Current Situation in the Neutrino (& Charged-Lepton) Sectors · Current Situation in the Neutrino...

Andre de Gouvea Northwestern

Current Situation in the Neutrino(& Charged-Lepton) Sectors

Andre de Gouvea

Northwestern University

Workshop on an European Strategy for Future Neutrino Physics

CERN, October 1–3, 2009

October 1, 2009 ν (and `) Physics


Neutrinos:

Where We Are, Where We Want to Go, and Why?



[Maltoni and Schwetz, arXiv: 0812.3161]

[Details in next three talks (Ranucci, Lasserre, Touramanis)]



We often assume two-flavor mixing. Of course, there are three neutrinos. . .

Phenomenological Understanding of Neutrino Masses & Mixing

νe

νµ

ντ

=

Ue1 Ue2 Ue3

Uµ1 Uµ2 Uµ3

Uτ1 Uτ2 Uτ3

ν1

ν2

ν3

Definition of neutrino mass eigenstates (who are ν1, ν2, ν3?):

• m21 < m2

2 ∆m213 < 0 – Inverted Mass Hierarchy

• m22 −m2

1 � |m23 −m2

1,2| ∆m213 > 0 – Normal Mass Hierarchy

tan2 θ12 ≡ |Ue2|2

|Ue1|2 ; tan2 θ23 ≡ |Uµ3|2|Uτ3|2 ; Ue3 ≡ sin θ13e

−iδ

[for a detailed discussion see AdG, Jenkins, arXiv:0804.3627]



Three Flavor Mixing Hypothesis Fits All Data Really Well.

⇒ Good Measurements of Oscillation Observables

[1] Schwetz, Tortola and Valle, arXiv:0808.2016

[2] Gonzalez-Garcia and Maltoni, arXiv:0704.1800




What We Know We Don’t Know (1): Missing Oscillation Parameters

(∆m2)sol

(∆m2)sol

(∆m2)atm

(∆m2)atm

νe

νµ

ντ

(m1)2

(m2)2

(m3)2

(m1)2

(m2)2

(m3)2

normal hierarchy inverted hierarchy

[Driving Force of Next-Generation Oscillation Program (see next three talks)]

• What is the νe component of ν3?(θ13 6= 0?)

• Is CP-invariance violated in neutrinooscillations? (δ 6= 0, π?)

• Is ν3 mostly νµ or ντ? (θ23 > π/4,θ23 < π/4, or θ23 = π/4?)

• What is the neutrino mass hierarchy?(∆m2

13 > 0?)

⇒ All of the above can “only” be

addressed with new neutrino

oscillation experiments

Ultimate Goal: Not Measure Parameters but Test the Formalism (Over-Constrain Parameter Space)



“Hint” for non-zero sin2 θ13? You decide. . . (see claim by Fogli et al., arXiv:0806.2649)




The “Holy Graill” of Neutrino Oscillations – CP Violation

In the old Standard Model, there is only onea source of CP-invariance violation:

⇒ The complex phase in VCKM , the quark mixing matrix.

Indeed, as far as we have been able to test, all CP-invariance violating

phenomena agree with the CKM paradigm:

• εK ;

• ε′K ;

• sin 2β;

• etc.

Neutrino masses and lepton mixing provide strong reason to believe that other

sources of CP-invariance violation exist.

[for details on how we plan to do this, see talk by Schwetz-Mangold]

amodulo the QCD θ-parameter, which will be “willed away” as usual.



What We Know We Don’t Know (2): How Light is the Lightest Neutrino?

(∆m2)sol

(∆m2)sol

(∆m2)atm

(∆m2)atm

νe

νµ

ντ

(m1)2

(m2)2

(m3)2

(m1)2

(m2)2

(m3)2

normal hierarchy inverted hierarchy

m2 = 0 ——————

——————↑↓

m2lightest = ?

So far, we’ve only been able to measure

neutrino mass-squared differences.

The lightest neutrino mass is only poorly

constrained: m2lightest < 1 eV2

qualitatively different scenarios allowed:• m2

lightest ≡ 0;

• m2lightest � ∆m2

12,13;

• m2lightest � ∆m2

12,13.

Need information outside of neutrino oscillations.

[talks by Cremonesi, Hannestad]



What We Know We Don’t Know (3) – Are Neutrinos Majorana Fermions?

