home.fnal.govhome.fnal.gov/~jkopp/pdf/ids2008.pdf · 2015. 11. 17. · Optimization of a neutrino factory for non-standard interactions Joachim Kopp Max-Planck-Institut für Kernphysik,

Optimization of a neutrino factoryfor non-standard interactions

Joachim Kopp

Max-Planck-Institut für Kernphysik, Heidelberg, Germany

IDS-NF Plenary Meeting, June 2008, Fermilab

arXiv:0804.2261 (to be published in Phys. Rev. D)Phys. Rev. D76 (2007) 013001 (hep-ph/0702269)Phys. Rev. D77 (2008) 013007 (arXiv:0708.0152)

in collaboration with M. Lindner, T. Ota, J. Sato, and W. Winter

J. Kopp (MPI Heidelberg) Optimization of a NF for NSI June 2008

Outline

1 Non-standard interactions in oscillation experimentsThe general formalismNSI in a neutrino factoryAnalytical treatment of NSI in a neutrino factory

2 Optimization of a neutrino factory in the presence of NSISimulation detailsOptimization of muon energyOptimization of baselines

3 Summary and conclusions


Non-standard interactions in oscillation experiments

Outline





Non-standard interactions in oscillation experiments The general formalism

Outline






The general formalism

“New physics” often leaves low-energy fingerprints in the form ofeffective, non-standard 4-fermion interactions (NSI).⇒ Modification of weak interaction Lagrangian

NSI can affect neutrino production, propagation, and detectionGrossman PL B359 (1995) 141Wolfenstein PR D17 (1978) 2369, Valle PL B199 (1987) 432, Guzzo Masiero Petcov PL B260 (1991) 154, Roulet PR D44 (1991) R935, etc.

Lagrangian:

LNSI =GF√

2

∑f,f ′

εs,f,f ′

αβ

[νβγρ(1− γ5)`α

][f ′γρ(1− γ5)f

]+

GF√2

∑f

εm,fαβ

[ναγρ(1− γ5)νβ

][fγρ(1− γ5)f

]+ h.c.,

Lorentz structures different from (V −A)(V −A) are possible, but notconsidered in this talk.see e.g. JK Lindner Ota Sato, arxiv:0708:152 for a discussion of NSI with non-(V − A)(V − A) Lorentz structure.

We will focus on NSI in the propagation (NC NSI) in the following.




“New physics” often leaves low-energy fingerprints in the form ofeffective, non-standard 4-fermion interactions (NSI).⇒ Modification of weak interaction LagrangianNSI can affect neutrino production, propagation, and detectionGrossman PL B359 (1995) 141Wolfenstein PR D17 (1978) 2369, Valle PL B199 (1987) 432, Guzzo Masiero Petcov PL B260 (1991) 154, Roulet PR D44 (1991) R935, etc.

Lagrangian:

LNSI =GF√

2

∑f,f ′

εs,f,f ′

αβ


][f ′γρ(1− γ5)f

]+

GF√2

∑f

εm,fαβ


][fγρ(1− γ5)f

]+ h.c.,







Lagrangian:

LNSI =GF√

2

∑f,f ′

εs,f,f ′

αβ


][f ′γρ(1− γ5)f

]+

GF√2

∑f

εm,fαβ


][fγρ(1− γ5)f

]+ h.c.,







Lagrangian:

LNSI =GF√

2

∑f,f ′

εs,f,f ′

αβ


][f ′γρ(1− γ5)f

]+

GF√2

∑f

εm,fαβ


][fγρ(1− γ5)f

]+ h.c.,







Lagrangian:

LNSI =GF√

2

∑f,f ′

εs,f,f ′

αβ


][f ′γρ(1− γ5)f

]+

GF√2

∑f

εm,fαβ


][fγρ(1− γ5)f

]+ h.c.,





NSI in oscillation experiments

Compared to charged lepton flavour violation experiments: Interferencebetween standard and non-standard amplitudes is possible⇒ NSI effects suppressed only by |ε| instead of |ε|2.Grossman 1995, Wolfenstein 1977, Valle 1987, Guzzo 1991, Roulet 1991, Bergmann 1999, Gago 2001.

Possible consequences in oscillation experiments:

Poor quality of standard oscillation fit (⇒ Detection of NSI possible)Offset: Wrong reconstruction of neutrino mixing parametersMismatch between standard oscillation fits to different experimentsDifferent optimization strategy





Possible consequences in oscillation experiments:

Poor quality of standard oscillation fit (⇒ Detection of NSI possible)Offset: Wrong reconstruction of neutrino mixing parametersMismatch between standard oscillation fits to different experimentsDifferent optimization strategy





Possible consequences in oscillation experiments:Poor quality of standard oscillation fit (⇒ Detection of NSI possible)

Offset: Wrong reconstruction of neutrino mixing parametersMismatch between standard oscillation fits to different experimentsDifferent optimization strategy





Possible consequences in oscillation experiments:Poor quality of standard oscillation fit (⇒ Detection of NSI possible)Offset: Wrong reconstruction of neutrino mixing parameters

Mismatch between standard oscillation fits to different experimentsDifferent optimization strategy





Possible consequences in oscillation experiments:Poor quality of standard oscillation fit (⇒ Detection of NSI possible)Offset: Wrong reconstruction of neutrino mixing parametersMismatch between standard oscillation fits to different experiments

Different optimization strategy





Possible consequences in oscillation experiments:Poor quality of standard oscillation fit (⇒ Detection of NSI possible)Offset: Wrong reconstruction of neutrino mixing parametersMismatch between standard oscillation fits to different experiments

0.02 0.05 0.1 0.2Sin22Θ13

0

50

100

150

200

250

300

350

∆C

P

T2K � Double Chooz H90% C.L.L

0

50

100

150

200

250

300

350

Cho

oz90

%E

xclu

ded

ÈΕeΤm È = 0.5

argHΕeΤm L = -Π�2

Reactor

Beam NH

Beam IH

"True"params

GLoBES

0.01 0.02 0.05 0.1Sin22Θ13

0

50

100

150

200

250

300

350

∆C

P

T2K � Double Chooz H90% C.L.L

0

50

100

150

200

250

300

350

Cho

oz90

%E

xclu

ded

ΕeΤs= ΕΤe

d= 0.05

Reactor

Beam NH

Beam IH

"True"params

GLoBES

JK Ota Lindner Phys. Rev. D77 (2008) 013007

Different optimization strategy





Possible consequences in oscillation experiments:Poor quality of standard oscillation fit (⇒ Detection of NSI possible)Offset: Wrong reconstruction of neutrino mixing parametersMismatch between standard oscillation fits to different experimentsDifferent optimization strategy


Non-standard interactions in oscillation experiments NSI in a neutrino factory

Outline






NSI in the NF appearance channel

µ+ νe∼ 1

θ13

θ13

νe

νµ

ντ

1 + εmee

εmeµ

εmeτ

εmeµ 1 + εm

µµ

εmµτ

εmeτ

εmµτ

1 + εmττ

νe

νµ

ντ

θ13

θ23

θ23

νµ µ−

Standard path (suppressed by θ13): µ+ → νeθ13−−→ νµ → µ−

Assume ε ∼ θ13

NSI paths with same level of suppression as standard path:

