Towards precision lepton flavour physics

Some reflections… have brought us many clues for a deeper understanding in the SM and continue to do so: They were the key to the weak interactions first "almost" invisible carriers of energy first realization of an “almost” Weyl fermion: only one helicity state! first state with only a chiral gauge charge

We got the SM but not quite a deeper understanding chiral gauge theories are finely tunned and extremely hard to get as effective theories: anomaly cancellation complex vacuum structure that we naively describe with one boring scalar (hierarchy problem) problem and many free parameters to parametrize our ignorance (flavour puzzle)

It seemed that could not tell us anything about the vacuum because they could not feel it but they do…again in a extremely weak way

The “other” helicity states non-decoupling physics (scales at or below v): at least three new fundamental s=1/2 fields with no charge m= Weyl  no new scale M=0  L conserved Majorana  new scale M  0  L violated These could be furthermore coupled to a hidden sector: gauge interactions, more fermions, scalars… only linked to the visible sector through neutrino masses

decoupling L-violating physics:  >> v mixture: decoupling and not decoupling +… Weinberg

If M>> v the see-saw solution New scale solution M  v,  =O(  : m ~ v 2 /M  decoupling effect No new scale solution M ~ v: m ~  2 v  Yukawa smallness ( if  e  m ~ O(1 eV) ) why are masses so small ?

what value of M is more natural ? M << v is natural because of L symmetry M>>v is not  hierarchy problem: Casas, Espinosa, Hidalgo

Whether the new physics is associated to just a high scale or there is a hidden sector around the corner, its (strongest) link to the visible world is the mass matrix: Generically non-unitary PMNS matrix Flavour structure in neutral currents Mixing O( v/M) ~O(m  v)

and not just a typical CKM… (|U fi |,|U fj |,|U fk |) Maximal mixing in the 23 sector seems to imply redundancy: symmetry ?

The fundamental questions: what are the “other” helicity states: Weyl, Majorana or decoupling physics what are the scales and dynamics involved in the interactions of these new fields? Is it a decoupling scale  >>v or is there a hidden sector at low scales is there a L number conserved ? are relevant in cosmology and in the genesis of baryons ? The answers will provide a new perspective into the flavour puzzle and the hierarchy problem

Einstein’s dream Photomultiplier Solving the Flavour Puzzle

Our safest bet is to measure precisely the light  mass matrix: overconstrain the PMNS matrix to see that it is not the whole story… test symmetries: CP, CPT, maximal mixing…to give us a clue on the new interactions

Standard 3  scenario The observables: Masses Angles CP-phases m 1 2 < m 2 2, m 3 2          

The unknowns…        Hierarchy 0  m 2 1, m 2 3 Precise oscillations 0  Cosmology sign(cos   

The knowns…     |  m  2 23 |,  m  2 12 Precise oscillations More precision and overconstraining the known parameters will also be important: to resolve correlations with the unknown ones search for new physics or symmetries: test of unitarity of the PMNS, establish maximal mixing

The challenge… Measure small oscillation probabilities or measure large ones with high accuracy There are only two mass splittings: |  m  2 23 | >>  m  2 12 Tunning E /L ~  m 2  ij we can enhance different terms even in the same channel

ee e   e      1 1     1 1   sign(         sign(cos2     1   1   Sensitivity to unknows at E /L ~|  m 2 23 | in matter vac/matter   small parameters       Golden Silver

Sensitivity to knowns at E /L ~|  m 2 23 |   small parameters       ee e   e   m      1  1  sin 2 2    1  1   m     1 1   sin 2 2     1 1  

Sensitivity at E /L ~  m 2 12 ee e            sign(       sign(cos     1 1   ee e    m       sin 2 2    1   m    1  sin 2 2    1 

Correlations and degeneracies At fixed E  L: P  (    eas 1 P  (    eas 2 Generically two solutions: true and intrinsic degeneracy Burguet-Castell, Gavela, Gomez-Cadenas,P.H.,Mena Including the discrete ambiguities eight-fold P  (      cos 2    eas 1 P  (      cos 2    eas 2 Barger,Marfatia, Whisnant Minakata, Nunokawa

    rue  Fake    wrong octant Position of depend strongly on the E,L and channel Fake do not depend on E and L are the ones that increase the error on    In vacuum all are CP violating or all CP conserving:  fake  wrong sign

Terrestrial precision oscillation experiments

Ultimate reactors E /L ~|  m 2 23 | ? L(km) sin 2 2   DChooz 1.1 ~ 0.03 UR 1.7 ~ No sensitivity to the other unknowns No dependence on  If   large, great synergies with superbeams to resolve degeneracies Minakata, et al Anderson et al  90%CL < 1% syst

