Origin of Neutrino Mass: Will We Ever Know?

Origin of neutrino mass: will we ever know?

Ray Volkas School of Physics The University of Melbourne

CERN Theory Colloquium at “Neutrinos: the quest for a new physics scale”, 29 March 2017. 1. What we know, don’t know and want to know. 2. Theνexperimental program. 3. Schemes for Majoranaνmass generation: A. Type-1,2,3 seesaw models. B. Inverse and linear seesaw mechanisms. C. Radiative neutrino mass models. 4. Beyond theνexperimental program. 5. Will we ever know? 1. What we know, don’t know and want to know. On the origin of mass in general:

A. Nucleon mass

QCD field energy.

Non-perturbative.

Dynamical chiral symmetry breaking.

Fundamental parameter

is ΛQCD ~ 220 MeV. Dimensional transmutation.

Low masses of pions are Credit: universe-review.ca understood. B. Quark, charged-lepton, W, Z masses

Higgs-induced spontaneous EW symmetry breaking.

Tree-level perturbative.

Fundamental parameter is Higgs VEV ~ 250 GeV.

W, Z, t masses are near this scale. Others a lot smaller: ascribed to small Yukawa coupling constants. C. Dark matter mass(es)

Unknown.

Speculations range from 10-5 eV axions to 105 solar mass primordial black holes!

But we do know that ρdark ≈ 5ρbaryon. If ρi= mi ni then this observation suggests ndark ~ nbaryon and mdark ~ mproton – asymmetric dark matter. Is mdark explained by strong QCD-like dynamics? D. Neutrino masses (and mixings)

We have now measured some, but not all, neutrino parameters quite precisely.

Review in coming slides.

Credit: Mainz U

The absolute neutrino mass scale has a lab upper limit of 2 eV and cosmo limit of about 0.2 eV.

How do nu masses arise, and why are they so small?

Credit: KATRIN Recent global fits to neutrino flavour-transformation data: Esteban+ 1611.01514, JHEP 1701 (2017) 087 Capozzi+ 1601.07777, NPB 908 (2016) 218 Forero+ 1405.7540, PRD90 (2014) 093006

Definition of PMNS matrix:

⌫e Ue1 Ue2 Ue3 ⌫1 ⌫1,2,3 mass Δm2 = solar ⌫ = U U U ⌫ 12 µ µ1 µ2 µ3 2 estates Δm2 ~Δm2 = atmos. 2 3 2 3 2 3 32 31 ⌫⌧ U⌧1 U⌧2 U⌧3 ⌫3 m1,2,3 4 5 4 5 4 5 Standard parameterisation:

i c12c13 s12c13 s13e 10 0 s c c s s ei c c s s s ei s c 0 ei↵1/2 0 2 12 23 12 23 13 12 23 12 23 13 23 13 3 2 3 s s c c s ei c s s c s ei c c 00ei↵2/2 12 23 12 23 13 12 23 12 23 13 23 13 4 5 4 5 ✓12 = solar angle = Dirac phase ✓ = atmospheric angle 23 ↵1,2 = Majorana phases ✓13 = reactor angle Oscillation probability formula:

2 2 mijL P↵ = ↵ 4 Re(U↵⇤iUiU↵jU⇤j)sin ! 4E i>j ! X 2 mijL +2 Im(U ⇤ U U U ⇤ )sin ↵i i ↵j j 2E i>j ! X

m2 m2 m2 ij ⌘ i j m2L m2 L GeV 1.27 4E ' eV2 km E From the most recent global fit (Esteban+):

Interesting preference for δ≈ 270°. A selection of what we don’t know:

• Dirac or Majorana? • The value of absolute neutrino mass scale. • Leptonic CP violation not quite confirmed. • Normal or inverted ordering?

• θ23 < π/4 or > π/4? • Whether or not the LSND/MiniBooNE, reactor and gallium anomalies are due to eV-scale sterile neutrinos. • The origin of the neutrino mass scale. • Are the mixing parameters and mass splittings free parameters, or is there a flavour symmetry or some other deep dynamics? • Is lepton mass/mixing connected to quark mass/mixing? • Is neutrino mass tree-level or radiative? • What role does the 126 GeV Higgs play in neutrino mass? • Are there other as-yet undiscovered particles that play a role in neutrino mass generation? • Is dark matter a 10 keV-scale sterile neutrino? • Did leptogenesis seed baryogenesis? • And so on. Ultimate goal has to be = + + LBSM LSM L⌫ mass LDM,Bgen,inﬂation,... where “ν mass” may contain DM and/or Bgen.

All we can put in current textbooks is a bunch of empirical facts and a plethora of theoretical speculations.

By the way, just in case it is necessary, I want to ν convince you of something: The discovery of mass is most certainly the discovery of new physics.

Sometimes you hear the view, “We always expected neutrinos to have mass, so what’s the big deal?” As everyone knows, the original SM has no RH neutrinos, no Y=2 Higgs triplet, and nothing else that breaks Le,μ,τor Ltot, so neutrinos are exactly massless.1

Massive neutrinos may be Dirac or Majorana.

If neutrinos are Majorana, they are the first such states to be discovered: new physics.

If neutrinos are Dirac, then the gauge-invariant RH neutrino Majorana mass terms must be omitted. This means a global symmetry – U(1)L – must be imposed: a new principle, hence new physics.

Also: RH neutrinos are new dofs, like any new particles: new physics. Majorana mass generation requires RH neutrinos or a Y=2 Higgs triplet, or any of a bunch of other new particles: new physics.

1. Exercise for the listener: do sphalerons generate neutrino masses? 2. The neutrino experimental program

NEMO Double Beta Decay (82Se, 100Mo, 150Nd) (Home, INSPIRE) References Experiments FNAL-E-0531 Accelerator SBL Oscillations (INSPIRE) References NEOS Reactor Short-Baseline Oscillations (INSPIRE) References FNAL-E-0613 Accelerator SBL Oscillations (INSPIRE) References Filter this page Neutrino-4 Reactor SBL Oscillations (INSPIRE) References (Note: The process can take some time.) Frejus Atmospheric Neutrinos, Proton Decay (INSPIRE) References 136 51 NEXT Double Beta Decay ( Xe) (Home) References Search Reset GALLEX Solar Neutrinos, SBL Oscillations with Cr Neutrino Source (Home, INSPIRE) Thanks to Carlo References NOMAD Accelerator SBL Oscillations (Home, INSPIRE) References Types of Neutrino Experiments Gargamelle Accelerator SBL Oscillations, Neutrino Interactions (INSPIRE) References NOVA Accelerator Long Baseline Oscillations (Home, INSPIRE) References Giunti for keeping Accelerator Beam Dump Astrophysical Neutrinos Atmospheric Neutrinos 187 Genova Re Electron Neutrino Mass (Home, INSPIRE) References Nucifer Reactor SBL Oscillations (INSPIRE, Wikipedia) References Electron Neutrino Long-Baseline Neutrino Oscillations Muon Neutrino GERDA Double Beta Decay (76Ge) (Home) References NUSEX Atmospheric Neutrinos, Proton Decay (INSPIRE) References a nice … long list! Neutrinoless Double Beta Decay Short-Baseline Neutrino Oscillations Solar Neutrinos GEMMA Reactor Electron Antineutrino - Electron Scattering References NuTeV Accelerator Muon Neutrino - Nucleon Scattering (Home, INSPIRE) References Supernova Neutrinos Tau Neutrino GLUE High-Energy Astrophysical Neutrinos (Home, INSPIRE) References OPERA Accelerator Long Baseline Oscillations (Home, INSPIRE) References EXPAND ALL COMPRESS ALL GNO Solar Neutrinos (Home, INSPIRE) References Palo Verde Reactor Long Baseline Oscillations (Home, INSPIRE) References