νL

you

νR? ν

L?

you

__

A massive charged fermion (s=1/2) isdescribed by 4 degrees of freedom:

(e−L ← CPT→ e+R)

l “Lorentz”

(e−R ← CPT→ e+L)

A massive neutral fermion (s=1/2) isdescribed by 4 or 2 degrees of freedom:

(νL ← CPT→ νR)

l “Lorentz” ‘DIRAC’

(νR ← CPT→ νL)

(νL ← CPT→ νR)

‘MAJORANA’ l “Lorentz”

(νR ← CPT→ νL)How many degrees of freedom are requiredto describe massive neutrinos?



Why Don’t We Know the Answer?

If neutrino masses were indeed zero, this is a nonquestion: there is nodistinction between a massless Dirac and Majorana fermion.

Processes that are proportional to the Majorana nature of the neutrinovanish in the limit mν → 0. Since neutrinos masses are very small, theprobability for these to happen is very, very small: A ∝ mν/E.

The “smoking gun” signature is the observation of LEPTON NUMBERviolation. This is easy to understand: Majorana neutrinos are their ownantiparticles and, therefore, cannot carry “any” quantum numbers —including lepton number.

[talks by Cremonesi, Zuber]



Search for the Violation of Lepton Number (or B − L)

10−4 10−3 10−2 10−1 1lightest neutrino mass in eV

10−4

10−3

10−2

10−1

1

|mee

| in

eV

90% CL (1 dof)

∆m232 > 0

disfavoured by 0ν2β

disfavouredby

cosmology

∆m232 < 0

Helicity Suppressed Amplitude ∝ meeE

Observable: mee ≡∑i U

2eimi

⇐ no longer lamp-post physics!

Best Bet: search for

Neutrinoless Double-Beta

Decay: Z → (Z + 2)e−e− ×

←(next)

←(next-next)



What We Are Trying To Understand:

⇐ NEUTRINOS HAVE TINY MASSES

⇓ LEPTON MIXING IS “WEIRD” ⇓

VMNS ∼

0.8 0.5 0.2

0.4 0.6 0.70.4 0.6 0.7

VCKM ∼

1 0.2 0.001

0.2 1 0.01

0.001 0.01 1

1

10-5

10-4

10-3

10-2

10-1

1

10

10 2

10 3

10 4

10 5

10 6

10 7

10 8

10 9

10 10

10 11

10 12

0 1 2 3 4fermion

mas

s (e

V)

t

bτ

µ

c

s

du

e

ν3

ν2

ν1

TeV

GeV

MeV

keV

eV

meV

What Does It Mean?



Who Cares About Neutrino Masses: Only∗ “Palpable” Evidenceof Physics Beyond the Standard Model

The SM we all learned in school predicts that neutrinos are strictlymassless. Massive neutrinos imply that the the SM is incomplete andneeds to be replaced/modified.

Furthermore, the SM has to be replaced by something qualitativelydifferent.

——————∗ There is only a handful of questions our model for fundamental physics cannot

explain properly. These are, in order of “palpability” (my opinion):

• What is the physics behind electroweak symmetry breaking? (Higgs or not in SM).

• What is the dark matter? (not in SM).

• Why does the Universe appear to be accelerating? Why does it appear that the

Universe underwent rapid acceleration in the past? (not in SM – is this “particle

physics?”).



What is the New Standard Model? [νSM]

The short answer is – WE DON’T KNOW. Not enough available info!

mEquivalently, there are several completely different ways of addressingneutrino masses. The key issue is to understand what else the νSMcandidates can do. [are they falsifiable?, are they “simple”?, do theyaddress other outstanding problems in physics?, etc]

We need more experimental input, and it looks like it may be coming inthe near/intermediate future! ⇒ This is why we are talking here today!



Options include:

• modify SM Higgs sector (e.g. Higgs triplet) and/or

• modify SM particle content (e.g. SU(2)L Triplet or Singlet) and/or

• modify SM gauge structure and/or

• supersymmetrize the SM and add R-parity violation and/or

• augment the number of space-time dimensions and/or

• etc

Important: different options → different phenomenological consequences

[talks by Altarelli, Strumia, Gavela]



Most Popular νSM

SM as an effective field theory – non-renormalizable operators

LνSM ⊃ −λij LiHLjH2Λ +O ( 1Λ2

)+H.c.

There is only one dimension five operator [Weinberg, 1979]. If Λ� 1 TeV, itleads to only one observable consequence...

after EWSB LνSM ⊃ mij2 νiνj ; mij = λij

v2

Λ .

• Neutrino masses are small: Λ� v → mν � mf (f = e, µ, u, d, etc)

• Neutrinos are Majorana fermions – Lepton number is violated!

• νSM effective theory – not valid for energies above at most Λ/λ.

• What is Λ? First naive guess is that M is the Planck scale – does notwork. Data require Λ ∼ 1014 GeV (anything to do with the GUTscale?).

