4.4 Deep inelastic scattering and structure functions

Deep inelastic scattering reveals the inner workings of hadrons by smashing high-energy particles into them. It's like using a super-powered microscope to peek inside protons and neutrons, showing they're made of smaller bits called quarks and gluons.

This discovery was huge for quantum chromodynamics (QCD), the theory of strong interactions. It proved QCD's ideas about quarks and gluons were right, and helped scientists understand how these tiny particles behave inside bigger ones.

Deep Inelastic Scattering

Process and Significance

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• Deep inelastic scattering (DIS) involves high-energy collisions between leptons and hadrons to probe particle substructure
• "Deep" refers to high momentum transfer, "inelastic" indicates target hadron breakup
• Incoming lepton (electron or muon) exchanges virtual photon with quark inside hadron
• Quark ejection causes hadron fragmentation
• Cross-section depends on Q² (four-momentum transfer squared) and x (Bjorken scaling variable)
• Reveals hadrons composed of point-like constituents (partons) later identified as quarks and gluons
• Provides direct evidence for quark model
• Scaling behavior in cross-sections at high Q² led to parton model development and QCD formulation

Experimental Insights

• Different energy scales probe various aspects of hadron structure
• Moderate Q²: valence quark distributions
• Higher Q²: sea quarks and gluons
• DIS experiments confirm quarks as point-like hadron constituents
• Validates key prediction of QCD and Standard Model
• Scaling violations in structure functions evidence running coupling constant and asymptotic freedom in QCD
• Reveals sea quark and gluon content, confirming rich QCD vacuum structure
• Small x values show rapid gluon density rise
  • Leads to gluon saturation concept
  • Necessitates resummation techniques in QCD calculations

Structure Functions of Hadrons

Fundamental Concepts

• Structure functions describe hadron internal structure in terms of constituent partons
• Dimensionless quantities relating to parton momentum fraction probability
• Main functions: F₁(x,Q²) and F₂(x,Q²)
• F₁(x,Q²) relates to hadron transverse structure
• F₂(x,Q²) provides longitudinal and transverse structure information
• Parton model directly relates structure functions to quark and antiquark momentum distributions
• Weighted by electric charges squared
• Callan-Gross relation: $F₂(x) = 2xF₁(x)$
  • Holds in simple parton model
  • Evidences spin-1/2 nature of quarks

Advanced Characteristics

• Structure functions exhibit scaling violations (Q² dependence)
• Caused by gluon radiation and quark-antiquark pair production
• Described by DGLAP evolution equations in QCD
• Longitudinal structure function F_L(x,Q²) arises from gluon contributions
• Important at small x and high Q²
• Q² evolution of structure functions described by DGLAP equations
• Demonstrates QCD's predictive power
• Sum rules provide constraints on structure function integrals
  • Test fundamental aspects of hadron structure
  • Examples: Gottfried sum rule, Adler sum rule

Hadron Structure from Data

Experimental Analysis

• DIS data analysis measures differential cross-section
• Extracts structure functions using reduced cross-section formula
• x and Q² dependence of structure functions reveals momentum distributions of parton flavors
• Scaling violations at small x and high Q² expose sea quarks and gluons
• Allows determination of gluon distribution functions
• Global analyses of DIS data determine parton distribution functions (PDFs)
• Uses fitting procedures
• Includes other high-energy scattering processes
• Polarized DIS experiments measure spin-dependent structure functions
• Provides information on hadron spin structure
• Reveals parton contributions to nucleon spin
• Neutrino DIS experiments enable flavor separation of quark distributions
• Offers unique information on nucleon strange quark content

Nuclear Effects

• DIS on nuclear targets reveals parton distribution modifications in nuclei (EMC effect)
• Provides insights into QCD dynamics of confined systems
• Allows study of nuclear medium effects on quark and gluon distributions
• Important for understanding collective behavior in heavy-ion collisions
• Enables investigation of nuclear shadowing and anti-shadowing phenomena
• Crucial for interpreting results from high-energy nuclear collisions (LHC, RHIC)

Implications for Quantum Chromodynamics

Theoretical Validations

• DIS results confirm key QCD predictions
• Existence of quarks as point-like hadron constituents
• Running coupling constant and asymptotic freedom
• Rich vacuum structure with sea quarks and gluons
• DGLAP equations successfully describe Q² evolution of structure functions
• Demonstrates QCD's ability to make quantitative predictions
• Precision DIS measurements allow accurate αs (strong coupling constant) determinations
• Tests QCD factorization theorems
• Crucial for validating perturbative QCD calculations

Frontier Areas

• Small-x physics reveals limitations of standard perturbative QCD approach
• Leads to development of new theoretical frameworks (BFKL, CGC)
• Nuclear DIS provides insights into QCD in dense environments
• Important for understanding early stages of heavy-ion collisions
• DIS at future electron-ion colliders will probe gluon saturation regime
• May reveal new aspects of strong interaction dynamics
• Precision structure function measurements constrain PDFs
• Essential for accurate predictions at hadron colliders (LHC)
• Spin-dependent DIS contributes to understanding proton spin puzzle
• Challenges conventional understanding of nucleon structure