July 9th and 10th, 2007NUSS2007@Fermilab

Neutrino Cross SectionsNeutrino Cross Sections

Tsuyoshi NAKAYA (Kyoto University)

1

OutlineOutline1. Introduction

1. Neutrino Oscillation Experiments2. Role of neutrino cross sections3. !+e! !+e scattering

2. Cross Sections of ~MeV neutrinos2. Cross Sections of MeV neutrinos3. Cross Sections of ~GeV neutrinos4 C S ti f 10 100G V t i4. Cross Sections of 10~100GeV neutrinos5. Cross Sections of >TeV neutrinos6. Experiments for neutrino cross sections.7. Summaryy

2

Revolution of Neutrino PhysicsRevolution of Neutrino Physicsyy• Discovery of Neutrino mass.• Discovery of Neutrino Mixing.

• Unresolved Problems!– Neutrino Mass TypeNeutrino Mass Type– Neutrino Mixing Scheme (3 generation)– CP ViolationCP Violation– Sterile Neutrinos– Non-standard ! interactions?Non-standard ! interactions?–

Neutrino Oscillation Experiments are important!!Neutrino Oscillation Experiments are important!! 3

1. Introduction1. Introduction--11Neutrino Oscillation Experiments.

SuperSuper--KKK2KK2K

41.4

m

!2!1 !3

K2KK2K

Neutrino massesNeutrino masses ("m122 "m23

2)

39m

4 !2!1 !3

"m223

!# !$

!eNeutrino massesNeutrino masses ("m12 , "m23 )Mixing AnglesMixing Angles (%12, %23)

"m212

% & '44

SNOSNOKamLANDKamLAND

%13 & '

1 Introduction (1 1)1 Introduction (1 1)1. Introduction (1.1)1. Introduction (1.1)Neutrino Oscillation Experiments.Neutrino Oscillation Experiments.• Experimental condition:

– Solar Neutrinos ( )E!~ , L~ , "m2 ~ , (! ~ .! !

– Reactor Neutrinos ( )E ~ L~ "m2 ~ ( ~E!~ , L~ , "m ~ , (! ~ .

– Atmospheric Neutrinos ( , , , )2E!~ , L~ , "m2 ~ , (! ~ .

– Accelerator Neutrinos ( , , , )E!~ , L~ , "m2 ~ , (! ~ .

5

• Neutrino Targets:g– Solar Neutrinos:

• Gallex(GNO), SAGE, Homesatke, Kamiokande, Super-K, SNO

,Reactor Ne trinos:– Reactor Neutrinos:

• CHOOZ, KamLAND,

– Atmospheric Neutrinos:• Soudan2, Kamioaknde, Super-K, MINOS, MACRO, , p , ,

,– Accelerator Neutrinos:

• LSND, MiniBooNE, K2K, MINOS, OPERA, CCFR, CHORUS, NOMAD

,

6

• Neutrino Flux:– Solar Neutrinos:– Reactor Neutrinos:– Atmospheric Neutrinos:– Accelerator Neutrinos:Accelerator Neutrinos:

HOMEWORK: See the reference.

7

1. Introduction1. Introduction--22oduc ooduc o• Role of Neutrino Cross Sections

– In order to understand the results of neutrino oscillations including experimental designs andoscillations including experimental designs and methods, the understanding of neutrino interaction (cross section) is essential.(cross section) is essential.

– For experimentalists• It is essential for you to design an experiment and get• It is essential for you to design an experiment and get

reliable results.

For theorists– For theorists• The neutrino cross section is often used to estimate the

systematic error on the sensitivity of neutrino oscillationsystematic error on the sensitivity of neutrino oscillation. 8

N i f ti f ill ti t dNecessary information for oscillation study: • Neutrino flux measurement

C ti– Cross section• Neutrino energy measurement (reconstruction)

I t ti d ith th ti– Interaction modes with the cross sections.• What is the target?• KinematicsKinematics• How interaction modes will vary as a function of neutrino

energy?B k d ti t (& S t ti )• Background estimate (& Systematic errors)– Interaction modes with the cross sections.