What else is this “good for”? Depends on the ultraviolet completion!



How Do We Learn More?

In order to learn more, we need more information. Any new data and/oridea is welcome, including

• measurements of the cosmic neutrino background (indirect, of course,via CMB, large-scale structure, relic abundances, etc)

• searches for lepton number violation;

(neutrinoless double beta decay, etc)

• precision measurements of the neutrino oscillation parameters;

(νs from reactors, accelerators, sun, atmosphere, supernovae(?), etc)

• searches for fermion electric/magnetic dipole moments;

(electron edm, muon g − 2, etc)



• precision studies of neutrino – matter interactions;

(Minerνa, NuSOnG, etc)

• collider experiments:

(LHC, etc)

– Can we “see” the physics responsible for neutrino masses at the LHC?– YES!Must we see it? – NO, but we won’t find out until we try!

– we need to understand the physics at the TeV scale before we canreally understand the physics behind neutrino masses (is therelow-energy SUSY?, etc).

[talks by Strumia, Gavela, Hannestad, et alia]



[another crucial activity that may help reveal the origin of neutrino masses, in detail]

Charged-Leptons:

More specifically, charged-lepton flavor violation (CLFV)

(and, even more specifically, muons)

What is the connection?

• Both neutrinos and charged-leptons are, well, leptons;

• Facilities required for next-next generation oscillation experiments are also

ideal for next-generation CLFV.

& (not necessarily related to neutrino physics)

• Searches for CLFV provide unique, perhaps invaluable, opportunity for

running into new, heavy physics at or beyond the electroweak scale.



Searches for Lepton Number Violation

10-19

10-17

10-15

10-13

10-11

10-9

10-7

10-5

10-3

10-1

1950 1960 1970 1980 1990 2000 2010

Year

UL

Bra

nc

hin

g R

ati

o (

Co

nv

ers

ion

Pro

ba

bil

ity

)

µ → e γ

µ- N→ e

- N

µ+e

-→ µ

-e

+

µ → e e e

KL → π+ µ e

KL → µ e

KL → π0 µ e

(µ and e)

[hep-ph/0109217]October 1, 2009 ν (and `) Physics


SM Expectations?

In the old SM, the rate for charged lepton flavor violating processes is trivial to

predict. It vanishes because individual lepton-flavor number is conserved:

• Nα(in) = Nα(out), for α = e, µ, τ .

But individual lepton-flavor number are NOT conserved– ν oscillations!

Hence, in the νSM (the old Standard Model plus operators that lead to neutrino

masses) µ→ eγ is allowed (along with all other charged lepton flavor violating

processes).

These are Flavor Changing Neutral Current processes, observed in the quark

sector (b→ sγ, K0 ↔ K0, etc).

Unfortunately, we do not know the νSM expectation for charged lepton flavor

violating processes → we don’t know the νSM Lagrangian !



One contribution known to be there: active neutrino loops (same as quark sector).

In the case of charged leptons, the GIM suppression is very efficient. . .

e.g.: Br(µ→ eγ) = 3α32π

∣∣∣∑i=2,3 U∗µiUei

∆m21i

M2W

∣∣∣2 < 10−54

[Uαi are the elements of the leptonic mixing matrix,

∆m21i ≡ m2

i −m21, i = 2, 3 are the neutrino mass-squared differences]



10-16

10-15

10-14

10-13

10-12

10-11

10-10

10-9

20 40 60 80 100 120 140 160 180 200m4 (GeV)

MA

X B

(CLF

V)

τ→ µγ

τ→ µµµ

µ→ eγ

µ→ eee

µ→e conv in 48Ti

e.g.: SeeSaw Mechanism [minus “Theoretical Prejudice”]

arXiv:0706.1732 [hep-ph]



Independent from neutrino masses, there are strong theoretical reasons tobelieve that the expected rate for flavor changing violating processes ismuch, much larger than naive νSM predictions and that discovery is justaround the corner.

Due to the lack of SM “backgrounds,” searches for rare muon processes,including µ→ eγ, µ→ e+e−e and µ+N → e+N (µ-e–conversion innuclei) are considered ideal laboratories to probe effects of new physics ator even above the electroweak scale.

Indeed, if there is new physics at the electroweak scale (as many theoristswill have you believe) and if mixing in the lepton sector is large“everywhere” the question we need to address is quite different:

Why haven’t we seen charged lepton flavor violation yet?



