Weak Interactions: towards the Standard Model of Physics


 Jasmine Gilbert
 2 years ago
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1 Weak Interactions: towards the Standard Model of Physics Weak interactions From βdecay to Neutral currents Weak interactions: are very different world CPviolation: power of logics and audacity Some experimental consequences K  oscillations Setting the stage for the Standard Model 1
2 The Fundamental Forces Presently: we see four forces in nature Force Strength* Theory Mediator Strong 1 Chromodynamics (QCD) Gluon Electromagnetic 12 Electrodynamics (QED) Photon Weak 113 (Flavordynamics) W, Z GlashowWeinbergSalam Gravitational 142 General Theory of Relativity Graviton Strength: to be taken as an indication; depends on force, energy, distance (and maybe on time!) 2
3 Effective range of Fundamental Forces Strong interaction Potential 1/r Electrom. interaction Weak interaction M(gluon)=; but range limited by Gluongluon selfinteraction Range limited due to heavy IVB Potential 1/r 3
4 Quantum Electrodynamics (QED) Oldest, simplest, most successful of the dynamical theories All electromagnetic processes are ultimately reducible to the process represented by the diagram below  Convention for interpreting the diagram time flows horizontally the charged particle enters emits (or absorbs) a photon the charged particle exists charged particle could be  charged lepton  a quark 4
5 Quantum Chromodynamics (QCD) o o in QCD: color plays the role of charge fundamental vertex o Analogous to Bottom diagram p. 66 o o bound state of force between two quarks is mediated by the exchange of gluons 5
6 Quantum Chromo Dynamics QCD: Fundamental differences to QED QED: one type of charge, i.e. one number (+, ); photon is neutral QCD: three kinds of color: red, green, blue  Fundamental process q q + : color of quark (not its flavor may change e.g.: blue upquark red upquark color is conserved gluon carries away the difference gluons are bicolored with one positive and negative unit (e.g.: one unit of blueness and minus one unit of redness) 3 x 3 = 9 possibilities experimentally only 8 different gluons observed; ninth gluon would be color singlet and therefore observable not observed, i.e. does not exist g 6
7 β Decay: experimental facts Fundamental reaction n p + e + v n ( u, d, d) p ( u, u, d) + e + In the quark picture:  This particular weak interaction process changes quark flavor However, the following weak interaction process preserves quark flavor ν µ p ν + + µ  Neutrinoproton scattering: hint of two different types of processes (in modern language: Mediators ) Observation of kinematics of βdecay led to neutrino hypothesis  Is the neutrino really massless? The happy end to a 4year struggle will be discussed later Observation of (maximal) parity violation in βdecay (first observed in the decay of 6 Co) p v 7
8 Neutron decay through weak interactions βdecay of neutron : n p + e  + anti ν e apart from strong interaction contamination from the spectator quarks is related in structure to µ decay and to piondecay 8
9 Neutron decay through weak interactions Measurements of neutron decay parameters and their correlations are a very active area of research These measurements probe Standard Model Parameters, like quark coupling; they are also sensitive to Physics Beyond Standard Model, e.g. Supersymmetry or other new particles (Axions) 9
10 β Decay: attempting to measure the mass of neutrinos 1
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12 Neutrinos: There is much more to it µ e + γ not observed, although charge and Lepton numbers are conserved Why? famous rule of thumb (Feynman):  whatever is not expressively forbidden, is mandatory (in physics) Absence of µ e + γ conservation of muonness  but µ e + ν + ν Perhaps: two kinds of neutrinos?  one associated with e ν e (L e = +1)  one associated with µ ν µ (L µ = +1) 12
13 Neutrinos: There is much more to it Answer: conservation of electron number and muon number n p + + e + ν e π µ + ν µ ; π + µ + + ν µ µ e _ + ν e + ν µ ; µ + e + + ν e + ν µ Lepton quantum number is attached to leptons and is conserved (however: see later: neutrino oscillations) 13
