Deep Inelastic Scattering José Repond Argonne National Laboratory CTEQ Summer School 2002, Madison, Wisconsin, June 2- 20, 2002
Jan 06, 2018
Deep Inelastic Scattering
José RepondArgonne National Laboratory
CTEQ Summer School 2002, Madison, Wisconsin, June 2- 20, 2002
June 2, 2002 J Repond - DIS 2
Introduction: What is Deep Inelastic Scattering?
γ*
Q2 = -q2 … mass of exchanged γ* squared ~ energy of photon in p rest mass Probing the proton with a wavelength or resolving power λ = ħ/√Q2
e.g. Q2 = 10 5 GeV2: λ ~ 10-18 m or 10-3 ·Rp
Consider electron – proton scattering
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 3
More variables…
Consider elastic e – q scattering with x the momentum fraction of the proton carried by the struck q
4- momentum of outgoing quark xP+q mass of outgoing quark 0 = (xP + q)2 ~ q2 + 2xP·q
x = Q2/2P·q … Bjorken x
s = (k + p)2 ~ 4EeEp …total center of mass energy squared
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 4
Relations between variables…
Q2 = sxy
W2 ≈ Q2(1-x)/x
Easy to show that…
only 2 independent Q2, x variables needed x, y W2, Q2
….
At fixed center of mass energy s
to describe inclusive deep inelastic scattering
ee’(θ,E)
June 2, 2002 J Repond - DIS 5
Introduction: History of Deep Inelastic Scattering
1911 Rutherford Elastic scattering of α – particles on atoms Discovery of atomic nucleus Size of nucleus 10-5 size of atom
1968 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 6
1973 Gargamelle (Bubble chamber at CERN)
Observation of ÷ö + N ! ÷ö + hadrons
With no outgoing μ!!!
Discovery of neutral current interactions (mediated by Z0 boson)
Distance in detector
ν ν
p
hadrons
Z0
June 2, 2002 J Repond - DIS 7
1988 European Muon Collaboration at CERN
Scattering of
Study of spin asymmetries
Integral of spin structure function g_1 related to contributions of quarks to p spin
(Expected Σ =1 from valence quarks) Contribution of quarks to p spin small
ö~+ N~! ö + X
Rgp1(x)dx = 0:123æ0:013æ0:019
Î = É u + É d + É s = 0:12æ0:16
June 2, 2002 J Repond - DIS 8
Introduction: The HERA Collider
First and only ep collider e± p
27.5 GeV 920 GeV√s = 318 GeV
Equivalent to fixed target experiment with 50.6 TeV e±
Located in Hamburg (Germany)
June 2, 2002 J Repond - DIS 9
World’s most complicated collider
ZEUS
HERA-B
HERMES
H1H1 – ZEUS
Colliding beam experiments
HERA-B
Uses p beam on wire target Goal: B - physics
HERMES
Uses e± beam on gas jet target Both lepton and target polarized Measurement of polarized structure functions
Two independent storage rings
June 2, 2002 J Repond - DIS 10
HERA Performance and Future
Commissioned in 1992Ran almost continuously until 2000Performance improved over yearsDelivered
RLdt = 27pbà1(electrons)RLdt = 166pbà1(positrons)
Total RLdt = 193pbà1
Shutdown in September 2000Insertion of quadropoles close to IR → Increase of Luminosity by a factor of 5Insertion of spin rotators around H1-ZEUS → Longitudinally polarized e±
HERA II Program
To be completed by 2006/7Expect RLdt ø 1fbà1
June 2, 2002 J Repond - DIS 11
Introduction: The Collider Experiments
H1 DetectorComplete 4π detector with
Tracking Si-μVTX Central drift chamber
Liquid Ar calorimeter
Rear Pb-scintillator calorimeter
î E=E = 12%= E[GeV ]p
