Experimental methods Experimental methods for direct measurements for direct measurements

of the Neutrino Massof the Neutrino Mass

Part - 1Part - 1

Como – 30/05/2006

2

Standard modelStandard model

WEAK INTERACTIONS PARTICLE :

“Neutrino” Pauli (1930) – postulated to reconcile data on radioactive decay of nuclei with energy conservation

• No Strong or Electromagnetic Interactions (singlet of SU(3)C x U(1)EL)

• Non-Sterile Neutrino Has Left – Handed Weak Interactions (SU(2)L) “Weak” Partner of charged leptons

• Massless due to SM gauge group: GSM= SU(3)C x SU(2)L x U(1)Y )fermions have no bare mass terms (are in chiral

representation of gauge group)

Charged Fermions Mass arise from Yukawa interactions after spontaneous symmetry breaking Massless neutrino

L

ll l

L

,,el

3

These currents give all the neutrino interactions within the standard model

Measurement of Z0 weak-decay invisible width (measured at e+- e- annihilation)

only 3 light ( M ≤ MZ / 2 ) neutrinos

N = 3.00 ± 0.06

Standard modelStandard model

WEAK INTERACTIONS : Neutrino current interactions terms (mathematically speaking)

..cos

..

L

L

CHZg

CHWlg

Llll

WNC

LllCC

0

2

2

Charge current

Neutral current

4

Standard modelStandard model

Standard model is not a complete picture of Nature:

• fine-tuning problem of Higgs mass (supersimm.)• gauge coupling unification & many gauge representation (GUT)• baryogenesis by heavy singlet fermions (leptogenesis)• Gravity (string theories)

A true possibility: standard model must be thought as a low energy theory

scale energy NP under which SM is a valid approximation

A possible extension of SM is the seesaw mechanism, where the break of

total lepton number and lepton flavour symmetry occurs. The basic assumption

is the existence of heavy sterile neutrinos that involves small mass-neutrinos.

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Standard model extensionStandard model extensionNeutrino mass pattern & mixing matrixNeutrino mass pattern & mixing matrix

Neutrino oscillations

neutrino flavors are superposition of states of definite mass

ilil U

U is unitary neutrino flavor is not a conserved quantity so 'll

Where:

• 3 mix angles 13, 23, 12 (sij and cij are the respective sin and cosine) (unknown 13)

• 2 Squared mass difference (m2big - m2

small) (from oscillation experiments)

• CP violating phase (unknown)

• 2 Majorana phases 1, 2 (unknown – -0 experiments for Majorana neutrinos)

• Absolute mass scale and hierarchy (normal, inverted or degenerate)

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No information about the absolute value

of the neutrino masses

direct measurements

Hierarchy or Degeneracy are competitive scenarios

M1 M2 M3

Mi < Mj < Mk

M

(eV

)

Mass state

Standard model extensionStandard model extensionElectronic neutrinoElectronic neutrino

Information on the neutrino mass spectrum:MBig

2 5 x 10-3 eV2

MSmall2 10-4 eV2

So, for electronic neutrino:222iei mUm

e

(Majorana terms are not considered)

Role of the indirect constraintsRole of the indirect constraints

There are many indirect constraints on the absolute neutrino mass scale

We will consider here two of them:

Neutrinoless Double Beta Decay

it is a rare nuclear process that, if observed, would imply that neutrinos are massive neutrino is a Majorana particle = C

present results: M < ~0.5 eV IF neutrino is a Majorana particle

Cosmic Microwave Background measurement

WMAP results imply that, assuming neutrino full degeneracy,M < 0.23 eV

(assumption of CDM cosmological model and use of Galaxy Redshift Surveys)

necessity of direct measurement at this scale

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Basic ideas for direct neutrino mass measurementBasic ideas for direct neutrino mass measurement

kinematics of processes involving neutrinos in the final state

+ + + for M

- m + n0 + vfor M

use dispersion in Time Of Flight of neutrinos from supernova explosion

From SN1987A in Small Magellanic Cloud neutrinos were observed. Studying the spread in arrival times over 10 s leads to

Me < 23 eVHowever, not better than 1 eV uncertainties in time emission spectrum

(A,Z) (A,Z+1) + e- + e for Me

use only: E2 = M2c4 + p2c2 IT IS MODEL INDEPENDENT !