Reactors at E/L ~  m 2 12 SK-Gd can reach a sensitivity to  m % (3  CL   Choubey,Petcov The sensitivity to sin 2   can reach 2% (1  CL) in a reactor experiment tuned to the oscillation maximum SADO Minakata, Nunokawa, Teves, Zukanovich Funchal L=(50-70)km [8 x eV 2 /  m 2 12 ] 4% syst. Stat: (~1700 events/y) 0.5 kton y (SADO) ≈1.4 kton y(KL)

Superbeams Off-axis Use the conventional (more intense) beams: p  Target  K,  , % e

  e L(km) sin 2 2    sign(    sign(cos2    T2K-I (2008) 295 ~   some - Sensitivity to   strongly depends on  in both cases and also on  sign(    in  T2K upgrade of K2K with a more intense beam and OA NO  upgrade of MINOS with a better detector and OA  CL

Hierarchy at   Only for sin 2 2   > 0.04 and some values of 

   The atmospheric parameters can be measured with high precision (per cent level): But the sensitivity to maximal mixing is not as good:   =  /4   sin 2 2   = 1-O(   ) T2K-I:

Sensitivity to sin 2   Minakata,Sonoyama Fernandez-Martinez et al For 42º <    50º the error on s 2 23 remains O(10-20%) which is not much better than the present error!

The new era (discovery) (roughly…depends on the actual value of the parameters)     sign(      ~2013 > 4ºmarginal  13 > 6º (0%)  13 >13º(50%) 40º-50º deg. T2K-I seems to be a rather optimal setup for the next generation superbeam…should start taking data in 2008

The new era (precision) (roughly…depends on the actual value of the parameters) |  m 2 23 | sin 2    m 2 12 sin 2   ~2013 ~1% ~2%-16% ~1%~2% T2K-I + reactors seem to be a rather optimal combination of setups for the next generation…

Next-to-new era Superbeams: still room for improvement with a significant increase in power and/or detector: JPARC: 0.75  4MW, HyperK (Megaton!) NUMI: factor 4 with new Fermilab proton driver CERN-SPL: 4MW, Megaton Huge statistics, but systematics is critical ! T2K-II best sensitivity to    but not to hierarchy

The race for the hierarchy  : a second detector at the second oscillation maximum No a proposal

T2K-II: half of detector in Korea (2nd oscillation peak) 22 33 Ishitsuka,Kajita,Minakata,Nunokawa

Combination with atmospheric Comes for free! Huber, Maltoni,Schwetz T2K-II+atmospheric data Also helps in resolving the   octant:  if |s | > 0.1

The known realm…   |  m  2 23 | :  Maximal mixing can be established at % level only with a per mil sensitivity to sin 2 2   T2K-I vs II Fernandez-Martinez et al  per mil 

The purists… At accelerators we can also do electron (anti)-neutrino beams above  threshold that are pure! from  decay: a magnetized detector indispensable! from radioactive ions:

 beam FACT A significant investment in accelerator infrastructure

Very well-known fluxes

Not so different starting point since the detector can be made more massive for the  -beam (it does not need magnetization) CERN-Canaries  p L(km) Det. mass FACT KTon  -beam 60/ KTon In both cases, there is an associated superbeam (SPL) that can be combined CERN-Frejus

Higher   -beam at longer baseline are possible and much better more signal because of higher cross-sections easier to measure the energy dependence more significant matter effects  max  e)/L   GeV) SPS150/300km0.6 SPS- upgrade 350/700km1.3 LHC2500/3000km9.4 Burguet-Castell, et al CERN-Canfranc ?

Comparing  -beams Hierarchy, t23 Sin 2 2    x

Degeneracies at  beam

Ultimate anti-degeneracy machine FACT &40KTon iron calorimeter 2800km (Golden)  e    FACT & 4Ton Emulsion 730km(Silver) e    SPL&Megaton Cerenkov (Bronce) 130km   e The intrinsic and the   octant ambiguities are resolved (up to uncertainties) if the e  and e  are combined Donini, Meloni, Migliozzi

Hierarchy and octant solved for    º  º   sensitivity down to 0.3º ! Overconstraining: e  ee,e  e,  for  and !

The new era (discovery) (roughly…depends on the actual value of the parameters)    sign(      ~2013 > 4ºmarginal  13 > 6º (0%)  13 >13º(50%) 40º-50º deg. ~202?> º  º large    13 > 1º- 2º(100%) While T2K-I seems to be a rather optimal setup for the next generation superbeam, the “optimal” next-to-new generation experiment is still under investigation

There are good ideas to reach the per cent sensitivity in the mass matrix in the next years The lepton flavour sector might turn out to be uninspiring…

Approximate oscillation probabilities O(    Cervera et al. Akhmedov et al Extremely useful to optimize the observables and experiments understand correlations existence of approximately degenerate solutions: set of oscillation parameters that give the same probabilities