General Considerations NP search strategies µ − e universality in RK = Γ(K → eνe )/Γ(K → µνµ ) SM prediction for RK ,πSUSY effects in Kaon physics: Lepton Universalitytests and rare decays
P. Paradisi
TU of Munich

KAON ’09
TSUKUBA, JAPAN 12 June 2009

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KAON ’09

P. Paradisi

SUSY effects in Kaon physics: Lepton Universality tests and ra

General Considerations NP search strategies µ − e universality inGeneralRK =Considerations
Γ(K → eνe )/Γ(K → µνµ ) SM prediction for RK ,πGeneral Considerations

Flavor Physics in the LHC era
High energy experiments are the key tool to determine theenergy scale Λ by direct production of NP particles.
Low energy experiments are a fundamental ingredient todetermine the symmetry properties of the new d.o.f. via
their virtual effects in precision observables.

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KAON ’09

P. Paradisi

SUSY effects in Kaon physics: Lepton Universality tests and ra

General Considerations NP search strategies µ − e universality inGeneral
RK =Considerations
Γ(K → eνe )/Γ(K → µνµ ) SM prediction for RK ,πGeneral Considerations

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KAON ’09

P. Paradisi

SUSY effects in Kaon physics: Lepton Universality tests and raGeneral Considerations NP search strategies µ − e universality in RK = Γ(K → eνe )/Γ(K → µνµ ) SM prediction for RK ,πNP search strategies
Where to look for New Physics?

Processes very suppressed or even forbidden in the SM0FCNC processes (µ → eγ, τ → µγ, Bs,d→ µ+ µ− , K → πν ν̄)CPV effects (electron/neutron EDMs, de,n ....)
CPV in Bs,d decay/mixing amplitudes

Processes predicted with high precision in the SM
EWPO as ∆ρ, (g − 2)µ ....
e/µLU tests in RM = Γ(K (π) → eν)/Γ(K (π) → µν)
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KAON ’09

P. Paradisi

SUSY effects in Kaon physics: Lepton Universality tests and ra

General Considerations NP search strategies µ − e universality in RK = Γ(K → eνe )/Γ(K → µνµ ) SM prediction for RK ,πLU tests with K `3 and k`2 modes

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KAON ’09

P. Paradisi

SUSY effects in Kaon physics: Lepton Universality tests and ra

General Considerations NP search strategies µ − e universality in RK = Γ(K → eνe )/Γ(K → µνµ ) SM prediction for RK ,πµ − e universality in RK = Γ(K → eνe )/Γ(K → µνµ )e/µPDG 2006
NA48/2 ’03 prel.
NA48/2 ’04 prel.
KLOE prel.
SM prediction(RK )exp. [10−5 ]2.45 ± 0.11
2.416 ± 0.043 ± 0.024
2.455 ± 0.045 ± 0.041
2.55 ± 0.05 ± 0.05
2.477 ± 0.001

e/µ(RK )exp. = (2.457 ± 0.032) × 10−5
A dedicated run (of 4 month) for RK by P326/NA62(former NA48) has been performed @ the CERN.
Goal: the error @ 0.3%!
Rπexp. = (1.230 ± 0.004) · 10−4
KAON ’09

P. Paradisi

PDG

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SUSY effects in Kaon physics: Lepton Universality tests and raLFV
LFV
LFV
General Considerations NP search strategies µ − e universality inRKRK in= SUSY
Γ(K → Reνin SUSY→ µνRµK) SMin SUSYprediction
LU forat aR(SupK ,πK e )/Γ(KSM prediction for RK ,πRKSM = (2.472 ± 0.001) · 10−5

SMRπSM = (1.2354 ± 0.0002) · 10−4

SMMarciano Sirlin ’93, Finkemeyer ’96
RKSM = (2.477 ± 0.001) · 10−5

SMRπSM = (1.2352 ± 0.0001) · 10−4

SM

Cirigliano Rossell ’07
The total errors in RK ,π are dominated by the EXP. ERRORS!!!