(e:m:)î E=E = 50%= E[GeV ]
p(had)
î E=E = 7:5%= E[GeV ]p
(e:m:)
μ chambers
and much more…
June 2, 2002 J Repond - DIS 12
ZEUS Detector
Complete 4π detector with
Tracking Si-μVTX Central drift chamber
Uranium-Scintillator calorimeter
î E=E = 18%= E[GeV ]p
(e:m:)î E=E = 35%= E[GeV ]
p(had)
μ chambers
and much more…Both detectors asymmetric
June 2, 2002 J Repond - DIS 13
Introduction: Physics Processes
Neutral Current Interactions e’e
γ, Z0
qq’
Photoproduction
Q2 ~ 0 GeV2 (real γ)
e p
Deep Inelastic Scattering
Q2 ≥ 4 GeV2 (virtual γ*, Z0)
pT of events balanced
e pe’
e’
June 2, 2002 J Repond - DIS 14
Charged Current Interactions
e p
pT of events not balanced
e
W±
qq’
ν
Inclusive scattering described by 2 variables e.g. x, Q2
Details of hadronic final state ignored Charged current kinematics reconstructed with hadronic final state
ν
ee’(θ,E)
June 2, 2002 J Repond - DIS 15
Studies of Hadronic Final State in DISMulti-jet Production in NC events
Processes in Leading – Order in αS
e
γ, Z0
g
e’e
γ, Z0
g
e’
αS
Boson-gluon Fusion QCD Compton
Need additional variables to describe events e.g. NJet, ηJet, pT
Jet… Thrust, Sphericity… Ncharged tracks, Nπ…
June 2, 2002 J Repond - DIS 16
Diffractive eventse
e p
Gap in rapidity η
e’
γ, Z0
p p
Color neutral exchange: P or 2 gluons
Proton stays intactApproximately 10% of the events
Additional variables: xP, ηmax, β…
June 2, 2002 J Repond - DIS 17
Kinematic Regions of DIS
Previous fixed target experiments
Reaching values of x < 10-6
Reaching values of Q2 > 104 GeV2
HERA: extension by several orders of magnitude
Kinematic limit defined by Q2 = sxysHERA = 100000 GeV2
June 2, 2002 J Repond - DIS 18
Outline of Lectures
Inclusive measurementsExclusive measurements
Total γp cross sectionNeutral 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 photoproductionHeavy flavor production Charm production cross sections Interpretations Charm fragmentation Beauty production cross sections J/ψ production cross sectionsDiffraction Rate of inclusive diffraction Interpretations Vector-meson production
Exotic searches Leptoquarks, SUSY signatures, Contact Interactions…
Outlook and conclusionsPolarized structure functions
June 2, 2002 J Repond - DIS 19
Total γP cross section
Most fundamental measurement at HERAConsider e± as source of (real ) photons Inclusive measurement with only 1 variable
WγP … center of mass of γ and proton
or
… Inelasticity
= E eE pyp
y = 1à E e0=E e
June 2, 2002 J Repond - DIS 20
Measurement
dydûep
tot(y) = LA eN e(y)
Tag events at low Q2 < 0.02 GeV2
with e± tagger at 35 m from IP
35 m
Require O(1GeV) in calorimeter
Count events Ne(y)
Bethe-Heitler Bremsstrahlungs process ep → eγp
105 m
e’
γ
Count events Nγ
(syst) nb-
1
L = ûB HáA íN í = 49:26æ0:54
Can be calculated with high accuracyAcceptance: real challenge!
Reconstruct W from Ee’
γ tagger
June 2, 2002 J Repond - DIS 21
Reliably calculable for 12 < Ee’ < 16 GeV corresponds to
0.56 > y > 0.42 or 225 > W > 194 GeV
Acceptance Ae = A35m ACAL
Requires simulation of all physics processes
Fraction determined
in separate measurements in fits to detector observables
Major uncertainty of measurement!
June 2, 2002 J Repond - DIS 22
Extraction of γP Cross SectionMeasurement of How to extract σγP(W) ???
