Probing Majorana Neutrinos (in Rare Decays of Mesons) 11/17/2011 - DBD11 C. S. Kim arXiv:1005.4282...
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![Page 1: Probing Majorana Neutrinos (in Rare Decays of Mesons) 11/17/2011 - DBD11 C. S. Kim arXiv:1005.4282 (PRD82,053010,2010) G. Cvetic, C. Dib, S.K. Kang, C.S.](https://reader036.fdocuments.net/reader036/viewer/2022081516/56649eb35503460f94bba99a/html5/thumbnails/1.jpg)
Probing Majorana Neutrinos (in Rare Decays of Mesons)
11/17/2011 - DBD11C. S. Kim
arXiv:1005.4282 (PRD82,053010,2010)
G. Cvetic, C. Dib, S.K. Kang, C.S. Kim
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Outline
1. Prologue
2. Issues on neutrino masses
3. Probing Majorana neutrinos via (a) 0nbb (b) K, D, Ds, B, Bc meson RARE de-cays (c) at the LHC (and ILC)
4. Concluding remarks
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Neutrinos are massless in the SM
1. Prologue
• No right-handed ’s Dirac mass term is not allowed.
• Conserves the SU(2)_L gauge symmetry, and only con-tains
the Higgs doublet (the SM accidently possesses (B - L) symmetry); Majorana mass term is forbidden.
Historic Era in Neutrino Physics
• Atmospheric nm’s are lost. (SK) (1998)
• converted most likely to n t (2000)
• Solar ne is converted to either nm or nt (SNO) (2002)
• Only the LMA solution left for solar neutrinos (Homestake+Gallium+SK+SNO) (2002)• Reactor anti-ne disappear (2002) and reappear (KamLAND)
(2004)
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4
What we have learned
• Lepton Flavor is not conserved• Neutrinos have tiny mass, not very hierarchical• Neutrinos mix a lot• Very different from quark sectors
the first evidence for incompleteness of Minimal Standard Model
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What we don’t know
absolute mass scale of neutrinos remains an open ques-tion.
m1 and m3, which is bigger? normal or inverted hier-archy?
What is the value of q13? Is it zero or not? how small?
Reactor & accelerator -oscillation experiments can an-swer, but possibly estimated from a global fit Why q23 and q12 are large and close to special values?
Very strong hints at a certain (underlying) flavor sym-metry. Is CP violated in leptonic sector?
Neutrinos are Dirac or Majorana?
![Page 6: Probing Majorana Neutrinos (in Rare Decays of Mesons) 11/17/2011 - DBD11 C. S. Kim arXiv:1005.4282 (PRD82,053010,2010) G. Cvetic, C. Dib, S.K. Kang, C.S.](https://reader036.fdocuments.net/reader036/viewer/2022081516/56649eb35503460f94bba99a/html5/thumbnails/6.jpg)
6
Window to high energy physics beyond the SM!
Why are physicists interested in neutrino mass ?
How exactly do we extend it?
Without knowing if neutrinos are Dirac or Majo-rana, any attempts to extend the Standard Model are not successful.
2. Issues on neutrino masses
• Effective Observability of Difference between
Dirac and Majorana Nu is proportional to ( ) /D M m E
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7
2 possible types of neutrino masses
Dirac mass terms are invariant under a global symmetry , but Majorana mass terms are not so.
Thus Dirac mass can be associated with a conserved quantum number, but Majorana mass violates L number conserva-tion.
, : Majorana
,: Diracc
c
c
c
ie
etc ,)( : Majorana
,: Diracc
LL
LRRL
chiral projection :
![Page 8: Probing Majorana Neutrinos (in Rare Decays of Mesons) 11/17/2011 - DBD11 C. S. Kim arXiv:1005.4282 (PRD82,053010,2010) G. Cvetic, C. Dib, S.K. Kang, C.S.](https://reader036.fdocuments.net/reader036/viewer/2022081516/56649eb35503460f94bba99a/html5/thumbnails/8.jpg)
If Neutrinos are Majorana
• The mass eigenstates are self-conjugate up to a phase. The relative phases between two n’s be-come observable
3
2
1
Ue
U = UD X
The Majorana character is only observable for pro-cesses
ΔL=2 through the mass term that connects inter-acting neutrinos with antineutrinos:
AZ A(Z+2) + 2e-, μ- + AZ e+ + A(Z-2), etc.
