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Introduction to Modern Theoretical Physics Thomas Gajdosik, VU Introduction to Particle Physics Thomas Gajdosik Vilnius Universitetas Teorinės Fizikos Katedra The Particle Zoo Symmetries The Standard Model

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Introduction to Modern Theoretical Physics Thomas Gajdosik, VU The Particle Zoo

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Introduction to Modern Theoretical Physics Thomas Gajdosik, VU 1897 the electron e-e- Thomson

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Introduction to Modern Theoretical Physics Thomas Gajdosik, VU 1897 the photon Planck Einstein Compton e-e-

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Introduction to Modern Theoretical Physics Thomas Gajdosik, VU 1897 the proton e-e 1914 Rutherford p

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Introduction to Modern Theoretical Physics Thomas Gajdosik, VU 1897 the neutron e-e 1914 n p 1932 Chadwick

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Introduction to Modern Theoretical Physics Thomas Gajdosik, VU 1897 the muon e-e 1914 µ p 1932 n 1937 Who ordered that one? Hess Anderson, Neddermeyer Street, Stevenson spark chamber

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Introduction to Modern Theoretical Physics Thomas Gajdosik, VU 1897 the pion e-e 1914 p 1932 n 1937 µ 1947 Powell Yukawa predictiondiscovery

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Introduction to Modern Theoretical Physics Thomas Gajdosik, VU 1897 the positron (anti-matter) e-e 1914 e+e+ p 1932 n 1937 µ 1947 Anderson Dirac prediction discovery

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Introduction to Modern Theoretical Physics Thomas Gajdosik, VU 1897 the neutrino e-e 1914 p 1932 n 1937 µ 1947 e+e+ Fermi Pauli

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Introduction to Modern Theoretical Physics Thomas Gajdosik, VU 1897 strange particles e-e 1914 K K p 1932 n 1937 µ 1947 e+e+ Rochester, Butler,

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Introduction to Modern Theoretical Physics Thomas Gajdosik, VU 1897 „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.“ e-e 1914 K p 1932 n 1937 µ 1947 e+e Willis Lamb, in his Nobel prize acceptance speech 1955, expressed the mood of the time: Lamb

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Introduction to Modern Theoretical Physics Thomas Gajdosik, VU mean life time (s) n cc KLKL D KcKc KSKS 00 B J 1s 2s 3s 4s D* cc 00 mass (GeV/c 2 ) 1s 1 ms 1 µs s s s e-e- p 1 ns The Particle Zoo W ± Z o

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Introduction to Modern Theoretical Physics Thomas Gajdosik, VU + - e-e- 1V 1GeV = 10 9 eV the electron volt (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 = · J length[eV -1 ]1 cħ/eV = · m time[eV -1 ]1 ħ /eV = · s mass[eV]1 eV/c 2 = · kg temperature[eV]1 eV/k = · 10 4 K

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Introduction to Modern Theoretical Physics Thomas Gajdosik, VU Looking for some order in the chaos 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: neutralneutrons, neutrinos, photons... ±1 elementary chargeproton, electron, muon, …. ±2 elementary charge ++, c ++ order by spin: fermions (spin ½, 1½,...)electrons, protons, neutrinos, … bosons (spin 0, 1, …)photons, pions, … order by „strangeness“, parity,...

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Introduction to Modern Theoretical Physics Thomas Gajdosik, VU e e µ µ Decay e e 26 ns 2200 ns Scattering e-e- e+e+ e+e+ K K p p e-e- e+e+ e+e+ K K Observing particle decays and interactions:

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Introduction to Modern Theoretical Physics Thomas Gajdosik, VU Looking for some order in the chaos conservation laws for particle decays: conservation of energy: n p +...but not 0 conservation of charge: n p + e but not n p + e conservation of lepton number: n p + e - + but not n p + e - + conservation of baryon number: n p +... but notn + conservation of strangeness (only in „fast“ processes) fast K* K but only “slow” K

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Introduction to Modern Theoretical Physics Thomas Gajdosik, VU e e µ µ Decay e e 26 ns 2200 ns Scattering e-e- e+e+ e+e+ K K p p e-e- e+e+ e+e+ K K Observing particle decays and interactions

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Introduction to Modern Theoretical Physics Thomas Gajdosik, VU Symmetries as a guiding principle

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Introduction to Modern Theoretical Physics Thomas Gajdosik, VU 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!