• What is the target?• What is the target?• Kinematics• How interaction modes will vary as a function of neutrino

?energy?9

0

1

2

3

4

5

6

7

8

9

10

0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5E!

rec

Events

Normalized by areaExpectation

w/o oscillation

0

1

2

3

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5

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7

8

9

10

0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5E!

rec

Events

w/o oscillationBest Fit

0

1

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10

0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5E!

rec

Events

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0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5E!

rec

Events

0

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0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5E!

rec

Events

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• Keep the followings in your mind• Keep the followings in your mind.– Many types of neutrino targets, and they look different

with the neutrino energy.gy• Electron• quark

P t d N t• Proton and Neutron• Nucleus

– Charged current and Neutral Current Interactions.C a ged cu e t a d Neut a Cu e t te act o s.

Because of the above complexity the neutrino crossBecause of the above complexity, the neutrino cross section looks not easy for non-experts!

Let’s learn the physics of neutrino cross sections Let’s learn the physics of neutrino cross sections from the basic in this lecture!!from the basic in this lecture!!ff

11

1. Introduction1. Introduction--331. Introduction1. Introduction 33!!+e+e!! !!+e+e scatteringscattering

• Let’s review the QED process first, assuming m m m =0:assuming m!, me,m#=0:– e+e-!#+#- #e

qMif

4

2222

2

)*

+,

-.

1e e

sut

psee

dd

8)cos1(

4)(

2

2

22

2

22

2 *%*##(//0

+112

, 3-3-&

45353

#e2

1q

see

34)(

2)*##( -& 5353

12

• Review the QED process,– e-#+!e-#+6Text example (not real process)s!-t e e222*( /

+1, 3usds t e e

7 89 :21

8)(

42

22

%*

*##(//0

+112

, 3-&

43535

tus

pee

dd

e

Lab frame (muon rest frame).7 8 7 89 :2cos1

2sin84

42 %%

3-p

E %1'

# #EE

ypEpEe

e

%%

%.%. ##

1cos12cos1,2),cos1(

2

'

3

5---5- e

7 8 dydd

y

)%)

%%

4cos2

12cos1

2cos2

--4

5-3

-

22d 7 89 :24

2

112)( yq

seedyd

53-& 3535 )*##(

13

)4( 2

2

) pqy -

4)0,(

)4(

4

2

2

)*##()

qyee

dqd

p

-&& 3535

07 82sin4 222 %pqt --

• y!0– No muon recoil " Rutherford Scattering Formula

• Basic essence of lecture is all shown here.You are ready to look into neutrino cross sections with– You are ready to look into neutrino cross sections with this knowledge. If you cannot follow my lecture, please review

• “Introduction to High Energy Physics” by D.H. Perkins, Chapter 5

• “Quarks and Leptons” by F. Halzen and A.D. Martin, ChapterQuarks and Leptons by F. Halzen and A.D. Martin, Chapter 6 and 12

14

• QED! Weak InteractionQED ! Weak Interaction

7 8 222 ggM ;-

!eg7 8

222 2 WWif MMq

M ;3

-

W

! e7 8

2

3222

2 222)(

fif dq

ddEdppM

vee

dqd

+,

4-& 55

))!!( g

! e

2

222

2

2

82,

82

WW MgGG

Mg

<-//0

+112

,-

)) G=1.16639(1)=10-5GeV-2

sGeesGeedyd

)!!(

)!!((

22

)(,)( -&-& 5555

!!! EmmEmpps eeee 22)( 22 ;3-3-2

222 4dqsdy

sqpqy-

--

15The cross section is proportional to the neutrino energy!The cross section is proportional to the neutrino energy!

! e• How is anti-neutrino?– s!-t

! e

g gW

!7 81)( 2

255 5-& ysGee

dyd

)!!((

g

!e)(

31

3)(

25555 &--& eesGee !!(

)!!(

– At y=(Ee/E!)=1, the cross section is zero.– The average energy is E!/4. (Homework?)g gy ! ( )– Review the QED process

16

Charged+Neutral CurrentCharged+Neutral Current9 : 7 89 : 9 :>? @AG 17 89 : 7 89 : 7 8 7 89 :

BC>

DE?