Neutrino Experiments Gosgen Reactor SBL Oscillations (INSPIRE) References RENO Reactor LBL Oscillations (Home) References Future experiments AMANDA High-Energy Astrophysical Neutrinos, Supernova Neutrinos (Home, INSPIRE) Gotthard Double Beta Decay (136Xe) (Home) References References RICE High-Energy Astrophysical Neutrinos, Supernova Neutrinos (Home, INSPIRE) References Heidelberg-Moscow Double Beta Decay (76Ge) (Home) References ANTARES High-Energy Astrophysical Neutrinos (Home, INSPIRE) References constitute another Rovno Reactor SBL Oscillations (INSPIRE) References Solar Neutrinos (INSPIRE) References ARIANNA High-Energy Astrophysical Neutrinos (Home, INSPIRE) References Homestake SAGE Solar Neutrinos (Home, INSPIRE) References ArgoNeuT Neutrino Interactions (INSPIRE) References ICARUS Accelerator Long Baseline Oscillations, Supernova Neutrinos, Proton Decay (Home, long, but shorter, list. INSPIRE) References Reactor SBL Oscillations (INSPIRE) References Baikal High-Energy Astrophysical Neutrinos, Supernova Neutrinos (Home, INSPIRE) Savannah River References IceCube High-Energy Astrophysical Neutrinos (Home, INSPIRE) References SciBooNE Accelerator Muon Neutrino - Nucleon Scattering (Home, INSPIRE) Baksan Atmospheric and Supernova SN1987A Neutrinos (Home, INSPIRE) References IGEX Double Beta Decay (76Ge) (INSPIRE) References References BOREXino Solar Neutrinos (Home, INSPIRE) References IHEP-JINR Accelerator SBL Oscillations, Neutrino-Nucleon Interactions (INSPIRE) SKAT Accelerator SBL Oscillations, Neutrino-Nucleon Interactions (INSPIRE) References References BEBC Accelerator SBL Oscillations, Neutrino Interactions (INSPIRE) References ILL Reactor SBL Oscillations (INSPIRE) References SNO Solar and Supernova Neutrinos (Home, INSPIRE) References BNL-E-734 Neutrino Interactions (INSPIRE) References 150 IMB Atmospheric Neutrinos, Supernova SN1987A Neutrinos, Proton Decay (Home, INSPIRE) SNO+ Neutrinoless Double Beta Decay ( Nd), Solar, Reactor, Geo and Supernova Neutrinos BNL-E-776 Accelerator SBL Oscillations (INSPIRE) References References (Home) References

116116 BNL-E-816 Accelerator SBL Oscillations (INSPIRE) References K2K Accelerator Long Baseline Oscillations (Home, INSPIRE) References Solotvina Double Double Beta Beta Decay Decay ( ( Cd)Cd) References References

Kamiokande Solar, Atmospheric and Supernova SN1987A Neutrinos, Proton Decay (Home, Soudan 2 Atmospheric Neutrinos, Proton Decay (Home, INSPIRE) References Bugey Reactor SBL Oscillations (INSPIRE) References INSPIRE) References Super-Kamiokande Solar and Atmospheric Neutrinos, Proton Decay (Home, INSPIRE) Accelerator SBL Oscillations, Muon Neutrino - Nucleon Scattering (Home, INSPIRE) KamLAND Reactor Long Baseline Oscillations, Supernova Neutrinos (Home, INSPIRE) CCFR References References References

KamLAND-Zen Double Beta Decay (136Xe) (Home) References T2K Accelerator Long Baseline Oscillations (Home, INSPIRE) References CDHSW Accelerator SBL Oscillations, Muon Neutrino - Nucleon Scattering (INSPIRE) References KARMEN Accelerator SBL Oscillations (Home, INSPIRE) References TEXONO Electron Neutrino Interactions (Home, INSPIRE) References

CERN-PS-191 Accelerator SBL Oscillations (INSPIRE) References Krasnoyarsk Reactor SBL Oscillations (INSPIRE) References TGV Double Beta Decay (48Ca, 106Cd) References

CHARM Accelerator SBL Oscillations (INSPIRE) References LAMPF-0645 Accelerator SBL Oscillations (INSPIRE) References Troitsk Electron Neutrino Mass (Home, INSPIRE) References

LAMPF-0764 Accelerator SBL Oscillations (INSPIRE) References Chooz Reactor LBL Oscillations (Home, INSPIRE) References LSD Supernova SN1987A Neutrinos, Astrophysical Neutrinos (INSPIRE) References CHORUS Accelerator SBL Oscillations (Home, INSPIRE) References LSND Accelerator SBL Oscillations (Home, INSPIRE) References COBRA Double Beta Decay (70Zn, 116Cd, 128Te, 130Te) (Home) References LVD Supernova Neutrinos, Astrophysical Neutrinos (Home, INSPIRE) References 130 Rather than comment on individual CUORE Double Beta Decay ( Te) (Home) References MACRO Atmospheric Neutrinos (Home, INSPIRE) References CUORICINO Double Beta Decay (130Te) (Home) References Mainz Electron Neutrino Mass (Home, INSPIRE) References projects, I’ll remark on how this DANSS Reactor SBL Oscillations (INSPIRE) References MiBeta Electron Neutrino Mass (Home) References

Daya Bay Reactor LBL Oscillations (Home) References MicroBooNE Accelerator SBL Oscillations, Neutrino Interactions (Home) References MINERvA Neutrino Interactions (Home, INSPIRE) References program can help us uncover the DONUT Tau Neutrino Interactions (Home, INSPIRE) References MiniBooNE Accelerator SBL Oscillations, Supernova Neutrinos (Home, INSPIRE) Double Chooz Reactor LBL Oscillations (Home) References References

Accelerator Long Baseline Oscillations, Atmospheric Neutrinos (Home, INSPIRE) Double Beta Decay (48Ca, 100Mo) References MINOS origin of neutrino mass. ELEGANT References

136 EXO Double Beta Decay ( Xe) (Home) References MUNU Reactor Electron Antineutrino - Electron Scattering (Home, INSPIRE) References FNAL-E-0053 Accelerator SBL Oscillations (INSPIRE) References NEMO Double Beta Decay (82Se, 100Mo, 150Nd) (Home, INSPIRE) References FNAL-E-0531 Accelerator SBL Oscillations (INSPIRE) References

Future Neutrino Experiments

100 AMoRE Double Beta Decay ( Mo) References An impressive range of experiments are

ANITA High-Energy Astrophysical Neutrinos (Home, INSPIRE) References underway or planned which either will or can 51 BEST SBL Oscillations with Cr Neutrino Source (INSPIRE) References address the following from the earlier list: 48 CANDLES Double Beta Decay ( Ca) References

CLEAN Solar and Supernova Neutrinos (Home) References DCBA Double Beta Decay (150Nd) References 1. Dirac or Majorana?

DUNE Accelerator LBL Oscillations, Atmospheric and Supernova Neutrinos, Proton Decay (Home, INSPIRE, WikipediA) References 2. Absolute neutrino mass scale.

ECHO Electron Neutrino Mass (Home, INSPIRE) References 3. Leptonic CP violation.

HOLMES Electron Neutrino Mass (Home, INSPIRE) References 4. Normal or inverted ordering?

JUNO Reactor Long-Baseline Oscillations, Atmospheric, Solar, Geo Neutrinos (Home, INSPIRE, WikipediA) References 5. θ23 < π/4 or > π/4? K ATRIN Electron Neutrino Mass (Home, INSPIRE) References 6. LSND/MiniBooNE, reactor, gallium anomalies.

