Interazioni di neutrino

pπ0

π+γe+

e-

µ+

νµ

9

Ordini di grandezza delle sezioni d’urto di particelle subnucleari

• Al fine di avere un’idea delle diverse intensità delle interazioni fondamentali, consideriamo proiettili di tipo diverso (p, γ e ν)che urtino contro lo stesso bersaglio, un protone.

• Le sezioni d’urto, in genere, dipendono dall’energia. Poiché la variabile fisicamente rilevante è l’energia nel centro di massa, concentriamoci su uno stesso valore, ad es.: √s = 10GeV

• Assegnamo a un protone una dimensione dell’ordine di rn= 1fm=10-13 cm*.• La tipica sezione d’urto geometrica che ci aspettiamo è dell’ordine di

σG= π rn2 ≈ 3fm2=3 10-26cm2.• Dalle sezioni d’urto misurate σ potremo estrarre una probabilita’ di interazione

comew= σ / σG .

• *un protone, in realtà, non ha un raggio definito come quello di una sfera rigida, e le sue dimensioni dipendono dalla sonda con cui lo si guarda. Lo studio della diffusione elastica di elettroni su protoni fornisce un raggio medio per la distribuzione di carica all’interno di un protone un raggio medio rp=0.8 fm

10

La sezione d’urto protone protone

pL[GeV/c]

√s[GeV]

• Il grafico mostra σel e σtot in funzione dell’impulso del protone proiettile pLe dell’ energia equivalente nel c.m. √s*• Le σ sono misurate in millibarn, sottomultiplo di un’unitàfrequentemente utilizzata in fisica nucleare e subnucleare:

1 barn=10-24cm2 →1mb=10-27cm2.• La sezione d’urto elastica decresce all’aumentare dell’energia, in conseguenza del

fatto che all’aumentare dell’energia di collisione diventa sempre più improbabile lasciare intatte le particelle che urtano.

• La sezione d’urto totale, al di sopra di √s≈ 3 GeV è approssimativamente costante. Dunque aumenta σin, come conseguenza delle produzione di particelle, principalmente pioni**

*Ricordare che s=2mpEL+2mp2 e inoltre EL=(mp2+ pL2)1/2.** Calcolare il valore di soglia per la produzione di 1 pione, e confrontarlo col picco di σinin figura.

11

La probabilita’ di interazione protone protone

• Su un ampio intervallo di energie sopra la soglia per la produzione di pioni la sezione d’urto totale è approssimativamente costante

• A √s =10 GeV ho σtot (pp)=4 10-26 cm2. La probabilità media di interazione èdunque:

w(pp) = σtot (pp) / σG ≈ 1• cioè due protoni, se si avvicinano a distanze dell’ordine di un fermi interagiscono

con probabilità dell’ordine di uno.

pL[GeV/c]

√s[GeV]

12

La sezione d’urto fotone protone

• La sezione d’urto totale fotone protone ha un comportamento simile a quella pp: si notano i picchi della fotoproduzione di pioni e altri mesoni, quindi una zona in cui σ(γp) è essenzialmente piatta e infine una lenta risalita.

• La carattersitica principale è che, come ordine di grandezza, a parità di s:σtot (γp) ≈1/400 σtot (pp)

• Cioè la probabilità di interazione di un fotone è circa 400 volte inferiore a quella di un protone:

w(γp) ≈1/400 w(pp)

10-2

10-1

13

Le sezioni d’urto neutrino protone

• La sezione d’urto totale neutrino ( o antineutrino) protone ha un comportamento ben diverso da quello della pp, in quanto cresce linearmente con l’energia Eν del neutrino incidente

• Dunque cresce con il quadrato dell’energia nel c.m. poiché per energie alte s= 2Eνmp +mp2 ≈ 2Eνmp

14

La probabilita’ di interazioneneutrino protone

• A √s =10 GeV corrisponde un energia dei neutrini Eν= 50GeV.

• La sezione d’urto di neutrini èdunque σtot= 3.5 10-37cm2, mentre per la collisione pp era dell’ordine di 4 10-26 cm2.