5FG@

HIA 5355- eggeeeGH AVllee

FeffW 555 1

21211

25 ..!..!J..!!.. ##

##

1 22

### %

%ZJJgi EM

WW

)sin(cos

23 551

sin221sin2

3

223

5--5-

35-K5-3-

Tggg

QTggg

RLA

WWRLV %%

2230sin2 -%W23Tggg RLA

!e !eLM!#L !$ !eLM!#L !$

223.0sin -W%

W Z0CC NC

17! e e e

NC couplingsNC couplings223.0sin2 -W%

gL gR

e, #LM$ -½+sin2%W sin2%W

! ½ 0u,c,t ½-2/3*sin2%W -2/3*sin2%W

d,s,b -½+1/3*sin2%W 1/3*sin2%W

### %

%ZJJgi EM

WW

)sin(cos

23 55

18

7 89 : 7 89 : 7 8 7 89 :eggeeeGH AVlleeFeff

W 555 121211

25 ..!..!J..!!.. ##

##BC>

DE?

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# 5FG@

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• cv = Jgv+1 !ee- (!#e-: no -1: NC only)• cA= JgA+1 !ee- (!#e-: no -1: NC only)A JgA e ( # y)

– cL = ½*(cV +cA)=gL+1 for !e=gL for !#gL #

– cR = ½*(cV -cA)=gR 223.0sin2 -W%

@A mEmG 112 2

FG

@HI

A53-

!

!

)(

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RLRLe

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312 22

20

2 Cross Sections of ~2 Cross Sections of ~MeVMeV neutrinosneutrinos2. Cross Sections of ~2. Cross Sections of ~MeVMeV neutrinosneutrinos

• Neutrino SourcesNeutrino Sources– Solar Neutrinos (!e)– Reactor Neutrinos (!e)– Supernova Neutrinos (!e, !e, !#, !# , !$, !$)e e # # $ $

• How to detect the neutrinos?• How to detect the neutrinos?

21

Solar Neutrinos• Water Cherenkov Detector (Super-K, …)

+ ! + tt i d b th l t– !+e! !+e scattering, and observe the electron.– You already learn

• ((!e+e! !e+e ) ~ 6= ((!#+e! !#+e ) – How many neutrino events / day [Homework?]y y– Why do experimentalists work hard to lower the

threshold?threshold?• Super-K: Eth~5MeV or less • Kamiokande: Eth~6 5MeVKamiokande: Eth 6.5MeV• Super-K-II Eth~7.0MeV

22

23

• Detection of anti-neutrinosDetection of anti-neutrinos.– Is the cross section smaller than !+e!!+e scattering?

( ) 3 ( )• ((!e+e! !e+e ) ~ 3= ((!e+e! !e+e ) – We can use a proton in H2O or CH(KamLAND, ..)!

• Inverse beta decay: !p!e+n.• Native expectation (assuming a proton as a Dirac particle):

sGnepsGee)

!()

!!(3

~)(3

)(22

355 &N-&

• In reality, the proton is NOT a Dirac particle.!!! EmmEmpps pepepepe )(

2)()(

2)( 22)( ;3-3-

y, p p

7 89 : 7 89 :)(1)'(12

cos5

5 pugpueGH AeCFeff

W ..!..% ## 55-

24

• The matrix element (same as O decay) isThe matrix element (same as O decay) is

7 8 FG

@HI

A/0+

12, 533- %O%O%

! cos3

13cos182

cos21 2

222

AeCF gEEGT F

GHI 02 322

7 87 8

7 8 7 8 23

3

212

2221 TmmEE

Epd

Enep npe

ee 535-& 3 P !

!

'))

!(7 8

7 8222

31cos

2222

gEEG

EE

ACpeF

e

3-

!

%)

)

N f

– NOTE:

22

42

101030.9 cm

MeVE

/0+

12,=; 5 !

7 8 7 8

No free neutron

– NOTE: 7 8 7 8%

!(!(267.1,974.0cos --&-& 53

gpennep

AC

ee

Well known process and reliable calculation for the %%( cos104.01 5Qdd

low energy anti-neutrino (~MeV)!25

• For the higher energy anti-neutrinos, we must take into g gy ,account of the nucleon structure (form factor).

