Introduction to Particle Physics

Introduction to Particle Physics The Particle Zoo Symmetries The Standard Model Thomas Gajdosik Vilnius UniversitetasTeorinėsFizikosKatedra

The Particle Zoo

e- the electron Thomson 1897

e- g the photon Einstein Planck Compton 1900-1924 1897

e- g p the proton Rutherford 1914 1897 1900-1924

e- g p n the neutron Chadwick 1932 1914 1897 1900-1924

Hess • Anderson, • Neddermeyer e- g • Street, Stevenson p n µ the muon Who ordered that one? spark chamber 1937 1914 1897 1900-1924 1932

e- g p n µ p the pion prediction discovery Powell Yukawa 1947 1937 1914 1897 1900-1924 1932

e- g p p n µ e+ the positron(anti-matter) discovery Anderson prediction Dirac 1932 1947 1914 1897 1937 1900-1924

e- g p p n µ e+ n the neutrino Pauli Fermi 1932 1947 1914 1897 1937 1900-1924

L e- g K n p µ n p e+ S Rochester, Butler, ... strange particles 1947-... 1947 1914 1932 1897 1937 1900-1924

L e- g K n p p n µ e+ S Willis Lamb, in his Nobel prize acceptance speech 1955, expressed the mood of the time: „I have heard it said that the finder of a new elementary particle used to be rewarded by a Nobel Prize, but such a discovery now ought to be punished by a $10,000 fine.“ Lamb 1947-... 1947 1914 1932 1897 1937 1900-1924

mean life time (s) 100000 e- p The Particle Zoo n 1s 1 ms m 1 µs KL Kc pc Sc 1 ns W- KS B D t 10-15s p0 h S0 3s 1s 2s J/y 10-20s D* 4s f w W± Zo r 10-25s mass (GeV/c2)

the electron volt (eV) + e- 1V - 1GeV = 109 eV • side note: • Natural Units in Particle Physics • the fundamental constants c and ħ are set to 1 and are dimensionless • the only remaining dimension is energy, which is measured in units of eV • all other dimensions can be expressed in powers of [eV]: energy [eV] 1 eV = 1.60328·10-13 J length [eV-1] 1 cħ/eV = 1.97327·10-7 m time [eV-1] 1 ħ/eV = 6.58212·10-16 s mass [eV] 1 eV/c2 = 1.78266·10-36 kg temperature [eV] 1 eV/k = 1.16044·104 K

Looking for some order in the chaos... • 1. properties of particles: • order by mass(approximately, rather to be seen historically) : • leptons (greek: „light“) electrons, muons, neutrinos, ... • mesons („medium-weight“) pions, kaons, ... • baryons („heavy“) proton, neutron, lambda, .... • order by charge: • neutral neutrons, neutrinos, photons ... • ±1 elementary charge proton, electron, muon, …. • ±2 elementary charge D++, Sc++ • order by spin: • fermions (spin ½, 1½, ...) electrons, protons, neutrinos, … • bosons (spin 0, 1, …) photons, pions, … • order by „strangeness“, parity, ...

e e- e- p µ p p e+ e+ nm nm Observing particle decays and interactions: ne Decay  26 ns  2200 ns K K Scattering p

Looking for some order in the chaos... • 2. conservation laws for particle decays: • conservation of energy: • n  p + ...butnot p0  p+ + ... • conservation of charge: • n  p + e- + ...butnot n  p + e+ + ... • conservation of lepton number: • n  p + e- + nbutnot n  p + e- + n • conservation of baryon number: • n  p + ...butnot n  p+ p- + ... • conservation of strangeness (only in „fast“ processes) • fastK*  Kp but only “slow” K  pp

e e- e- p µ p p e+ e+ nm nm Observing particle decays and interactions ne Decay  26 ns  2200 ns K K Scattering p ?

Symmetriesas a guidingprinciple

Symmetries & where do we find them?  everywhere in nature: • snow flakes exhibit a 6-fold symmetry • crystals build lattices  symmetries of the microcosm are also visible in the macrocosm!

How do symmetries look like in theory? • symmetries are described by symmetry transformations: Example 1: Butterflysymmetry transformation S1:mirror all points at a line! formally: W=„original picture“  W‘=„mirrored picture“ apply symmetry in operator notation: S1W=W‘ symmetry is given if and only ifS1W=W!

How do symmetries look like in theory? • symmetries are described by symmetry transformations: Example 2: crystal latticesymmetry transformation S2:move all points by same vector! formally: W=„original picture“  W‘=„moved picture“ apply symmetry in operator notation: S2W=W‘ symmetry is given if and only ifS2W=W!

