Quark Flavour Quantum Numbers
Y2 Neutrino Physics (spring term 2016)
Lecture 2
Fundamental particles and interactions
Dr E Goudzovski [email protected]
http://epweb2.ph.bham.ac.uk/user/goudzovski/Y2neutrino
Previous lecture
The natural system of units (ħ=c=1) is used in particle physics: all quantities are expressed in powers of energy (GeV).
By the Heisenberg’s uncertainty principle, momentum required to probe a distance scale is p 1/ (in natural units). Particle accelerators are the most powerful microscopes.
Elementary particles often travel at speeds close to c: relativistic (rather than classical) kinematics applies.
Lorentz-invariance and conservation of the 4-momenta provide a useful tool to solve simple kinematic problems (reaction thresholds, accelerator energy reach, etc.)
1 This lecture
Introduction to particle physics (continued)
The fundamental particles: quarks and leptons.
Forces, their strengths and ranges.
Internal quantum numbers and conservation laws.
Feynman diagrams.
Examples of electromagnetic processes.
Textbooks:
B.R. Martin and G. Shaw. Particle physics. Chapters 1, 2, 8. D. Perkins. Introduction to high energy physics. Chapters 1, 2. D. Griffiths. Introduction to Elementary Particles. Chapters 1, 2. 2 Fermions: 1st generation Point-like spin-1/2 fundamental fermions (1) Leptons: Electron (e ) and its neutrino (e). Particle Symbol Electric Type charge (q) (2) Quarks: Electron e 1 Up (u) and down (d). Lepton They form bound states (hadrons), Neutrino e 0 e.g. nucleons (p, n). Up quark u +2/3 Quark Down quark d 1/3 Proton (q=+1) Neutron (q=0) Example: the nuclear beta decay …at the nuclear level:
Beta decay …at the nucleon level:
…at the fundamental fermion level: 3 Fermions: the 3 generations
st nd rd 1 generation 2 generation 3 generation Electrical charge (q) Electron e Muon Tauon 1
Electron neutrino e Muon neutrino Tau neutrino 0 Up quark u Charm quark c Top quark t +2/3
Down quark d Strange quark s Bottom quark b 1/3
Higher generations:
Copies of (e , e, u, d).
Undergo identical interactions.
The principal difference among the generations: masses.
Generations are successively heavier.
Therefore particles of higher generations are unstable. Example: (mean lifetime ~106 s)
Why exactly three generations? We do not know. 4 Fermion mass spectrum
TeV 197Au nucleus eV H O molecule Composite 2 objects Quarks
p,n GeV Mass, Mass,
Leptons
MeV
keV
eV
Generations 5 Antimatter Antimatter: antiparticles of “ordinary” particles. Positron (e+) track
Predicted within relativistic field theory (for fermions: P. Dirac, 1929; Nobel prize 1933) First antiparticle discovered: the positron (e+) (C. Anderson, 1932; Nobel prize 1936) Compared to its matter partner, an antiparticle has: Pb plate equal mass and spin; opposite electric charge; Cloud chamber photograph opposite internal quantum numbers. of the first identified positron Track curvature: due to magnetic field. Baryon asymmetry: antimatter does not exist in large Direction: change of curvature quantities in the observable Universe. when crossing the Pb plate. (Baryon = bound state of 3 quarks, e.g. proton, neutron) The charge can then be inferred. Antiparticles of the first generation fermions:
Examples for hadrons: 6 Interactions (forces) Classical description of interactions: Field of a source charge acting on other charges. Force is proportional to field intensity.
Quantum field theory description: Discontinuous exchange of “virtual” field quanta (gauge bosons). Force = rate of exchange of momentum.
Interaction Couples to; Boson mass Comment [GeV/c2] gauge boson(s) Mass; Negligible on Gravity 0 graviton G (?) particle physics scale Electromagnetic Electric charge; (almost all extranuclear 0 phenomena) photon All fundamental Weak Massive carriers: (e.g. nuclear beta-decays, fermions; 80.4, 91.2 limited range nuclear fusion) W, Z0 Colour (r, g, b); Gluon charge: rg, etc. Strong 0 (binds nucleons in nuclei) 8 gluons Self-coupling of gluons. Gravity vs electrostatic force
Gravitational attraction vs Coulomb repulsion between two protons:
(SI units)
~1036 [the hierarchy problem] However gravity must be weak for a complex universe to exist
Q: Why is gravity dominant in everyday experience?
A: Matter is electrically neutral: cancellation of attraction and repulsion. Gravity is cumulative: no repulsion no cancellation. The weak and strong forces have limited (sub-atomic) range. 8 Standard Model vertices
NC = neutral current CC = charged current
9 Ranges of forces
Neutron decay: Heisenberg’s uncertainty principle: Et ~ ħ. p(u) Massive force carrier limited range.
