Particle Physics Status and Perspectives

Particle Physics Status and Perspectives 142.095 Claudia-Elisabeth Wulz Institute of High Energy Physics Austrian Academy of Sciences c/o CERN/PH, CH-1211 Geneva 23 Tel. 0041 22 767 6592, GSM: 0041 75 411 0919 E-mail: Claudia.Wulz@cern.ch http: //home.cern.ch/~wulz 1 June 2017 Part 3

Literature A. Pich: The Standard Model of Electroweak Interactions, http://arxiv.org/abs/0705.4264 W. Hollik: Electroweak Theory, http://dx.doi.org/10.1088/1742-6596/53/1/002 T. Morii, C.S. Lim, S.N. Mukherjee: The Physics of the Standard Model and Beyond, World Scientific Publishing Co. (2004) D. Griffiths: Introduction to Elementary Particles, Wiley VCH, (2008)

The Standard Model of Particle Physics The Standard Model is a theory of the strong, weak and electromagnetic forces, formulated in the language of quantum gauge field theories, and of the elementary particles that take part in these interactions. It does, however, not include gravity. Interactions are mediated by the exchange of virtual particles. FORCE Fundamental forces RELATIVE STRENGTH RANGE CARRIER Strong 1 10-15 m Gluons Weak 10-6 10-18 m W, Z Electromagnetic α (10-2 ) infinite Photon Gravitational 10-38 infinite Graviton? 2

Particle Content of the Standard Model Matter particles: Fermions (half-integer spin, s = ½ħ) and their antiparticles. There are 3 families (generations) of fermion fields, which are identical except for their masses. Fermions come as leptons and quarks. Mediator particles: Gauge bosons (integer spin, s = 1ħ). There are 3 types of gauge bosons, corresponding to the 3 interactions described by the Standard Model. Higgs particle: Needed to explain that the symmetries of the electroweak theory are broken to the residual gauge symmetry of QED. Particles that interact with the Higgs field cannot propagate at the speed of light and acquire masses through coupling to the Higgs boson (s = 0ħ). 3

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History of the Standard Model 1964 Quarks (u,d,s) are postulated by M. Gell-Mann and G. Zweig. 1964 R. Brout, F. Englert, P. Higgs, G. Guralnik, C. Hagen, T. Kibble develop the mechanism to generate mass (now called BEH mechanism) 1965 Color is postulated by O. W. Greenberg, M. Y. Han, Y. Nambu. 1967 S. Weinberg, Sh. Glashow and A. Salam develop the electroweak theory, which unifies electromagnetic and weak interactions (Nobel prize 1979), and incorporate the BEH mechanism to generate mass for W, Z and fermions (not neutrinos). 1969 J. Friedman, H. Kendall, R. Taylor discover that the proton has a substructure (evidence of quarks) in a deep elastic scattering experiment. 1970 GIM mechanism: Introduction of a 4 th quark (c) allows a theory which suppresses flavor-changing neutral currents mediated by the Z boson. 1970 Formulation of a quantum theory of the strong interaction (QCD, quantum chromodynamics) by H. Fritzsch and M. Gell-Mann. 1971 Renormalizability of Yang-Mills theories with spontaneous symmetry breaking (G. t Hooft, M. Veltman) 5

History of the Standard Model 1974 Asymptotic freedom by D. Politzer, D. Gross, F. Wilczek. 1974 The Standard Model of particle physics in its modern form is presented by J. Iliopoulos. 1974 The charm quark is found at SLAC (B. Richter et al.) and in Brookhaven (S. Ting et al.), through the discovery of the J/ψ. 1975 Discovery of the tau lepton at SLAC (M. Perl et al.). 1977 Discovery of the bottom quark (postulated 1973 by M. Kobayashi, T. Maskawa) at Fermilab (L. Lederman et al.). 1983 The W- and Z bosons, mediators of the weak interaction, are discovered at CERN (C. Rubbia et al.). 1995 Discovery of the top quarks, the last missing quark, at Fermilab. 2000 Discovery of the tau neutrino, the last missing leptons, at the DONUT experiment at Fermilab. 2012 Discovery of the Higgs boson at CERN. Today Measurement of Higgs properties and search for physics beyond the Standard Model 6

