
HERA II Program
To be completed by 2006/7
Expect
R
Ldt ø 1fb à 1
10
Introduction: The Collider Experiments
H1 Detector
Complete 4π detector with
Tracking
Si-μVTX
Central drift chamber
Liquid Ar calorimeter
î E=E = 12%=
p
î E=E = 50%=
p
E[GeV ] (e:m:)
E[GeV ] (had)
Rear Pb-scintillator calorimeter
î E=E = 7:5%=
p
E[GeV ] (e:m:)
μ chambers
and much more…
June 2, 2002
J Repond - DIS
11
ZEUS Detector
Complete 4π detector with
Tracking
Si-μVTX
Central drift chamber
Uranium-Scintillator calorimeter
î E=E = 18%=
î E=E = 35%=
p
p
E[GeV ] (e:m:)
E[GeV ] (had)
μ chambers
and much more…
Both detectors asymmetric
June 2, 2002
J Repond - DIS
12
Introduction: Physics Processes
Neutral Current Interactions
e’
e
γ, Z0
Photoproduction
Q2
~0
GeV2
q
(real γ)
q’
Deep Inelastic Scattering
e
e’
p
Q2 ≥ 4 GeV2 (virtual γ*, Z0)
e’
e
p
pT of events balanced
June 2, 2002
J Repond - DIS
13
Charged Current Interactions
ν
e
ν
W±
e
q
p
q’
pT of events not balanced
Inclusive scattering described by 2 variables
e.g. x, Q2
e
e’(θ,E)
Details of hadronic final state ignored
Charged current kinematics reconstructed
with hadronic final state
June 2, 2002
J Repond - DIS
14
Studies of Hadronic Final State in DIS
Multi-jet Production in NC events
Boson-gluon Fusion
e’
e
γ, Z0
QCD Compton
e’
e
αS
γ, Z0
Need additional variables
to describe events
g
g
e.g. NJet, ηJet, pTJet…
Thrust, Sphericity…
Ncharged tracks, Nπ…
Processes in Leading – Order in αS
June 2, 2002
J Repond - DIS
15
Diffractive events
e
e’
γ, Z0
e
p
p
p
Gap in rapidity η
Color neutral exchange: P or 2 gluons
Approximately 10% of the events
Proton stays intact
Additional variables:
June 2, 2002
xP, ηmax, β…
J Repond - DIS
16
Kinematic Regions of DIS
Reaching values of Q2 > 104 GeV2
Kinematic limit
defined by
Q2 = sxy
sHERA = 100000 GeV2
Previous fixed target experiments
Reaching values of x < 10-6
HERA: extension by several orders of magnitude
June 2, 2002
J Repond - DIS
17
Outline of Lectures
Exclusive measurements
Inclusive measurements
Total γp cross section
Neutral current scattering
Structure function F2
Interpretations
Extraction of parton densities
Measurements of FL
Measurement of xF3
Valence quarks
Contributions of charm to F2
Charged current scattering
Jet production
Jets in DIS
Extraction of αS
Jets in photoproduction
Heavy flavor production
Charm production cross sections
Interpretations
Charm fragmentation
Beauty production cross sections
J/ψ production cross sections
Diffraction
Rate of inclusive diffraction
Interpretations
Vector-meson production
Outlook and conclusions
Exotic searches
June 2, 2002
Polarized structure functions
Leptoquarks, SUSY signatures, Contact Interactions…
J Repond - DIS
18
Total γP cross section
Most fundamental measurement at HERA
Consider e± as source of (real ) photons
Inclusive measurement with only 1 variable
WγP … center of mass of γ and proton
p
= E eE p y
or
y = 1 à E e0=E e … Inelasticity
June 2, 2002
J Repond - DIS
19
Measurement
dû ep
t ot (y)
dy
=
Tag events at low Q2 < 0.02 GeV2
with e± tagger at 35 m from IP
e’
N e(y)
LA e
Reconstruct
W from Ee’
35 m
Bethe-Heitler Bremsstrahlungs process
ep → eγp
Require O(1GeV) in calorimeter
Count events Ne(y)
105 m
γ
γ tagger
Count events Nγ
L=
Nн
û B H áA н
= 49:26 æ0:54
(syst) nb-1
Acceptance: real challenge!
Can be calculated with high accuracy
June 2, 2002
J Repond - DIS
20
Acceptance Ae = A35m ACAL
Major uncertainty of measurement!
Reliably calculable for 12 < Ee’ < 16 GeV
corresponds to
Requires simulation of all physics processes
0.56 > y > 0.42
225 > W > 194 GeV
or
Fraction determined
in separate measurements
in fits to detector observables
June 2, 2002
J Repond - DIS
21
Extraction of γP Cross Section
Measurement of
How to extract σγP(W) ???