KM3NeT High-Energy Astrophysical Neutrinos (Home) References

Supernova Neutrinos References LAND

LANNDD Supernova Neutrinos (Home) References Importance for origins question? 82 LUCIFER Double Beta Decay ( Se) (Home) References

Majorana Double Beta Decay (76Ge) (Home, INSPIRE) References 1. Crucial. Electron Neutrino Mass (Home) References MARE 100 2. Already know 0.05-0.2 eV assuming standard MOON Double Beta Decay ( Mo) (Home) References

NuMass Muon Neutrino Mass (Home) cosmology.

OMNIS Supernova Neutrinos (Home) References 3. Expected. Important for flavour symmetry High-Intensity Stopped-Pion Neutrino Facility (Home, INSPIRE) References ORLaND

PINGU models and leptogenesis. PROSPECT Reactor Short-Baseline Oscillations (INSPIRE) References 4. Important for 1. Model discrimination. SBN Acclerator Short-Baseline Oscillations (Home, INSPIRE) References

Reactor Short-Baseline Oscillations (INSPIRE) References SoLid 5. Flavour symmetry models.

144 144 SOX SBL Oscillations with Ce- Pr Anti-Neutrino Source (INSPIRE) References 6. New ball game!

STEREO Reactor Short-Baseline Oscillations (INSPIRE) References

UNO Atmospheric, Solar and Supernova Neutrinos, Nucleon Decay (Home) References

136 XMASS Double Beta Decay ( Xe) References

3. Schemes for Majorana neutrino mass generation.

I want to outline a story about good options for Majorana νmass.

It is a story, not the story. I have to omit many interesting subplots, including: flavour symmetries, DM-νmass connection (scotogenesis), explicit SUSY approaches, GUT perspectives, extra-d mechanisms, …

I will provide a perspective on: Tree-level seesaw models. Radiative models.

Key issues will be: Why are nu masses so small? Experimental testability of models. Why not Dirac?

Dirac masses with Yukawas ~ 10-12. Possible, but unappealing. There are more sophisticated Dirac ideas out there, but today we’ll follow a more conventional line of thinking:

Of all the fermions, only neutrinos may be Majorana. Could that be why neutrinos have such small masses?

Tree-level: Type-1,2,3, inverse, linear etc. seesaw mechanisms. Nu mass goes inversely as some power of a high mass scale. Inverse and linear cases also have technically-natural small parameters.

Radiative: Loop factors, multiplication of coupling constants, high-ish mass of new physics. ΔL=2 SM effective operators can be used to systematically study a large class of models of Majorana neutrino mass generation.

These operators have mass dimension d = 5, 7, 9, …

At d = 5, there is only the Weinberg operator: (1/M) LLHH M is the scale of new physics.

2 It gives neutrino mass directly, via the see-saw formula mν~ /M

Underlying renormalisable theories yielding LLHH are constructed by “opening up” the operator. The type-1,2,3 see-saw models are the minimal, tree-level ways to open up LLHH.

OtherΔL=2 SM effective operators require external legs (quarks, additional leptons) to be closed off in loops to give neutrino mass: radiative neutrino mass generation.

The effective operator is still minimally opened up at tree-level.

A. Type-1,2,3 seesaw models: Type 1

⌫ (1, 1)(0) R ⇠ “Open up” LLHH in all minimal, tree-level ways. Type 2

(1, 3)(2) ⇠

An advantage of this approach to Type 3 constructing models is that you don’t miss any. f (1, 3)(0) R ⇠ Can we know if any of these mechanisms is true?

2 As you know, the seesaw formula mν~ /M has the tinyνmass explained by the inverse relationship with the scale of new physics M.

-10 2 14 Using mν~ 0.1 eV = 10 GeV and ~ 10 GeV you get M ~ 10 GeV, an extremely high mass scale, putting the new physics extremely out of range of accelerator experiments.*

Diluting the purity of the seesaw idea, you can put a small λwith 2 2 -6 mν~ λ / M. A λ~10 brings the new physics into the LHC range. This is an electron-Yukawa-like parameter magnitude, so not ridiculous.

Type 2 and 3 are more testable than type 1 because the new physics couples with EW interactions. If e.g. RH weak interactions were to exist at the few-TeV scale, then type-1 would become more testable.

*Note: there are interesting motivations for using the type-1 seesaw Lagrangian in the different, low-M parameter regime, e.g.νSM of Shaposhnikov+, the Akhmedov, Rubakov, Smirnov leptogenesis scenario. Relevant experiments: SHiP, SBN, FCC-ee. In general, one may do high precision searches for low mass, weakly-coupled new physics associated withνmass. Example of search and bound: type 3 seesaw. He+, Z. Phys. C44 (1989) 441

+ 0 - fR~(1,3)(0) = (L ,N ,L ) Heavy lepton EW pair production.

CMS-PAS-EXO-16-002 Flavour democratic BR choice

ATLAS, PRD29 (2015) 032001 Melbourne contribution through P. Urquijo, L. Strang. Benchmark branching ratio Type 1 seesaw is very compelling: just add Majorana RH neutrinos. Has added major benefit of baryogenesis via leptogenesis.

Minkowski; Yanagida; Gell-Mann, Ramond, Slansky; Glashow; Senjanovic, Mohapatra; Fukugita, Yanagida.

Are there any theoretical reasons to doubt this minimal scenario?

Tension between leptogenesis and naturalness: Vissani PRD57 (1998) 7027 i lL 1 1 ij ij∗ 2 3 2 φφyν yν µ m M < 1 TeV ' 4⇡2 2 ⌫ N pp h i 7 j mN < 3 10 GeV νR ) ⇥

Standard hierarchical, thermal leptogenesis: Davidson, Ibarra 8 9 Giudice+ Bound for N1 leptogen mN > 5 x 10 – 2 x 10 GeV

7 Going to 3 flavours doesn’t help: M 4 10 GeV Clarke+ PRD91 (2015) 073009 N1 . ⇥ 1 1 3 2 2 7 Mj mi Rij < 1 TeV , 4⇡2 2 | | MN2 . 7 10 GeV 1 h i i ⇥ 0.05 eV 3 X 1 7 3 7 0.05 eV MN3 . 3 10 GeV Mj . 2.9 10 GeV 2 ⇥ mmin ) ⇥ i mi Rij ✓ | | ◆ R=Casas-Ibarra matrix ✓ ◆ P Much less minimal in most extended gauge models:

Start at LR symmetric model level: SU(2)L SU(2)R U(1)B L ⇥ ⇥ ⌫ ⌫ L (2, 1)( 1) R (1, 2)( 1) eL ⇠ eR ⇠ ✓ ◆ ✓ ◆

c c (3, 1)(2) (2, 2)(0) (⌫L) ν mass matrix: ⌫L, (⌫R) (2, 2)(0) (1, 3)(2) ⌫R ⇣ ⌘  ✓ ◆ scalar multiplets

As well as νR, you also need (1,3)(2) scalar.

Going all the way to SO(10): 126 10 + 120 You need a 126. 10 + 120 126  126 (1, 3, 1)(2) + (1, 1, 3)(2) + stu↵ you do not need ! Of course you can live with this. But there is an interesting alternative. B. Inverse and linear seesaw mechanisms:

In LRSM, add a gauge singlet fermion SR:

c (3, 1)(2) (2, 2)(0) (2, 1)( 1) (⌫L) c c ⌫L, (⌫R) (SR) (2, 2)(0) (1, 3)(2) (1, 2)( 1) ⌫R 2 (2, 1)( 1) (1, 2)( 1) (1, 1)(0) 3 0 S 1 ⇣ ⌘ R 4 5 @ A The triplets are not needed. Doublets suffice.

