QCD and parton distribution functions

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QCD and parton distribution functions

• Zdenko van Kesteren
• Sascha Caron

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Outline

• Structure of hadronic cross sections
• as and renormalization scale
• p.d.f.s and factorization scales
• How do the p.d.f.s look like

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QCD

• Essentially all LHC physics is controlled by
• interaction between quarks gluons...
• Interaction with color-charges
• 3 colors ? SU(3) symmetry
• Color octet (? 8 gluons)

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Naive Parton Model

• Assumptions
• Hadrons consist of partons (quarks and gluons)
  which are structureless.
• Partons interact as if they were free particles.
• Scattering between hadrons translates to
  scattering between partons ?
• Cross section of hadron-hadron scattering is the
  incoherent sum of parton-parton scattering.

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Hadronic cross section
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Divergencies ? renormalization

• UV divergencies
• Included into definition of as

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Renormalization scale µr
as(µrMz) 0.1180.002 ? 200 MeV
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Run, as, run!!

• Running coupling constant as(µr,?)
• µr large ? small as(µr,?)
• asymptotic freedom
• Nobel prize physics 2004

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Improved parton model

• In proton, partons are not free, but bound
• In the limit of a hard probe (µr2 gtgt mp),
• there is no time for the partons to
• negotiate a coherent response.
• More divergencies occur in calculation
• (initial collinear gluon radiation)

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Factorization

• Initial state collinear gluon
• radiation ? divergencies
• in calculation M / s

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Measured p.d.f.s
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p.d.f. evolution equations

• DGLAP integro-differential equations

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derived p.d.f.s
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p.d.f.s at LHC

• We need measured p.d.f.s
• from former experiments
• to extrapolate the
• p.d.f.s for LHC
• (smaller x, larger µf)

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Hadronic cross section

• Function of renormalization/factorization
• scales hide the divergent terms of the
• cross section in
• measurable parameters a(µr) and fi(x, µf)

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Things to know

• Different renormalization schemes
• MS, MS, DIS, LO, etc
• Schemes pdfs must match scheme cross section.
• P.d.f.s fitted by different groups
• CTEQ, MRST, Botje

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Uncertainty parton luminosity
Centre of mass energy of hard scattering