QCD: Quantum Chromo Dynamics
Quarks exist in three colors (red, blue, green)
Physics is invariant under rotation in color space. SU(3) color is an exact symmetry! - No way to distinguish red, blue and green quarks.8 generators of SU(3): Gell-Mann matrices (in 3D representation)
To determine color states of gluons and quarks, study combination of color and anti-color
[Some freedom of convention to define the color states, this representation used throughout the lecture]
Due to exact symmetry, no mixed states (of color octet and singluet) exist in nature.
All bound (observed) particles are colorless (invariant under rotation in phase space).
Gluons carry color and form a color octet [number of 8 gluons direct consequence of the 8 non-abelian generators of SU(3)]
Symmetries define interactions
If physics is invariant under a symmetry transformation, the Lagrangian must be invariant under this transformation. Lagrangian of free particle is NOT invariant under anysymmetry transformation. Thus need to add (interaction) terms to construct a invariant Lagrangian. The Lagrangian defines the allowed elements of the Feynman-diagrams.
QED: U(1) QCD: SU(3)
Gell-Mann matrices
two transformation commute two transformation in general do not commute
introduce 1 photon field A to get introduce 8 gluon fields Gi to get invariant
invariant Lagrangian Lagrangian
L = “ψψ” + e”ψψA” + “A2”
--------
L = “qq” + “G2” + g”qqG” + g”G3” + g2”G4”
What are the coupling “constants”?
How does the potential look like?
What is the energy dependence of coupling “constants”?
Can we experimentally confirm to have a SU(3)?
Connection Gluon Colour and Gell-Mann matrices
potential at small scales
potential is attractive ifquarks form singlet state !
Color Factors
Color factors are result of SU(3). A different symmetry group, would give different color factors!
Di-Jet event at UA1 (1984)
How to determine Bjorken x in a proton-antiproton collisions
Angular distribution of 2-jet events at CERN UA1
ignoring effect of spinof quarks and gluon(only very little impact at small scatter angles)
same dependence on
for QCD and QED cross-section
→ same potential
Spectroscopy of heavy hadrons
Study strong IA potential by studying excited states of resonances and comparethem to QED (e.g. hydrogen atom)
Spectroscopy of heavy hadrons
Measurement of and discovery of Gluons
Spin of the Gluon
Reminder on running coupling for QED
Running of coupling constant
Running of coupling constant
Is strong IA described by SU(3) – measure colour factors?
Is strong IA described by SU(3) ?
0.375 (SU(3))
2.25 (SU(3))
TF/C
F
NC/C
F