SO(10) level: 126 10 + 120 16 126 can be replaced by 16. 10 + 120 126 16 2 16 16 1 3

4 16 (1, 2, 1)(51) + (1, 1, 2)(1) + (3, 2, 1)(1/3) + (3⇤, 1, 2)( 1/3) ! 0 mmL Putting in mass scales: m 0 m 2 R 3 mL mR µ 4 5

Inverse seesaw: mL = 0 and μ << m << mR

Wyler, Wolfenstein NPB 218 (1983) 205

Double suppression: small μ and m/mR. Light neutrino mass: 2 Sterile admixture ~ m/mR, so relatively large m if m ~ few TeV. m µ R ⌫ ⇠ m ✓ R ◆ Smallμexplicitly violates L. Technically natural.

Scale of new physics can be few TeV. Linear seesaw: μ=0, mL ≤ m << mR

Akhmedov+ PRD53 (1996) 2752 Malinksý, Ramão, Valle PRL 95 (2005) 161801

mmL Light neutrino mass: m⌫ ⇠ mR

mL=0 restores L conservation, so mL << m technically natural.

Thus double suppression possible: small mL and m/mR.

Scale of new physics can again be relatively low. ISS & LSS produce small mν without tinyνDirac masses, and with low scale of new physics, but at the expense of introducing (technically natural) small L-violation scales μand mL.

Are they improvements over regular Dirac neutrinos?

4 -10 Put new-physics scale mR ~ 10 GeV, and mν~ 10 GeV.

µ 10 ISS: So,μdoes not have to be ridiculously small. MeV ⇠ (m/GeV)2

m 10 3 LSS: L m in keV range is reasonable. MeV ⇠ m/GeV L C. Radiative neutrino mass models:

Opening up operator O1=LLHH at tree-level produced the type-1,2,3 seesaw models at the minimal level.

Inverse, linear seesaws are examples of non-minimal tree-level options.

Now let’s look at how more complicated ΔL=2 operators lead to radiative models.

Assumptions: SM gauge group Single Higgs doublet No RH neutrinos List ofΔL=2 operators: Babu, Leung NPB619 (2001) 667 See also: de Gouvêa, Jenkins PRD77 (2008) 013008 Winter+ With gauge fields: Bhattacharya, Wudka PRD94 (2016) 055022 Henning+ 1512.03433 Lc Lc

LLc L L

Lc L L

Historic example: Doubly-charged Singly-charged Zee-Babu model scalar k scalar h

ec ec hh c e ec k L L

L L LL L L ec ec L L LL

HH c c O9 = LLLe Le 9 EffectiveO op Opening it up 2-loop nu mass diagram

The exotics (k, h in this case) can be searched for at the LHC. 4

102 Table 1 Lower mass limits at 95% CL on H±± bosons decaying to Observed 95% CL upper limit e±e±, µ±µ±, or e±µ± pairs. Mass limits are derived assuming branch- ) [fb]

± Expected 95% CL upper limit ++ e ATLASing ratios bounds to a given decay on mode k offrom 100%, 33%,like-sign 22%, or 11%. Both ± Expected limit ± 1σ e expected and observed limits are given. Expected limit ± 2σ → dilepton searches. ++ −− ±± ± σ(pp → H H ), BR(H → e±e±)=1 ± 10 L L L ++ −− ±± ± ± σ(pp → H HR ), BR(H → e e )=1 R R BR(H±± ⇥ ⇥ ) 95% CL lower limit on m(H±±) [GeV] L ⌅ ± ⇧± L BR(H

× The bounds depend on BR ) e e e − ± ± µ±µ± ±µ± − exp. obs. exp. obs. exp. obs. H 1 assumption. See back-up slides. ++ ATLAS 100% 407 409 401 398 392 375 H -1 → ∫ Ldt = 4.7 fb Strong Melbourne33% role: Nuti318, Scutti317, P. Taylor,317 Barberio290 , 279 276 22% 274 258 282 282 250 253 (pp s = 7 TeV EPJ C72 (2012) 2244 Rodd, Hamano. σ -1 11% 228 212 234 216 206 190 10 100 200 300 400 500 ±± BR(H±± ⇥ ⇥ ) 95% CL lower limit on m(H±±) [GeV] m(H ) [GeV] R ⌅ ± ⇧± R (a) e±e± µ±µ± e±µ± exp. obs. exp. obs. exp. obs. 102 100% 329 322 335 306 303 310 Observed 95% CL upper limit

) [fb] 33% 241 214 247 222 220 195

± Expected 95% CL upper limit µ 22% 203 199 223 212 194 187 ± Expected limit ± 1σ µ 11% 160 151 184 176 153 151 Expected limit ± 2σ → ++ −− ±± ± ± ± σ(pp → H HL ), BR(H → µ µ )=1 ± 10 L L ++ −− σ(pp → H H ), BR(H±±→ µ±µ±)=1 R R R BR(H × ) −

− e±e± and µ±µ± ﬁnal states and 11% for the e±µ± ﬁnal

H 1

++ state. In addition, the same mass limits can be placed on the ATLAS H -1 singlet H±± in the Zee-Babu model as its production cross → ∫ Ldt = 4.7 fb sections and decay kinematics are the same as for H±±. Fig-

(pp s = 7 TeV L σ -1 ure 3 shows the mass limits as a function of the branching 10 100 200 300 400 500 600 ATLAS-CONF-2016-051 ratio into each of the three ﬁnal states. m(H±±) [GeV] In conclusion, a search for doubly-charged Higgs bosons (b) decaying to e±e±, e±µ±, or µ±µ± has been performed by searching for a narrow resonance peak in the dilepton mass 102 Observed 95% CL upper limit distribution. No such peak was observed in a data sample ) [fb]

± Expected 95% CL upper limit 1 µ corresponding to an integrated luminosity of 4.7 fb of pp ± Expected limit ± 1σ e Expected limit ± 2σ collisions at ⌃s = 7 TeV recorded by the ATLAS detector → ++ −− ±± ± ± ± σ(pp → H H ), BR(H → e µ )=1 ± 10 L L L at the LHC in 2011. Cross-section limits between 17 fb and ++ −− ±± ± ± σ(pp → H HR ), BR(H → e µ )=1 R R 0.6 fb are set depending on the mass of the H±± boson and BR(H

× the final state. Assuming pair production, couplings to left- ) − − handed fermions, and a branching ratio of 100% for each H 1 ++ ATLAS final state, masses below 409 GeV, 398 GeV, and 375 GeV H -1 → ∫ Ldt = 4.7 fb are excluded at 95% CL for e±e±, µ±µ±, and e±µ± final

(pp s = 7 TeV states, respectively. Lower mass limits are also set for sce- σ -1 10 100 200 300 400 500 600 narios with right-handed couplings or smaller branching ra- m(H±±) [GeV] tios. The limits on HL±± bosons also apply to the singlet in the Zee-Babu model. (c)

Fig. 2 Upper limit at 95% CL on the cross section times branching Acknowledgements We thank CERN for the very successful oper- ratio for pair production of H±± bosons decaying to (a) e±e±, (b) ation of the LHC, as well as the support staff from our institutions µ±µ±, and (c) e±µ± pairs. The observed and median expected limits without whom ATLAS could not be operated efﬁciently. are shown along with the 1⇥ and 2⇥ variations in the expected limits. We acknowledge the support of ANPCyT, Argentina; YerPhI, Ar- In the range 70 < m(H±±) < 110 GeV, no limit is set in the e±e± chan- menia; ARC, Australia; BMWF and FWF, Austria; ANAS, Azerbai- nel. Also shown are the theoretical predictions at next-to-leading order jan; SSTC, Belarus; CNPq and FAPESP, Brazil; NSERC, NRC and for the pp H H cross section for H±± and H±± bosons. The ⌅ ±± ⇤⇤ L R CFI, Canada; CERN; CONICYT, Chile; CAS, MOST and NSFC, variation from bin to bin in the expected limits is due to ﬂuctuations in China; COLCIENCIAS, Colombia; MSMT CR, MPO CR and VSC the background yields derived from small MC samples. CR, Czech Republic; DNRF, DNSRC and Lundbeck Foundation, Den- mark; EPLANET and ERC, European Union; IN2P3-CNRS, CEA- DSM/IRFU, France; GNSF, Georgia; BMBF, DFG, HGF, MPG and CMS search also includesτfinal states:

