CP-volaton from Non-Untary Lptonc Mxng Jacobo Lópz Pavón IFT UAM/CSIC XLIIIrd Rncontrs d MORIOND Elctrowak Ssson La Thul, March 1-8, 008 S. Antusch, C. Bggo, E. Frnándz-Martínz and M.B. Gavla JHEP 0610:084,006 E. Fdz-Martnz, M.B. Gavla and O. Yasuda Phys.Ltt.B 649:47-435,007
Motvatons Nutrno masss and mxng vdnc of Physcs Byond th SM Typcal xplanatons nvolv Nw Physcs at hghr nrgs Ths NP oftn nducs dvatons from untarty of th PMNS at low nrgy W wll analyz th prsnt constrants on th mxng matrx wthout assumng untarty Study of CP volaton n th contxt of non-untarty
Usual Analyss 1 g g L = ( α / α αmαββ hc..) ( Wlαγ PLα hc..) ( Zαγ PLα hc..)... cosθ W l α CC W - α NC Z Dagonalzng α α L 1 g ( ) g ( = ) / m Wlαγ PU L α Zγ PL hc..... cosθ W U α = U Th mxng matrx s untary n th usual analyss wth 3 lght α
Th gnral da W - gγ PU L α l α cc sc s U= s c s s c c c s s s s c ss csc sc css cc δ 13 1 1 13 13 δ δ 1 3 3 13 1 1 3 3 13 1 3 13 δ δ 3 1 3 13 1 3 1 3 13 1 3 13 α β 1 W - l α gγ PN L α N N N N N N N N N N 1 3 = 1 3 1 3
Effctv Lagrangan allowng non-untarty L 3 lght Assum NP at Λ >> Λ EW. In th flavor bass, 1 c g g = ( α / Kαββ αmαββ hc..) ( W lαγ PLα hc..) ( Zαγ PLα hc..)... cosθ W α = N α L 1 g g = ( / m) ( Wlαγ PLNα) ( Zγ PL( N N) j j) hc..... cosθ W unchangd N non-untary = δ j j
Th ffcts of non-untarty appar n th ntractons W - Z l α N α j ( NN) j W can bound untarty wth wak dcays α 1 = N α N α δ β α α β P = L= 0= = αβ β α ( L) ) N N β N α N * α β E N N α m N L * α β N β Zro Dstanc Effct
Constrants on Untarty from wak dcays W l α Z nvsbl unvrsalty tsts rar lpton dcays NN 0.994± 0.005 < 7.1 10 < 1.6 10 < 7.1 10 0.995± 0.005 < 1.0 10 < < ± 5 5 1.6 10 1.0 10 0.995 0.005 90% C.L. N s untary at % lvl
In th futur γ γ TESTS OF UNITARITY RARE LEPTON DECAYS NN < 10 6 NN < 1.6 10 (MEG) (BABAR) γ NN < 1.0 10 (Bll)
In th futur TESTS OF UNITARITY γ γ γ RARE LEPTON DECAYS NN < 10 NN < 1.6 10 6 NN < 1.0 10 (MEG) (BABAR) (Bll) ZERO-DISTANCE EFFECT @ NF 4 ( NN ) <.3 10 3 ( NN ) <.9 10 3 NN <.6 10
In th futur TESTS OF UNITARITY γ γ γ RARE LEPTON DECAYS NN < 10 NN < 1.6 10 6 NN < 1.0 10 (MEG) (BABAR) (Bll) ZERO-DISTANCE EFFECT @ NF 4 ( NN ) <.3 10 3 ( NN ) <.9 10 3 NN <.6 10
In th futur TESTS OF UNITARITY γ γ γ RARE LEPTON DECAYS NN < 10 NN < 1.6 10 6 NN < 1.0 10 (MEG) (BABAR) (Bll) ZERO-DISTANCE EFFECT @ NF 4 ( NN ) <.3 10 3 ( NN ) <.9 10 3 NN <.6 10 PHASES phass apparanc xprmnts: NUFACTs, b-bams