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KAON ’09

P. Paradisi

SUSY effects in Kaon physics: Lepton Universality tests and ra

LFV
LFV
LFV
General Considerations NP search strategies µ − e universality inRKRK in= SUSY
Γ(K → Reνin SUSY→ µνRµK) SMin SUSY
prediction
LU forat aR(SupK ,πK e )/Γ(KRK @ NA62ape-logo infn-logo

KAON ’09

P. Paradisi

SUSY effects in Kaon physics: Lepton Universality tests and ra

LFV
LFV
LFV
General Considerations NP search strategies µ − e universality inRK
RK in= SUSY
Γ(K → Reνin SUSY→ µνRµK) SMin SUSYprediction
LU forat aR(SupK ,πK e )/Γ(KRK @ KLOE

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KAON ’09

P. Paradisi

SUSY effects in Kaon physics: Lepton Universality tests and ra

LFV
LFV
LFV
General Considerations NP search strategies µ − e universality inRK
RK in= SUSY
Γ(K → Reνin SUSY→ µνRµK) SMin SUSYprediction
LU forat aR(SupK ,πK e )/Γ(Kµ − e universality in M → lνAny deviation from the SM expectation for RK ,π due to NPcan be written ase−µRK ,π = RKSM
1+∆r,πK ,π NP ,Violations of LU in CCI can be classified asi) Corrections to (V −A)×(V −A) interaction through W `ν`vertex correction induced by a loop of NP particles!
2mW
α2 m̃µ2 − m̃e2e−µ≤ 10−4∆rSUSY ∼24π m̃µ2 + m̃e2 MSUSYii) New Lorentz Structures, i.e. scalar CCI withH`ν ∼ m` tan β.

KAON ’09

P. Paradisi

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SUSY effects in Kaon physics: Lepton Universality tests and ra

LFV
LFV
LFV
General Considerations NP search strategies µ − e universality inRKRK in= SUSY
Γ(K → Reνin SUSY→ µνRµK) SMin SUSY
prediction
LU forat aR(SupK ,πK e )/Γ(Kµ − e universality in M → lν
Four-Fermi interaction for M → `ν induced by W ± , H ±4GFµ2 md m`√ Vud (uγµ PL d)(`γ PL ν` ) − tβ(uPR d)(`PL ν` )2mH2±PCAC’sµ< 0|uγµ γ5 d|M >= ifM pM

m2

M< 0|uγ5 d|M >= −ifM md +mu

H ± (W± ) amplitude is proportional to m` because of theYukawa coupling (helicity suppression)" 2 #2±±mM
ΓH +W (M → `ν)
md= rM = 1 − tβ2.
±2W
mu +md mH
Γ (M → `ν)±
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Tree level H ± effects (rM ) are lepton flavour blind
KAON ’09

P. Paradisi

SUSY effects in Kaon physics: Lepton Universality tests and raLFV
LFV
LFV
General Considerations NP search strategies µ − e universality inRKRK in= SUSY
Γ(K → Reνin SUSY→ µνRµK) SMin SUSYprediction
LU forat aR(SupK ,πK e )/Γ(Kµ − e universality in M → lν
WHAT ARE WE MISSING ?...........

RKEXP. =Γ(K → eνe ) + Γ(K → eνµ ) + Γ(K → eντ )Γ(K → µνµ ) + Γ(K → µνe ) + Γ(K → µντ )...........EXPERIMENTALLY THE NEUTRINO FLAVOUR IS
UNDETERMINED !!
Masiero, Paradisi, Petronzio, ’06
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KAON ’09

P. Paradisi

SUSY effects in Kaon physics: Lepton Universality tests and ra

LFV
LFV
LFV
General Considerations NP search strategies µ − e universality inRKRK in= SUSY
Γ(K → Reνin SUSY→ µνRµK) SMin SUSY
prediction
LU forat aR(SupK ,πK e )/Γ(Kµ − e universality in M → lν
WHAT ARE WE MISSING ?...........

RKEXP. =Γ(K → eνe ) + Γ(K → eνµ ) + Γ(K → eντ )Γ(K → µνµ ) + Γ(K → µνe ) + Γ(K → µντ )...........EXPERIMENTALLY THE NEUTRINO FLAVOUR IS
UNDETERMINED !!
Masiero, Paradisi, Petronzio, ’06
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KAON ’09

P. Paradisi

SUSY effects in Kaon physics: Lepton Universality tests and ra

LFV
LFV
LFV
General Considerations NP search strategies µ − e universality inRK
RK in= SUSY
Γ(K → Reνin SUSY→ µνRµK) SMin SUSY
prediction
LU forat aR(SupK ,πK e )/Γ(Kµ − e universality in M → lν
WHAT ARE WE MISSING ?...........

