PHYSICS OF THE NEUTRINO FACTORY (AND FRIENDS) J.J. Gmez Cadenas - - PowerPoint PPT Presentation

SLIDE 1

PHYSICS OF THE NEUTRINO FACTORY (AND FRIENDS)

J.J. Gómez Cadenas IFIC (CSIC-UV) Lecture II

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LECTURE II

• Matter matters
• Degenerate physics
• Design your experiment

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TRAVEL IN MATTER

• In a NuF, rates grow with muon energy (flux

& cross sections increase with E)

• To work at the oscillation peak one needs

long baselines (~5000 km at 10 GeV)

• This implies that the neutrino beam travels

through Earth.

• But Earth is less transparent to νe than to

νμ, ντ

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THE MATTER PARAMETER A

• The fact that νe (both neutrinos and antineutrinos) have charged current elastic scattering

interactions on the Earth electrons introduce effective “masses” for the electron neutrinos m= ± 2EA, where A is the matter parameter

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MATTER IMPORTANT AT LARGE L

A = 2GFne ne is electron number density

eV 2 GeV

km

A increases with L Matter effects important at large L

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P

atm = sin223 sin2 213 sin2 1.267matm 2 L

E

• s23

2 sin2 213 sin2 23L

2

• ,

23 = 2.534matm

2

E P

sun = cos223 sin2 212 sin2 1.267msol 2 L

E

• c23

2 sin2 212 sin2 12L

2

• ,

12 = 2.534msol

2

E P

int = J cos ± 1.267matm 2 L

E

• 1.267msol

2 L

E

• sin 1.267matm

2 L

E

• J 12L

2

• sin 23L

2

• cos ± 23L

2

• Matter : B = A 23

A 0 B = 23 A 23 B is different for and : "Fake CP violation effect" Matter effects can be described by the following (golden) formula: A 12 : Effective neutrino mass shorten solar oscillation B 23 :Matter distinguishes between and P

atm = s23 2 sin2 213

23 B

• 2

sin2 BL 2

• P

atm is now different for and

P

sun = c23 2 sin2 212

12 A

• 2

sin2 AL 2

• P

sol amplitude controlled by A not by 12

P

int = J 12

A

• 23

B

• sin AL

2

• sin BL

2

• cos ± 23L

2

• Extra "fake" CP violation in P

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L=300 KM, NEGLIGIBLE EFFECT

• -- Patm
• -- Patm
• -- Psol

in matter

• -- Psol

in vacuum

• -- Pint
• -- Pint
• -- Ptot
• -- Ptot

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L=1000 KM, ATM TERM SEES EFFECT

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L=3000 KM STRONG ATM EFFECT

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L=10,000 KM ALL IS MATTER

• At L=10000 Km (E=30GeV) matter effects are also important for solar term and will

mask completely any oscillation effect

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L=300 KM NO FAKE CP

• -- Ptot, = 90 in vacuum
• -- Ptot, = 90 in vacuum
• -- Ptot, = 0 in matter
• -- Ptot, = 0 in matter
• -- Ptot, = 90 in matter
• -- Ptot, = 90 in matter

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L=1000 KM, TRUE CP LARGER THAN MATTER CP

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L=3500 KM, TRUE CP SAME ORDER THAN MATTER CP

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L=10,000 KM, TRUE CP MUCH SMALLER THAN MATTER CP

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MEASURING THE SIGN OF MATTER

• The bad news: Matter effects are large at

large distances. For a high energy neutrino factory one is prevented to go to the

• scillation peak and has to work in the

“lineal region” where one is less sensitive to ACP.

• The good news: Because matter effects are

large, one can use them to find out the mass hierarchy, that is the so-called, “sign of matter”.

• Notice that B changes sign depending on

whether the sign of matter is “positive” or negative”.

Matter : B = A 23

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SLIDE 16

matm

2

> 0 matm

2

> 0 matm

2

< 0 matm

2

< 0

L = 300Km L = 300Km L = 800Km L = 800Km

MEASURING THE SIGN OF MATTER

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MEASURING THE SIGN OF MATTER

matm

2

> 0 matm

2

> 0 matm

2

< 0 matm

2

< 0

L = 3500Km L = 3500Km L =10000Km L =10000Km

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SLIDE 18

HOMEWORK

• You are the owner of a tunable beta-beam facility.
• Choose a neutrino beam energy
• Choose baseline
• Choose detector technology (explain your reasons)
• Explain your physics program
• Repeat the game for a tunable neutrino-factory.
• Compare both facilities
• Since matter matters. What is your criteria now to choose a baseline?

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