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M. Cobal, PIF 2006/7 Units and kinematics

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M. Cobal, PIF 2006/7 Units in particle physics

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M. Cobal, PIF 2006/7 Other Units

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M. Cobal, PIF 2006/7 QuantityUnits HEUnits SI Lenght1 fm10 -15 m Energy1 GeV=10 9 eV1.602x10 -10 J Mass1 GeV/c 2 1.78x10 -27 Kg h6.59x10 -25 GeVs1.055x10 -34 J s c2.998x10 23 fms -1 2.998x10 8 ms -1 hc0.1975 GeV fm3.162x10 -26 J m Natural Units = c = 1 Mass 1 GeV Lenght 1 GeV -1 Time 1 GeV -1 1 Volt - + U = 1 eV Units in particle physics

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M. Cobal, PIF 2006/7 Co-moving coordinate systems v S S’ x x’’ Example: Muons, 2. 10 -6 s, in cosmic ray p =10 GeV l v 60 km (not. 600 m) Lorentz contraction: length reduction with motion Time dilatation: Lenght at rest Time at rest Lorentz transformation

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M. Cobal, PIF 2006/7 Relativistic kinematics

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M. Cobal, PIF 2006/7 4-vector Invariant for rotations : Introducing the metric : Lorentz-invariant in terms of scalar, 4-vectors Contro-variant 4-vec Co-variant 4-vec Notation

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M. Cobal, PIF 2006/7 Four vectors

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M. Cobal, PIF 2006/7 Four vectors addition

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M. Cobal, PIF 2006/7 Kinematics example

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M. Cobal, PIF 2006/7

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Observables

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M. Cobal, PIF 2006/7

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mAmA mBmB mCmC c.m. frame Example EE EeEe 2-Body Decay

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M. Cobal, PIF 2006/7

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Decay Width

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M. Cobal, PIF 2003 Resonances - If cross section for muon pairs is plotted one find the 1/s dependence -In the hadronic final state this trend is broken.

M. Cobal, PIF 2003 Resonances - If cross section for muon pairs is plotted one find the 1/s dependence -In the hadronic final state this trend is broken.

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