• A questa energia le probabilità di interazione dei neutrini sono dunque

w(νp) ≈ 10-11.• Le probabilità di interazione dei

neutrini crescono con la loro energia (e dunque con l’energia nel centro di massa).

• Questo comportamento non può valere per energie arbitrariamente alte, perché una probabilità non può superare l’unità.

• Sappiamo che per energie nel c.m del ordine di √s ≈ 100 GeV (Eν ≈ 500GeV) il comportamento cambia, e le probabilità di interazione dei neutrini diventano dello stesso ordine di grandezza di quelle di fotoni ed elettroni.

√s =10 GeV

26

La diffusione di neutrini in una proto-stella di neutroni• I neutrini possono attraversare generalmente enormi distanze

senza effettuare urti, e dunque possono essere usati come “sonda”dell’interno di una stella come il sole, ma non sempre è così…

• Nell’esplosione di una supernova si forma una “protostella di neutroni”, un sistema estremamente denso ( M≈Msole e raggio r ≈ 10 km) caldo. Nella formazione di questo sistema si produce un’energia E ≈ GM2sole /r ≈ 4 1046J (confrontabile con quella prodotta da tutta la galassia in 30 anni), irraggiata principalmente sotto forma di neutrini, perché la stella è estremamente opaca alla radiazione e.m.

• Stimiamo il tempo necessario perché i neutrini possano emergere da questo sistema e dunque raffreddare la stella.

• Le densità di nucleoni sono: n ≈ 1057/ (4 1018cm3) ≈ 2.5 1038cm-3• Le temperature del sistema sono dell’ordine T ≈ 4 1011 oK kT ≈ 30 MeV e

vengono prodotti neutrini con energie dell’ordine di kT• Neutrini con queste energie* (termiche) hanno σ ≈ 10-40cm2 e dunque lunghezze

di collisione :λ=1/nσ ≈ 1/[(10-40 cm2)(2.5 1038cm-3 )] -> λ ≈ 40 cm

• Poiché λ

NeutrinoLand

νe

Sun

νµ, νµ-barνe, νe-bar

Atmosphere(Cosmic Rays)

νe, νe-baretc...

SupeNovae

Natural Sources

νe-bar

Reactors

νµ-baretc...

Beam Dump

νµ

Short/Long Baseline

Accelerators

Artificial Sources

Neutrino Sources

100 KeV 1 MeV 10 MeV 100 MeV 1 GeV 10 GeV 100 GeV 1 TeV

Eν

Neutrino interactions from 100 keV to 100 GeV

from the“Standard Solar Model”

BP00: astro-ph/0010346

%10±

%1± %10±

%5.1±

%16%20

−+

?±

The Solar Neutrino Spectrum

Neutrino Cross Section

Neutrino Cross Sections are as important as Stellar Models in determining the predicted rates in solar neutrino detectors

(often uncertainties in ν cross sections are larger than uncertainties from solar model fluxes)

Three types of reactions have to be considered (in the “Low Energy” range):

νe + AZ → e− + AZ +1

ν x + AZ → νx + AZ

ν x + e− → νx + e

−

Absorption reaction on nuclei A(Charged Current - e-flavor)

Elastic scattering on electrons(Charged Current - e-flavor

and Neutral Current - x=e,µ,τ flavors)

Elastic scattering on nuclei A(Charged Current - e-flavor

and Neutral Current - x=e,µ,τ flavors

Fundamental couplings. There is until now no indication that neutrinos interact by any other nonstandard way.

Charged current

Neutral current

(1) Absorption Reactions (Inverse β decay)

Absorption Reactions: the incoming ν is absorbed, an electron is created, and a neutron in thetarget Nucleus (A) is transformed into a proton. (with detection of electron and/or of AZ+1)

Dominant transitions are ALLOWED transitions:

∆ J = 0 (Fermi Trans.), ±1 (Gamow- Teller Trans.)

