Searching for Majorana neutrinos

with cryogenic detectorsMarco Vignati, INFN-Roma

International School of Subnuclear PhysicsErice, 26/6/2013

Majorana neutrinosIf the total lepton number is not a conserved quantity, we could have

that neutrinos are equal to anti-neutrinos:

It is still not clear today whether neutrinos are Dirac or Majorana particles

The only way we know to answer this question is to observe a rare nuclear process, the neutrinoless double beta decay (0νDBD)

2

Double beta decay happens in very few natural isotopes:130Te, 76Ge, 136Xe,100Mo,82Se, ...and not many other of exp. interest.

1) 2ν mode - standard model allowed: (A,Z) → (A,Z+2) + 2 e- + 2 ν

2) 0ν mode - lepton number violation: (A,Z) → (A,Z+2) + 2 e-

The decay half-life is the measurable quantity. It depends on the effective Majorana mass of the neutrino exchanged between the two electron vertexes:

m��

�0�1/2

Phase space factor: ~ Q5

Nuclear Matrix element

Effective neutrino mass

3

Double beta decay

mmin [eV]

|m``

| [

eV]

NS

IS

Cosm

ological Limit

Current Bound

10<4 10<3 10<2 10<1 110<4

10<3

10<2

10<1

1

1m2m3m

Present limits on mββ

Cuoricino-130Te

Exo-136XeHeidelberg Moscow-76Ge

KamlandZen-136XeKK evidence -76Ge

Inverted hierarchy of neutrino masses:present challenge

4

Bilenky Giunti (arXiv:1203.5250v3)

Normal hierarchy:still a dream

• Experiments measure the sum of the kinetic energies of the two emitted βs.

‣ Signature: monochromatic line at theQ-value of the decay.

• Half-life sensitivity @1σ:

Isotope abundance (%)Detector mass (100 kg)

Measurement time (y)

Atomic massBackground (counts/keV/kg/y)

Energy Resolution (keV)

S0� = ln 2NA · a

A

�Mt

B�E

⇥1/2

· � detectionefficiency

5

0νDBD in Experiments

• Particle energy converted into phonons → temperature variation.

• TeO2 crystals (dielectric, diamagnetic)• 0νDBD emitter: 130Te (isotopic abundance: 34%)

• Detector response in this configuration: ~ 0.2 mK / MeV • Resolution @0νDBD energy (2527 keV) ~ 0.2% FWHM

Heat bath ~ 8mK

Weak thermal coupling

Thermometer:NTD Ge thermistor

R ~ 100 MΩ

Absorber CrystalTeO2 C~10-9 J/K

Energy release

6

Bolometric technique

detector = source

Energy [keV]2480 2500 2520 2540 2560 2580

Rat

e [c

ount

s/ (1

keV

)]

05

101520

253035

404550

Best Fit68% C.L.90% C.L.

0νDBD

60Co γ + γ Cuoricino

• Past: Cuoricino (2003-2008)‣ 62 bolometers

11 kg (130Te)×2y, Bkg: 0.16 cpy/keV/kg

‣ T0ν1/2 > 2.8×1024 years (90% CL)〈mββ〉< 300~700 meV

• Future: Cuore (data taking in 2015)‣ Expected bkg: 0.01~0.04 cpy/keV/kg‣ Exp. T0ν1/2 > 1.6 ×1026 years 〈mββ〉< 40~94 meV

• Present: Cuore-0, a CUORE-like tower.‣ same mass of Cuoricino, ‣ Expected bkg: 0.05 cpy/keV/kg.

130Te CUORE

7

CUORE - @Gran Sasso

CUORE: 988 bolometers

750 kg TeO2

200 kg 130Te

• MC: most of the background in CUORICINO is due to degraded α (surface contaminations, mainly in copper).

• TeO2 bolometers, per se, do not allow to discriminate β and α particles.

‣ α bkg. partially reduced by cleaning the detector parts.‣ β/γ smaller in CUORE thanks also to the self-shielding geometry.

