Neutrinoless Double Beta Decay from Lattice QCD Amy Nicholson UC - - PowerPoint PPT Presentation

Neutrinoless Double Beta Decay from Lattice QCD

Amy Nicholson UC Berkeley Lattice 2016 Southampton, UK

History

Pauli 1930 Chadwick 1932 Fermi 1934 Majorana 1937 Goppert-Mayer 1935 Racah 1937

μ+ μ- 𝜌- 𝜉μ μ- μ+ 𝜌+ 𝜉μ 𝜉R 𝜉 𝜉

Lepton Number

Neutrinos have no known charge or other additively conserved quantum number

μ+ μ- 𝜌- 𝜉R μ- μ+ 𝜌+ 𝜉L 𝜉R 𝜉R 𝜉R

Lepton Number

Neutrinos have no known charge or other additively conserved quantum number

F

• r

b i d d e n b y h e l i c i t y ?

𝜉R 𝜉R 𝜉L x

Neutrinos have masses!

Takaaki Kajita (Super-K) Arthur B. McDonald (SNO) Nobel Prize, 2015

μ+ μ- 𝜌- 𝜉R μ- μ+ 𝜌+ 𝜉L 𝜉R 𝜉R 𝜉L x ~ mββ

Lepton Number

Neutrinos have no known charge or other additively conserved quantum number

But they’re tiny!

• scillation experiments

don’t tell us absolute mass scale 0𝝃𝛾𝛾 will!

• Anything not forbidden by

symmetry should occur in nature

• Why are neutrinos so

light?

• Dirac mass on its own

requires fine-tuning

Majorana or Dirac?

L5 = −m ⇣ ¯ L ˜ H ⌘ ⇣ ˜ HL ⌘†

• Anything not forbidden by

symmetry should occur in nature

• Why are neutrinos so

light?

• Dirac mass on its own

requires fine-tuning

✓ ML MD MD MR ◆

Majorana or Dirac?

L5 = −m ⇣ ¯ L ˜ H ⌘ ⇣ ˜ HL ⌘†

• Anything not forbidden by

symmetry should occur in nature

• Why are neutrinos so

light?

• Dirac mass on its own

requires fine-tuning

✓ ML MD MD MR ◆

Majorana or Dirac?

L5 = −m ⇣ ¯ L ˜ H ⌘ ⇣ ˜ HL ⌘†

dim-4 operator not allowed

• Anything not forbidden by

symmetry should occur in nature

• Why are neutrinos so

light?

• Dirac mass on its own

requires fine-tuning

✓ ML MD MD MR ◆

Majorana or Dirac?

L5 = −m ⇣ ¯ L ˜ H ⌘ ⇣ ˜ HL ⌘†

• Anything not forbidden by

symmetry should occur in nature

• Why are neutrinos so

light?

• Dirac mass on its own

requires fine-tuning

✓ ML MD MD MR ◆

ml ∼ M 2

D/MR

mh ∼ MR

Majorana or Dirac?

L5 = −m ⇣ ¯ L ˜ H ⌘ ⇣ ˜ HL ⌘†

• Anything not forbidden by

symmetry should occur in nature

• Why are neutrinos so

light?

• Dirac mass on its own

requires fine-tuning

✓ ML MD MD MR ◆

ml ∼ M 2

D/MR

mh ∼ MR

Majorana or Dirac?

MR ∼ 1015GeV

MD ∼ 200GeV

ml ∼ 0.05eV

L5 = −m ⇣ ¯ L ˜ H ⌘ ⇣ ˜ HL ⌘†

If observed, could help explain matter/anti-matter asymmetry in the universe!

