Direct27

Neutrinogy Physics
r
e
n
E
h
g
i
H
Advances in

Mass
150

Cl K 𝛼@ 1.5 keV
ΔE ≈ 28 eV𝜏 R ≈ 1 ms

Measurements

100
CountsSi K𝛼Al K 𝛼50

20th Lomonosov Conference
0

0

500

1000

2000
1500
Energy (eV)
(b)

(a)

2500

3000

Joseph A. Formaggio

1 ms (a).
≈
𝜏
,
V
e
𝑅
k
47 eV at 2.6 of Technology
Massachusetts
Institute
≈
𝐸
Δ
e
iv
g
sable pixels

de
n
a
k
o
i
m
a
Super-K

A myriad of experiments
demonstrated thatneutrinos transmute
flavor (oscillations).

The Sudb
ury Neutrino
Observat
ory

There are predictions
that stem from alterationof the Standard Model.
de
n
a
k
o
i
m
a
Super-K

SNO

However, oscillation
experiments cannot
reveal the neutrino massscale.

Takaaki Kajita(Super-Kamiokande)

Arthur B. McDonald(Sudbury Neutrino Observatory)

So… how do we access what is the scaleof neutrino masses?

nde
a
k
o
i
m
a
K
Super-

de
n
a
k
o
i
m
a
Super-K

MethodObservable

Neutrino
Oscillations

Neutrinolessdouble beta decay
Cosmology

Nat. Commun. 6:6935 doi: 10.1038/ncomms7935 (2015)

m2ij ⌘ m2i
m

⌘
⌃⌘

X

(Uei )2 mi

i

X
i

m2j

mi

As mentioned, neutrino oscillations
provide our most accurate measurementof neutrino masses, but are only sensitive
to mass differences.
However, they simplify the problem:
measuring one mass scale yields all theneutrino masses.
The ordering (IMO or NMO) can also be
uncovered, if matter effects are at play.

Credit: Facility for Rare Isotope Beams

MethodObservable

Neutrino
Oscillations

Neutrinolessdouble beta decay
Cosmology

m2ij ⌘ m2i
m

⌘
⌃⌘

X

(Uei )2 mi

i

X
i

m2j

mi

These are really our most powerfulprobes for lepton number conservation(ΔL = 2).
If Majorana-neutrino exchange is thedominant contribution to 0νββ, the rate
for 0νββ is a function of the neutrino
masses.

CUORE

MethodObservable

Neutrino
Oscillations

Neutrinolessdouble beta decay
Cosmology(Z, A) ! (Z + 2, A) + e

m2ij ⌘ m2i
m

⌘
⌃⌘

X

2

(Uei ) mi

i

X
i

m2j

mi

+e

Large uncertainties in the determinationof the matrix elements that govern themeasured decay rate.
No guarantee that neutrino mechanism isdominant (or that neutrinos are Majorana
particles).
Inverted ordering in reach for next
generation of experiments.

PLANCK’s image of the microwave sky

MethodObservable

Neutrino
Oscillations

Neutrinolessdouble beta decay
Cosmology

m2ij ⌘ m2i
m

⌘
⌃⌘

X

(Uei )2 mi

i

X
i

m2j

mi

Neutrinos are also remnants of the Big
Bang; their masses contributing to thematter density of the observable universe.
The neutrino energy density can beconstrained by observations of the CMB,
the distribution of clusters of galaxies,
and the Lyman-alpha forest.

Zyla et al. Prog Theor. Exp. Phys 083C01 (2020).

MethodObservable

Neutrino
Oscillations

Neutrinolessdouble beta decay
Cosmology

Measured as part of a full fit to ΛCDM
model. This introduces dependencies onother cosmological parameters.

m2ij ⌘ m2i
m

⌘
⌃⌘

X

(Uei )2 mi

i

X
i

m2j

Limits on the neutrino mass scale fromcosmology are affected by model
extensions (such as additionalparameters) or new physics (neutrino selfinteraction or dark matter interactions).

Current Limits ~ 0.2 eVmiProjected Limits ~ 0.05 eV!!

