towards precision lepton flavour physics. some reflections… have brought us many clues for a...
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Towards precision lepton flavour physics
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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
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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 could not tell us anything about the vacuum because they could not feel it but they do…again 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 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
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• decoupling L-violating physics: >> v
• mixture: decoupling and not decoupling
+…
Weinberg
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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 ?
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what value of M is more natural ?
M << v is natural because of L symmetryM>>v 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 mass matrix:
• Generically non-unitary PMNS matrix• Flavour structure in neutral currents • Mixing O(v/M) ~O(mv)
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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 >>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
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Einstein’s dream Photomultiplier
Solving the Flavour Puzzle
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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
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Standard 3scenario
The observables:
Masses Angles CP-phases
m12
< m22, m3
2
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The unknowns…
Hierarchy 0
m21, m2
3
Precise oscillations
0
Cosmologysign(cos
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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
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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
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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
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Sensitivity to knowns at E/L ~|m223|
small parameters
ee e e m
1 1
sin22 1 1
m 1 1
sin22 1 1
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Sensitivity at E/L ~m212
ee e
sign(
sign(cos 1 1
ee e m
sin22 1
m 1
sin22 1
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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
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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
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Terrestrial precision oscillation experiments
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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
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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)
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Superbeams Off-axis
Use the conventional (more intense) beams: p Target K, , % e
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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
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Hierarchy at
Only for sin22> 0.04 and some values of
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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:
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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!
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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
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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…
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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 sensitivityto but not to hierarchy
Para ver esta película, debedisponer de QuickTime™ y deun descompresor TIFF (LZW).
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The race for the hierarchy
: a second detector at the second oscillation maximum
Noa proposal
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T2K-II:half of detector in Korea (2nd oscillation peak)
23
Ishitsuka,Kajita,Minakata,Nunokawa
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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
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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
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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:
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beam FACT
A significant investment in accelerator infrastructure
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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 -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
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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 ?
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Comparing -beams
Hierarchy, t23
Sin22x10-3 0.04
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Degeneracies at beam
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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
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Hierarchy and octant solved for ºº
sensitivity down to 0.3º !
Overconstraining: eee,ee,for and !
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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
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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…
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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