qcd: quantum chromo dynamics - physi.uni-heidelberg.demenzemer/pp_ss2012/qcd_17.pdf · qcd: quantum...
TRANSCRIPT
![Page 1: QCD: Quantum Chromo Dynamics - physi.uni-heidelberg.demenzemer/PP_SS2012/QCD_17.pdf · QCD: Quantum Chromo Dynamics Quarks exist in three colors (red, blue, green) Physics is invariant](https://reader030.vdocuments.mx/reader030/viewer/2022040712/5e156d2a2d5cde7cc42d92e5/html5/thumbnails/1.jpg)
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)]
![Page 2: QCD: Quantum Chromo Dynamics - physi.uni-heidelberg.demenzemer/PP_SS2012/QCD_17.pdf · QCD: Quantum Chromo Dynamics Quarks exist in three colors (red, blue, green) Physics is invariant](https://reader030.vdocuments.mx/reader030/viewer/2022040712/5e156d2a2d5cde7cc42d92e5/html5/thumbnails/2.jpg)
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”
![Page 3: QCD: Quantum Chromo Dynamics - physi.uni-heidelberg.demenzemer/PP_SS2012/QCD_17.pdf · QCD: Quantum Chromo Dynamics Quarks exist in three colors (red, blue, green) Physics is invariant](https://reader030.vdocuments.mx/reader030/viewer/2022040712/5e156d2a2d5cde7cc42d92e5/html5/thumbnails/3.jpg)
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)?
![Page 4: QCD: Quantum Chromo Dynamics - physi.uni-heidelberg.demenzemer/PP_SS2012/QCD_17.pdf · QCD: Quantum Chromo Dynamics Quarks exist in three colors (red, blue, green) Physics is invariant](https://reader030.vdocuments.mx/reader030/viewer/2022040712/5e156d2a2d5cde7cc42d92e5/html5/thumbnails/4.jpg)
Connection Gluon Colour and Gell-Mann matrices
![Page 5: QCD: Quantum Chromo Dynamics - physi.uni-heidelberg.demenzemer/PP_SS2012/QCD_17.pdf · QCD: Quantum Chromo Dynamics Quarks exist in three colors (red, blue, green) Physics is invariant](https://reader030.vdocuments.mx/reader030/viewer/2022040712/5e156d2a2d5cde7cc42d92e5/html5/thumbnails/5.jpg)
potential at small scales
potential is attractive ifquarks form singlet state !
![Page 6: QCD: Quantum Chromo Dynamics - physi.uni-heidelberg.demenzemer/PP_SS2012/QCD_17.pdf · QCD: Quantum Chromo Dynamics Quarks exist in three colors (red, blue, green) Physics is invariant](https://reader030.vdocuments.mx/reader030/viewer/2022040712/5e156d2a2d5cde7cc42d92e5/html5/thumbnails/6.jpg)
Color Factors
Color factors are result of SU(3). A different symmetry group, would give different color factors!
![Page 7: QCD: Quantum Chromo Dynamics - physi.uni-heidelberg.demenzemer/PP_SS2012/QCD_17.pdf · QCD: Quantum Chromo Dynamics Quarks exist in three colors (red, blue, green) Physics is invariant](https://reader030.vdocuments.mx/reader030/viewer/2022040712/5e156d2a2d5cde7cc42d92e5/html5/thumbnails/7.jpg)
Di-Jet event at UA1 (1984)
![Page 8: QCD: Quantum Chromo Dynamics - physi.uni-heidelberg.demenzemer/PP_SS2012/QCD_17.pdf · QCD: Quantum Chromo Dynamics Quarks exist in three colors (red, blue, green) Physics is invariant](https://reader030.vdocuments.mx/reader030/viewer/2022040712/5e156d2a2d5cde7cc42d92e5/html5/thumbnails/8.jpg)
How to determine Bjorken x in a proton-antiproton collisions
![Page 9: QCD: Quantum Chromo Dynamics - physi.uni-heidelberg.demenzemer/PP_SS2012/QCD_17.pdf · QCD: Quantum Chromo Dynamics Quarks exist in three colors (red, blue, green) Physics is invariant](https://reader030.vdocuments.mx/reader030/viewer/2022040712/5e156d2a2d5cde7cc42d92e5/html5/thumbnails/9.jpg)
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
![Page 10: QCD: Quantum Chromo Dynamics - physi.uni-heidelberg.demenzemer/PP_SS2012/QCD_17.pdf · QCD: Quantum Chromo Dynamics Quarks exist in three colors (red, blue, green) Physics is invariant](https://reader030.vdocuments.mx/reader030/viewer/2022040712/5e156d2a2d5cde7cc42d92e5/html5/thumbnails/10.jpg)