All these methods indirectly access theneutrino mass scale (usually under someunderlying model assumption).

A direct method must rely on kinematics
to determine the neutrino mass.

First suggested by Francis Perrin in 1933
“On peut essayer de d́eduire de la forme desspectres continus d’́emission une indication sur
la valeur de cette masse inconnue...”[One could attempt to deduce from the shape ofthe continuous emission spectra an indication of
the value of this unknown mass... ]Enrico Fermi independently came to the same conclusion in his
seminal 1934 paper on weak decay.

“Arriviamo cosi a concludere che l a massa del neutrino euguale a zero o, in ogni caso, piccola in confronto dellamassa dell'elettrone (~) ...”

[We thus conclude that the mass of the neutrino is equal to zeroor, in any case, small enough in comparison to the mass of theelectron.]In his paper, Fermi already sketches out how one can use
the weak decay to explore the neutrino mass scale.

Tritium beta decay

Holmium electron capture

νe

163Ho

3

H

3

He

+

+ e

+ ¯e

163

163Dy*

Ho + e ! 163 Dy⇤ + ⌫e

For both beta decay (left) and electron capture (right), theinformation about the neutrino mass comes from the phase spacedependence on the neutrino momentum.

Tritium beta decay

Holmium electron capture

count rate

Electron Energy
0.2

In both cases,

0.15

differential spectrum
depends on the
0.1

neutrino momentum.

0.05

0
0

5

10

15

20

25

kinetic energy (keV)Ṅ / p⌫ E⌫

For both beta decay (left) and electron capture (right), theinformation about the neutrino mass comes from the phase spacedependence on the neutrino momentum.

Tritium beta decay

Holmium electron capture

count rate

Electron Energy
0.2

ν
β
ν
β

0.15

ν
β

0.1

0
0

β

0.05

5

10

15

20

25
<latexit sha1_base64="frksUZcBW2zPUlBuY6zxjmy1bBE=">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</latexit>

kinetic energy (keV)

m =

sX
i

|Uei |2 m2i

We define mβ as the incoherent weighted sum of the neutrino mass eigenvalues
associated with the electron.
The neutrino mass effect is most pronounced at the end of the beta or electron
capture portion of the decay spectrum.

3H

2

18.5 keV𝛕1/2 12.3 yrs

163Ho

2.83 keVFirst,
pick a source…

𝛕1/2 4570 yrs
187Re

2.5 keV𝛕1/2 4.5 Gyrs
115In

135Cs

155 eV440 eV𝛕1/2 4.4x1014 yrs

𝛕1/2 1.5x106 yrs

Amount needed
to see 1 event per
day in last eV
135Cs and 115In look attractive for their low endpoint and because

decays can be tagged. But they suffer from minuscule branchingratios.
Issues with 187Re make it impractical.
That mainly leaves tritium and holmium.

Electron transfers all of its energy tothe absorbing medium.

Calorimetric(Cryogenic Bolometers)

Electromagnetic filtering of electrons of
selected energy.

Electromagnetic Collimation(MAC-E Filter)
Use photon spontaneous emission fromelectron in magnetic field.

Frequency-Based(Cyclotron Radiation Emission Spectroscopy)Electron transfers all of its energy tothe absorbing medium.

Calorimetric(Cryogenic Bolometers)

Calorimetric approaches convert
the total deposited energy of the
decay into heat (phonons).
Usually very small detectors
operated at extremely low(< 100 mK) temperatures.

Small detectors(small heat
capacitance)
Cryogenic
temperatues
Highly sensitive
thermal detectors

Sensitivity of the detectors governed by the totalheat capacitance (Ctot) of the detector and thethermal coupling (G) to the thermal bath.
Superconductors
and semi-conductors

