Workshop Neckarzimmern. Symmetries Standard Model Langrangian Higgs Coupling to Quarks and Mass Generation CKM Matrix Unitarity Triangles Mixing

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1 Workhop Nkarzrn Syr Sanar Mol angrangan gg Couplng o Quark an Ma Gnraon CKM Marx Unary Trangl Mxng

2 Syr T.D.: Th roo o all yry prnpl l n h aupon ha pobl o obrv ran ba quan; h non-obrvabl Thr ar four an yp of yry: Pruaon yry: o-enn an Fr-Dra Sa Connuou pa- yr: ranlaon, roaon, alraon, Dr yr: pa nvron, nvron, harg nvron Unary yr: gaug nvaran: U harg, SU opn, SU olor,.. Nohr Thor: yry onrvaon law

3 Non-obrvabl Dffrn bwn nal parl Abolu paal poon Abolu Abolu paal ron Abolu rgh or lf Abolu gn of lr harg lav pha bwn a of ffrn harg Q lav pha bwn a of ffrn baryon nubr lav pha bwn a of ffrn lpon nubr Dffrn bwn ffrn ohrn xur of p an n a Syry Tranforaon Pruaon Spa ranlaon T ranlaon oaon r r r r ψ ψ ψ Q θ N θ θ r r ur r r τ ψ ψ ψ p p U n n Conrvaon aw or Slon ul.-e. or F.-D. a onu nrgy angular onu pary harg onjugaon harg baryon nubr lpon nubr opn

4 an an / x q x q x x x x x q x q l l l l λ ω pon / baryon nubr onrvaon:

5 Dkr Syrn C, P, T Pary, P Pary rfl a y hrough h orgn. Convr rgh-han oorna y o lf-han on. or hang gn bu axal vor ran unhang x x, p -p, bu x p Charg Conjugaon, C Charg onjugaon urn a parl no an-parl, K K T vral, T Chang, for xapl, h ron of oon of parl Dr yr ulplav quanu nubr

6 Tranforaon Propr P C r r r x, x, x, r r r Salar Fl : φ, x φ x, φ, x r r r Puo Fl : P x, P x, P x, r r r Dra Fl ψ x ψ x ψ x T :,,, r r r :,,, r :, x r, A x r, or Fl x x x Axal Fl A x A Tranforaon propr of Dra pnor blnar: P C CP T CPT S : P : : A: T : ψψ ψψ ψψ ψψ ψψ ψψ ψψ ψψ ψ ψ ψ ψ ψψ ψ ψ ψ ψ ψψ ψψ ψψ ψψ ψψ ψ ψ ψ ψ ψ ψ ψ ψ ψ ψ ψ ψ ν ν ψσ ψ ψσ ψ ψσ ψ ψ σ ψ ψ σ ψ ψ σ ψ ν ν ν ν * *

7 T vral Wgnr foun ha T opraor anunary: ψ ' φ' ψt Tφ ψ φ * Th lav h phyal onn of a y unhang, n: ψ ' φ' φ ψ ψ φ Anunary opraor ay b nrpr a h prou of an unary opraor by an opraor whh oplx-onjuga. A a onqun, T anlnar: * * T C ψ C φ C T ψ C T φ

8 Pary olaon n Wak Inraon Charg urrn ν ν τ ν τ ν,,ν τ τ,ν W ν u b u,, b, W ν Maxal olaon of P an C

9 ν S : P : : A: T : Charg rang urrn: ψ ψ ψ ψ 5 5 ψ ψ ψ ψ P ψ ψ ψψ ψψ ψ ψ 5 5 ψ σ ψ ψ σ ψ ν ν W 5 J ψ ν ψ ν Charg lowrng urrn: W ν J 5 ψ ψν ν