10 3

10 4

10-2

10-1

1 10 102

κ

Λ (

TeV

)

B(µ→ eγ)>10-13

B(µ→ eγ)>10-14

B(µ→ e conv in 48Ti)>10-16

B(µ→ e conv in 48Ti)>10-18

EXCLUDED

Model Independent Considerations

LCLFV =mµ

(κ+1)Λ2 µRσµνeLFµν+

+ κ(1+κ)Λ2 µLγµeL

(uLγ

µuL + dLγµdL)

• µ→ e-conv at 10−17 “guaranteed” deeper

probe than µ→ eγ at 10−14.

• We don’t think we can do µ→ eγ better than

10−14. µ→ e-conv “only” way forward after MEG.

• If the LHC does not discover new states

µ→ e-conv among very few process that can

access 1000+ TeV new physics scale:

tree-level new physics: κ� 1, 1Λ2 ∼

g2θeµM2

new.



[Agashe, Blechman, Petriello, hep-ph/0606021]

Randall-Sundrum Model

(fermions in the bulk)

- dependency on UV-completion(?)

- dependency on Yukawa couplings

- “complementarity” between µ→ eγ,

µ− e conv

SUSY GUT

- dependency on choice for

neutrino Yukawa couplings

- scan restricted to scenarios

LHC discovers new states.

[Calibbi et al, PRD74, 116002 (2006)]October 1, 2009 ν (and `) Physics


What is This Good For?

While specific models (see last slide) provide estimates for the rates forCLFV processes, the observation of one specific CLFV process cannotdetermine the underlying physics mechanism (this is always true when allyou measure is the coefficient of an effective operator).

Real strength lies in combinations of different measurements, including:

• kinematical observables (e.g. angular distributions in µ→ eee);

• other CLFV channels;

• neutrino oscillations;

• measurements of g − 2 and EDMs;

• collider searches for new, heavy states;

• etc.



CONCLUSIONS

The venerable Standard Model has finally sprung a leak – neutrinos arenot massless!

1. we have a very successful parametrization of the neutrino sector,

and we have identified what we know we don’t know → Well-defined

experimental program.

2. neutrino masses are very small – we don’t know why, but we think it

means something important.

3. we need a minimal νSM Lagrangian. In order to decide which one is

“correct” we need to uncover the faith of baryon number minus

lepton number (0νββ is the best [only?] bet).



4. We know very little about the new physics uncovered by neutrino

oscillations.

• It could be renormalizable → “boring” Dirac neutrinos

• It could be due to Physics at absurdly high energy scales M � 1 TeV →high energy seesaw. How can we ever convince ourselves that this is correct?

• It could be due to very light new physics. Prediction: new light propagating

degrees of freedom – sterile neutrinos

• It could be due to new physics at the TeV scale → either weakly coupled, or

via a more subtle lepton number breaking sector. Predictions: charged

lepton flavor violation, collider signatures!

5. We need more experimental input – and more seems to be on the way

(this is a data driven field). We only started to figure out what is going on.

6. There is plenty of room for surprises, as neutrinos are very narrow but

deep probes of all sorts of physical phenomena. Remember that neutrino

oscillations are “quantum interference devices” – potentially very sensitive

to whatever else may be out there (e.g., Λ ' 1014 GeV).



7. We know that charged lepton flavor violation must occur. Naive

expectations are really tiny in the νSM (neutrino masses too small).

8. If there is new physics at the electroweak scale, we “must” see CLFV very

soon (MEG taking date – stay tuned!). ‘Why haven’t we seen it yet?’

9. It is fundamental to probe all CLFV channels. While in many scenarios

µ→ eγ is the “largest” channel, there is no theorem that guarantees this

(and many exceptions).

10. CLFV may be intimately related to new physics unveiled with the discovery

of non-zero neutrino masses. It may play a fundamental role in our

understanding of the seesaw mechanism, GUTs, the baryon-antibaryon

asymmetry of the Universe. We won’t know for sure until we see it! ⇒October 1, 2009 ν (and `) Physics


11. Complementary to LHC and other searches for new physics. Guaranteed to

learn something regardless of scenario:

• New d.o.f. at LHC and positive signal for next-generation CLFV: best case

scenario. Differentiate new scenarios for the new physics. Connections to

neutrino masses?

• New d.o.f. at LHC and negative signal for next-generation CLFV: New

physics flavor blind. Why? Neutrino masses are very high energies?

Leptogenesis disfavored? Neutrino Mass Physics Weakly Coupled?

• No new d.o.f. at LHC and positive signal for next-generation CLFV: New

physics beyond the reach of LHC. Can we learn more? How?

• No new d.o.f. at LHC and negative signal for next-generation CLFV:

Next-next generation CLFV (possibly µ→ e-conversion) among very few

probes of new physics scales (along with neutrino oscillation experiments,

astrophysics, cosmology, etc). How do we learn more?