Leptons There are 6 leptons (and their antiparticles), classified by lepton number (L e, L µ, L τ ) and electric charge (Q). Lepton L e L µ L τ Q Mass e - +1 0 0-1 0.511 MeV _ ν e -1 0 0 0 < 3 ev e + -1 0 0 +1 0.511 MeV ν e +1 0 0 0 < 3 ev µ - 0 +1 0-1 105.7 MeV _ ν µ 0-1 0 0 < 0.19 MeV µ + 0-1 0 +1 105.7 MeV ν µ 0 +1 0 0 < 0.19 MeV τ - 0 0 +1-1 1.777 GeV _ ν τ 0 0-1 0 < 18.2 MeV τ + 0 0-1 +1 1.777 GeV ν τ 0 0 +1 0 < 18.2 MeV 7

Quarks There are 6 quarks (and 6 antiquarks), in three colors (and anticolors), with baryon number B = ±1/3 and non-integer electric charges. Quark B Q Masse u 1/3 2/3 2.3 + 0. 7 0.5 MeV _ u -1/3-2/3 2.3 + 0. 7 0.5 MeV d 1/3-1/3 4.8 + 0. 7 0.3 MeV _ d -1/3 1/3 4.8 + 0. 7 0.3 MeV c 1/3 2/3 1.275 ± 0.025 GeV _ c -1/3-2/3 1.275 ± 0.025 GeV s 1/3-1/3 95 ± 5 MeV _ s -1/3 1/3 95 ± 5 MeV t 1/3 2/3 173.5 ± 0.6 ± 0.8 GeV _ t -1/3-2/3 173.5 ± 0.6 ± 0.8 GeV b 1/3-1/3 4.18 ± 0.03 GeV _ b -1/3 1/3 4.18 ± 0.03 GeV 8

Quark model s =0 d u s = 1 s Quarks Antiquarks s = -1 s Q = 2/3 s =0 u d Q = -1/3 S: Strangeness (S = - 1 for the s quark) Q = -2/3 Q = 1/3 Mesons consist of quark-antiquark pairs, baryons of 3 quarks. Q Q Q Q Q 9

Strong Isospin Protons and neutrons have about the same mass. Therefore it was obvious to arrange them in a doublet: p n This means, they are the same particle regarding the strong interaction (same strong isospin I), but with different 3 rd component (I 3 ). For quarks isospin is a quantum number which characterizes flavor. Each of the 3 light quarks has a different orientation of I 3 : I 3 (u) = ½, I 3 (d) = -½, I 3 (s) = 0 Many particle properties can be related with special symmetries. 10

Hadrons: Mesons and Baryons Examples: meson nonet (octet plus singlet) and baryon decuplet. - 0 :(uū d d)/ 2 :(uū + d d 2s s)/ 6 :(uū + d d + s s)/ 3 Q = I 3 +Y/2 3 3 = 1 8 Quarks: spin 1/2! Pauli principle -> COLOR (O.W. Greenberg et al.) Gell-Mann-Nishijima formula - Hypercharge Y = B+S I 3 : Strong isospin (3 rd component), S: Strangeness 11

Interactions Interaction Mediator Mass Action on Electromagnetic Weak γ Photon W +, W -, Z 0 Intermediate vector bosons 0 Charged particles 80.4 GeV 91.2 GeV Left-handed particles or right-handed antiparticles with flavor Strong g 1,, g 8 Gluons 0 Particles with color charge Neutrinos have only weak interactions, charged leptons experience weak and electromagnetic interactions. Quarks have strong, weak and electromagnetic interactions. In the classical Standard Model neutrinos are massless. Fermions must be grouped into left-handed weak isospin doublets or right-handed singlets, quarks into color triplets. 12