(A,Z) + e-at (A,Z-1) + + e for Me

electron capture withinner bremsstrahlung

not useful to reach the desired sub-eV sensitivity range, due to the high energyof the decay products with respect to the expected neutrino mass scale

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0.7 - 1 eV

0.5 eV

2.2 eV

0.1 eV

0.05 eV

0.2 eV

Presentsensitivity

Future sensitivity

(a few year scale)

Cosmology (CMB + LSS)

Neutrinoless Double Beta Decay

Single Beta Decay

Tools

Model dependentDirect determinationLaboratory measurements

Tools for the investigation of the Tools for the investigation of the mass scale mass scale

Neutrino oscillations cannot provide information about a crucialparameter in neutrino physics: the absolute neutrino mass scale

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The nuclear beta decay and the neutrino massThe nuclear beta decay and the neutrino mass

Fermi theory of weak interaction (1932)

(A,Z) (A,Z+1) + e- + e

Q = Mat(A,Z) – Mat(A,Z+1) Ee + E

(Q – Ee) (Q – Ee)2 – M2c4

finite neutrino mass

(Q – Ee)2

dNdp

GF2 |Mif|2 p2 (Q – Ee)2 F(Z,p) S(p,q)

electron momentum distribution

dNdE

GF2 |Mif|2 (Ee+mec2) (Q – Ee)2 F(Z,Ee) S(Ee) [1 + R(Z,Ee)]

electron kinetic energy distribution

zero neutrino mass

only a small spectral region very close to Q is affected

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The nuclear beta decay and the neutrino massThe nuclear beta decay and the neutrino mass

So, the energy spectrum of emitted electron is:

dE

dN

Phase space term

Coulombian correction term (relativistic, finite size nucleus, no e- shielding)

Form factor term

Radiative electromagnetic correction term

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Spectral effects of a finite neutrino massSpectral effects of a finite neutrino mass

The more relevant part of the spectrum is a range of the order of [Q – Mc2 , Q]

The count fraction laying in this range is (MQ)3 low Q are preferred

Q

E – Q [eV]

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Effects of a finite neutrino mass on the Kurie plot Effects of a finite neutrino mass on the Kurie plot

The Kurie plot K(Ee) is a convenient linearization of the beta spectrum

QQ

Q–Mc2 Q

K(E

)

zero neutrino mass

finite neutrino mass

effect of: background energy resolution excited final states

K(E)

dNdE

GF |Mif|2 (Ee+mec2)F(Z,Ee) S(Ee) [1 + R(Z,Ee)]

1/2

(Q – Ee) (Q – Ee)2 – M2c4

1/2

Q-E

Q

(dN/dE) dE 2(E/Q)3

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Mass hierarchyMass hierarchyIn case of mass hierarchy: the Kurie plot superposition of three different sub - Kurie plots each sub - Kurie plot corresponds to one of the three different mass eigenvalues

The weight of each sub – Kurie plot will be given by |Uej|2, where

|e = Uei |Mi i=1

3

This detailed structure will not be resolved with present and

planned experimental sensitivities(~ 0.3 eV)

K(E

e)

Ee

Q – M3

Q – M2

Q – M1

Q Ee

K(Ee)

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Mass degeneracyMass degeneracy

In case of mass degeneracy:the Kurie-plot could be described in terms of a single mass parameter, a mean value of the three mass eigenstates

Q – M

K(E

e)

Q Ee

this is the only mechanismwhich can assure discovery

potential to the direct measurement of neutrino mass

with the present sensitivities,at least in the “standard” three

light neutrino scenario

M = Mi |Uei|2

|Uei|2

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Experimental searches based on nuclear beta decayExperimental searches based on nuclear beta decay

Requests: high energy resolution a tiny spectral distortion must be observed high statistics in a very narrow region of the beta spectrum well known response of the detector spectral output for an energy function input control of any systematic effect that could distort the spectral shape