∆ π = 0

Nuclear spin change

Nuclear parity (no change)

Absorption Cross Section can be written in terms of atomic and kinematic factorstimes the nuclear matrix element (representing the n-p transformation):

σ = σ o × pe We F Z,We( )σo = k Mi → f

2

M 2 = B F( ) + B GT( )

where

F : Fermi function

σo 10−46cm 2[ ]: transition matrix element

B(F) : Fermi Matrix Elements B(GT) : Gamow - Teller Matrix Elements

In particular, SUPER-ALLOWED transitions: ∆I = 0 (Isotopic Analogue State Trans.)

νe + AZ → e− + AZ +1

B(F) and B(GT) (⇒ σo) can be evaluated with shell-model calculations (high precisionfor B(F)) and comparedwith experimental data from half-life measurements of inverse nuclear processes (e.g. Electron Capture) by symmetry relations.

• The emitted electron energy We is given by:

We = Eν − ∆Enucl with ∆Enucl being the nuclear mass difference

• The Fermi function F(Z, We) takes into account corrections due to finite nuclear size and electron screening (important effect for high Z materials)

(FORBIDDEN reactions provide small corrections in the “Low energy” range)

Target Nuclei in some present (past & “future”) experiments

• 71Ga : GALLEX (now GNO) and SAGE

• 37Cl : HOMESTAKE

• 2H : SNO

• 40Ar : ICARUS

3/2-

1/2-

71Ga

71Ge 0.233 MeV

0.500 MeV

3/2-

3/2+

3/2+

37Cl

37Ar

0.814 MeV

0+

4+

40Ar 40K 1.505 MeV

4.384 MeV

0+ 40K*

IAS

IAS

ν D p

p+ e

•  The simplest hadronic system – a single nucleon at low (a few MeV) energies

The neutron decay and the antineutrino capture on proton are governed by the same hadronic matrix element: n → p + e- + νe (neutron decay) νe + p → n + e+ (inverse neutron decay)

Knowing the neutron lifetime, τn = 885.7(0.8), f = 1.715, fixes the cross section for the relevant energies: σtot=(2π2/me5)/fτn x Eepe or [2π2(hc)3]/[(mec2)5fτnc]pecEe (Ee,pe are the energy and momentum of the positron, Ee = Eν - (Mn - Mp + me))

Note, however, that life is not simple even in this “classical” case. The measurement of Serebrov et al. (2005) gives τn = 878.5 ± 0.7±0.3, which differs from the official 885.7±0.8 by ~9σ; it is not yet clear which is correct.

The neutron lifetime fixes cross section of all processes involving a single nucleon, e.g., νe + n → p + e- or ν + p(n) → ν + p(n) (neutral current)

Neutrino interaction with the simplest nucleus, deuteron, at low energy:

There are no bound states in d, the only open channel is the deuteron disintegration. Consider the CC scattering νe + d p + p + e-

The tree level cross section at low energies is

(dσ/dE)tree= 2GF2/π Vud2gA2MppeEep |I(p2)|2,

where p is the relative momentum of the outgoing protons and the overlap integral is I(p2) = ∫ u*cont(pr) ud(r) dr,

This integral depends on the pp scattering length, effective radius, and on the deuteron binding energy. It is peaked at low values of p2/Mp and is about 1 MeV wide in that variable

What about ν interaction with complex nuclei?

At lowest energies we must consider exclusive scattering to specific bound (or resonance) nuclear states. At somewhat higher energies we are typically interested in the inclusive scattering, summing over all possible nuclear final states.

The initial state is usually the nuclear ground state. However, in various astrophysics applications the temperature might be high enough that excited states are populated as well.

Essentially absent is the truly elastic (NC) scattering, never observed as yet. Note that at low energies (Eν < 50 MeV) such scattering is coherent with the maximum nuclear recoil energy of only ~Eν2/(Axmp), thus very difficult to observe, even though the cross section is enhanced σtot ~ GF2 Eν2 N2/4π .

Expected rates calculations

ν Absorption cross-section “averaged” over single flux component energy spectrum

σ f = σ Eν( ) λ f Eν( )Eν

min

Eνmax

∫ dEν ; f = pp, 7Be, 8B, ...

