Introduction 1 Particle Physics 2

• [0] L.Wainstein and V.Zubakov, Extraction of signals from noise, ISBN 0-486-62625-3

• The course PHZ 7357 is taught from the phenomenological and experimental perspectives, covering in depth the underlying theoretical and experimental concepts in particle physics.

Prof. S. Klimenko PHZ 7357, Fall 2017 Time line of particle discoveries 2

X-rays

nt H

Prof. S. Klimenko PHZ 7357, Fall 2017 Standard Model building blocks 3

matter force

strong

electromag.

weak

weak

Prof. S. Klimenko PHZ 7357, Fall 2017 Where are we today? 4 • All particles are made up of spin ½ fermions (leptons & quarks – are there other building blocks?) • Quarks and leptons appear to be fundamental (point-like) – no evidence for their constituents • Fundamental “matter” is organized in 3 generations (why 3?) • Carriers of force are integer spin bosons Ø quark interactions are strong (g), weak (W,Z), EM (g) and gravity Ø lepton interactions are weak (W,Z), EM (g) and gravity

Ø strong & EM forces are long-range – mg=mg=0 Ø weak force is short-range – mw~mz ~ 90 GeV Ø the 4th force of nature – gravity – is not part of SM • All other particles are hadrons Ø mesons - �� quarks bounded state, like K,p,.. Ø baryons – 3 quarks bounded state, like proton, neutron, .. Ø no free quarks have been observed. • Neutrinos have small mass - why so small? • ….

Prof. S. Klimenko PHZ 7357, Fall 2017 Standard Model Interactions 5 • Fundamental interaction force is given by charge g related to dimensionless ag. • for the EM force: in � = � = 4�� • Properties of the gauge bosons and nature of the interaction between the bosons and fermions determine the properties of the interaction

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Prof. S. Klimenko PHZ 7357, Fall 2017 Units for High Energy Physics 6

• The most convenient energy unit for HEP is Ø typical nuclear binding energies are MeV (106 eV) Ø mass of electron = 0.51 MeV/c2 = 9.1x10-31 kg Ø mass of proton = 938 MeV/c2 = 1.67x10-27 kg • Natural UNITS Ø Planck’s constant ℏ = = 1, c=1, energy in eV (or MeV) Ø Also � = 1 and � = 1 Ø Energy of relativistic particle � = �� + �� → � + � ℏ Ø Thompson x-section � = → , FS constant α = → ℏ • Conversion back to MKS ! = M 1L2T -1 and c = M 0 L1T -1 and Energy = M 1L2T -2 • Convenient conversion factors Ø Time 1 ��� = 6.58×10� Ø Length 1 ��� = 0.197 ��, 1�� = 10� Ø X-section 1 ��� = 0.38 ��, 1 �� = 0.1��

Prof. S. Klimenko PHZ 7357, Fall 2017 Relativistic Kinematic 7 • Lorentz transformation – M&S p383,.. æ 1 0 0 0 ö ç 0 -1 0 0 ÷ • µ g = Energy-momentum 4-vector p = (E,px,py,pz) µn ç 0 0 -1 0 ÷ ç ÷ • Scalar product è 0 0 0 -1ø 3 3 µ n µ n µ o o 1 1 2 2 3 3 ab = aµb = å ågµna b º gµna b = a b - a b - a b - a b µ=0 n=0 µ • aµb is Lorentz invariant • Energy-momentum 4-vector pµ = (E,px,py,pz) 2 µ Ø p =pµ p is the invariant mass • Sum of two 4-vectors a+b is also 4-vector 2 2 Ø s=(p1+p2) =(p3+p4) - invariant mass 2 2 Ø t=(p1-p3) =(p4-p2) - (4-momentum transfer)^2 2 2 Ø u=(p1-p4) =(p3-p2) s,t,u – Mandelstam variables • Examples, p – particle momentum 2 2 2 Ø Fix target: E2=m2 , p2=0, s=(p1+p2) =(E1+m2) -|p1| =2m2E1 2 2 Ø Colliding beams: p1=p2, s=(p1+p2) =(E1+E2)

Prof. S. Klimenko PHZ 7357, Fall 2017