Particle Physics The Basics Particle Physics arises from

Particle Physics The Basics • Particle Physics arises from the combination of special relativity and quantum mechanics Particles are described by a list of properties: • Mass, a positive number or zero, describing the minimum energy of the particle – Always given in metric multiples of e. V/c 2, like Me. V/c 2 and Ge. V/c 2 • Spin, which describes the internal angular momentum of the particle – Written as s , but we abbreviate this by just giving s, where s > 0 – s is always an integer (0, 1, 2, 3, …) or half-integer (1/2, 3/2, 5/2, …) • Electric charge, which is a multiple of the fundamental charge e – We normally give just Q, and the charge is Qe – Q is an integer. It can be positive, negative, or zero • Other properties exist, which we will discuss as they come up

Fermions and Bosons Fermions • Fermions are particles that obey the Pauli Exclusion Principle – You can’t put two of the same kind in the same quantum state – Fermions always have half-integer spin • Bosons are particles that violate the Pauli Exclusion Principle – They actually prefer being in the same quantum state – Bosons always have integer spin Some Particles (masses in Me. V/c 2) Name Sym. Spin Q Mass Proton p+ ½ +1 938. 27 Neutron n 0 ½ 0 939. 57 Electron e½ -1 0. 511 Neutrino ½ 0 2 10 -6 Photon 1 0 0 Pi-plus + 0 +1 139. 57 Pi-zero 0 0 0 134. 98 Pi-minus 0 -1 139. 57

Anti-Particles • All particles have anti- For each of the particles below particles • What is the spin, charge, and mass of the anti-particle • Anti-particles have the • Which might be their own anti-particles? same mass and spin, • Which might be anti-particles of each other? but opposite charge • Usually named by prefixing with “anti-” • Some particles are their own anti-particles Name Sym. Spin Q Mass Proton p+ ½ +1 938. 27 ½ – 1 938. 27 Neutron n 0 ½ 0 939. 57 Electron e½ – 1 0. 511 ½ +1 0. 511 Neutrino ½ 0 2 10 -6 Photon 1 0 0 Pi-plus + 0 +1 139. 57 0 – 1 139. 57 anti Pi-zero 0 0 0 134. 98 Pi-minus 0 – 1 139. 57 0 +1 139. 57 pair

Conservation Laws Energy and Momentum • Energy and Momentum are conserved + p • We’ll use only energy conservation • Consider a frame where the initial proton is at rest p+ • Is the following interaction possible? p+ + n 0 + + + – + 0 • Energy • Momentum • Angular Momentum • Electric Charge • Baryon Number • Strangeness • Energy doesn’t preclude it because the particles on the left can have kinetic energy in addition to their rest energy For decays only: Mass of initial particle – There is not necessarily must exceed sum of masses of final particles any frame where these particles are at rest

Angular Momentum • Total angular momentum is conserved n 0 p+ + e- • Consider angular momentum around z-axis • Energy • Momentum • Angular Momentum • Electric Charge • Baryon Number • Strangeness • All of the orbital angular momenta (L’s) are integer multiples of • Because the neutron, proton and electron are all fermions, the internal angular momenta (S’s) are all half-integer multiples of • Right side is an integer, left side is not Total number of fermions (particles with half-integer spin) on left plus right must be even

Electric Charge • Electric charge is conserved Charge is conserved Why is the electron stable? e- ? • Energy • Momentum • Angular Momentum • Electric Charge • Baryon Number • Strangeness • By energy conservation, whatever is on the right must be lighter • By charge conservation, something on the right must be charged • No such particle exists, so electron is stable

Baryon Number • Consider nuclear reactions – – decay: (Z, A) (Z+1, A) – + decay: (Z, A) (Z– 1, A) – decay: (Z, A) (Z– 2, A-4) + (2, 4) – decay: (Z, A)* (Z, A) • Total protons plus neutrons (call p+ + pthis baryons) remains constant? • Maybe anti-protons count as negative baryons? p+ + p+ n 0 + ++ + • Energy • Momentum • Angular Momentum • Electric Charge • Baryon Number • Strangeness Baryon number is conserved • Maybe there are other particles that count as baryons too? • There a group of particles called baryons – They each have baryon number +1 Why is the proton stable? • For every baryon, there is an anti-baryon – They each have baryon number – 1 • There is no lighter baryon

Baryons, Anti-Baryons, and Mesons • The strong nuclear force is what holds the nucleus together – It is must be strong and fast to do so • Some particles (photon, electron, neutrino) do not seem to be affected by it The particles that feel strong forces come in three categories: • Baryons have baryon number +1 • Anti-baryons are their anti-particles and have baryon number – 1 • Mesons have baryon number 0 – Anti-mesons are mesons Reactions that occur very quickly are believed to be mediated by this strong force • The rho-mesons, for example, decay very fast + + + 0 A strong interaction • The kaons, by comparison, decay very slowly K+ + + 0 A weak interaction

Strangeness • Why do some reactions involving strongly interacting particles occur so slowly? • It was speculated that some baryons and mesons had a property called strangeness that also had to be violated only in weak interactions Strangeness is conserved in all interactions except weak interactions Important notes: • Strangeness only applies to strongly interacting particles; other particles have S = 0 • Strangeness can only be changed by weak interactions • The strangeness of an anti-particle is the opposite of the strangeness of the particle • Energy • Momentum • Angular Momentum • Electric Charge • Baryon Number • Strangeness Symbol +, 0, K+ , K 0 K -, K 0 p+, n 0 +, 0 0, - S 0 0 +1 -1 0 -1 -1 -2

Types of Interactions THE STRONG FORCE • Involves only strongly interacting particles: baryons, anti-baryons, and mesons • Conserves strangeness ELECTROMAGNETISM + + e e µ µ + + • Affects all charged particles • Always involves photons (though this isn’t always obvious) e- µ+- e+ THE WEAK FORCE • Affects essentially all particles except photons • The only force that affects neutrinos • The only force that violates strangeness Which force is at work in a given reaction? • The stronger a force is, the more likely it is to be at work – Strong > Electromagnetism > Weak

Which Force? A step-by-step procedure for determining which force is at work • If charge conservation is violated Impossible • Else if baryon number is violated Impossible • Else if odd # fermions (left + right) Impossible • Else if decay and insufficient energy Impossible • Else if strangeness violated Weak • Else if all particles are strong Strong • Else if neutrinos are involved Weak • Else Electromagnetism

Sample Problems Classify the reactions below: p+ + K- 0 + K 0 Strong 0 0 + e + + e Electromagnetism • • Charge: (+1) + (-1) = 0 + 0 • Baryons: (+1) + 0 = (+1) + 0 • Fermions: [1+0] + [1+0] = 2 = even • Not a decay • Strangeness: 0 + (-1) = (-2) + (+1) • All particles are strong Charge: 0 = 0 + (+1) + (-1) Baryons: (+1) = (+1) + 0 Fermions: [1] + [1+1+1] = 4 = even Energy: 1193 > 1116 + 0. 5 Strangeness: 1 = 1 + 0 All particles are strong Neutrinos are involved (the n 0 and the p- are the anti • Charge: 0 = (-1) + (+1) Impossible -particles of the neutron and • Baryons: (-1) = (-1) + 0 proton) • Fermions: [1] + [1+1] = 3 = odd