Towards precision lepton flavour physics

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Towards precision lepton flavour physics
n
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Some reflections

• n 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

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• 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)

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It seemed that n could not tell us anything
about the vacuum because they could not feel it
but they doagain in a extremely weak way
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• The other helicity states
• non-decoupling physics (scales at or below v)
  at least three new fundamental s1/2 fields with
  no charge
• m
• Weyl ? no new scale M0 ? 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

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• decoupling L-violating physics M gtgt v
• mixture decoupling and not decoupling

Weinberg
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why are n masses so small ?

• If Mgtgt ln v the see-saw solution
• New scale solution M ?? v, ln O(1)
• mn v2/M ? decoupling
  effect
• No new scale solution M v
• mn ln2 v ? Yukawa
  smallness
• ( if lnle ? mn O(1 eV) )

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what value of M is more natural ?
M ltlt v is natural because of L symmetry Mgtgtv is
not ? hierarchy problem
Casas,
Espinosa, Hidalgo
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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 n mass matrix

• Generically non-unitary PMNS matrix
• Flavour structure in neutral currents
• Mixing O(lnv/M) O(mn/ lnv)

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

Maximal mixing in the 23 sector seems to imply
redundancy
symmetry ?
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• 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 M gtgtv or is there a hidden
  sector at low scales
• is there a L number conserved ?
• are n relevant in cosmology and in the genesis
  of baryons ?
• The answers will provide a new perspective into
  the flavour puzzle and the hierarchy problem

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Solving the Flavour Puzzle
Photomultiplier
Einsteins dream
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• Our safest bet is to measure precisely the light
  n mass matrix
• overconstrain the PMNS matrix to see that it is
  not the whole story
• test symmetries CP, CPT, maximal mixingto give
  us a clueon the new interactions

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Standard 3n scenario
The observables
Masses Angles CP-phases
m12 lt m22, m32 q12,q23,q13 d, a1, a2
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The unknowns


q13 a1, a2
d
Hierarchy 0nbb
m21, m23
0nbb, bb Cosmology
sign(cosq23)
Precise n oscillations

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The knowns

• q23 , q12, Dm 223, Dm 212
• Precise n 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

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The challenge
Measure small oscillation probabilities or
measure large ones with high accuracy

• There are only two mass splittings Dm 223 gtgt
  Dm 212
• Tunning En/L Dm2 ij we can enhance different
  terms even in
• the same channel
• 
  

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Sensitivity to unknows at En/L Dm223 in matter
ee em mm et mt
q13 e2 1 e2 1 e2
d ? 1 e2 1 e2
sign(D23) -/e2 -/1 e -/1 e
sign(cos2q23) ? 1 e2 1 e2
Golden
Silver
e ? small parameters q13, D12/D23

vac/matter
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Sensitivity to knowns at En/L Dm223
ee em mm et mt
Dm223 e2 1 1 1 1
sin22q23 - 1 1 1 1
Dm212 e2 1 e2 1 e2
sin22q12 e2 1 e2 1 e2

e ? small parameters q13, D12/D23


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Sensitivity at En/L Dm212
e? q13
ee em mm
q13 e2 e e
d ? e e
sign(D23) ? ? ?
sign(cosq23) - 1 1

ee em mm
Dm223 - - -
sin22q23 - 1 1
Dm212 1 1 1
sin22q12 1 1 1
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Correlations and degeneracies
At fixed En, L Pnab(q13 ,d ) Meas1 Pnab(q13
,d ) Meas2 Generically two solutions true and
intrinsic degeneracy Burguet-Castell, Gavela,
Gomez-Cadenas,P.H.,Mena
Including the discrete ambiguities
eight-fold

• Pnab(q13 ,d ,?D23, ?cos 2q23) Meas1
• Pnab(q13 ,d ,?D23, ?cos 2q23) Meas2

Barger,Marfatia, Whisnant Minakata, Nunokawa
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Dq13
d True
d
Fake p-d
d p-d
wrong sign
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 q13,d
• In vacuum all are CP violating or all CP
  conserving dfakep-d

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Terrestrial precision n oscillation experiments
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Ultimate reactors En/L Dm223 ?