Equivalent Photon Approximation relates the two
Qmax … maximum Q defined by experimental conditions
Qmin … minimum Q given by finite e± massσT … cross section for transversely polarized γσL … cross section for longitudinally polarized γ → expected to be very small
Integration over Q2
Photon flux factor fγ(y)
June 2, 2002 J Repond - DIS 23
Resultûí p(W = 209GeV ) = 174æ1(stat) 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 24
Proton Structure Function from NC DIS
Cross section calculated as convolution of Lμν Lepton tensor calculable in QED
Wμν Hadron tensor contains 3 ‘a priori’ unknown 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)
Coupling
Propagator
June 2, 2002 J Repond - DIS 25
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
Measurement of F2(x,Q2)
dxdQ2d2ûep
Difficult measurements:
Nevertheless high precision: errors of 2-3%
June 2, 2002 J Repond - DIS 26
June 2, 2002 J Repond - DIS 27
Scaling and its violations
Elastic scattering off pointlike and free partons → does not depend on Q2
‘a point is a point’
Scaling
Scaling violations
Scaling violations
Result of emission of gluons from partons inside proton
(non) – dependence on Q2
Depletion at high x → quarks emit gluonsIncrease at low x → quarks having emitted gluons
Effect increases with αslog Q2
June 2, 2002 J Repond - DIS 28
Interpretation: DGLAP evolutionF2(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 pQCDDokshitzer, 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
Pij(x/z) … Splitting functions
Quark-Parton Model (QPM)
…in DIS scheme
June 2, 2002 J Repond - DIS 29
Probability of parton i going into parton j with momentum fraction z
Calculable in pQCD as expansions in αS
In Leading Order Pij(z) take simple forms
Pqq Pqg Pgq Pgg
Splitting Functions Pij(z)
June 2, 2002 J Repond - DIS 30
b) Sum i) over q and q separately
Fit to DGLAP equations
c) Define: Valence quark density
Singlet quark density
I) Rewrite DGLAP equations
a) Simplify notation
Nf … number of flavors
i)
ii)
ia)
ib)
← u,u,d
June 2, 2002 J Repond - DIS 31
II) DGLAP equations govern evolution with Q2
Do not predict x dependence: Parameterize x-dependence at a given Q2 = Q2
0 = 4 – 7 GeV2
d) Rewrite DGLAP equations
Valence quark density decouples from g(x,Q2) Only evolves via gluon emission depending on Pqq
55 parameters
Low x behaviour High x behaviour: valence quarks
June 2, 2002 J Repond - DIS 32
III) Sum rules and simplifying assumptions
Valence distributions 2 valence up-quarks
1 valence down quarks
Symmetric sea
Treatment of heavy flavors (different treatments available…) Below mHF:
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 33
Results of fits I
Several groups perform global fits CTEQ: currently CTEQ6 MRS: currently MRST2001 GRV: currently GRV98 Experiments: H1, ZEUSOverall good agreement between fitsDespite some differenent assumptions
Fit quality: excellent everywhere! → no significant deviationsEvolution 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 → expected to work only for Q2 ≥ 10 GeV2
June 2, 2002 J Repond - DIS 34
Results of fits II
Quark and gluon densities
Valence quarks
Gluon density
Inferred from QCD fit not probed directly by γErrors of order 4% at Q2 = 200 GeV2
Strong coupling constant
Based on NLO pQCD including terms of αS
2
Scale error reduced with NNLO not yet available
CTEQ6
June 2, 2002 J Repond - DIS 35
Universality of Parton Density Functions
Determined with DIS data and pQCD fitsCan now be used to calculate any process involving protons
Higgs production at LHC
W± Production at the Tevatron
Jet production at HERAAnd yetanother success
of pQCD…
June 2, 2002 J Repond - DIS 36
Other interpretationsDGLAP formalism
Standard approach: Equations to NLO Include all terms O(αS
2) 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 37
BFKL formalism
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,kT
2,Q2)
Y Balitskii, V Fadin, L Lipatov, E Kuraev
CCFM formalism
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
kT Factorization results in kT unintegrated gluon distributions g(x,kT
2,Q2)
Easier to implement in MC programs, e.g. CASCADE
Low x: approaches BFKL
High x: approaches DGLAP
x
Q2
DGLAPCCFM
BFKL
June 2, 2002 J Repond - DIS 38
Asymmetric sea
Measurement of Drell-Yan production with H2 and D2 targets p N →μ+ μ- X
FNAL fixed target experiment E-866
…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 39
Longitudinal Structure Function FL from NC DIS
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
Disentangle F2(x,Q2) and FL(x,Q2)
…ignore xF3 at lower Q2
June 2, 2002 J Repond - DIS 40
H1 Analysis
Determine PDFs using only low y data contribution from FL negligibleEvolve PDFs to high y region according to DGLAP equationsSubtract 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 41
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 42
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?
