“Fisica Sperimentale Nucleare e Subnucleare”Lezione 14

Marina Cobal,UniUD e INFN Trieste

How to probe the nucleon / quarks?

m 10 18−≈=∝p

d probed

• Scatter high-energy lepton off a proton:

Deep-Inelastic Scattering (DIS)

• In DIS experiments point-like leptons + EM interactions which are well understood are used to probe hadronic structure (which isn’t).

• Relevant scales:

large momentum -> short distance

(Uncertainty Principle at work!)

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e-p scattering

DIS (deep inelastic scattering)

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Electron - proton inelastic scattering

• Bloom et al. (SLAC-MIT group) in 1969 performed an experiment with high-energy electron beams (7-18 GeV).

• Scattering of electrons from a hydrogen target at 60 and 100.

• Only electrons are detected in the final state - inclusive approach.

• The data showed peaks when the mass W of the produced hadronic system corresponded to the mass of the known resonances.

e-p scattering

• Rutherford x-sec:– e: non-relativistic– p: does not recoil

• Mott x-sec:– e: relativistic– p does not recoil

• DIS e-p scattering:– e relativistic– p recoil– spin-spin effect

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Energyincrease

e-p Kinematics

• Four-momentum transfer:

• Mott Cross Section (!c=1):

q2 = (E −E ')2 − (k −k ') ⋅ (

k −k ') =

=me2 +me '

2 − 2(EE '− |k | |

k ' | cosθ ) =

≈ − 4EE 'sin2 θ2 ≡ −Q

2

sorhadron ten :

sorlepton ten :

µν

µν

WL

a virtual photon of four-momentum q is able to resolve structures of the order !/√q2

Form Factors

Point-like e-p scattering

If the proton recoils:

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Electron-Proton ScatteringMeasuring GE(q2) and GM(q2)

Electron-Proton ScatteringHigh q2 results

Electron-Proton ScatteringSummary of elastic scattering

Electron-Proton ScatteringScattering at very high q2

Scattering at very high q2

Kinematics of inelastic scattering

Relationship between kinematics variables

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Elastic and quasi-elastic scattering

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Inelastic scattering

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Inelastic cross section

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First SLAC experiment (‘69):– expected from proton form factor steep decrease in cross section vs Q2

• First data show big surprise:– very weak Q2-dependence– form factor -> 1!– scattering off point-like objects?

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Deep inelastic scattering

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Measuring the structure functions

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Bjorken scaling and the Callan-Gross relation

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The quark parton model

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Valence and Sea quarks

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Parton distribution functions (PDF)

X

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Scaling violation

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F2(x, Q2) results

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Origin of scale violation

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Summary