Double Beta Decay: Theory Motivation
versus the experimental Challenge
Manfred Lindner
M. Lindner, MPIK
BLV2015
1
The Standard Picture of Double Beta Decay
2nbb
2nbb decay seen for diff. isotopes (Kirsten,…)
T1/2 = O(1018 - 1021 years)  up to 1011 TUniverse
SM
0nbb decay
0nbb
2nbb decay
Majorana
mass
• observe 2nbbsignal
• look for 0nbbsignal at Qbb
• large amount of 76Ge nuclei
• extreme low backgrounds!
M. Lindner, MPIK
BLV2015
2
More general: L Violating Processes
2nbb
2nbb decay seen for diff. isotopes (Kirsten,…)
T1/2 = O(1018 - 1021 years)  up to 1011 TUniverse
SM
0nbb decay
0nbb
2nbb decay
BSM
T1/2 > O(1024y)
0nbb
• observe 2nbbsignal
• look for 0nbbsignal at Qbb
• large amount of 76Ge nuclei
• extreme low backgrounds!
some
DL=2
operator
M. Lindner, MPIK
BLV2015
3
mee: The Effective Neutrino Mass
0nbb by Majorana masses
 limits on mee
• cosmology  limit on m
assumption: no *other*
DL=2 physics, no sterile
neutrinos up to TeV,...
M. Lindner, MPIK
BLV2015
4
Double Beta Decay Processes
Standard Model:
+
 2 electrons + 2 neutrinos
2nbb
Majorana n-masses or other DL=2 physics:  2 electrons
0nbb
…
Majorana
neutrino masses
 Dirac?
M. Lindner, MPIK
SM+Higgs
SM
+ Higgs triplet
SUSY SUSY
important connections to LHC and LFV …
sub eV Majorana mass  TeV scale physics
BLV2015
5
Interference of DL=2 Operators
Usually
with interferences
= overall phase space factor
 determined by parameters of new physics
me ~ (Lnew)-5 m0nbb = 1 eV  Lnew ~ TeV
M. Lindner, MPIK
BLV2015
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m’ee
me
interferences
growing me for fixed 0nbb
 shifts of masses,
mixings and CP phases
 sensitivity to TeV physics
M. Lindner, MPIK
BLV2015
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Does 0nbb Decay Imply Majorana Masses?
• Standard picture: Majorana neutrinos  0nbb.
 If 0nbb is observed then we proof the Majorana
nature of neutrinos?  no, only some DL=2 operator
• What if some other new DL=2 operator from some BSM
model would completely explain an observed 0nbb
signal?
 `Schechter-Valle Theorem’: Any DL=2 operator
which mediates the decay induces via loops Majorana
mass terms  unavoidable!  Majorana nature …!?
M. Lindner, MPIK
BLV2015
8
The Schechter-Valle Theorem induced Mass
- any DL=2 operator which leads to 0nbb decay induces
via loops a Majoarana mass
- assume a 0nbb signal  how big is the induced mass?
Dürr, ML, Merle
4 loops  dmn = 10-25 eV  very tiny (academic interest)
 cannot explain observed n masses and splittings
explicit Dirac neutrino mass operators required
Extreme possibility:
- 0nbb = L violation = other BSM physics
- neutrino masses = Dirac (plus very tiny correction)
M. Lindner, MPIK
BLV2015
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Neutrino Mass Terms & L Violation
Simplest possibility: assume 3 right handed singlets (1L)
nL gN nR
x
nR
x
nR
_
 n L
Majorana
L
/
<f> = v
like quarks and charged
leptons  Dirac mass terms
(including NMS mixing)
+9+ new ingredients:  SM+
1) Majorana mass = scales
2) lepton number violation
Or: add scalar triplets (3L) nL
or fermionic 1L or 3L
x
3
nL
x
left-handed Majorana mass term:
M. Lindner, MPIK
_c  0
n R )
 mD
BLV2015
mD n Lc 
 
MR n R 
6x6 block mass matrix
block diagonalization
MR heavy  3 light n’s
nL
1,3
x
x
nL
_ c
 MLLL
10
Both nR and new singlets / triplets:
 see-saw type II, III mn=ML - mDMR-1mDT
Higher dimensional operators: d=5, …
_
Radiative neutrino mass generation
 MLLLc
Extra gauge groups, SUSY, extra dimensions, …
 neutrino masses can/may solve two of the SM problems:
- leptogenesis (BAU) - keV sterile neutrinos as (WDM)
 assumptions = new physics  connections to LFV, LHC, ...