C(T ) / T 3

Metals<latexit sha1_base64="Gzev73CC15RLtPv0JPjj5tNUfdM=">AAACIXicdVBLSwMxGMz6rPW11qOXYBHqZclaH7ueCr14rNCqYGvJptkams2GJCuWYn+KFw/6V7yJN/GPeDStFazoQGCY+QYmE0nOtEHozZmZnZtfWMwt5ZdXVtfW3Y3CmU4zRWiDpDxVFxHWlDNBG4YZTi+kojiJOD2PetWRf35DlWapqJu+pK0EdwWLGcHGSm23MBxWS/Vd2JQqlSaF9aty2y0iLwwPAhRA5AUI+ahsSTkMw+AA+h4aowgmqLXdj2YnJVlChSEca33pI2laA6wMI5ze5ZuZphKTHu7SS0sFTqhuDcbd7+COVTowTpV9wsCx+jMxwInW/SSylwk21/q3NxL/9GLaF4m01phgATsMd5VNTPcxcdAaMCEzQwX5qhNnHNopRnPZkKLE8P4oTRSzP4LkGitMjB01b6f63gP+T872PP/Q2z9FxcrxZLQc2ALboAR8cAQq4ATUQAMQcAvuwSN4ch6cZ+fFef06nXEmmU0wBef9E/zWo0g=</latexit><latexit sha1_base64="bpqeeHDNS7ZUC1MiY5t9Qk0AkE4=">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</latexit>

C(T ) / T

In 1981, DeRujula proposed an alternate method for measuring
the neutrino mass.
Make use of the internal bremsstrahlung in electron capture(IBEC), with a spectrum analogous to beta decay.

<latexit sha1_base64="S1F8k8L0swkRVJymglgRzq5BwvI=">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</latexit>

d EC
dEc

=

G2F |Vud |2(Q Ec ) ⇥
3
2⇡
X
2
2
C
|M
|
j0
j j
4(Ec
j
X
2⇥
|Uei | (Q Ec )2ijEj ) 2 +

j

2 ⇥

⇤

2 1/2
mi

Neutrino phase space termThis opened up the possibility of using 163Ho as asource for calorimetric detectors.

Modern Calorimetric Experiments

Micro calorimeters which are sensitive to changes in temperature(energy deposition).
Contain the full decay energy.

Modern Calorimetric Experiments

MMC response(ECHO)TES Resolution(HOLMES)

163Ho is implanted onto gold absorbers and cooled to cryogenic temperatures

for energy readout.
Need very high energy resolution (for spectrum) and fast timing resolution (toavoid pile-up of events).

Modern Calorimetric Experiments

Aim of 1st gen.
ECHo & HOLMES

See L. Gastaldo’s talk(Friday)

Upcoming generation of ECHo & HOLMES aim at the eV neutrino mass scale.
Sub-eV sensitivity is within reach for next-generation large array of detectors.

Electromagnetic filtering of electrons of
selected energy.

Electromagnetic Collimation(MAC-E Filter)Electrostatic
potential (U)High Magnetic
Field (Bs)

Low Field
BA

High Magnetic
Field (Bs)

Magnetic Adiabatic Collimation
withElectrostatic Filtering(only electrons with enough energy can overcome potential barrier)

High Magnetic
Field (Bs)
1011 e- / second

μe

μe

Low Field
BA
μe

μe

High Magnetic
Field (Bs)μe
1 e- / second

High Magnetic
Field (Bs)
1011 e- / second

μe

μe

Low Field
BA
μe

μe

High Magnetic
Field (Bs)μe
1 e- / second

Predecessors: Mainz & Troitsk (Limit mβ < 2 eV)

After all critical systema(inelastic scattering, sel

m2() = -0.6 ± 2.2 ± 2

C. Kraus et al.
28

The Spectrometers&
Detector

The
KATRIN
Experiment

e-

eeThe
Tritium Source&
Gas retention
systemTime (h)Residuals ( )Count rate (cps)

KATRIN’s 1st Results++

KATRIN data with 1
Fit result

10 1

error bars

50

10 0

-40

m  1.1 eV (90% C.L.)
-30

-20

-10

0

10

20

Stat.

2

30

40

Stat. + syst.

