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: 5 eV 2 ( best fit) solar ν e ν others : θ 12 33 , ∆ m 2 7 . 5 10 12 3 eV 2 (best fit) atmospheric ν µ ν τ : θ 23 40 or 50 , ∆ m 2 2 . 4 10 23 reactor ¯ ν others : θ 13 ν e ¯ 8 . 7 (best fit) accelerator ν µ ν others Oscillations Non-diagonal charged currents g U ji ν ¯ 2 U ji U ji L int � j γ µ P L ν i W µ h . c . ν ν 3 mass eigenstates ν i ν 1 , ν 2 , ν 3 different from the interaction eigenstates ν α ν e , ν µ , ν τ U α i U α i U α i ν α ν ν i ν ν U ν U ν is a 3 3 unitary matrix, the PMNS matrix U ν

Leptonic kaon decays Focus on K �ν decays, more precisely on: Γ K e ν R K Γ K µ ν Well measured by the NA62 collaboration [Lazzeroni et al. , 2013] : R exp 5 2 . 488 0 . 010 10 K SM prediction is very precise [Finkemeier, 1996, Cirigliano and Rosell, 2007] : R SM 5 2 . 477 0 . 001 10 K New Physics: R NP R SM 1 ∆ r K K K tree-level corrections are usually lepton universal higher-order corrections are limited by other observables ( e.g. 3 in unconstrained minimal SUSY models ∆ r K 10 [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: U ν becomes a 3 n ν non-unitary matrix with n ν 3 Could affect at tree-level many observables containing a W � ν vertex [Schrock, 1980, 1981] ν i K W � j

Deviation from universality Summing over all the kinematically accessible neutrinos (from 1 to N e max , N µ max the heaviest kinematically allowed neutrino) : N e U 1 i 2 G i 1 max i 1 ν R K with N µ max U 2 k 2 G k 2 k 1 ν 1 2 G ij m 2 K m 2 m 2 m 2 m 2 2 m 2 m 2 m 2 2 4 m 2 l j m 2 l j l j K l j ν i ν i ν i ν i m 2 m 2 m 2 2 In the SM, R SM e K e K m 2 m 2 m 2 µ 2 K µ G j 1 and n ν because G i 1 1 U 1 i 2 U ν U ν 11 1 i ν 2 ways to deviate from universality: - (A) sterile neutrinos are lighter than m K , with m active m ν s m K ν - (B) sterile neutrinos are heavier than m K

∆ r K 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 µ X 1 Y ij ν ¯ L i ˜ 2 µ Xij ¯ X c h.c. L ISS L SM H ν Rj M Rij ¯ ν Ri X j i X j R NP R SM 1 ∆ r K K K Scenario (A) Scenario (B) 10 2 10 0 10 0 10 � 2 10 � 2 � r K � r K 10 � 4 10 � 4 10 � 6 10 � 6 10 � 8 10 � 8 10 � 7 10 � 6 10 � 5 10 � 4 10 � 3 10 � 2 10 � 1 10 0 10 � 7 10 � 6 10 � 5 10 � 4 10 � 3 10 � 2 � � Η Η Contributions to ∆ r K in the inverse seesaw as a function of Det ˜ 1 U PMNS ˜ η

Conclusion Sterile neutrinos can lead to a large violation of lepton universality at tree-level R K particularly well-suited for this search Large deviations from the SM can be found ( ∆ r K 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: M R 1 TeV with natural Yukawa Y ν 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 ν Ri ( L 1 , i 1 , 2 , 3 ) and X i ( L 1 , i 1 , 2 , 3 ) [Mohapatra and Valle, 1986] 1 Y ij X c ν ¯ L i ˜ 2 µ Xij ¯ H ν Rj M Rij ¯ ν Ri X j i X j h.c. L ISS L SM 0 m D 0 m T With m D Y ν v , M 0 M R D H H M T 0 µ X R M R M R µ X m 2 D µ X m ν ν R ν R X X m 2 M 2 D R M 2 L L R µ X m 2 M 2 m 1 , 2 D R 2 m 2 M 2 D R