CUORICINO data

CUORE: the α nightmare

8

α continuum

TeO2 TeO2

Cu

α

α α

[keV]2Heat in TeO0 1000 2000 3000 4000 5000

Det

ecte

d Li

ght [

keV

]

-0.3

-0.2

-0.1

0

0.1

0.2

0.3

0.4

β/γ source

α contaminations

Light@0νββ: 100 eV

Heat in TeO2 [keVee]

Germanium bolometric

light detector

TeO2 wrapped with Teflon

R&D on CUOREDiscrimination of α interactions in CUORE: MeV βs (signal) emit a little Čerenkov light, αs (background) do not.

9

The light is visible but event by event discrimination is not possible: the noise of the light detector is high (100 eV RMS) compared to the Čerenkov signal (100 eV). J. W. Beeman, M. Vignati (c.a.), et al., “Discrimination of α and β/γ interactions in a TeO2 bolometer,” Astropart. Phys. 35 (2012) 558.

10

CREATE a new kind of light detector with a factor >10 better resolution: Noise ΔE < 20 eV RMS, Area=5x5 cm2, Twork=10 mK

scalable to 1000 detectors

[keV]2Heat in TeO0 1000 2000 3000 4000 5000

Det

ecte

d Li

ght [

keV

]

-0.3

-0.2

-0.1

0

0.1

0.2

0.3

0.4

Heat in TeO2 [keVee]

Det

ecte

d lig

ht [k

eV]

0νDBD in CUORE: reject completely the background from α particles.

Challenge: detect the small amount of Čerenkov light from βs (100 eV@2.5 MeV).

Our objective

10

CREATE a new kind of light detector with a factor >10 better resolution: Noise ΔE < 20 eV RMS, Area=5x5 cm2, Twork=10 mK

scalable to 1000 detectors

[keV]2Heat in TeO0 1000 2000 3000 4000 5000

Det

ecte

d Li

ght [

keV

]

-0.3

-0.2

-0.1

0

0.1

0.2

0.3

0.4

Heat in TeO2 [keVee]

Det

ecte

d lig

ht [k

eV]

0νDBD in CUORE: reject completely the background from α particles.

Challenge: detect the small amount of Čerenkov light from βs (100 eV@2.5 MeV).

✓ Kinetic Inductance Detectors (KID): new technology invented at Caltech

‣ Excellent energy resolution and reliability.

‣ Easy readout: FPGAs and 1 cold amplifier, high multiplexing. Tremendous evolution, very successful in astrophysical applications:

‣ Not yet ported to Particle Physics: time is now.

Our objective

KID: Working principle Day et al., Nature 425 (2003) 817

J Low Temp Phys

dimensionless factors describing the dissipative and frequency response from Mattis-Bardeen theory [9, 12]. β = S2/S1 ∼2.5 is the ratio of the response in the frequencyand dissipation directions. The total resonator quality factor, Q−1

r = Q−1c + Q−1

i ,depends both on the quality factor due to coupling to the feedline, Qc , and that due tointernal losses in the resonator, Qi . The factor χBW = τqp/(τph + τqp) ≤ 1 accountsfor the degradation in resolution when the phonon energy arrives as an exponentialwith fall time τph rather than as a δ-function energy deposition.

Resolving the few µs pulse rise times requires a resonator time constant, τr =Qr/πfr ≈ 1 µs, or Qc ! 104 for fr ∼ 3 GHz. In the limit that the conductivity tothe thermal bath is low, so that the phonon decay time is dominated by creation ofquasiparticles in the MKIDs, and τqp % τph, we can rewrite (1) as:

σE = (2.4 eV)

(1

ηph

√1

αpt

)(2.5

β(ω, T )

)(*

200 µeV

)

×√

Asub

8 cm2

λpb

1 µm3 GHz

fr

100 µsτqp

TN

3 K1.22

S1(ω, T )(2)

where pt is the phonon transmission probability from the substrate to the MKID,λpb is the phonon pair-breaking length in the MKID, Asub is the surface area ofthe substrate, and the resolution has been numerically evaluated for the expectedparameters for our prototype 20 mm × 20 mm devices, conservatively assumingηread = 1. Equation (2) indicates that the resolution is expected to degrade as√

Asub , so that a more massive detector with Asub ∼ 100 cm2 would still haveσE ≈ 10 eV/(ηph

√αpt ).