0
-2
-40

-30

-20

-10

0

10

20

30

40

-30

-20

-10

0

10

20

30

40

40
20
0
-40

Results from first measurement
campaign yielded an eV scale limit

Retarding energy - 18574 (eV)Phys.Rev.D 104 (2021) 1, 012005

KATRIN’s 2nd Results

Results from first measurement
campaign yielded an eV scale limitm  1.1 eV (90% C.L.)
Phys.Rev.D 104 (2021) 1, 012005

Recently, a statistically improved limit
was also released…

m  0.8 eV (90% C.L.)<latexit sha1_base64="cRgcZJusJCvCOjbJIilKb6JXm/Y=">AAACNHicdVA9SwNBFNzz2/gVtbRZDAFtjj0xmlgJNhYWCiYKXgh7m3dxcXfv3N0TwpH8AX+NjYX+EsFObK0t3cQIKjrwYJh5A+9NlApuLCFP3tj4xOTU9MxsYW5+YXGpuLzSMEmmGdRZIhJ9HlEDgiuoW24FnKcaqIwEnEVXBwP/7Aa04Yk6td0UmpJ2FI85o9ZJrWJZtsIILMWhgGtM/GoeatnvQ6O/USNhuX/gH/mbvVaxRPwKCWo7gdshQziyVSG1KsHBSCmhEY5bxfewnbBMgrJMUGMuApLaZk615UxArxBmBlLKrmgHLhxVVIJp5sN3erjslDaOE+1GWTxUvydyKo3pyshtSmovzW9vIP7pxdBVMnXWkFCF25x2tEv8vMfG1WbOVZpZUOzznDgT2CZ40KALaWBWdAdpprn7CLNLqimzrueCq+qrD/w/aWz5wY6/fUJK+3uj0mbQGlpHGyhAu2gfHaJjVEcM3aI79IAevXvv2XvxXj9Xx7xRZhX9gPf2AYkfqhE=</latexit>

See A. Lokhov’s talk(Friday)e-Print: 2105.08533 [hep-ex]

KATRIN Outlook
KATRIN continues to collect data.

Target Sensitivity:
Comprehensive campaign to reduce and mitigate
backgrounds, including radon and Rydberg events.

200 meV (90% C.L.)

Better measurement/control of plasma instabilities in source.

Increased statistics

Background mitigation

Assessment ofplasma effects

Use photon spontaneous emission fromelectron in magnetic field.

Frequency-Based(Cyclotron Radiation Emission Spectroscopy)Cyclotron Radiation
EmissionSpectroscopy(CRES)“Nevermeasureanything but
frequency.”

A. L. Schawlow

O. Heaviside

Project
8:
Cyclotron
radiatUse frequency measurement of cyclotron
radiation from single electrons:

Novel approach: J. Formtransparent to• Source• Cyclotron radiation f
microwave radiation• Source transparent ttransport
from from• No •e- No
e- transport
source to detector• Highly precise freque• Leverages precision
Frequency Approach3

H

3

He+ + e+ ¯einherent in frequency
1
techniquesfc,0

fc =

eB
=
2⇡ me + E

B. Monreal and JAF, Phys. Rev D80:051301

1
eB
fc,0
Cyclotron Radiation=fc =2⇡ me c2 + Ekin
Emission
Project
8:
Cyclotron
radiation
emissio
Spectroscopy(CRES)

Novel approach: J. Formaggio and B. Monreal, P• Cyclotron radiation from single electron• Source transparent to microwave radiat• No e- transport from source to detector• Highly precise frequency measurement
fc,0

1
eB
11 eB
= 491 10(6) GHz⇡fc,0fc==27.992
T 2⇡ m2
2⇡ me + Ekin /ce1<latexit sha1_base64="JSkeLJxIEE6oyTAfk3N/rj0ySlg=">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</latexit>• Narrow band region of interest (@26 GHz).
• Small, but detectable power emitted.
Frequency Approach3

H

3

He+ + e+ ¯e

P (17.8 keV, 90 , 1 T) = 1 fW
P (30.2 keV, 90 , 1 T) = 1.7 fW

Sm
stat

energy changing gas collisions

Energy (keV)

sudden onset of power

Radiative energy loss

! =<latexit sha1_base64="5VsIhGCKufN4n6YePdsRQdLZADs=">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</latexit>

A “typical” event(actually, this was our first event)

eB
eB
=
me
me + K/c2

Project 8 Phase II

Trapping coilsarranged to provide
deep and shallow
traps.
Commissioned using
krypton gas, but
optimized for tritium
gas flow.