14 MEG Collaboration Question: is Lepton number conservation a PERFECT symmetry? Search for Lepton Flavor violating reaction μ + e + + γ Present upper limit on Branching ratio B: B < 2.4 * 112 Top view Front view LXe Photon Detector 14
15 Neutral KMeson System revisited: Oscillations K and K can be produced in strong interaction processes  K  + p K + n; K + + n K + p;..  Kaons are produced in states of unique strangeness  K (S= 1) is antiparticle of K (S=+1) Neutral kaons are unstable and decay through weak interaction  Experimentally observed: two different decay times Possible, if these states consist of a superposition of two distinct states with different lifetimes  a shortlived one, originally labeled K 1  a longlived one, originally labeled K 2 K and K are eigenstates of the Strong Hamiltonian, but not eigenstates of the Weak Hamiltonian K 1 and K 2 are eigenstates of the weak Hamiltonian Eigenstates of weak Hamiltonian are different from those of st.h. Weak interaction does not conserve strangeness: K + > π +π +
16 Neutral KSystem K s are pseudoscalars P K = K P K = K C K = K C K = K CP K = K CP K = K The normalized eigenstates of CP are (assuming CP is good symmetry) ( )( ) ( ) ( ) 1 1 K K K = K K + 1 = 2 2 K 2 CP K1 = K1 CP K2 = K2 If CP is conserved in weak interactions  K 1 can decay only in CP = +1 state  K 2 can decay only in CP = 1 state Kaons typically decay into (P π =  π C π = π ) 2 π state (CP = +1) 3 π state (CP = 1) Conclusion: K 1 2π, K 2 3π 16
17 K 1, K 2 2π decay is much faster (larger phase space, more energy available) Start with K beam  component will decay quickly, leaving more s K 1 ( 1 )( K K ) 1964: Cronin, Fitch and collaborators observe CP violation K  beam: by letting the K 1 component decay can produce arbitrarily pure K 2  beam; K 2 is a CP=1 state; can only decay into CP=1 (3 pions), if CP is conserved K Observation: 227 3πdecays and 45 2πdecays = 2 Longlived K 2 is NOT perfect eigenstate of CP, contains a small admixture of K K 2 17
18 Oscillations in the neutral KSystem Inverting the eigenstates of CP ( )( ) ( ) ( ) 1 1 K = K K K 2 2 = K + 2 one obtains K o 1 K = ( 1 )( ) ( ) ( ) K + K, K = 1 K K 2 Can be seen as : the strong interaction eigenstates, K and K are superpositions of the weak eigenstates K 1 and K At time of production the K and K states correspond to the superposition of K 1 and K states; K 2 1 component will decay much faster, the component will become enriched; BUT is an equal admixture of K and K 2 K An initially pure K or K state will evolve into a mixture of these two states! K K (or strangeness ) oscillations 2 K
19 Oscillations in the neutral KSystem: time evolution The states and are stable with respect to strong interactions, but decay weakly; decays phenomenologically described with an effective Hamiltonian in the timedependent Schrödinger equation Hamiltonian involves the masses and lifetimes of the two states and After a few pages of matrix manipulation and algebra one obtains for the timedependent probabilities of the and states: 19 K K ) ( ) ( t H t t i eff ψ ψ = K L K S K K + + = + t m e e e t K P L S L S t t cos ), ( 1 1 ( 2 1 τ τ τ τ S L t t m m m t m e e e t K P L S L S = + = + cos 2 4 ), ( 1 1 ( 2 1 τ τ τ τ κ
20 Oscillations in the neutral KSystem: time evolution If the states K and K had the same masses, the beam intensities would exhibit the sum of two exponential decays, corresponding to the two characteristic decay times Experimentally observed are oscillations between the two states, implying a finite mass difference, for which one obtains m = m L m S 3.5 * 112 MeV/ c 2 (recall: mass K = MeV/ c 2 ) This mass difference can be converted into an upper limit on the K K mass difference of < 118 m K implying a very stringent on the validity of CPT Similar physics also observed in the B B system  Studied at Beauty Factories  Babar at SLAC (terminated)  Belle and 2 nd generationexperiment Belle II HEPHY is leading institute in Belle and Belle II, offering outstanding research opportunities 2