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Introduction to Modern Theoretical Physics Thomas Gajdosik, VU How do symmetries look like in theory? symmetries are described by symmetry transformations: Example 1: Butterfly symmetry transformation S 1 : mirror all points at a line! formally: W=„original picture“ W‘=„mirrored picture“ apply symmetry in operator notation: S 1 W=W‘ symmetry is given if and only if S 1 W=W!

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Introduction to Modern Theoretical Physics Thomas Gajdosik, VU How do symmetries look like in theory? symmetries are described by symmetry transformations: Example 2: crystal lattice symmetry transformation S 2 : move all points by same vector! formally: W=„original picture“ W‘=„moved picture“ apply symmetry in operator notation: S 2 W=W‘ symmetry is given if and only if S 2 W=W!

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Introduction to Modern Theoretical Physics Thomas Gajdosik, VU Which types of symmetries do we encounter 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

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Introduction to Modern Theoretical Physics Thomas Gajdosik, VU 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 we encounter in particle physics? discrete symmetry transformations:

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Introduction to Modern Theoretical Physics Thomas Gajdosik, VU 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- e+e+ electron positron Which types of symmetries do we encounter in particle physics? discrete symmetry transformations:

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Introduction to Modern Theoretical Physics Thomas Gajdosik, VU (symmetry transformations that can be performed in arbitrarily small steps) time: physics(today) physics(tomorrow) more accurate: shift by a time-step Δt: e Δt / 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): e Δr W(t,x,y,z) = W(t,x+Δx,y+Δy,z+Δz) Which types of symmetries do we encounter in particle physics? continuous symmetry transformations:

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Introduction to Modern Theoretical Physics Thomas Gajdosik, VU orientation: physics(north) physics(west) more accurate: rotation around an arbitrary axis in space: DW(t,x,y,z) = W(t,x‘,y‘,z‘) (symmetry transformations that can be performed in arbitrarily small steps) Which types of symmetries do we encounter in particle physics? continuous symmetry transformations:

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Introduction to Modern Theoretical Physics Thomas Gajdosik, VU 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 : U(1) (t,x,y,z)=e i (t,x,y,z) dėmesio, sudėtinga! 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. Re Im 1 eiei =| |· e i (symmetry transformations that can be performed in arbitrarily small steps) Which types of symmetries do we encounter in particle physics? continuous symmetry transformations:

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Introduction to Modern Theoretical Physics Thomas Gajdosik, VU to each continuous symmetry of a field theory corresponds a certain conserved quantity, i.e. a conservation law that means: if a field theory remains unchanged under a certain symmetry transformation S, then there is a mathematical procedure to calculate a property of the field which does not change with time, whatever complicated processes are involved. Emmy Noether The fundamental importance of symmetries Noether's theorem:

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Introduction to Modern Theoretical Physics Thomas Gajdosik, VU also tomorrow the sun will rise the conservation of energy E = mc 2...and that's it! e Δt / t W(t,x,y,z) = W( t+Δt, x,y,z) = W(t,x,y,z) ! the laws of physics do not change with time more accurate: the corresponding field theory is invariant under time shifts: From Noether‘s theorem follows the conservation of a well-known property: energy! The fundamental importance of symmetries applications of Noether's theorem:

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Introduction to Modern Theoretical Physics Thomas Gajdosik, VU 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! just to be clear: we are talking about properties of the underlying theory, not a certain physics scenario

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Introduction to Modern Theoretical Physics Thomas Gajdosik, VU 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: e Δr W(t,x,y,z) = W(t,x+Δx,y+Δy,z+Δz) = W(t,x,y,z) ! The fundamental importance of symmetries applications of Noether's theorem: From Noether‘s theorem follows the conservation of another well-known property: momentum!

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Introduction to Modern Theoretical Physics Thomas Gajdosik, VU 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 theory is invariant under rotations: DW(t,x,y,z) = W(t,x,y,z) ! The fundamental importance of symmetries applications of Noether's theorem: From Noether‘s theorem follows the conservation of yet another well-known property: angular momentum!

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Introduction to Modern Theoretical Physics Thomas Gajdosik, VU even more abstract symmetries get a meaning: the conservation of charge as it turns out, the field theory of electro-dynamics is invariant under a global * U(1) transformation: U(1) (t,x,y,z)=e i (t,x,y,z) W‘=W ! The fundamental importance of symmetries applications of Noether's theorem: * global means affecting all space-points (t,x,y,z) the same From Noether‘s theorem follows the conservation of charge!