Jansen (1996) Bödeker, Moore, Rummukainen (2000) Fodor (2000)

Experiment

Nuclear physics gives us a natural filter for the process

Two broken pairs All nucleons paired A=76

Experiment

Nuclear physics gives us a natural filter for the process

Two broken pairs All nucleons paired A=76

Energetically forbidden

Experiment

Nuclear physics gives us a natural filter for the process

Two broken pairs All nucleons paired A=76

Second order, allowed

Neutrinoless mode can be isolated using spectroscopic methods

Experiment

Neutrinoless mode can be isolated using spectroscopic methods

Experiment

Neutrinoless mode can be isolated using spectroscopic methods

Experiment

0𝜉𝛾𝛾 decay Experiment

nEXO

136Xe

Sno+

130Te

Gerda

76Ge

Cuore

130Te

How can LQCD contribute?

gA gA gA ~ ~

Standard picture: long-range contribution

Jμ

gA

A

n n

(p2)

l

Short-range contribution: probe for heavy physics

Valle & Schecter, Fig.: H. Päs, W. Rodejohann New J.Phys. 17 (2015) no.11, 115010

Black box:

l

Short-range contribution: probe for heavy physics

~1/MR

Valle & Schecter, Fig.: H. Päs, W. Rodejohann New J.Phys. 17 (2015) no.11, 115010

Black box:

l

Short-range contribution: probe for heavy physics

~1/MR m𝛾𝛾 ~1/MR x

Valle & Schecter, Fig.: H. Päs, W. Rodejohann New J.Phys. 17 (2015) no.11, 115010

Black box:

l

Short-range contribution: probe for heavy physics

Black box: ~1/MR

Valle & Schecter, Fig.: H. Päs, W. Rodejohann New J.Phys. 17 (2015) no.11, 115010

Short-range contribution: probe for heavy physics

Black box: ~1/MR

0𝝃𝛾𝛾 experiments may help constrain R-parity violating coefficients

Valle & Schecter, Fig.: H. Päs, W. Rodejohann New J.Phys. 17 (2015) no.11, 115010

Short-range contribution: probe for heavy physics

O(p-2) O(p0) O(p0) O(p2)

Prezeau, Ramsey-Musolf, Vogel (2003)

~1/MR Chiral EFT

Short-range contribution: probe for heavy physics

O(p-2) O(p0) O(p0) O(p2)

Prezeau, Ramsey-Musolf, Vogel (2003)

~1/MR Chiral EFT

• Nine operators:
• 𝜌 → 𝜌: only need

parity even

• Vector operators

suppressed by me

Prezeau, Ramsey-Musolf, Vogel (2003)

Effective Lagrangian

• Nine operators:
• 𝜌 → 𝜌: only need

parity even

• Vector operators

suppressed by me

Prezeau, Ramsey-Musolf, Vogel (2003)

Effective Lagrangian

• Nine operators:
• 𝜌 → 𝜌: only need

parity even

• Vector operators

suppressed by me

Prezeau, Ramsey-Musolf, Vogel (2003)

Effective Lagrangian

Calculate LECs; EFT then determines nn → pp transition via pion exchange diagram

✔ ✔ ✔ ✔ ✔

Left-right symmetric models

Prezeau, Ramsey-Musolf, Vogel (2003), Savage (1999)