10 C an P olaon π τ ν τ Auf rn lk hn hwah Whlwrkung nvaran unr CP. π τ ν τ P C π τ ν τ P π τ ν τ C W τ ν τ u π

11 Pary olaon n Nural Currn? Ina of g l an g h vor an axal vor ouplng ar ofn u: g g g A g g g w f f w Q T g g g θ θ n o : w f w Q g g g θ θ n o :..7 : : g g g g ν pl: f f Z? f A f g g J ψ ψ ~ 5

12 Z M Z σ ~ oθ o θ 8 A F oθ wh A F σ F σ F σ σ σ F σ F

13 CPT Syr oal Fl hor alway rp: ornz Invaran Syry unr CPT opraon an lron a poron ravllng bak n > Conqun: a of parl a of an-parl: ür, Paul, Shwngr M p p p p CPT CPT CPT CPT p p CPT CPT p p p M p an-unary > Slarly h oal ay-ra of a parl qual o ha of h an-parl Quon : Th a ffrn bwn K an K S :.5 x -6 > CPT volaon? Quon : ow o h lf of K S.89 n whl h lf of h K 5.7 n? Quon : aar aur ay ra -> J/ψ K S an bar-> J/ψ K S. Clarly no h a: how an b?

15 Dra Equaon for fr Spn ½ Fron ψ ψ Soluon ψ ar four-oponn pnor. Thy rb h funanal pn ½ parl: ψ ψ ψ ψ ψ 4 Wh ajon pnor ψ ψ ψ Exrly opr rpon j...4 : 4 k jk x δ jk ψ k

16 Gaa Mar 5,,, βα β an β σ σ α..., 5 σ σ ,..,,,, for, ν ν ν ν ν ν k g k k k k ul

17 Connuy Equaon ψ ψ ψ ψ ψ ψ ψ ψ j Fron urrn hr : > > ψ ψ ψ ψ ψ ψ ρ j j

18 angrangan oal fl hor work wh agrangan n: x r, x r,, x r, φ j φj r wh φ j x,, j,,..., N h fl akn a, Th funanal quany, whn ung yr h Aon:, 4 A x x r r x If h aon no nvaran unr a yry opraon hn h yry n quon a goo brokn on > Unary of h nraon rqur h agrangan o b ran S xpa S arx hory n

19 Toy Thory Conr a pn-/ Dra parl nulon nrang wh a pn- Salar obj on ψ r r r r r x, ψ x, ψ x, ψ x, ψ x, r r r φ φ φ r r r ψ ψ φ x, x, x, x, a b x, x, 5 M φ Inraon: Salar an puo alar ouplng

20 oal Gaug Invaran agrangan u b nvaran unr loal gaug ranforaon Thory of al Fron: ψ α global U gaug ranforaon: ψ x ψ x ψ x loal U gaug ranforaon: ψ x ψ ψ ψ α x x x I h agrangan nvaran? ; ψ ψ ψ ψ α x x x x α x x α x α x ψ x ψ x ψ x α x Thn: ψ ψ ψ ψ ψ ψ α x No nvaran!

21 Gaug Fl > Inrou h ovaran rvav: D A A A A α x an an ha Α ranfor a: Conluon: Inrou harg fron fl lron Dan nvaran unr loal gaug ranforaon U Th pr o pay ha a gaug fl A an h IA wh h fl u b nrou a h a. Anon: Ma r ar no gaug nvaran!

22 Sanar Moll agrangan f, G f, G, G f fron quark, lpon G gaug boon W, gg oubl q j,, q j q j j,, q j 5 5 q q q q angrangan forally vola P an C, bu onrv CP

23 gg gg an Syr rakng φ φ D D gg φφ λ φφ φ φ φ gg gg φ φ φ φ φ φ D D gg φφ λ φφ > : < ϕ > φ Pha hang SS < : < ϕ > v φ φ φ v λ ~ 46 G Sponanou Syry rakng: Th gg fl aop a non-zro vauu xpaon valu No gg CP onrvng