Approximate approach to evaluate sensitivity to neutrino mass M

Require that the deficit of counts close to the end point due to neutrino mass beequal to the Poissonian fluctuation of number of counts in the massless spectrum

It underestimates the sensitivity,but it is very useful to understand

the general trends and the difficultyof this experimental search

M1.6 Q3 E

A TM4

energy resolutiontotal source activity

live time

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electron kinetic energy distribution with zero neutrino mass and background B

dNdE

GF2 |Mif|2 (Ee+mec2) (Q – Ee)2 F(Z,Ee) S(Ee) [1 + R(Z,Ee)] + B

dNdE

GF2 |Mif|2 (Ee+mec2) (Q – Ee) 2 1 – F(Z,Ee) S(Ee) [1 + R(Z,Ee)]

(Q – Ee) 2

M2c4

electron kinetic energy distribution with non-zero neutrino mass

Effect of the background Effect of the background

GF2 |Mif|2 (Ee+mec2) (Q – Ee)2 1+

B

GF2 |Mif|2 (Ee+mec2) (Q – Ee)2 FS[1 + R]

FS[1 + R]

can be re-written as:

unaccounted background gives negative neutrino mass squared

M2c4 –

2 B

GF2 |Mif|2 (Ee+mec2) FS [1 + R]

< 0

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Two complementary experimental approachesTwo complementary experimental approaches

determine electron energy by means of a selection on the beta electrons operated by proper electric and magnetic fields

measurement of the electron energy out of the source

present achieved sensitivity: 2 eV

future planned sensitivity: 0.2 eV

determine all the “visible” energy of the decay with a high resolution low energy “nuclear” detector

magnetic and electrostatic spectrometers

bolometers

present achieved sensitivity: 10 eV

future planned sensitivity: 0.2 eV(5y MARE)

measurement of the neutrino energy

source coincident with detector (calorimetric approach)

source separate from detector (the source is always T)

completely different systematic uncertainties

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Historical improvement in T beta spectroscopyHistorical improvement in T beta spectroscopywith magnetic / electrostatic spectrometers with magnetic / electrostatic spectrometers

M2

(eV

2)

Experimental results on M

n.b.: neutrino mass squared is theexperimentally accessible parameter

all the experiments but one finds M

Tret’yakov magnetic spectrometers (1983-1993)

ITEP (Moscow) (valine source) ~ 30 eVZurich (T2 implanted source) < 12 eVLos Alamos (T2 gaseous source) < 9 eVLivermore (T2 gaseous source) < 7 eV

Electrostatic spectrometers (1993-2000)

Troitsk (T2 gaseous source) < 3 eVMainz (T2 solid source) < 2 eV

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Beta spectroscopy Beta spectroscopy with magnetic / electrostatic spectrometers with magnetic / electrostatic spectrometers

Experimental procedure T spectrum is scanned by stepping the selected energy from Emin to Q Emax > Q to monitor the background At each Ee step, acquisition lasts a time interval t, with t increasing with Ee

Source Electron analyzer Electron counter

T2

high activity

high luminosity L/4(fraction of transmitted

solid angol)

high energy resolutiontwo types: differential: select Ee window integral: select Ee > Eth

high efficiency low background

source and spectrometer time stability – excellent live time control

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The problem of the excited states The problem of the excited states

A good control of molecular excited states is necessary to understand spectral shapes

Suppose to have N excited states Ei with transition probability Wi

Ee

K(E

e)

Q – E1

Q – E2

Q

Q’

M > 0

It can be shown that:

M2 – 2(Ei2 – Ei

2 )

Q’ Q – Ei

spectrum superposition of N spectra with end point Q-Ei, each weighted by Wi

less kinetic energy available for e and

The concavity of the Kurie plotis changed to positive close to Q

fake M2 < 0

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Excited states and other spectral factors in T Excited states and other spectral factors in T

Final state distribution is very difficult to calculate for complex molecules

Detailed calculations are available only for the process

T2 3HeT+ + e- +

Other factors Spectral shape S(E)=1 foR T (super-allowed transition) Fermi function F(Z=1,E) Radiative corrections

