Weak Interactions. Chapter 8 M&S

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1 Some weak interaction baic: Weak force i reponible for β decay e.g. n pev (1930 ). Interaction involve both qark and lepton. Not all qantm nmber are conerved in weak interaction: parity, charge conjgation, CP iopin flavor (trange, charm, bottom, top) Weak (+EM) are completely decribed by the Standard Model. Weak interaction ha a very rich hitory: 1930 : Fermi theory decribed β decay : V-A (vector-axial vector) theory: Yang & Lee decribe parity violation. Feynman and Gell-Mann decribe mon decay and decay of trange meon 1963: N. Cabibbo propoe qark mixing : explain why rate for decay with ΔS = 0 > ΔS = 1: BR(K µ ν µ ) = 63.5% Weak Interaction Chapter 8 M&S BR(π µ ν µ ) = 99.9% Qark in trong interaction are not the ame a the one in the weak interaction: weak interaction bai different than trong interaction bai: (K 0,K 0 ) (K S,K L ) K.K. Gan L10: Weak Interaction 1

2 Weinberg-Salam-Glahow (Standard Model today): nify weak and EM force predict netral crrent (Z) reaction give relationhip between ma of W and Z predict/explain lot of other tff, e.g. no flavor changing netral crrent predict exitence of Higg ( generate ma in Standard Model) contrct renormalizable gage theory The pictre i till incomplete: Weak Interaction mt inpt lot of parameter into the Standard Model (e.g. mae) where the Higg and how many are there? how many generation of qark and lepton are there? how to explain the ma pattern of qark and lepton? netrino have ma! CP violation oberved with qark! i there CP violation with lepton? K.K. Gan L10: Weak Interaction 2

3 Weak Interaction Claification of weak interaction Type Comment Example Leptonic lepton only µ e v e v µ v e e v e e Semileptonic lepton and qark n pe v e (Δ = 0) K + µ + v µ (Δ =1) B D 0 µ v µ (Δb =1) Non - leptonic qark only Λ π p & K + π + π 0 Qark and lepton are groped into doblet (SU(2)). Sometime called familie or generation. For every qark doblet there i a lepton doblet: Q(e) c t 2 3 d b 1 3 e µ τ 1 ν µ 0 ν e ν τ Charged crrent interaction involve the exchange of a W boon. τ - τ - W cople to lepton in the ame doblet. W copling to lepton/qark i a combination of vector and axial vector (V-A) term: J = γ (1- γ 5 ) parity violating charged crrent K.K. Gan L10: Weak Interaction 3 ν e e - ν µ µ - ν τ Allowed ν µ,τ e - ν e,τ µ - ν e,µ Not Allowed

4 Cabibbo conjectre (1963): Cabibbo Model qark participating in weak interaction are a mixtre of qark that participate in the trong interaction explain certain decay pattern in the weak interaction originally had only to do with the d and qark: d' = d coθ + inθ the form of the interaction (charged crrent) ha an extra factor for d and qark d qark : J γ (1 γ 5 )coθ c qark : J γ (1 γ 5 )inθ c = d d coθ c + inθ c The Cabibbo angle i important for determining the rate of many reaction. The Cabibbo angle can meared ing data from the following reaction: BR(K + µ + v µ ) BR(π + µ + v µ ) = in2 θ c m K 1 (m µ /m K ) 2 2 co 2 θ c m π 1 (m µ /m π ) 2 coθ c or inθ c From the above branching ratio we find: θ c = 0.27 radian We can check the above by mearing the rate for θ c = 0.25 radian d coθ c K π o e ν e and π π o e ν e : K.K. Gan L10: Weak Interaction 4 inθ c Prely leptonic decay (e.g. mon decay) do not contain the Cabibbo factor µ + W + ν µ d,

5 Extenion to Cabibbo Model Cabibbo model cold eaily be extended to 4 qark: = d d d coθ c + inθ c c c c = coθ c d inθ c d = coθ c inθ c inθ c coθ c d Adding a forth qark actally olved a long tanding pzzle in weak interaction: abence (i.e. very mall BR) of decay with a flavor (e.g. trangene) changing netral crrent: BR(K 0 µ + µ ) BR(K + µ + v µ ) = M&S ection Cabibbo model cold not incorporate CP violation 1977: there wa evidence for 5 qark! Cabibbo name CKM model: wa added to Kobayahi and Makawa extended Cabibbo idea to ix qark in make CKM Thi i two year before dicovery of charm! 2x2 3x3 matrix that mixe the weak qark and the trong qark The matrix i nitary. 1 parameter (Cabibbo angle) 3 angle (generalized Cabibbo angle) + 1 phae The phae allow for CP violation. Jt like θ c, the matrix element of the CKM matrix mt alo be obtained from experiment. K.K. Gan L10: Weak Interaction 5

