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NEUTRINOS �IN NUCLEAR PHYSICS

BJPJ

3

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THE ZOO OF 0NUBB SEARCHES

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Many completely different technologies…

CUORE/CUPID

GERDA/MAJORANA/

Legend

EXO/nEXO

Kamland Zen

SNO+

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THE ZOO OF 0NUBB SEARCHES

3

Many completely different technologies…

CUORE/CUPID

GERDA/MAJORANA/

Legend

EXO/nEXO

Kamland Zen

SNO+

This lecture, like life, is too short.

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Instead, try to explain the physics that connects them all

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RELATIVISTIC QUANTUM

MECHANICS

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DIRAC EQUATION

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Spin ½ fermions satisfy an equation of motion called the Dirac equation:

The solution can be written as an object with four components called a Dirac spinor:

The Schrodinger Eq. of relativistic spin ½ fermions

How much of this kind of particle is where

Paul Dirac

???

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WHAT DO THE FOUR DEGREES OF FREEDOM OF THE DIRAC SPINOR MEAN?

  • With a judicious choice of basis (Weyl):

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  • Dirac spinor breaks into two components for a spin-up particle and two components for a spin-down particle.

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  • But why are there two kinds of field for each spin?

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Two left spinning things

Two right spinning things

(when relativistic)

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ANTIMATTER

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  • Each pair has a positive energy part and a negative energy part.

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  • The negative energy part represents antimatter.
    • Matter moving backward in time, according to the Feynman Stueckelberg interpretation.

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Ψ= Ψ0e-i E t / ℏ

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  • The positron is the electrons antiparticle. It was predicted by Dirac (1928) before it was discovered by Anderson (1932).

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First positron detection, 1932

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NOT SO FAST!

Four numbers at each point in space? I’ll do it with two!

But, Ettore Majorana found a new class of solutions to Dirac’s equation using only two degrees of freedom.

Four-component object built using some two-component ⍵(x)

Ettore Majorana

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CHARGE CONJUGATION

  • For Majorana’s solution:

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  • Whereas for a general Dirac solution:

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Definition of charge conjugation operation:

transform particles 🡨🡪 antiparticles

It’s antiparticle is the particle!

Two degrees of freedom correspond to

left and right of a “particle-antiparticle-thing”

Distinct particle and antiparticle

Four degrees of freedom correspond to

left and right of particle and antiparticle.

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IN SHORT, WHAT ARE MAJORANA FERMIONS:

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We call it a particle

(behaves like matter)

We call it an antiparticle

(behaves like antimatter)

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WHO CARES?

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Each term represents some interaction between quantum fields.

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After quantizing the theory, this becomes an interaction between particles.

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The standard model Lagrangian

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  • Mercifully, there is a recipe for writing down that Lagrangian.

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  • Write down all terms that are:

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  • 1) Consistent with the symmetries of nature

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  • 2) Renormalizible

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+ Lorentz invariance

Gauge invariance:

All appear in nature, except 1 mystery absentee (strong CPV).

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IS THERE MORE?

  • We’ve never seen a particle interaction not predicted by the SM. But we suspect there is new physics out there…
    • Dark matter
    • Hierarchy problem
    • Gauge unification
    • Etc…

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  • Lots of ideas:
    • SUSY
    • Extra dimensions
    • String theory
    • Lorentz violation
    • [your favorite theory]

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Evidence for dark matter from gravitational lensing

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  • We believe that whatever the new physics is, it kicks in a high energies (that’s why we build accelerators).

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  • Technically we say the SM is likely a “low energy effective theory”.

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At high energies:

At low energies:

COMPLETE THEORY, VALID AT ALL ENERGIES

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At high energies:

At low energies:

  • As a point of reference, here is another low energy effective theory:

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At high energies:

At low energies:

“dimension-4 correction”

  • As a point of reference, here is another low energy effective theory:

And, we can test the high energy theory by confirming these corrections.