90CL
L(km) sin22q13
DChooz 1.1 0.03
UR 1.7 0.017
lt 1 syst

• No sensitivity to the other unknowns
• No dependence on d
• If q13 large, great synergies with superbeams to
  resolve degeneracies Minakata, et al
• 
  Anderson et al

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Reactors at E/L Dm212
SK-Gd can reach a sensitivity to Dm212 2.8 (3s
CL)
Choubey,Petcov The
sensitivity to sin2 q12 can reach 2 (1sCL) in a
reactor experiment tuned to the oscillation
maximum SADO
Minakata, Nunokawa, Teves, Zukanovich Funchal
L(50-70)km 8 x 10-5 eV2/Dm212
4 syst. Stat (1700 events/y) 0.5
kton y (SADO) 1.4 kton y(KL)
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Superbeams Off-axis
Use the conventional (more intense) beams
p ? Target ? K,p nm, ne
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nm ? ne

T2K upgrade of K2K with a more intense beam and OA
NOnA upgrade of MINOS with a better detector and
OA
3s CL
L(km) sin22q13 d sign(D23) sign(cos2q23)
T2K-I (2008) 295 0.01 0.02 - - -
NOnAI (2011) 810 0.003 0.02 - some -
Sensitivity to q13 strongly depends on d in both
cases and also on sign(D23) in NOnA
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Hierarchy at NOnA-I
NOnA-I
Only for sin22q13 gt 0.04 and some values of d
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nm ? nm
The atmospheric parameters can be measured with
high precision (per cent level)
T2K-I
But the sensitivity to maximal mixing is not as
good q23p/4?? ? sin2 2q23 1-O(e2)
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Sensitivity to sin2q23
Minakata,Sonoyama

Fernandez-Martinez et al For 42º lt q23 lt 50º the
error on s223 remains O(10-20) which is not
much better than the present error!
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The new era
(discovery) (roughlydepends on the actual
value of the parameters)
q13(3s) d sign(D23)(95) q23
2013 gt 4º marginal q13 gt 6º (0) q13 gt13º(50) 40º-50º deg.
T2K-I seems to be a rather optimal setup for the
next generation superbeamshould start taking
data in 2008
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The new era
(precision) (roughlydepends on the actual
value of the parameters)
Dm2 23 sin2 q23 Dm2 12 sin2 q12
2013 1 2-16 1 2
T2K-I reactors seem to be a rather optimal
combination of setups for the next generation
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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 q13, d, but
• not to hierarchy

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The race for the hierarchy

• NOnA a second detector at the second oscillation
  maximum

Nona proposal
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T2K-IIhalf of detector in Korea (2nd oscillation
peak)
3s
2s
Ishitsuka,Kajita,Minakata,Nunokawa
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Combination with atmospheric n
T2K-IIatmospheric data
Huber, Maltoni,Schwetz
Comes for free!
Also helps in resolving the q23 octant 3s if
s232-0.5 gt 0.1
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The known realm

• q23 , Dm 223 Maximal mixing can be
  established at level
• only with a per mil sensitivity to sin22q23
• 
  T2K-I vs II
• 
  

T2K-II e 2 per mil - 1
Fernandez-Martinez et al
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The purists

• At accelerators we can also do electron
  (anti)-neutrino beams
• above m threshold that are pure!
• from m decay
• a magnetized detector indispensable!
• from radioactive ions

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A significant investment in accelerator
infrastructure
nFACT
b-beam
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Very well-known fluxes
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Not so different starting point since the
detector can be made more massive for the b-beam
(it does not need magnetization)

CERN-Canaries
gp L(km) Det. mass
nFACT 200-500 3000 40KTon
b-beam 60/100 130 440KTon
CERN-Frejus
In both cases, there is an associated superbeam
(SPL) that can be combined
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Higher g b-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

gmax(He)/L En(GeV)
SPS 150/300km 0.6
SPS-upgrade 350/700km 1.3
LHC 2500/3000km 9.4
CERN-Canfranc ?
Burguet-Castell, et al
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Comparing b-beams
Hierarchy, t23
Sin22q13 5x10-3 0.04
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Degeneracies at b-beam

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Ultimate anti-degeneracy machine
nFACT 40KTon iron calorimeter 2800km (Golden)
ne ? nm nFACT 4Ton Emulsion 730km(Silver) ne
? nt SPLMegaton Cerenkov (Bronce) 130km nm ? ne
The intrinsic and the q23 octant ambiguities are
resolved (up to uncertainties) if the em and et
are combined
Donini, Meloni, Migliozzi

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q13 sensitivity down to 0.3º !
Hierarchy and octant solved for q13 gt 1º-2º
!
Overconstraining em,ee,et,mt,me,mm for n and n
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The new era
(discovery) (roughlydepends on the actual
value of the parameters)
q13 d sign(D23) q23
2013 gt 4º marginal q13 gt 6º (0) q13 gt13º(50) 40º-50º deg.
202? gt0.3-0.6º dgt 10º large q13 q13 gt 1º- 2º(100) q13 gt 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
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There are good ideas to reach the per cent
sensitivity in the n mass matrix in the next
10-20 years
The lepton flavour sector might turn out to be
uninspiring
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Approximate oscillation probabilities O(e2)

• 
  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