µ+ → νe

εmeµ−−→ νµ → µ−

µ+ → νeεm

eτ−−→ ντθ23−−→ νµ → µ−




µ+ νe∼ 1

θ13

θ13

νe

νµ

ντ

1 + εmee

εmeµ

εmeτ

εmeµ 1 + εm

µµ

εmµτ

εmeτ

εmµτ

1 + εmττ

νe

νµ

ντ

θ13

θ23

θ23

νµ µ−


Assume ε ∼ θ13


µ+ → νe


µ+ → νeεm

eτ−−→ ντθ23−−→ νµ → µ−




µ+ νe∼ 1

θ13

θ13

νe

νµ

ντ

1 + εmee

εmeµ

εmeτ

εmeµ 1 + εm

µµ

εmµτ

εmeτ

εmµτ

1 + εmττ

νe

νµ

ντ

θ13

θ23

θ23

νµ µ−


Assume ε ∼ θ13


µ+ → νe


µ+ → νeεm

eτ−−→ ντθ23−−→ νµ → µ−




µ+ νe∼ 1

θ13

θ13

νe

νµ

ντ

1 + εmee

εmeµ

εmeτ

εmeµ 1 + εm

µµ

εmµτ

εmeτ

εmµτ

1 + εmττ

νe

νµ

ντ

θ13

θ23

θ23

νµ µ−


Assume ε ∼ θ13


µ+ → νe


µ+ → νeεm

eτ−−→ ντθ23−−→ νµ → µ−



NSI in the NF disappearance channel

µ+ νµ

θ13

θ23

θ23

νe

νµ

ντ

1 + εmee

εmeµ

εmeτ

εmeµ 1 + εm

µµ

εmµτ

εmeτ

εmµτ

1 + εmττ

νe

νµ

ντ

θ13

θ23

θ23

νµ µ+

Standard path (unsuppressed): µ+ → νµ → νµ → µ+

Dominant NSI paths:

µ+ → νµ

εmµµ−−→ νµ → µ+

µ+ → νµθ23−−→ ντ

εmττ−−→ ντ

θ23−−→ νµ → µ+

µ+ → νµ

εmµτ−−→ ντ

θ23−−→ νµ → µ+




µ+ νµ

θ13

θ23

θ23

νe

νµ

ντ

1 + εmee

εmeµ

εmeτ

εmeµ 1 + εm

µµ

εmµτ

εmeτ

εmµτ

1 + εmττ

νe

νµ

ντ

θ13

θ23

θ23

νµ µ+


Dominant NSI paths:

µ+ → νµ


µ+ → νµθ23−−→ ντ


θ23−−→ νµ → µ+

µ+ → νµ


θ23−−→ νµ → µ+




µ+ νµ

θ13

θ23

θ23

νe

νµ

ντ

1 + εmee

εmeµ

εmeτ

εmeµ 1 + εm

µµ

εmµτ

εmeτ

εmµτ

1 + εmττ

νe

νµ

ντ

θ13

θ23

θ23

νµ µ+


Dominant NSI paths:

µ+ → νµ


µ+ → νµθ23−−→ ντ


θ23−−→ νµ → µ+

µ+ → νµ


θ23−−→ νµ → µ+



Classification of NSI in a neutrino factory

Relevant NSI in appearance channel: εmeµ, εm

eτ

Relevant NSI in disappearance channel: εmµµ, εm

ττ , εmµτ

Combination of appearance and disappearance channels provides ahandle on all εm parameters except εm

ee (which is special anyway, beingintimately correlated with the standard matter potential).Already at this level, one can see that the Silver channel is not needed todetect NSI.





eτ


ττ , εmµτ







eτ


ττ , εmµτ


ee (which is special anyway, beingintimately correlated with the standard matter potential).

Already at this level, one can see that the Silver channel is not needed todetect NSI.





eτ


ττ , εmµτ





Relevant oscillation channels for εmeτ and εm

ττ sensitivity

-0.4 -0.2 0 0.2 0.4ΕΤΤ

m

-0.02

-0.01

0

0.01

0.02

Ε eΤm

Golden+Disappearance

GLoBES 2008

-0.1 -0.05 0 0.05 0.1ΕΤΤ

m

0

0.005

0.01

0.015

0.02

ÈΕ e

ΤmÈ

Golden+Disappearance

GLoBES 2008

ΦeΤm marginalized

ΕeΤm sensitivity

-0.1 -0.05 0 0.05 0.1ΕΤΤ

m

0

0.005

0.01

0.015

0.02

ÈΕ e

ΤmÈ

Golden+Disapp.+Silver*

GLoBES 2008

ΦeΤm marginalized

ΕeΤm sensitivity

-0.4 -0.2 0 0.2 0.4ΕΤΤ

m

-0.02

-0.01

0

0.01

0.02

Ε eΤm

L=4000km, Golden channel only

3Σ 2Σ

1Σ

GLoBES 2008

-0.4 -0.2 0 0.2 0.4ΕΤΤ

m

-0.02

-0.01

0

0.01

0.02

Ε eΤm

L=7500km, Golden channel only

GLoBES 2008

-0.4 -0.2 0 0.2 0.4ΕΤΤ

m

-0.02

-0.01

0

0.01

0.02

Ε eΤm

L=4000km+7500km, Golden channel only

GLoBES 2008

Ribeiro Minakata Nunokawa Uchinami Zukanovich-Funchal JHEP 0712 (2007) 002, JK Ota Winter arXiv:0804.2261



Further restrictions

εmee: Effect equivalent to systematically biased matter density

εmeµ: Strong existing bounds from charged LFV (εm

eµ < 5× 10−4)Davidson Pena-Garay Rius Santamaria JHEP 03 (2003) 011

εmµµ: effect very similar to εm

ττ

Most interesting

εmeτ

εmµτ

εmττ








ττ

Most interesting

εmeτ

εmµτ

εmττ








ττ

Most interesting

εmeτ

εmµτ

εmττ








ττ

Most interesting

εmeτ

εmµτ

εmττ








ττ

Most interesting

εmeτ

εmµτ

εmττ








ττ

Most interesting

εmeτ

εmµτ

εmττ








ττ Most interesting

εmeτ

εmµτ

εmττ



Classification of NSI in a neutrino factory — Summary

For the NF optimization, we need to consider only εmeτ , εm

µτ , and εmττ .

We expect:The Golden channel will be sensitive to εm

eτ .The Silver channel will be sensitive to εm

eτ , but will not be needed.The disappearance channel will be sensitive to εm

µτ and εmττ .