• Form Factor of the proton:p– Fourier transformation of the charge distribution.– In the case of exponential distribution: JM(r)=J(0)exp(-mr)

7 8 7 8 cos1232 )(cos2 eddrerNxdeeNqF rqimrxqimr -- 5K5 P PP %) %!!7 8 7 87 8 7 89 : 7 8

1

82

)(cos2

NeerdrN

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--

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P PP))

%)

N li ti

9 : 7 822230 1 mqmeerdr

qi 3P

33 81P NdN mrNormalization:

7 8 22

33

1

81

-

-N-P 5

qF

mNxdeN mr )

26

7 8 2

2

2

1 //0

+112

,5

mq

q

• In QEC (ep scattering), we can study vector form factorform factor.

• In the neutrino scattering, we study both vector and axial-vector form factors.– MV=0.84GeV/c2

V• The rms radius of the charge distribution is 0.8 fm.

– MA=1.05S0.05GeV/c2A

•!p!e+n is a good mode to detect the anti-neutrinos (Reactor and (Super-nova) because the higher cross section and the association of a neutron7 8 2421030.9 cmnepe

53 =;&!(

277 8 2421009.0 cmee ee

5=;& !!(

• How to detect the low energy solar neutrinos?– Use a NucleusUse a Nucleus

7 8 7 8T 35- eeeeiCF EZFmEEMG ,1cos 21222

22

!)%(

M!i: Nuclear Matrix element.F F i f ti f th ti f C l b

Ti)

F : Fermi function for the correction of Coulomb attraction between the electron and nucleus.

The point is that the proton in !+n!e+p must be at t t i th lsome state in the nucleus.

– We have to know the probability of transition b t t tbetween states.

28

• Example: Devis’s experiment– !e+37Cl !e-+37Ar– The lowest 37Ar state is not high g

transition probability.• Naive idea: The lowest state is

often occupied by a proton in advance.

• The coupling must be known.

!+n!e+pp

p n

29

• The cross section is not the sum of neutrons.• The accurate estimation of the cross section is• The accurate estimation of the cross section is

very difficult.– Need the experimental input of the nuclear matrix

element.

30

Dominant transitionDominant transition

• The cross section estimate is not simple.• The differential cross section as a function of• The differential cross section as a function of

energy is not simple, neither. 31

• In order to measure the lower energy gyneutrinos:– 71Ge is the ideal target nucleus– Ge is the ideal target nucleus.

– Gallex(GNO), SAGE

32

33

70!570!4 70!570!4

• Measurement of neutral current for neutrino oscillationoscillation.– !e! !e or !#, !$

N t i ill ti b ll fi d b– Neutrino oscillation can be well confirmed by measuring !# and !$ by NC.

• Deuterium (D O): SNO• Deuterium (D2O): SNO– CC: !+d!#$%&%&

NC +d! % % ( d d t t th t )– NC: !+d!!%&%' (and detect the neutron)

35

70!570!4 70!570!4

Cross Sections of 10~100MeV neutrinosCross Sections of 10~100MeV neutrinos• Nucleus Target

– Reliable calculation of cross section is not easy!

37

3. Cross Sections of ~3. Cross Sections of ~GeVGeV neutrinosneutrinos• It is the energy of accelerator neutrinos for the

long baseline.g• Dominant Interaction Mode

– Elastic scattering.g• CC: Quasi-elastic scattering.• NC: Elastic scattering.

1 d ti ith h d– 1 ) production with hadron resonance.– 1 ) production in coherent scattering.

Deep inelastic scattering– Deep inelastic scattering.• Not only the baseline interaction, but the

secondary interaction in the nucleus makes thesecondary interaction in the nucleus makes the story difficult– Tutorial by J. Morfin?

38

u o a by J. o ?

K2K Neutrino Energy U!M Reconstruction

+ + #-

CC quasi elastic (QE) CC inelastic

#-!# + n! # + p #

p

(E#, p#)%# !# + n! # + p + )

!