λ f = normalized energy spectrum

Eνmin = ∆Enucl + me + Ethr( )

Nevt = SNU × Ntarg × ∆t ; Ntarg =N AvA

g−1[ ]× 106 × MDet t[ ]

SNU 10-36s −1[ ] = σ f 10-46cm 2[ ] × Φ f 1010cm 2s−1[ ]

e.g. ≈ 30 evtt ⋅ yr

of Ga target, ≈ 2 evtt ⋅ yr

of Ar target

Elastic Scattering on Electrons

ν x + e− → νx + e

−

Important Diagnostic Features:• angular distribution, strongly peaked in the forward direction of the Earth-Sun axis• electron energy spectrum, reflecting the solar neutrino spectrum• cross-section magnitude, sensitive to neutrino flavor• time information, sensitive to flux modulation.

CC+NC (purely leptonic F. Diagrams)

Main characteristic (vs Absorption reactions):(neglecting atomic binding) there is nothreshold on the ν minimal energy in producing Electron (i.e. Eνmin=0.)

The actual ν energy defines the max value of the electron kinetic energy:

Temax =

2Eν2

me + 2Eν

The total cross-section, calculated at specific ν energy, parametrically depends on the minimal kinetic energy of the emitted electron

σES = σ e f Eν ;Temin( ) ; where : f Eν ;Temin = 0.( )≈ 1k MeV ][ ]Eν

The differential cross-section for producing a recoil electron with kinetic energy Teby scattering with a neutrino of initial energy Eν is:

dσ ESdTe

= σ e × gL2 + gR

2 1 − TeEν

2

− gLgRmeTeEν

2

where : gL = ± 12 + sin2 θW( ) ; gR = sin2 θW

+ ⇒ νe ; − ⇒ νµ ,τ

and : σe = cost 10-46cm 2[ ]

Target material in present (past & “future”) experiments

• H2O : SuperKamiokande (SK)(Kamiokande)

• 2H2O : SNO

• 40Ar18 : ICARUS

ZH2O = 2 + 8 = 10 ; EthrSK = 5MeV

ZH2O = 2 + 8 = 10 ; EthrSNO = 5MeV

ZAr = 18 ; EthrICARUS = 5 ÷ 7MeV

Expected rates calculations

ν Elastic Scattering cross-section “averaged” over single flux component energy spectrum

σ f = σ Eν( ) λ f Eν( )Eν

min

Eνmax

∫ dEν ; f = 7Be( ), 8B, hep

λ f = normalized energy spectrum

Eνmin = E

thr

Detector

SNU = σ f 10-46 cm 2[ ] × Φf 1010cm −2s−1[ ]

Nevt = SNU × Ne -targ × ∆t ; N e -targ = ZN AvA

g−1[ ]× 106 × MDet t[ ]

e.g. ≈ 12 evtt ⋅ yr

reducing to ≈ 1 evtt ⋅ yr

for E ethr = 5MeV

Reactor are emitted in the same (“Low”)energy range of Solar-ν: the interaction cross-sections with matter are established by the theoretical models discussed in the Solar neutrino section

The average energy distribution for the energy released per fission with a thermal neutron in uranium-235

The tremendous anti-neutrino flux produced by nuclear reactors ( per second for a 2800 MW reactor) already led to the neutrino experimental discovery.

Energy Spectrum

~2 < Eν < 9 MeV

Source Flux

[1010 cm-2 s-1]

EnergySpectrum

EnergyMean Value

(Eν>2MeV)[MeV]

Energy

End Point[MeV]

235U239Pu

Fission- 2000 Cont. - 3 - 9

λR

Source

Flux

[1010 cm-2 s-1]

Energy Spectrum

Energy

Mean Value

(E>2MeV) [MeV]

Energy

End Point [MeV]

235U 239Pu Fission

≈ 2000

Cont.

≈ 3

≈ 9

leaving as signature a prompt light pulse corresponding to the positron annihilationfollowed by a delayed light pulse from the de-excitation after neutron capture.