Equivalent Photon Approximation relates the two
Qmin … minimum Q given by finite e± mass
σT … cross section for transversely polarized γ
σL … cross section for longitudinally polarized γ
→ expected to be very small
Integration over Q2
Qmax … maximum Q defined by experimental conditions
Photon flux factor fγ(y)
June 2, 2002
J Repond - DIS
22
Result
ûí p(W = 209GeV ) = 174 æ1(st at ) æ13(syst )öb
Rise parameterized as sα
with
α = 0.08
Same value as in pp, pp, πp, Kp
γp scattering behaves like
hadron-hadron scattering
At low Q2: γ is just a hadron
June 2, 2002
J Repond - DIS
23
Proton Structure Function from NC DIS
Lμν
Cross section calculated as convolution of
Lepton tensor
calculable in QED
Wμν Hadron tensor
contains 3 ‘a priori’ unknown
Coupling
Propagator
structure functions Fi
Helicity structure: Jz= 0 → 1
1 → (1 - y)2
F2 … Parity conserving structure function (γ and Z0 exchange plus interference)
FL … Longitudinal structure function (exchange of longitudinally polarized γ/Z0)
xF3 … Parity violating structure function (pure Z0 exchange and interference)
June 2, 2002
J Repond - DIS
24
Measurement of F2(x,Q2)
For Q2 « MZ2 → xF3 negligible
FL only important at high y
Both FL and xF3 ~ calculable in QCD
Correct for higher order QED radiation
Extract F2(x,Q2) from measurement of
d 2 û ep
dxdQ 2
Difficult measurements:
Nevertheless high precision: errors of 2-3%
June 2, 2002
J Repond - DIS
25
June 2, 2002
J Repond - DIS
26
Scaling and its violations
(non) – dependence on Q2
Elastic scattering off pointlike
and free partons
→ does not depend on Q2
‘a point is a point’
Scaling
violations
Scaling
Result of emission of gluons
from partons inside proton
Scaling
violations
Depletion at high x
→ quarks emit gluons
Increase at low x
→ quarks having emitted gluons
Effect increases with αslog Q2
June 2, 2002
J Repond - DIS
27
Interpretation: DGLAP evolution
F2(x,Q2) can in principle be calculated on the Lattice
→ Some results emerged in the last few years
Standard analysis assumes that F2(x,Q2) not calculable
However: evolution with Q2 calculable in pQCD
Dokshitzer, Gribov, Lipatov, Altarelli, Parisi (DGLAP):
Parton Density Functions (PDFs)
qi(x,Q2) … Density of quark i at given x, Q2
g(x,Q2) … Density of gluons at given x, Q2
Quark-Parton Model (QPM)
Pij(x/z) … Splitting functions
…in DIS scheme
June 2, 2002
J Repond - DIS
28
Splitting Functions Pij(z)
Probability of parton i going into parton j with momentum fraction z
Pqq
Pqg
Pgq
Pgg
Calculable in pQCD as expansions in αS
In Leading Order Pij(z) take simple forms
June 2, 2002
J Repond - DIS
29
Fit to DGLAP equations
I) Rewrite DGLAP equations
a) Simplify notation
i)
ii)
b) Sum i) over q and q separately
ia)
ib)
Nf … number of flavors
← u,u,d
c) Define: Valence quark density
Singlet quark density
June 2, 2002
J Repond - DIS
30
d) Rewrite DGLAP equations
Valence quark density decouples from g(x,Q2)
Only evolves via gluon emission depending on Pqq
II) DGLAP equations govern evolution with Q2
Do not predict x dependence:
Parameterize x-dependence at a given Q2 = Q20 = 4 – 7 GeV2
55 parameters
Low x behaviour
June 2, 2002
High x behaviour: valence quarks
J Repond - DIS
31
III) Sum rules and simplifying assumptions
Valence distributions
2 valence up-quarks
1 valence down quarks
Symmetric sea
Treatment of heavy flavors
Below mHF:
(different treatments available…)
Above mHF: generate
dynamically via DGLAP evolution
Momentum sum rule: proton momentum conserved
Effect number of parameters:
55 (parameters) – 3 (sum rules) – 13 (symmetric sea) – 22(heavy flavors) = 17
Difficult fits, involving different data sets with systematic errors…
June 2, 2002
J Repond - DIS
32
Several groups perform global fits
CTEQ: currently CTEQ6
MRS: currently MRST2001
GRV: currently GRV98
Experiments: H1, ZEUS
Overall good agreement between fits
Despite some differenent assumptions
Results of fits I
June 2, 2002
Fit quality: excellent everywhere!
→ no significant deviations
Evolution with Q2: 5 orders of magnitude
QCDs greatest success!!!