21 (uds) (uud) + (u bar,d) 21 21
22 22
23 From Cabibbo to GIM Cabbibo s suggestion was very successful, explaining a number of decay rates, except:  Within this description K would decay into μ + μ  with a rate far larger than experimentally measured Solution proposed in 197 by Glashow, Iliopoulos, Maiani (GIM);  In the GIM mechanism a fourth quark, charm was introduced, four years before first experimental indications  Approximate cancellation between the two diagrams resulting in a rate consistent with experiment 23
24 24
25 Conclusions so far Eigenstates of the Weak Hamiltonian are different to those of the Strong Hamiltonian Eigenstates of the Weak Hamiltonian do not have unique Strangeness Transposed to the quark level (more on this topic later):  Quark Doublets of the Weak Hamiltonian are mixed states of these doublets u d ' c s t ' b 25
26 Unifying Interactions Maxwell (1865): electricity and magnetism described by one single theory involving a vector field, the electromagnetic field, interacting between electric charges and currents Maxwell equations involve arbitrary constants: e.g. velocity of light c and electric charge e, to be determined experimentally Einstein (and others): dream of unified field theory of all four intersections Unifying electromagnetic and weak interactions into electroweak :  Fundamental idea: symmetry between electromagnetic and weak interactions manifest at large momentum transfers (q 2 >>1 4 GeV 2 )  At low energies: symmetry is broken First ideas for unified treatment of electromagnetic and weak interactions :  Schwinger (1957): first conceptual work  Glashow (1961)... 26
27 From Fermi to GlashowSalamWeinberg: from Weak to Electroweak Interactions Fermi theory of weak interactions:  Fermions involved have point (contact) interaction; no mediating particle required  Excellent approximation for lowenergy phenomena, such as βdecay  At high energy: ν e + e  ν e + e  has total cross section σ(ν e e) = G 2 s/π; G Fermi coupling constant; s (total cms energy) 2 cross section depends on coupling G and energy ~ s (phase space) Catastrophic problem:  This cross section exceeds Unitarity limit : total scattered intensity is larger than incident intensity for s >~ 3 GeV/c 2  Fundamentally: the Fermi contact interaction has divergent higher order terms  Introducing the concept of an exchange interaction with a heavy, mass M, particle (gauge boson) being exchanged spreads the interaction over range ~ 1/M and saturates cross section at G 2 M 2 / π
28 From Fermi to GlashowSalamWeinberg: from Weak to Electroweak Interactions Remember Yukawa s problem with the strong interactions  Estimate of the mass of the exchanges particle (the pion) based on the range of the strong force: approximately size of nucleon Problem for weak interactions: no equivalent way to estimate range of weak interaction (no weakly bound states)  Exchange particle was given the (not very imaginative) name: Intermediate Vector Boson (IVB) (remember: photon is vector boson)  Estimate of mass initially based on educated guesses, i.e. limits obtained by experiments searching for existence of IVBs Emergence of the electroweak theory, formulated by Glashow, Weinberg and Salam (end of 196 s)  Three IVB s: W +, W , Z (plus photon) Note the presence of charged and neutral mediators! Neutral mediator is a novel feature of this theory 28
29 Electroweak unification Glashow (1961): aim to unify electromagnetic and weak interactions in a single theoretical description, building on work by Schwinger Several difficulties had to be overcome...  Enormous difference in strength of em and weak interactions  Glashow (and others) recognized that this could be solved, if the weak interactions were mediated by extremely massive particle  Glashow (and all other physicists!) did not know how to introduce a heavy mediator into the theory: Quoting Glashow: Is is a stumbling block, we must overlook  Difference in electromagnetic (only vector coupling γ μ ) and weak vertex factors γ μ (1 γ 5 )  γ μ represents the vector coupling, as in QED; γ μ γ 5 axial coupling which violates parity  This problem was formally treated with the spinor concept, as sketched on following transparencies 29