Anti-neutrinos interact with protons in the target through the inverse beta decay reaction:

The reaction has a threshold on neutrino energy:

The detection technique is generally very similar to that pioneered by Reines and Cowan experiment: a large tank of liquid scintillator(CnH2n+2 hydrocarbon molecule rich in H, n >20) doped with an element (Cd) adequate for neutron capture is exposed to the neutrino flux.

ν e + p → e+ + n

Eν Thr = Mn − Mp( )+ me = 1.805 MeV

The gold-plated reaction!!

•Precise cross-section calculation•Low threshold•Unambiguous signature•Target availability

Fermi Theory:In 1933 E. Fermi assumed that an electron and anantineutrino are produced in the process

eν

n

pand calculated the n-decay matrix element.

Cross Section

σ = σ 0 × pe We ; where σ 0 10-42 cm 2[ ]: trans. matrix element

and We = Eν - (Mn - Mp )

ν e + p → e+ + n

σR = σ Eν( )∫ λR Eν( ) dEν ≈ 2 ×10−45cm2 averaged over Reactor ν-flux

"SNU" 10−36 s−1[ ]= σR × ΦR ≈ 4 ×104

Evt. Rate : Nevth

≈ 3 − 4 for a detector Mass of 0.2 t

If the interaction responsible for the decay of the neutron is known, one can connect the cross section of theprocess, at the small reactor energies, with the lifetime of the neutron.

Neglecting small corrections due to neutron recoil, the total cross section of the process is given by:

νµ

νµDetectorνµ

Neutrino fluxes from decay of Pion and Muon at rest (“beam dump neutrinos”) have well defined energy spectra (and angular distributions). The neutrino energy range encompasses the solar & reactor range and extends up to about 50 MeV (the “Moderate Energy” range). The interaction cross-sections with matter can be established by the theoretical models discussed in the Solar&Reactor neutrino sections…. but need some further deepening.

p-beamπ µ

e

νε

Cu Block

νµ

p

H2O

π − → µ− + ν µ ; µ− → e− + ν e + νµ

π + → µ+ +νµ ; µ+ → e+ + νe +ν µ

Weak Processes: leptonic decay

µ-νµ

e-

νe

W-

π−d

uµ-

νµ

Range of investigation

DominantChannel:• N(π+) > N (π- )• π- and µ- are captured

Shape of theNeutrino Flux

The signature for a interaction in a liquid scintillator detector is the reaction:ν e

followed by n + p d + γ (2.2 MeV)

… the same signature exploited with reactor neutrinos at lower ν energy.

The reaction has a threshold on neutrino energy:

ν e + p → e+ + n

Eν Thr = Mn − Mp( )+ me = 1.805 MeV

LSND Experiment@ Los Alamos Meson Physic Facility:

• 200 m3 of Liq.Scint. (ρ=0.85)

σBD = σ Eν( )∫ λR Eν( ) dEν ≈ 4 ×10−41cm2 averaged over BeamDump ν-flux

"SNU" 10−36 s−1[ ]= σBD × ΦBD ≈ 0.1

Cross Section (Fermi Theory):

See formulas from “Reactor Neutrino” section

σ = σ 0 × pe We ; where σ 0 10-42 cm 2[ ]: trans. matrix element

and We = Eν - (Mn - Mp )

NB: σ increases ≈ quadratically with ν energy. Compared to the Reactor experiments,at the higher energies (>36 MeV) investigated at beam dump experiments, larger cross section compensate lower flux(… but cross-section calculation with Fermi Theory not fully adequate).

The negligible expected rate makes the search for oscillationvery effective due to the much larger flux (22 events have been detected !! by LSND).

Evt. Rate : Nevtyr

≈ 4 − 5 (!!!) for a detector Mass of 180 t

ν e ν µ → ν eν µ

• SN-type II: temperature hierarchy among ν flavors (Tνe < Tνµ)

• Tνe = 3.5 MeV ⇒ = 11 MeV• Tνµ = 8.0 MeV ⇒ = 25 MeV

• Energy spectra: Fermi-Dirac distribution• SN @ 10kpc (53% of stars in the galactic disk), E=3X1053 erg

Supernova Neutrinos in the SN “electron neutrino heating “ hypothesis

Among SN detectors, only ICARUS has a signal dominated by νe flux !!!

