m. lindner, mpikblv20151 double beta decay: theory motivation versus the experimental challenge...

M. Lindner, MPIK BLV2015 1

Double Beta Decay: Theory Motivation versus the experimental Challenge

Manfred Lindner

Majorana mass

The Standard Picture of Double Beta Decay

2nbb decay

0nbb decay

2nbb decay seen for diff. isotopes (Kirsten,…)

T1/2 = O(1018 - 1021 years) up to 1011 ⊗ TUniverse

• observe 2 nbb signal• look for 0 nbb signal at Qbb

• large amount of 76Ge nuclei• extreme low backgrounds!


2 nbb

0nbb

SM

More general: L Violating Processes

2nbb decay

0nbb decay

2nbb decay seen for diff. isotopes (Kirsten,…)

T1/2 = O(1018 - 1021 years) up to 1011 ⊗ TUniverse

• observe 2 nbb signal• look for 0 nbb signal at Qbb

• large amount of 76Ge nuclei• extreme low backgrounds!


2 nbb

0nbb

0nbb

SM

BSM

someDL=2

operator

T1/2 > O(1024y)

mee: The Effective Neutrino Mass


assumption: no *other* DL=2 physics, no sterile neutrinos up to TeV,...

0nbb by Majorana masses limits on mee

• cosmology limit on m

Double Beta Decay Processes


+ 2 electrons + 2 neutrinos2nbb

Standard Model:

SM+Higgs triplet SUSY

…

SM + Higgs triplet SUSY

Majorana n-masses or other DL=2 physics: 2 electrons 0nbb

important connections to LHC and LFV …sub eV Majorana mass TeV scale physics

Majorananeutrino masses Dirac?

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


mem’ee

interferencesgrowing me for fixed 0nbb shifts of masses, mixings and CP phases

sensitivity to TeV physics

Does 0nbb Decay Imply Majorana Masses?

• Standard picture: Majorana neutrinos 0 .nbb 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 …!?


The Schechter-Valle Theorem induced Mass

M. Lindner, MPIK BLV2015

- 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 splittingsexplicit Dirac neutrino mass operators required

Extreme possibility: - 0nbb = L violation = other BSM physics - neutrino masses = Dirac (plus very tiny correction)

9

Neutrino Mass Terms & L Violation

M. Lindner, MPIK BLV2015

Majorana L

xx

nL nR

<f> = v

nR nRgN

/

R

L

RD

DRL Mm

m

0 _ _

cc

Simplest possibility: assume 3 right handed singlets (1L)

like quarks and chargedleptons Dirac mass terms(including NMS mixing)

+9+ new ingredients: SM+1) Majorana mass = scales2) lepton number violation

6x6 block mass matrixblock diagonalizationMR heavy 3 light n’s

10

Or: add scalar triplets (3L) or fermionic 1L or 3L

nL nL

left-handed Majorana mass term: MLLLc_x x

nL nL

x x1,3

3


mn=ML - mDMR-1mD

T see-saw type II, III

Both nR and new singlets / triplets:

Higher dimensional operators: d=5, …

MLLLc_

Extra gauge groups, SUSY, extra dimensions, …

Radiative neutrino mass generation

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

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…


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 ?

M. Lindner, MPIK 13BLV2015

• 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

SM:Triviality and Vacuum Stability

M. Lindner, MPIK 14

l

ln( )m

L(GeV)

RGE arguments seem to work we need some embeding no BSM physics observed! just a SM Higgs

SM does not exist w/o embeding- U(1) copling , Higgs self-coupling

Landau pole

ML ‘86

126 GeV < mH < 174 GeV

Lvacuum stavility

triviality

allowed

126 GeV is here! l(Mpl) ~ 0- EW-SB radiative- just SM?Holthausen, ML, Lim (2011)

BLV2015

Is the Higgs Potential at MPlanck flat?