If w paramtrz Can w masur th phass of N? E. Fdz-Martnz, M.B. Gavla, J. Lópz-Pavón and O.Yasuda hp-ph/0703098 ph/0703098 N = (1 η) U whr U U PMNS η η η * η = η η η * * η η η and η = η If Δ E ml Δ<< 1 SM * ( L = A O ) η η α β αβ αβ P αβ only dpnds on ηαβ
Can w masur th phass of N? E. Fdz-Martnz, M.B. Gavla, J. Lópz-Pavón and O.Yasuda hp-ph/0703098 ph/0703098 For nstanc, for two famls: Δ P αβ = sn ( θ)sn 4 η αβ sn( δ αβ )sn( θ)sn Δ 4 η αβ SM CP volatng ntrfrnc Zro dstanc ffct η αβ δ η αβ αβ Nw CP-volaton sgnals Δ =ΔmL E 1 j j
Whch s th bst channl???? < 3.5 10 η 5 < 8.0 10 η 3 < 5.1 10 η 3 Δ sn θ sn 4 η snδ sn θ sn 4 η 31 P 3 3 Δ 31 P Ths s th bst channl to masur nw CP phass: P 8 η snδ sn( θ )sn Δ 3 13
Th CP phas δ can b probd N N 8 η snδ sn( θ )sn Δ 3 13 1. Confuson btwn sgn sgn. Dgnracy δ δ 180º δ Δ 3σ 13 @ a Nutrno Factory wth L = 130 Km
Th CP phas δ can b probd 3σ Prsnt bound from γ Snstvty to η Snstvty to δ For non-trval δ, on ordr of magntud mprovmnt for η
Conclusons Analyz nutrno data wthout assumng untarty. W startd th frst analyss and conclud that, at prsnt: -EW dcays confrms untarty at % lvl -Prsnt bounds on untarty ar strong nough to match th untarty analyss CP-asymmtry s a clan prob of th nw phass. Non-untary ffcts n typcal modls ar too small to b dtctd at prsnt xprmnts. Thy could b szabl n xtnsons/othrs modls wth M~ TV, ). -> kp trackng thm n th futur. Thy ar xcllnt sgnals of nw physcs.
Back-up slds
Constrants on untarty < 3 η < 3.510 5 η < 8.010 3 5 3 η < 5.1 10 3 < 3 < 3 < 3 η 5.510 < 3.510 < 5.010 η 8.0 10 η 5.1 10 η 5.0 10 η η η
Lptonc Mxng Matrx Elmnts From Oscllatons N N N N N N N 1 3 = 1 3 N N N 1 3
CHOOZ: KamLAND: Δ 13 from KK SNO: P 0.1 N 0.9 N N lmnts from oscllatons: -row ( ) 4 ( ) cos( Δ ) ( ) 4 4 4 cos( Δ ) P N N N N N 1 3 1 1 1 P N N N N N N 1 3 1 3 13 KamLANDCHOOZKK Δ j = Δm j L E SNO all N dtrmnd
Pˆ N lmnts from oscllatons: -row Atmosphrc KK: Δ 1 0 Δ j = Δm j L E 4 N N N N N N ( Δ ) 1 3 1 3 cos 3 1. Dgnracy N N 1 3 N UNITARITY. 1, N N cannot b dsntangld
N lmnts from oscllatons only = OSCILLATIONS [ N N 1 N wthout untarty 0.75 0.89? 1/ = 0.45 0.66 0.57 0.86? ] < 0.34 0.57 0.86? 3σ wth untarty OSCILLATIONS U 0.79 0.86 0.50 0.61 < 0.0 = 0.5 0.53 0.47 0.73 0.56 0.79 0.10.51 0.4 0.69 0.610.83 Gonzálz-García, Malton 07
Dcays W - l α ( W l ) Γ α ( NN ) αα ( NN ) ( NN ) l α W - γ Br l l β ( α lβγ ) ( NN ) βα ( NN ) ( NN ) m O MW αα ββ ( NN) j, j Z nvsbl unvrsalty tsts NN NN ( NN ) ( NN ) αα ββ
