Transcript Document

Theoretical Aspects of Neutrino Mass
Zhi-zhong Xing (邢志忠)
IHEP, Beijing
E. Witten–Opening Talk at Neutrino 00 [hep-ph/0006332]
I’ll cover some aspects of interesting attempts.
OCPA Workshop on Underground Science, 21-23 July 08, HK
2
Neutrino Astronomy
UHE

Underground Business
3
Physics Potential of a large multi-purpose underground infrastructure
with a sufficiently big detector (100 – 1000 ktons?):
◆ Solar interior: various solar neutrinos and precision test of the SSM;
◆ Atmospheric neutrinos: high-statistics study;
◆ Earth interior: geo-neutrinos;
◆ Supernova neutrinos: information on the dynamics of SN explosion;
◆ Dark matter search: with / without the help of detecting neutrinos;
◆ Reactor and accelerator neutrinos: long-baseline oscillations;
◆ Proton decay: better sensitivity;
◆ ……
What / where / how can we do?
中科院未来五十年战略发展: 重大交叉学科之“宇宙起源, 超
弦理论, 中微子, 暗物质与暗能量”路线图: 建立国家地下实
验室?
4
My Focus
Part (A): free parameters of known (light) neutrinos:
3
masses
3
mixing
3
CP phases
angles
Part (B): heavy Majorana neutrinos: ≤ TeV or ≥ EeV?


LHC TeV
  

Part (A)
(Smirnov 07)
Masses
6
Neutrinos are massless in the SM, a result of the SM’s simple structure:
---- it has no right-handed ’s (weak-interaction experiments have not
required them, so theorists did not introduce them into the SM);
Dirac mass term is not allowed.
---- it conserves the SU(2)_L gauge symmetry, and it only contains the
Higgs doublet (the SM accidently possesses (B - L) symmetry);
Majorana mass term is forbidden.
A pure Dirac mass term added into the SM is theoretically not favored:
---- it worsens the problem of the large lepton & quark mass hierarchy;
---- it violates ‘t Hooft’s naturalness criterion, as a Majorana mass term
of right-handed ’s is not forbidden by the SM gauge symmetry;
---- it imposes the ad hoc assumption of L conservation on the theory.
And thus most theorists believe that massive ’s are Majorana particles
and their salient feature is lepton number violation.
Masses: Known
7
(1) 3 -masses m_1, m_2 and m_3 must have non-degenerate values;
2
2
m21
~ 8  105 eV2 , | m32
| ~ 2.5 103 eV2
(2) One of them must be about or larger than 0.05 eV;
(3) The upper bound of m_i is expected to be about 1 eV, or even less.
Latest global 3-oscillation analysis (Fogli et al., arXiv:0805.2517):
m 2  m 22  m12
m 2  | m 32  ( m12  m 22 )/2 |
Absolute mass scale:
: single  decay;
0: neutrinoless  decay;
CMB: cosmological constraints.
8
Combined Constraints
Constraints from -oscillations +  + 0 claim + CMB (Fogli et al., 08)
CMB+HST+SN-Ia+BAO+Ly
 mi  0.19e V
CMB
 mi  1.19e V
i
i
1
1
HM claim: 0.16 – 0.52 eV m1  m2  m3 HM claim
101
m 
(e V)
101
IH
m 
(e V)
IH
102
global
102
NH
NH
95% C.L.
3
10
1
10
i
1
95% C.L.
3
10
 mi (eV)
 2 fit
101
 m (eV)
i
i
1
9
Masses: Unknown
A: If the HM (Heidelberg-Moscow) claim is not true, then the absolute
mass scale of 3 neutrinos remains an open question.
Comment: I personally like a near mass degeneracy of 3 neutrinos, in
particular if neutrinos are Majorana particles.
Dirac (charged) fermions: strong mass hierarchy ---- limit 0 : 0 : 1;
Majorana (neutral) neutrinos: near mass degeneracy ---- limit 1 : 1 : 1.
B: m_1 and m_3, which is bigger? ---- normal or inverted hierarchy?
Comment: Long-baseline neutrino oscillations + matter effect can tell.
C: Can one mass be vanishing (or vanishingly small)? ---- it is possible.
Comment: Flavor symmetry may work to assure m_1 = 0 or m_3 = 0.
NH
IH
m_1 = 0 or m_3 = 0
10
Example: Friedberg-Lee symmetry on the effective -mass operator at
low energy scale (hep-ph/0606071):
Translational FL symmetry:
   z
Mass matrix:
Det(M )  m1m2 m3  0
one neutrino is massless!
Comment 1: it is easy to extend the FL symmetry to the Majorana case;
Comment 2: one may obtain an effective -mass matrix with m_1 = 0 /
m_3 = 0 by combining the FL symmetry with the seesaw mechanism.
The FL symmetry forces one massless heavy
Majorana neutrino to decouple: M_R rank 2.
Xing, Zhang, Zhou (PLB 06)
Luo, Xing, (PLB 07)
Jarlskog (PRD 08)
Liao et al (PRD 08)
11
Angles
Flavor mixing signifies a mismatch between the weak-interaction states
and the mass (or free propagation) states of leptons.
Neutrino Oscillations
Neutrino Flavor Violation
Lepton Flavor Violation
  e
Phenomenological assumption: neutrino flavor mixing can be described
by a 3 × 3 unitary matrix containing 3 mixing angles and 3 CPV phases.
Warning: the dynamics of flavor mixing relies on the theory of -mass
generation. Hence we don’t know if this assumption is correct or not.
12
Angles: Known
(a) Angle theta_23 is large and close to /4, suggestive of something?
(b) Angle theta_12 is large and seems to lie between /6 and 35.3°.
(c) Angle theta_13 is not large and its upper bound is about 10°.
Latest global 3-oscillation analysis (Fogli et al., arXiv:0805.2517):
Observations:
theta_23: seems < /4 (at < 1  C.L.);
theta_12: is quite close to ~ 35.3°;
theta_13: hints of > 0 (at ~ 1  C.L.).
(Fogli et al., arXiv:0806.2649)
95% C.L. (2)
Hints of theta_13 > 0
Fogli et al.,
arXiv:0806.2649
13
14
Angles: Unknown
A: What is the value of theta_13? Is it small? And how small is small?
Comment: Reactor & accelerator -oscillation experiments can answer,
but can they answer before a global fit yields definite “prediction”?
B: Why theta_12 and theta_23 are large and close to 2 special values?
Comment: Very strong hints at a certain (underlying) flavor symmetry.
mysterious
35.3°
T.D. Lee,
hep-ph/0605017
Tri-bimaximal Mixing
15
Flavor Symmetry
S3 , S4 , A4 ,
Z2 , …... U(1)F ,
SU(2)F , .…..
Friedberg-Lee, …...
Tri-bimaximal -mixing
One may play games with a few small integers & their square roots (an
economical group language)
Example:
(Harrison, Perkins,
0, 1, 2, 3.
Scott 02; Xing 02)
Guiding Principle
A realization of the tri-bimaximal -mixing in the Friedberg-Lee model:
 2/ 6
1/ 3
0   cos 0  sin  - symmetry breaking





