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

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

Lepton Number Neutrinos have no known charge or other additively conserved quantum number 𝜉 𝜉 R 𝜉 μ - μ + 𝜌 - μ - μ + 𝜌 + 𝜉 μ 𝜉 μ

Lepton Number Neutrinos have no known charge or other additively conserved quantum number y b n e d d ? i b y t r 𝜉 R i o c i F l e 𝜉 R 𝜉 R h μ - μ + 𝜌 - μ - μ + 𝜌 + 𝜉 R 𝜉 L

Neutrinos have masses! Takaaki Kajita 𝜉 R x 𝜉 R 𝜉 L (Super-K) Arthur B. McDonald (SNO) Nobel Prize, 2015

Lepton Number Neutrinos have no known charge or other additively conserved quantum number But they’re oscillation experiments don’t tell us absolute tiny! 𝜉 R x ~ m ββ mass scale 𝜉 R 𝜉 L 0 𝝃𝛾𝛾 will! μ - μ + 𝜌 - μ - μ + 𝜌 + 𝜉 R 𝜉 L

Majorana or Dirac? • Anything not forbidden by symmetry should occur in nature ⌘ † ⇣ ⌘ ⇣ L ˜ ¯ ˜ L 5 = − m H HL • Why are neutrinos so light? • Dirac mass on its own requires fine-tuning

Majorana or Dirac? • Anything not forbidden by symmetry should occur in nature ✓ ◆ M L M D ⌘ † ⇣ ⌘ ⇣ L ˜ ¯ ˜ L 5 = − m H HL M D M R • Why are neutrinos so light? • Dirac mass on its own requires fine-tuning

Majorana or Dirac? • Anything not forbidden by symmetry should occur in dim-4 operator not allowed nature ✓ ◆ M L M D ⌘ † ⇣ ⌘ ⇣ L ˜ ¯ ˜ L 5 = − m H HL M D M R • Why are neutrinos so light? • Dirac mass on its own requires fine-tuning

Majorana or Dirac? • Anything not forbidden by symmetry should occur in nature ✓ ◆ 0 M L M D ⌘ † ⇣ ⌘ ⇣ L ˜ ¯ ˜ L 5 = − m H HL M D M R • Why are neutrinos so light? • Dirac mass on its own requires fine-tuning

Majorana or Dirac? • Anything not forbidden by symmetry should occur in nature ✓ ◆ 0 M L M D ⌘ † ⇣ ⌘ ⇣ L ˜ ¯ ˜ L 5 = − m H HL M D M R • Why are neutrinos so m l ∼ M 2 D /M R m h ∼ M R light? • Dirac mass on its own requires fine-tuning

Majorana or Dirac? • Anything not forbidden by symmetry should occur in nature ✓ ◆ 0 M L M D ⌘ † ⇣ ⌘ ⇣ L ˜ ¯ ˜ L 5 = − m H HL M D M R • Why are neutrinos so m l ∼ M 2 D /M R m h ∼ M R light? • Dirac mass on its own m l ∼ 0 . 05 eV M D ∼ 200 GeV requires fine-tuning M R ∼ 10 15 GeV

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 A=76 paired

Experiment Nuclear physics gives us a natural filter for the process Two broken pairs Energetically forbidden All nucleons A=76 paired

Experiment Nuclear physics gives us a natural filter for the process Second order, Two broken pairs allowed All nucleons A=76 paired

Experiment 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 Cuore 0 𝜉𝛾𝛾 decay 130 Te Gerda 76 Ge Sno+ 130 Te nEXO 136 Xe

How can LQCD contribute?