CMS-PAS-HIG-16-036

Early CMS search: EPJ C72 (2012) 2189. Pre-2015 analyses B=Babu J=Julio L=Leung Z=Zee d=detailed, b=brief d f operator(s) scale from mν model(s)? comments (TeV) (incomplete) 7 7 4 O = LLLecH 10 Z (1980,d) pure leptonic, 2 1-loop 105,8 BJ (2012,d) 2012 = 2-loop O = LLQdcH(2) 3 BL (2001,b) 2001 = 1-loop ¯ c 107,9 BL (2001,b) 1-loop O4 = LLQu¯ H(2) vector leptoquarks c c c 104 BJ (2010,d) 2-loop O8 = Le¯ u¯ d H

9 4 c 106 BL (2001,b) 1-loop O5 = LLQd HHH¯

c 107 O6 = LLQ¯u¯ HHH¯

c 102 O7 = LQe¯ QHHH¯

c 105 purely leptonic O61 =(LLHH)(Le H¯ )

c 106 O66 =(LLHH)(Qd H¯ )

c 7 O71 =(LLHH)(Qu H) 10 BL (2001,b) 1-loop A=Angel et al dGJ=deGouvêa+Jenkins

d f operator(s) scale from mν model(s)? comments (TeV) c c 3 2-loop, purely leptonic 9 6 O9 = LLLe Le 10 BZ (1988,d)

c c 4 O10 = LLLe Qd 10 BL (2001,b) two 2-loop models

O = LLQdcQdc(2) 30, 104 BL (2001,b) three 2-loop models 11 A (2013,d) one 2-loop model

c c 4,7 O12 = LLQ¯u¯ Q¯u¯ (2) 10 BL (2001,b) 2-loop

c c 4 O13 = LLQ¯u¯ Le 10

¯ c c 3,6 O14 = LLQu¯ Qd (2) 10

c c O15 = LLLd L¯u¯ 103 3-loop

c c c c O16 = LLe¯ d e¯ u¯ 2 3-loop

c c ¯c c O17 = LLd d d u¯ 2 3-loop

c c c c O18 = LLd u u¯ u¯ 2 3-loop

c c c c O19 = LQd d e¯ u¯ 1 dGJ (2008,b) 3-loop

c c c c O20 = Ld Q¯u¯ e¯ u¯ 40 3-loop In Cai, Clarke, Schmidt, RV JHEP 1502 (2015) 161, arXiv:1410.0689 we finished the job of constructing all minimal models from d = 7 ops:

0 = LLHHHH˜ O1 = LLLeH,¯ = LLQdH,¯ = LLQ†u¯†H, = Ld¯e¯†u¯†H O2 O3 O4 O8

Scalar-only extension:

Scalar Scalar Operator Zee (1,2,1/2) (1,1,1) O2,3,4

(3,2,1/6) (3,1,-1/3) O3,8 Babu, Leung, Julio

(3,2,1/6) (3,3,-1/3) O3 Scalar + fermion extension:

Dirac fermion Scalar Operator

(1,2,-3/2) (1,1,1) O2

(3,2,-5/6) (1,1,1) O3

(3,1,2/3) (1,1,1) O3 Babu, Julio (3,1,2/3) (3,2,1/6) O3

(3,2,-5/6) (3,1,-1/3) O3,8 Cai, Clarke, Schmidt, RV

(3,2,-5/6) (3,3,-1/3) O Detailed collider and LFV 3 pheno on this model is done in the paper cited earlier: (3,3,2/3) (3,2,1/6) O3 see back-up slides.

(3,2,7/6) (1,1,1) O4

(3,1,-1/3) (1,1,1) O4

(3,2,7/6) (3,2,1/6) O8

(1,2,-1/2) (3,2,1/6) O8 Scalar + fermion extension:

Dirac fermion Scalar Operator

(1,3,-1) (1,4,3/2) O’1

Clearly, a large variety of scalar and fermion exotics can be associated with radiative neutrino mass generation.

Including new gauge bosons expands the list: RH weak, vector LQs, etc.

General searches for the production of exotic particles at the energy frontier can also be searches for radiative neutrino mass generation. Radiative models are in general more testable than seesaw models:

• Exotics that interact under all SM forces • Scale of new physics in general is lower • Implications for flavour experiments

4-loop models are probably ruled out because the scale of new physics has to be too low.

3-loop models deserve attention, therefore. See, for example, papers by: Krauss, Nasri, Trodden Aoki, Kanemura, Seto Ahriche, Nasri, McDonald+ Gustafsson, No, Rivera

4. Beyond theνexperimental program

We can classifyνmass models into 3 categories:

1. High-scale (> 106 GeV): Traditional seesaw idea. New physics at accelerator-inaccessible mass scale. Can have important cosmological implications.

2. Intermediate-scale (102-6 GeV): Radiative models. Low-scale seesaw variants such as inverse and linear seesaw.

3. Very low-scale (<102 GeV): Seesaw structure but radically different parameter space. New physics is very weakly coupled: hidden sector. The very low scale, hidden-sector possibilities could be probed by the very interesting SHiP experiment at CERN and SBN at Fermilab (also FCC-ee) (talks by J. Salvado and P. Ballett at our workshop) – beyond my scope.

Intermediate-scale regime:

• General collider searches for exotics (ATLAS, CMS). • Often connection betweenνmass/mixing fitting and decay BRs of exotics. • LFV effects: μèeγ, μèeee, μNèeN, τèμγ etc. (Mu2/3E, COMET, Belle 2). • Can have LFV in Higgs decays (ATLAS, CMS). • Lepton universality violation, quark flavour violation (LHCb, Belle 2). • Newνphysics could contribute to (g-2)μ(E989 at Fermilab, E34 at J-PARC).

It is clear that the search for the origin of neutrino mass involves basically the whole experimental HEP program! A probably falsifiable case: extended Zee model

Herrero-García, Ohlsson, Riad, Wirén 1701.05345

Φ1,2 Two Higgs doublets and a singly-charged scalar.

Φ− h− 1,2 Implications: L L eR L Significant charged LFV. Potentially significant Higgs LFV. Φ1,2 All scalars must be below 2.5 TeV.

-2 2 region 1 region According to their analysis:

)) -4 ⌧ µ NO case can be almost completely tested if expected Belle 2 !

h -9 ( τèμγ sensitivity of O(10 ) achieved. Br (

10 -6 log NO IO case already disfavoured. Would be ruled out by θ23>π/4. Future μNèeN should be able to rule it out completely. -8 -12.0 -10.5 -9.0 -7.5 log (Br(⌧ µ)) 10 !

Let me briefly turn to some current excitement in flavour physics … 0.5

Belle II Projection ICHEP 2016 Preliminary Scalar leptoquarks, which abound in radiative R(D*) Belle Combination 0.45 Babar LHCb νmass models, are of considerable interest World Combination 0.4 SM prediction: PRD92 054410 (2015), PRD85 094025 (2012) for current flavour anomalies: charged-lepton universality violation hints. 0.35

0.3 + (B¯ Kµ¯ µ) 0.25 R ! σ K ¯ ¯ + 1 σ contours >3 ⌘ (B Ke e) 0.2 ! 0.25 0.3 0.35 0.4 0.45 0.5 0.55 0.6 SM : 1.0003 0.0001 2.6σ R(D) ± Credits: Belle 2 and P. Urquijo +0.090 SuperKEKB luminosity projection LHCb : 0.745 0.074 0.036 ±

Goal of Be!e II/SuperKEKB"

) -1 (ab ¯ ( )

Integrated luminosity (B D ⇤ ⌧⌫¯) 9 months/year R ( ) ! 20 days/month D ⇤ ¯ ( ) ⌘ (B D ⇤ `⌫¯) !