3 Experimental Setup

Figure 1 shows the layout of prototype phonon-mediated MKID devices. The deviceconsists of 20 LEKIDs capacitively coupled to a coplanar-strip (CPS) feedline. Theinductive section of each resonator consists of a 70 µm wide meander with 10 µmspacing between the meanders, which has a total area of ∼0.98 mm2. The capacitivesection consists of four, 70 µm wide fingers spaced by 20 µm.

Fig. 1 (Color online) (a) Chip layout for prototype devices. Twenty LEKID resonators are arranged in arectangular grid and capacitively coupled to a CPS feedline. (b) Device mounted in housing for testing

Moore et al., Appl. Phys. Lett, 100 (2012) 232601

11

J Low Temp Phys

dimensionless factors describing the dissipative and frequency response from Mattis-Bardeen theory [9, 12]. β = S2/S1 ∼2.5 is the ratio of the response in the frequencyand dissipation directions. The total resonator quality factor, Q−1

r = Q−1c + Q−1

i ,depends both on the quality factor due to coupling to the feedline, Qc , and that due tointernal losses in the resonator, Qi . The factor χBW = τqp/(τph + τqp) ≤ 1 accountsfor the degradation in resolution when the phonon energy arrives as an exponentialwith fall time τph rather than as a δ-function energy deposition.

Resolving the few µs pulse rise times requires a resonator time constant, τr =Qr/πfr ≈ 1 µs, or Qc ! 104 for fr ∼ 3 GHz. In the limit that the conductivity tothe thermal bath is low, so that the phonon decay time is dominated by creation ofquasiparticles in the MKIDs, and τqp % τph, we can rewrite (1) as:

σE = (2.4 eV)

(1

ηph

√1

αpt

)(2.5

β(ω, T )

)(*

200 µeV

)

×√

Asub

8 cm2

λpb

1 µm3 GHz

fr

100 µsτqp

TN

3 K1.22

S1(ω, T )(2)

where pt is the phonon transmission probability from the substrate to the MKID,λpb is the phonon pair-breaking length in the MKID, Asub is the surface area ofthe substrate, and the resolution has been numerically evaluated for the expectedparameters for our prototype 20 mm × 20 mm devices, conservatively assumingηread = 1. Equation (2) indicates that the resolution is expected to degrade as√

Asub , so that a more massive detector with Asub ∼ 100 cm2 would still haveσE ≈ 10 eV/(ηph

√αpt ).

3 Experimental Setup

Figure 1 shows the layout of prototype phonon-mediated MKID devices. The deviceconsists of 20 LEKIDs capacitively coupled to a coplanar-strip (CPS) feedline. Theinductive section of each resonator consists of a 70 µm wide meander with 10 µmspacing between the meanders, which has a total area of ∼0.98 mm2. The capacitivesection consists of four, 70 µm wide fingers spaced by 20 µm.

Fig. 1 (Color online) (a) Chip layout for prototype devices. Twenty LEKID resonators are arranged in arectangular grid and capacitively coupled to a CPS feedline. (b) Device mounted in housing for testing

Cooper pairs (cp) in a superconductor act as an inductance (L).

Absorbed photons change cp density and L.

High quality factor (Q) resonating circuit biased with a microwave (GHz):

signal from amplitude and phase shift.

L C

KID: Working principle Day et al., Nature 425 (2003) 817

J Low Temp Phys

dimensionless factors describing the dissipative and frequency response from Mattis-Bardeen theory [9, 12]. β = S2/S1 ∼2.5 is the ratio of the response in the frequencyand dissipation directions. The total resonator quality factor, Q−1

r = Q−1c + Q−1

i ,depends both on the quality factor due to coupling to the feedline, Qc , and that due tointernal losses in the resonator, Qi . The factor χBW = τqp/(τph + τqp) ≤ 1 accountsfor the degradation in resolution when the phonon energy arrives as an exponentialwith fall time τph rather than as a δ-function energy deposition.

