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2004, Torino Aram Kotzinian 2
HERAHERA KINEMATICKINEMATIC PLANEPLANE
• Accessible Kinematic Plane now almost completely covered
• Measurements extend to cover high y, high x and very high Q2
• Probe distances to ~ 1/1000th of proton size
2004, Torino Aram Kotzinian 8
The data show that F2 depends more and more steeply on Q2 as x falls. These logarithmic scaling violations are predicted by QCD. The driver is gluon emission from the quark lines - the gluons in turn spilt into quark-antiquark pairs, which in turn radiate gluons - and so on, ad infinitum. At each branching, the energy is shared, so the result is to throw more and more partons to lower and lower x - the “steep rise in F2” which is one of the mostsignificant discoveries of HERA.
2004, Torino Aram Kotzinian 9
Scaling and its violations
Elastic scattering off pointlike and free partons → does not depend on Q2
‘a point is a point’
Scaling
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
2004, Torino Aram Kotzinian 10
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 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
Pij(x/z) … Splitting functions
Quark-Parton Model (QPM)
…in DIS scheme
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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)
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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
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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
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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…
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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 different 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
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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
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Other interpretations
DGLAP 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?
2004, Torino Aram Kotzinian 18
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
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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
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Longitudinal Structure Function FL from NC DIS
Need to vary y, keeping x, Q2 fixed
→ vary s
Disentangle F2(x,Q2) and FL(x,Q2)
Data from SLAC and CERN: e/μ scattering on fixed targets with different beam energies
Measurement of R(x,Q2): Ratio of longitudinal and transverse cross section