If w paramtrz Can w masur th phass of N? E. Fdz-Martnz, M.B. Gavla, J. Lópz-Pavón and O.Yasuda hp-ph/0703098 ph/0703098 N Normalzaton factors = (1 η) U whr U U PMNS η η η * η = η η η * * η η η and η = η O( η ) Standard ampltud If Δ E ml Δ<< 1 SM Aαα 1 η SM Aαβ αβ << 1 SM * ( L = A O ) η η α β αβ αβ P αβ only dpnds on ηαβ
Whch s th bst channl???? Constrants on untarty: η 5.5 10 η η < 3.5 10 η < 5.0 10 η 8.0 10 η 5.1 10 η 5.0 10 3 5 3 < η < 3.5 10 η < 8.0 10 5 3 3 η < 5.1 10 3 3 3 < < < 90% C.L. η << η, η
Whch s th bst channl???? P P SM s c η c sn δ δ sn θ Δ η sn θ snδ Δ 4 η 3 13 31 3 13 1 1 Δ =Δ mle<< 1 j j sn θ Δ s supprssd by th small paramtrs Δ 1 and 13 31
Our analyss wll also apply to non-standard or xotc nutrno ntractons. (Grossman, Gonzalz-Garca t al., Hubr t al., Ktazawa t al., Davdson t al. Blnnow t al...) Thy add 4-frmon xotc oprators whch affct producton or dtcton or propagaton n mattr Ψ Ψ Ψ Ψ
NSI nutrno ntractons vs NonUntarty SM Dtcton @ NF: d l u α α d u Producton @ convntonal-bams supr-bams Producton @ NF: Mattr ffcts: α=β=
NSI nutrno ntractons vs NonUntarty Exotc Intractons Add nw ffctv 4-frmon oprators whch affcts to: Producton Dtcton d αd lα u u Mattr ffcts f f
NSI nutrno ntractons vs NonUntarty SM Exotc Intractons Exotc Intractons Non-Untarty
NSI nutrno ntractons vs NonUntarty Exotc Intractons Non-Untarty ε p αβ No rlatonshp btwn and ε d βα η αβ = η * βα If ε = ε p d* αβ βα P EXOTIC = P NON UNITARITY Our constrants apply to Exotc Intractons! If not Idm, barrng xtrm fn tund canclatons
Oscllaton Probablty n Mattr 1 L = Gnγ P Gn γ P nt 0 0 ff F L F n α L α α V CC V NC d dt = N E 0 0 ( N ) 1 * 1 * E ( NN ) ( NN ) ( VCC VNC )( NN ) VNC ( NN ) ( NN ) ( Vcc VNC ) ( NN ) VNC ( NN ) ( NN ) Effctv Evoluton 1. non-dagonal lmnts. NC ffcts do not dsappar
Mattr ffcts n Δ, Δ, AL Kpng only trms to scond ordr n 1 31 and and frst n η (sttng η = 0): αβ sn θ 13 sn θ 10 Δ AL 10 Δ 10 η < ~ 10 1 3.5 13 31 1 αβ
Aproxmat xprsson for P Δ31 Δ1 3 sn θ13 3 sn θ1 P c s Δ1 Δ31 c13 sn θ1 sn θ3 sn θ13 cosδ η c sn θ sn δ δ Δ η sn θ snδ Δ 4 η s c 3 13 31 3 13 1 1 ( ; ; η η ) P = P s c c s 3 3 3 3
Analyss of 3σ 3σ Th zro dstanc ffct domnats ovr CP volatng ntrfrnc trm - No nformaton on δ 3 η 10 - Snstvts to around
Som dtals about th xprmnt @ NF W study a NF bam rsultng from th dcay of 50 GV muons: 10 - Assumng usful dcays/yar - 5 yars runnng wth ach polarty - 5 Kt Opra-lk dtctor -L=130 km 0 5 - snstvts and backgrounds = ( snstvts and backgrounds) hp-ph/0305185