V  1 / 6 1 / 3 1 / 2  0
1
0 
3 (c  b)

 
tan
2



1
/
6

1
/
3
1
/
2
sin

0
cos



(b  c )  2a


Tetra-maximal Mixing?
16
Noise to Tri-bimax: 0, 1, 2 and i (Xing, arXiv:0805.0416, PRD in press):
Predictions:
1
J 
 3%
32
-mass matrix:
17
Phases
(a) Phase  is relevant to the strength of CP violation in -oscillations;
(b) Phases  and  are associated with the LN-violating 0-process;
(c) They are entangled with one another in the RGE running.
Three phases are entirely unconstrained by current experimental data.
Jarlskog parameter is a rephasing-invariant measure of CP / T violation
in neutrino oscillations:
J is maximal when theta_12 = theta_23
= /4, theta_13 = 35.3°and delta = /2.
It will be impossible to see CP Violation if
theta_13 is too small.
J max 
1
6 3
 9.6%
More on Majorana
18
Neutrino masses, if they are of Majorana nature, must have a different
origin compared to the masses of charged leptons and quarks.
The observation of 0 must imply the Majorana nature of ’s, but it
may not uniquely & directly point to -masses and mixing parameters.
Given the SM interactions, a massive Dirac
neutrino can get tiny (one-loop) magnetic
dipole moment:
m
3eGF
 20
 ~
m  3  10
B
2
0.1 e V
8 2
A massive Majorana neutrino cannot have magnetic and electric dipole
moments, because its anti-particle is just itself.
More on Dipole Moment
19
Both Dirac and Majorana ’s can have transition
dipole moments, of a size comparable with _ .
The electro-magnetic dipoles of massive ’s can
produce a variety of rare processes:
---- neutrino decays;
---- scattering with electrons;
---- interaction with an external magnetic field
(sun, supernovae, red-giant stars, …);
---- contributions to neutrino masses.
Current experimental bound on dipole moments (Kayser, Neutrino 08):
New Physics?
D :   1015 B
M :   Bound
Model Building?
20
A Theoretician’s Personal Roadmap of Model Building (King 08)
where are the signposts?
LHC
numerous -experiments
Part (B)
(P5 Report 08)
LHC
The Money Frontier
^_^
Why Seesaws?
22
A natural theoretical way to understand why 3 -masses are very small.
Type-one Seesaw (Minkowski 77, Yanagida 79, Glashow 79, Gell-Mann,
Ramond, Slanski 79, Mohapatra, Senjanovic 79).
Fer
mi
scal
e
Triplet Seesaw (Magg, Wetterich 80, Schechter, Valle 80, Lazarides,
Shafi, Wetterich 80, Mohapatra, Senjanovic 80, Gelmini, Roncadelli 80).
Type-II Seesaw (a few right-handed Majorana neutrinos and one Higgs
triplet are both added into the SM).
23
Why TeV Seesaws?
Is the seesaw scale very close to a fundamental physics scale?
How heavy are the heavy Majorana
neutrinos or the Higgs triplet?
Planck
GUT
to unify strong, weak & electromagnetic forces?
Conventional (Type-one) Seesaw Picture: close to the GUT scale
TeV Seesaw Idea: driven by testability at LHC
TeV
Fermi
to solve the unnatural gauge hierarchy problem?
Naturalness?
Testability?
Type-I Seesaw
24
Natural case: no large cancellation in the leading seesaw term.
M  MD MR-1 MDT
0.01 eV
100 GeV
R ~ S ~ M D / M R ~ 1013
-26
Unitarity Violation ~ 10
1015 GeV
Unnatural case: large cancellation in the leading seesaw term.
1
T
M  MD MR MD
0.01 eV
1 TeV
100 GeV
R ~ S ~ M D / M R ~ 101
2
Unitarity Violation ~ 10
TeV-scale (right-handed) Majorana neutrinos: small masses of
light Majorana neutrinos come from sub-leading perturbations.
Structural Cancellation
25
Given diagonal M_R with 3 eigenvalues M_1, M_2 and M_3, the leading
(i.e., type-I seesaw) term of the light neutrino mass matrix vanishes, if
and only if M_D has rank 1,
and if
MD
Mν  MD MR-1 MDT  0
(Buchmueller, Greub 91; Ingelman, Rathsman 93; Heusch, Minkowski
94; ……; Kersten, Smirnov 07).
Tiny -masses can be generated from tiny corrections to this complete
“structural cancellation”, by deforming M_D or M_R .
Simple example:
26
Type-II Seesaw
Incomplete cancellation between two leading terms of the light neutrino
mass matrix in type-II seesaw scenarios. The residue of this incomplete
cancellation generates the neutrino masses:
tiny mass
not
not
collider
generation
small
small
signature
(Chao, Luo, Z.Z.X., Zhou, PRD 08)