Electrons are magnetically trapped inside a circular waveguide to allow
enough time to reconstruct event.
Microwave photons from electron provide energy reconstruction.

First CRES Tritium Measurement
Linearity with 83mKr Spectroscopy
gas inlet

trap coils

calibration port

Model
• “Shallow trap”Dataconfiguration• System is extremely linear:!2/ndf = 0.3• 32-keV " energy: 32153.6 ± 2.4 eV

B ~ 1T

ESR magnetometers

waveguide terminator

Phase II Insert

PRELIMINARY§ Vénos, et al: 32151.7 ± 0.5 eV
Appl. Radiat. Isot. 63 323-7 (2005)

High resolution

See poster by C. Claessens and Y.-H. Sun(session 4, #400)
Noah S. Oblath -- XXIX International Conference on Neutrino Physics and Astrophysics

Phase II CRES instrument provides 1mm3
inside waveguide
Permits measurements of 83mKr and T2
Shallow trap configurations sacrificeefficiency for instrumental resolution, as
good as 2.0 ± 0.1 eV (83mKr, above)
First endpoint CRES measurement
conducted with no observed background.

Low backgroundJunFirstCRES
Tritium
Measurement
Preliminary Measurement of theT2 Endpoint
gas inlet

trap coils

calibration port

Energy spectrum and posterior fit

B ~ 1T

ESR magnetometers

waveguide terminator

Phase II Insert

Plot by T. Weiss

PRELIMINARY

T2 endpoint result:+! = -.//0. 1'#$.("#$.& eV
Background rate:≤ 3×-5")! eV "*s "* (90% C.I.)
Preliminary
Posterior distribution
Plot by T. Weiss

PRELIMINARY

Phase II CRES instrument provides 1mm3
inside waveguide
Permits measurements of 83mKr and T2
Shallow trap configurations sacrificeefficiency for instrumental resolution, as
Final
beeV
completedthis summer
goodanalysis
as 2.0 ±will
0.1(83mKr, above)

Bodine, et al.: Phys. Rev. C 91 (2015)

Noah S. Oblath -- XXIX International Conference on Neutrino Physics and Astrophysics

First endpoint CRES measurement
conducted with no observed background.

Low background

June 22, 2020

20

An Open Antenna Array(Phase III)

CRES must be scaled to much larger volumes 1 mm3 → 1 m3
Must leave waveguide for free space observed with antennas
Active signal processing techniques focus and reconstruct source volume:
Permits simultaneous electron events
Confines B-field uniformity requirement to single voxels

An Open Antenna Array(Phase III)

CRES must be scaled to much larger volumes 1 mm3 → 1 m3
Must leave waveguide for free space observed with antennas
Active signal processing techniques focus and reconstruct source volume:
Permits simultaneous electron events
Confines B-field uniformity requirement to single voxels

Bodine, Parno and Robertson,
Phys. Rev. C 91 (2015).

T+T
Edissoc(T2)

Any experiment with amolecular tritium (T2) source
will have a systematic penalty
associated with uncertainty inthe width of rotational andvibrational states of thedaughter 3He+T populated in
the decay.

4.590 eV

Q(T)

QA

T2

18591.3(10) eV
3He+ + T + e-

Q(T2)Eioniz(3He)
24.59 eV

3HeT2+ + e- + e3He + T+ + e-

Eioniz(T)13.60 eV

Edissoc(3HeT+)
1.897 eV

Eioniz(3HeT+)
45.16 eV

3HeT+ + e3He + T

Comparison of T2 andT decay schemes

In order to push to the next
target mass scale (IO), onewill need to switch to an
atomic tritium source.

rotation and vibration ofmolecular 3HeT+ daughter

Doss et al., Phys.
Rev. C 73 (2006)

Bodine, Parno and Robertson,
Phys. Rev. C 91 (2015).