24 f, an Syr rakng hnvaran Sponanou Syry rakng: φ φ υ φ,,, φ φ φ φ υ Ean up by W ± an Z boon bong av u-yp υ jk Y jk υ jk Y jk Quark a ar Non phyal quark fl

25 Phyal Quark Fl Dagonalz a ar: U U D Dag,, onvnon. u arx hory: pobl w/ hlp of unary a U U D Dag.,, b U U Subung no f, on oban for u-yp quark: analog for -yp quark q j U jk q phy q k DU q U q q q U q phy q q U q q U u U U U U q q Slar rlaon alo for rgh-han quark

26 Ma r Subuon no f,: ark: 5 q 5 q q q No: phy f, onrv C an P paraly, an hrfor alo CP.

27 Charg Currn Inraon wh U U an unary J C u,, u u ub b b b

28 CP olaon an Mxng Marx X C axally P an C volang an CP onrvaon rqur o b ral W CP W CP olaon Pha, π

29 Parar of h CKM Marx Unary N N Marx: N Parar: N 9 N N - / Eulr angl roaon angl anng parar ar pha: 6 N- ar unaurabl pha ff 5 N obrvabl parar 4

30 Unobrvabl Pha Pha of lf-han fl n J C ar unobrvabl: pobl rfnon u u u φ φ φ φ φ b b b φ al nubr Unr pha ranforaon: b b b ub u u u φ φ φ φ φ φ j j j α α φ φ α ] xp[, G f phy nvaran, f aff. rphang q

31 CP volaon wh fal CKM Pha δ,π CP olaon No fully orr! Au ha an b quark hav h a a: xra yry roaon n /b quark pa Nw -quark: nw ~ u ub b u-quark only oupl wo an nw bu no o b nw Nw xng arx: onru fro row ung unary oθ nθ nθ oφ oθ oφ nθ nφ oθ nφ NO CP olaon nφ oφ

32 Nary bu no uffn onon for CP olaon u u b b

33 CKM Pararzaon PDG ho b b ' ' ' δ δ δ δ δ δ δ j j j j θ θ n, o whr

34 CKM Pararzaon 4 λ λ η ρ λ λ λ λ η ρ λ λ λ O A A A A CKM non Wolfnn 98: λ, A, ρ, η hrarhy xpr by orr of λ nθ.

35 CKM Pararzaon PDG ho Wolfnn npr pararzaon λ nδ oδ Aλ η Aλ ρ Aλ n Oλ qual o Wolfnn pararzaon.

36 Unary Trangl b n Oλ * u u * ub * * * b * * * * b u u ub b b u ub * b * b * Unarärk

37 Angl α In oplx plan: Angl αβ bwn wo vor A a an β b I α β A / A u arg * ub * b η u ub * * b α β ρ * b * b α arg u b * * ub β arg b * * b

38 CKM Pha an Angl β - - b u CKM Phan β α * * b ub u * * b b η I ρ λ η ρ λ λ λ λ η ρ λ λ λ A A A A CKM

39 All rangl b b ub u u b η ρ λ λ η ρ λ A A A b b ub u u η ρ λ λ η ρ λ A A A b ub u u O λ Th Unary Trangl

40 Jarlkog Invaran 5 6 I ± η λ A J kj l kl j b b ub u u ara J all rangl b b u u J CP olaon:

41 b Trangl n ghr Orr u ub I b Aλ ρ η Aλ Aλ ρ η 5 A λ ρ η Aλ 5 ρ η η η λ ρ ρ λ b Aλ ρ η Aλ Aλ ρ η O λ 7 O λ O λ 5 O λ 7 b * u * ub * b η α β ρ * b

42 u u u ub b A λ ρ η A λ A λ ρ 5 5 A λ ρ η Aλ ρ η I η O λ O λ 5 O λ 7 η α λ ρλ ηλ ρ β β β λ η u Aλ

43 Sanar Moll. CP xplly brokn. Thr a ngl our of CP volaon: δ CKM. CP volaon appar only n harg urrn nraon of quark 4. CP volaon loly rla o flavor hangng nraon