Left-handed doublets, right-handed singlets Left-handed (chiral) fermion doublets and right-handed singlets: # νl & L = % ( R = l R, ν l R (l = e, µ, τ ) $ l ' L If neutrinos were massless like in the classical Standard Model, there would only be R = l R. T 3 3 rd component of the weak isospin # T 3L = % $ 1 2 1 2 & ( T 3R = 0 ' Similarly for quarks:! u # $ & " d% L Only left-handed particle states (and right-handed antiparticle states) take part in the weak interaction.! c # $ & " s% L! t # $ & " b%, u R, d R, c R, s R, b R, t R L 13

Weak Isospin Leptons and quarks have another quantum number, the weak isospin T. It links quark- and lepton doublets of left-handed particles, in each generation. Left-handed fermions (fermions with negative chirality) have T = ½ and can be grouped into doublets with T 3 = ± ½. They act, however, in the same way with respect to the weak interaction. T 3 (u L ) = T 3 (c L ) = T 3 (t L ) = ½, T 3 (d L ) = T 3 (s L ) = T 3 (b L ) = -½ T 3 (e - L ) = T 3 (µ- L ) = T 3 (τ- L ) = -½, T 3 (ν el ) = T 3 (ν µl ) = T 3 (ν τl ) = ½ In analogy to the Gell-Mann-Nishijima formula (Q = I 3 + Y/2; Y = B+S): Y W weak hypercharge Y W = 2 (Q-T 3 ) 14

Helicity Helicity (h) corresponds to the sign of the projection of spin on the direction of movement. It is however not Lorentz invariant. This becomes evident if the inertial system in the right-handed case moves with a higher speed than v : h changes from +1 to -1. v v v s s s : h = +1 ( right-handed ) h = - 1 ( left-handed ) For a massless particle there is no inertial system that can move faster than the speed of light, therefore for such particles h is Lorentz invariant. For massless particles helicity is identical with chirality. 15

Spinors, Dirac Equation Dirac equation for a free fermion with mass m: (iγ µ µ m) ψ (x) = 0 ψ (x)... 4-component Dirac spinor, x = (t,x,y,z) 4 fundamental solutions: u 1 = N 1 0 p z /( E + m) (p x + ip y )/( E + m) v 1 = N p z /( E + m) (p x + ip y )/( E + m) 1 0 1 = u 1 e i( p r Et) 2 = u 2 e i( p r Et) u 2 = N v 2 = N (x) = 1 2 0 1 (p x ip y )/( E + m) p z /( E + m) (p x ip y )/( E + m) p z /( E + m) 0 1 3 4 3 = v 1 e i( p r Et) 4 = v 2 e i( p r Et) N = E +m 2m E = E + = E u 1, u 2 describe a particle, v 1, v 2 an antiparticle. The spins of u 1, v 1 are in +z direction, the spins of u 2, v 2 in z direction. 16

Dirac- and Pauli matrices Dirac matrices γ (4 x 4) 0 = 1 0 0 0 0 1 0 0 0 0 1 0 0 0 0 1 i = 0 i i 0 5 = i 0 1 2 3 = 0 1 1 0 Pauli matrices σ (2 x 2) 1 = 0 1 1 0 2 = 0 i i 0 3 = 1 0 0 1 17

Chirality The eigenstates of the chirality operator γ 5 are defined as left-handed (u L, v L ) and right-handed (u R, v R ) chiral states: 5 u R =+u R, 5 u L = u L, 5 v R = v R, 5 v L =+v L Projection operators project the chiral eigenstates: P R = 1 2 (1 + 5 ) P L = 1 2 (1 5 ) P R u R = u R P R u L =0 P L u R =0 P L u L = u L P R v R =0 P R v L = v L P L v R = v R P L v L =0 P R projects right-handed particle and left-handed antiparticle states. We can compose any spinor from its chiral components: = R + L = 1 2 (1 + 5 ) + 1 2 (1 5 ) 18

Group Structure of the Standard Model In a gauge theory there is a group of transformations of field variables (gauge transformations), which leave the physics of the quantum field unchanged. This property is called gauge invariance. The Standard Model is a gauge theory. It is based on the symmetry group: SU(3) C SU(2) L U(1) Y The gauge symmetry is broken by the vacuum. The electroweak group is broken down to the electromagnetic subgroup by spontaneous symmetry breaking (SSB): SU(3) C U(1) QED SSB generates the masses of the weak gauge bosons and leads to a scalar particle, the Higgs particle. Fermion masses are also generated through SSB. 19