Looking only at below the last 20 eV should allow to skip

excited state problemA fraction of only 3x10-10 counts

lays in the last 10 eV

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Tritium sources Tritium sources

Requests

High specific activity Low self-absorption and inelastic scattering Control of excited states use of molecular tritium T2

+ low inelastic scattering probability+ source homogeneity– backscattering from substrate– solid state excitation effects– source charging– surface roughening

+ highest specific activity+ lowest inelastic scattering probability+ no backscattering+ no source charging+ source homogeneity+ calibration with radioactive gasses– source strength stability

Solid frozen T2 source Gaseous windowless T2 source

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Electrostatic spectrometers Electrostatic spectrometers with Magnetic Adiabatic Collimation (MAC-E-filter) with Magnetic Adiabatic Collimation (MAC-E-filter)

These instruments enabled a major step forward in sensitivity after 1993They are the basic devices for next generation experiments aiming at the sub-eV range

High magnetic field Bmax at source anddetector. Low field Bmin at center.

All electrons emitted in the forward hemisphere spiral from source to detector

In the adiabatic limit

Ek / B = constant

Ek(center) = Ek(source) (Bmin/Bmax)

Since Ee = Ek + Ek= constant efficient collimation effect in the center

The retarding electric field at the center hasmaximum potential U0 and admits electrons with

Ek> eU0

Integral spectrometer

Resolving power: E / E = Bmin / Bmax 2 x 10-4

magnetic bottle

E 4 eV at E 18 keV

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The experimental beta spectrum with spectrometers The experimental beta spectrum with spectrometers

R(eU) is fitted with A, Q, B, M2 as free parameters

dNtheo

dE(Q, M

2) Ftrans(eU-E) Feloss(E) Fbsc(E) Fcharge(E) Fdet(E) + B=A R(eU)

counting rate for a retarding potential eU

theoretical beta spectrum, including radiative corrections and excited final states

spectrometer transmission function

energy loss in the source

backscattering on the source substrate(for frozen source only)

potential distribution in the T film(for frozen source only)

detector efficiency

spectrometer response function r (eU-E) = Ftrans(eU-E) Feloss(E) Fbsc(E) Fcharge(E)

r(eU-E)

eU – E (eV)

1

0

ideal response function

real response function

It is determined experimentally with monochromatic electron sourcesand at least for some effects it can be determined numerically

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Experiments with MAC electrostatic spectrometersExperiments with MAC electrostatic spectrometers

In the 90’s two experiments based on the same principle improved limit on neutrino mass down to about 2 eV at 95% c.l.

Both experiments have reached their final sensitivity

KATRINKATRINKAKArlsruhe rlsruhe TRITRItium tium NNeutrino experimenteutrino experiment

new generation experiment aiming at afurther factor 10 improvement in sensitivity

Mainz (Germany)Mainz (Germany) frozen T2 source complicated systematic in the source solved

Troitsk (Russia)Troitsk (Russia) gaseous T2 source unexplained anomaly close to the end point

collaborations has joined + other institutions (large international collaboration)

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MAC electrostatic spectrometer withwindowless gaseous T2 source

240 days of measurement(from Jan 1994 to Dec 1999)

Troitsk experiment: the set-upTroitsk experiment: the set-up

Differentially pumped gaseous T2

source with magnetic transportL = 3 m - = 50 mmp = 10-2 mbarT = 26 – 28 KT2 : HT : H2 = 6 : 8 : 2

L = 6 m - = 2 mP = 10-9 mbar

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Troitsk experiment: the calibrationTroitsk experiment: the calibration

Energy resolution: EFW = 3.5 – 4 eV

Monochromatic 0.5 eV energy-spread electrons from electron gun

eU0 (eV)

Careful measurement of theresponse function, without T2 gas

and with T2 gas at different pressures

r

eU – E (eV)

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Troitsk experiment: the anomalyTroitsk experiment: the anomaly

eU0 (eV)

Rat

e

Elow (eV)

M2

(eV

2)

relative intensity: 6x10-11

peak position change with time

collected data present an anomalyintegral spectrum must be fitted

with a step function 5-15 eV below Q

a peak in the differential spectrum

without step function M2 is negative

and not compatible with 0

with step function included in the fit:

M2 = -1.9 3.4 2.2 eV2

M < 2.5 eV (95% c.l.)