RKEXP. =Γ(K → eνe ) + Γ(K → eνµ ) + Γ(K → eντ )Γ(K → µνµ ) + Γ(K → µνe ) + Γ(K → µντ )...........EXPERIMENTALLY THE NEUTRINO FLAVOUR IS
UNDETERMINED !!
Masiero, Paradisi, Petronzio, ’06
ape-logo infn-logo

KAON ’09

P. Paradisi

SUSY effects in Kaon physics: Lepton Universality tests and ra

LFV
LFV
LFV
General Considerations NP search strategies µ − e universality inRK
RK in= SUSY
Γ(K → Reνin SUSY→ µνRµK) SM
in SUSY
prediction
LU forat aR(SupK ,πK e )/Γ(KRKLFV in SUSYPK → eνiΓSM (K → eνe ) + Γ(K → eντ )RKLFV = P i',K→µνΓSM (K → µνµ )iisReR,µRg2 mτ 31∆R tan2 βeH ± ντ → √M2 W
α2 31
∆31
δ
R ∼
4π RR

H+uL

ντ

∆rKe−µSUSY '4mK
MH4 ±−2∆rKe−µSUSY ≈ 10=⇒

KAON ’09

i = e, µ, τ−4∆31tβ = 40 MH ± = 500GeVR ∼ 5·10!

mτ2me2⇓26−2|∆31
R | tan β ≈ 10

Br th.(exp.) (τ → eX ) ≤ 10−10(−7)

P. Paradisi

ape-logo infn-logoSUSY effects in Kaon physics: Lepton Universality tests and raLFV
LFV
LFV
General Considerations NP search strategies µ − e universality inRKRK in= SUSY
Γ(K → Reνin SUSY→ µνRµK) SMin SUSY
prediction
LU forat aR(SupK ,πK e )/Γ(KRKLFV in SUSYe−µWhich is the sign of ∆rNP?

LFV effects to LFC channels in RM
mτ ``g2 m`tanβ 1 +∆ tanβ`H ν` → √m` RL
2 MW±∆``
RL ∼(` = e, µ)α1 `3 3`δ δ floop ≤ 10−44π RR LLDeviations from µ − e universality in Kl2 and πl2224RKLFVmτ2 mK ,π 31 2mτ mK ,π 11,π36'1−∆ tan β + 2 4 |∆R | tan β
me MH2 ± RL
me MH ±RKSM,πRKLFV ' RKSM (1 − 0.032) ,KAON ’09

P. Paradisi

RπLFV ' RπSM (1 − 0.0021)ape-logo infn-logo

SUSY effects in Kaon physics: Lepton Universality tests and ra

LFV
LFV
LFV
General Considerations NP search strategies µ − e universality inRKRK in= SUSY
Γ(K → Reνin SUSY→ µνRµK) SMin SUSY
prediction
LU forat aR(SupK ,πK e )/Γ(KRKLFV in SUSYBlack points explain the (g − 2)µ anomaly

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Masiero, P.P., Petronzio, ’08
KAON ’09

P. Paradisi

SUSY effects in Kaon physics: Lepton Universality tests and ra

LFV
LFV
LFV
General Considerations NP search strategies µ − e universality inRK
RK in= SUSY
Γ(K → Reνin SUSY→ µνRµK) SMin SUSY
prediction
LU forat aR(SupK ,πK e )/Γ(KRKLFV in SUSYBlack points explain the (g − 2)µ anomalyape-logo infn-logo

Masiero, P.P., Petronzio, ’08
KAON ’09

P. Paradisi

SUSY effects in Kaon physics: Lepton Universality tests and ra

LFV
LFV
LFV
General Considerations NP search strategies µ − e universality inRK
RK in= SUSY
Γ(K → Reνin SUSY→ µνRµK) SMin SUSY
prediction
LU forat aR(SupK ,πK e )/Γ(KLU at a (Super)B factoriesµ/eRτ= Γ(τ → µν ν̄)/Γ(τ → eν ν̄)Rτµ/e ' 1 − 10−3tβ50

2 200GeVMH ±2Mursula et al. ’83
τ /`RB→D = Γ(B → Dτ ν)/Γ(B → D`ν)
Hou ’92, Tanaka ’95, Kiers & Soni ’97
τ /µRB→Dτ /µ' 1 − 0.3

RB→D |SMtβ50

2 200GeV
MH ±

2

Nierste et al.’08, Kamenik & Mescia ’08
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KAON ’09