44 Mxng of nural on Nural on: P : K D u b b P : K D u b b Sanar Mol pr ollaon of nural Mon: b W b u,, u,, u,, W W W b u,, b Tranon an b rb by arx ln: W

45 Phnonologal rpon of xng Shröngr quaon for unabl on: Γ ψ ψ ψ Γ Γ ψ ψ ψ ψ Γ Γ Γ CPT CP W M an Γ hran: * * Γ Γ Γ Γ Γ Γ * * P P P P P P P P P P Γ M,,,,,,, D D K K For nural on onr opon. Pha φ

46 P P p q Ma gna by agonalzng arx avy an lgh a gna: p P p P q P q P wh, wh Γ, oplx offn Γ Γ,, Γ x Parar of h a a ± Γ Γ Γ I Γ un 4I y Γ Γ P P P p P q P P > 4.4 p Γ / Γ <.7 9% C Γ Nural on.5 ±.7 p / Γ PDG PDG.9 ±.64 Moron7

47 ,, f q p f f p q f q p b q p b p p ψ ψ b b,,,,,,, Γ [ ] / / f Γ Γ ± ±,, f p q P f P,, f q p P f P T voluon Gnr parl bfor P

48 Mxng of nural on T voluon of ra: [ ] P P Γ Γ Γ Γ o 4 / [ ] [ ] q p P p q P Γ Γ Γ Γ Γ Γ Γ Γ o 4 o 4 / / CPT CP, T- volaon n xng: p q P P

49 Mxng Mhan η q p Γ Γ Γ 4I x Γ un y Γ Γ prv aborbv If CP onrv: Two xng han: Γ y O Mxng hrough ay Γ Mxng hrough ollaon x O Γ η K, K, φ η, D, D,,, how ffrn ollaon bhavor K π π K long an, on-hll a For K poran, for nglgbl K W u,, hor an, vrual a K

51 , Mxng Mxng han: Mxng hrough ay: any pobl haron ay Γ larg n aon ay lk ππ ar uppr y Γ Γ for all O. for on' xp xng va ay Mxng hrough ollaon b u,,, u,, b Sgnfan onrbuon only fro op loop b u,, u,, b

52 Marx Eln Π Propagaor

53 gh Quark Conrbuon For : Π Π Π u u lar o GIM ub Ung unary: u b b Corrpon o ngl arx ln w/ nnr fron u

54 G F π φ CP b W [ f ] [ S / W η QCD ] CP Pha nrou whl val. haron par of arx ln Elrowak an QCD orron aron par of arx ln:

55 Para all, Moron 7

56 ξ wh ξ f f ~ 6 ξ.4 ±.7.56 ±.6 ± -.4 p 7.77 ±.a. ±.7y. - p X 5

57 D Mxng Foral

60 D D K π π

61 ξ λ ρ λ Sau aufgrun CP rhalnr Mgrößn

62 Couplng n lrowak Thor Y Q T T 4 τ τ ν ν ν τ b u b u I II III ponn Quark Dubl Sngl Dubl Sngl

63 . Phoonkopplung an Fronn an un Fronn glh ~ Q f. W-Kopplung an Fronn nur an Fronn ~ T g T. Z-Kopplung an Fronn an un Fronn vrhn nθ w : : g g g oθ w g oθ w g g f T Q n Q f f θ n θ w w pl: ν : : g g g.7 g. äufg wrn a g l un g auh kor un Axalvkorkopplungn vrwn: g g g g g g A

1. Quark mixing and CKM matrix

1. Quark mixing and CKM matrix Avan arl hy: IX. Flavor Ollaon an C olaon IX. Flavor ollaon an C volaon. Quark xng an h CM arx. Flavor ollaon: Mxng o nural on 3. C volaon. Nurno ollaon. Quark xng an CM arx. Quark xng: Ma gna ar no ual