Group theory Let us consider a transformation U of a wave function ψ: ψʹ=uψ If U is a continuous transformation, then U takes the form: U=e iλ Λ operator e i (i ) = n n! If Λ is a hermitian operator (Λ= Λ + = Λ *T n=0 ) then U is a unitary transformation: U=e iλ U + =(e iλ ) *T = e -iλ*t = e -iλ UU + = e iλ e -iλ =1 Remark: U is not a hermitian operator since U U + Λ is called a generator of U. The following 4 properties define a group: 1) Closure: If A and B are elements of the group, then AoB is also an element 2) Neutral element I: For all group elements A: IoA=A 3) Inverse Element: For each group element there is an inverse element such that AA -1 =I 4) Associativity: If A,B,C are group elements, then Ao(BoC)=(AoB)oC are elements as well The group is Abelian if also the commutation relation is true: AoB= BoA The group is special if the determinant det U = 1. The transformation with only one Λ forms the unitary Abelian group U(1). The group SU(2) is a non-abelian group. 20

Symmetries Interactions between fundamental particles are described by symmetry principles. Every continuous symmetry in nature leads to a conservation law, every conservation law reveals an underlying symmetry (Noether s theorem). Examples: Symmetry Time translation Spatial translation Rotation Gauge transformation Conservation law Energy Momentum Angular momentum Charge All fundamental interactions are invariant under local gauge transformations. The dynamics of fundamental particles is described by the Lagrangian density or Lagrangian, which depends on the field variable and its derivative. Lagrangian of a free fermion with mass m: L 0 = i (x) µ µ (x) m (x) (x) = 0 Adjunct spinor 21

Example: Momentum Conservation δh = Spatial translation Example: classical mechanics 3 i=1 H dq i + q i 3 i=1 y H p i dp i + a y' Hamilton operator: H = H(p i, q i, t) The object should move independent of the coordinate system! q i = H p i = H p i q i 3 3 H t dt δh = H dq i = p i dq i = 0 q i a d dt 3 p i = 0 i=1 Translational invariance Conservation of linear momentum i=1 i=1 ( p i dp i dt ) 22

Global and Local Gauge Transformations Transformation: U U: Group of all unitary matrices. Simplest case: U(1), U = e iθ, θ = real constant. L 0 is invariant under global U(1) transformations: (x) (x) =e i (x) L 0 = i (x) µ µ (x) m (x) (x) L 0 ie i (x) µ e i µ (x) me i (x)e i (x) =L 0 If the phase transformations depend on space-time (θ =θ(x)), L 0 is no longer invariant under such local transformations: µ (x) e i (x) ( µ + i µ ) (x) This would mean that once a certain phase convention for a reference point was chosen, the same one must be chosen for all points -> unnatural! The gauge principle is the requirement that the U(1) phase invariance must also hold locally. 23

Covariant Derivative We try to add a spin-1 field A µ (x) to the Lagrangian, which transforms as follows: A µ (x) A µ (x) =A µ (x) 1 e µ We define also the so-called covariant derivative: D µ (x) := [ µ + iea µ (x)] (x) The covariant derivative transforms in the same way as the field: D µ (x) (D µ ) (x) =e i D µ (x) One obtains a Lagrangian which is invariant under local gauge transformations: L = i (x) µ D µ (x) m (x) (x) =L 0 ea µ (x) (x) µ (x) 24

Quantum Electrodynamics (QED) Through the gauge principle an interaction between the Dirac spinor and the gauge field A µ was created. In order to obtain the complete Lagrangian of QED, we must add a kinetic term and in principle also a mass term : L kin = 1 4 F µ (x)f µ (x) F µ = µ A A µ electromagnetic field strength tensor L mass = 1 2 m2 A Aµ A µ This term violates gauge invariance, therefore the photon mass must be 0! L QED = (x)(i µ D µ m) (x) 1 4 F µ (x)f µ (x) µ F µ = J = e Maxwell equations J ν Electromagnetic fermion current 25