No deviations at high Q2:
→ no new physics:
no contact interactions
no leptoquarks
Fit includes data with low Q2: αS(Q2) large
→ surprise
J Repond
- DIS to work only for Q2 ≥ 10 GeV2
→ expected
33
Results of fits II
Gluon density
Quark and gluon densities
Inferred from QCD fit
not probed directly by γ
Errors of order 4% at Q2 = 200 GeV2
CTEQ6
Valence quarks
Strong coupling constant
Based on NLO pQCD
including terms of αS2
Scale error reduced with NNLO
not yet available
June 2, 2002
J Repond - DIS
34
Universality of Parton Density Functions
Determined with DIS data and pQCD fits
Can now be used to calculate any process involving protons
W± Production at the Tevatron
Higgs production at LHC
Jet production at HERA
June 2, 2002
J Repond - DIS
And yet
another
success
of
pQCD…
35
Other interpretations
DGLAP formalism
Standard approach: Equations to NLO
Include all terms O(αS2)
Calculation of NNLO corrections
First results by the MRST group
Effects seem small, but will reduce uncertainties
Collinear Factorization
DGLAP also resums terms proportional (αS log Q2)n
corresponds to gluon ladder with kT ordered gluons
kT,n >> kT,n-1 … >> kT,0
struck parton collinear with incoming proton
Does not resum terms proportional to (αS log 1/x)n
→ Is this ok at small x?
June 2, 2002
J Repond - DIS
36
BFKL formalism
Q2
Y Balitskii, V Fadin, L Lipatov, E Kuraev
Resums terms proportional to (αs log 1/x)n
gluons in ladder not kT ordered, but ordered in x
x1 >> x2 … >> xn
Predicts x, but not Q2 dependence
kT Factorization
results in kT unintegrated gluon distributions g(x,kT2,Q2)
DGLAP
CCFM
BFKL
CCFM formalism
x
S Catani, M Ciafaloni, F Fiorani, G Marchesini
Resums terms proportional to (αs log 1/x)n and (αs log 1/(1-x))n
gluons in ladder now ordered in angle
Low x: approaches BFKL
High x: approaches DGLAP
kT Factorization
results in kT unintegrated gluon distributions g(x,kT2,Q2)
Easier to implement in MC programs, e.g. CASCADE
June 2, 2002
J Repond - DIS
37
Asymmetric sea
FNAL fixed target experiment E-866
Measurement of Drell-Yan production with H2 and D2 targets
p N →μ+ μ- X
…with x = x1 – x2
Sea not flavor symmetric!!!
Explanations: Meson clouds
Chiral model
Instantons
More data to come: P-906 at the Main Injector
June 2, 2002
J Repond - DIS
38
Longitudinal Structure Function FL from NC DIS
…ignore xF3 at lower Q2
Disentangle F2(x,Q2) and FL(x,Q2)
Need to vary y, keeping x, Q2 fixed
→ vary s
lower Ep to say 920 → 450 GeV
Involves large effort
- Machine tuning
- Detector acceptance for lower Ee’
- Large statistics needed
Not yet done at HERA
June 2, 2002
J Repond - DIS
39
H1 Analysis
Determine PDFs using only low y data
contribution from FL negligible
Evolve PDFs to high y region according to DGLAP equations
Subtract prediction of F2 from measurements at high y → FL
Yellow line:
Result of DGLAP fit including FL
Points:
Subtraction technique
ZEUS:
No comparable analysis
Circularity?
At small x:
Fit at low y already determines FL
June 2, 2002
J Repond - DIS
40
Low Energy Results
Data from SLAC and CERN
Electron/μ scattering on fixed targets with different beam energies
Measurement of R(x,Q2)
Ratio of longitudinal and transverse cross section
June 2, 2002
J Repond - DIS
41
Measurements at high x > 0.1
but low Q2 < 80 GeV2
Curves
Rfit … fit to empirical function
RQCD … prediction based on
PDFs from F2data
RQCD+TM … same as above, corrected
for target mass effects
Differences between data and QCD
higher twist effects?
decrease as 1/Q2
g
Important to measure at HERA!!!
June 2, 2002
J Repond - DIS
42
xF3 Structure Function from NC DIS
Cross section for scattering of Left, Right – handed electrons
FL(x,Q^2) … ignored (small at high Q2)
Parity conserving
Parity violating
… sum over all q and q
…sum over the 2 valence distributions
At high Q2: weak terms non-negligible
electromagnetic
June 2, 2002
interference
pure weak
interference
J Repond - DIS
pure weak
43
Up to now: no longitudinal polarization for H1/ZEUS
→ How to measure xF3(x,Q2) ???