Backup Slides . . .



High-energy seesaw has no observable consequence other than non-zero neutrino

masses, except, perhaps,

Baryogenesis via Leptogenesis

One of the most basic questions we are allowed to ask (with any real hopeof getting an answer) is whether the observed baryon asymmetry of theUniverse can be obtained from a baryon–antibaryon symmetric initialcondition plus well understood dynamics. [Baryogenesis]

This isn’t just for aesthetic reasons. If the early Universe undergoes aperiod of inflation, baryogenesis is required, as inflation would wipe outany pre-existing baryon asymmetry.

It turns out the seesaw mechanism contains all necessary ingredients toexplain the baryon asymmetry of the Universe as long as the right-handedneutrinos are heavy enough – M > 109 GeV (with some exceptions that Iwon’t have time to mention).



In the old SM, (electroweak) baryogenesis does not work – not enoughCP-invariance violation, Higgs boson too light.

Neutrinos help by providing all the necessary ingredients for successfulbaryogenesis via leptogenesis.

• Violation of lepton number, which later on is transformed into baryonnumber by nonperturbative, finite temperature electroweak effects (inone version of the νSM, lepton number is broken at a high energyscale M).

• Violation of C-invariance and CP-invariance (weak interactions, plusnew CP-odd phases).

• Deviation from thermal equilibrium (depending on the strength of therelevant interactions).



L

LN1

AH

H

AH

N1 L

H

HA

N1 L

H

HN1

AL

L

AL

N1 H

L

LA

N1 H

H

N1 U3

Q3L

H

L

U3

N1

Q3

H

L

Q3

N1

U3

N1, 2, 3

LL

HH

N1, 2, 3

H

H L

L

N1, 2, 3

H

HL

L

N1

L

H

N1N2, 3

L

L

H

H

N1 N2, 3

LL

HH

E.g. – thermal seesaw leptogenesis, L ⊃ −yiαLiHNα − MαβN

2 NαNβ +H.c.

• L-violating processes

• y ⇒ CP-violation

• deviation from thermal eq.constrains combinations of

MN and y.

• need to yield correct mν

not trivial!

[G. Giudice et al, hep-ph/0310123]

[Fukugita, Yanagida]



0.08 0.1 0.12 0.14 0.16heaviest ν mass m3 in eV

10−10

10−9

10−8

max

imal

nB

/nγ

SM

3σ ranges

0.08 0.1 0.12 0.14 0.16heaviest ν mass m3 in eV

10−10

10−9

10−8

max

imal

nB

/nγ

MSSM

3σ ranges

E.g. – thermal, seesaw leptogenesis, L ⊃ −yiαLiHNα − MαβN

2 NαNβ +H.c.

[G. Giudice et al, hep-ph/0310123]

It did not have to work – but it does

MSSM picture does not quite work – gravitino problem

(there are ways around it, of course...)



Fourth Avenue: Higher Order Neutrino Masses from ∆L = 2 Physics.

Imagine that there is new physics that breaks lepton number by 2 units atsome energy scale Λ, but that it does not, in general, lead to neutrinomasses at the tree level.

We know that neutrinos will get a mass at some order in perturbationtheory – which order is model dependent!



9

TABLE I: Dimension-five through dimension-eleven LNV operators analyzed in this survey. The first two columns display theoperator name and field structure, respectively. Column three presents the induced neutrino mass expressions, followed bythe inferred scale of new physics, Λν . Column five lists favorable modes of experimental exploration. Column six describes anoperator’s current status according to the key U (Unconstrained), C (Constrained) and D (Disfavored). See text for details.

