Refer to Chapter 8 Kaon system Oscillations and CKM mixing matrix Neutrinos

Transcription

1 Chaptr 1

2 Rfr to Chaptr 8 Kaon systm Oscillations and CKM mixing matrix Nutrinos

3 " # K 1 = 1 $ K K " # K = 1 $ K K C K = K ; C K = K P K = K ; P K = K % ' & % ' & K andk ar not ignstats of CP : CP K = K ; CP K = K K 1 andk ar ignstats of CP : CP K 1 = K 1 ; CP K = K K 1 and K ar lik ral particls to th wak intraction as ar K and K bar to th strong CP π π = π π ; CP π π = π π CP π π π = π π π ; CP π π π = π π π K 1 and K hav diffrnt masss K 1 ππ K πππ m K m π MV $ & % m K 3m π 9MV '& Γ 1 > Γ τ 1 < τ K & S K 1, K -& L K Mor in 1.

4 π p Λ K τ 1 < τ K S K 1 ;K L K K N Λ π K bar highr cross sction than K t = K () = 1 $ K 1 () K () " At t 1 $ a (t) K 1 1 () a (t) K () a α (t) = Probability # oscillating tim factor " # im αc t/ "# $ %$ Γ αt/ "#$ = im αt ; M α = m α iγ α / # #" ### $ particl dcays 1 a α (t) = 1 Γ αt/ dcrass xponntially with τ = Γα 1 7/5/15 F. Ould- Saada 4 % ' & % ' & α=1,

5 ( ) ( ) P(K K ) = 1 % 4 Γ 1t Γt ( Γ 1Γ )t/ & cos Δmc t P(K K ) = 1 % 4 Γ 1t Γt ( Γ 1Γ )t/ & cos Δmc t Δm m 1 m ; Δm τ S =.5 ' ( ' ( Intnsity of th componnts I(K ) = f (distanc from K sourc) K p π Λ, π Σ Δm K = (3.483±.6) 1 1 MV / c Δm K / m K = /5/15 F. Ould- Saada 5

6 If CP wr consrvd, K 1 dcays into 3 pions, and K dcays into pions would b forbiddn. It was such a forbiddn dcay that was obsrvd in 1964, showing that CP is not consrvd In th xprimnt, K bam was allowd to travl ~18m to nsur as fw K 1 prsnt as possibl Th products of th particl dcays of K bam wr thn obsrvd in dtctors Obsrvation: 5 K à π π - out of 3 dcays K S = 1 K # 1ε 1 ε K " K L = 1 K # 1ε ε K " 1 $ & % $ & % ( * ) * ε 1 3 ε = ε iϕ

7 K L = 1 1 ε K ε K 1 K S = 1 1 ε K 1 ε K (a) Indirct CP violation by Mixing CP- forbiddn K 1 componnt in K L dcays via CP- allowd procss K 1 à ππ, giving contribution proportional to probability ε of finding K 1 componnt in K L ΔS= à paramtr ε (a) ε (1 ε ) 1 ε (b) Dirct CP violation ΔS=1 Pnguin diagrams through g, γ, Z à paramtr ε << ε CP- allowd K componnt in K L dcays via CP- violating raction K à ππ 7/5/15 7

8 η = (.33±.1) 1 3 ; η = (. ±.1) 1 3 ϕ = (43.5 ±.5) ϕ = (43.5 ±.6) ε = (.9 ±.1) 1 3 R(ε '/ε) = (1.65±.6) 1 3 What was masurd xprimntally: Ratio R, Asymmtry A à xtract CP violation paramtrs η = η iϕ η = η iϕ = A(K L π π ) A(K S π π ) = ε ε ' = A(K L π π ) A(K S π π ) = ε ε ' 8

9 CKM quark- mixing matrix V αi =probability (αà iw transition) Kobayashi Maskawa_matrix Phas( iδ ) rsponsibl for CP violation) 9