Non-standard interactions in oscillation experiments Analytical treatment of NSI in a neutrino factory

Outline






Modified neutrino oscillation probabilities

Standard oscillations

Pνα→νβ= |〈νβ |e−iHL|να〉|2

Oscillations with neutral current NSI

Pνsα→νd

β= |〈νβ |e−i(H+VNSI)L|να〉|2

VNSI =√

2GF Ne

εmee εm

eµ εmeτ

εm∗eµ εm

µµ εmµτ

εm∗eτ εm∗

µτ εmττ



Modified neutrino oscillation probabilities

Standard oscillations

Pνα→νβ= |〈νβ |e−iHL|να〉|2

Oscillations with neutral current NSI

Pνsα→νd

β= |〈νβ |e−i(H+VNSI)L|να〉|2

VNSI =√

2GF Ne

εmee εm

eµ εmeτ

εm∗eµ εm

µµ εmµτ

εm∗eτ εm∗

µτ εmττ



Analytic expression for Peµ including |εmeτ |

P NSIeµ ' P SO

eµ − 2 |εmeτ | sin 2θ13 sin 2θ23 s23 sin(δCP + φm

eτ )FMB FRes sin∆

− 2 |εmeτ | sin 2θ13 sin 2θ23 s23 cos(δCP + φm

eτ )FMB FRes cos∆

+ 4 |εmeτ | sin 2θ13 c23 s2

23 cos(δCP + φmeτ ) A

`FRes´2

− 2 |εmeτ |α sin 2θ12 sin 2θ23 c23 sin φm

eτ FMB FRes sin∆

+ 2 |εmeτ |α sin 2θ12 sin 2θ23 c23 cos φm

eτ FMB FRes cos∆

− 4 |εmeτ |α sin 2θ12 s23 c2

23 cos φmeτ

1

A

`FMB´2

+ 4 |εmeτ |2 c2

23 s223 A2 `

FRes´2

− 2 |εmeτ |2 sin2 2θ23 AFMB FRes cos∆

+ 4 |εmeτ |2 s2

23c223

`FMB´2

.

A ≡ ±aCC/∆m231 = ±2

√2EGF Ne/∆m

231, Matter potential

∆ ≡ ∆m231L/4E , Vacuum oscillation phase

FRes≡ sin[(1 − A)∆]/(1 − A) , Maximal at matter resonance

FMB≡ sin(A∆) = sin

„± GF√

2NeL

«. Vanishes at magic baseline



Analytic expressions for Peµ and Peτ including |εmeτ |

„P NSI

eµ

P NSIeτ

«'

„P SO

eµ

P SOeτ

«∓ 2 |εm

eτ | sin 2θ13 sin 2θ23 s23 sin(δCP + φmeτ )FMB FRes sin∆

∓ 2 |εmeτ | sin 2θ13 sin 2θ23 s23 cos(δCP + φm

eτ )FMB FRes cos∆

+ 4 |εmeτ | sin 2θ13 c23

„s2

23

c223

«cos(δCP + φm

eτ ) A`FRes´2

∓ 2 |εmeτ |α sin 2θ12 sin 2θ23 c23 sin φm

eτ FMB FRes sin∆

± 2 |εmeτ |α sin 2θ12 sin 2θ23 c23 cos φm

eτ FMB FRes cos∆

− 4 |εmeτ |α sin 2θ12 s23

„c223

s223

«cos φm

eτ1

A

`FMB´2

+ 4 |εmeτ |2 c2

23

„s2

23

c223

«A2 `

FRes´2

∓ 2 |εmeτ |2 sin2 2θ23 AFMB FRes cos∆

+ 4 |εmeτ |2 s2

23

„c223

s223

« `FMB´2

.

Strong correlations, even at magic baselineφm

eτ can yield CP violation even for θ13 = 0.For θ23 = π/4, Peµ and Peτ differ only in the signs of certain terms.For θ23 = π/4, Peµ and Peτ are identical at the magic baseline.(⇒ Silver channel at magic baseline would be useless.). . .




P NSI

eµ

P NSIeτ

!'

P SOeµ

P SOeτ

!∓ 2 |εm

eτ | sin 2θ13 sin 2θ23 s23 sin(δCP + φmeτ )FMB FRes sin ∆

∓ 2 |εmeτ | sin 2θ13 sin 2θ23 s23 cos(δCP + φ

meτ )FMB FRes cos ∆

+ 4 |εmeτ | sin 2θ13 c23

s223

c223

!cos(δCP + φ

meτ ) A

`FRes´2

∓ 2 |εmeτ |α sin 2θ12 sin 2θ23 c23 sin φ

meτ F

MB FRes sin ∆

± 2 |εmeτ |α sin 2θ12 sin 2θ23 c23 cos φ

meτ F

MB FRes cos ∆


c223

s223

!cos φ

meτ

1A

`FMB´2

+ 4 |εmeτ |

2c223

s223

c223

!A

2 `FRes´2∓ 2 |εm

eτ |2 sin2 2θ23 AFMB FRes cos ∆

+ 4 |εmeτ |

2s223

c223

s223

! `FMB´2

.

Strong correlations, even at magic baseline

φmeτ can yield CP violation even for θ13 = 0.

For θ23 = π/4, Peµ and Peτ differ only in the signs of certain terms.For θ23 = π/4, Peµ and Peτ are identical at the magic baseline.(⇒ Silver channel at magic baseline would be useless.). . .




P NSI

eµ

P NSIeτ

!'

P SOeµ

P SOeτ

!∓ 2 |εm




+ 4 |εmeτ | sin 2θ13 c23

s223

c223

!cos(δCP + φ

meτ ) A

`FRes´2


meτ F

MB FRes sin ∆


meτ F

MB FRes cos ∆


c223

s223

!cos φ

meτ

1A

`FMB´2

+ 4 |εmeτ |

2c223

s223

c223

!A

2 `FRes´2∓ 2 |εm


+ 4 |εmeτ |

2s223

c223

s223

! `FMB´2

.


eτ can yield CP violation even for θ13 = 0.

For θ23 = π/4, Peµ and Peτ differ only in the signs of certain terms.For θ23 = π/4, Peµ and Peτ are identical at the magic baseline.(⇒ Silver channel at magic baseline would be useless.). . .




P NSI

eµ

P NSIeτ

!'

P SOeµ

P SOeτ

!∓ 2 |εm




+ 4 |εmeτ | sin 2θ13 c23

s223

c223

!cos(δCP + φ

meτ ) A

`FRes´2


meτ F

MB FRes sin ∆


meτ F

MB FRes cos ∆


c223

s223

!cos φ

meτ

1A

`FMB´2

+ 4 |εmeτ |

2c223

s223

c223

!A

2 `FRes´2∓ 2 |εm


+ 4 |εmeτ |

2s223

c223

s223

! `FMB´2

.


eτ can yield CP violation even for θ13 = 0.For θ23 = π/4, Peµ and Peτ differ only in the signs of certain terms.

For θ23 = π/4, Peµ and Peτ are identical at the magic baseline.(⇒ Silver channel at magic baseline would be useless.). . .




P NSI

eµ

P NSIeτ

!'

P SOeµ

P SOeτ

!∓ 2 |εm




+ 4 |εmeτ | sin 2θ13 c23

s223

c223

!cos(δCP + φ

meτ ) A

`FRes´2


meτ F

MB FRes sin ∆


meτ F

MB FRes cos ∆


c223

s223

!cos φ

meτ

1A

`FMB´2

+ 4 |εmeτ |

2c223

s223

c223

!A

2 `FRes´2∓ 2 |εm


+ 4 |εmeτ |

2s223

c223

s223

! `FMB´2

.


eτ can yield CP violation even for θ13 = 0.For θ23 = π/4, Peµ and Peτ differ only in the signs of certain terms.For θ23 = π/4, Peµ and Peτ are identical at the magic baseline.(⇒ Silver channel at magic baseline would be useless.)

. . .




P NSI

eµ

P NSIeτ

!'