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Troitsk experiment: the speculationTroitsk experiment: the speculation

13 orders of magnitude higher thanforeseen by standard cosmology

hypotheses: neutrinos are bound in the solar system in a cloud the binding energy varies within the cloud semiannual effect

probably, experimental artifact

position Q – Estep changes periodicallywith T = 0.5 y between 5 and 15 eV

attempts to correlate with Mainzmeasurement mostly failed

neutrino density ~ 0.5 x 1015 cm-3

exotic explanation

e + T 3He + e-

= 0.77 x 10-44 cm2

Q

Q + M - EbQ + M

Q + M – Ebound Q + M

Q

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MAC electrostatic spectrometer with frozen solid T2 source

Mainz experiment: the set-upMainz experiment: the set-up

Segmented Si detector to help background

rejection

L = 2 m - = 0.9 mp = 0.5 x 10-10 mbarBmin = 5x10-4 T

T2 film quench-condensedon a graphite substrate Tsource = 1.86 K thickness = 45 nm 130 mL area = 2 cm2

activity = 20 mCi

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Mainz experiment: control of the systematicMainz experiment: control of the systematic

systematic constantly improved M2, significantly negative at the beginning,

is now statistically compatible with zero

Signal to background ratio – improved by: background reduction maximization of source strength

Detailed study of the systematic inducedby the quench condensed source

Source roughening (which induces dispersion in energy losses) is reduced by cooling the T2 film down to 1.2 K

The source charging and the related potential profile is modeled and included in the analysis Fcharge

Energy loss in the source was studied with different source thicknesses Feloss

r

eU0 (keV)

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Mainz experiment: the resultsMainz experiment: the results

M2 = -1.2 2.2 2.1 eV2 M < 2.2 eV (95% c.l.)

Final experimental sensitivity reached

Rat

e

eU0 (keV)

sourcecharging

effect

Clear improvement in signal-to-background ratio from 1994 set-up to 1998-2001 set-up

To reduce systematic uncertainties, only the final 70 eV are used M2 ~ 0

M2

(eV

2)

Elow (keV)

100 eV

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Next generation of MAC spectrometer:Next generation of MAC spectrometer:the KATRIN proposalthe KATRIN proposal

Strategy better energy resolution EFW ~ 1 eV higher statistic stronger T2 source – longer measuring times better systematic control in particular, improve background rejection

Goal: to reach sub-eV sensitivity on M

letter of intenthep-ex/0109033

Double sourcecontrol of systematic

Pre-spectrometerselects electrons with E>Q-100 eV

(10-7 of the total)

Better detectors: higher energy resolution time resolution (TOF) source imaging

Main spectrometer high resolution ultra-high vacuum (p<10-11 mbar) high luminosity

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KATRIN sensitivityKATRIN sensitivity

In addition, no excited states below 27 eV

Simulation to evaluate sensitivityE = 1 eV spect = 7 m (10 m) Background = 11 mHz Source: area 29 cm2

column density 5 x 1017 molecule/cm2

Sensitivity on M2: 0.35 eV

with spec = 10 m sensitivity down to 0.25 eV

Schedule: 2003: proposal + pre-spectrometer 2004: application for funds 2007: start

No electron inelastic scattering is possiblein T2 with energy loss lower than 12 eV

The response function is flat forQ – 12 eV < eU0 < Q

Use small region below end-pointof the order of 20 eV

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Neutrino is at the frontier of particle physics Its properties have strong relevance in cosmology and astrophysics

Absolute mass scale, a crucial parameter, is not accessible via flavor oscillations

Direct measurement through single beta decay is the only genuine model independent method to investigate the neutrino mass scale

Conclusion

Neutrino needs more research and researchers, even if it cannot interact with.