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Neutrino masses, if neutrinos are of Majorana nature, must
have a different origin compared to the masses of charged leptons and quarks. A natural theoretical way to understand why 3 -masses
are very small : Seesaw mechanism
• Type-I : Right-handed Majorana neu-
trinos.
• Type-II : Higgs triplet.
• Type-III : Triplet fermions.
ν
:
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Fundamental physics and seesaw scale
• For k order of one, seesaw scale : 1013-14 GeV.
no hope of direct observation
• We may keep L free and look for theoretical pre-dictions
TeV scale seesaw
• For testability, low scale seesaw is desirable
it may harms naturalness prob-lem
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• Loop Models: Light neutrino masses are radiatively in-duced.
Ma
• RPV: Sneutrino gets small VeVs inducing a mixing between n & c.
Alternative mechanisms for majorana nmass
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Lepton number violation by 2 units plays a crucial role
to probe the Majorana nature of ’s,
Provides a promising lab. method for determining the absolute neutrino mass scale that is complementary to other measurement techniques
2L
Black Box 0
(a) The observation of 0
,
3. Probing Majorana neutrinos
![Page 13: Probing Majorana Neutrinos (in Rare Decays of Mesons) 11/17/2011 - DBD11 C. S. Kim arXiv:1005.4282 (PRD82,053010,2010) G. Cvetic, C. Dib, S.K. Kang, C.S.](https://reader036.fdocuments.net/reader036/viewer/2022081516/56649eb35503460f94bba99a/html5/thumbnails/13.jpg)
Opening Black Box 0
• exchange of a virtual light neu-trino
• Helicity mismatch mass mecha-nism
• Neutrino Majorana particle
L/R symmetric models
• Exchange of a massive neutrino• Constraints on the model pa-
rameters:
R
R
![Page 14: Probing Majorana Neutrinos (in Rare Decays of Mesons) 11/17/2011 - DBD11 C. S. Kim arXiv:1005.4282 (PRD82,053010,2010) G. Cvetic, C. Dib, S.K. Kang, C.S.](https://reader036.fdocuments.net/reader036/viewer/2022081516/56649eb35503460f94bba99a/html5/thumbnails/14.jpg)
the half-life time, ,of the 0nbb decay can be factor-ized as :
2/10T
: phase space fac-tor
: Nuclear matrix ele-ment
depends on neutrino mass hierarchy
2200
012/10 ||||),(][
eemMZEGT
3121 233
222
211
ie
ieeee eUmeUmUmm
In the limit of small neutrino masses :
: effective neutrino mass (model inde-pendent)
![Page 15: Probing Majorana Neutrinos (in Rare Decays of Mesons) 11/17/2011 - DBD11 C. S. Kim arXiv:1005.4282 (PRD82,053010,2010) G. Cvetic, C. Dib, S.K. Kang, C.S.](https://reader036.fdocuments.net/reader036/viewer/2022081516/56649eb35503460f94bba99a/html5/thumbnails/15.jpg)
• Estimate by using the best fit values of parameters including uncertainties in Majorana phases
Long Baseline
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Large uncertianties in NME
About factor of 100 in NME affect order 2-3 in |< mn>|
Uncertianties (O.Cremonesi, 05)
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Best present bound :
eV 50.035.0 m
eeSeGe 7676 Heidelberg-Mos-cow
Ge76 Half-life ysT 252/1 102.1
consistent with cosmological bound
eV 0.2 im
![Page 18: Probing Majorana Neutrinos (in Rare Decays of Mesons) 11/17/2011 - DBD11 C. S. Kim arXiv:1005.4282 (PRD82,053010,2010) G. Cvetic, C. Dib, S.K. Kang, C.S.](https://reader036.fdocuments.net/reader036/viewer/2022081516/56649eb35503460f94bba99a/html5/thumbnails/18.jpg)