10 Wolfnstin paramtrisation λ = s 1 Aλ = s 3 Aλ 3 (ρ iη) = s 13 i δ Unitarity conditions Equation of triangl Th position of th apx is fixd by various xprimnts and provids a consistncy chck of th SM If, for x., β > à CP violation If triangl closd à 3 gnrations

11 Th position of th apx is fixd by various xprimnts and provids a consistncy chck of th SM. - If, for x., β > à CP violation - If triangl closd à 3 gnrations

12 Various masurmnts to dtrmin CKM paramtrs

13 What is a nutral B- mson? Short liftim à no bams of B msons B- factoris Υ(4s): M=1.58GV, Γ=MV Υ(4s) B J PC = 1 d B d ; B B B (579.58) db ; B bd B (579.6) ub ; B bu B = 1 B = 1 τ B ~ 1.5ps Analogof K S, K L B L, B H 7/5/15 F. Ould- Saada 13

14 Othr dcays studid whr CP violation masurd B / B J / ΨK S BaBar at PEP- II, SLAC, US BELLE at KEK- B, Japan ) ( ) ( ) ( ) ( ± = Γ Γ Γ Γ π π π π π π K K A K B K B K B K B A Qustion: how do w know that a B (or anti- B) is producd?

15 Tag on B mson and study th othr: Sign of K, µ Asymmtric collidr B J / ΨK S µ µ π π B D π µ µ ; D π K βγ >>1 Δt = t t 1 = z z 1 βγc

16 From othr dcay final stats

17 Th Low Enrgy Anti- proton Ring (LEAR) Vry activ in tsting discrt symmtris CPLEAR xprimnt provd in 1998 that tim rvrsal symmtry, T, is not consrvd in wak procsss involving K msons T- invarianc would rquir sam probability for th invrs transformations K K & K K Rad nxt slid and study th th principl od th masurmnt

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19 CP- violation in Standard Modl Kaon and B- mson systms not nough to xplain th mattr- antimattr asymmtry in th Univrs. Still unknown, sourcs of CP- violation Nutrino masss, oscillations and CP- violation Suprsymmtry and or thoris byond SM In 1967, Sakharov, 1967 CP- violation is a ncssary condition for baryognsis à 13.6 Th Big Bang and th Primordial Univrs lptognsis in addition to baryognsis?

20 Sakharov: ncssary to hav (a) an intraction that violats baryon numbr (b) an intraction that violats charg conjugation C and CP (c) a non- quilibrium situation to sd th procss Currnt situation CP violation obsrvd in K and B dcays but not nough Unknown sourcs of CP violations? Such in SUSY thoris Gnration of non- quilibrium? Mayb b within Baryon- violating intractions of GUTs, or Lptognsis? Mattr- Antimattr asymmtry rmains a srious unsolvd problm kt > M X X X mattr radiation kt << M X no profuction norannihilation of X X X X CP violating dcays mor mattr than antimattr 7/5/15 F. Ould- Saada

21 In SM m = But if nutrino has non- zro mass à oscillations may occur Bam of 1 typ nutrino ( µ ) dvlops componnts of othr typs ( / τ ) For this to happn à nutrino mixing Flavour stats (, µ, τ ) coupling to (, µ, τ) don t hav dfinit masss but ar linar combinations of ( 1,, 3 ) with dfinit masss m 1, m, m 3, (ignstats of mass) α, α=1,,3 ar flavour ignstats (of th wak intraction) i, i=1,,3 ar mass ignstats (of th strong intraction, also ignstats of Hamiltonian) 3 nutrinos à 3 mixing angls à 3X3 matrix Simpl cas of flavour stats à on mixing angl θ ij à X matrix 6/5/15 F. Ould- Saada 1