#(E#, p#)%#

## 5-2mEm

E2

N

p !p)’s

###! %35-

cospEmE

N inelastic

Rate(E!LNear) & V7E!LWear)X

QE

((QE), ((nonQE)

39

Q

CC Quasi-elastic scattering with nucleus• A Fermi gas model

– The interaction take place through quasi-free p g qscattering of nucleons contained in the non-interacting Fermil gas.g g

!kFB

#

40

• Nucleons in the initial state have momentum (Fermi momentum) ~200MeV/c

• The nucleon in the final state must have theThe nucleon in the final state must have the momentum above Fermi momentum surface.

P li bl ki " l Q2 i– Pauli blocking " low Q2 suppression.

41

• We must take into account of the form factors of a nucleon.7 8 2

2

2

22

1

1

//0

+112

,3

-5-V

MQ

qQF

7 8 22

2

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1

//+

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353

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EmQFFFmQF

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)(2)(24

)(22 F

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HI

353N

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N

NW mE

FFFm

F!

!

)()( 22 QFQF VW Q

F W k ti t tFW:Weak magnetism tensor term

42

• I wrote thatMA=1.05S0.05 GeV.

• However, each measurement has large error, and there may be nuclear dependence.

43

• CC quasi-elastic is one of the most well measured cross section in this energy range. Even so, the precision is NOT great!g– One of the study items in the next generation

experiment.experiment.

44

• CC 1) production: !N!#N)CC 1) production: !N!#N)(– The amplitude is sum of I=1/2 and 3/2 processes

t ib ticontributions.

2321)( AcNNA

ssI

II-&-T)#!

0

23

23,21

3232)(

)(

AApNA

ApNAsI

-&

-&"&5

35335

-

)#!

)##!

2123

2123

3231)(

3232)(

AAnNA

AApNA

3-&

5-&35 )#!

)#!

– C3/2 for " p3- )23,

23

pn

pn

5

3

3-5

3-

))

))

31

32

21,

23

32

31

21,

23

0

0

45n5-5 )

23,

23

3322

• The scattering matrix element through "++ isThe scattering matrix element through " is)()1()'(||

2 5 kkNAVGT F #..! Y#YY 55"-

• By introducing form factors,)(

2222

AN tCmmmsGd//+

11, 35 ""(

9 :2)()(

)(24

222

22

52

AA

AN

N

mmmmtCG

tCmmsdt

33//+

11,

-

//0

1125

;"

""

(

)

• (~4=10-38cm2 is good agreement with the

9 :2)()(72 5 AN

N

mmmm

tC 33//0

112

- ")(

• (~4=10 cm is good agreement with the !p!#-p)+ experiment for mp)<1.4GeV.

46

47

• For " resonance, we have 14 final state overall (6CC and 8NC)( )

48

• For other ) production process, we mustFor other ) production process, we must consider other " resonance including off-shell "’s" s.– What is the effect of A1/2?– R=|A1/2|/| A3/2 |=0.68S0.04

• The experimental result is consistent with a resonant I=3/2 amplitude in the presence of a large non-resonant I=1/2 background.

• Experimental results:1)(

0 -35 )#( n for A3/2

but experimental result is 0.96S0.122)( 05 )#( p 3/2

49

Coherent ) productionCoherent ) productionCC-coherent ) (!+A!#+A+))

#

!

)

Neutrino interacts coherently with nucleons bound in the nucleus, producing pion.

• may be too details as a lecture.

50

• DIS (Deep Inelastic Scattering) will be discussed in the next chapter since it is a dominant cross section at the high energy.g gy

51

4. Cross Sections of 10~100GeV neutrinos4. Cross Sections of 10~100GeV neutrinosC oss Sect o s o 0 00Ge eut osC oss Sect o s o 0 00Ge eut os• Deep inelastic scattering

– Scattering with a quark in a nucleusExample: a proton with the ! beamExample: a proton with the !# beam– !#+d! #5+u scattering

Gdd C%( 222 cos)(

• x (Feynman x) is the momentum fraction of the quark i th t

xsGuddxdyd C

)%#!((

#cos)( -& 5

in the proton.

– Anti-quarks exist in a proton as a sea quark.