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Introduction to Modern Theoretical Physics Thomas Gajdosik, VU Overview symmetries and conservation laws contnuous symmetryconservation law time translationenergy space translationmomentum rotationangular momentum U(1) phasecharge

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Introduction to Modern Theoretical Physics Thomas Gajdosik, VU 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 small imperfections make it more interesting...

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Introduction to Modern Theoretical Physics Thomas Gajdosik, VU originally, all experiments indicated that the microcosmic world is perfectly mirror-symmetric 1956 Tsung-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 Co e-e- P e-e- beta-decay Tsung-Dao Lee & Chen Ning Yang Are symmetries perfect? the Wu experiment

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Introduction to Modern Theoretical Physics Thomas Gajdosik, VU 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-neutrino does not exist in nature at all! therefore, P-symmetry is said to be maximally violated 60 Co e-e- right-handed anti-neutrino left-handed anti-neutrino Are symmetries perfect? a deeper understanding of the Wu experiment

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Introduction to Modern Theoretical Physics Thomas Gajdosik, VU there is no left-handed anti-neutrino, but there is a left-handed neutrino (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: right-handed anti-neutrino left-handed neutrino CP Are symmetries perfect? P violation - but maybe a CP symmetry? right-handed anti-neutrino left-handed anti-neutrino left-handed neutrino

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Introduction to Modern Theoretical Physics Thomas Gajdosik, VU the kaon experiment of 1964 Rene Turlay James Cronin *1931 Val Fitch *1923 KLKL long-lived kaon decay into pions 99,8% KLKL 0,2% 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, P = - therefore, CP is conserved for the decay of the long-lived kaon into three pions, but not for the decay into two CP-Symmetry is (slightly) violated Are symmetries perfect?

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Introduction to Modern Theoretical Physics Thomas Gajdosik, VU why CP-violation is important for our existence: Andrej Sacharow 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! implications of CP-violation in cosmology Are symmetries perfect?

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Introduction to Modern Theoretical Physics Thomas Gajdosik, VU 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!“ "last hope" CPT-symmetry? Are symmetries perfect?

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Introduction to Modern Theoretical Physics Thomas Gajdosik, VU Overview discrete symmetries symmetryvalid in the universe? P (mirroring) C (exchange matter/anti-matter) T (time inversion) CP (combination of C and P) CPT (combination of C,P & T)

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Introduction to Modern Theoretical Physics Thomas Gajdosik, VU The Standard Model – Particle content

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Introduction to Modern Theoretical Physics Thomas Gajdosik, VU fermions (spin ½)bosons (spin 1,2) strong weak e charge 0 +2/3 -1/3 gravity ? weak force W, Z electromagnetic strong force g e d u s c b t +1/ d u d u u d u d proton neutron q q q q q The Standard Model - Overview particles interactions charge leptonsquarks generation1 st 2 nd 3 rd 1 st 2 nd 3 rd

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Introduction to Modern Theoretical Physics Thomas Gajdosik, VU fermions (spin ½)bosons (spin 1,2) strong weak e charge gravity ? weak force W, Z electromagnetic strong force g e d u s c b t The Standard Model - Overview anti particles interactions charge leptonsquarks generation1 st 2 nd 3 rd 1 st 2 nd 3 rd e /3 +1/3 e d u s c b t +1 pion ( ) d u

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Introduction to Modern Theoretical Physics Thomas Gajdosik, VU ++ u u u d d d u s u u s c d DD s u b b

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Introduction to Modern Theoretical Physics Thomas Gajdosik, VU ++ u u u u d d u s c d DD s u b b d u u d u d protonneutron mesons baryons... nucleus He-nucleus ( -particle) atom matter

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Introduction to Modern Theoretical Physics Thomas Gajdosik, VU Particles of the Standard Model: Fermions 1.reminder about the particles from the historical introduction 2.the ordering principle example: electron and neutrino 3.the systematics extending the ordering to all fermions counting the degrees of freedom 4.overview

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Introduction to Modern Theoretical Physics Thomas Gajdosik, VU 1897 the electron e-e- Thomson

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Introduction to Modern Theoretical Physics Thomas Gajdosik, VU 1897 the positron (anti-matter) e-e 1914 e+e+ p 1932 n 1937 µ 1947 Anderson Dirac prediction discovery

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Introduction to Modern Theoretical Physics Thomas Gajdosik, VU 1897 the neutrino e-e 1914 p 1932 n 1937 µ 1947 e+e+ Fermi Pauli