Which types of symmetries do weencounter in particle physics? discrete symmetry transformations: parity transformation P • to mirror at a plane, e.g. a mirror, is easy to understand, but depends on the (arbitrary) position and orientation of the plane. • more general definition: mirror at origin (space inversion, parity transformation):PW(t,x,y,z) := W(t,-x,-y,-z) • parity transformations correspond to a rotation followed by a mirroring at a plane

Which types of symmetries do weencounter in particle physics? discrete symmetry transformations: Reversion of time‘s arrow: time inversion T • corresponds to a movie played backwards • in case of a movie (= everday physics), this is spotted at once (i.e. there is no symmetry) • however, the laws of mechanics are time- symmetric! (example: billiard) • definition: TW(t,x,y,z) := W(-t,x,y,z)

Which types of symmetries do weencounter in particle physics? discrete symmetry transformations: anti-matter : charge conjugation C • for every known particle, there is also a anti-partner • anti particles are identical to their partners with respect to some properties (e.g. mass), and opposite w.r.t. others (e.g. charge) • charge conjugation exchanges all particles with their anti partners (and vice versa) • definition: CW(t,x,y,z) := W(t,x,y,z) e- e+ electron positron

Which types of symmetries do weencounter in particle physics? continuous symmetry transformations: (symmetry transformations that can be performed in arbitrarily small steps) • time: physics(today)  physics(tomorrow)more accurate: shift by a time-step Δt:eΔt /t W(t,x,y,z) = W(t+Δt,x,y,z) • space: physics(here)  physics(there)more accurate: displacement in space by a vector Δr=(Δx, Δy, Δz): • eΔr  W(t,x,y,z) = W(t,x+Δx,y+Δy,z+Δz)

Which types of symmetries do weencounter in particle physics? continuous symmetry transformations: (symmetry transformations that can be performed in arbitrarily small steps) • orientation: physics(north)  physics(west) • more accurate: rotation around an arbitrary axis in space:DW(t,x,y,z) = W(t,x‘,y‘,z‘)

insertion: particles are represented by fields in quantum field theory. At each point in space and time, the field can have a certain complex phase. =| |·eia Im eia a 1 Re Which types of symmetries do weencounter in particle physics? continuous symmetry transformations: (symmetry transformations that can be performed in arbitrarily small steps) • U(1) transformation: • does not affect the outer coordinates t,x,y,z, but inner properties of particles • U(1) is a transformation, which rotates the phase of a particle field (denoted as ) by an angle a:U(1)(t,x,y,z)=eia(t,x,y,z) dėmesio, sudėtinga!

The fundamental importanceof symmetries Noether's theorem: to eachcontinuoussymmetryof a fieldtheorycorrespondsa certainconservedquantity, i.e. a conservationlaw Emmy Noether 1882-1935 that means: if a field theory remains unchanged under a certain symmetry transformationS, then there is a mathematical procedure to calculate a property of the field which does not change with time, whatever complicated processes are involved.

eΔt /t W(t,x,y,z) = W(t+Δt,x,y,z) = W(t,x,y,z) ! The fundamental importanceof symmetries applications of Noether's theorem: also tomorrow the sun will rise the conservation of energy • the laws of physics do not change with time • more accurate: the corresponding field theory is invariant under time shifts: E = mc2 ...and that's it! From Noether‘s theorem follows the conservation of a well-known property: energy!

just to be clear: we are talking about properties of theunderlying theory, not a certain physics scenario • Example: chess • there is virtually an infinite number of ways a game of chess can develop • a game tomorrow can be completely different from that today • but: • the rules of chess remain the same, they are invariant under time shifts!

The fundamental importanceof symmetries applications of Noether's theorem: it‘s the same everywhere the conservation of momentum • the laws of physics do not depend on where you are • more accurate: the corresponding field theory is invariant under space displacements: • eΔr W(t,x,y,z) = W(t,x+Δx,y+Δy,z+Δz) = W(t,x,y,z) ! From Noether‘s theorem follows the conservation of another well-known property: momentum!

The fundamental importanceof symmetries applications of Noether's theorem: going round and round – the conservation of angular momentum • the laws of physics do not depend on which way you look • more accurate: the corresponding field theoryis invariant under rotations: • DW(t,x,y,z) = W(t,x,y,z) ! From Noether‘s theorem follows the conservation of yet another well-known property: angular momentum!