P SOeµ

P SOeτ

!∓ 2 |εm




+ 4 |εmeτ | sin 2θ13 c23

s223

c223

!cos(δCP + φ

meτ ) A

`FRes´2


meτ F

MB FRes sin ∆


meτ F

MB FRes cos ∆


c223

s223

!cos φ

meτ

1A

`FMB´2

+ 4 |εmeτ |

2c223

s223

c223

!A

2 `FRes´2∓ 2 |εm


+ 4 |εmeτ |

2s223

c223

s223

! `FMB´2

.


eτ can yield CP violation even for θ13 = 0.For θ23 = π/4, Peµ and Peτ differ only in the signs of certain terms.For θ23 = π/4, Peµ and Peτ are identical at the magic baseline.(⇒ Silver channel at magic baseline would be useless.). . .J. Kopp (MPI Heidelberg) Optimization of a NF for NSI June 2008

Optimization of a neutrino factory in the presence of NSI

Outline





Optimization of a neutrino factory in the presence of NSI Simulation details

Outline






Numerical simulation techniques

All simulations have been performed with GLoBES 3.0Huber Lindner Winter Comput. Phys. Commun. 167 (2005) 195,Huber JK Lindner Rolinec Winter Comput. Phys. Commun. 177 (2007) 432http://www.mpi-hd.mpg.de/∼globes

Event rate based simulations (no Monte Carlo)χ2 analysis includes

Systematical errorsParameter correlationsDegeneraciesExternal input on those parameters which cannot be determined by theexperiment under consideration





Event rate based simulations (no Monte Carlo)

χ2 analysis includes













Systematical errors

Parameter correlationsDegeneraciesExternal input on those parameters which cannot be determined by theexperiment under consideration






Systematical errorsParameter correlations

DegeneraciesExternal input on those parameters which cannot be determined by theexperiment under consideration






Systematical errorsParameter correlationsDegeneracies

External input on those parameters which cannot be determined by theexperiment under consideration









Neutrino factory setup (IDS-NF 1.0 baseline)

Two 50 kt magnetized iron detectors @ L1 = 4000 km, L2 = 7500 km.

Optional 10 kt silver channel detector (emulsion cloud chamber)Hypothetical Silver* detector (signal ×5, background ×3) incorporateshadronic τ decay channels2.5× 1021 useful muon decays per baseline and polarityMuon energy: Eµ = 25 GeVGolden (νe → νµ), Silver (νe → ντ ), and Disappearance (νµ → νµ)channels simulatedCharge ID in Golden and Silver channels, but not in disappearancechannel




Two 50 kt magnetized iron detectors @ L1 = 4000 km, L2 = 7500 km.Optional 10 kt silver channel detector (emulsion cloud chamber)

Hypothetical Silver* detector (signal ×5, background ×3) incorporateshadronic τ decay channels2.5× 1021 useful muon decays per baseline and polarityMuon energy: Eµ = 25 GeVGolden (νe → νµ), Silver (νe → ντ ), and Disappearance (νµ → νµ)channels simulatedCharge ID in Golden and Silver channels, but not in disappearancechannel




Two 50 kt magnetized iron detectors @ L1 = 4000 km, L2 = 7500 km.Optional 10 kt silver channel detector (emulsion cloud chamber)Hypothetical Silver* detector (signal ×5, background ×3) incorporateshadronic τ decay channels

2.5× 1021 useful muon decays per baseline and polarityMuon energy: Eµ = 25 GeVGolden (νe → νµ), Silver (νe → ντ ), and Disappearance (νµ → νµ)channels simulatedCharge ID in Golden and Silver channels, but not in disappearancechannel




Two 50 kt magnetized iron detectors @ L1 = 4000 km, L2 = 7500 km.Optional 10 kt silver channel detector (emulsion cloud chamber)Hypothetical Silver* detector (signal ×5, background ×3) incorporateshadronic τ decay channels2.5× 1021 useful muon decays per baseline and polarity

Muon energy: Eµ = 25 GeVGolden (νe → νµ), Silver (νe → ντ ), and Disappearance (νµ → νµ)channels simulatedCharge ID in Golden and Silver channels, but not in disappearancechannel




Two 50 kt magnetized iron detectors @ L1 = 4000 km, L2 = 7500 km.Optional 10 kt silver channel detector (emulsion cloud chamber)Hypothetical Silver* detector (signal ×5, background ×3) incorporateshadronic τ decay channels2.5× 1021 useful muon decays per baseline and polarityMuon energy: Eµ = 25 GeV

Golden (νe → νµ), Silver (νe → ντ ), and Disappearance (νµ → νµ)channels simulatedCharge ID in Golden and Silver channels, but not in disappearancechannel




Two 50 kt magnetized iron detectors @ L1 = 4000 km, L2 = 7500 km.Optional 10 kt silver channel detector (emulsion cloud chamber)Hypothetical Silver* detector (signal ×5, background ×3) incorporateshadronic τ decay channels2.5× 1021 useful muon decays per baseline and polarityMuon energy: Eµ = 25 GeVGolden (νe → νµ), Silver (νe → ντ ), and Disappearance (νµ → νµ)channels simulated

Charge ID in Golden and Silver channels, but not in disappearancechannel




Two 50 kt magnetized iron detectors @ L1 = 4000 km, L2 = 7500 km.Optional 10 kt silver channel detector (emulsion cloud chamber)Hypothetical Silver* detector (signal ×5, background ×3) incorporateshadronic τ decay channels2.5× 1021 useful muon decays per baseline and polarityMuon energy: Eµ = 25 GeVGolden (νe → νµ), Silver (νe → ντ ), and Disappearance (νµ → νµ)channels simulatedCharge ID in Golden and Silver channels, but not in disappearancechannel


Optimization of a neutrino factory in the presence of NSI Optimization of muon energy

Outline






Optimization of muon energy

20 40 60 80 10010-3

10-2

10-1

EΜ @GeVD

Sens

itivi

tytoÈΕΑΒ

mÈ

IDS-

NF

GLoBES 2008

sin2 2Θ13true = 0.001

∆CPtrue = 3Π�2

ÈΕeΤm È

ÈΕΜΤm È

ÈΕΤΤm È

Improvement bySilver detector � 4000 km

Improvement bySilver* detector � 4000 km

20 40 60 80 10010-3

10-2

10-1

EΜ @GeVD

Sens

itivi

tytoÈΕΑΒ

mÈ

IDS-

NF

GLoBES 2008

sin2 2Θ13true = 0.01

∆CPtrue = 0

ÈΕeΤm È

ÈΕΜΤm È

ÈΕΤΤm È

JK Ota Winter arXiv:0804.2261

Eµ = 25 GeV is optimal.(Eµ > 25 GeV → no significant improvementEµ < 25 GeV → sensitivity decreases dramatically)Silver channel only useful at Eµ � 25 GeV.




20 40 60 80 10010-3

10-2

10-1

EΜ @GeVD

Sens

itivi

tytoÈΕΑΒ

mÈ

IDS-

NF

GLoBES 2008

sin2 2Θ13true = 0.001

∆CPtrue = 3Π�2

ÈΕeΤm È

ÈΕΜΤm È

ÈΕΤΤm È



20 40 60 80 10010-3

10-2

10-1

EΜ @GeVD

Sens

itivi

tytoÈΕΑΒ

mÈ

IDS-

NF

GLoBES 2008


∆CPtrue = 0

ÈΕeΤm È

ÈΕΜΤm È

ÈΕΤΤm È


Eµ = 25 GeV is optimal.(Eµ > 25 GeV → no significant improvementEµ < 25 GeV → sensitivity decreases dramatically)

Silver channel only useful at Eµ � 25 GeV.




