Weak Interactions Kihyeon Cho

2 입자의 표준모형 (The Standard Model)

3 기본상호작용

HEP Journal Club 표준모형 (Standard Model) What does world made of? –6 quarks u, d, c, s, t, b Meson (q qbar) Baryon (qqq) –6 leptons e, muon, tau e, , 

What holds it together? (The four interactions)

Weak Interactions Some Weak Interaction basics Weak force is responsible for  decay e.g. n → pev (1930’s) interaction involves both quarks and leptons not all quantum numbers are conserved in weak interaction: parity, charge conjugation, CP isospin flavor (strangeness, bottomness, charm) Weak (+EM) are “completely” described by the Standard Model Weak interactions has a very rich history 1930’s: Fermi’s theory described  decay. 1950’s: V-A (vector-axial vector) Theory: Yang & Lee describe parity violation Feynman and Gell-Mann describe muon decay and decay of strange mesons 1960’s: Cabibbo Theory N. Cabibbo proposes “quark mixing” (1963) "explains" why rates for decays with  S =0 >  S =1 Quarks in strong interaction are not the same as the ones in the weak interaction: weak interaction basis different than strong interaction basis previous example: Chapter 8 M&S Chapter M&S

Weak Interactions Weinberg-Salam-Glashow (Standard Model 1970’s-today) unify Weak and EM forces predict neutral current (Z) reactions gives relationship between mass of W and Z predict/explain lots of other stuff!..e.g. no flavor changing neutral currents existence of Higgs (“generates”mass in Standard Model) Renormalizable Gauge Theory But the picture is still incomplete: must input lots of parameters into the Standard Model (e.g. masses) where’s the Higgs and how many are there ? how many generations of quarks and leptons are there ? mass pattern of quarks and leptons ? neutrinos have mass! CP violation observed with quarks! is there CP violation with leptons?

Weak Interactions Classification of Weak Interactions TypeCommentExamples Leptonicinvolves only leptonsmuon decay (   evv) e e -  e e - Semileptonicleptons and quarksneutron decay (  s=0) K +   +  (  s=1) (  b=1) Non-Leptonicinvolves only quarks    - p & K +   +  o Some details of Weak Interactions quarks and leptons are grouped into doublets (SU(2)) (sometimes called families or generations) For every quark doublet there is a lepton doublet Charged Current Interactions (exchange of a W boson) W’s couple to leptons in the same doublet The W coupling to leptons/quarks is a combination of vector and axial vector terms: J u = ug u (1- g 5 )u (parity violating charged current) e e-e- W-W-  -- W-W-  -- W-W- ,  e-e- W-W- e,  -- W-W- e,  -- W-W- Allowed NOT Allowed

9 CKM Matrix Original 2X2 Cabibbo angle CKM 3X3 Matrix

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Intro. to elementary particle physics Y. Kwon 11/24/2003 Universality of weak interactions? Do all leptons and quarks carry the same unit of weak charge?  Yes, for leptons and no for quarks for quarks, the couplings to the weak gauge bosons depend on the quark flavors, due to “quark-mixing”  CKM mechanism

Intro. to elementary particle physics Y. Kwon 11/24/2003 Weak decays of quarks Consider the (semileptonic) weak decay Assuming universality of weak decays of quarks, we expect both decays would happen in similar rate, but...

Intro. to elementary particle physics Y. Kwon 11/24/2003 Weak decays of quarks (2)

Intro. to elementary particle physics Y. Kwon 11/24/2003 Weak decays of quarks (3) So, what are we going to do? Discard the universality of weak interaction? It was also noticed that the value of the Fermi constant G F deduced from nuclear  -decay was slightly less than that obtained from muon decay.

Intro. to elementary particle physics Y. Kwon 11/24/2003 Cabibbo theory Try to keep the universality, but modify the quark doublet structure… Assume that the charged current (W  ) couples the “rotated” quark states where d’, s’ (weak interaction eigenstates) are linear combinations of mass eigenstates d, s

What we have done is to change our mind about the charged current: “Cabibbo-favored” vs. “-suppressed” effective weak coupling for  S=0 (d  uW) is cos  c effective weak coupling for  S=1 (s  uW) is sin  c Cabibbo theory (2)

Cabibbo theory (3) (Ex) What is the relationship between the weak couplings for muon decay (G  =G F ) and nuclear  -decay (G  ) ?

Intro. to elementary particle physics Y. Kwon 11/24/2003 Suppression of flavor-changing neutral currents a very stringent suppression of flavor-changing neutral current reactions (Ex) Draw the decay diagrams for the above two reactions! Is it easy to understand this stringent suppression?

The GIM Mechanism In Glashow, Iliopoulos, and Maiani (GIM) proposed a solution to the to the K 0  +  - rate puzzle. The branching fraction for K 0  +  - was expected to be small as the first order diagram is forbidden (no allowed W coupling). ++ u W+W+ s  ++ d ?? 0 s -- K + allowed K 0 forbidden The 2 nd order diagram (“box”) was calculated & was found to give a rate higher than the experimental measurement! amplitude  sin  c cos  c GIM proposed that a 4 th quark existed and its coupling to the s and d quark was: s’ = scos  - dsin  The new quark would produce a second “box” diagram with amplitude  sin  c cos  c These two diagrams almost cancel each other out. The amount of cancellation depends on the mass of the new quark A quark mass of  1.5GeV is necessary to get good agreement with the exp. data. First “evidence” for Charm quark!

