Transcript Physics potential of very long neutrino factory baselines

Phenomenology of q13
q13 half-day meeting
Oxford, UK
September 24, 2007
Walter Winter
Universität Würzburg
Contents
Introduction
 The measurement of q13:
Reactor versus beam experiments
 Performance indicators for q13
… and comparison of experiments
 The “farer” future: what if q13 is very small?
 Beyond q13: Mass hierarchy and CP violation
 Summary

Sept. 24, 2007
Oxford 2007 - Walter Winter
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Neutrino mixing
Use standard parameterization - as for CKM matrix:
(sij = sin qij cij = cos qij)
=


(
)(
x
)(
x
)
Three mixing angles q13, q12, q23; one CP phase dCP
Difference to quarks: Two mixing angles large: q12, q23
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Neutrino mass

Mass hierarchy:
Normal or inverted?
8

Theory: Dirac or
Majorana mass terms?

To independent mass
squared differences
relevant for oscillations:
|Dm212 | << |Dm312|
8
|a| = Dm212/|Dm312| ~ 3%

Mass spectra: Difference to origin? Degenerate masses?
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Neutrino oscillations with two flavors
Mixing and mass squared difference:
na “disappearance”:
~Frequency
Amplitude
nb “appearance”:
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Baseline:
Source Detector
Energy
5
Picture of three-flavor oscillations
Atmospheric
oscillation:
Amplitude: q23
Frequency: Dm312
Subleading
effect: dCP
Solar
oscillation:
Amplitude: q12
Frequency: Dm212
Coupling strength: q13
Magnitude of q13 is key to
“subleading” effects:
 Mass hierarchy
determination
 CP violation
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Use ne transitions on
atmospheric oscillation scale
(“Oscillation maximum”)
Oxford 2007 - Walter Winter
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Matter effects in n-oscillations (MSW)




Ordinary matter
contains electrons,
but no m, t
Coherent forward
scattering in matter
(Wolfenstein, 1978; Mikheyev, Smirnov, 1985)
has net effect on electron flavor because of CC (rel. phase shift)
Matter effects proportional to electron density and baseline
Hamiltonian in matter:
Y: electron
fraction ~ 0.5
(electrons per
nucleon)

The matter potential is not CP-inv.! Source of many problems!
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Oxford 2007 - Walter Winter
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The measurement of q13
Experiment classes
Experiment classes by source
Source
Production
… and Detection
Limitations
L
<E>
Reactor
Systematics
1-2 km
~4 MeV
Superbeam
Intrinsic
beam BG,
systematics
1002,500 km
0.5 – 5
GeV
Neutrino
factory
Charge
700identification, 7,500 km
NC BG
b-beam
Source
luminosity
For leading atm. params
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Signal prop. sin22q13
Oxford 2007 - Walter Winter
5-50
GeV
1000.3 – 10
2,000 km GeV
Contamination
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Disappearance measurements

Use expansions in small parameters:

Short baseline reactor experiments:
D31 = Dm312 L/(4E)
No dCP,
No mass
hierarchy!

2nd term small for sin22q13 >> 10-3!
Long baseline accelerator experiments:
(see e.g. Akhmedov et al., hep-ph/0402175)
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A multi-detector reactor experiment
… for a “clean” measurement of q13
See also Lisa
Falk-Harris‘ talk!
Identical detectors, L ~ 1.1-1.7 km
Daya Bay
size
NB: No
sensitivity
to dCP and
mass hierarchy!
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Double Chooz
size
(Minakata et al, 2002; Huber, Lindner, Schwetz, Winter, 2003)
Oxford 2007 - Walter Winter
Unknown
systematics
important for
large
luminosity
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Appearance channels: nm ne
Antineutrinos
(Cervera et al. 2000; Freund, Huber, Lindner, 2000; Freund, 2001)

Complicated, but all interesting information there:
q13, dCP, mass hierarchy (via A)
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See also
Dave Wark‘s talk!
Neutrino beams
nb?
Acceleratorbased neutrino
source
na
Far detector
Often: near detector
(measures flux times
cross sections)
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Baseline:
L ~ E/Dm312
(Osc. length)
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Running example: MINOS


Measurement of atmospheric
parameters with high precision
Flavor conversion
?
Near detector: 980 t
Beam line
Fermilab - Soudan
L ~ 735 km
Far detector: 5400 t
735 km
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q13 performance indicators
…and comparison of experiments
q13 exclusion/sensitivity limit
q13 discovery potential
Predictions for future experiments

Existing experiments:
?