20 40 60 80 10010-3

10-2

10-1

EΜ @GeVD

Sens

itivi

tytoÈΕΑΒ

mÈ

IDS-

NF

GLoBES 2008

sin2 2Θ13true = 0.001

∆CPtrue = 3Π�2

ÈΕeΤm È

ÈΕΜΤm È

ÈΕΤΤm È



20 40 60 80 10010-3

10-2

10-1

EΜ @GeVD

Sens

itivi

tytoÈΕΑΒ

mÈ

IDS-

NF

GLoBES 2008


∆CPtrue = 0

ÈΕeΤm È

ÈΕΜΤm È

ÈΕΤΤm È


Eµ = 25 GeV is optimal.(Eµ > 25 GeV → no significant improvementEµ < 25 GeV → sensitivity decreases dramatically)Silver channel only useful at Eµ � 25 GeV.J. Kopp (MPI Heidelberg) Optimization of a NF for NSI June 2008

Optimization of a neutrino factory in the presence of NSI Optimization of baselines

Outline






Optimization of Silver channel baseline

2000 4000 6000 8000 10 000 12 000Baseline of Silver* Detector @kmD

10-3

5×10-3

10-2

Sens

itivi

tytoÈΕ eΤmÈ

sin2 2Θ13true=0.001, ∆CP

true=0

IDS-

NF

base

line

GLoBES 2008

EΜ=25 GeV

EΜ=50 GeV

EΜ=100 GeV


10-3

5×10-3

10-2

Sens

itivi

tytoÈΕ eΤmÈ


true=3Π�2

GLoBES 2008

Conclusion: Silver channel only useful at L = 4000 km and Eµ � 25 GeV.⇒ We can omit the Silver channel in the rest of our discussion.





10-3

5×10-3

10-2

Sens

itivi

tytoÈΕ eΤmÈ


true=0

IDS-

NF

base

line

GLoBES 2008

EΜ=25 GeV

EΜ=50 GeV

EΜ=100 GeV


10-3

5×10-3

10-2

Sens

itivi

tytoÈΕ eΤmÈ


true=3Π�2

GLoBES 2008

Conclusion: Silver channel only useful at L = 4000 km and Eµ � 25 GeV.

⇒ We can omit the Silver channel in the rest of our discussion.





10-3

5×10-3

10-2

Sens

itivi

tytoÈΕ eΤmÈ


true=0

IDS-

NF

base

line

GLoBES 2008

EΜ=25 GeV

EΜ=50 GeV

EΜ=100 GeV


10-3

5×10-3

10-2

Sens

itivi

tytoÈΕ eΤmÈ


true=3Π�2

GLoBES 2008

Conclusion: Silver channel only useful at L = 4000 km and Eµ � 25 GeV.⇒ We can omit the Silver channel in the rest of our discussion.



Optimization of baselines for θ13, MH, CPV

2000 4000 6000 8000 10 000 12 000

2000

4000

6000

8000

10 000

12 000

L1 @kmD

L2@k

mD

sin2 2Θ13 sensitivity

Symmetr

y axis

Magic baseline

GLoBES 2008

æ

æ

ìì

ì

EΜ = 25 GeV

sin2 2Θ13 < 10-3.4

Standard Fit

sin2 2Θ13 < 10-3.2

Fit including ΕeΤm

2000 4000 6000 8000 10 000 12 000

2000

4000

6000

8000

10 000

12 000

L1 @kmD

L2@k

mD

Normal MH sensitivity Hfor ∆CPtrue = 3Π�2L

Symmetr

y axis

Magic baseline

GLoBES 2008

æ

æ

ì

ì

ì

ì

EΜ = 25 GeV

Discovery for sin2 2Θ13 > 10-3.8

Standard Fit



2000 4000 6000 8000 10 000 12 000

2000

4000

6000

8000

10 000

12 000

L1 @kmD

L2@k

mD

Max. CPV sensitivity Hfor ∆CPtrue = 3Π�2L

Symmetr

y axis

Magic baseline

GLoBES 2008

æ

æ

ì

ì

ì

ì

EΜ = 25 GeV


Standard Fit



2000 4000 6000 8000 10 000 12 000

2000

4000

6000

8000

10 000

12 000

L1 @kmD

L2@k

mD

All performance indicators

Core crossing

Symmetr

y axis

Magic baseline

GLoBES 2008

æ

æ

EΜ = 25 GeV


Performance indicators:

sin2 2θ13 sensitivity:What is the newexclusion limit ifθtrue13 = 0?

Normal MH/max. CPVsensitivity: How largedoes sin2 2θ13 have to beto guarantee detectionof NH/max. CPV?

Conclusion:L1 = 4000 km, L2 = 7500 kmis close to optimal even ifNSI are included in the fit.(We checked this also for theother εm

αβ)




2000 4000 6000 8000 10 000 12 000

2000

4000

6000

8000

10 000

12 000

L1 @kmD

L2@k

mD


Symmetr

y axis

Magic baseline

GLoBES 2008

æ

æ

ìì

ì

EΜ = 25 GeV

sin2 2Θ13 < 10-3.4

Standard Fit

sin2 2Θ13 < 10-3.2


2000 4000 6000 8000 10 000 12 000

2000

4000

6000

8000

10 000

12 000

L1 @kmD

L2@k

mD


Symmetr

y axis

Magic baseline

GLoBES 2008

æ

æ

ì

ì

ì

ì

EΜ = 25 GeV


Standard Fit



2000 4000 6000 8000 10 000 12 000

2000

4000

6000

8000

10 000

12 000

L1 @kmD

L2@k

mD


Symmetr

y axis

Magic baseline

GLoBES 2008

æ

æ

ì

ì

ì

ì

EΜ = 25 GeV


Standard Fit



2000 4000 6000 8000 10 000 12 000

2000

4000

6000

8000

10 000

12 000

L1 @kmD

L2@k

mD


Core crossing

Symmetr

y axis

Magic baseline

GLoBES 2008

æ

æ

EΜ = 25 GeV


Performance indicators:

sin2 2θ13 sensitivity:What is the newexclusion limit ifθtrue13 = 0?



αβ)




2000 4000 6000 8000 10 000 12 000

2000

4000

6000

8000

10 000

12 000

L1 @kmD

L2@k

mD


Symmetr

y axis

Magic baseline

GLoBES 2008

æ

æ

ìì

ì

EΜ = 25 GeV

sin2 2Θ13 < 10-3.4

Standard Fit

sin2 2Θ13 < 10-3.2


2000 4000 6000 8000 10 000 12 000

2000

4000

6000

8000

10 000

12 000

L1 @kmD

L2@k

mD


Symmetr

y axis

Magic baseline

GLoBES 2008

æ

æ

ì

ì

ì

ì

EΜ = 25 GeV


Standard Fit



2000 4000 6000 8000 10 000 12 000

2000

4000

6000

8000

10 000

12 000

L1 @kmD

L2@k

mD


Symmetr

y axis

Magic baseline

GLoBES 2008

æ

æ

ì

ì

ì

ì

EΜ = 25 GeV


Standard Fit



2000 4000 6000 8000 10 000 12 000

2000

4000

6000

8000

10 000

12 000

L1 @kmD

L2@k

mD


Core crossing

Symmetr

y axis

Magic baseline

GLoBES 2008

æ

æ

EΜ = 25 GeV


Performance indicators:sin2 2θ13 sensitivity:What is the newexclusion limit ifθtrue13 = 0?