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Introduction to Modern Theoretical Physics Thomas Gajdosik, VU there is no left-handed anti-neutrino, but there is a left-handed neutrino (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: right-handed anti-neutrino left-handed neutrino CP Are symmetries perfect? P violation - but maybe a CP symmetry? right-handed anti-neutrino left-handed anti-neutrino left-handed neutrino Reminder:

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Introduction to Modern Theoretical Physics Thomas Gajdosik, VU Ordering principle discreet symmetries Parity P –left handed or right handed Charge Conjugation C –particle or antiparticle Charge Q or Flavour –possible values: Generation –first – second – third 0 ⅔ -⅓-⅓ eud e eLeL eReR _

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Introduction to Modern Theoretical Physics Thomas Gajdosik, VU Particles of the Standard Model: Fermions Antiparticle Particle RightLeft eReR - eReR + e eLeL - eLeL + e _

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Introduction to Modern Theoretical Physics Thomas Gajdosik, VU 1897 the proton e-e 1914 Rutherford p

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Introduction to Modern Theoretical Physics Thomas Gajdosik, VU 1897 the neutron e-e 1914 n p 1932 Chadwick

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Introduction to Modern Theoretical Physics Thomas Gajdosik, VU partons / parton model e-e- p n µ e+e+ Richard Feynman

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Introduction to Modern Theoretical Physics Thomas Gajdosik, VU Particles of the Standard Model: Fermions Antiparticle Particle RightLeft eReR - eReR + e eLeL - eLeL + e _ uLuL dLdL uRuR dRdR

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Introduction to Modern Theoretical Physics Thomas Gajdosik, VU 1897 the pion e-e 1914 p 1932 n 1937 µ 1947 Powell Yukawa predictiondiscovery

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Introduction to Modern Theoretical Physics Thomas Gajdosik, VU Particles of the Standard Model: Fermions Antiparticle Particle RightLeft eReR - eReR + e eLeL - eLeL + uLuL dLdL uLuL _ _ dLdL uRuR dRdR uRuR _ _ dRdR

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Introduction to Modern Theoretical Physics Thomas Gajdosik, VU 1897 the muon e-e 1914 µ p 1932 n 1937 Who ordered that one? Hess Anderson, Neddermeyer Street, Stevenson spark chamber

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Introduction to Modern Theoretical Physics Thomas Gajdosik, VU Particles of the Standard Model: Fermions RR - RR + LL - LL + Antiparticle Particle RightLeft eReR - eReR + e eLeL - eLeL + uLuL dLdL uLuL _ _ dLdL uRuR dRdR uRuR _ _ dRdR

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Introduction to Modern Theoretical Physics Thomas Gajdosik, VU 1897 strange particles e-e 1914 K K p 1932 n 1937 µ 1947 e+e+ Rochester, Butler,

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Introduction to Modern Theoretical Physics Thomas Gajdosik, VU Particles of the Standard Model: Fermions RR - RR + LL - LL + Antiparticle Particle RightLeft sLsL _ sLsL sRsR _ sRsR eReR - eReR + e eLeL - eLeL + uLuL dLdL uLuL _ _ dLdL uRuR dRdR uRuR _ _ dRdR

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Introduction to Modern Theoretical Physics Thomas Gajdosik, VU 1897 antineutrino e-e 1914 p 1932 n 1937 µ 1956 e+e+ reactors: Clyde Cowan, Frederick Reines _

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Introduction to Modern Theoretical Physics Thomas Gajdosik, VU Particles of the Standard Model: Fermions RR - RR + LL - LL + Antiparticle Particle RightLeft _ sLsL _ sLsL sRsR _ sRsR eReR - eReR + e eLeL - eLeL + e _ uLuL dLdL uLuL _ _ dLdL uRuR dRdR uRuR _ _ dRdR

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Introduction to Modern Theoretical Physics Thomas Gajdosik, VU charm quark: J/Ψ e-e- p n µ e+e+ Burt Richter (SLAC), Samuel Ting (BNL) 1974 c

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Introduction to Modern Theoretical Physics Thomas Gajdosik, VU Particles of the Standard Model: Fermions RR - RR + LL - LL + Antiparticle Particle RightLeft _ cLcL sLsL cLcL _ _ sLsL cRcR sRsR cRcR _ _ sRsR eReR - eReR + e eLeL - eLeL + e _ uLuL dLdL uLuL _ _ dLdL uRuR dRdR uRuR _ _ dRdR

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Introduction to Modern Theoretical Physics Thomas Gajdosik, VU tau lepton: e-e- p n µ e+e+ Martin Perl (SLAC-LBL) 1975