O Operator mαβ Λν (TeV) Best Probed Disfavored

4a LiLjQiucHkεjk

yu

16π2

v2

Λ 4 × 109 ββ0ν U

4b LiLjQkucHkεijyug2

(16π2)2v2

Λ 6 × 106 ββ0ν U

5 LiLjQkdcH lHmHiεjlεkmyd

(16π2)2v2

Λ 6 × 105 ββ0ν U

6 LiLjQkucH lHkHiεjlyu

(16π2)2v2

Λ 2 × 107 ββ0ν U

7 LiQj ecQkHkH lHmεilεjm y%β

g2

(16π2)2v2

Λ

“1

16π2 + v2

Λ2

”4 × 102 mix C

8 LiecucdcHjεij y%β

ydyu

(16π2)2v2

Λ 6 × 103 mix C

9 LiLjLkecLlecεijεkly2

"(16π2)2

v2

Λ 3 × 103 ββ0ν U

10 LiLjLkecQldcεijεkly"yd

(16π2)2v2

Λ 6 × 103 ββ0ν U

11a LiLjQkdcQldcεijεkly2

dg2

(16π2)3v2

Λ 30 ββ0ν U

11b LiLjQkdcQldcεikεjly2

d(16π2)2

v2

Λ 2 × 104 ββ0ν U

12a LiLjQiucQjuc y2

u(16π2)2

v2

Λ 2 × 107 ββ0ν U

12b LiLjQkucQlucεijε

kl y2ug2

(16π2)3v2

Λ 4 × 104 ββ0ν U

13 LiLjQiucLlecεjl

y"yu

(16π2)2v2

Λ 2 × 105 ββ0ν U

14a LiLjQkucQkdcεijydyug2

(16π2)3v2

Λ 1 × 103 ββ0ν U

14b LiLjQiucQldcεjl

ydyu

(16π2)2v2

Λ 6 × 105 ββ0ν U

15 LiLjLkdcLiucεjkydyug2

(16π2)3v2

Λ 1 × 103 ββ0ν U

16 LiLjecdcecucεijydyug4

(16π2)4v2

Λ 2 ββ0ν, LHC U

17 LiLjdcdcdcucεijydyug4

(16π2)4v2

Λ 2 ββ0ν, LHC U

18 LiLjdcucucucεijydyug4

(16π2)4v2

Λ 2 ββ0ν, LHC U

19 LiQjdcdcecucεij y%β

y2dyu

(16π2)3v2

Λ 1 ββ0ν, HElnv, LHC, mix C

20 LidcQiucecuc y%β

ydy2u

(16π2)3v2

Λ 40 ββ0ν, mix C

21a LiLjLkecQlucHmHnεijεkmεlny"yu

(16π2)2v2

Λ

“1

16π2 + v2

Λ2

”2 × 103 ββ0ν U

21b LiLjLkecQlucHmHnεilεjmεkny"yu

(16π2)2v2

Λ

“1

16π2 + v2

Λ2

”2 × 103 ββ0ν U

22 LiLjLkecLkecH lHmεilεjmg2

(16π2)3v2

Λ 4 × 104 ββ0ν U

23 LiLjLkecQkdcH lHmεilεjmy"yd

(16π2)2v2

Λ

“1

16π2 + v2

Λ2

”40 ββ0ν U

24a LiLjQkdcQldcHmHiεjkεlmy2

d(16π2)3

v2

Λ 1 × 102 ββ0ν U

24b LiLjQkdcQldcHmHiεjmεkly2

d(16π2)3

v2

Λ 1 × 102 ββ0ν U

25 LiLjQkdcQlucHmHnεimεjnεklydyu

(16π2)2v2

Λ

“1

16π2 + v2

Λ2

”4 × 103 ββ0ν U

26a LiLjQkdcLiecH lHmεjlεkmy"yd

(16π2)3v2

Λ 40 ββ0ν U

26b LiLjQkdcLkecH lHmεilεjmy"yd

(16π2)2v2

Λ

“1

16π2 + v2

Λ2

”40 ββ0ν U

27a LiLjQkdcQidcH lHmεjlεkm

g2

(16π2)3v2

Λ 4 × 104 ββ0ν U

27b LiLjQkdcQkdcH lHmεilεjmg2

(16π2)3v2

Λ 4 × 104 ββ0ν U

28a LiLjQkdcQjucH lHiεkl

ydyu

(16π2)3v2

Λ 4 × 103 ββ0ν U

28b LiLjQkdcQkucH lHiεjlydyu

(16π2)3v2

Λ 4 × 103 ββ0ν U

28c LiLjQkdcQlucH lHiεjk

ydyu

(16π2)3v2

Λ 4 × 103 ββ0ν U

29a LiLjQkucQkucH lHmεilεjmy2

u(16π2)2

v2

Λ

“1

16π2 + v2

Λ2

”2 × 105 ββ0ν U

29b LiLjQkucQlucH lHmεikεjm

g2

(16π2)3v2

Λ 4 × 104 ββ0ν U

30a LiLjLiecQkucHkH lεjly"yu

(16π2)3v2

Λ 2 × 103 ββ0ν U

30b LiLjLmecQnucHkH lεikεjlεmn y"yu

(16π2)2v2

Λ

“1

16π2 + v2

Λ2

”2 × 103 ββ0ν U

31a LiLjQidcQkucHkH lεjl

ydyu

(16π2)2v2

Λ

“1

16π2 + v2

Λ2

”4 × 103 ββ0ν U

Effective

Operator

Approach

(∆L = 2)

AdG, Jenkins,

0708.1344 [hep-ph]