αβ)




2000 4000 6000 8000 10 000 12 000

2000

4000

6000

8000

10 000

12 000

L1 @kmD

L2@k

mD


Symmetr

y axis

Magic baseline

GLoBES 2008

æ

æ

ìì

ì

EΜ = 25 GeV

sin2 2Θ13 < 10-3.4

Standard Fit

sin2 2Θ13 < 10-3.2


2000 4000 6000 8000 10 000 12 000

2000

4000

6000

8000

10 000

12 000

L1 @kmD

L2@k

mD


Symmetr

y axis

Magic baseline

GLoBES 2008

æ

æ

ì

ì

ì

ì

EΜ = 25 GeV


Standard Fit



2000 4000 6000 8000 10 000 12 000

2000

4000

6000

8000

10 000

12 000

L1 @kmD

L2@k

mD


Symmetr

y axis

Magic baseline

GLoBES 2008

æ

æ

ì

ì

ì

ì

EΜ = 25 GeV


Standard Fit



2000 4000 6000 8000 10 000 12 000

2000

4000

6000

8000

10 000

12 000

L1 @kmD

L2@k

mD


Core crossing

Symmetr

y axis

Magic baseline

GLoBES 2008

æ

æ

EΜ = 25 GeV





αβ)




2000 4000 6000 8000 10 000 12 000

2000

4000

6000

8000

10 000

12 000

L1 @kmD

L2@k

mD


Symmetr

y axis

Magic baseline

GLoBES 2008

æ

æ

ìì

ì

EΜ = 25 GeV

sin2 2Θ13 < 10-3.4

Standard Fit

sin2 2Θ13 < 10-3.2


2000 4000 6000 8000 10 000 12 000

2000

4000

6000

8000

10 000

12 000

L1 @kmD

L2@k

mD


Symmetr

y axis

Magic baseline

GLoBES 2008

æ

æ

ì

ì

ì

ì

EΜ = 25 GeV


Standard Fit



2000 4000 6000 8000 10 000 12 000

2000

4000

6000

8000

10 000

12 000

L1 @kmD

L2@k

mD


Symmetr

y axis

Magic baseline

GLoBES 2008

æ

æ

ì

ì

ì

ì

EΜ = 25 GeV


Standard Fit



2000 4000 6000 8000 10 000 12 000

2000

4000

6000

8000

10 000

12 000

L1 @kmD

L2@k

mD


Core crossing

Symmetr

y axis

Magic baseline

GLoBES 2008

æ

æ

EΜ = 25 GeV




Conclusion:L1 = 4000 km, L2 = 7500 kmis close to optimal even ifNSI are included in the fit.

(We checked this also for theother εm

αβ)




2000 4000 6000 8000 10 000 12 000

2000

4000

6000

8000

10 000

12 000

L1 @kmD

L2@k

mD


Symmetr

y axis

Magic baseline

GLoBES 2008

æ

æ

ìì

ì

EΜ = 25 GeV

sin2 2Θ13 < 10-3.4

Standard Fit

sin2 2Θ13 < 10-3.2


2000 4000 6000 8000 10 000 12 000

2000

4000

6000

8000

10 000

12 000

L1 @kmD

L2@k

mD


Symmetr

y axis

Magic baseline

GLoBES 2008

æ

æ

ì

ì

ì

ì

EΜ = 25 GeV


Standard Fit



2000 4000 6000 8000 10 000 12 000

2000

4000

6000

8000

10 000

12 000

L1 @kmD

L2@k

mD


Symmetr

y axis

Magic baseline

GLoBES 2008

æ

æ

ì

ì

ì

ì

EΜ = 25 GeV


Standard Fit



2000 4000 6000 8000 10 000 12 000

2000

4000

6000

8000

10 000

12 000

L1 @kmD

L2@k

mD


Core crossing

Symmetr

y axis

Magic baseline

GLoBES 2008

æ

æ

EΜ = 25 GeV





αβ)



Optimization of baselines for NSI


L1 = 4000 km, L2 = 7500 km is OK for εmeτ

For εmµτ and εm

ττ , larger baselines are preferred.Note: NSI sensitivity could be improved if longer baselines werecombined with higher Eµ.






For εmµτ and εm







For εmµτ and εm

ττ , larger baselines are preferred.

Note: NSI sensitivity could be improved if longer baselines werecombined with higher Eµ.






For εmµτ and εm



Summary and conclusions

Outline







10-5 10-4 10-3 10-2 10-1

10-5 10-4 10-3 10-2 10-1

sin2 2Θ13

H5ΣL

NH for ∆CPtrue = 3Π�2

H5ΣL

CPV for ∆CPtrue = 3Π�2

H5ΣL

sin2 2Θ13

H5ΣL


H5ΣL


H5ΣL

ÈΕeem È H3ΣL

ÈΕeΤm È H3ΣL

ÈΕΜΤm È H3ΣL

ÈΕΤΤm È H3ΣL

ÈΕΑΒmÈ

sin2 2Θ13

GLoBES 2008

better

5 GeV

25 GeV

50 GeV

Improvement bySilver* � 4000 km

sin2

2Θ13

reac

hno

NSI

sin2

2Θ13

reac

hfi

tinc

ludi

ngΕ eΤm

ÈΕΑΒ

mÈre

ach

ν-fact is a powerful tool tosearch for NSI, in particularεm

eτ , εmµτ , and εm

ττ .Eµ = 25 GeV is OK.L1 = 4000 km,L2 = 7500 km is OK forsin2 2θ13, MH, and CPV, andNSI.Some NSI slightly preferlonger baselines andhigher energies.Silver channel can beomitted for standardphysics and NSI, unless Eµ

is increased significantly.




10-5 10-4 10-3 10-2 10-1

10-5 10-4 10-3 10-2 10-1

sin2 2Θ13

H5ΣL


H5ΣL


H5ΣL

sin2 2Θ13

H5ΣL


H5ΣL


H5ΣL

ÈΕeem È H3ΣL

ÈΕeΤm È H3ΣL

ÈΕΜΤm È H3ΣL

ÈΕΤΤm È H3ΣL

ÈΕΑΒmÈ

sin2 2Θ13

GLoBES 2008

better

5 GeV

25 GeV

50 GeV


sin2

2Θ13

reac

hno

NSI

sin2

2Θ13

reac

hfi

tinc

ludi

ngΕ eΤm

ÈΕΑΒ

mÈre

ach



ττ .

Eµ = 25 GeV is OK.L1 = 4000 km,L2 = 7500 km is OK forsin2 2θ13, MH, and CPV, andNSI.Some NSI slightly preferlonger baselines andhigher energies.Silver channel can beomitted for standardphysics and NSI, unless Eµ





10-5 10-4 10-3 10-2 10-1

10-5 10-4 10-3 10-2 10-1

sin2 2Θ13

H5ΣL


H5ΣL


H5ΣL

sin2 2Θ13

H5ΣL


H5ΣL


H5ΣL

ÈΕeem È H3ΣL

ÈΕeΤm È H3ΣL

ÈΕΜΤm È H3ΣL

ÈΕΤΤm È H3ΣL

ÈΕΑΒmÈ

sin2 2Θ13

GLoBES 2008

better

5 GeV

25 GeV

50 GeV


sin2

2Θ13

reac

hno

NSI

sin2

2Θ13

reac

hfi

tinc

ludi

ngΕ eΤm

ÈΕΑΒ

mÈre

ach



ττ .Eµ = 25 GeV is OK.