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If SM is a low energy effective theory:

Dimension-5 terms

Dimension-6 terms

Etc…

Enew > 10 TeV Seems likely (LHC)

Enew ~ 1013 TeV Maybe? (GUT scale)

Standard model

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  • The only dimension-5 operator one can add obeying SM gauge symmetry:

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  • This term does an important thing - it makes neutrinos Majorana particles, with mass suppressed by the new physics scale.

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  • And it makes the theory non-renormalizible – implying there must be something else at high scale.

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Weinberg 1979.

If SM is a low energy effective theory:

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DOUBLE-BETA DECAY

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A rare radioactive process, energetically allowed for some even-even nuclei where mZ+1 > mZ > mZ+2

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(Z,A) → (Z+2,A) + e-1 + ν1 + e-2 + ν2

(NB: this decay mode has nothing to do with Majorana neutrinos, but we’ll get back to them soon)

Maria Goeppert Mayer

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Observed in 82Se, 52 years after prediction.

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Half-life is ~1013 times age of Universe.

Discovery of double beta decay

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DOUBLE BETA WITH NO NEUTRINOS?

  • This can only happen if the neutrino is its own antiparticle.

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  • Observation of double beta decay with no neutrinos would prove the neutrino to be a Majorana fermion.

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How fast will this decay go? Lets find out!

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TIME FOR MATH INTERLUDE 2

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DOUBLE BETA ISOTOPES

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  • Larger G 🡪 higher rate

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  • Helps if Q is above most background γ rays

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  • Abundance, cost, and ease of enrichment are also factors influencing isotope choice.

Phase space factor

Energy of peak

Natural abundance

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NUCLEAR MATRIX ELEMENTS

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1

2

3

+

+

2

Γ ⍺

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1

2

3

+

+

2

Γ ⍺

(Ue1)2m1

(Ue2)2m2

(Ue3)2m3

+

+

2

=

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1

2

3

+

+

2

Γ ⍺

(Ue1)2m1

(Ue2)2m2

(Ue3)2m3

+

+

2

=

c122c132e2i⍺ m1

s132m3

+

+

2

=

c122s122e2iβ m2

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1

2

3

+

+

2

Γ ⍺

(Ue1)2m1

(Ue2)2m2

(Ue3)2m3

+

+

2

=

c122c132e2i⍺ m1

s132m3

+

+

2

=

c122s122e2iβ m2

=

mββ

2

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1

2

3

+

+

2

Re(M)

Im(M)

Γ ⍺

Normal Ordering

(angles are unknown CP phases)

Re(M)

Im(M)

Inverted Ordering

(angles are unknown CP phases)

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Inverted

Normal

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WHAT IF THERE ARE ADDITIONAL NEUTRINOS?

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1

2

3

+

+

2

Γ ⍺

Re(M)

Im(M)

IO, 4 neutrinos

(angles are unknown CP phases)

4

+

Re(M)

Im(M)

IO, 3 neutrinos

(angles are unknown CP phases)

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WITH A STERILE NEUTRINO:

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Inverted

Normal

But this gets less difficult!

Now you can close the loop here after all

mββ

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If SM is a low energy effective theory:

You can also get it from up here

So really we need to consider 0nubb as a discovery search – just hit the longest half lives possible!

https://arxiv.org/pdf/1708.09390.pdf

BSM theory with lepton number violation at high energy makes SM Wilson coefficients in the EFT expansion

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  • Given a high energy model, the kinematics of the final electrons can be predicted.

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  • If 0nubb is seen, measuring the opening angle and energy sharing could illuminate the mechanism.