Flavor-changing neutral currents (FCNC) Neutral-current reactions for (u,d’) quarks In this picture, FCNC is perfectly allowed by theory ??? Perkins 7.11 For all neutral current process

GIM mechanism for FCNC suppression In 1970, Glashow, Iliopoulos & Maiani (GIM) proposed the introduction of a new quark of Q=+2/3, with label c for ‘charm’. With this new quark, a second quark doublet is also introduced. Then we have additional terms for the neutral current reactions. Perkins 7.11

GIM mechanism (2) FCNC has disappeared!

Intro. to elementary particle physics Y. Kwon 11/24/2003 GIM mechanism (3) At the price of a new quark ‘charm’ and another quark doublet, the (experimentally) unwanted FCNC has been removed! Later, in 1974, the bound state of charm  anti-charm was discovered: J/  Indeed, just before this discovery, it had been possible to estimate the mass of the new quark!!  by considering mixing

25 quark  anti quark  quark  anti quark ……  decay Time We are all the children of Broken symmetry Just tiny deviation from perfect symmetry seems to have been enough

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27 노벨 물리학상 2008 Citation: 5483

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Cabibbo Angle 29

30 V ub

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32 The CKM Matrix Unitary with 9*2 numbers  4 independent parameters Many ways to write down matrix in terms of these parameters

CKM Matrix The CKM matrix can be written in many forms: 1) In terms of three angles and phase: The four real parameters are ,  12,  23, and  13. Here s=sin, c=cos, and the numbers refer to the quark generations, e.g. s 12 =sin  12. This matrix is not unique, many other 3X3 forms in the literature. This one is from PDG ) In terms of coupling to charge 2/3 quarks (best for illustrating physics!) 3) In terms of the sine of the Cabibbo angle (  12 ). This representation uses the fact that s 12 >>s 23 >>s 13. “Wolfenstein” representaton Here =sin  12, and A, ,  are all real and approximately one. This representation is very good for relating CP violation to specific decay rates.

CKM Matrix The magnitudes of the CKM elements, from experiment are (PDG2000): There are several interesting patterns here: 1)The CKM matrix is almost diagonal (off diagonal elements are small). 2)The further away from a family, the smaller the matrix element (e.g. V ub <<V ud ). 3)Using 1) and 2), we see that certain decay chains are preferred: c  s over c  d D 0  K -  + over D 0   -  + (exp. find 3.8% vs 0.15%) b  c over b  uB 0  D -  + over B 0   -  + (exp. find 3x10 -3 vs 1x10 -5 ) 4)Since the matrix is supposed to be unitary there are lots of constraints among the matrix elements: So far experimental results are consistent with expectations from a Unitary matrix. But as precision of experiments increases, we might see deviations from Unitarity.

35 Heavy Flavor Physics 정밀측정으로 표준모형의 검증 => 새로운 물리 현상 Foundation New Physics

Decays of b quark Then how does b decay at all? Note: b  W  t but m(t) >> m(b) For quarks,  mass eigenstates  weak interaction eigenstates  flavor mixing through CKM matrix weak interaction eigenstates mass eigenstates very important for CP study responsible for most b decays

CKM matrix CKM is 3x3 and unitary –only 3 generations in the SM CKM is almost 1, but not exactly V ii  1, V ij  0 for i  j How do we determine the CKM matrix elements?

38 F. Di Lodovico, ICHEP 2008

Measuring the CKM Matrix No one knows how to calculate the values of the CKM matrix. Experimentally, the cleanest way to measure the CKM elements is by using interactions or decays involving leptons.  CKM factors are only present at one vertex in decays with leptons. V ud : neutron decay: n  pev d  uev V us : kaon decay: K 0   + e - v e s  uev V bu : B-meson decay: B -  (  or  + )e - v e b  uev V bc : B-meson decay: B -  D 0 e - v e b  cev V cs : charm decay: D 0  K - e + v e c  sev V cd : neutrino interactions:  d   - c d  c “Spectator” Model decay of D 0  K - e + v e c u s u e,  W K-K- D0D0 V cs Amplitude  V cs Decay rate  V cs   For massless neutrinos the lepton “CKM” matrixis diagonal Called a “spectator” diagram because only one quark participates in the decay, the other “stands around and watches”.

Extension of Cabibbo theory to 3 quark generations Leptons are not involved in the strong interactions Quarks & Leptons do not change its flavor when interacting with neutral gauge bosons –quarks do not change flavor under strong int. –leptons & quarks do not change flavor when interacting with  or Z 0 –leptons & quarks change flavor only when interacting with W , and only within its family WW tb' W+W+

Expt’l determination of CKM elements V ud - from nuclear b-decay V us –from –results of K + and K 0 decays agree V cd –from charm meson production via neutrino scattering

Expt’l determination of CKM elements V cs –from semileptonic decay of D meson –unitarity constraint assuming only 3 generations gives a much tighter bound

Expt’l determination of CKM elements Intro. to elementary particle physics Y. Kwon 11/24/2003 V cb : from and HQET

Expt’l determination of CKM elements V ub : from

Expt’l determination of CKM elements V tb : from t-quark decay, assuming only 3 generations at the Tevatron collider at Fermi Lab, top quarks are produced mainly in pairs Assuming one could obtain a pure sample of (Ref. hep-ex/ )

Expt’l determination of CKM elements V td and V ts (1) (2) V td (s)(s) (s)(s)

Exp. determination of CKM elements & phase (7)

References 48 I.S.Cho’s talk (2008) Class P by Richard Kass (2003) B.G Cheon’s Summer School (2002) S.H Yang’s Colloquium (2001) Class by Jungil Lee (2004) PDG home page ( Newton (2009.1) Youngjoon Kwon’s Lecture (2003)

Thank you.