Spectroscopy of heavy hadrons
Study strong IA potential by studying excited states of resonances and comparethem to QED (e.g. hydrogen atom)
![Page 11: QCD: Quantum Chromo Dynamics - physi.uni-heidelberg.demenzemer/PP_SS2012/QCD_17.pdf · QCD: Quantum Chromo Dynamics Quarks exist in three colors (red, blue, green) Physics is invariant](https://reader030.vdocuments.mx/reader030/viewer/2022040712/5e156d2a2d5cde7cc42d92e5/html5/thumbnails/11.jpg)
Spectroscopy of heavy hadrons
![Page 12: QCD: Quantum Chromo Dynamics - physi.uni-heidelberg.demenzemer/PP_SS2012/QCD_17.pdf · QCD: Quantum Chromo Dynamics Quarks exist in three colors (red, blue, green) Physics is invariant](https://reader030.vdocuments.mx/reader030/viewer/2022040712/5e156d2a2d5cde7cc42d92e5/html5/thumbnails/12.jpg)
Measurement of and discovery of Gluons
![Page 13: QCD: Quantum Chromo Dynamics - physi.uni-heidelberg.demenzemer/PP_SS2012/QCD_17.pdf · QCD: Quantum Chromo Dynamics Quarks exist in three colors (red, blue, green) Physics is invariant](https://reader030.vdocuments.mx/reader030/viewer/2022040712/5e156d2a2d5cde7cc42d92e5/html5/thumbnails/13.jpg)
Spin of the Gluon
![Page 14: QCD: Quantum Chromo Dynamics - physi.uni-heidelberg.demenzemer/PP_SS2012/QCD_17.pdf · QCD: Quantum Chromo Dynamics Quarks exist in three colors (red, blue, green) Physics is invariant](https://reader030.vdocuments.mx/reader030/viewer/2022040712/5e156d2a2d5cde7cc42d92e5/html5/thumbnails/14.jpg)
Reminder on running coupling for QED
![Page 15: QCD: Quantum Chromo Dynamics - physi.uni-heidelberg.demenzemer/PP_SS2012/QCD_17.pdf · QCD: Quantum Chromo Dynamics Quarks exist in three colors (red, blue, green) Physics is invariant](https://reader030.vdocuments.mx/reader030/viewer/2022040712/5e156d2a2d5cde7cc42d92e5/html5/thumbnails/15.jpg)
![Page 16: QCD: Quantum Chromo Dynamics - physi.uni-heidelberg.demenzemer/PP_SS2012/QCD_17.pdf · QCD: Quantum Chromo Dynamics Quarks exist in three colors (red, blue, green) Physics is invariant](https://reader030.vdocuments.mx/reader030/viewer/2022040712/5e156d2a2d5cde7cc42d92e5/html5/thumbnails/16.jpg)
Running of coupling constant
![Page 17: QCD: Quantum Chromo Dynamics - physi.uni-heidelberg.demenzemer/PP_SS2012/QCD_17.pdf · QCD: Quantum Chromo Dynamics Quarks exist in three colors (red, blue, green) Physics is invariant](https://reader030.vdocuments.mx/reader030/viewer/2022040712/5e156d2a2d5cde7cc42d92e5/html5/thumbnails/17.jpg)
Running of coupling constant
![Page 18: QCD: Quantum Chromo Dynamics - physi.uni-heidelberg.demenzemer/PP_SS2012/QCD_17.pdf · QCD: Quantum Chromo Dynamics Quarks exist in three colors (red, blue, green) Physics is invariant](https://reader030.vdocuments.mx/reader030/viewer/2022040712/5e156d2a2d5cde7cc42d92e5/html5/thumbnails/18.jpg)
Is strong IA described by SU(3) – measure colour factors?
![Page 19: QCD: Quantum Chromo Dynamics - physi.uni-heidelberg.demenzemer/PP_SS2012/QCD_17.pdf · QCD: Quantum Chromo Dynamics Quarks exist in three colors (red, blue, green) Physics is invariant](https://reader030.vdocuments.mx/reader030/viewer/2022040712/5e156d2a2d5cde7cc42d92e5/html5/thumbnails/19.jpg)
![Page 20: QCD: Quantum Chromo Dynamics - physi.uni-heidelberg.demenzemer/PP_SS2012/QCD_17.pdf · QCD: Quantum Chromo Dynamics Quarks exist in three colors (red, blue, green) Physics is invariant](https://reader030.vdocuments.mx/reader030/viewer/2022040712/5e156d2a2d5cde7cc42d92e5/html5/thumbnails/20.jpg)
Is strong IA described by SU(3) ?
0.375 (SU(3))
2.25 (SU(3))
TF/C
F
NC/C
F