T+T
Edissoc(T2)

Any experiment with amolecular tritium (T2) source
will have a systematic penalty
associated with uncertainty inthe width of rotational andvibrational states of thedaughter 3He+T populated in
the decay.

4.590 eV

Q(T)

QA

T2

18591.3(10) eV
3He+ + T + e-

Q(T2)Eioniz(3He)
24.59 eV

3HeT2+ + e- + e3He + T+ + e-

Edissoc(3HeT+)

Eioniz(T)1.897 eV

13.60 eV

Eioniz(3HeT+)
45.16 eV

3HeT+ + e3He + T

Comparison of T2 andT decay schemes
10

Relative probability

In order to push to the next
target mass scale (IO), onewill need to switch to an
atomic tritium source.

8

Atomic T

T2

6

4

Comparison ofT2 and T
ground states

2

0
-10

-8

-6

-4

-2

0

2

Relative Extrapolated Endpoint (eV)Any experiment with amolecular tritium (T2) source
will have a systematic penalty
associated with uncertainty inthe width of rotational andvibrational states of thedaughter 3He+T populated in
the decay.

In order to push to the next
target mass scale (IO), onewill need to switch to an
atomic tritium source.

Molecular sensitivity

Atomic sensitivity

A large scale atomic experiment to reach the inverted scale.

Known as Phase IV, Project 8 hopes to break throughthe degeneracy scale toward the inverted (40 meV)

Target Mass
Sensitivitymβ < 40 meVCurrent experiments have broken the eV scale…

… and a future atomic T experiment could
break the inverted scale.
nu-fit v 3.1
NO
IO

Mainz & Troitsk limits (95% CL)
100

KATRIN 2021 upper
limit (90% CL)

KATRIN design
sensitivity (90% CL)
10 1

10 2

10 1

Σmi [eV/c2]

Planck limit

Project 8 design
sensitivity (90% CL)
Cosmology
disfavoredmβ-decay [eV/c2]

ECHo/ Holmes
Projected100

27
gy Physics
r
e
n
E
h
g
i
H
Advances in150@ 1.5 keV
ΔE ≈ 28 eV𝜏 R ≈ 1 ms

100
CountsSi K𝛼Al K 𝛼500(a)This is a good decadefor direct neutrino massmeasurements, withseveralexperiments
Cl K 𝛼reaching for the sub-eV
scale and beyond.

0

500

1000

KATRIN, Project 8,
ECHo and HOLMES all
3000
2500
0
0
0
2
1500
ramping and taking
Energy (eV)data in the near future.
(b), 𝜏𝑅 ≈ 1 ms
V
e
k
.6
2
t
a
Δ𝐸 ≈ 47 eV
e
iv
g
ls
e
ix
p
sable

(a).

27
gy Physics
r
e
n
E
h
g
i
H
Advances in
150

Cl K 𝛼@ 1.5 keV
ΔE ≈ 28 eV𝜏 R ≈ 1 ms

Thanks for yourSi K𝛼attention!

Counts100
Al K 𝛼

50

0

0

500

1000

2000
1500
Energy (eV)
(b)

(a)

2500

3000

, 𝜏𝑅 ≈ 1 ms
V
e
k
.6
2
t
a
Δ𝐸 ≈ 47 eV
e
iv
g
ls
e
ix
p
sable

(a).

References(Normally, I would give a full list, but we just finished a hugereview, and it has almost 300 references).

That might be more useful.

Direct measurements of neutrino mass,
Physics Reports, Volume 914, 2021, Pages 1-54,
https://doi.org/10.1016/j.physrep.2021.02.002.

Event reconstruction is a bit more
complex

Oscillations

Cosmology0νββ

5m ββ (eV)Σ (eV)

1
0.50

Cosmology Limits
0.10
0.05

0.01

Inverted
Normal1
0.500

Inverted
Normal0.05

0.10m β (eV)

0.50

1

0.100
0.050

GERDA Limits

0.010
0.005
0.01

0.05

0.10
m β (eV)

0.50

Combining all the approaches provides a more
complete picture of the neutrino mass scale1