30 From weak to electroweak interaction Quarks and leptons are arranged in doublets  Lepton generations  Quark generations (weak interaction generation) Reminiscent of spin, isospin structure for hadrons, represented by SU(2) transformation properties  Strong interaction isospin used to classify hadrons; good symmetry, if electromagnetic interaction is ignored ( turned off ) Weak isospin classifies leptons and quarks  Up and down states of leptons and quarks are the same, if electromagnetic interaction is turned off Weak Hypercharge : Y= 2(QJ 3 ) Q = J 3 + Y/2; 3
31 Weak Hypercharge and lefthanded and righthanded particles Example : (ν, e  ) doublet: Y(ν) = 2(1/2) = 1; Y(e  ) = 2 (1+1/2) = 1 (u,d) quark doublet : Y(u) = 2(2/31/2) = 1/3; Y(d) = 2 (1/3+1/2) = 1/3 weak hypercharge quantum number is the same for both members of a doublet In the Standard Model only lefthanded leptons and quarks have doublet structure  Isospin doublets Righthanded quarks and righthanded charged leptons are  Isospin I= singlets Weak interactions have doublet (SU L (2) symmetry) and singlet (U Y (1)) structure Electromagnetic interaction is U(1) invariant > can be regarded as a particular combination of weak isospin and weak hypercharge 31
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33 Weak Interactions mediated by heavy exchange particle 33
34 Electroweak Theory Developed by S. Weinberg and A. Salam, applying new ideas about gauge theories originally developed by S. Glashow. All three received Nobel Prize in 1979 Weinberg was actually studying Strong Interactions, until he realized that his concept corresponded to Weak Interactions! Theory has 4 mediators of electroweak force ( gauge bosons )  Photon γ (m=)  three heavy IVB s (W +, W , Z ) required to make theory consistent EW Theory predicts  M Z = 92 GeV/c 2 M W = M Z cos θ W ;  θ W = ; M W = 82 GeV/c 2 ;  sinθ w is parameter in theory which must be be measured experimentally Actual measured values 34
35 Weak Interactions The newly developed electroweak theory predicts two kinds of weak interactions: charged and neutral Neutral weak interactions (actually discovered much later than charged WI)  fundamental vertex  f (fermion) can be any lepton or any quark  Z (one of the four bosons responsible for the electroweak interaction) mediates a new kind of weak force, resulting in processes such as Example: neutrinoelectron scattering 35
36 Neutral Weak Interactions Middle p. 73 neutrino proton scattering two spectator quarks go along, bound by Strong Interaction to d quark Similarly: Note: any process mediated by photon could also be mediated by Z example: electronelectron scattering very minute corrections to Coulomb law observed in e + + e  > μ + + μ  36
37 First Observation of Weak Neutral Current Interaction (CERN 1973) Muon antineutrino electron scattering producing energetic electron and antineutrino First event: beginning of several months of intensive further searches and a violent scientific controversy with an US Collaboration which originally reported no evidence for this type of interactions Joke: the US physicists had identified Alternating neutral currents The confirmation of neutral current reactions provided a major additional contribution to the emergent idea of electroweak theory Unified physics theory confirmed a finding of historic importance (New 37 York Times, 1973)
38 Charged Weak Interactions Electromagnetic, strong and neutral weak interactions:  Quark or lepton not changed: same quark (lepton) in same out  Strong interaction only changes color of quark, not its flavor New effect in charged weak interactions  Charged weak interactions are the only interactions that change the flavor true decay of a particle Fundamental charged lepton vertex o negative lepton converts into corresponding neutrino with emission of W  Neutrinomuon scattering (difficult to study ) 38
