Lepton universality in K decays JHEP02(2013)048 / arXiv:1211.3052 C - - PowerPoint PPT Presentation

Lepton universality in K decays

JHEP02(2013)048 / arXiv:1211.3052

C´ edric Weiland

in collaboration with A. Abada, D. Das, A.M. Teixeira and A. Vicente Laboratoire de Physique Th´ eorique d’Orsay, Universit´ e Paris-Sud 11, France

Rencontres de Moriond 2013 La Thuile, March 3rd, 2013

Neutrino oscillations and masses

Neutrino oscillations: solar νe νothers: θ12

33 , ∆m2

12

7.5 10

5eV2 ( best fit)

atmospheric νµ ντ : θ23

40 or 50 , ∆m2

23

2.4 10

3eV2 (best fit)

reactor ¯ νe ¯ νothers: θ13

8.7 (best fit)

accelerator νµ νothers Oscillations Non-diagonal charged currents Lint

g 2Uji ν

Uji

ν

Uji

ν ¯

jγµPLνiWµ h.c. 3 mass eigenstates νi ν1, ν2, ν3 different from the interaction eigenstates να νe, νµ, ντ να Uαi

ν

Uαi

ν

Uαi

ν νi

Uν Uν Uν is a 3 3 unitary matrix, the PMNS matrix

Leptonic kaon decays

Focus on K ν decays, more precisely on: RK Γ K e ν Γ K µ ν Well measured by the NA62 collaboration [Lazzeroni et al., 2013]: Rexp

K

2.488 0.010 10

5

SM prediction is very precise [Finkemeier, 1996, Cirigliano and Rosell, 2007]: RSM

K

2.477 0.001 10

5

New Physics: RNP

K

RSM

K

1 ∆rK

tree-level corrections are usually lepton universal higher-order corrections are limited by other observables (e.g. ∆rK 10

3 in unconstrained minimal SUSY models

[Fonseca et al., 2012])

Impact of singlet neutrinos

Singlet neutrino Interaction eigenstate with no coupling to gauge bosons (e.g. fermionic singlet in type-I seesaw) Modification of the charged weak current: Uν becomes a 3 nν non-unitary matrix with nν 3 Could affect at tree-level many observables containing a W

• ν vertex [Schrock, 1980, 1981]

W K j νi

Deviation from universality

Summing over all the kinematically accessible neutrinos

(from 1 to N e

max, N µ max the heaviest kinematically allowed neutrino) :

RK

N e

max

i 1

U1i

ν 2Gi1 N µ

max

k 1

U2k

ν 2Gk2

with Gij m2

K m2 νi

m2

lj

m2

νi

m2

lj 2

m2

K

m2

lj

m2

νi 2

4m2

ljm2 νi 1 2

In the SM, RSM

K m2

e

m2

µ

m2

K

m2

e 2

m2

K

m2

µ 2

because Gi1 Gj1 and

nν i 1 U1i ν 2

UνUν 11 1

2 ways to deviate from universality:

• (A) sterile neutrinos are lighter than mK, with mactive

ν

mνs mK

• (B) sterile neutrinos are heavier than mK

∆rK in the inverse seesaw model

Inverse seesaw: low-scale seesaw mechanism

Add fermionic singlets Smallness of the active neutrino mass related to the smallness of the Majorana mass µX LISS LSM Yij

ν¯

Li ˜ HνRj MRij ¯ νRiXj 1 2µXij¯ Xc

i Xj

h.c. RNP

K

RSM

K

1 ∆rK

Scenario (A)

107 106 105 104 103 102 108 106 104 102 100 102 Η

• r K

Scenario (B)

107 106 105 104 103 102 101 100 108 106 104 102 100 Η

• r K

Contributions to ∆rK in the inverse seesaw as a function of ˜ η 1 Det ˜ UPMNS

Conclusion

Sterile neutrinos can lead to a large violation of lepton universality at tree-level RK particularly well-suited for this search Large deviations from the SM can be found (∆rK O 1 , already excluded by NA62) Can appear in other leptonic or semileptonic meson decays

Backup–Constraints

Direct sterile neutrino searches (monochromatic lines in meson decays): scenario (A) and (B) Non-unitarity of the leptonic mixing matrix: scenario (B) Lepton flavour violation: scenario (A) and (B) LHC SM scalar searches and electroweak precision data: scenario (B) Cosmological observations: scenario (A) and (B) but disappear in non-standard cosmology (e.g. low reheating temperature)

The Inverse Seesaw Mechanism

Inverse seesaw: MR 1 TeV with natural Yukawa Yν O 1 cLFV is much less suppressed Might be testable at the LHC and future B factories (Belle II) Inverse seesaw Consider fermionic gauge singlets νRi (L 1, i 1, 2, 3) and Xi (L 1, i 1, 2, 3)

[Mohapatra and Valle, 1986]

LISS LSM Yij

ν¯

Li ˜ HνRj MRij ¯ νRiXj 1 2µXij¯ Xc

i Xj

h.c. With mD Yνv , M mD mT

D

MR MT

R

µX mν m2

DµX

m2

D

M2

R

m1,2 m2

D

M2

R

M2

RµX

2 m2

D

M2

R

νR X νR X H L H L µX MR MR