Standard picture: long-range contribution g A ~ g A ~ g A l g A A J μ (p 2 ) n n

Short-range contribution: probe for heavy physics l Black box: Valle & Schecter, Fig.: H. Päs, W. Rodejohann New J.Phys. 17 (2015) no.11, 115010

Short-range contribution: probe for heavy physics ~1/M R l Black box: Valle & Schecter, Fig.: H. Päs, W. Rodejohann New J.Phys. 17 (2015) no.11, 115010

Short-range contribution: probe for heavy physics x m 𝛾𝛾 ~1/M R ~1/M R l Black box: Valle & Schecter, Fig.: H. Päs, W. Rodejohann New J.Phys. 17 (2015) no.11, 115010

Short-range contribution: probe for heavy physics ~1/M R Black box: Valle & Schecter, Fig.: H. Päs, W. Rodejohann New J.Phys. 17 (2015) no.11, 115010

Short-range contribution: probe for heavy physics 0 𝝃𝛾𝛾 experiments may help ~1/M R constrain R-parity violating coefficients Black box: Valle & Schecter, Fig.: H. Päs, W. Rodejohann New J.Phys. 17 (2015) no.11, 115010

Short-range contribution: probe for heavy physics ~1/M R Chiral EFT O (p -2 ) O (p 0 ) O (p 0 ) O (p 2 ) Prezeau, Ramsey-Musolf, Vogel (2003)

Short-range contribution: probe for heavy physics ~1/M R Chiral EFT O (p -2 ) O (p 0 ) O (p 0 ) O (p 2 ) Prezeau, Ramsey-Musolf, Vogel (2003)

Effective Lagrangian Prezeau, Ramsey-Musolf, Vogel (2003) • Nine operators: • 𝜌 → 𝜌 : only need parity even • Vector operators suppressed by m e

Effective Lagrangian Prezeau, Ramsey-Musolf, Vogel (2003) • Nine operators: • 𝜌 → 𝜌 : only need parity even • Vector operators suppressed by m e

Effective Lagrangian Prezeau, Ramsey-Musolf, Vogel (2003) • Nine operators: • 𝜌 → 𝜌 : only need parity even • Vector operators suppressed by m e Calculate LECs; EFT then determines nn → pp transition via pion exchange diagram

✔ ✔ ✔ ✔ ✔ Left-right symmetric models O ++ O ++ 1+ 3+ Prezeau, Ramsey-Musolf, Vogel (2003), Savage (1999)

Contractions • Exact momentum projection at source 𝛒 - t=t f and sink spin color • Must add color mixed versions of Prezeau, Ramsey-Musolf, Vogel ops 1&2 O i t=0 q L τ − γ µ q L � � ⇥ ⇤ O −− 1+ = ¯ q R τ − γ µ q R ¯ O 0�� q L τ � γ µ q L � ⇤ ⇥ � q R τ � γ µ q R 1+ = ¯ ¯ � � ⇥ ⇤ � � ⇥ ⇤ O −− 2+ = q R τ − q L ¯ q R τ − q L ¯ + q L τ − q R ¯ q L τ − q R ¯ 𝛒 - t=N t - t i O 0�� � ⇤ ⇥ � � ⇤ ⇥ � q R τ � q L q R τ � q L q L τ � q R q L τ � q R 2+ = ¯ ¯ + ¯ ¯ q L τ − γ µ q L q R τ − γ µ q R � � ⇥ ⇤ � � ⇥ ⇤ O −− 3+ = ¯ q L τ − γ µ q L ¯ + ¯ q R τ − γ µ q R ¯

Contractions • Exact momentum projection at source 𝛒 - t=t f and sink spin color • Must add color mixed versions of Prezeau, Ramsey-Musolf, Vogel ops 1&2 O i t=0 q L τ − γ µ q L � � ⇥ ⇤ O −− 1+ = ¯ q R τ − γ µ q R ¯ O 0�� q L τ � γ µ q L � ⇤ ⇥ � q R τ � γ µ q R 1+ = ¯ ¯ � � ⇥ ⇤ � � ⇥ ⇤ O −− 2+ = q R τ − q L ¯ q R τ − q L ¯ + q L τ − q R ¯ q L τ − q R ¯ 𝛒 - t=N t - t i O 0�� � ⇤ ⇥ � � ⇤ ⇥ � q R τ � q L q R τ � q L q L τ � q R q L τ � q R 2+ = ¯ ¯ + ¯ ¯ q L τ − γ µ q L q R τ − γ µ q R � � ⇥ ⇤ � � ⇥ ⇤ O −− 3+ = ¯ q L τ − γ µ q L ¯ + ¯ q R τ − γ µ q R ¯