39 This image cannot currently be displayed. Charged weak interactions of quarks Leptonic weak vertices connect members of the same generation (e  ν e emitting W , μ  μ  emitting Z ): electron never goes to muon, etc. Quarks: fundamental charged quark vertex quark (⅓, d, s, b) quark (⅔, u, c, t) Surprise: flavor is NOT conserved in charged weak interactions! (far end of the Wline can couple to lepton ( semileptonic process) or to other quarks (purely hadronic interaction) 39
40 Example: Muon decay Calculations proceed analogously to QED calculations  Feynman rules are the same as for QED, apart from the modifications in vertex factor and propagator Muon decay: with the matrix element (compare the QED calculation for e + µ e + µ) M Decay rate Γ(Fermi s Golden Rule )  Γ ~ M 2 * Phase factor  With the result for total decay rate  Note that only the ratio g W /M W enters 4
41 Ultima ratio: power of logic 1973: Kobayashi and Maskawa Structure of Weak Charged Current was established GIM mechanism successful: mixing of quarks good strategy Kobayashi, Maskawa: aim to treat CP violation in Standard Model  Discover that treatment of CP violation within the SM framework requires a complex number in the rotation matrix; nontrivial only in a 3*3 matrix 3 generation of quarks and leptons: implemented by Kobayashi and Maskawa in 1973 before the discovery of c, b, tquark! Requires 3x3 Matrix, which can be parameterized with three parameters, which are obtained from measurements  one parameter is a phase, which generates CP violation in the Standard Model These measurements are a very active research area CP violation Nobel Prize 28 for Kobayashi and Maskawa 41
42 Quark Mixing in the Weak Interaction Sector Mixing of the mass eigenstates is expressed with the matrix V CKM c ij cos θ ij; s ij...sin θ ij ; if θ 23 = θ 13 = CabibboGIM picture Elements of this matrix reflect the coupling of the W boson to all the quark pairs: e.g. V ud :coupling of u to d: d u + W  Transition rate q i q j is proportional to [V ij ] 2 Dominant transitions in Wdecay are to members of the same doublet 42 diagonal matrix elements close to unity; offdiagonal small
43 CKM Matrix Weak eigenstates d, s, b are linear combinations of the mass eigenstates d, s, b CKM Matrix V CKM = 43
44 Quark Mixing: CabibboKobayashiMaskawa matrix Mixing of the mass eigenstates is expressed with the matrix V CKM Alternate representation Matrix can be parameterized with three parameters (three generalized Cabibbo angles ),to be determined by experiment, and one phase In the Standard Model, CPviolation can be explained by a nontrivial complex phase iη in this matrix This would not be possible with only two generations 44
45 Quark Mixing: CabibboKobayashiMaskawa matrix Matrix desribes a mixture of states whose total number does not change; so the matrix has to be unitary: V V + = V + V = 1 this yields the relation which can be graphically represented in the form of one of six socalled unitarity triangles 45
46 46
47 The unitarity triangle: measurements Measurements have confirmed with high precision the unitarity of the triangle: the red ellipse is the 1 σ error contour; Next steps: increase the precision by factor ten to search for significant deviations: physics beyond Standard Model should be reflected also in deviations from the SM description of CP violation
48 !: The Inexorable Rise of the Standard Model (SM) Today s physics world as described by the Standard Model, is made of  four interactions: (gravitation), weak, electromagnetic, strong  12x3 quarks and 12 leptons  4 IVB s for ew force  8 gluons, mediating the strong force  Higgs particle (explained later) There are 61 particles  is this really the hallmark of a fundamental description? The obvious question: why 3 generations of quarks  perhaps: matterantimatter symmetry? After the ProtonAntiproton collider, the Discovery Machine LEP e + e  collider was the next logical step to perform precise tests of the Standard Model LHC to complete the Standard Model This will be the story of the next lectures 48
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