(there are 129

of them if you

discount different

Lorentz structures!)

classified by Babu

and Leung in

NPB619,667(2001)



να νβ

LNVOperator

(a)(b)

νβνα

yv yv

(c)

νβνα

yv yv

yH−

eyβ

(d) (e)

γ, g

W, Z

να νβ

vv

W, Z

γ, g

νβνα

yyH−

e e

v v

H+

yβyαh0h0h0

h0



0

0.2

0.4

0.6

0.8

1

1.2

1.4

20 40 60 80 100 120m4 (GeV)

MA

X Γ

(H→

νN)/

Γ(H

→bb

- )

MH=120 GeV

Weak Scale Seesaw, and Accidentally Light Neutrino Masses[AdG arXiv:0706.1732]

What does the seesaw Lagrangian predict

for the LHC?

Nothing much, unless. . .

• MN ∼ 1− 100 GeV,

• Yukawa couplings larger than naiveexpectations.

⇐ H → νN as likely as H → bb!

(NOTE: N → `q′q or ``′ν (prompt)

“Weird” Higgs decay signature! )

ALSO: “Majorana neutrinos at the LHC,”

see Han, Zhang, hep-ph/0604064

et cetera



(a) (b) (c)

q

q qq ℓℓ

g gg

qq ℓν

q

g g

q qqq ℓ ℓ

LNV at Colliders ⇒ LHC: pp→ `±`±+ multi-jets

OK OK ν in final state



H

H

φ1

φ2

φ3

φ4

Q

L

dc dc

ec dc

Order-One Coupled, Weak Scale Physics

Can Also Explain Naturally Small

Majorana Neutrino Masses:

Multi-loop neutrino masses from lepton number

violating new physics.

−LνSM ⊃∑4

i=1Miφiφi + iy1QLφ1 + y2dcdcφ2 + y3ecdcφ3 + λ14φ1φ4HH + λ234Mφ2φ3φ4 + h.c.

mν ∝ (y1y2y3λ234)λ14/(16π)4 → neutrino masses at 4 loops, requires Mi ∼ 100 GeV!

WARNING: For illustrative purposes only. Details still to be worked out. Scenario most

likely ruled out by charged-lepton flavor-violation, LEP, Tevatron, and HERA.

[arXiv:0708.1344]



CP-invariance Violation in Neutrino Oscillations

The most promising approach to studying CP-violation in the leptonicsector seems to be to compare P (νµ → νe) versus P (νµ → νe).

Aµe = U∗e2Uµ2

(ei∆12 − 1

)+ U∗e3Uµ3

(ei∆13 − 1

)where ∆1i = ∆m2

1iL2E , i = 2, 3.

The amplitude for the CP-conjugate process is

Aµe = Ue2U∗µ2

(ei∆12 − 1

)+ Ue3U

∗µ3

(ei∆13 − 1

).

[remember: according to unitarty, Ue1U∗µ1 = −Ue2U∗µ2 − Ue3U∗µ3]



In general, |A|2 6= |A|2 (CP-invariance violated) as long as:

• Nontrivial “Weak” Phases: arg(U∗eiUµi) → δ 6= 0, π;

• Nontrivial “Strong” Phases: ∆12, ∆13 → L 6= 0;

• Because of Unitarity, we need all |Uαi| 6= 0 → three generations.

All of these can be satisfied, with a little luck: given that two of the threemixing angles are known to be large, we need |Ue3| 6= 0.

The goal of next-generation neutrino experiments is to determine themagnitude of |Ue3|. We need to know this in order to understand how tostudy CP-invariance violation in neutrino oscillations!



In the real world, life is much more complicated. The lack of knowledgeconcerning the mass hierarchy, θ13, and θ23, for example, leads to severaldegeneracies and ambiguities.

Note that, in order to see CP-invariance violation, we need the“subleading” terms (and need to make sure that the leading atmosphericterms do not average out)!

In order to ultimately measure a new source of CP-invariance violation,we will need to combine different measurements:– oscillation of muon neutrinos and antineutrinos,– oscillations at accelerator and reactor experiments,– experiments with different baselines (or broad energy spectrum),– etc.



Most direct probe of the lightest neutrino mass – β-decay spectrum

Kinemarical Effect of Non-Zero mν . In practice sensitive to “electron neutrino mass”:

m2νe ≡

∑i|Uei|2m2

i Next Generation m2νe < (0.2 eV)2

E0 = 18.57 keV

t1/2 = 12.32 years

e

e



Big Bang Neutrinos are Warm Dark Matter

• Constrained by the Large Scale

Structure of the Universe.