O++

3+

O++

1+

𝛒- 𝛒- t=0 t=tf t=Nt - ti

Oi

• Exact momentum projection at source

and sink

• Must add color mixed versions of

Prezeau, Ramsey-Musolf, Vogel ops 1&2

Contractions

O−−

2+ =

• ¯

qRτ −qL ⇥ ¯ qRτ −qL ⇤ +

• ¯

qLτ −qR ⇥ ¯ qLτ −qR ⇤ O0

2+ =

• ¯

qRτ qL ⇤ ⇥ ¯ qRτ qL

• +
• ¯

qLτ qR ⇤ ⇥ ¯ qLτ qR

• O0

1+ =

• ¯

qLτ γµqL ⇤ ⇥ ¯ qRτ γµqR

• O−−

1+ =

• ¯

qLτ −γµqL ⇥ ¯ qRτ −γµqR ⇤ O−−

3+ =

• ¯

qLτ −γµqL ⇥ ¯ qLτ −γµqL ⇤ +

• ¯

qRτ −γµqR ⇥ ¯ qRτ −γµqR ⇤

spin color

𝛒- 𝛒- t=0 t=tf t=Nt - ti

Oi

• Exact momentum projection at source

and sink

• Must add color mixed versions of

Prezeau, Ramsey-Musolf, Vogel ops 1&2

Contractions

O−−

2+ =

• ¯

qRτ −qL ⇥ ¯ qRτ −qL ⇤ +

• ¯

qLτ −qR ⇥ ¯ qLτ −qR ⇤ O0

2+ =

• ¯

qRτ qL ⇤ ⇥ ¯ qRτ qL

• +
• ¯

qLτ qR ⇤ ⇥ ¯ qLτ qR

• O0

1+ =

• ¯

qLτ γµqL ⇤ ⇥ ¯ qRτ γµqR

• O−−

1+ =

• ¯

qLτ −γµqL ⇥ ¯ qRτ −γµqR ⇤ O−−

3+ =

• ¯

qLτ −γµqL ⇥ ¯ qLτ −γµqL ⇤ +

• ¯

qRτ −γµqR ⇥ ¯ qRτ −γµqR ⇤

spin color

• Möbius DWF on HISQ
• Gradient flow method for smearing configs
• mres < 0.1 ml for moderate L5
• Wall + point sources for pions
• ~ 1000 cfgs, 1 source/cfg

163 × 48, mπL ∼ 3.78 243 × 48, mπL ∼ 3.99 323 × 48, mπL ∼ 3.25 243 × 64, mπL ∼ 3.22 243 × 64, mπL ∼ 4.54 323 × 64, mπL ∼ 4.29 483 × 64, mπL ∼ 3.91 403 × 64, mπL ∼ 5.36 323 × 96, mπL ∼ 4.50 483 × 96, mπL ∼ 4.73

MILC Collaboration Phys. Rev. D87 (2013) 054505 Narayanan, Neuberger (2006), Luscher (2010)

• K. Orginos, C. Monahan (private communication)

10 15 20 0.3 0.4 0.5 0.6 0.7 0.8 tf O2+ 5 10 15 20

• 0.35
• 0.30
• 0.25
• 0.20
• 0.15
• 0.10
• 0.05

tf O'2+

Wall Point

Signals

• m𝜌 ~ 135 MeV
• L = 5.76 fm
• a = 0.12 fm

5 10 15 20

• 0.2

0.0 0.2 0.4 0.6 0.8 tf Oi+

O1+, O0

1+

O2+, O0

2+

O3+

Preliminary!

5 10 15 20

• 0.2

0.0 0.2 0.4 0.6 0.8 tf Oi+

O1+, O0

1+

O2+, O0

2+

O3+

5 10 15 20

• 0.008
• 0.006
• 0.004
• 0.002

0.000 0.002 0.004 tf O3+

Preliminary!

2.5 3.0 3.5 4.0 4.5 5.0 5.5 6.0

• 0.2

0.0 0.2 0.4 0.6 0.8 1.0 mpL Oi+

O1+, O0

1+

O2+, O0

2+

O3+

Preliminary!

2.5 3.0 3.5 4.0 4.5 5.0 5.5 6.0

• 0.2

0.0 0.2 0.4 0.6 0.8 1.0 mpL Oi+

O1+, O0

1+

O2+, O0

2+

O3+

2.5 3.0 3.5 4.0 4.5 5.0 5.5 6.0

• 0.014
• 0.012
• 0.010
• 0.008
• 0.006
• 0.004
• 0.002

0.000 mpHMeVL O3+

Preliminary!

100 150 200 250 300 350

• 0.2

0.0 0.2 0.4 0.6 0.8 1.0 1.2 mpHMeVL Oi+

O1+, O0

1+

O2+, O0

2+

O3+

Preliminary!