think of options for L violation  talks at this conference
M. Lindner, MPIK
BLV2015
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How things might be different…
• The standard picture is that neutrinos are Majorana
particles and (most often) no other L-violation exists
• There exist many interesting questions concerning the
ultimate role of L:
GUTs, low lying L-embedinggs (Fileviez Perez et al.),
sphalerons & B+L violation, GR & global symmetries,
… with and without SUSY, extra dimensions etc.
 some talks at this conference
• Even without that naive expectations may turn out to be
wrong
• Example: Nothing new is found at the LHC
 new ways of EW symmetry breaking  neutrinos…
M. Lindner, MPIK
BLV2015
12
The LHC (so far…) and the SM as a QFT
• The SM itself (without embedding) is a QFT like QED
- infinities, renormalization  only differences are calculable
- SM itself is perfectly OK  many things unexplained…
• New or special features
- Higgs field (scalar), potential & SSB
- fermion masses via Yukawa couplings  no explicit fermion masses  reps
- besides m no scale  all masses: g*VEV  one scale theory
- hierarchy problem ?
•
•

•
Renormalizable QFT  no cutoff L physics of an embedding
Two scalars j, F ; masses m, M and a mass hierarchy m << M
j+j and F+Fare singlets  lmix(j+j)(F+F)must exist
Quantum corrections ~M2 drive both masses to the heavy scale
 two vastly different scalar scales are generically unstable
 not
a SM problem  embedding with a 2nd much heavier
scalar
BLV2015
M. Lindner, MPIK
13
SM:Triviality and Vacuum Stability
L(GeV)
126 GeV < mH < 174 GeV
SM does not exist w/o embeding
- U(1) copling , Higgs self-coupling
l
Landau
pole
triviality
allowed
ML ‘86
M. Lindner, MPIK
126 GeV is here!
 l(Mpl) ~ 0
- EW-SB radiative
- just SM?
Holthausen, ML, Lim (2011)
BLV2015
vacuum stavility
lnm)
L
 RGE arguments seem to work
 we need some embeding
 no BSM physics observed!
 just a SM Higgs
14
Is the Higgs Potential at MPlanck flat?
Buttazzo, Degrassi, Giardino, Giudice, Sala, Salvio, Strumia
Holthausen, ML, Lim
difference
12 loop
2-loop
as error
Notes:
- remarkable relation between weak scale, mt, couplings and MPlanck precision
- strong cancellations between Higgs and top loops
 very sensitive to exact value and error of mH, mt, as = 0.1184(7)  currently 1.8s in mt
- other physics: DM, mn … axions, …Planck scale thresholds… SM+  l = 0
 top mass errors: data  LO-MC  translation of mpole  MS bar
 be cautious about claiming that metastability is established
M. Lindner, MPIK
BLV2015
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Is there a Message?
 l(MPlanck) ~ 0?  flat potential at Mplanck
 flat Mexcican hat at the Planck scale

• if in addition m2 = 0  V(MPlanck) ~ 0?