Anomalous Magnetic Moment The most stringent experimental tests of QED come from precision measurements of the magnetic moment of the electron (and the muon): µ e = 1 2 gµ 0 µ 0 = e 2m e c Anomaly of the magnetic moment: Bohr s magneton 9. 10-24 JT -1 g = 2 (classically) a = g 2 2 a e stems entirely from virtual electrons and photons. These contributions up to O(α 4 ) are entirely known; α = e 2 /4πε 0 hc 1/137 is the coupling constant (fine structure constant) of QED. a e = ( 1 159 652 180.85 ± 0.76 ). 10-12 a e also allows the most precise determination of α: a e = 2 (1-loop approximation) α -1 = 137.035 999 719 ± 0.000 000 096 26

Quantum Chromodynamics Besides the electric charge quarks also have a color charge. Gluons also have color charges, but these are not pure but mixed. The theory of the strong interaction is also called Quantum Chromodynamics. Color Anticolor q q u RED BLUE CYAN YELLOW q q d q GREEN MAGENTA Baryons Mesons 27

Introduction of Color To satisfy Fermi-Dirac statistics, quarks are assigned 3 color degrees of freedom: N C = 3 (red, bue, green). " 1% $ ' 0 $ ' # 0& " 0% $ ' 1 $ ' # 0& q(r) = q(b) = q(g) = Example Δ ++ = u u u > J P = 3/2 + " 0% $ ' 0 $ ' # 1& Angular momentum J Parity P: mirror symmetry (x x, y y, z z) The wave function of the Δ ++ is fully symmetric without color: ψ qqq = ψ Raum ψ Spin ψ Flavor The asymmetry is restored by introducing the fully antisymmetric color wave function ψ Color : ψ qqq = ψ Space ψ Spin ψ Flavor ψ Color 28

Color and Confinement For baryons and mesons (quarks q α, α = 1,2,3 for red, green, blue) the color term can be written as: B = 1 6 q q q M = 1 3 q q ε αβγ (epsilon tensor) is +1 for even permutations of α,β,γ (1,2,3; 2,3,1; 3,1,2), -1 for odd permutations (1,3,2; 3,2,1; 2,1,3), and 0 for α=β or β=γ or γ=α. δ αβ (Kronecker delta) is 1 for α=β, and 0 for α β. Summing over identical indices is implied. Baryons and mesons only appear in color singlet combinations. No particles with net color have been seen. Free quarks can therefore not be observed, they are locked into the hadrons, just like the gluons (Confinement). 29

Gluons have composite colors: Gluons The red quark becomes a blue quark by emitting a red-antiblue gluon. b r g rb - - r b + rb Are there 9 gluons? : r r, r b, rḡ, b r, b b, bḡ, g r, g b, gḡ With respect to SU(3) C color symmetry, these 9 states form a color octet ( 1> 8>) and a singlet ( 9>): Confinement requires that all naturally 1 =(r b + b r)/ 2 appearing particles are color singlets 2 = i (r b b r)/ 2 (color invariant), therefore the octet states 3 =(r r b b)/ 2 never appear as free particles. But 9> is a 4 =(rḡ + g r)/ 2 singlet! Could it be the photon or another 5 = i (rḡ g r)/ 2 6 =(bḡ + g b)/ 2 particle that mediates large-range forces 7 = i (bḡ g b)/ 2 and strong coupling? 8 =(r r + b b 2gḡ)/ 6 NO! Our world would be different 9 =(r r + b b + gḡ)/ 3 30

Experimental Observation of Color Measurement of the ratio of the total cross sections for e + e - annihilation into hadrons and muons: R = σ (e + e - hadrons) σ (e + e - µ + µ - ) f N C Quark flavors u, d, s, c, b, t Number of colors Since the 3 color states have the same electric charge, the cross section for producing quark pairs of a defined flavor type should be proportional to the number of colors N C. (e + e q q) =N C (q 2 u + q 2 d + q2 s...) (e + e µ + µ ) R 0 = (e + e q q)/ (e + e µ + µ )=N C (q 2 u + q 2 d + q2 s...) If we take into account higher orders (3-jet events and others) we get: R = R Q 2 0 (1 + s (Q 2 )/ +...) Momentum transfer 31