Discrete flavor symmetries may be used to arrange the textures of two
mass terms, but fine-tuning seems unavoidable in the (Big – Big) case.
Collider signatures: both heavy Majorana neutrinos and doubly-charged
scalars are possible to be produced at the LHC (e.g., Azuleos et al 06;
del Aguila et al 07; Han et al 07; ….). But decoupling between collider
physics & the mechanism of neutrino mass generation is very possible.
Lessons
27
Lesson 1: two necessary conditions to test a seesaw model with heavy
right-handed Majorana neutrinos at the LHC:
(A) Masses of heavy Majorana neutrinos must be of O (1) TeV or below;
(B) Light-heavy neutrino mixing (i.e., M_D/M_R) must be large enough.
Lesson 2: LHC-collider signatures of heavy Majorana ’s are essentially
decoupled from masses and mixing parameters of light Majorana ’s.
Lesson 3: non-unitarity of the light neutrino flavor mixing matrix might
lead to observable effects in neutrino oscillations and rare processes.
Lesson 4: nontrivial limits on heavy Majorana neutrinos can be derived
at the LHC, if the SM backgrounds are small for a specific final state.
L = 2 like-sign dilepton events
Collider Signature
Lepton number violation: like-sign
dilepton events at hadron colliders,
such as Tevatron (~2 TeV) and LHC
(~14 TeV).
collider analogue to 0 decay
dominant channel
N can be produced on resonance
28
29
Just for Illustration
Han, Zhang (hep-ph/0604064, PRL): cross sections are generally smaller
for larger masses of heavy Majorana neutrinos.
Del Aguila et al (hep-ph/0606198): signal & background cross sections
(in fb) as a function of the heavy Majorana neutrino mass (in GeV).
Chao, Si, Xing, Zhou
Tevatron
arXiv:0804.1265
A single heavy N
(minimal Type-II)
LHC
Non-unitarity of V ?
30
Example A: light sterile neutrinos --- no good TH / EX motivation today.
Example B: heavy Majorana neutrinos --- popular seesaw mechanisms.
Example C: whole tower of KK states --- models with extra dimensions.
The scheme of Minimal Unitarity Violation (Antusch et al 07):
---- Only 3 light neutrino species are considered;
---- Sources of non-unitarity are allowed only in those terms of the
SM Lagrangian which involve neutrinos.
Constraint on the 3×3
-mixing matrix V ---data on -oscillations,
W and Z decays, rare
LFV modes and lepton
universality tests, …...
(Antusch et al 07):
Charged Current Interactions
31
Correlated CC-interactions:
light
heavy
Standard Parametrization of V and R (Xing, PLB 08):
V = A V_0
The deviation of A from 1 measures the
strength of unitarity violation of V .
A and R contain 9 new mixing angles
and 9 new CP-violating phases.
A and R
32
All 9 rotation angles are expected to be small, at most of O(0.1),
9 CPV phases may be large to generate new CP-violating effects.
Observations:
If the unitarity violation of V is close to the percent level, then elements
of R can reach order of 0.1, leading to appreciable collider signatures for
TeV-scale Majorana neutrinos.
New CP-violating effects, induced by the non-unitarity of V, may show
up in (short-baseline) neutrino oscillations.
Such a parametrization turns out to be very useful in –phenomenology.
UV-induced CPV
33
Example: V_0 takes the tri-bimaximal mixing pattern which has
Non-unitary
V takes the
simple form
CP violation (9 Jarlskog invariants):
New CPV
O(≤1%)
Neutrino Oscillations
34
Oscillation probability in vacuum (e.g., Antusch et al 06, Z.Z.X. 08):
Short- or medium-baseline experiments in the neglect of matter
effects (Fernandez-Martinez et al 07). In particular (Z.Z.X. 08),
≈1
UV-induced CPV at 1% level?
Numerical Illustration
35
Example: an experiment with E  a few GeV & L ~ a few 100 km.
Neutrino
Factory?
Sensitivity ≤ 1% ?
36
Matter Effects
Illustration: one heavy Majorana neutrino and constant matter density.
 e ,  , 
 e ,  , 
e
e , p,n
e
e
e
W
W
Z
e , p,n
e e
e
e
(Goswami, Ota 08; Luo 08)
Genuine CPV
Matter effect
The same matter-effect term appears in _  _ oscillations (Luo 08).
37
CPV at Colliders?
CP violation: interference between tree and one-loop amplitudes of N.
l
W
Nj
W
Ni