(Remember: m is the only single scale of the SM)
 conformal symmetry as potential solution to the HP
• Conceptual aspects
• Realizations & implications for neutrino masses
M. Lindner, MPIK
BLV2015
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Conformal Symmetry & EW Symmetry Breaking
M. Lindner, MPIK
BLV2015
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Conformal Symmetry as Protective Symmetry
- Exact (unbroken) CS
 absence of L2 and ln(L) divergences
 no preferred scale and therefore no scale problems
- Conformal Anomaly (CA): Quantum effects explicitly break CS
existence of CA  CS preserving regularization does not
exist
- dimensional regularization is close to CS and gives only
ln(L)
- cutoff reg.  L2 terms; violates CS badly  Ward Identity
Bardeen: maybe CS still forbids L2 divergences
 CS breaking  b-functions  ln(L) divergences
 anomaly induced spontaneous EWSB
NOTE: asymmetric logic! The fact the dimensional regularization
M. Lindner, MPIK
2
BLV2015
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Looking at it in different Ways…
• Basics of QFT: Renormalization  commutator
- [F(X),P(y)] ~ d3(x-y)  delta funtion  distribution
- freedom to define d*d  renormalization  counterterms
- along come technicalities: lattice, L, Pauli-Villars, MS-bar, …
• Reminder: Technicalities do not establish physical existence!
• Conceptiully most clear  BPHZ-renormalization
• Symmetries are essential!
Question: Is gauge symmetry spoiled by discovering
massive gauge bosons?  NO  Higgs mechanism
 non-linear realization of the underlying symmetry
 important consequence: naïve power counting is wrong
Gauge invariance  only log sensitivity
M. Lindner, MPIK
BLV2015
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Versions of QCD…
• QCD with massless (chrial) fermions
 gauge + conformal symmetry
 dimensional transmutation  LQCD (2 scales: <
> , <GG>)
 reference scale ; everything else is scale ratios
 no L2 sensitivity – there is no other physical scale!
 no hierarchy problem
Question:Do fundamental theories require absolute scales?
Why not everything in relative terms?
Don’t blame a theory forthe scale problems which you
invented in your head (a lattice, a cutoff, …)
Important: The conformal anomaly
 dimensional transmutation b-fcts.  logs
M. Lindner, MPIK
BLV2015
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Now massless scalar QCD…
• Massless scalar field instead of chiral fermions
• Gauge and conformal symmetry
• Technically there seems to be a L2 divergence
 but this has no meaning since (if) there is no other
explicit physical reference scale
• Dimensional transmutation  LQCD
 reference scale ; everything else is scale ratios
 conformal anomaly  b-functions  only logs
Relict of conformal symmetry
 only log sensitivity
M. Lindner, MPIK
BLV2015
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Implications
Gauge invariance  only log sensitivity
If conformal symmetry is realized in a
non-linear way  protective relic of
conformal symmetry  only log sensitivity
 reflects anomaly – there is nothing more
• No hierarchy problem, even though there is the the conformal
anomaly = logs  b-functions
• Dimensional transmutation due to log running like in QCD
 scalars can condense and set scales like fermions
 use this in Coleman Weinberg effective potential calculations
 most attractive channels (MAC)  b-functions
M. Lindner, MPIK
BLV2015
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Let’s try to implement the idea…
M. Lindner, MPIK
BLV2015
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Why the minimalistic SM does not work
Minimalistic:
SM + choose m= 0  CS
Coleman Weinberg: effective potential
 CS breaking (dimensional transmutation)
 induces for mt < 79 GeV
a Higgs mass mH = 8.9 GeV
This would conceptually realize the idea, but:
Higgs too light and the idea does not work for mt> 79 GeV
Reason for mH << v: Veff flat around minimum
 mH ~ loop factor ~ 1/16p2
AND: We need neutrino masses, dark matter, …
M. Lindner, MPIK
BLV2015
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Realizing the Idea via Higgs Portals
• SM scalar F plus some new scalar j(or more scalars)
• CS  no scalar mass terms
• the scalars interact  lmix(j+j)(F+F)must exist
 a condensate of <j+j> produces lmix<j+j>(F+F)=m2(F+F)
 effective mass term for F
• CS anomalous …  breaking  only ln(L)
 implies a TeV-ish condensate for jto obtain <F>=246 GeV
• Model building possibilities / phenomenological aspects:
- jcould be an effective field of some hidden sector DSB
- further particles could exist in hidden sector; e.g. confining…
- extra hidden U(1) potentially problematic  U(1) mixing
- avoid Yukawas which couple visible and hidden sector
 phenomenology safe due to Higgs portal, but there is TeV-ish new physics!