100 150 200 250 300 350

• 0.2

0.0 0.2 0.4 0.6 0.8 1.0 1.2 mpHMeVL Oi+

O1+, O0

1+

O2+, O0

2+

O3+

100 150 200 250 300 350

• 0.030
• 0.025
• 0.020
• 0.015
• 0.010
• 0.005

0.000 mpHMeVL O3+

Preliminary!

50 100 150 200 250 300 350

• 0.2

0.0 0.2 0.4 0.6 0.8 1.0 1.2 mpHMeVL Oi+

Preliminary!

O1+, O0

1+

O2+, O0

2+

O3+

Oi = c0 + c2m2

π

50 100 150 200 250 300 350

• 0.2

0.0 0.2 0.4 0.6 0.8 1.0 1.2 mpHMeVL Oi+

Preliminary!

O1+, O0

1+

O2+, O0

2+

O3+

O3 = c2m2

π + c4m4 π

50 100 150 200 250 300 350

• 0.030
• 0.025
• 0.020
• 0.015
• 0.010
• 0.005

0.000 mpHMeVL O3+

Oi = c0 + c2m2

π

• 0𝜉𝛾𝛾: search for Majorana mass signature
• Lepton number violation could be source of matter/anti-matter

asymmetry

• Huge experimental efforts planned/underway
• LQCD can make major impact on understanding of short-range
• perators
• Preliminary results for 𝜌- → 𝜌+ matrix element
• Multiple pion masses, lattice spacings, volumes
• Pion mass dependence as expected from chiral EFT counting
• To do:
• Renormalization
• Extrapolations in pion mass/lattice spacing
• Other contact operators....

Summary

Buras, Misiak, Urban (2000), Tiburzi (2012)

Contact

• perators

O(p-2) O(p0) O(p0) O(p2)

• LO almost c︎omplete!

Contact

• perators

O(p-2) O(p0) O(p0) O(p2)

✔

• NLO: disconnected diagrams
• LO almost c︎omplete!

Contact

• perators

O(p-2) O(p0) O(p0) O(p2)

✔

• NLO: disconnected diagrams
• LO almost c︎omplete!

Contact

• perators

O(p-2) O(p0) O(p0) O(p2)

✔

• Don’t contribute to 0+ → 0+

nuclear transitions

• NLO: disconnected diagrams
• LO almost c︎omplete!

Contact

• perators

O(p-2) O(p0) O(p0) O(p2)

✔

• Don’t contribute to 0+ → 0+

nuclear transitions

• nn → pp contact operators

*Doi & Endres, Originos et. al., Günther et. al.

• Isospin limit: 576 contractions
• Extension of unified contraction method*
• Need position space

source & sink

• otherwise all-to-all

propagators connect to 4-quark operator

• stochastically project onto

zero total momentum

Contractions

n n n n

Iso-clover cfgs (W. Detmold, R.Edwards, D. Richards, K. Orginos)

momentum + displaced local + local momentum + displaced displaced + displaced

n n n n

Need displaced operators!

Iso-clover cfgs (W. Detmold, R.Edwards, D. Richards, K. Orginos)

momentum + displaced local + local momentum + displaced displaced + displaced

n n n n n n

p p

Finite volume formalism for 2 → 2 matrix elements completed:

• R. Briceño, M. Hansen Phys.Rev. D94

(2016) no.1, 013008 Renormalization known in MS:

• B. Tiburzi Phys.Rev. D86 (2012) 097501

momentum + displaced local + local momentum + displaced displaced + displaced

Stay tuned!

• LBL/UCB: Chia Cheng Chang, AN, André Walker-Loud,
• LLNL: Evan Berkowitz, Enrico Rinaldi, Pavlos Vranas
• NERSC: Thorsten Kurth
• JLab: Balint Jóo
• CCNY: Brian Tiburzi
• nVidia: Kate Clark