) -1 s -2 Phase-1 Confirm B→D*τν (cm New physics Peak luminosity

Calendar Year 5. Will we ever know? 5. Will we ever know?

It should be obvious that the answer is: 5. Will we ever know?

It should be obvious that the answer is: MAYBE! Back-up slides Doubly-charged scalar search 4

102 Table 1 Lower mass limits at 95% CL on H±± bosons decaying to Observed 95% CL upper limit e±e±, µ±µ±, or e±µ± pairs. Mass limits are derived assuming branch- ) [fb]

± Expected 95% CL upper limit e ing ratios to a given decay mode of 100%, 33%, 22%, or 11%. Both ± Expected limit ± 1σ e expected and observed limits are given. Expected limit ± 2σ → ++ −− ±± ± σ(pp → H H ), BR(H → e±e±)=1 ± 10 L L L ++ −− σ(pp → H H ), BR(H±±→ e±e±)=1 R R R BR(H±± ⇥ ⇥ ) 95% CL lower limit on m(H±±) [GeV] L ⌅ ± ⇧± L BR(H × ) e e e − ± ± µ±µ± ±µ± − exp. obs. exp. obs. exp. obs. H 1 ++ ATLAS 100% 407 409 401 398 392 375 H -1 → ∫ Ldt = 4.7 fb 33% 318 317 317 290 279 276 22% 274 258 282 282 250 253 (pp s = 7 TeV σ -1 11% 228 212 234 216 206 190 10 100 200 300 400 500 ±± BR(H±± ⇥ ⇥ ) 95% CL lower limit on m(H±±) [GeV] m(H ) [GeV] R ⌅ ± ⇧± R 4 4 (a) e±e± µ±µ± e±µ± 2 Table 1 Lower mass limitsexp. at 95%obs. CL onexp.H bosonsobs. decayingexp. obs. to 10 102 ±± Table 1 Lower mass limits at 95% CL on H±± bosons decaying to 2 Observed 95% CL upper limit e±e±, µ±µ±, or e±µ± pairs. Mass limits are derived assuming branch- ) [fb] 10 100% 329 322Observed 95%335 CL upper306 limit 303 310e±e±, µ±µ±, or e±µ± pairs. Mass limits are derived assuming branch- ± Expected 95% CL upper limit ) [fb] ± e Dependence of mass Observed 95% CL upper limit ing ratios to a given decay mode ofExpected 100%, 95% 33%, CL upper 22%, limit or 11%. Both ± e ) [fb] 33% 241 214 247 222 220 195ing ratios to a given decay mode of 100%, 33%, 22%, or 11%. Both

Expected limit ± 1σ ± ± e Expected 95% CL upper limit expected and observed limits are given.Expected limit ± 1σ µ

e 22% 203 199 223 212 194 187 ± Expected limit ± 2σ expected and observed limits are given. →

Expected limit ± 1σ µ ++ −− Expected limit ± 2σ

±± →

± ± ±

σ(pp → H H ), BR(H → e e )=1 limits 11% on charge-2160 151 184 176 153 151 ± 10 L ++ −− ±± ExpectedL limit ± 2σL ± (pp H H ), BR(H e±e±)=1 → ++ −− σ → → ±± ± ± ± 10 L L L σ(pp → H H++R ), −BR(H− →± ±e e )=1± ± ± R R ++ −− ±± σ(pp → H HL ), BR(H → µ µ )=1 ( ⇥ ⇥ ) ( ± ± ) ± 10 H m H L L BR L±± ± ⇧± 95% CLσ lower(pp → H limit HR ), onBR(H → eL±±e )=1[GeV] ++ −− R R σ(pp → H H ), BR(H±±→ µ±µ±)=1 ⌅ BR(H±± ⇥±⇥⇧±) 95% CL lower limit on m(H±±) [GeV]

BR(H L L R R R scalar on BR

× ⌅ BR(H ) e e e − ± ± µ±µ± ±µ± × BR(H − ) e e e

− µ µ µ

× ± ± ± ± ± ± )

− exp. obs. exp. obs. exp. obs. H − 1 assumption. Early − ++ e e and µ µ ﬁnal states and 11% for the e µ ﬁnal exp. obs. exp. obs. exp. obs. H ± ± ± ± ± ± ATLAS 1

H 100% 407 409 401 398 392 375 H 1 ++

++ -1 state.ATLAS In addition, the same mass limits can be placed on the

→ 100% 407 409 401 398 392 375 LdtATLAS = 4.7 fb H 33% 318 EPJ317 C72317 (2012)290 2244 279 276 H ∫ Run 1 data.-1 -1 → singlet22%LdtH ±±= 4.7 infb the Zee-Babu274 258 model282 as its282 production250 253 cross 33% 318 317 317 290 279 276 → (pp s = Ldt7 TeV = 4.7 fb ∫ σ ∫ 22% 274 258 282 282 250 253 -1 (pp sections11%s = and7 TeV decay kinematics228 212 are234 the same216 as for206H±±190. Fig-

10(pp s = 7 TeV L 100 200 300 400 500 σ σ -1 11% 228 212 234 216 206 190 10-1 10ure 3 shows the mass limits as a function of the branching 100 200 300 400 500±± 600 BR(H±±100 ⇥ ⇥ 200) 95%300 CL lower400 limit on 500m(H±±) [GeV] m(H ) [GeV] R ⌅ ± ⇧± R ratio into each of the three ﬁnal states. ±± (H ⇥ ⇥ ) m(H ) m(H±±) [GeV] m(H ) [GeV] BR R±± ± ⇧± 95% CL lower limit on R±± [GeV] (a) In conclusion, a searche±e± for doubly-chargedµ±µ± Higgse±µ bosons± ⌅ (b) exp.(a) obs. exp. obs. exp. obs. e±e± µ±µ± e±µ± decaying to e±e±, e±µ±, or µ±µ± has been performed by 102 100% 329 322 335 306 303 310 exp. obs. exp. obs. exp. obs. 2 Observed 95% CL upper limit searching2 for a narrow resonance peak in the dilepton mass ) [fb] 10 10 33% 241 214 247 222 220 195 100% 329 322 335 306 303 310 ± Expected 95% CL upper limit µ Observed 95% CL upper limit distribution.22% No such203 peak199 wasObserved observed223 95% CL 212upper in limit a194 data sample187 ± ) [fb] Expected limit ± 1σ ) [fb] 33% 241 214 247 222 220 195 ± µ ± 1 Expected 95% CL upper limit Expected 95% CL upper limit µ 11% 160 151 184 176 153 151 µ corresponding to an integrated luminosity of 4.7 fb of pp ± Expected limit ± 2σ 22% 203 199 223 212 194 187 ± → Expected limit 1 ++ −− ± σ Expected limit ± 1σ µ e ±± ± ± ± σ(pp → H HL ), BR(H → µ µ )=1

± 10 ExpectedL limit ± 2σL collisions at ⌃s = 7 TeV recorded by the ATLAS detector 11% 160 151 184 176 153 151 → ++ −− ±± ± ± Expected limit ± 2σ

σ(pp → H H++ ), −BR(H− →± ±µ µ )=1 → R ± ± ± σ(pp →R H H ), BR(HR → e µ )=1 ++ −− ±± ± ± ±