16 3 × 48 , m π L ∼ 3 . 78 24 3 × 48 , m π L ∼ 3 . 99 32 3 × 48 , m π L ∼ 3 . 25 24 3 × 64 , m π L ∼ 3 . 22 24 3 × 64 , m π L ∼ 4 . 54 32 3 × 64 , m π L ∼ 4 . 29 48 3 × 64 , m π L ∼ 3 . 91 40 3 × 64 , m π L ∼ 5 . 36 32 3 × 96 , m π L ∼ 4 . 50 48 3 × 96 , m π L ∼ 4 . 73 • Möbius DWF on HISQ • Gradient flow method for smearing configs • m res < 0.1 m l for moderate L 5 • Wall + point sources for pions • ~ 1000 cfgs, 1 source/cfg MILC Collaboration Phys. Rev. D87 (2013) 054505 Narayanan, Neuberger (2006), Luscher (2010) K. Orginos, C. Monahan (private communication)

Signals - 0.05 - 0.10 - 0.15 O' 2 + - 0.20 Wall - 0.25 0.8 Point - 0.30 0.7 - 0.35 0 5 10 15 20 0.6 t f O 2 + 0.5 • m 𝜌 ~ 135 MeV 0.4 • L = 5.76 fm 0.3 10 15 20 • a = 0.12 fm t f

Preliminary! O 2+ , O 0 2+ O 1+ , O 0 0.8 1+ O 3+ 0.6 0.4 O i + 0.2 0.0 - 0.2 5 10 15 20 t f

Preliminary! 0.004 0.002 O 2+ , O 0 2+ O 1+ , O 0 0.000 0.8 1+ O 3+ O 3 + - 0.002 - 0.004 0.6 - 0.006 - 0.008 0.4 5 10 15 20 t f O i + 0.2 0.0 - 0.2 5 10 15 20 t f

Preliminary! O 2+ , O 0 1.0 2+ O 1+ , O 0 1+ O 3+ 0.8 Ê Ê Ê 0.6 Ê Ê Ê 0.4 O i + Ê Ê 0.2 Ê 0.0 Ê Ê Ê Ê Ê Ê - 0.2 2.5 3.0 3.5 4.0 4.5 5.0 5.5 6.0 m p L

Preliminary! 0.000 - 0.002 O 2+ , O 0 1.0 2+ - 0.004 O 1+ , O 0 1+ O 3+ - 0.006 Ê O 3 + 0.8 Ê Ê Ê - 0.008 Ê Ê - 0.010 0.6 Ê - 0.012 Ê Ê - 0.014 2.5 3.0 3.5 4.0 4.5 5.0 5.5 6.0 m p H MeV L 0.4 O i + Ê Ê 0.2 Ê 0.0 Ê Ê Ê Ê Ê Ê - 0.2 2.5 3.0 3.5 4.0 4.5 5.0 5.5 6.0 m p L

Preliminary! O 2+ , O 0 1.2 2+ O 1+ , O 0 1+ O 3+ 1.0 Ê Ù ‡ Ù 0.8 ‡ Ê ‡ ‡ ‡ Ê 0.6 Ê Ê Ê Ù Ù O i + 0.4 Ê Ù ‡ Ù 0.2 Ê ‡ Ê 0.0 ‡ Ê Ù Ê ‡ Ù Ê ‡ Ù Ù Ê Ê Ê ‡ - 0.2 ‡ ‡ 100 150 200 250 300 350 m p H MeV L