Resolving the few µs pulse rise times requires a resonator time constant, τr =Qr/πfr ≈ 1 µs, or Qc ! 104 for fr ∼ 3 GHz. In the limit that the conductivity tothe thermal bath is low, so that the phonon decay time is dominated by creation ofquasiparticles in the MKIDs, and τqp % τph, we can rewrite (1) as:

σE = (2.4 eV)

(1

ηph

√1

αpt

)(2.5

β(ω, T )

)(*

200 µeV

)

×√

Asub

8 cm2

λpb

1 µm3 GHz

fr

100 µsτqp

TN

3 K1.22

S1(ω, T )(2)

where pt is the phonon transmission probability from the substrate to the MKID,λpb is the phonon pair-breaking length in the MKID, Asub is the surface area ofthe substrate, and the resolution has been numerically evaluated for the expectedparameters for our prototype 20 mm × 20 mm devices, conservatively assumingηread = 1. Equation (2) indicates that the resolution is expected to degrade as√

Asub , so that a more massive detector with Asub ∼ 100 cm2 would still haveσE ≈ 10 eV/(ηph

√αpt ).

3 Experimental Setup

Figure 1 shows the layout of prototype phonon-mediated MKID devices. The deviceconsists of 20 LEKIDs capacitively coupled to a coplanar-strip (CPS) feedline. Theinductive section of each resonator consists of a 70 µm wide meander with 10 µmspacing between the meanders, which has a total area of ∼0.98 mm2. The capacitivesection consists of four, 70 µm wide fingers spaced by 20 µm.

Fig. 1 (Color online) (a) Chip layout for prototype devices. Twenty LEKID resonators are arranged in arectangular grid and capacitively coupled to a CPS feedline. (b) Device mounted in housing for testing

Moore et al., Appl. Phys. Lett, 100 (2012) 232601

11

J Low Temp Phys

dimensionless factors describing the dissipative and frequency response from Mattis-Bardeen theory [9, 12]. β = S2/S1 ∼2.5 is the ratio of the response in the frequencyand dissipation directions. The total resonator quality factor, Q−1

r = Q−1c + Q−1

i ,depends both on the quality factor due to coupling to the feedline, Qc , and that due tointernal losses in the resonator, Qi . The factor χBW = τqp/(τph + τqp) ≤ 1 accountsfor the degradation in resolution when the phonon energy arrives as an exponentialwith fall time τph rather than as a δ-function energy deposition.

Resolving the few µs pulse rise times requires a resonator time constant, τr =Qr/πfr ≈ 1 µs, or Qc ! 104 for fr ∼ 3 GHz. In the limit that the conductivity tothe thermal bath is low, so that the phonon decay time is dominated by creation ofquasiparticles in the MKIDs, and τqp % τph, we can rewrite (1) as:

σE = (2.4 eV)

(1

ηph

√1

αpt

)(2.5

β(ω, T )

)(*

200 µeV

)

×√

Asub

8 cm2

λpb

1 µm3 GHz

fr

100 µsτqp

TN

3 K1.22

S1(ω, T )(2)

where pt is the phonon transmission probability from the substrate to the MKID,λpb is the phonon pair-breaking length in the MKID, Asub is the surface area ofthe substrate, and the resolution has been numerically evaluated for the expectedparameters for our prototype 20 mm × 20 mm devices, conservatively assumingηread = 1. Equation (2) indicates that the resolution is expected to degrade as√

Asub , so that a more massive detector with Asub ∼ 100 cm2 would still haveσE ≈ 10 eV/(ηph

√αpt ).

3 Experimental Setup

Figure 1 shows the layout of prototype phonon-mediated MKID devices. The deviceconsists of 20 LEKIDs capacitively coupled to a coplanar-strip (CPS) feedline. Theinductive section of each resonator consists of a 70 µm wide meander with 10 µmspacing between the meanders, which has a total area of ∼0.98 mm2. The capacitivesection consists of four, 70 µm wide fingers spaced by 20 µm.