7 82222

1cos)( yxsGdudxdyd C 5-& 5

)%#!((

#

52

53

– In the proton, we define the quark distribution function: u(x), d(x), s(x), …. The cross section with a proton is

– In the case of neutron by using the isospin7 89 :2

222

1)()(cos)( yxuxdxsGpdxdyd C 53-

)%!((

#

In the case of neutron, by using the isospinsymmetry (dn (x)=up(x)),

7 89 :2222

1)()(cos)( dGd C 3%!(

– In the case of isoscalar target (Tn= Tp)7 89 :1)()()( yxdxuxsn

dxdyC 53-

)!( #

9 : 9 :7 8Z [2222

1)()()()(2

cos)( yxdxuxdxuxsGNdxdyd C 5333-

)%!((

#

– For anti-neutrinos,9 :7 8 9 :Z [)()(1)()(cos)( 2

222

ddGNd C 333%!(

54

9 :7 8 9 :Z [)()(1)()(2

)( xdxuyxdxuxsNdxdy

C 3353-)

!( #

9 : 9 :+,

3-3- PPEG

dxxdxuxQdxxdxuxQ ,)()(,)()(22 %7 8

7 8 +,

/0+

12, 3-

EmG

QQEmG

N pC

1cos31cos

22

22

%)%

!(

7 8 7 8

7 8 /0+

12, 3- QQ

EmGN pC

31cos

)%

!(

7 8 7 815.0

2;N

=;

QQNN !(!(

• This example is CC

QQ

This example is CC current.

55

• NC current:• NC current:

9 :)()1()( 12

1

22

xqyxxxqsGd53-//

+11,

J( 9 :

9 : 9 :9 : 9 : )()()(4)()()(4)(

)()()(4)()()(4)(

)()()(4

2222

22221

11

ddxqdgugxqdgugxq

qyqdxdy

RRLL

NN

333-

//0

112 &

J)!!

– What is gL(u), gR(u), gL(d), gR(d)?

9 : 9 : )()()(4)()()(4)( 22221 xqdgugxqdgugxq RRLL 333-

### %

%ZJJgi EM

WW

)sin(cos

23 55%Wcos

gL gR

M ½+ i 2% i 2%e, #LM$ -½+sin2%W sin2%W

! ½ 02 2

56

u,c,t ½-2/3*sin2%W -2/3*sin2%W

d,s,b -½+1/3*sin2%W 1/3*sin2%W

XNXNNR CC

NC

)()()(

3&3&

-!!(!

9 :XN

rXN

NCWW

CC

)(

sin)1(95sin21)(

42 335-

3&

J%%#!(

9 :XNXNNR CC

NC

i)11(95i21)()()(

42

3&3&

-

%%#!(!!(!

9 :

QQQQ

XNXNr

r WW

3131

)()(,

sin)11(95sin21 42

3-

3&-

335-

5

3#!(

J%%

QQXN 31)( 33& #!(

• FNAL NuTeV experiment measured this quantitiesquantities.

57

NuTeV results on R! and R!barNuTeV results on R! and R!bar

• NuTeV result:

0016.02277.0.)(0009.0.)(0013.02277.0sin )(2

S-SSS-5 syststatshellon

W%

• Standard model fit (LEPEWWG): 0.2227 S 0.00037A 3( discrepancy…

R

differenceSMR

S

\

S-

0027040500

3)3950.0:(

0013.03916.0exp

!

!

(

agreementGoodSMR

\

S-

)4066.0:(

0027.04050.0exp

58

5 Cross Sections of >5 Cross Sections of >TeVTeV neutrinosneutrinos5. Cross Sections of >5. Cross Sections of >TeVTeV neutrinosneutrinos

• Neutrinos are an important particle to search for astrophysical sources.p y– Example: ICE-Cube experiment.

The energy of neutrino is much higher than that– The energy of neutrino is much higher than that available by an accelerator.B i i i i DIS i h i– Basic interaction is DIS with some corrections.

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HOMEWORK: For an example how long is theHOMEWORK: For an example, how long is the interaction length of 100TeV neutrino in ice?

60

6 Experiments for neutrino cross sections6 Experiments for neutrino cross sections6. Experiments for neutrino cross sections 6. Experiments for neutrino cross sections • Neutrino detectors in the short baseline oscillation

experiment– NuTeV, NOMAD, CHORUS, MiniBooNE

• Near neutrino detectors in the long baseline oscillation experiment.– K2K, MINOS, T2K, NO!A

• Dedicated experiments to measure the neutrino ticross section

– SciBooNE, MINER!A!SNS– !SNS

• study the cross section of ~O(10MeV) for Supernova detection.