ICARUS: νe + 42Ar ⇒ e + 40K (F + GT)(Q = 5.9 - 4.2÷7.9 MeV)

• SN signal is usually dominated by νe on free proton• Detector based on νe reactions may contribute significantly

in case of “νe MSW oscillation mechanism”: SuperK: νe + 16O ⇒ e + 16F (Q=15.4 MeV) LVD, Borexino, KamLand, Baksan :

νe + 12C ⇒ e + 12B (Q=17.4 MeV) SNO: νe + D ⇒ e + p + p (Q=1.4 MeV)

•Statistics (no threshold): ES - 13 evt/kTonAbs (F+GT) - 50 evt/kTon

ν Cross-Sections: • El. Scattering on el. [linear increase with Eν, all flavors]• Absorption on Ar nuclei (F + GT transitions)

[˜ quadratic increase with Eν, CC-νe only]

ν µνe ν µν µ

π − → µ− + ν µ ; µ− → e− + ν e + νµ

π + → µ+ +νµ ; µ+ → e+ + νe +ν µ

µ-νµ

e-

νe

W-d

uµ-

νµ

Cosmic Rays (p, A-nuclei) after entering the atmosphere collide with nuclei in the air(NB: Primary C.R. Fluxes suffer large uncertainties and Hadronic Interaction cross-section at extremely high energies are poorly known).

Pions and Kaons in the hadronic cascades decay in flight producing ν’s and µ’s. Muons can in turn decay into ν’s.

π- W-

The ν-flavor Ratio at Earth surface is approximately constant R =νµ +ν µνe +ν e

≅ 2

.. however for Eν≈ 1 GeV, the parent muon reaches the surface of the Earthbefore it decays ⇒ the e-neutrino fluxes decreases and R becomes larger

Upward-going ν

Downward-going ν

Earth (atmosphere around)

UndergroundDetector

Precise calculation of the atmospheric ν-flux required a tremendous effort of many different groups (it took about 20 yr of re-iterated discussions and checks)[e.g. 1D vs 3D models]

Differential ν-flux energy distributions at fixed zenith angles (1D model - Bartol Group, Honda et al., Volkova)

The energy spectrum covers many orders of magnitude. The largest fraction is concentrated below 1 GeV.

The explored range (present & past experiments) is:

≈ 400 MeV ≤ Eν ≤ ≈10 GeV

… but future experiment(s) willcover soon the lower energypart of the atm. ν-spectrum

The “Intermediate Energy” range

Cross SectionIn the “Intermediate Energy” range (100 MeV

For atmospheric neutrinos•QEL (“quasi-elastic” scattering) channel is dominant (65% of the rate)•RES (“resonance excitation” production) channel is sub-dominant (30%)•DIS (Deep Inelastic Scattering) is almost negligible (5%)

⇒ only QEL will be discussed in details

Dynamics of QEL interaction is described by “current-current” Lagrangian (valid in the limit of Q2

dσ = 12π( )2 δ4 Pf − Pi( ) 12Eν 2mN

Mfi FV1, FV

2 ,FA1( )2 d

p

2E

dp ′ N

2E ′ N

where :

Mfi =G2

u γµ (1− γ 5 ) uν[ ] cosθc u p Γµ un[ ]

Γµ function of the Nucleon Weak Form Factors

After integration over final state kinematics:

σQEL Eν( ) 10-38cm 2[ ]

From Q.F. Theory:

CC-QEL thresholds: νe : Eν

thr = 0.