P. Paradisi

SUSY effects in Kaon physics: Lepton Universality tests and ra

LFV
LFV
LFV
General Considerations NP search strategies µ − e universality inRK
RK in= SUSY
Γ(K → Reνin SUSY→ µνRµK) SMin SUSY
prediction
LU forat aR(SupK ,πK e )/Γ(KSUSY MFV scenario @ large tan β
How natural is the MFV SUSY scenario @ large tan β?
Top-Bottom Yukawa unification in GUT ⇒ tan β = (mt /mb )mh > 114GeV constraint better satisfied∆aµ = (g − 2)µ /2 = (3 ± 1) × 10−9 naturally explained
WMAP constraints ”naturally” satisfied

Ellis et al.

Correlations between BR(B → τ ν) and BR(B → Xs γ),∆MBs ,BR(Bs,d → `+ `− ), (g − 2)µ and mh0
Isidori, P.P., ’06
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KAON ’09

P. Paradisi

SUSY effects in Kaon physics: Lepton Universality tests and ra

LFV
LFV
LFV
General Considerations NP search strategies µ − e universality inRKRK in= SUSY
Γ(K → Reνin SUSY→ µνRµK) SMin SUSY
prediction
LU forat aR(SupK ,πK e )/Γ(KLightest Higgs boson mass WMAP & (g − 2)µ−9∆aµ ' 3 × 10µ=500 GeV

400GeVm̃2 tβ50sign µM1

500
450
400



coannihilation

350300    

250200150   100
50200

400

600

800

1000

1200

MH

ape-logo infn-logotβ = 20 (green), 30 (red), 50 (black)
KAON ’09

P. Paradisi

Isidori et al., 06’,’07

SUSY effects in Kaon physics: Lepton Universality tests and ra

LFV
LFV
LFV
General Considerations NP search strategies µ − e universality inRK
RK in= SUSY
Γ(K → Reνin SUSY→ µνRµK) SMin SUSY
prediction
LU forat aR(SupK ,πK e )/Γ(KConstraints

B → Xs γ:[1.01 < RBsγ < 1.24]

SM[2 < 10−9 (aexpµ − aµ ) < 4]aµ :B → µ+ µ− :∆MBs :[B exp < 8.0 × 10−8 ][∆MBs = 17.35 ± 0.25 ps−1 ]B → τν :[0.8 < RBτ ν < 0.9]
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KAON ’09

P. Paradisi

SUSY effects in Kaon physics: Lepton Universality tests and raLFV
LFV
LFV
General Considerations NP search strategies µ − e universality inRK
RK in= SUSY
Γ(K → Reνin SUSY→ µνRµK) SMin SUSY
prediction
LU forat aR(SupK ,πK e )/Γ(KB-physics & (g − 2)µ under WMAP constraints

MH ∼ 2M1
KAON ’09

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Isidori, Mescia, P.P., Temes, 07
P. Paradisi

SUSY effects in Kaon physics: Lepton Universality tests and ra

General Considerations NP search strategies µ − e universality in RK = Γ(K → eνe )/Γ(K → µνµ ) SM prediction for RK ,πK → πν ν̄ in the SMK → πνν processes offer a unique possibility in probing theunderlying flavour mixing mechanism:
No SM tree-level contributions (FCNC decays );One-loop SM contributions CKM-suppressed (V∗ts Vtd ∼ λ5 );High precision of the SM prediction thanks to short distance(e.w.) dynamics dominance:(s.d.)

Heff=XVts∗ Vtd [XL (s̄d)V −A + XR (s̄d)V +A ] (ν̄l νl )V −Al=e,µ,τBr (K → πνν) ∼ (X = XL +XR )2y 2 V ∗ VtdX ∼ cSM t 2ts 2
16π MW
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XLSM = 1.464±0.041 , XRSM = 0
KAON ’09

P. Paradisi

SUSY effects in Kaon physics: Lepton Universality tests and ra

General Considerations NP search strategies µ − e universality in RK = Γ(K → eνe )/Γ(K → µνµ ) SM prediction for RK ,π

K → πν ν̄ and NPK → πνν has a high sensitivity to NP effects of many
theories as SUSY, LHT, Z’ models.....
δ21y 2 V ∗ Vtd
X (s → d)FCNC ∼ cSM t 2ts 2 + cNP
16π 2 ΛNP216π MW