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Introduction to Modern Theoretical Physics Thomas Gajdosik, VU Particles of the Standard Model: Fermions RR - RR + LL - LL + Antiparticle Particle RightLeft _ cLcL sLsL cLcL _ _ sLsL cRcR sRsR cRcR _ _ sRsR RR - RR + LL - LL + eReR - eReR + e eLeL - eLeL + e _ uLuL dLdL uLuL _ _ dLdL uRuR dRdR uRuR _ _ dRdR

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Introduction to Modern Theoretical Physics Thomas Gajdosik, VU bottom quark e-e- p n µ e+e+ E288 (Fermilab) 1977 b

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Introduction to Modern Theoretical Physics Thomas Gajdosik, VU Particles of the Standard Model: Fermions RR - RR + LL - LL + Antiparticle Particle RightLeft _ cLcL sLsL cLcL _ _ sLsL cRcR sRsR cRcR _ _ sRsR RR - RR + LL - LL + bLbL _ bLbL bRbR _ bRbR eReR - eReR + e eLeL - eLeL + e _ uLuL dLdL uLuL _ _ dLdL uRuR dRdR uRuR _ _ dRdR

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Introduction to Modern Theoretical Physics Thomas Gajdosik, VU top quark e-e- p n µ e+e+ t CDF, D0 (Fermilab)

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Introduction to Modern Theoretical Physics Thomas Gajdosik, VU Particles of the Standard Model: Fermions RR - RR + LL - LL + Antiparticle Particle RightLeft _ cLcL sLsL cLcL _ _ sLsL cRcR sRsR cRcR _ _ sRsR RR - RR + LL - LL + t L bLbL __ bLbL t R bRbR __ bRbR eReR - eReR + e eLeL - eLeL + e _ uLuL dLdL uLuL _ _ dLdL uRuR dRdR uRuR _ _ dRdR

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Introduction to Modern Theoretical Physics Thomas Gajdosik, VU tau neutrino: e-e- p n µ e+e+ DONUT (Fermilab) 2000

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Introduction to Modern Theoretical Physics Thomas Gajdosik, VU Particles of the Standard Model: Fermions RR - RR + LL - LL + Antiparticle Particle RightLeft _ cLcL sLsL cLcL _ _ sLsL cRcR sRsR cRcR _ _ sRsR RR - RR + LL - LL + _ t L bLbL __ bLbL t R bRbR __ bRbR eReR - eReR + e eLeL - eLeL + e _ uLuL dLdL uLuL _ _ dLdL uRuR dRdR uRuR _ _ dRdR

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Introduction to Modern Theoretical Physics Thomas Gajdosik, VU solve the “solar neutrino puzzle” neutrinos have a tiny mass there exist also right-handed neutrinos but they have: no charge, no hypercharge, and no color no interaction, except the mass-term their existence does not change the Standard Model ! neutrino oscillations: e ↔ ↔ x

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Introduction to Modern Theoretical Physics Thomas Gajdosik, VU Particles of the Standard Model: Fermions RR - RR + R LL - LL + Antiparticle Particle RightLeft R _ cLcL sLsL cLcL _ _ sLsL cRcR sRsR cRcR _ _ sRsR RR - RR + R LL - LL + _ t L bLbL __ bLbL t R bRbR __ bRbR eReR - eReR + eR eLeL - eLeL + _ uLuL dLdL uLuL _ _ dLdL uRuR dRdR uRuR _ _ dRdR e _ _ e _

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Introduction to Modern Theoretical Physics Thomas Gajdosik, VU Symmetries as a guiding principle: leading to gauge bosons

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Introduction to Modern Theoretical Physics Thomas Gajdosik, VU How symmetries make theories remember: physics is invariant under a U(1)-transformation of the particle field , U(1) (t,x,y,z) = e i (t,x,y,z) the phase here is global, that means a synchronous phase transformation of all particles in the whole universe! the idea: replace global transformation by a local one: U(1) (t,x,y,z) = e i t,x,y,z (t,x,y,z) ? QED, the quantum theory of light ( different particles at different positions get transformed independently)

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Introduction to Modern Theoretical Physics Thomas Gajdosik, VU consequence of a local U(1) transformation: if only particles are transformed (not including their electromagnetic interaction), then the theory is not invariant under local U(1) transformations! however, if electromagnetic interaction is included, then the theory is locally U(1) symmetric! this works only, because the electromagnetic interaction has just the right form How symmetries make theories QED, the quantum theory of light coincidence or deeper truth?