ν µ : Eνthr =110. MeV

ντ : Eνthr = 3.45 GeV

In atmospheric ν experiments however nucleon targets are bound in Nuclei AZTherefore QEL interactions are:

ν + AZ → − + p + A −1( )Z and ν + AZ →

+ + n + A −1( )Z −1

This introduces some constraints on both initial and final state kinematicsdue to Nuclear Effects (i.e. cross-section is reduced):

• Fermi Motion of the nucleon N in AZ• Binding Energy of the Nucleus• Pauli blocking

Different types of nuclear target (O, Fe, Ar,…) introduce second order corrections to the QEL cross section (and additional uncertainty).

Best suited techniques for cross-section calculation are MonteCarlo calculations(a big effort is being produced by the “neutrino community” to reach a commonframework to define cross sections … but new dedicated measurements are indeednecessary).

Several theoretical models are available to describe nucleonic states inside Nuclei.The easiest (i.e. the most commonly used) is the “modified- Fermi Gas Model”:• incoherent impulse approximation (hit nucleon off-shell + spectator (A-1) on-shell)• Fermi momentum distribution flat up to kF, and modified with high momentum tail (N-N correlation)

Atmospheric neutrino event rate in present (“future”) experiments

Nuclear targets in use in present experiments:• O (Oxygen in H2O) ⇐ SupeKamiokande (Kamiokande and IMB)• Fe ⇐ SOUDAN • Ar ⇐ ICARUS• [O(50%) + Si(30%) + … (Rock) ⇐ MACRO

in high en range]

For the event rate calculation, Z/A ratio is more important than differences from nuclear effects (kF, EB).

σAtm = σ QELCC Eν( )∫ λAtm Eν ,cosθZ( ) dEν d cosθZ ≈ 1.2 ×10−38cm2

"SNU" 10−36 s−1[ ]= σAtm × ΦAtm ≈ 0.033

Summing up contributions of QEL (CC only) reactions from ν µ 47%( ), ν µ 15%( ), νe 30%( ), ν 8%( )

Oscillation (50% suppression of νµ rate) effect ARE NOT included!!

Evt. Rate : Nevtyr

≈ 300 for a detector Mass of 1 kt (!!!); εDet = 1, EDet

thr = 0. (ideal case)

σ Beam = σ DISCC Eν( )∫ λBeam Eν( ) dEν ≈ 2.2 ×10−38cm2

"SNU" 10−36 s−1[ ]= σ BeamDIS × ΦBeamNuMI ≈1.14 ×104

Evt. Rate : Nevtyr

≈ 8.5 ×107 for a detector Mass of 1 kt (!!!);

εDet =1, EDetthr = 0. (ideal case)

Huge unprecedented Rate is expected at the close station

With the “High Energy option” of NuMI Beam a much larger rate can be obtained (… but it is less attractive for present oscillation studies).

Obviously the Flux at far distance (730 Km) is MUCH smaller due to the divergence of the neutrino beam.

Summary• Guided tour of NeutrinoLand• Artificial/Natural ν sources• Cross-section from various model

calculations• ν interaction counting rate• New physics beyond Standard

Model? YES (ν oscillations is now a well established effect ⇒ mν≠0)

• New generation experiments are now in preparation … but a very accurate control of cross-section(and fluxes)is a mandatory request.

• … we still need to further probe standard neutrino properties!!! from both the experimental and the theoretical sides

Source SNU [10-36 s-1]

Solar – pp (Ge absorption channe l) 128

Solar – 8B (Ar absorption channe l) 11.1

Solar – 8B (elastic e-channe l) 1

Reactor (reaction of free p) 4 x 104

Beam Dump (reaction of free p) 0.1

Atmospheric (quasi-elastic on N ) 0.033

Long Baseline Beam (Deep Inelastic) 1.14 x 104

Source

SNU [10-36 s-1]

Solar – pp (Ge absorption channel)

128

Solar – 8B (Ar absorption channel)

11.1

Solar – 8B (elastic e-channel)

1

Reactor (reaction of free p)

4 x 104

Beam Dump (reaction of free p)

0.1

Atmospheric (quasi-elastic on N)

0.033

Long Baseline Beam (Deep Inelastic)

1.14 x 104

an10an10coverInterazioni di neutrino

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an10theo

an10endDiapositiva numero 1Diapositiva numero 2Diapositiva numero 3