M. Lindner, MPIK
BLV2015
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Realizing
Realizing this
the Idea:
Idea: Left-Right
Left-Right Extension
Extension
M. Holthausen, ML, M. Schmidt
Radiative SB in conformal LR-extension of SM
(use isomorphism SU(2) × SU(2) ~ Spin(4)  representations)
 the usual fermions, one bi-doublet, two doublets
 a Z4 symmetry
 no scalar mass terms  CS
M. Lindner, MPIK
BLV2015
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 Most general gauge and scale invariant potential respecting Z4
 calculate Veff
 Gildner-Weinberg formalism (RG improvement of flat directions)
- anomaly breaks CS
- spontaneous breaking of parity, Z4, LR and EW symmetry
- mH << v ; typically suppressed by 1-2 orders of magnitude
Reason: Veff flat around minimum
 mH ~ loop factor ~ 1/16p2
 generic feature  predictions
- everything works nicely…
v
requires moderate parameter adjustment for the separation
of the LR and EW scale… PGB…?
M. Lindner, MPIK
BLV2015
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Rather minimalistic: SM + QCD Scalar S
J. Kubo, K.S. Lim, ML New scalar representation S  QCD gap
equation:

C2(L) increases with larger representations
 condensation for smaller values of running a
q=3
S=15
M. Lindner, MPIK
BLV2015
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Realizing the Idea: Examples for other Directions
SM + extra singlet: F,j
Nicolai, Meissner, Farzinnia, He, Ren, Foot, Kobakhidze, Volkas, …
SM + extra SU(N) with new N-plet in a hidden sector
Ko, Carone, Ramos, Holthausen, Kubo, Lim, ML, (Hambye, Strumia) , …
SM embedded into larger symmetry (CW-type LR)
Holthausen, ML, M. Schmidt
SM + colored scalar which condenses at TeV scale
Kubo, Lim, ML
Since the SM-only version does not work  observable effects:
- Higgs coupling to other scalars (singlet, hidden sector, …)
- dark matter candidates  hidden sectors & Higgs portals
- consequences for neutrino masses
M. Lindner, MPIK
BLV2015
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Conformal Symmetry & Neutrino Masses
ML, S. Schmidt and J.Smirnov
• No explicit scale  no explicit (Dirac or Majorana) mass term
 only Yukawa couplings ⊗ generic scales
• Enlarge the Standard Model field spectrum
like in 0706.1829 - R. Foot, A. Kobakhidze, K.L. McDonald, R. Volkas
• Consider direct product groups: SM ⊗ HS
• Two scales: CS breaking scale at O(TeV) + induced EW scale
Important consequence for fermion mass terms:
 spectrum of Yukawa couplings ⊗ TeV or EW scale
 interesting consequences  Majorana mass terms are no
longer expected at the generic L-breaking scale  anywhere
M. Lindner, MPIK
BLV2015
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Implications for Neutrino Mass Spectra
3x3 matrix
3xN NxN
0…N
3
(
_
_
n L n cR
)
æ ML m
D
ç
ç mD MR
è
ö
÷
÷
ø
MR singular
singular-SS
ML = MR = 0
Dirac
ML = M R = e
pseudo Dirac
active
sterile
ML=0, mD = MW,
MR=high: see-saw
öæ n c
֍ L
֍ n R
øè
Usually:
ML tiny or 0, MR heavy
 see-saw & variants
light sterile: F-symmetries...