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Introduction to Modern Theoretical Physics Thomas Gajdosik, VU the modern view: for a given global symmetry, it is postulated that it is also valid locally from this, one gets automatically an interaction connected with this symmetry in addition, one gets additional particles (force carriers, for U(1) it is the photon), which mediate the interaction How symmetries make theories QED, the quantum theory of light each local symmetry produces an interaction plus new particles which mediate it

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Introduction to Modern Theoretical Physics Thomas Gajdosik, VU experiments showed that protons (and neutrons) have an inner structure the observed symmetries suggested the postulation of the existence of 3 quarks inside the nucleon. quarks have an additional property, called color there are three color states: red, green, blue qqq How symmetries make theories Quantum-Chromo-Dynamics (QCD) the theory of the strong force

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Introduction to Modern Theoretical Physics Thomas Gajdosik, VU idea: there is a symmetry between different color states, i.e. they can be arbitrarily re-mixed without changing the theory: q q q qqq A rr +A rg +A rb qqq A gr +A gg +A gb qqq A br +A bg +A bb mathematically, this corresponds to a 3x3 matrix A, and the symmetry group is known as SU(3) How symmetries make theories Quantum-Chromo-Dynamics (QCD) the theory of the strong force = = = „new colors“

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Introduction to Modern Theoretical Physics Thomas Gajdosik, VU by postulating a local SU(3) symmetry, one automatically gets a new kind of interaction between the quarks it is known as strong force, the corresponding force carriers are called gluons it is responsible for the binding of mesons and baryons and as well for the stability of nuclei the color symmetry of quarks enables the existence of atoms! How symmetries make theories Quantum-Chromo-Dynamics (QCD) the theory of the strong force

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Introduction to Modern Theoretical Physics Thomas Gajdosik, VU fermions (spin ½) e charge 0 +2/3 -1/3 e d u s c b t charge leptonsquarks generation1 st 2 nd 3 rd 1 st 2 nd 3 rd How symmetries make theories sketch of electro-weak interaction postulating a local SU(2) symmetry between up- and down-type particles produce a new kind of interaction for leptons and quarks however, since only left-handed neutrinos exist, this symmetry can only involve left-handed electrons for right-handed particles, a separate U(1)-symmetry is postulated together they form the electro-weak theory of the standard model A uu +A ud A du +A dd = = e e e e e e A uu +A ud A du +A dd = = u d du du

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Introduction to Modern Theoretical Physics Thomas Gajdosik, VU Overview Symmetries and Interactions gauge symmetryinteraction U(1) (symmetry of all leptons and quarks) U(1) Y SU(2) (symmetry of only left-handed leptons and quarks ) weak SU(3) (symmetry of quarks) strong ? (is it a symmetry of space-time geometry itself, or something qualitatively different?) (quantum-) gravity electro-weak

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Introduction to Modern Theoretical Physics Thomas Gajdosik, VU symmetry breaking example: chess the rules of chess are in principle absolutely symmetric for both players i.e. the rules how the pieces move are the same for black and white but: symmetry is broken at the beginning, due to the initial setup of the pieces therefore, e.g. a bishop never can change the color of the field it is standing on

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Introduction to Modern Theoretical Physics Thomas Gajdosik, VU spontaneous symmetry breaking energy Higgs-field hot universe (shortly after big bang) 0 particles are massless cold universe (condensed into an asymmetric state) particles get a mass In the standard model, the particle‘s masses are an effect of symmetry breaking: originally, all particles are massless but there is an additional interaction with the so-called Higgs-field if there were no Higgs-field, the interaction would have no effect however, due to a spontaneous symmetry breaking, the whole universe is filled with a non-zero Higgs-field the interaction with this omni-present field produces what we know as mass of particles symmetry breaking the origin of mass

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Introduction to Modern Theoretical Physics Thomas Gajdosik, VU the result of the search for the higgs will be one of the most important scientific results of 2012! the existence of the Higgs-field is up to today not experimentally confirmed! a theory of a omni-present, static field, whose only effect is giving particles their mass can not be falsified by principle however, a consistent theory also predicts excitations of the Higgs-field: Higgs particles the interaction of these Higgs particles with ordinary particles (and its strength) is completely determined by theory, and controlled by just one parameter, the value of the background Higgs field the necessary energy and luminosity for the hunt for the higgs will be provided by the LHC (Large Hardon Collider) at CERN symmetry breaking the search for the higgs

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Introduction to Modern Theoretical Physics Thomas Gajdosik, VU

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Particle Physics Nuclear Physics all other Physics

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