22 Simpl cas of flavour stats à mixing angl θ ij α = i cosθ ij j sinθ ij β = i sinθ ij j cosθ ij # % $ α β & # ( = % ' % $ cosθ ij sinθ ij sinθ ij cosθ ij &# (% ( ' $ i j & ( ' α producd (through WI) at t= with momntum p, E i = p m i i and j hav slightly diffrnt nrgis E i and E j (m i slightly diffrnt from m j, slightly diffrnt frquncis) à mass ignstats propagat indpndntly tim t, original bam α dvlops componnt β whos intnsity oscillats 6/5/15 F. Ould- Saada

23 " $ α () = i () cosθ ij j () sinθ ij t = :# %$ β () = i () sinθ ij j () cosθ ij = Tim volution of mass ignstats: i, j (t) = i E i, j t i, j (o) α (t) = i (t) cosθ ij j (t) sinθ ij = i E it i () cosθ ij i E jt j () sinθ ij = i E it " # α () cosθ ij β () sinθ ij $ % cosθ ij i " # α () sinθ ij β () cosθ ij $ % sinθ ij " = α () i E it cos θ ij i E jt $ sin θ ij #& %' () " β #& = A(t) α () B(t) β () β () = α (t) = α () " #& i E it cos θ ij i E jt $ sin θ ij %' 6/5/15 F. Ould- Saada 3 E j t i E i t i E jt $ %' sinθ cosθ ij ij ) " α (t) α (t) = A(t) = α () α () cos 4 θ ij sin 4 θ ij cos θ ij sin θ ij i (E j E i )t i(e je i )t $ - *., #& %' / ) P( α α ) = 1 sinθ ij sin (E E )t - j i *., / =1 P( α β ) P( α β ) = sin θ ij sin (E j E i )t

24 β (t) = i (t) sinθ ij j (t) cosθ ij = i E it i () sinθ ij i E jt j () cosθ ij = i E it " # α () cosθ ij β () sinθ ij $ % sinθ ij i " # α () sinθ ij β () cosθ ij $ % cosθ ij " = α () sinθ ij cosθ ij i E it i E jt $ #& %' () " β #& " β () = β (t) = α () sinθ ij cosθ ij i E it i E jt $ #& %' "( E β (t) α (t) = P( α β ) = sin (θ ij )sin j E i )t $ & ' #& %' i E j t E i t sin θ ij i E jt $ cos θ ij %' 6/5/15 F. Ould- Saada 4

25 At t= α producd with p (assum β =, i.. bam is pur α ) At tim t > Mass ignstats i and j propagat with nrgis E i and E j α (t) not anymor pur α but a combination of α and β #( E P( α β ) = sin (θ ij )sin j E i )t & % ( $ % '( P( α α ) =1 P( α β ) P( β ) oscillats with tim whil P( α ) rducs by corrsponding oscillating factor P( α ) =1- P( β ) Oscillation vanishs if mixing angl is zro OR mass ign- stats ar qual, in particular if m 1 =m = Possibl nhancmnt if oscillations in mattr 6/5/15 F. Ould- Saada 5

26 m vry small E i, j >> m i, j c (E pc;t L / c) E i, j = p c m i, jc 4 1 m i, j c4 pc E j E i m j c 4 m i c 4 pc = Δm ijc 4 pc # P( α β ) sin (θ ij )sin % $ Oscillations dtctd xprimntally and non- zro nutrino mass stablishd L L & ( with L = ' # P( α β ) sin (θ ij )sin 1.7 Δm # ij % $ $ % E GV V & ' [ ] L [ km ] 4E c Δm ij c 4 & ( '( 6/5/15 F. Ould- Saada 6

27 Atmosphric nutrinos stm from dcays of chargd pions (and kaons), which ar producd through intractions btwn primary cosmic rays and th atmosphr 6/5/15 7 F. Ould- Saada ~ = N N R µ µ π µ µ π π,k,... N p µ µ µ µ µ R = N µ N " # # $ % & & ~

28 l N l N' l =,µ 5 tons ultra pur Watr: h=4m, Ø=4m Dpth: 7 mw 13 photomultiplirs à Crnkov radiation N N R( µ µ / xpctd ) ~ ( µ / ) ( µ / ) masurd simulatd < 1 6/5/15 F. Ould- Saada 8