Fig. 1 (Color online) (a) Chip layout for prototype devices. Twenty LEKID resonators are arranged in arectangular grid and capacitively coupled to a CPS feedline. (b) Device mounted in housing for testing

Cooper pairs (cp) in a superconductor act as an inductance (L).

Absorbed photons change cp density and L.

High quality factor (Q) resonating circuit biased with a microwave (GHz):

signal from amplitude and phase shift.

Problem Direct photon detection:

maximum area of few mm2 (wavelength limited)

L C

Our goals

12

Proposing indirect detection: use a few KIDs (NK =10-20) and athermal phonons in the substrate as mediators:

State of the art goal Area

ΔE [eV RMS] Twork [mK]

few mm2 5x5 cm2 difficult< 1 < 20 achievable80 10 pro

Problem of direct photon detection: area cannot be covered with 103 KIDs, too demanding for electronics (in the future we will need 103 light detectors).

Substrate of silicon,sapphire...

(5x5cm2 x100-300µm)

KIDs of Al, TiN... (~1mm2 x 40-200nm)

Incident photons convert into phonons

Diffused phonons can be absorbed

by the KIDs

supports (glue, clamps...)

Scientific challengeNew problem: loss of phonon collection efficiency (ε) through the supports and via thermalization:

13

Substrate R&D: maximize transmission to the KIDs (pK). Minimize support area (Asupp), transmission prob. to supports (psupp) and substrate thickness (tsub).

KID R&D: ε loss compensated by KID sensitivity:1) Maximize film quality factor: Q > 105.2) High inductivity (L) and low Tc superconductors thanks to Twork =10 mK:

Al TiN (non stoich.) Ti+TiN (stoich.) Hf

Tc [K]

L [pH/square]

1.2 0.9 >0.4 0.12

0.5 3 30 3

Asupp

t sub

AK

Roberta Bagni, PhD Roma, 20/06/2013

FABBRICAZIONE KID

Prove di taglio chip allo scriber previa stesura resist per protezione

Prove di Bonding

Ulteriori test eseguiti sui chip realizzati:

Prova saldatura su campione sospeso

Prova di tenuta Al dopo stacco della saldatura

(Dispositivi finali verranno tagliati mediante microsega)

First 2x2 cm2

Al prototype ready:test next month

INFN, Sapienza U., Genova U.,IFN-CNR

Started in April 2013

14

Cryogenics testsalmost finished

mmin [eV]

|m``

| [

eV]

NS

IS

Cosm

ological Limit

Current Bound

10<4 10<3 10<2 10<1 110<4

10<3

10<2

10<1

1

1m2m3m

normal

invertedCUORE-130TeCUORE

(*) lines indicate average of max/min 130Te nuclear matrix elements.

0νDBD: CUORE improvementsKK evidence -76Ge

15

mmin [eV]

|m``

| [

eV]

NS

IS

Cosm

ological Limit

Current Bound

10<4 10<3 10<2 10<1 110<4

10<3

10<2

10<1

1

1m2m3m

normal

invertedCUORE-130TeCUORE

CUORE+enrichment

(*) lines indicate average of max/min 130Te nuclear matrix elements.

0νDBD: CUORE improvementsKK evidence -76Ge

15

mmin [eV]

|m``

| [

eV]

NS

IS

Cosm

ological Limit

Current Bound

10<4 10<3 10<2 10<1 110<4

10<3

10<2

10<1

1

1m2m3m

normal

invertedCUORE-130TeCUORE

CUORE+enrichmentCUORE+enrichment

+Cherenkov with KIDs

(*) lines indicate average of max/min 130Te nuclear matrix elements.