Br (K → πνν) ∼ (X = XL + XR )2

XL = XLSM + XLNP ,XR = XRNP

Large NP effects only if δ21  Vts∗ Vtd (beyond MFV)
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see the talk by Buras
KAON ’09

P. Paradisi

SUSY effects in Kaon physics: Lepton Universality tests and ra

General Considerations NP search strategies µ − e universality in RK = Γ(K → eνe )/Γ(K → µνµ ) SM prediction for RK ,πK → πν ν̄ in MFV

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KAON ’09

P. Paradisi

SUSY effects in Kaon physics: Lepton Universality tests and ra

General Considerations NP search strategies µ − e universality in RK = Γ(K → eνe )/Γ(K → µνµ ) SM prediction for RK ,πGaugino mediated K → πν ν̄The dominant effects to K → πν ν̄ arise from χ̃/ũ diagramswith double-MIA[Colangelo, Isidori ’98].
Gluino-type amplitudes (LL, RR and LR-down squarks typemixings) essentially negligible contrary to K , b → sγ,
B 0 − B¯0Minor effects within pure MFV.
The maximal sensitivity to theup-type trilinear terms is obtainedforLight stop and charginos
small tan β
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KAON ’09

P. Paradisi

SUSY effects in Kaon physics: Lepton Universality tests and ra

General Considerations NP search strategies µ − e universality in RK = Γ(K → eνe )/Γ(K → µνµ ) SM prediction for RK ,πK → πν ν̄ in SUSY beyond MFV

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KAON ’09

P. Paradisi

SUSY effects in Kaon physics: Lepton Universality tests and ra

General Considerations NP search strategies µ − e universality in RK = Γ(K → eνe )/Γ(K → µνµ ) SM prediction for RK ,πChargino mediated K → πν ν̄G.Isidori, F.Mescia, P.P., C.Smith, S.Trine, ’06
KAON ’09

P. Paradisi

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SUSY effects in Kaon physics: Lepton Universality tests and ra

General Considerations NP search strategies µ − e universality in RK = Γ(K → eνe )/Γ(K → µνµ ) SM prediction for RK ,πChargino mediated K → πν ν̄G.Isidori, F.Mescia, P.P., C.Smith, S.Trine, ’06
KAON ’09

P. Paradisi

ape-logo infn-logo

SUSY effects in Kaon physics: Lepton Universality tests and ra

General Considerations NP search strategies µ − e universality in RK = Γ(K → eνe )/Γ(K → µνµ ) SM prediction for RK ,πChargino mediated K → πν ν̄G.Isidori, F.Mescia, P.P., C.Smith, S.Trine, ’06
KAON ’09

P. Paradisi

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SUSY effects in Kaon physics: Lepton Universality tests and ra

General Considerations NP search strategies µ − e universality in RK = Γ(K → eνe )/Γ(K → µνµ ) SM prediction for RK ,πHiggs mediated K → πν ν̄ape-logo infn-logo

KAON ’09

P. Paradisi

SUSY effects in Kaon physics: Lepton Universality tests and raGeneral Considerations NP search strategies µ − e universality inConclusion
RK = Γ(K → eνe )/Γ(K → µνµ ) SM prediction for RK ,πConclusion
Where to look for New Physics?
e/µLU breaking @ % in RK

from SUSY LFV effectse/µ

LU breaking @ % in RK implies MH ± < 1TeV and it can becompatible with the (g − 2)µ anomaly
e/µLU breaking @ % in RK⇒ BR(τ → eγ) > 10−9e/µThe relevant SUSY parameter space for RK @ % is allowedby the constraints of rare LFV decays, B-physics observables
and Dark Matter⇓e/µRK

ape-logo infn-logooffers a great chance to probe SUSY LFV .
KAON ’09

P. Paradisi

SUSY effects in Kaon physics: Lepton Universality tests and raGeneral Considerations NP search strategies µ − e universality inConclusion
RK = Γ(K → eνe )/Γ(K → µνµ ) SM prediction for RK ,πConclusion
Where to look for New Physics?
K → πνν is a golden channel where to look for NP because:K → πνν is predicted with high resolution in the SM
K → πνν has a high sensitivity to NP effects of many
theories as SUSY, LHT, Z’ models.....

⇓Kaon Physics will play a major role in the LHC ERA to unveil
and to understand NP
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KAON ’09

P. Paradisi

SUSY effects in Kaon physics: Lepton Universality tests and ra