± 10 L L L at the LHC in 2011. Cross-sectionσ(pp → H limits HL ), BR(H between→ µ µ )=1 17 fb and

± 10 ++ −− ±± ± ± L L σ(pp → H H ), BR(H → e µ )=1 ++ −− ±± ± ±

BR(H R R R σ(pp → H HR ), BR(H → µ µ )=1 × 0.6 fb are set depending on the massR of theR H±± boson and ) − BR(H − e±e± and µ±µ± final states and 11% for the e±µ± final BR(H × the final state. Assuming pair production, couplings to left- ) × H −

1 ) − − ++ state. In addition, the same mass limits can be placed on the ATLAS − handed fermions, and a branching ratio of 100% for eache±e± and µ±µ± final states and 11% for the e±µ± final H H 1 H ++ -1 singlet1 H±± in the Zee-Babu model as its production cross → Ldt = 4.7 fb ATLAS ++ final state, masses below 409 GeV, 398 GeV, and 375 GeVstate. In addition, the same mass limits can be placed on the H ∫ ATLAS

-1 H sections and decay kinematics are the same as for H±±. Fig- →

(pp s = Ldt7 TeV = 4.7 fb L are excluded at-1 95% CL for e±e±, µ±µ±, and e±µ± ﬁnalsinglet H±± in the Zee-Babu model as its production cross σ ∫ → Ldt = 4.7 fb -1 ure 3 shows the mass limits as a function of the branching

(pp ∫ 10 100s = 7 TeV200 300 400 500 600 states, respectively. Lower mass limits are also set for sce- σ sections and decay kinematics are the same as for H±±. Fig- -1 (pp s = 7 TeV L

10 σ ratio into each of the three final states. 100 200 300 400 m(H500±±) [GeV]600 10narios-1 with right-handed couplings or smaller branching ra-ure 3 shows the mass limits as a function of the branching In conclusion,100 200 a search300 for doubly-charged400 500 Higgs600 bosons m(H±±) [GeV] tios. The limits on HL±± bosons also apply to the singlet in (b) ±± ratio into each of the three final states. decaying to e e , e µ , or µ µ has beenm(H performed) [GeV] by the Zee-Babu± model.± ± ± ± ± In conclusion, a search for doubly-charged Higgs bosons (c) searching for a narrow resonance peak in the dilepton mass 2 (b) 10 decaying to e±e±, e±µ±, or µ±µ± has been performed by Upper limit at 95% CL on theObserved cross section95% CL upper times limit branching distribution. No such peak was observed in a data sample Fig.) [fb] 2 Acknowledgements We thank CERN for the very successful oper- ± Expected 95% CL upper limit 1 searching for a narrow resonance peak in the dilepton mass ratioµ for pair production of H±± bosons decaying to (a) e±e±, (b) corresponding2 to an integrated luminosity of 4.7 fb of pp ± 10 Expected limit ± 1σ ation of the LHC, as well as the support staff from our institutions µ±µ e ±, and (c) e±µ± pairs. The observed and median expected limits collisions at ⌃s = 7 TeV recordedObserved by 95% the CL upper ATLAS limit detector distribution. No such peak was observed in a data sample Expected limit ± 2σ ) [fb] without whom ATLAS could not be operated efficiently. → ±

1 ++ −− ±± ± ± Expected 95% CL upper limit ± are shown along with the 1⇥ and 2⇥ variationsσ(pp → H H in), theBR(H expected→ e µ )=1 limits. µ corresponding to an integrated luminosity of 4.7 fb of pp ± 10 L L L ± at theWe LHC acknowledge in 2011. Cross-sectionthe support of ANPCyT, limits between Argentina; 17 YerPhI, fb and Ar- ++ −− ±± ± ± Expected limit ± 1σ

In the range 70 < m(H±±) < 110 GeV, noσ(pp limit → H isH set), BR(H in the→ eeµ±)=1e± chan- e R R R menia; ARC, Australia; BMWF and FWF, Austria; ANAS, Azerbai- 0.6 fb are set depending on theExpected mass limit of ± the 2σ H±± boson and collisions at ⌃s = 7 TeV recorded by the ATLAS detector →

nel. Also shown are the theoretical predictions at next-to-leading order ++ −− ±±

BR(H ± ± ± jan; SSTC, Belarus; CNPq and FAPESP,σ(pp → H H Brazil;), BR(H NSERC,→ e µ )=1 NRC and

± 10 L × the ﬁnal state. Assuming pair production,L couplingsL to left- at the LHC in 2011. Cross-section limits between 17 fb and for the) pp H H cross section for H±± and H±± bosons. The ±± ⇤⇤ L R ++ −− ±± ± ± − CFI, Canada; CERN; CONICYT,σ(pp Chile; → H HR CAS,), BR(H MOST→ e µ )=1 and NSFC,

− ⌅ variation from bin to bin in the expected limits is due to fluctuations in handed fermions, and a branching ratioR ofR 100% for each 0.6 fb are set depending on the mass of the H±± boson and H 1 China; COLCIENCIAS, Colombia; MSMT CR, MPO CR and VSC BR(H the++ background yields derived from small MC samples. ATLAS × finalCR, state, Czech masses Republic; below DNRF, 409 DNSRC GeV, and 398 Lundbeck GeV, and Foundation, 375 GeV Den-the final state. Assuming pair production, couplings to left- ) H −

-1 −

→ mark; EPLANET and ERC, European Union; IN2P3-CNRS, CEA- Ldt = 4.7 fb are excluded at 95% CL for e±e±, µ±µ±, and e±µ± ﬁnal handed fermions, and a branching ratio of 100% for each ∫ H DSM/IRFU,1 France; GNSF, Georgia; BMBF, DFG, HGF, MPG and ++ (pp s = 7 TeV states, respectively.ATLAS Lower mass limits are also set for sce-

σ final state, masses below 409 GeV, 398 GeV, and 375 GeV -1 H 10 -1 100 200 300 400 500 600 → narios with∫ Ldt = right-handed 4.7 fb couplings or smaller branching ra- are excluded at 95% CL for e±e±, µ±µ±, and e±µ± final ±± m(H ) [GeV] (pp tios. Thes = limits 7 TeV on HL±± bosons also apply to the singlet in states, respectively. Lower mass limits are also set for sce- σ the10-1 Zee-Babu model. (c) 100 200 300 400 500 600 narios with right-handed couplings or smaller branching ra- m(H±±) [GeV] tios. The limits on HL±± bosons also apply to the singlet in Fig. 2 Upper limit at 95% CL on the cross section times branching Acknowledgements We thank CERN for the very successful oper- the Zee-Babu model. ratio for pair production of H±± bosons decaying to (a) e±e±, (b) ation of the LHC, as well(c) as the support staff from our institutions µ±µ±, and (c) e±µ± pairs. The observed and median expected limits without whom ATLAS could not be operated efficiently. are shown along with the 1⇥ and 2⇥ variations in the expected limits.Fig. 2 UpperWe acknowledge limit at 95% the CL support on the of cross ANPCyT, section Argentina; times branching YerPhI, Ar- Acknowledgements We thank CERN for the very successful oper- In the range 70 < m(H±±) < 110 GeV, no limit is set in the e±e± chan-ratio formenia; pair ARC,production Australia; of H BMWF±± bosons and FWF,decaying Austria; to (a) ANAS,e±e±, Azerbai- (b) ation of the LHC, as well as the support staff from our institutions nel. Also shown are the theoretical predictions at next-to-leading orderµ±µ±,jan; and SSTC, (c) e±µ Belarus;± pairs. CNPq The observed and FAPESP, and median Brazil; expected NSERC, limits NRC and without whom ATLAS could not be operated efficiently. for the pp H±±H⇤⇤ cross section for HL±± and HR±± bosons. Theare shownCFI, along Canada; with CERN; the 1⇥ and CONICYT, 2⇥ variations Chile; in CAS, the expected MOST and limits. NSFC, variation from⌅ bin to bin in the expected limits is due to fluctuations in We acknowledge the support of ANPCyT, Argentina; YerPhI, Ar- In the rangeChina; 70 COLCIENCIAS,< m(H±±) < 110 Colombia; GeV, no limit MSMT is set CR, in MPOthe e± CRe± chan- and VSC the background yields derived from small MC samples. menia; ARC, Australia; BMWF and FWF, Austria; ANAS, Azerbai- nel. AlsoCR, shown Czech are Republic; the theoretical DNRF, DNSRCpredictions and at Lundbeck next-to-leading Foundation, order Den- jan; SSTC, Belarus; CNPq and FAPESP, Brazil; NSERC, NRC and for the mark;pp EPLANETH H cross and ERC, section European for H±± Union;and H IN2P3-CNRS,±± bosons. The CEA- ⌅ ±± ⇤⇤ L R CFI, Canada; CERN; CONICYT, Chile; CAS, MOST and NSFC, variationDSM/IRFU, from bin to France; bin in the GNSF, expected Georgia; limits BMBF, is due DFG, to fluctuations HGF, MPG in and China; COLCIENCIAS, Colombia; MSMT CR, MPO CR and VSC the background yields derived from small MC samples. CR, Czech Republic; DNRF, DNSRC and Lundbeck Foundation, Den- mark; EPLANET and ERC, European Union; IN2P3-CNRS, CEA- DSM/IRFU, France; GNSF, Georgia; BMBF, DFG, HGF, MPG and 4