Future experiments:
Input parameters
Data
Simulated data
Fit parameters to data:
Precision of quantity
of interest
Fit parameters to data:
Precision of quantity
of interest
Performance indicators depend on input param. hypothesis!
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Simulated versus fit parameters
Fit parameters



Simulated/true params
Determine the
precision of the
quantity of interest
“Unused” parameteres
are usually
marginalized over
(projection onto
axis/plane of interest)
Source of correlations!
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




Represent the values
implemented by nature
Known within current limits
Change the event rates, top.
Have to be interpreted like
“If the value of … is …,
then the performance will be
…” - Luck or not luck?
Used for risk minimization!
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q13 exclusion/sensitivity limit (1)




Describes the new q13 limit for the simulation of no
signal (q13=0)
Define as largest fit value of q13, which fits true q13=0
Straightforward inclusion of correlations
and degeneracies
Does not depend on the simulated dCP
and mass hierarchy!
systematics
correlations
degeneracies
sin22q13
statistical limit
(all parameters fixed)
Sept. 24, 2007
limit for
(sin22q13)eff
limit for sin22q13 from
*THIS* experiment only
Oxford 2007 - Walter Winter
(from hep-ph/0403068, App. C)
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q13 exclusion/sensitivity limit (2)



Simulated parameters:
q13=0, dCP meaningless
Relatively “simple”
parameter dependencies
No dependence on dCP,
mass hierarchy


Fit parameters:
All six parameters
Correlations and
degeneracies affect
this performance
indicator
Small for
T2K etc.;
Rate ~ 0
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Look for any
combination of
parameters which
“fake” the smallest
rate
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q13 exclusion: Problems with degeneracies



Connected (green) or
disconnected (yellow)
degenerate solutions in
parameter space
Affect measurements
Example: q13-sensitivity
(exclusion limit)
Discrete degeneracies:
(d,q13)-degeneracy
(Burguet-Castell et al, 2001)
sgn-degeneracy
(Huber, Lindner, Winter, 2002)
(Minakata, Nunokawa, 2001)
(q23,p/2-q23)-degeneracy
(Fogli, Lisi, 1996)
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Degeneracy resolution important
topic in recent years!
Example: Neutrino factory (later)
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q13 discovery limit



Simulated parameters:
Hypothesis: Certain q13>0,
dCP, mass hierarchy
Can we establish q13>0 for
this hypothesis?
Maximize parameter space
for discovery


Fit parameters:
Relatively simple as
long as “solar term”
negligible
Small impact of
correlations
Simulated rate
depends on all
parameters
Sept. 24, 2007
Oxford 2007 - Walter Winter
Small for
NOvA
etc.;
Rate ~ 0
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q13 discovery: CP fraction plots
Sensitive
region as
function of true
q13 and dCP
Read: For
sin22q13=0.04, we
expect a discovery
for 20% of all
values of dCP
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Oxford 2007 - Walter Winter
Fraction of dCP for
successful discovery
dCP values now
stacked for
each q13
“Typical dCP”:
CP fraction
50%
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Evolution of q13 discovery limit?
Specific scenario
 Bands reflect
dependence on dCP

GLoBES 2005
(NOvA)
(from: FNAL Proton Driver Study)
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Discovery versus exclusion power
(Huber, Kopp, Lindner, Rolinec, Winter, 2006)
Beams: discovery machines?
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Reactor experiments:
Exclusion instruments?
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The „farer“ future?
Experiments for very small q13
Superbeam upgrades: Examples

discovery



Bands reflect
variation of
systematical errors:
2%-5%-10%
Dots: Nominal L
Typical dCP, 3s
Discovery of sin22q13
downto ~10-3
(Barger, Huber, Marfatia, Winter, hep-ph/0610301, hep-ph/0703029)
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Neutrino factory



