Towards precision lepton flavour physics

Some reflections…

have brought us many clues for a deeper understandingin 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 ~ v2/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 symmetryM>>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(mv)

and not just a typical CKM… (|Ufi|,|Ufj|,|Ufk|)

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 clueon the new interactions

Standard 3scenario

The observables:

Masses Angles CP-phases

m12

< m22, m3

2

The unknowns…

Hierarchy 0

m21, m2

3

Precise oscillations

0

Cosmologysign(cos

The knowns…

|m223|, m2

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: |m223| >> m2

12

Tunning E/L ~ m2

ij we can enhance different terms even inthe same channel

ee e e 1 1

1 1

sign(

sign(cos2 1 1

Sensitivity to unknows at E/L ~|m223| in matter

vac/matter small parameters

Golden Silver

Sensitivity to knowns at E/L ~|m223|

small parameters

ee e e m

1 1

sin22 1 1

m 1 1

sin22 1 1

Sensitivity at E/L ~m212

ee e

sign(

sign(cos 1 1

ee e m

sin22 1

m 1

sin22 1

Correlations and degeneracies

At fixed EL:

P(eas1

P(eas2

Generically two solutions: trueand intrinsic degeneracy Burguet-Castell, Gavela, Gomez-Cadenas,P.H.,Mena

Including the discrete ambiguities eight-fold

P(cos 2eas1

P(cos 2eas2

Barger,Marfatia, WhisnantMinakata, 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 ~|m223| ?

L(km) sin22DChooz 1.1 ~ 0.03

UR 1.7 ~ 0.017

• 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 ~m212

SK-Gd can reach a sensitivity to m212 2.8% (3CL

Choubey,Petcov

The sensitivity to sin2 can reach 2% (1CL) in a reactor experiment tuned to the oscillation maximum

SADO Minakata, Nunokawa, Teves, Zukanovich Funchal

L=(50-70)km [8 x 10-5 eV2/m212]

Para ver esta película, debedisponer de QuickTime™ y deun descompresor TIFF (LZW).

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) sin22 sign( sign(cos2

T2K-I

(2008)

295 ~0.01

0.02 - - -

810 0.003

0.02 - some -

Sensitivity to strongly depends on in both cases and

also onsign(in

T2K upgrade of K2K with a more intense beam and OA

NOupgrade of MINOS with a better detector and OA CL

Hierarchy at

Only for sin22> 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 sin2 2 = 1-O()

T2K-I:

Sensitivity to sin2

Minakata,Sonoyama Fernandez-Martinez et al

For 42º < 50º the error on s223 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 > 4º marginal 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)

|m2 23| sin2 m2

12 sin2

~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 sensitivityto but not to hierarchy

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The race for the hierarchy

: a second detector at the second oscillation maximum

Noa proposal

T2K-II:half of detector in Korea (2nd oscillation peak)

23

Ishitsuka,Kajita,Minakata,Nunokawa

Combination with atmospheric

Comes for free! Huber, Maltoni,Schwetz

T2K-II+atmospheric data

Also helps in resolving the octant: if |s232-0.5| > 0.1

The known realm…

• |m223|: Maximal mixing can be established at % level

only with a per mil sensitivity to sin22 T2K-I vs II

Fernandez-Martinez et alper 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 200-500 3000 40KTon

-beam 60/100

130 440KTon

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

maxe)/L GeV)

SPS 150/300km 0.6

SPS-upgrade

350/700km 1.3

LHC 2500/3000km 9.4

Burguet-Castell, et al

CERN-Canfranc ?

Comparing -beams

Hierarchy, t23

Sin22x10-3 0.04

Degeneracies at beam

Ultimate anti-degeneracy machine

FACT &40KTon iron calorimeter 2800km (Golden)eFACT & 4Ton Emulsion 730km(Silver) eSPL&Megaton Cerenkov (Bronce) 130km e

The intrinsic and the octant ambiguities are resolved (up to uncertainties) if the eand e are combined

Donini, Meloni, Migliozzi

Hierarchy and octant solved for ºº

sensitivity down to 0.3º !

Overconstraining: eee,ee,for and !

The new era (discovery) (roughly…depends on the actual value of the parameters)

sign( ~2013 > 4º marginal 13 > 6º (0%)

13 >13º(50%)

40º-50º

deg.

~202? >0.3-0.6º º large

13 > 1º- 2º(100%)

While T2K-I seems to be a rather optimal setup for the nextgeneration 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 10-20 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