L1 = 4000 km,L2 = 7500 km is OK forsin2 2θ13, MH, and CPV, andNSI.Some NSI slightly preferlonger baselines andhigher energies.Silver channel can beomitted for standardphysics and NSI, unless Eµ





10-5 10-4 10-3 10-2 10-1

10-5 10-4 10-3 10-2 10-1

sin2 2Θ13

H5ΣL


H5ΣL


H5ΣL

sin2 2Θ13

H5ΣL


H5ΣL


H5ΣL

ÈΕeem È H3ΣL

ÈΕeΤm È H3ΣL

ÈΕΜΤm È H3ΣL

ÈΕΤΤm È H3ΣL

ÈΕΑΒmÈ

sin2 2Θ13

GLoBES 2008

better

5 GeV

25 GeV

50 GeV


sin2

2Θ13

reac

hno

NSI

sin2

2Θ13

reac

hfi

tinc

ludi

ngΕ eΤm

ÈΕΑΒ

mÈre

ach



ττ .Eµ = 25 GeV is OK.L1 = 4000 km,L2 = 7500 km is OK forsin2 2θ13, MH, and CPV, andNSI.

Some NSI slightly preferlonger baselines andhigher energies.Silver channel can beomitted for standardphysics and NSI, unless Eµ





10-5 10-4 10-3 10-2 10-1

10-5 10-4 10-3 10-2 10-1

sin2 2Θ13

H5ΣL


H5ΣL


H5ΣL

sin2 2Θ13

H5ΣL


H5ΣL


H5ΣL

ÈΕeem È H3ΣL

ÈΕeΤm È H3ΣL

ÈΕΜΤm È H3ΣL

ÈΕΤΤm È H3ΣL

ÈΕΑΒmÈ

sin2 2Θ13

GLoBES 2008

better

5 GeV

25 GeV

50 GeV


sin2

2Θ13

reac

hno

NSI

sin2

2Θ13

reac

hfi

tinc

ludi

ngΕ eΤm

ÈΕΑΒ

mÈre

ach



ττ .Eµ = 25 GeV is OK.L1 = 4000 km,L2 = 7500 km is OK forsin2 2θ13, MH, and CPV, andNSI.Some NSI slightly preferlonger baselines andhigher energies.

Silver channel can beomitted for standardphysics and NSI, unless Eµ





10-5 10-4 10-3 10-2 10-1

10-5 10-4 10-3 10-2 10-1

sin2 2Θ13

H5ΣL


H5ΣL


H5ΣL

sin2 2Θ13

H5ΣL


H5ΣL


H5ΣL

ÈΕeem È H3ΣL

ÈΕeΤm È H3ΣL

ÈΕΜΤm È H3ΣL

ÈΕΤΤm È H3ΣL

ÈΕΑΒmÈ

sin2 2Θ13

GLoBES 2008

better

5 GeV

25 GeV

50 GeV


sin2

2Θ13

reac

hno

NSI

sin2

2Θ13

reac

hfi

tinc

ludi

ngΕ eΤm

ÈΕΑΒ

mÈre

ach



ττ .Eµ = 25 GeV is OK.L1 = 4000 km,L2 = 7500 km is OK forsin2 2θ13, MH, and CPV, andNSI.Some NSI slightly preferlonger baselines andhigher energies.Silver channel can beomitted for standardphysics and NSI, unless Eµ




Thank you!


Backup slides

Optimization of baselines for NSI (Eµ = 50 GeV)



Backup slides

Qualitative arguments (NSI in source in detector)

N∗

1 + εs∗ee

εs∗eµ

εs∗eτ

νe

νµ

ντ

cos 2θ13 ∼ 1

sin 2θ13

sin 2θ13

νe

νµ

ντ

1 + εd∗ee

εd∗µe

εd∗τe

e+

Standard path: N∗ → νe → νe → e+

NSI production processes: N∗ εs∗ee−−→ νe N∗ εs∗

eµ−−→ νµ N∗ εs∗eτ−−→ ντ

NSI detection processes: νeεd∗

ee−−→ e+ νµ

εd∗µe−−→ e+ ντ

εd∗τe−−→ e+

νe ↔ νµ and νe ↔ ντ oscillations are suppressed by θ13.Assume only one ε parameter is sizeable

N∗ εs∗ee−−→ νe → νe → e+ O(ε) but: absorbed in flux uncertainty

N∗ → νe → νeεd∗

ee−−→ e+ O(ε) but: absorbed in flux uncertainty

N∗ εs∗eµ−−→ νµ

sin θ13−−−→ νe → e+ O(ε sin θ13)

N∗ εs∗eτ−−→ ντ


N∗ → νesin θ13−−−→ νµ

εd∗µe−−→ e+ O(ε sin θ13)

N∗ → νesin θ13−−−→ ντ

εd∗τe−−→ e+ O(ε sin θ13)


Backup slides


N∗

1 + εs∗ee

εs∗eµ

εs∗eτ

νe

νµ

ντ

cos 2θ13 ∼ 1

sin 2θ13

sin 2θ13

νe

νµ

ντ

1 + εd∗ee

εd∗µe

εd∗τe

e+





ee−−→ e+ νµ
















Backup slides


N∗

1 + εs∗ee

εs∗eµ

εs∗eτ

νe

νµ

ντ

cos 2θ13 ∼ 1

sin 2θ13

sin 2θ13

νe

νµ

ντ

1 + εd∗ee

εd∗µe

εd∗τe

e+





ee−−→ e+ νµ
















Backup slides


N∗

1 + εs∗ee

εs∗eµ

εs∗eτ

νe

νµ

ντ

cos 2θ13 ∼ 1

sin 2θ13

sin 2θ13

νe

νµ

ντ

1 + εd∗ee

εd∗µe

εd∗τe

e+





ee−−→ e+ νµ



νe ↔ νµ and νe ↔ ντ oscillations are suppressed by θ13.

Assume only one ε parameter is sizeableN∗ εs∗

ee−−→ νe → νe → e+ O(ε) but: absorbed in flux uncertainty












Backup slides


N∗

1 + εs∗ee

εs∗eµ

εs∗eτ

νe

νµ

ντ

cos 2θ13 ∼ 1

sin 2θ13

sin 2θ13

νe

νµ

ντ

1 + εd∗ee

εd∗µe

εd∗τe

e+





ee−−→ e+ νµ
















Backup slides


N∗

1 + εs∗ee

εs∗eµ

εs∗eτ

νe

νµ

ντ

cos 2θ13 ∼ 1

sin 2θ13

sin 2θ13

νe

νµ

ντ

1 + εd∗ee

εd∗µe

εd∗τe

e+













Backup slides


N∗

1 + εs∗ee

εs∗eµ

εs∗eτ

νe

νµ

ντ

cos 2θ13 ∼ 1

sin 2θ13

sin 2θ13

νe

νµ

ντ

1 + εd∗ee

εd∗µe

εd∗τe

e+













Backup slides

Discovery reach for εmeµ in a neutrino factory

Discovery reach for εmeµ: Minimum value of |εm

eµ| which can no longer befitted with εm

eµ = 0 at a given C.L.

