Quantum Numbers. Elementary Particles Properties. F. Di Lodovico c 1 EPP, SPA6306. Queen Mary University of London. Quantum Numbers. F.

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1 Elementary Properties 1 1 School of Physics and Astrophysics Queen Mary University of London EPP, SPA6306

2 Outline

3 Most stable sub-atomic particles are the proton, neutron (nucleons) and electron. Study of the proton and neutron revealed other less-stable particles. grouped into two broad categories: leptons (light-weight particles) and hadrons. Leptons are considered to be fundamental (not made of other particles). Hadrons are considered not to be fundamental.

4 The Hadrons The number of different types of leptons is small (6 types). However, there are many hadrons. The hadrons can be further sub-divided into baryons (heavy-weight particles) and mesons (middle-weight particles). Baryons all have half-integer spin (e.g. p (spin 1/2), + (spin 3/2) etc). Mesons all have integer spin (e.g. π + (spin 0), ρ + (spin 1) etc).

5 The Quarks The large number of hadrons suggests they are made from a smaller number of particles (quarks). So far, only 6 different types of quarks are needed to create all the observed hadrons. No free quarks have been observed so far. The parallels between the quarks and leptons are quite striking. Generation Charge First Second Third Quark +2/3 u (up) c (charm) t (top) Quark -1/3 d (down) s (strange) b (bottom) Lepton e e (electron) µ (muon) τ (tau) Lepton 0 ν e (electron ν µ (muon ν τ (tau neutrino) neutrino) neutrino)

6 Quarks and Leptons All quarks have spin 1/2. The masses of these basic building blocks are found to be: Quarks Leptons Type Mass (GeV) Type Mass (GeV) u e d µ s τ 1.78 c 1.27 ν e 0 b 4.2 ν µ 0 t 171 ν τ 0 The masses of the quarks are not measured directly, but through studies of particle interactions.

7 Quarks and Leptons The baryons are made of three quarks and the mesons are made of a quark and antiquark. You will notice that the sum of the masses of a particles constitent quark s does not equal the measured mass of the particle. The gluon (the mediator of the strong force) is considered responsible for the larger, missing mass which arises from quark-gluon and gluon-gluon interactions in the particle.

8 We can view particle interactions in light of Newton s Third Law: for every action there is an equal and opposite reaction. The repulsion between two electrons (the reaction) can be viewed as the exchange of a photon (the intermediate vector boson) between the two electrons (the action). One electron emits a photon towards other electron. The net result is the first electron moves away from the second. The other electron absorbs the photon. The net result is the second electron moves away from the first. All particle interactions can be described by four forces.

9 The Forces Force Intermediate Range Relative Vector Boson Strength Strong gluon m 1 Electromagnetic photon Infinite 10 2 Weak W ±, Z m 10 6 Gravity graviton Infinite All strengths relative to that of the strong force. The strong force extends to approximately the size of the nucleus. There are theories that assume all forces originally were unified. Theory has successfully unified the electomagnetic and weak forces. Although gravity is experienced by all particle interactions it s effect is so tiny compared to experimental precision it is usually ignored.

10 Rules Based on the experimental observation of particle interactions a number of particle properties (quantum numbers) were seen to be conserved. Not all interactions conserve all quantum numbers. The quantum numbers and their rules of conservation are useful to predict which interactions can occur. The rules of convervation were observed experimentally.

11 Rules of Conservation Quantity Strong EM Weak Charge Q Baryon Number B Lepton Number L Isospin I X X Isospin 3rd Cpt I 3 X Strangeness S X Parity P X Charge Conjugation C X Time Reversal T

12 Fermions and Bosons From quantum mechanics we know that two particles can exist in either a symmetric (S) or anti-symmetric (A) state. ψ S = 1 2 (ψ 1 (A)ψ 2 (B) + ψ 2 (B)ψ 1 (A)) ψ A = 1 2 (ψ 1 (A)ψ 2 (B) ψ 2 (B)ψ 1 (A)) Interchanging particles 1 2 and 2 1 has no effect on the symmetric state, but the antisymmetric state changes sign. If the two particles are in the same state (ie A = B) then the antisymmetric state disappears.

13 with an antisymmetric wave-function are called fermions. They have half-integer spin. with a symmetric wave-function are called bosons. They have integer spin. All hadrons and leptons can be classified as bosons or fermions. Fermions obey the Pauli Exclusion principle: no two fermions can exist can occupy the same quantum mechanical state. When constructing particles from quarks we need to be careful to take account of the Pauli exclusion principle (we will come back to this when we talk about quark colour).

14 Examples A hadronic strong interaction obeys the conservation of all quantum numbers: π + p K 0 + Λ 0 π p K 0 Λ 0 Q B S I /2-1/2 0 A hadronic weak interaction violates some quantum numbers: K 0 π + + π K 0 π + π Q B S strangeness not conserved I 3-1/ I 3 not conserved

15 CPT Symmetry The operations of Charge-Parity (C), Parity (P) and Time-Reversal (T) act on different parts of a particles state. P and T act on extrinsic or external properties such as the spatial or temporal coordinates whereas C acts on intrinsic or internal properties (the quantum numbers). Operation Charge Extrinsic Intrinsic P Invariant r r Invariant T Invariant t t Invariant C q q Invariant q numbers -(q numbers)

16 Each particle has an antiparticle. In some cases (some neutral mesons) the antiparticle is the same as the particle. An antiparticle has the same mass and spin as its corresponding particle.

17 Antibaryons In the case of baryons the antibaryons have the same quantum number, but with opposite sign. Quantity Antiparticle Charge Q q -q Baryon Number B b -b Lepton Number L l -l Isospin I I I Isospin 3rd Cpt I 3 I 3 -I 3 Strangeness S s -s Parity P p -p Charge Congugation C c -c E.g. the proton has baryon number 1, the antiproton has baryon number -1.

18 Antileptons For the leptons each particle has a distinct antilepton. Generation Charge First Second Third +e e + (positron) µ + (antimuon) τ + (antitau) 0 ν e (electron ν µ (muon ν tau (tau antineutrino antineutrino antineutrino

19 Antiquarks The quarks also have a corresponding antiparticle with the same mass, spin and opposite charge. Quarks Antiquarks Type Charge Type Charge u +2/3 u -2/3 d -1/3 d +1/3 s -1/3 s +1/3 c +2/3 c -2/3 b -1/3 b +1/3 t +2/3 t -2/3 The proton consists of uud and has a charge of +2/3 + 2/3 1/3 = +1. The antiproton consists of uud and has a charge of 2/3 2/3 + 1/3 = 1

20 Mesons and Anti-mesons Mesons are made from a quark and antiquark. In some cases a meson is its own antiparticle. E.g the π 0 because it contains the same type of quark and antiquark: uu. But, this is not true for all neutral mesons. E.g. the K 0 (us) has antiparticle K 0 (us). The Parity and Charge Conjugation for an anti-meson is the same as that of the corresponding meson. The baryon number is 0. The strangeness and I 3 for an antiparticle have the opposite sign of the values for the particle (e.g. S = +1 for the K + but S = 1 for the K ).