29 .9 sin ; ) θ ( Δm c V. Δm. 6/5/15 9 F. Ould- Saada 17 sin sin j i ij ij ij τ µ m m Δm ] Δm [V E[GV] L[km]. ) θ ( ) P(

30 Th Homstak solar nutrino xprimnt, R. 1st obsrvation of Solar Nutrino Dficit Dtctor: 615 tons C Cl 4 Apparanc of atoms of radioactiv 37 Ar 37 Cl à - 37 Ar, E thrshold =.814 MV Exprimnt obsrvd an vnt rat of:.56±.3 SNU 1 SNU = 1-36 intractions / targt atom s Standard Solar Modl flux prdiction: SNU Factor of thr discrpancy solar nutrino problm SNP inspird so much of modrn nutrino physics. SNP confirmd by various xprimnts 6/5/15 F. Ould- Saada 3

31 p p H.4MV pp 99.75% p p H 1.44MV pp.5% 3 3 H p H γ 5. 49MV 86% 14% hp.4* H H α p 1. 86MV H α B γ 1. 59MV 3 H p α 7 7 B 99.89% 7 B Li γ. 8617MV 7 Li p α α MV % 8 B p B γ. 14MV 8 B.11% 8 B B 14. 6MV 8 B α α 3MV 6/5/15 F. Ould- Saada 31

32 6/5/15 3 F. Ould- Saada MV B B MV n p d MV B B MV p p d MV B B MV MV d p p MV G Ga MV Li B MV B B MV Ar Cl x x x x E Sun procss Thrshold E Exprimnt procss ma n

33 6/5/15 F. Ould- Saada 33

34 SNO (Sudbury Nutrino Obsrvatory) mbddd 7 m in th Crighton min at Sudbury, Ontario, Canada Thrshold ~ 5 MV. Muon flux x smallr than SK. 1 tons D O 7 tons H O, 96 photomultiplirs. SNO s advantag: all nutrino favours can b masurd SNP dfinitly solvd through nutrino oscillations 6/5/15 F. Ould- Saada 34

35 Solar nutrino xprimnts KamLand (long baslin ractor xprimnt) Atmosphric nutrino xprimnt supportd by long baslin acclrator xprimnts Nuclar ractor Δm 3 tan 3 Δm ( θ 1 1 Δm ) ; ; sin sin (θ 13 ).1 V c 9 θ 3 ( θ 3 1 V c 35 ).9 Δm Δm θ 1 3 1, θ,, 13, θ 3 6/5/15 F. Ould- Saada 35

36 What is th right nutrino mass pattrn? Nutrino masss Oscillation data à mixing btwn all 3 nutrino mass stats Solar nutrino oscillation in mattr à sign of Sign of Δm 3 not dtrmind à solutions for mass hirarchy Δm 1 6/5/15 F. Ould- Saada 36

37 Dirct mass masurmnt But nutrino lctron = suprposition of 3 mass ignstats Howvr 5 5 V Δm V Δm Bounds from cosmology Analysis of larg scal structurs of Univrs à (indirct limit) c c V 1 c 6 m < 4 m m i > m j ( m i m j ) < m i m j m m 1 1 V / c m 3 m 5 1 V / c m i V / c << m l 3 m l 1V / c i=1 6/5/15 F. Ould- Saada 37

38 In a 3- framwork U U U µ τ U U U 1 3 = Uµ 1 Uµ Uµ 3 τ1 τ τ U 1 c s c s iρ iδ iσ = c3 s3 s1 c1 s3 c 3 s13 c θ 3 ~ 45 Atmosphric Acclrator θ 13 =? Ractor Acclrator θ 1 ~ 34 Solar Ractor ββ 6/5/15 F. Ould- Saada 38

39 Mattr- Antimattr asymmtry, nutrino mass and natur rmain srious unsolvd mystris as ar svral othr nigmas waiting for you 8/5/15 F. Ould- Saada 39