gdecrease as 1/Q2
Important to measure at HERA!!!
June 2, 2002 J Repond - DIS 43
xF3 Structure Function from NC DIS
FL(x,Q^2) … ignored (small at high Q2)
Cross section for scattering of Left, Right – handed electrons
Parity conserving
Parity violating
… sum over all q and q …sum over the 2 valence distributions
At high Q2: weak terms non-negligible
electromagneticinterference
pure weak interference pure weak
June 2, 2002 J Repond - DIS 44
Up to now: no longitudinal polarization for H1/ZEUS
→ How to measure xF3(x,Q2) ???
Consider Parity and CP Operations
Operation on e-L on xF3
P e-R -xF3
CP e+R xF3
P(CP) e+L -xF3
CP conserved in DIS
xF3(x,Q2) can be measured using difference of
Clear difference at high Q2
June 2, 2002 J Repond - DIS 45
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 46
Charm contribution to F2
Events with charm identified through
Mass plot of Δm = m(Kππ) – m(Kπ)Sharp peak at Δm = mD
* - mD = 145 MeV
Identify e± with dE/dx of central drift chamber
June 2, 2002 J Repond - DIS 47
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
Fixed Flavor Number Scheme FFNS
- 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
γ, Z0
c
γ, Z0
g
c
c
June 2, 2002 J Repond - DIS 48
Determination of Fc(x,Q2)
Charmed production measured in limited phase space e.g. 1.5 < pT(D*) < 15 GeV |η(D*)| < 1.5Extrapolation to full (pT,η) phase space model dependent!
2
ignored
Nice agreement with FFNS based on xg(x) from F2 fits
June 2, 2002 J Repond - DIS 49
Comparison of Schemes
FFNS VFNSVFNS
Some differences at 3 < Q2 < 32 GeV2
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 50
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 51
Propagator
NC
CC
Suppression at low Q2
Coupling
NC
CC
Approximately the same Unification of Electromagnetic and weak forces!!!
Charged Current DIS
…ignore FL and xF3
λ = ± 1 for left/right handed e-
For Q2 > MW:
Same propagator!!!
e
W±
qq’
ν
June 2, 2002 J Repond - DIS 52
Structure Function F2(x,Q2)
NC
CC e- p W- couples to
e+p W+ couples to
Dominated by flavor symmetric sea
Difference due to valence quarks 2u quarks versus 1d quark (1-y)2 suppression
June 2, 2002 J Repond - DIS 53
Flavor decomposition of proton
Use different angular dependence of valence and sea quarks both electron and positron data
Clearly need more data
→ HERA II
F2CC
June 2, 2002 J Repond - DIS 54
Outlook
HERA I Program
Shutdown period
Completed in September 2000
RLdt = 193pbà1
September 2001 – September 2001
New quadrupoles close to interaction region → increase of luminosity by factor ~5
Spin rotators around H1/ZEUS → rotate transverse spin into longitudinal
ZEUS upgrades → new μVTX detector → new forward tracker
Sokolov-Ternow Effect → Polarization build-up through emission of synchrotron radiation
June 2, 2002 J Repond - DIS 55
HERA II Program
Completed by 2006/7
RLdt = 1000pbà1 = 1fbà1
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 56
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