6 GIM Mechanim In , Glahow, Iliopolo, and Maiani (GIM) propoed a oltion to the K 0 µ + µ - rate pzzle: BR(K 0 µ + µ ) BR(K + µ + v µ ) = The branching fraction for K 0 µ + µ - wa expected to be mall. The firt order diagram i forbidden a thi i not a allowed W copling. µ + ν µ µ + µ - K + allowed W +? K 0 forbidden d The 2nd order diagram ( box ) wa calclated: amplitde inθ c coθ c Fond to give a rate higher than the experimental mearement! GIM propoed that a 4th qark exited and it copling to the and d qark wa: ' = coθ d inθ The new qark wold prodce a econd box diagram with amplitde -inθ c coθ c Thee two diagram almot cancel each other ot. The amont of cancellation depend on the ma of the new qark. A qark ma of 1.5 GeV i neceary to get good agreement with the experimental data. Firt evidence for Charm qark! K.K. Gan L10: Weak Interaction 6

7 CKM Matrix The CKM matrix can be written in many form: In term of three angle and phae: d c 12 c c e iδ 13 d Thi matrix i not niqe, b = 12 c 23 c e iδ 13 c 12 c e iδ many other 3x3 form in c c 12 c e iδ 13 c c e iδ 13 c 23 c 13 b the literatre. Thi one i from PDG2000. The for real parameter are δ, θ 12, θ 23, and θ 13. = in, c = co, and the nmber refer to the qark generation, e.g. 12 = inθ 12. In term of copling to charge 2/3 qark: d V d V V b d = V cd V c V b b V td V t V tb b Bet for illtrating phyic! In term of the ine of the Cabibbo angle (θ 12 ). d 1 λ 2 /2 λ Aλ 3 (ρ iη) d b = λ 1 λ 2 /2 Aλ 2 Wolfentein repreentaton Aλ 3 (1 ρ iη) Aλ 2 1 b Thi repreentation e the fact that 12 >> 23 >> 13. λ = inθ 12, and A, ρ, η are all real and approximately one. Thi repreentation i very good for relating CP violation to pecific decay rate. K.K. Gan L10: Weak Interaction 7

8 The magnitde of the meared CKM element (PDG2000): V d V V b (2 5) 10 3 V cd V c V cb V td V t V = ( ) 10 2 tb ( ) 10 2 ( ) There are everal intereting pattern: 1) The CKM matrix i almot diagonal (off diagonal element are mall). 2) The frther away from a family, the maller the matrix element (e.g. V b << V d ). 3) Uing 1) and 2), we ee that certain decay chain are preferred: c over c d: BR(D 0 K - π + ) ~ 3.8% BR(D 0 π - π + ) ~ 0.15% b c over b : BR(B 0 D - π + ) ~ 3x10-3 BR(B 0 π - π + ) ~ 1x10-5 4) Since the matrix i ppoed to be nitary there are lot of contraint among the matrix element: * V d + V * cd V cd + V * td V td =1 V d * V d + V cb * V cd + V tb * V td = 0 V b CKM Matrix So far experimental relt are conitent with expectation from a nitary matrix. A preciion of experiment increae, we might ee deviation from nitarity. K.K. Gan L10: Weak Interaction 8

9 Mearing the CKM Matrix No one know how to calclate the vale of the CKM matrix. Cleanet way to meare the CKM element i to e interaction or decay involving lepton. CKM factor are only preent at one vertex in decay with lepton. V d netron decay n pe v e d ev V kaon decay K 0 π + e v e ev V b B - meon decay B (ρ + or π + )e v e b ev V bc B - meon decay B D 0 e v e b cev V c charm decay D 0 K e + v e c ev V cd netrino interaction v µ d µ c d c Spectator model decay of D 0 K - e + v e Called a pectator diagram becae only one qark participate in the decay, the other tand arond and watche. v e,v µ W c Decay rate V c 2 V D 0 c K - K.K. Gan L10: Weak Interaction 9 e,µ For male netrino the lepton CKM matrix i diagonal