σ (e + e - hadrons) = σ (e + e - qq - + qqg - + qqgg - + qqqq - - + ) qq- σ (e R = + e - Hadronen) σ (e + e - µ + µ - ) R is almost constant, since e + e - qq - dominates. qq- qqg - 32

u, d, s: R 0 = 3 (q u 2 + q 2 d + q s2 ) = 2 u, d, s, c: R 0 = 3 (q u 2 + q 2 d + q 2 s + q c2 ) = 10/3 = 3.3 u, d, s, c, b: R 0 = 3 (q u 2 + q 2 d + q 2 s + q 2 c + q b2 ) = 11/3 = 3.7 u, d, s, c, b, t: R 0 = 3 (q u 2 + q 2 d + q 2 s + q 2 c + q 2 b + q t2 ) = 5 33

R obtained by different experiments N C = 3 W.-M. Yao et al., Rev. Part. Phys., J. Phys. G33 (2006) 1 34

Non-Abelian Gauge Symmetry of QCD Global SU(3) C transformations in color space for q fα, a quark field with flavor f and color α : q f (q f ) = U q f UU = U U =1 det U =1 The SU(3) C matrices can be written like this: U = exp{i a 2 a } θ a arbitrary parameters λ a /2 (a = 1,, 8) generators of the fundamental representation of SU(3) C λ a 3-dim. Gell-Mann matrices [ a, b c abc ]=if 2 2 2 f abc structure constants (real, antisymmetric) Like for QED we require that the QCD Lagrangian also be invariant under local SU(3) C transformations θ a = θ a (x), and make use of the covariant derivative again: D µ q f =[ µ + ig s g s is the strong coupling constant. Since there are 8 gauge parameters, we need 8 gluon fields (a=1,..,8): a 2 Gµ a(x)] q f G µ a(x)] 35

2-Jet- and 3-Jet-Events, α s From the ratio of the numbers of 3-jet- and 2-jet events α s = g s /4π can be determined. q e + α s e - Z 0 q - g e + q e - Z 0 q - 36

Running Coupling Constant α s (m Z2 ) = 0.118 ± 0.002 37

Gauge Transformations in QCD The gauge transformation of the gluon fields is more complicated than the one for the photon in QED, as the non-commutativity of the SU(3) C matrices leads to an additional term which contains the gluon fields themselves (infinitesimal transformation δθ): G µ a (G µ a) = G µ a 1 g s µ ( a ) f abc b G µ c We introduce field strengths for the formation of a gauge invariant term of the gluon fields: D µ q f =[ µ + ig s a 2 Gµ a(x)] q f =[ µ + ig s G µ (x)]q f G µ a (x) = µ G a G µ a g s f abc G µ b G c L QCD = 1 4 Gµ a G a µ + f q f (i µ µ m f )q f 38

Splitting of the QCD Lagrangian We can split L QCD into its different components: L QCD = 1 4 ( µ G a G µ a)( µ G a G a µ)+ g s G µ a f q f µ( a 2 ) q f f q f (i µ µ m f )q f (a) (b) + g s 2 f abc ( µ G a G µ a)g µ b G c g 2 s 4 f abc f ade G µ b G c G d µg e (c) (a) (b) (c) Kinetic terms for the gluon- and quark fields Color interaction between quarks and gluons Gluon self interactions of 3 rd and 4 th order 39

Electroweak Interaction Information from low-energy experiments was sufficient for the determination of the structure of modern electroweak theory. W- and Z-particles were introduced and their masses correctly predicted before their discovery. Neutral currents: f Z 0 f Fermion (quarks, leptons - including neutrinos) f Charged currents: ν l q j (+ 2/3) l ± W ± q i (- 1/3) W - l e, µ, τ q Quark ν Neutrino 40