M. Lindner, MPIK 15

2-loopas error

difference 12 loop

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

Buttazzo, Degrassi, Giardino, Giudice, Sala, Salvio, StrumiaHolthausen, ML, Lim

BLV2015

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


Conformal Symmetry & EW Symmetry Breaking


Conformal Symmetry as Protective Symmetry

M. Lindner, MPIK 18

- 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 kills a L2 dependence is well known. Argument goes the other way!

BLV2015

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

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


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 otherexplicit 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

Implications

M. Lindner, MPIK 22

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

BLV2015

Let’s try to implement the idea…


Why the minimalistic SM does not work

M. Lindner, MPIK 24

Minimalistic: SM + choose m= 0 CSColeman 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, …BLV2015

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 < > = 246F 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 26

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

Realizing this Idea: Left-Right ExtensionRealizing the Idea: Left-Right Extension

BLV2015

M. Lindner, MPIK 27

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…?BLV2015

New scalar representation S QCD gap equation:

C2(L) increases with larger representations condensation for smaller values of running a

q=3

LQCD LS

Rather minimalistic: SM + QCD Scalar S

M. Lindner, MPIK 28

S=15

J. Kubo, K.S. Lim, ML

BLV2015

Realizing the Idea: Examples for other Directions

M. Lindner, MPIK 29

SM + extra singlet: , F jNicolai, 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 scaleKubo, 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

BLV2015

Conformal Symmetry & Neutrino Masses

• 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 30

ML, S. Schmidt and J.Smirnov

BLV2015

Implications for Neutrino Mass Spectra

M. Lindner, MPIK

_ _c

c

3 0 … N3x3 matrix

3xN NxN

Usually: ML tiny or 0, MR heavy see-saw & variantslight sterile: F-symmetries... Now: ML, MR may have any value: diagonalization: 3+N EV 3x3 active almost unitary

ML=0, mD = MW, MR singular ML = MR = 0 ML = MR = eMR=high: see-saw singular-SS Dirac pseudo Dirac

acti

ve

ster

ile

31BLV2015

Examples

M. Lindner, MPIK 32

Yukawa seesaw:SM + nR + singlet

generically expect a TeV seesawBUT: yM might be tiny wide range of sterile masses including pseudo-Dirac case suppressed 0nbb

Radiative masses

or

pseudo-Dirac case

BLV2015

The punch line: all usual neutrino mass terms can be generated

suitable scalars no explicit massesall via Yukawa couplings different numerical expectations

Another Example: Inverse Seesaw


P. Humbert, ML, J. SmirnovSU(3)c × SU(2)L × U(1)Y × U(1)X

light eV “active” neutrino(s)two pseudo-Dirac neutrinos; m~TeVsterile state with μ ≈ keV Tiny non-unitarty of PMNS matrixTiny lepton universality violationSuppressed 0nbb decayLepton flavour violationTri-lepton production at LHCkeV neutrinos as warm dark matter


See talk by J. Smirnov

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


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 search2) Dirac masses + other L-violation

• Beware: The expectations for a L-violating signal depends on theoretical assumptions experimental effort…


Sensitivity & Background (for a Majorana Mass)


1000

100

NA = Avogadro’s numberW = atomic weight of isotopee = signal detection efficiencyM = isotope masst = data taking time

without background

with background N’ = N + Nbackground

c = cts/keV/kg/yr ; DE = ROIton-scale

Goals and hard Facts:


Testing IH 17 meV~ 1028y

Effort:1ty= 200kg*5y10ty = 1t * 10y

Ge76 lead time:O(100) kg/y

Summary

M. Lindner, MPIK 39

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…

BLV2015

Extra Slides


Implementing the Ideas at different Levels


SM SM+ mn

SM + DM SM + ?

SM + mn + DM + GR

at all levels: non-linear realization of conformal symmetry

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…


Phenomenology


m. lindner, mpikblv20151 double beta decay: theory motivation versus the experimental challenge...

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