Ni
l
W
W  , Z0 , H0
l
W
Ni
l  ,
Nj
l
Resonant enhancement with
4 heavy Majorana neutrinos.
(Bray, Lee, Pilaftsis 07)
38
Leptogenesis
Canonical idea (Fukugita, Yanagida 86):
●
Lepton number violation at the tree level of Majorana neutrino decays;
●
Direct CP violation at the one-loop level of Majorana neutrino decays;
●
At least 2 Majorana neutrinos are required.
CP violation
L-number asymmetry
B-number asymmetry
Developments and variations (Davidson, Nardi, Nir, Phys. Rept. 08):
Recent developments: spectator processes; finite temperature effects;
flavor effects; N_2 leptogenesis; resonant (TeV) leptogenesis; ……
●
Some variations: soft (SUSY) leptogenesis; type-II leptogenesis; Dirac
leptogenesis; electromagnetic leptogenesis; ……
●
Concluding Remarks
39
 Established new physics: at least 2 of 3 known ’s must be
massive. We wonder whether their tiny masses imply new DoF
such as heavy Majorana neutrinos (more exciting new physics).
 It seems that theorists are facing a new problem in looking
for the true theory of -mass generation, flavor mixing and CP
violation ---- uniqueness (or more credit?).
 Naturalness of the SM implies that there should exist a kind
of new physics at the TeV scale. We wonder whether it is also
responsible for the neutrino mass generation ---- TeV seesaws.
 It seems that theorists are struggling for a balance between
TH naturalness and EX testability as the guiding principle. Let’s
hope so in the era of LHC + precision -experiments!
Let’s Do Something Somewhere Underground!
感谢各位会议组织者朋友
感谢香港大学和中文大学