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HERA KINEMATIC PLANE. Accessible Kinematic Plane now almost completely covered Measurements extend to cover high y, high x and very high Q 2 Probe distances to ~ 1/1000 th of proton size. Q 2 = xys. Tevatron. COMPASS. - PowerPoint PPT Presentation
2004, Torino Aram Kotzinian 1

2004, Torino Aram Kotzinian 1

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• 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

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Q2 = xys


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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.

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Scaling and its violations

Elastic scattering off pointlike and free partons → does not depend on Q2

‘a point is a point’


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

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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





← 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


Scale error reduced with NNLO not yet available


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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?

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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


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


Easier to implement in MC programs, e.g. CASCADE

Low x: approaches BFKL

High x: approaches DGLAP





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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

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Measurements at high x > 0.1 but low Q2 < 80 GeV2


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