Consider Parity and CP Operations
on e-L
on xF3
P
e-R
-xF3
CP
e+R
xF3
P(CP)
e+L
-xF3
Operation
CP conserved in DIS
xF3(x,Q2) can be measured using difference of
Clear difference at high Q2
June 2, 2002
J Repond - DIS
44
First measurement on proton
No nuclear corrections
Agrees with expectations
based on PDFs from F2 fits
Clearly needs more statistics
→ HERA II program
June 2, 2002
J Repond - DIS
45
Charm contribution to F2
Events with charm identified through
Identify e± with dE/dx of central
drift chamber
Mass plot of Δm = m(Kππ) – m(Kπ)
Sharp peak at Δm = mD* - mD = 145 MeV
June 2, 2002
J Repond - DIS
46
Charm production mechanisms
Variable Flavor Number Scheme VFNS
- Charm treated as extra flavor c(x,Q2) in proton (mass ignored)
- c(x,Q2) assumed to be zero for scales μ < mc
- c(x,Q2) evolved to higher scales using DGLAP
→ this also resums (log(Q/mc)2)n
- Expect good description at large Q2 where log’s might be large
- Expect problems at Q ~ mc
γ, Z0
γ, Z0
c
Fixed Flavor Number Scheme FFNS
c
c
g
- no heavy quarks inside proton, only u, d, s quarks
- Charm produced via Boson-gluon fusion process (including masses)
- Expect good description for μ ~ mc
- Expect problems at large Q2, since log’s not resummed
Mixed Flavor Scheme MFS
- Uses best of both
June 2, 2002
J Repond - DIS
47
Determination of F2c(x,Q2)
Charmed production measured in limited phase space
e.g.
1.5 < pT(D*) < 15 GeV
|η(D*)| < 1.5
Extrapolation to full (pT,η) phase space
model dependent!
ignored
Nice agreement with FFNS
based on xg(x) from F2 fits
June 2, 2002
J Repond - DIS
48
Comparison of Schemes
Some differences at 3 < Q2 < 32 GeV2
FFNS
VFNS
VFNS
Data can not distinguish
→ HERA II
Agreement between schemes at large Q2
→ (log(Q/mc)2)n not important?
Plots from A Chuvakin, B Harris and J Smith
June 2, 2002
J Repond - DIS
49
Charm Fraction of Inclusive F2
Fraction increases with increasing Q2
→ as large as 30% !!!
Reproduced by FFNS calculations based
on xg(x,Q2) from fits to inclusive F2
June 2, 2002
J Repond - DIS
50
e
Charged Current DIS
ν
W±
q
…ignore FL and xF3
λ = ± 1 for left/right handed
q’
e-
Coupling
NC
CC
Approximately the same
Unification of Electromagnetic and weak forces!!!
Propagator
NC
CC
June 2, 2002
For Q2 > MW:
Same propagator!!!
J Repond - DIS
Suppression at low Q2
51
Structure Function F2(x,Q2)
Dominated
by flavor
symmetric
sea
NC
CC
e- p
W- couples to
e+p
W+ couples to
Difference due to valence quarks
2u quarks versus 1d quark
(1-y)2 suppression
June 2, 2002
J Repond - DIS
52
Flavor decomposition of proton
Use different angular dependence of valence and sea quarks
both electron and positron data
F2CC
Clearly need more data
→ HERA II
June 2, 2002
J Repond - DIS
53
Outlook
HERA I Program
R
L dt = 193pb à 1
Completed in September 2000
Shutdown period
September 2001 – September 2001
New quadrupoles close to interaction region
→ increase of luminosity by factor ~5
Sokolov-Ternow Effect
→ Polarization build-up
through emission of
synchrotron radiation
Spin rotators around H1/ZEUS
→ rotate transverse spin into longitudinal
ZEUS upgrades
→ new μVTX detector
→ new forward tracker
June 2, 2002
J Repond - DIS
54
HERA II Program
R
L dt = 1000pb à 1 = 1fb à 1
Completed by 2006/7
High precision F2(x,Q2) data
→ up to x = 0.65
→ up to Q2 of 40000 GeV2
Further constraints on PDFs
Δ[xg]/xg ≤ 3%
Determination of αs(MZ) to < 2%
(with NNLO formalism)
Charged current interactions
Disentangle flavor content of p
Search for deviations
Discovery or stringent limits
Leptoquarks
SUSY
Contact Interactions
Flavor changing NC
Excited fermions
…..
June 2, 2002
J Repond - DIS
55
Conclusions
Historically DIS has been a powerful for new discoveries
HERA has extended the reach in x, Q2
Precision measurements available from HERA I
Strong constraints on parton density functions
Tests of QCD over large kinematic range
Confrontation with different theoretical approaches
HERA II to start anytime now
Improved precision at very high Q2
June 2, 2002
J Repond - DIS
56