0νDBD: CUORE improvementsKK evidence -76Ge

15

Backup slides

Multiplexed readout of a KID array

O. Bourrion et al, JINST 6 (2011) 2011 JINST 6 P06012

Figure 2. Overview of the setup required to monitor a MKID array featuring the electronics generating thetwo frequency combs (each tone phase shifted by 90� between I and Q), the IQ up-mixer, the programmableattenuator for power adjustment, the cryostat, the low noise boost amplifier, the down mixer and the warmamplifier.

frequency comb must be generated at baseband and up-mixed to the frequency band of interest byhybrid mixers. The signal is then passed through the array at appropriate power level and finallyamplified and down-mixed back to baseband in order to be processed by the electronics.

The MKID array, operated at 70 mK, is followed by a low noise cold amplifier (LNA) operatedat 4 K and a warm amplifier. Typically, a combined total gain of 60 to 65 dB is used to boost theoutput signal and to adapt it to the ADC input dynamic range of 1 Vpp. Considering a white noise,the cold amplifier noise temperature of 5 K reported to the ADC input is equivalent to 1.3 mV forthe considered bandwidth. This yields a best achievable SNR of 57 dB which is much lower than the69 dB SNR of the chosen ADC. Measured performances and noise shape are detailed in section 7.2.

The programmable attenuator located before the transmission line coupled with the MKIDsadjusts the mean power per tone to an experimentally determined optimum of ⇠10 pW. Note thatthis value is adapted for typical ground based observations and that space based MKIDs wouldexhibit much lower saturation powers. Practical experience shows that driving the resonator withlower power degrades the SNR and using higher power makes the resonator unstable. This noisewhich is not related to the “two-level system noise” described in [16] is probably caused by insta-bilities in the thin superconducting film, and is associated to a strong deformation of the resonancecharacteristic in the complex plane.

It is important to note that the use of an IQ mixer is mandatory, because it presents the benefitto strongly attenuate the lower sideband and the carrier from the output up-mixed spectrum. Typicalrejection of -30 dB of the lower sideband can be obtained. As depicted on figure 3, the spectrumresulting from the down-mixing stage still contains residuals of the lower sideband due to the up-mixing. This part of the spectrum, unaffected by the MKID array, is folded on the tones of interestand reduces their available dynamic range, therefore degrading the SNR.

Another mixer side effect to consider, is their non linearity which creates inevitable intermod-ulation products. In the up-mixing part, those are not degrading the system performance, since theyare either off-resonance or in the worst case tuned to another MKID. In that case, the considered

– 4 –

2011 JINST 6 P06012

Figure 3. Illustration of the up and down-mixing of two tones f1 and f2 by a carrier flo with ideal mixers(no harmonics generated). Part (c) depicts the spectrum affected by the MKID array, only the green partis attenuated by a maximum of 2 to 10 dB (practical rejection values), i.e it still contains amplitudes 20 to28 dB larger than the residuals in red. As shown on (d), the tones affected by the MKID array and the imagefrequencies, i.e. the residuals (red), are summed because of the back folding due to the down-mixing.

intermodulation product is only adding a slight extra excitation and therefore is not adding anynoise nor crosstalk. In the down-mixing part however, an harmonic of a given MKID resonatorfrequency mixed to an harmonic of the local oscillator could fall on an other MKID resonance andthus create crosstalk. The probability of such an event is the ratio between the resonance widthand their mean separation, i.e. 50 kHz/2 MHz=2.5 %. Even in that case, this effect is not an issue,since the worst spurious suppression of the Intermediate Frequency harmonics (occurs when M=Nin M⇥ fRF±N⇥ fLO) was measured and is better than 45 dBc at the operated power.

4 Hardware development

The complexity of the design is directly driven by the targeted analog bandwidth and the number oftones to manage. The analog bandwidth puts hard constraints on the ADC and on the FPGA. On theFPGA side, unless each tone processing is parallelized, the limitation comes from the maximumrunning frequency of the multipliers used to perform the DDC. The FPGA size directly scales withthe number of tones to generate and process.

The hardware platform is FPGA centered and features a dual DAC for the frequency combgeneration, an ADC and a USB2 micro-controller for DAQ and slow control interfacing. A pictureof the board can be seen in figure 4. In order to demonstrate the concept feasibility and to keep thedesign simple, it was chosen to limit the sampling and processing frequency to 250 MHz (analog

– 5 –

17