102 Table 1 Lower mass limits at 95% CL on H±± bosons decaying to Observed 95% CL upper limit e±e±, µ±µ±, or e±µ± pairs. Mass limits are derived assuming branch- ) [fb]

± Expected 95% CL upper limit e ing ratios to a given decay mode of 100%, 33%, 22%, or 11%. Both ± Expected limit ± 1σ e expected and observed limits are given. Expected limit ± 2σ → EPJ C72 (2012) 2244 ++ −− ±± ± σ(pp → H H ), BR(H → e±e±)=1 ± 10 L L L ++ −− σ(pp → H H ), BR(H±±→ e±e±)=1 R R R BR(H±± ⇥ ⇥ ) 95% CL lower limit on m(H±±) [GeV] L ⌅ ± ⇧± L BR(H × ) e e e − ± ± µ±µ± ±µ± − exp. obs. exp. obs. exp. obs. H 1 ++ ATLAS 100% 407 409 401 398 392 375 H -1 → ∫ Ldt = 4.7 fb 33% 318 317 317 290 279 276 22% 274 258 282 282 250 253 (pp s = 7 TeV σ -1 11% 228 212 234 216 206 190 10 100 200 300 400 500 ±± BR(H±± ⇥ ⇥ ) 95% CL lower limit on m(H±±) [GeV] m(H ) [GeV] R ⌅ ± ⇧± R (a) e±e± µ±µ± e±µ± exp. obs. exp. obs. exp. obs. 102 100% 329 322 335 306 303 310 Observed 95% CL upper limit

) [fb] 33% 241 214 247 222 220 195

− e±e± and µ±µ± ﬁnal states and 11% for the e±µ± ﬁnal

H 1

(pp s = 7 TeV L σ 10-1 ure 3 shows the mass limits as a function of the branching 100 200 300 400 500 600 ratio into each of the three ﬁnal states. m(H±±) [GeV] In conclusion, a search for doubly-charged Higgs bosons (b) decaying to e±e±, e±µ±, or µ±µ± has been performed by searching for a narrow resonance peak in the dilepton mass 102 Observed 95% CL upper limit distribution. No such peak was observed in a data sample ) [fb]

Exotics: (3¯, 1, 1/3) , (3, 2, 5/6) ⇠ ⇠ Leptoquark scalar Vector-like quark

2 LQ L¯ d¯H = µ † + m ¯ + Y L Q + Y L ¯ † + Y d¯ H + h.c. L ij i j i i ij i j ⇣ e¯u¯ ⌘ + Yij e¯iu¯j† + h.c. Set to zero for simplicity b/c no role in nu mass gen ⇣ ⌘

Impose B-conservation to forbid proton-decay interactions allowed by the gauge symmetry: QQ† and d¯u¯ Neutrino mass generation:

Qi d¯ ¯ Prop to down quark masses L↵ L - dominated by b quark H H - for simplicity, have zero mixing h i h i of χ with 1st, 2nd gen quarks

2 3 LQ L¯ mbmB mB (m⌫ )ij = 2 Yi3 Yj +(i j) mbB 2 2 ln 2 16⇡ $ m mB m ⇣ ⌘ d¯H p mbB = Y3 v/ 2 (m m ,m ) b ⌧ B

B charge -1/3 mixing with b to give B = 0 Y charge -4/3 massive exotic quark ✓ ◆ One almost massless nu, and two massive T T m⌫ = a+a + a a+ outer product of vectors

1 1 NO ⇣± IO ⇣± a = (pm2u2⇤ ipm3u3⇤) ,a= (pm1u1⇤ ipm2u2⇤) ± p2 ± ± p2 ±

UPMNS =(u1 ,u2 ,u3 ) ζis a Casas-Ibarra-like, complex parameter not determined by Set lightest nu mass and all low-energy parameters PMNS phases to zero. Run-1 LHC constraints:

CMS search for vector-like B quark (no Y search has been done): B Zb, B Hb dominate ! ! 1.0

0.8 CMS # 0.6 bZ ! B

" 0.4 Br 0.2

0.0 400 500 600 700 800 900 1000 mB!GeV m 620 GeV B Leptoquark searches:

Pair production: gg fusion and q q-bar annihilation. Colour charge only, so σ(ppàφφ) depends on mφ only. σ(ppàφφ) = 82 (23.5) fb for mφ = 500 (600) GeV.

Decays: Lt, b⌫ L (e, µ, ⌧) ⌘ Consider! mY,B >> mφ only, so LY, Bυ final states not possible m 2 ( Lt)= Y LQ f(m ,m ,m ) ! 8⇡ L3 L t Also give nu mass

m 2 2 ( ⌫ b) Y LQc + Y L¯ s f(m ,m ,m ) ! L ' 8⇡ L3 2 L 1 ⌫L b ✓ ◆ BRs depend on |ζ|. Because of connection to nu mass generation, they are quite constrained. Next slide: region B (Br(φàbυ)≈100% ) and region T (Br(φàbυ)<100% )

Region B: pp bb +missingE ! ! T sbottom pair searches apply: mφ> 730 GeV at 95% C.L.

Region T: ATLAS,CMS limits on decays to all bυfinal states.

100

b⌫⌧ b⌫L bb + MET: m >520-600 GeV b⌫µ φ P

1 (e,μ) + MET + (b-)jets: mφ>580 GeV 10 t⌧ normal hierarchy b⌫ tµ e example + - (e,μ) (e,μ) + MET + jets: mφ>600 GeV te

2 10

m Charged LFV bounds and prospects:

Same model, flavour violation constraints: µ e,µ eee, µN eN ! ! !

grey = excluded region

Blue (B) allowed region has Br(φàbυ)≈100% Red (T) allowed region has Br(φàbυ)<100%

13 12 13 BR(µ e) < 5.7 10 BR(µ eee) < 10 BR(µAu eAu) < 7 10 ! ⇥ ! ! ⇥

16 BR(µTi eTi) 10 reach of Mu2E, COMET ! ⇠