Discovery of the neutral Currents at CERN 1973 - - ν µ + e - e - + ν µ ν µ e - ν µ Z 0 e - ν - µ For comparison: A charged current would lead to a muon in the final state: µ - µ - ν µ W + e - with E 400 MeV at an angle (1.5 ± 1.5) 0 with respect to the neutrino beam. e - identified by characteristic energy loss by bremsstrahlung and subsequent pair production. Hasert et al. ν µ 41

Bubble Chamber Gargamelle at CERN Filled with freon gas (CF3Br) 42

Cabibbo Angle Cabibbo suggested in 1963 (when only u, d, s were known) that the vertices d u + W - should get a factor cosθ C and s u + W - a factor sinθ C, to achieve identical couplings as for leptons. In this way the W s couple to the Cabibbo-rotated states just like to lepton pairs: d = d cosθ C + s sinθ C s = - d sinθ C + s cosθ C In matrix form:! d' $! # & = cosθ C sinθ C $ # " s' % " sinθ C cosθ C % &! # d$ " s & % Cabibbo angle θ C = 13.1 0 43

Cabibbo Theory u u cosθ C W - sinθ C W - d s ν l W ± l Through the Cabibbo theory many decay rates could be brought into relation with each other. But it was not understood, why the decay K 0 µ + µ - occurs less frequently than calculated. The decay amplitude should be proportional to sinθ C cosθ C. 44

µ - µ + d W cos θ C ν µ u K 0 = (ds) - W sin θ C s - K 0 µ + µ - GIM mechanism (Glashow, Iliopoulos, Maiani) µ - µ + ν µ GIM Mechanism Experimentally measured decay amplitude is not proportional to sinθ C cosθ C, but much smaller! introduction of the charm quark W W - sin θ C c cos θ C d K 0 = (ds) - s - This diagram cancels the previous one, but not completely because of the masse difference of m u and m c. 45

Discovery of the J/ψ (cc) - 1974 in Brookhaven - S.C.C. Ting et al. Fixed target experiment at the AGS p + p e + e - + X Proton beam p = 28.5 GeV/c Stationry Be target C. Cerenkov counter (threshold mode) M Magnets D. Drift chambers S.. Shower counters (calorimeter) J/ψ is short-lived (τ ~ 10-20 s) only decay products can be detected! 46

Discovery of the J/ψ (cc) - 1974 in Brookhaven e + e - pairs were selected. Invariant mass of the e + e - pair: W 2 = E 2 - p 2 = (E + + E - ) 2 - (p + + p - ) 2 = = 2 (m 2 + E + E - - p + p - cosθ) If the e + e - pair comes from the decay of a single particle with energy E und momentum p, W is constant due to energy and momentum conservation (E = E + + E -, p = p + + p - ): W 2 = m J/ψ 2 p ±. Laboratory momentum of e ± E ± Total energy of e ± θ. Angle between e + and e - 47

Discovery of the J/ψ (cc) - 1974 at SLAC B. Richter et al. Mark-I experiment e + e - - Collider SPEAR e + e - X Energy scan was made. W = m J/ψ J/ψ is produced at rest. m J/ψ = 3.097 GeV Γ J/ψ = 0.063 GeV 48

Charged Currents Only left-handed fermions and right-handed antifermions couple to the W. Therefore parity P and charge conjugation C (particle <-> antiparticle) are maximally violated. CP remains conserved, however. The W s couple to fermion doublets, where the electric charges of the two fermion partners differ by one unit. The decay channels of the W - are therefore: W e e,µ µ,,d ū, s c All fermion doublets couple to the W s with the same universal strength if the doublet partners of the u, c and t are mixtures of the three quarks with charge -1/3. The mixing is given by the unitary Cabibbo-Kobayashi-Maskawa matrix: d s b = V CKM d s b = V ud V us V ub V cd V cs V cb V td V ts V tb The weak eigenstates differ from the mass eigenstates. V characterizes flavor mixing, e.g. V ud specifies the coupling of u to d (d u +W - ). d s b M. Kobayashi T. Maskawa 2008 49