Ultimate “high precision” instrument!?
Muon decays in straight sections of storage ring
Technical challenges: Target power, muon
cooling, charge identification, maybe steep
decay tunnels
Decays
Target
p
p, K
Cooling
m-Accelerator
m
m
n
“Wrong sign”
“Right sign”
“Wrong sign”
“Right sign”
(from: CERN Yellow Report )
Sept. 24, 2007
(Geer, 1997; de Rujula, Gavela, Hernandez, 1998; Cervera et al, 2000)
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IDS-NF launched at NuFact 07
International design study for a neutrino factory

Successor of the International Scoping Study for a „future
neutrino factory and superbeam facility“:
Physics case made in physics WG report (~368 pp)
http://www.hep.ph.ic.ac.uk/ids



Initiative from ~ 2007-2012 to present a design report,
schedule, cost estimate, risk assessment for a neutrino
factory Ken Long (Imperial, RAL)
In Europe: Close connection to „Euronus“ proposal
within the FP 07; currently ranked #1, negotiating contract
In the US: „Muon collider task force“
How can a neutrino factory be „upgraded“ to a muon
collider?
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Resolving degeneracies
Example: „Magic“ baseline for NF


L= ~ 4000 km (CP) +
~7500 km (degs) today
baseline configuration of
a neutrino factory
(Huber, Winter, 2003)
(ISS study, 2006)
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Beyond q13 discovery
Mass hierarchy and CP violation
Precision measurements
Perspectives for MH and dCP
for the coming 5 to 10 years?

A mass hierarchy or CP violation measurement
will be unlikely or impossible from
– Beams+Reactor experiments
– Any other source alone (supernova etc.)
(from: Huber, Lindner, Rolinec, Schwetz, Winter, 2004)
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Help from outer space?
Astrophysical neutrino sources produce
certain flavor ratios of neutrinos (ne:nm:nt):
Neutron decays: (1:0:0)
Muon damped sources: (0:1:0)
Pion decays: (1:2:0)
~ cosd
 These ratios are changed at Earth through
averaged neutrino oscillations:
 Measure muon track to shower ratio at neutrino
telescope: R = fm/(fe+ft)
(conservative, since in future also flavors!?)

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Complementarity to beams

Use R to obtain
information on
osc. parameters?
Difficult, since
– Low statistics
– No spectral info
Total
Rates
(Serpico, Kachelriess, 2005;
Serpico, 2005)


R
But: Complementary
dependence
on dCP
Combine the
information from
multiple low
statistics exps?
(Winter, 2006)
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Early measurement of dCP
(Winter, 2006)
... using Double Chooz?


Sept. 24, 2007
Oxford 2007 - Walter Winter
Double Chooz
might be the first
experiment to
observe dCP
If more information:
possibly even CP
violation measurement:
(Blum, Nir, Waxman, 2007)
34
Future discovery of MH and dCP
Mass hierarchy discovery
CP violation discovery
Left end of band: Optimistic setup
Right end of band: Conservative setup
Sept. 24, 2007
Oxford 2007 - Walter Winter
(ISS study)
35
Beyond discovery:
Precision measurements at a NF
q13 precision
3s
dCP precision
dCP
dep.
(Huber, Lindner, Winter, 2004)
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Oxford 2007 - Walter Winter
(Gandhi, Winter, 2006)
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Summary
q13 will be tested in the near future by reactor
experiments and superbeams
 Reactor experiments provide very good limits
on q13, while a discovery may be more likely at
a beam experiment
 If not found, neutrino factories may probe
sin22q13 down to the level of 10-4 or 10-5
 The measurements of the mass hierarchy and
dCP will require the next generation of
experiments

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Oxford 2007 - Walter Winter
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Backup
Matter effects (two flavors, r const.)

Parameter mapping (same form):
Vacuum:
Matter:
Describes
ne – nm transitions
to 0th order in a:
q  q13
Dm2  Dm312
(except factor 0.5)
“Matter resonance”:
In this case:
- Effective mixing maximal
- Effective osc. frequency min.
Resonance energy:
Sept. 24, 2007
r ~ 4.5 g/cm3 (Earth’s mantle)
LBL osc.: E ~ 6.5 GeV
Oxford 2007 - Walter Winter
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Early mass hierarchy measurement?


Fake solution is running in dCP
as function of q13
Astrophysical source may help
mass hierarchy measurement
by constraining this running
Curves: Errors on R
5%
10%
20%
No constraint
(Winter, 2006)
MINOS+Double
Chooz+T2K+NOvA
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