Range of the weak force: n(d) W e R ct ħc / M weak W 3 200 MeV fm / 80 GeV 2×10 fm. e
(proton radius Rp= 0.9 fm ≫ Rweak)
Force Relative strength Range (fm) Strong (hadrons) 1 ~1 Electromagnetic ~102 ∞ Weak ~107 ~103 Gravity ~1039 ∞ 10 Internal quantum numbers
Discrete (quantized) quantities conserved in fundamental interactions:
widely known: the electric charge.
But there are others:
lepton family (flavour) numbers; total lepton number; quark flavour numbers; baryon number.
11 Lepton numbers (1) Lepton family (or lepton flavour) numbers (electronic number) (muonic number) (tauonic number) and the total lepton number
are conserved in all known interactions (not a fundamental conservation law: its origin is a puzzle)
Examples:
1) Violation of lepton flavour: [MEG experiment, PSI, Switzerland: Phys.Rev.Lett.110 (2013) 201801] 2) Violation of lepton number: [NA48/2 experiment, CERN, Switzerland: Phys.Lett.B697 (2011) 107]
3) Free neutron decay
Allowed: lepton flavour is conserved by the anti-neutrino emission. 12 Baryon number
(2) The baryon number
is conserved in all interactions.
Particles not formed of quarks (leptons, gauge bosons) have B=0. Mesons (quark-antiquark bound states) have B=0.
Examples:
1) The proton (p = uud) is the lightest baryon and is therefore stable.
Experimentally, (The age of Universe: ~ 1010 years)
2) Nucleon decays violating baryon number: never observed. FORBIDDEN: 13 Quark flavour (3) Quark flavour quantum numbers:
(“strangeness”) (“charm”) (“bottomness”) (“topness”) are conserved in strong and electromagnetic interactions (convention: flavour number and electric charge have the same sign) Example:
A number of strange particles (discovered in cosmic rays in 1947) are produced in pairs via the strong interaction (~1023 s), e.g.
but decay “slowly” (~1010 s) via the weak interaction (with strangeness not conserved), e.g.
14 Feynman diagrams Quantum field theories: interactions between particles proceed discontinuously by exchange of mediator particles.
A+B C+D Amplitude of a boson-mediated process
(in natural units):
A C space
ga virtual “mediator” x particle • ga, gb: the fundamental gb coupling strengths at the vertices;
B D • Squared momentum transfer (pA, pB, pC and pD are 4-vectors): 2 2 2 q = (pC pA) = (pD pB) ;
2 2 initial “how the final • 1/(q mx ): the boson propagator. state interaction state happened” The reaction rate is proportional to |A|2 time 15 Electromagnetic processes (1) Force carrier: photon (). Squared coupling constant (the fine structure constant): Example 1: e+e annihilation to photons e+ e e
+ e e
In general, is process of order (n2)
Higher-order electromagnetic processes are suppressed
QED is a “perturbative theory”: very precise predictions 16 Single photon emission
Q: Are e+e annihilation and e+e pair production (photon conversion) processes
involving real (rather than virtual) photons allowed?
e+ e
A: The photon is a massless: E = p in any reference frame.
+ + + + In e e COM frame, p(e e ) = 0; E(e e ) = m(e e ) 2me > 0.
+ + Therefore, E(e e ) > p(e e ), contradicting E = p.
Both processes are forbidden by energy-momentum conservation. 17 Electromagnetic processes (2) Example 2: e+e pair production (photon conversion)
is allowed in the field of a nucleus (energy-momentum conserved due to nuclear recoil) Reaction rate: e+ (Z: electric charge of the nucleus) The dominant photon interaction process at e high energies (E>100MeV);
Z-dependence is exploited for photon detection N N (e.g. Pb calorimeter pre-showers)
Example 3: Bremsstrahlung e e is also allowed in the presence of a nucleus Reaction rate: N N Practical uses: e.g. X-ray generation in medical imaging 18 Summary
The known matter is composed of 3 generations of fundamental fermions (leptons, quarks) and corresponding anti-particles. “Normal” matter is composed of 3 particle types: u, d, e.
Four fundamental interactions are known. Their ranges and strengths are vastly different. QFT interactions = discontinuous exchange of field quanta.
Internal quantum numbers: (a) lepton and baryon numbers: conserved in all interactions; (b) quark flavour numbers: conserved in all but weak interactions.
Feynman diagrams are a powerful tool for qualitative predictions.
Examples of electromagnetic processes: e+e annihilation, bremsstrahlung, photon conversion. 19