61

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63

MINER!A at NuMI (start in 2009)MINER!A at NuMI (start in 2009)

• Need a high granularity detector (like SciBar) but in aNeed a high granularity detector (like SciBar) but in a higher energy beam and with improved containment of . M)! M#of .LM) LM#

!

• MINER!A at NuMI" “chewy center” (active target)

12-15 August 2006 Kevin McFarland: Interactions of Neutrinos 64

" chewy center (active target)" with a crunchy shell of muon, hadron and EM absorbers

65

7. Summary7. Summaryyy• Understanding of neutrino cross section is a good

exercise to review the standard modelexercise to review the standard model.• In reality, the reliable estimation is not easy

because of the nuclear (and nucleon?) structurebecause of the nuclear (and nucleon?) structure.– Experimental Inputs and model buildings are essential!

• The next generation precision oscillationThe next generation precision oscillation experiments request the precise information of neutrino cross sections.– Including the final state kinematics (although I did not

fully cover this topics in the lecture).•

Play together with neutrinos!Play together with neutrinos!y gy g66

ReferenceReferenceReference Reference materialsmaterialsmaterialsmaterials

67

Neutrino ExperimentsNeutrino Experiments

• KamLAND, Super-K, SNO, Borexino, GNO, Homestake, one more,

• LSND, KarmenK2K T2K S K MINOS S d 2• K2K, T2K, Super-K, MINOS, Soudan2, MACRO, MiniBooNE

• NuTeV, CCFR, OPERA, CHORUS, NOMAD S iB NE MINER A• SciBooNE, MINERnA

68

SNOSNO

69

1 Introduction1 Introduction1. Introduction1. IntroductionNeutrino Oscillation Experiments.Neutrino Oscillation Experiments.• Experimental Condition:

– Solar Neutrinos (!e)E!~ 0.1~15MeV, L~1.5=108km, "m2 ~>10-11eV2, (! ~ 10-43cm2.

– Reactor Neutrinos (!e)E ~ 1~9MeV L~1~100km "m2 ~>10-5eV2 ( ~ 10-41cm2E!~ 1~9MeV, L~1~100km, "m2 ~>10 5eV2, (! ~ 10 41cm2.

– Atmospheric Neutrinos (!e, !e, !#, !#)E!~ 20~>105MeV, L~10~1=104km, "m2 ~>10-4eV2, (! ~ 10-42~10-36cm2.

– Accelerator Neutrinos (!e, !e, !#, !#)# #

E!~ 20~105MeV, L~0.01~1000km, "m2 ~>10-3eV2, (! ~ 10-42~10-36cm2.

• Neutrino Targets:• Neutrino Targets:– Solar Neutrinos:

• Gallex(GNO) SAGE Homesatke Kamiokande Super K• Gallex(GNO), SAGE, Homesatke, Kamiokande, Super-K, SNO

Ga, Cl, H2O, D2O and e- ,2 2

– Reactor Neutrinos:• CHOOZ, KamLANDC (Carbon),

– Atmospheric Neutrinos:• Soudan2, Kamioaknde, Super-K, MINOS, MACROFe, H2O , CH

Accelerator Neutrinos:– Accelerator Neutrinos:• LSND, MiniBooNE, K2K, MINOS, OPERA, CCFR,

CHORUS, NOMAD,Carbon, H, Fe, H2O, and other Nucleus

71

Neutrino FluxNeutrino Flux

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Reactor Neutrinos

• KamLAND Flux: 2=106cm-2s-1

– 70GW reactors at 100 – 250 km away74

Accelerator neutrino fluxAccelerator neutrino flux

75

Atmospheric neutrino fluxAtmospheric neutrino flux

76

Cosmic Ray fluxCosmic Ray flux

• Features of atmospheric neutrino fluxneutrino flux.

77

Supernova neutrino fluxSupernova neutrino flux

78

Geo neutrino fluxGeo-neutrino flux

79