Now:
ML, MR may have any value:
 diagonalization: 3+N EV
 3x3 active almost unitary
M. Lindner, MPIK
BLV2015
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Examples
Yukawa seesaw:
SM + nR + singlet
 generically expect a TeV seesaw
BUT: yM might be tiny
 wide range of sterile masses  including pseudo-Dirac case
 suppressed 0nbb
The punch line:
all usual neutrino mass
terms can be generated
Radiative masses
or
pseudo-Dirac case
M. Lindner, MPIK
BLV2015
 suitable scalars
 no explicit masses
all via Yukawa couplings
 different numerical
expectations
32
Another Example: Inverse Seesaw
SU(3)c × SU(2)L × U(1)Y × U(1)X
P. Humbert, ML, J. Smirnov
light eV “active” neutrino(s)
two pseudo-Dirac neutrinos; m~TeV
sterile state with μ ≈ keV
Tiny non-unitarty of PMNS matrix
Tiny lepton universality violation
Suppressed 0nbb decay
Lepton flavour violation
Tri-lepton production at LHC
keV neutrinos as warm dark matter 
M. Lindner, MPIK
BLV2015
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 See talk by J. Smirnov
M. Lindner, MPIK
BLV2015
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General Implications of CISS
• The usual expectation that sterile mass terms are
automatically very heavy is no longer fulfilled
• VEVs heavy, but Yukawa couplings may be anything
 various eV-evidences may or may not be correct
 any sterile mass natural: eV, keV, MeV, GeV, TeV, …
 cosmology… avoid thermalization and HDM
interesting theoretical and phenomenological options:
-TeV improved EW fits (Z-width, NuTeV, ALR, …
Akhmedov, Kartavtsev, ML, Michels, J. Smirnov ; Antusch, Fischer
- keV  warm dark matter
M. Lindner, MPIK
BLV2015
35
Messages
• Lepton number is important and L-violation is an
interesting subject!
• Unclear if Majorana masses exist and if the are the
only L-violating operator (most likely not!)
• Extreme cases:
1) Majorana masses only  usual scenario  search
2) Dirac masses + other L-violation
• Beware: The expectations for a L-violating signal
depends on theoretical assumptions
 experimental effort…
M. Lindner, MPIK
BLV2015
36
Sensitivity & Background (for a Majorana Mass)
without background
1000
NA = Avogadro’s number
W = atomic weight of isotope
e = signal detection efficiency
M = isotope mass
t = data taking time

with background
N’ = N + Nbackground
100

ton-scale 
M. Lindner, MPIK
BLV2015
c = cts/keV/kg/yr ; DE = ROI
37
Goals and hard Facts:
Testing IH
 17 meV
~ 1028y
Effort:
1ty= 200kg*5y
10ty = 1t * 10y
Ge76 lead time:
O(100) kg/y
M. Lindner, MPIK
BLV2015
38
Summary
 lepton number violation is a very important topic!
 goes beyond neutrino masses
 big new 0nbb experiments  search for L-violation
… are very hard (ultra low background)
… and expensive (large quantities of very special material)
… will take many years (complexity, R&D)
… while expectations will change:




LHC results/limits  n mass terms (SUSY, WR, nothing)
sterile neutrinos may be confirmed
the mass hierarchy will be known
indications for other L-violation?
 the 50 meV goal
is uncertain and very hard to reach
 effort…
M. Lindner, MPIK
BLV2015
39
Extra Slides
M. Lindner, MPIK
BLV2015
40
Implementing the Ideas at different Levels
SM
SM + DM
SM
+ mn
SM + ?
SM + mn
+ DM + GR
 at all levels: non-linear realization of conformal symmetry
M. Lindner, MPIK
BLV2015
41
Further general Comments
• New (hidden) sector  DM, neutrino masses, …
• Question: Isn’t the Planck-Scale spoiling things?
 non-linear realization…  conformal gravity…
ideas: see e.g. 1403.4226 by A. Salvio and A. Strumia …
K. Hamada, 1109.6109, 0811.1647, 0907.3969, …
• Question: What about inflation?
see e.g. 1405.3987 by K. Kannike, A. Racioppi, M. Raidal
or 1308.6338 by V. Khoze
• Unification …
• UV stability: ultimate solution should be asymptotically safe
(have UV-FPs) …  U(1) from non-abelian group
• Justifying classical scale invariance
 cancel the conformal anomaly
 nature of space time & observables…
M. Lindner, MPIK
BLV2015
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Phenomenology
M. Lindner, MPIK
BLV2015
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