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Opening angle

Energy sharing

E1

E2

θ

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CURRENT WORLD HEAVYWEIGHT CHAMPION

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WWE world heavyweight champion

Seth “Freakin” Rollins

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CURRENT WORLD HEAVYWEIGHT CHAMPION

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WWE world heavyweight champion

0nubb world heavyweight chamption

Seth “Freakin” Rollins

Kamland “Freakin” Zen

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From Neutrino2024

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News from Neutrino2024:

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CURRENT LIMITS

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KZ limit

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Inverted Heirachy

Going further:

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Inverted Heirachy

1000 kg experiment

Or to be specific:

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Run for 100 years

Run for 15 years

Run for 2-3 years

Run for 1000 years

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Where are the backgrounds from?

(nb: these are pre-Neutrino2024 numbers)

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Where are the backgrounds from?

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THE IDEAL EXPERIMENT:

  • MANDATORY:
    • Resolution better than ~2% FWHM to fully reject two-neutrino mode

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  • Then just watch and wait…

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Measuring Energy

CUORE

SNO+

GERDA

KZ

EXO-200

NEXT-White

Free from 2nubb

Once free from 2nubb, radioactive and cosmogenic backgrounds become dominant

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Measuring Energy

CUORE

SNO+

GERDA

KZ

EXO-200

NEXT-White

Solid state detectors are amazing for measuring energy.

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LEGEND

  • 200kg, eventually 1000kg, of enriched 76Ge crystals

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  • The king of excellent E resolution - 0.1%FWHM in the best crystals.

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LEGEND200 backgrounds and energy resolutions:

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Measuring Energy

CUORE

SNO+

GERDA

KZ

EXO-200

NEXT-White

Xenon gas much better energy resolution than liquid Xe, why?

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RECOMBINATION-LIMITED IONIZATION ENERGY RESOLUTION

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Recombination

Limited gas

Intrinsic (up to ~50 bar)

Liquid

Fluctuations in electron-ion recombination limit energy resolution for dense TPCs.

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Every event is a random microscopic shape, so each loses different amounts of charge to recombination.

e-

e-

e-

+

+

+

+

+

+

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Where are the backgrounds from?

Radiogenics

Solar neutrinos(!)

Cosmogenics

These will limit all future experiments.

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“100kg-class” experiments:

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NEXO

  • Proposed ton-scale liquid xenon detector.
  • Self-shielding of xenon from outer regions protects inner clean volume from backgrounds

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CUPID

  • Cryogenic bolometers coupled to light sensors
  • Precise calorimetry and optical handle on surface backgrounds advances on the CUORE approach.

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“100kg-class” experiments:

I work on this one, so I’m going to tell you about it.

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THE NEXT PROGRAM

  • Sequence of HPGXe TPCs, focused on achieving big, very low background xenon 0νββ detector

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🡪 NEXT-DBDM

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🡪 NEXT-DEMO

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🡪 NEXT-White

🡪 NEXT-100

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  • N-Ton Scale

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1800 SiPMs, 1cm pitch

10 kg active region (10bar) 50cm drift length

12 PMTs operating in vacuum (30% coverage)

SiPM feedthroughs

HV Connections

(Berkeley, US)

(Valencia, Spain)

(Canfranc, Spain)

(Canfranc, Spain)

NEXT-White operating now

Full underground technology demonstrator @10kg scale

R&D

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THE 208TL DOUBLE ESCAPE PEAK

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On double escape peak

Off double escape peak

15cm

15cm

208Tl double escape

Compton continuum

🡪 0.89% at Qbb

NEXT-White data

NEXT-White data

JHEP 2019, 52 (2019)

SM process that makes e+e- at a well-defined energy.

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We get to see energy resolution and topology all in one plot!

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TWO-NEUTRINO DOUBLE BETA DECAY EVENTS

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NEXT-White data

Topologically identified and away from double escape peaks

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BARIUM TAGGING

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Barium ion is only produced in a true ββ decay, not in any other radioactive event🡪

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Identification of Ba ion plus ~1% FWHM energy measurement would give a background-free experiment.

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Is it plausible to detect an individual barium ion or atom in a ton of material, inside a working xenon TPC?

