Energy and momentum units in particle physics, Lecture notes of Particle Physics

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Energy and momentum units in particle physics

Gron Tudor Jones UNIVERSITY OF BIRMINGHAM CERN HST

Use of ‘GeV-type’ units rather than SI in Particle Physics In ordinary Newtonian physics, given the kinetic energy E k of a particle (4 Joules, say) and its momentum p (4 kg m/s), one can calculate m = p 2 /2E k = 2 kg In highly relativistic collisions at the LHC, the total energy E of a particle is measured by detectors quaintly called ‘calorimeters’, and the momentum p by determining the curvature of charged tracks moving in a magnetic field. Then, using _E 2 = p 2 c 2

• m 2 c 4_ , we can calculate the mass m :

Particle physicists measure energies in GeV, where 1 GeV = 10 9 eV = energy gained by an electron or proton accelerated through 10 9 volts. How does one use **_E 2 = p 2 c 2

• m 2 c 4_** to measure mass using particle physicists’ units? For the units in each term of E 2 = p 2 c 2 +m 2 c 4 to be the same, p must be in GeV/c and m must be in GeV/c 2 . Then (^) E^2 (in GeV^2 ) = p^2 (in GeV^2 /c^2 ) c^2 + m^2 (in GeV^2 /c^4 ) c^4 Physicists ‘simplify’ this by writing it as E 2 (in GeV 2 ) = p 2 (in GeV 2 ) + m 2 (in GeV 2 ) So when you see E 2 = p 2
• m 2 think of

What is a highly relativistic particle? _p 2 c 2

m 2 c 4 E ~ pc_

E

2

= p

2

c

2

+ m

2

c

4

• Examples/discussion