Very challenging due to strong constraint εmeµ . 5× 10−4 (90% C.L.) from

charged lepton flavour violation. Davidson Pena-Garay Rius Santamaria JHEP 03 (2003) 011

Neutrino factory setup

Baseline 3000 km (1 detector only)Detector: 50 kt magnetized iron calorimeterParent muon energy: 50 GeVStored muons: 4× 1021 µ+, 4× 1021 µ−


Backup slides










Backup slides










Backup slides







Neutrino factory setupBaseline 3000 km (1 detector only)

Detector: 50 kt magnetized iron calorimeterParent muon energy: 50 GeVStored muons: 4× 1021 µ+, 4× 1021 µ−


Backup slides







Neutrino factory setupBaseline 3000 km (1 detector only)Detector: 50 kt magnetized iron calorimeter

Parent muon energy: 50 GeVStored muons: 4× 1021 µ+, 4× 1021 µ−


Backup slides







Neutrino factory setupBaseline 3000 km (1 detector only)Detector: 50 kt magnetized iron calorimeterParent muon energy: 50 GeV

Stored muons: 4× 1021 µ+, 4× 1021 µ−


Backup slides







Neutrino factory setupBaseline 3000 km (1 detector only)Detector: 50 kt magnetized iron calorimeterParent muon energy: 50 GeVStored muons: 4× 1021 µ+, 4× 1021 µ−


Backup slides


|εmeµ| = 0.5× 10−3

|εmeµ| too small

0 50 100 150 200 250 300 350∆CP

true @DegreesD

0

50

100

150

200

250

300

350

arg@HΕ

eΜmLt

rueD@D

egre

esD

1Σ

2Σ

3Σ

sin2 2Θ13true=0.01

dof=2

ÈHΕeΜm Ltrue È=0.0005


Backup slides


|εmeµ| = 0.5× 10−3

|εmeµ| too small

↓χ2 of standard oscillation fit isbelow 3σ for all true values of δCP

and arg εmeµ.

0 50 100 150 200 250 300 350∆CP

true @DegreesD

0

50

100

150

200

250

300

350

arg@HΕ

eΜmLt

rueD@D

egre

esD

1Σ

2Σ

3Σ

sin2 2Θ13true=0.01

dof=2



Backup slides


|εmeµ| = 0.5× 10−3

|εmeµ| too small

↓χ2 of standard oscillation fit isbelow 3σ for all true values of δCP

and arg εmeµ.↓

No chance for discovery

0 50 100 150 200 250 300 350∆CP

true @DegreesD

0

50

100

150

200

250

300

350

arg@HΕ

eΜmLt

rueD@D

egre

esD

1Σ

2Σ

3Σ

sin2 2Θ13true=0.01

dof=2



Backup slides


|εmeµ| = 0.6× 10−3

|εmeµ| becomes larger

↓For some combinations of δCP

and arg εmeµ, the standard

oscillation fit becomes worse than3σ (white islands appear).

↓Discovery possible for favorablephase combinations

0 50 100 150 200 250 300 350∆CP

true @DegreesD

0

50

100

150

200

250

300

350

arg@HΕ

eΜmLt

rueD@D

egre

esD

1Σ

2Σ

3Σ

sin2 2Θ13true=0.01

dof=2



Backup slides


|εmeµ| = 1× 10−3






0 50 100 150 200 250 300 350∆CP

true @DegreesD

0

50

100

150

200

250

300

350

arg@HΕ

eΜmLt

rueD@D

egre

esD

1Σ

2Σ

3Σ

sin2 2Θ13true=0.01

dof=2



Backup slides


|εmeµ| = 2× 10−3






0 50 100 150 200 250 300 350∆CP

true @DegreesD

0

50

100

150

200

250

300

350

arg@HΕ

eΜmLt

rueD@D

egre

esD

1Σ

2Σ

3Σ

sin2 2Θ13true=0.01

dof=2



Backup slides


|εmeµ| = 4× 10−3






0 50 100 150 200 250 300 350∆CP

true @DegreesD

0

50

100

150

200

250

300

350

arg@HΕ

eΜmLt

rueD@D

egre

esD

1Σ

2Σ

3Σ

sin2 2Θ13true=0.01

dof=2



Backup slides


|εmeµ| = 5× 10−3

|εmeµ| is large enough

↓χ2 of standard oscillation fitexceeds 3σ in the wholeparameter plane.

↓Discovery is possible for anyphase combination

0 50 100 150 200 250 300 350∆CP

true @DegreesD

0

50

100

150

200

250

300

350

arg@HΕ

eΜmLt

rueD@D

egre

esD

1Σ

2Σ

3Σ

sin2 2Θ13true=0.01

dof=2



Backup slides

Summary of the discovery reach for εmeµ

10-5

10-4

10-3

10-2

10-1

ÈHΕ eΜmLt

rueÈ

HΕeΜm Ltrue discovery reach H3ΣL for NuFact-II

Marginalize all Λ

sin2 2Θ13true=0.01

GLoBES

5× 10−3

?NSI effect can be discoveredfor all δtrue

CP and arg[(εmeµ)true].


Backup slides


10-5

10-4

10-3

10-2

10-1

ÈHΕ eΜmLt

rueÈ


Marginalize all Λ

sin2 2Θ13true=0.01

GLoBES

5× 10−3

?NSI effect can be discoveredfor all δtrue


5× 10−4

Hard to discover the NSI forany δtrue


6

Possible to observeNSI depending on δtrue

CP

and arg[(εmeµ)true].

��*


Backup slides


10-5

10-4

10-3

10-2

10-1

ÈHΕ eΜmLt

rueÈ


Systematics

Fix all Λ

Marginalize all Λ

sin2 2Θ13true=0.01

GLoBES

Discovery reach strongly depends onδtrueCP and arg[(εm

eµ)true].

Systematics and correlations in the fitdo not have a large impact.


Backup slides


10-5

10-4

10-3

10-2

10-1

ÈHΕ eΜmLt

rueÈ


Systematics

Fix all Λ

Marginalize all Λ

sin2 2Θ13true=0.1 sin2 2Θ13

true=0.01 sin2 2Θ13true=0.001

GLoBES

θtrue13 affects the discovery reach

only marginally

Signal ∝ θ13,Background (standard osc.) ∝ θ2

13


Backup slides

Discovery reach for εmeτ and εs

eµ in a neutrino factory

εmeτ εs

eµ

10-5

10-4

10-3

10-2

10-1

ÈHΕ eΜmLt

rueÈ


Systematics

Fix all Λ

Marginalize all Λ


true=0.01 sin2 2Θ13true=0.001

GLoBES

10-4

10-3

10-2

10-1

1ÈHΕ

eΤmLt

rueÈ

HΕeΤm Ltrue discovery reach H3ΣL for NuFact-II

Systematics

Fix all Λ

Marginalize all Λ


true=0.01 sin2 2Θ13

true=0.001

GLoBES


Documents

home.fnal.govhome.fnal.gov/~jkopp/pdf/ids2008.pdf · 2015. 11. 17. · Optimization of a neutrino factory for non-standard interactions Joachim Kopp Max-Planck-Institut für Kernphysik,