The fundamental importanceof symmetries applications of Noether's theorem: even more abstract symmetries get a meaning: the conservation of charge • as it turns out, the field theory of electro-dynamics is invariantunder a global* U(1) transformation: • U(1)(t,x,y,z)=eia(t,x,y,z)  W‘=W ! From Noether‘s theorem follows the conservation of charge! * global means affecting all space-points (t,x,y,z) the same

Overview symmetries and conservation laws

Are symmetries perfect? the small imperfections make it more interesting... is physics really perfectly symmetric? • obviously, many things in our macroscopic world are not symmetric • but is this also true for the fundamental laws of physics? •  Originally it seemed that nature does not only exhibit the previously discussed continuous symmetries, but the discrete symmetries as well: • P (parity = mirror symmetry) • T (time inversion) • C (charge conjugation)

Are symmetries perfect? the Wu experiment e- e- P  60Co 60Co beta-decay • originally, all experiments indicated that the microcosmic world is perfectly mirror-symmetric • 1956Tsung-Dao Lee and Chen Ning Yang postulated a violation of parity for the weak interaction • in the same year, Chien-Shiung Wu demonstrated the violation experimentally •  nature is not mirror-symmetric, • P-symmetry (parity) is violated Chien-Shiung Wu 1912-1997 Tsung-Dao Lee & Chen Ning Yang

Are symmetries perfect? a deeper understanding of the Wu experiment e- 60Co n n right-handed anti-neutrino left-handed anti-neutrino • also (undetected) anti-neutrinos are emitted • anti-neutrinos have a spin that is always orientated in the direction of movement (they are „right-handed“) • since a P-transformation changes the direction of movement, but not the spin, it produces a „left-handed“ anti-neutrino • as it turns out, a left-handed anti-neutrinodoes not exist in nature at all! • therefore, P-symmetry is said to be maximally violated

CP  n n right-handed anti-neutrino left-handed neutrino Are symmetries perfect? P violation - but maybe a CP symmetry? n n n right-handed anti-neutrino left-handed anti-neutrino left-handed neutrino • there is no left-handed anti-neutrino, but there is a left-handedneutrino(and only a such-handed!) • obviously, this violates C-symmetry (symmetrie between matter and anti-matter) • BUT: the combined symmetry transformation CP (exchange matter/anti-matter plus mirroring) works:

0,2% 99,8% p KL p Are symmetries perfect?  the kaon experiment of 1964 p KL p p James Cronin *1931 Val Fitch *1923 Rene Turlay 1932-2002 long-lived kaon decay into pions • if there is CP-symmetry in nature, by Noether‘s theorem there is also a corresponding conserved quantum number „CP“ • one has to know that mesons like the kaon or the pion are pseudo- scalars, which mean they change sign under a P-transformation: PK = -K, Pp = -p • therefore, CP is conserved for the decay of the long-lived kaon intothree pions, but not for the decay into two  CP-Symmetry is (slightly) violated

Are symmetries perfect?  implications of CP-violation in cosmology why CP-violation is important for our existence: • our universe consists – as far as we know – almost completely of matter • but where is the anti-matter? • and why haven‘t matter and anti-matter just annihilated? •  possible explanation: • at big bang, there have been large amounts of both matter and anti-matter • almost all of them annihilated • but smallest asymmetries in the laws of nature for matter and anti-matter left a tiny excess of matter: the matter our universe is made of! • 1967,Andrej Sacharow gave a list of conditions for this explanation • one of it is CP-violation • Without CP-violation, our universe would not be the one we know! Andrej Sacharow 1921-1989

Are symmetries perfect?  "last hope" CPT-symmetry? • the CPT-theorem states that under very general conditions, quantum field theories always have to exhibit CPT-symmetry • also experimentally, no violations have been observed so far  CPT-Symmetry is (as far as we know today)not violated • interesting side remark: as a consequence of CPT-symmetry together with CP-violation, there has to exist a violation of T-symmetry • that means: the fundamental laws of nature are not time-symmetric,there is a special direction of time even at microscopic level • „future IS different from the past, after all!“

Overview discrete symmetries

The Standard Model – Particle content

q q q q q g strong force g m t d d u s d u d u u u c b t d electromagnetic e weak force W, Z ? gravity nm nt ne The Standard Model - Overview particles fermions (spin ½) bosons (spin 1,2) leptons quarks charge charge strong 0 +2/3 -1 -1/3 1st 2nd 3rd generation 1st 2nd 3rd weak interactions +1 0 +1/3 proton neutron

u g strong force g t m m t d t b c s d t u b c s u electromagnetic e e weak force W, Z ? gravity nt nm nm ne ne nt d The Standard Model - Overview anti particles fermions (spin ½) bosons (spin 1,2) leptons quarks charge charge strong 0 -2/3 +1 +1/3 1st 2nd 3rd generation 1st 2nd 3rd weak interactions +1 pion (p)

u u u u s s u u d d c u d D++ s L0 d K- p0 b D+ b  S+

u c d u u u d d p+ K-  D+ d u d b ... mesons s b ... u u baryons s u u d proton neutron D++ L0 atom nucleus He-nucleus (a-particle) matter

reminder about the particles from the historical introduction the ordering principle example: electron and neutrino the systematics extending the ordering to all fermions counting the degrees of freedom overview Particles of the Standard Model: Fermions

e- the electron Thomson 1897

Introduction to Particle Physics