136Xe 🡪 136Ba + e + e

(My fave thing: forgive me for indulging ☺ )

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BA IMAGING IN XENON ICE

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nEXO has developed methods of imaging Ba+ and Ba0 in carefully grown xenon ice.

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Frozen Xe on cryo-probe

Ba

Xe

Xe

Xe

Xe

Xe

Xe

Xe

Xe

Xe

Xe

Xe

Xe

555nm

560nm

564nm

Colors show bleaching effect

Various types of defect sites

Individual Ba atoms imaged in frozen xenon matrices in vacuum

Single Ba2+ imaged in this site

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BA IMAGING IN XENON GAS

Individual Ba2+ ions imaged in 10 bar of xenon gas

NEXT has built microscopy systems capable of imaging individual barium ions in high pressure xenon gas environments.

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1mm x 1mm area can be scanned with single ion precision.

Ba2+

Ba2+

Xe

Xe

Xe

Xe

Xe

Xe

Xe

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TIRF

Single Ba2+ molecular complexes

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THE TON SCALE

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Ton Scale

We need to do this with multiple isotopes and techniques

Current limit

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NB: if you use these tons, the sensitivity will be better.

1016.05 kg

1000.00 kg

907.19 kg

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TOWARD NORMAL ORDERING

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Current limit

Ton Scale

Beyond ton-scale

Can we ever do this?

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ISOTOPES

  • Will need hundreds of tons of isotope. Current industrial production of any species is insufficient.

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  • There are difficulties with both acquisition of raw material and its enrichment.

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  • Some notable factoids:

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    • Tellurium: �Comes naturally enriched to 34%. So natural tellurium is the most viable for an unenriched experiment.
    • Molybdenum:�New capacity for enrichment of Molybdenum in 100Mo for nuclear medicine is needed. 0nubb may be parasitic?
    • Germanium:�Semiconductor industry enriches germanium already; 76Ge can in principle be extracted as byproduct?
    • Xenon:�Atmospheric carbon capture technology based on metal organic frameworks has plausible extendibility to capture atmospheric Xe. Free from steel industry capacity limit?

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  • Both enrichment R&D and new major facilities would be needed to produce isotope at the scale needed for a normal-ordering scale experiment.

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GIANT TPCS

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  • Radiogenics become totally irrelevant due to self shielding

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Cosmogenics and solar neutrinos become a serious concern!

If energy resolution achievable at scale, with kiloton masses, normal ordering parameter space is accessible.

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GIANT TPCS

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  • Radiogenics become totally irrelevant due to self shielding

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Cosmogenics and solar neutrinos become a serious concern!

If energy resolution achievable at scale, with kiloton masses, normal ordering parameter space is accessible.

…in salt caverns?

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ISOTOPE IN KTONS OF LIQUID SCINTILLATOR…

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Xe or Te loaded in kilotons of liquid scintillator🡪

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ISOTOPE IN KTONS OF LIQUID SCINTILLATOR…

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Xe or Te loaded in kilotons of liquid scintillator🡪

Much, much R&D…

Quantum dot doped liquid scintillator @NuDot

Dichroicon

Slow scintillator for Cerenkov separation

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ISOTOPE IN KTONS LS, OR IN LIQUID ARGON?

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Xe or Te loaded in kilotons of liquid scintillator🡪

  • Achieving this energy resolution in DUNE is an extreme challenge.

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Argon also needs to be depleted to remove background from 42Ar 🡪

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CONCLUSIONS

  • NDBD is the only sensitive known way to probe the Majorana nature of the neutrino.

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  • Experiments at the 100kg scale have demonstrated background indices in the range 2-200 ct/ton/ky/yr

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  • Ton-scale experiments plan to reduce backgrounds by 1.5-3 orders of magnitude relative 100kg phases and probe the inverted mass ordering range of parameter space.

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  • Beyond-ton-scale will require huge, ultra-low background detectors that we don’t yet know how to build, but need to figure out!

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