(NN ) and (N N) from dcays NN 1.00 ± 0.005 5 < 7. 10 < 1.6 10 < 7. 10 1.003 ± 0.005 < 1.3 10 5 < 1.6 10 < 1.3 10 1.003± 0.005 90% C.L. N = HV NN = H = 1 ε wth ε = ε N N = 1 V ε V = 1 ε ' ε ' j ε αβ 0. 03 αβ N N 1.00 ± 0.03 < 0.03 < 0.03 < 0.03 1.00 ± 0.03 < 0.03 < 0.03 < 0.03 1.00 ± 0.03 N s untary at % lvl
Low-nrgy thory..... cos.... 1 / = h c P Z g h c P l W g h c M K L L W L c α α α α β αβ α β αβ α γ θ γ Aftr EWSB:..... ) ( cos 1 / = h c N N P Z g N P l W g m L j j L W L c γ θ γ α α M αβ dagonalzd untary transformaton K αβ dagonalzd and normalzd untary transf. rscalng N non-untary
CHOOZ: systmatc rror hp-x\0301017 SNO: n n CC NC Som numbrs 1 N 0.9 N 0.1 Normalzaton flux ~.7% Enrgy ~ 1.1% w lt t vary % OPERA (NF): background: c-dcays / chargd currnt dcays ~ systmatc rror ~ 5% ffcncy ~ 0% hp-ph\0305185 KK: Statstcs hp-x\0411038 10 6 ZERO-DISTANCE EFFECT 40Kt Iron calormtr nar NUFACT 4 ( NN ) <.3 10 4Kt OPERA-lk nar NUFACT 3 ( NN ) <.9 10 NN <.6 10 3
(NN ) from dcays: G F W W dcays Z Invsbl Z Unvrsalty tsts ( NN ) αα l α ( NN ) ( NN ) ( N N ) j j j ( NN ) ( NN ) ( NN ) αα ( NN ) ββ Info on (NN ) aa G F s masurd n -dcay W N j 5 Fm Γ = N N 3 19π j N* j G j G F,xp GF = N N j j
Oscllaton Probablty n Vacuum d H dt = ^ = E δ = I fr j j j Effctv Evoluton E 0 0 E 1 1 0 0 d * * t = U 0 E α α dt 0( * U) 1 N 0 E 0 N α 0 0 E 0 0 E 3 3 = I P = L= 0= = αβ β α ( L) ) N N β N α N * α β E N N α m N L * α β N β Zro Dstanc Effct
Non-untarty from s-saw L = LSM NRdNR -Y L H NR -M NR NR Intgrat out N R L ff = L SM 1 d = 5 1 d = 6 L L MΛ MΛ... T YY/M (L LH H) _ YY/M (L H) d(h L) d=5 oprator t gvs mass to d=6 oprator t rnormalss kntc nrgy Broncano, Gavla, Jnkns 0
masss byond th SM Tr-lvl ralzatons N R N R Havy frmon snglt N R dvatons from untarty (Ssaw I) Havy scalar trplt Δ t R t R Y t Y t M t no dvatons from untarty Havy frmon trplt t R dvatons from untarty Abada, Antusch, Bggo, Bonnt, Hamby, M.B.G.
addng nar dtctors E, 0 = NN Tst of zro-dstanc ffct: αβ αβ P αβ δ MINOS: (NN ) =1±0.05 BUGEY: (NN ) =1±0.04 NOMAD: (NN ) <0.09 (NN ) <0.013 KARMEN: (NN ) <0.05 N = 0.75 0.89 0.00 0.69? 0.45 0.66 0. 0.81? < 0.7 0.57 0.85? also all N dtrmnd
Numbr of vnts n v Φ α d ( E) ~ de P αβ ( E, L) σ β ( E) ε ( E) de producd and dtctd n CC dφ dφ ~ de de SM σ β ~ σ β NN ( NN ) αα SM α α ββ n v SM ( NN ) P ( E, L) ( NN ) ( E) ε SM dφα ( E) ~ de αα αβ ββ σ β E de Excptons: masurd flux lptonc producton mchansm dtcton va NC Pˆ αβ ( E, L) = N * α P L N β
In th futur γ γ TESTS OF UNITARITY RARE LEPTON DECAYS NN < 7.1 10 5 NN < 1.6 10 (MEGA) (BABAR) γ NN < 1.0 10 (Bll)