Constraints depend on

• Data set analysed;

• “Bias” on other parameters;

• . . .

Bounds can be evaded with

non-standard cosmology. Will we

learn about neutrinos from

cosmology or about cosmology

from neutrinos?October 1, 2009 ν (and `) Physics


The Seesaw Lagrangian

A simplea, renormalizable Lagrangian that allows for neutrino masses is

Lν = Lold − λαiLαHN i −3∑i=1

Mi

2N iN i +H.c.,

where Ni (i = 1, 2, 3, for concreteness) are SM gauge singlet fermions. Lνis the most general, renormalizable Lagrangian consistent with the SMgauge group and particle content, plus the addition of the Ni fields.

After electroweak symmetry breaking, Lν describes, besides all other SMdegrees of freedom, six Majorana fermions: six neutrinos.

aOnly requires the introduction of three fermionic degrees of freedom, no new inter-

actions or symmetries.



To be determined from data: λ and M .

The data can be summarized as follows: there is evidence for threeneutrinos, mostly “active” (linear combinations of νe, νµ, and ντ ). Atleast two of them are massive and, if there are other neutrinos, they haveto be “sterile.”

This provides very little information concerning the magnitude of Mi

(assume M1 ∼M2 ∼M3).

Theoretically, there is prejudice in favor of very large M : M � v. Popularexamples include M ∼MGUT (GUT scale), or M ∼ 1 TeV (EWSB scale).

Furthermore, λ ∼ 1 translates into M ∼ 1014 GeV, while thermalleptogenesis requires the lightest Mi to be around 1010 GeV.

we can impose very, very few experimental constraints on M



What We Know About M :

• M = 0: the six neutrinos “fuse” into three Dirac states. Neutrinomass matrix given by µαi ≡ λαiv.

The symmetry of Lν is enhanced: U(1)B−L is an exact globalsymmetry of the Lagrangian if all Mi vanish. Small Mi values are’tHooft natural.

• M � µ: the six neutrinos split up into three mostly active, light ones,and three, mostly sterile, heavy ones. The light neutrino mass matrixis given by mαβ =

∑i µαiM

−1i µβi [m ∝ 1/Λ ⇒ Λ = M/µ2].

This the seesaw mechanism. Neutrinos are Majorana fermions.Lepton number is not a good symmetry of Lν , even thoughL-violating effects are hard to come by.

• M ∼ µ: six states have similar masses. Active–sterile mixing is verylarge. This scenario is (generically) ruled out by active neutrino data(atmospheric, solar, KamLAND, K2K, etc).



Why are Neutrino Masses Small? – Different Possibilities!

If µ�M , below the mass scale M ,

L5 =LHLH

2Λ.

Neutrino masses are small if Λ� 〈H〉. Data require Λ ∼ 1014 GeV.

In the case of the seesaw,

Λ ∼ M

λ2,

so neutrino masses are small if either

• they are generated by physics at a very high energy scale M � v

(high-energy seesaw); or

• they arise out of a very weak coupling between the SM and a new, hidden

sector (low-energy seesaw); or

• cancellations among different contributions render neutrino masses

accidentally small (“fine-tuning”).



10−2

10−1

100

101

102

103

104

νe

νµ

ντ

νs1

νs2

νs3

ν4

ν5

ν6

ν1

ν2

ν3

Mass (eV)

Low-Energy Seesaw [AdG, PRD72, 033005 (2005)]

[AdG, Jenkins, Vasudevan, PRD75, 013003 (2007)]

“Oscillation” Sterile States

Dark Matter?

Pulsar Kicks?

Also effects in 0νββ,

tritium beta-decay,

supernova neutrino oscillations,

NEEDS non-standard cosmology.



−1 0 1 2 3 4 5 6 7 8 9 10 11 120

5

10

15

20

25

30

35

40

45

Log( Λ/TeV)

Num

ber

Of O

pera

tors

Dim 5Dim 7Dim 9Dim 11

Beyond The Dim-5 Operator: AdG, Jenkins, 0708.1344[hep-ph]

“Directly Accessible”

Out of “direct” reach if not weakly-coupled (?)

|||||||

Colliders

g − 2 CLFVEDM ⇓

(seesaw)



Anomalous Magnetic Moment of the Muon, (g − 2)/2 ≡ aµ

PLUS: Interplay with LHC – if there is new physics at the TeV scale, aµ can differentiate

among different models, provide precision measurement of model parameters.October 1, 2009 ν (and `) Physics


∆aµ: we need to dig a little more!


Current Situation in the Neutrino (& Charged-Lepton) Sectors · Current Situation in the Neutrino...

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