21 : Processes 2 llMML
(b) Probe of Majorana neutrinos via rare decays of mesons
Taking mesons in the initial and final state to be pseudoscalar (M : K, D, Ds, B, Bc / M’=pi, K, D,…)
Not involve the uncertainties from nuclear ma-trix
elements in 0bnn
(G.Cvetic, C. Dib, S.Kang, C.S.Kim, arXiv:1005.4282 (PRD82,053010,2010))
![Page 19: Probing Majorana Neutrinos (in Rare Decays of Mesons) 11/17/2011 - DBD11 C. S. Kim arXiv:1005.4282 (PRD82,053010,2010) G. Cvetic, C. Dib, S.K. Kang, C.S.](https://reader036.fdocuments.net/reader036/viewer/2022081516/56649eb35503460f94bba99a/html5/thumbnails/19.jpg)
Effective Hamiltonian:
Decay Amplitude:
2 2
2
[ ]2
Feff t t s
N N
N Ns
N N
GH C O C O L
p m
p m im
*5[ (1 ) ]i i NL U U u v
2 1 2 1
2 1 2 1
*
*
t q q q Q q q q Q
s q q qQ q q qQ
O V V J J
O V V J J
5(1 )qQJ Q q
' '1 2 1 2( ) | |effA M M M H M
![Page 20: Probing Majorana Neutrinos (in Rare Decays of Mesons) 11/17/2011 - DBD11 C. S. Kim arXiv:1005.4282 (PRD82,053010,2010) G. Cvetic, C. Dib, S.K. Kang, C.S.](https://reader036.fdocuments.net/reader036/viewer/2022081516/56649eb35503460f94bba99a/html5/thumbnails/20.jpg)
transition rates are proportional to
production resonant for )()(
heavy for
light for
23
4
23
1
2
21
2121
NN
n
i i
ilil
iiililll
m
fNiN
m
UU
mUUm
2 2i j
Nl N l N
N N N
p mU U
p m im
,t sC C
![Page 21: Probing Majorana Neutrinos (in Rare Decays of Mesons) 11/17/2011 - DBD11 C. S. Kim arXiv:1005.4282 (PRD82,053010,2010) G. Cvetic, C. Dib, S.K. Kang, C.S.](https://reader036.fdocuments.net/reader036/viewer/2022081516/56649eb35503460f94bba99a/html5/thumbnails/21.jpg)
For example, leptonic current :
5 5(1 ) (1 )( )
2 2( )i i i iL U U v v
2 2* 5 5(1 ) (1 )
( )2 2
i i
i ii
i i
p m
pU U v
mu
2 2* 5(1 )
2i
i
ii
iiU U u
m
p mv
* 5 5(1 ) (1 )(( )
2 2)i i i iU U u v
iU iU
i i
![Page 22: Probing Majorana Neutrinos (in Rare Decays of Mesons) 11/17/2011 - DBD11 C. S. Kim arXiv:1005.4282 (PRD82,053010,2010) G. Cvetic, C. Dib, S.K. Kang, C.S.](https://reader036.fdocuments.net/reader036/viewer/2022081516/56649eb35503460f94bba99a/html5/thumbnails/22.jpg)
Model Independence of Effective Theory approach
This could be any gauge boson,e.g. ,…
'
'CKM
il
F NP
V V
U U
G G
This could be any Majorana particle,e.g. neutralino, heavy N,… , ,sterlie
, ', RW W W
Propagator changed
, 's tC C
![Page 23: Probing Majorana Neutrinos (in Rare Decays of Mesons) 11/17/2011 - DBD11 C. S. Kim arXiv:1005.4282 (PRD82,053010,2010) G. Cvetic, C. Dib, S.K. Kang, C.S.](https://reader036.fdocuments.net/reader036/viewer/2022081516/56649eb35503460f94bba99a/html5/thumbnails/23.jpg)
(i) Light neutrino case Mmmi
![Page 24: Probing Majorana Neutrinos (in Rare Decays of Mesons) 11/17/2011 - DBD11 C. S. Kim arXiv:1005.4282 (PRD82,053010,2010) G. Cvetic, C. Dib, S.K. Kang, C.S.](https://reader036.fdocuments.net/reader036/viewer/2022081516/56649eb35503460f94bba99a/html5/thumbnails/24.jpg)
Neutrinoless decay, e.g. with light neutrinos:
1 2B D
(In the limit of absorptive dominance, the amplitude can be ex-pressed in a model independent way.)
![Page 25: Probing Majorana Neutrinos (in Rare Decays of Mesons) 11/17/2011 - DBD11 C. S. Kim arXiv:1005.4282 (PRD82,053010,2010) G. Cvetic, C. Dib, S.K. Kang, C.S.](https://reader036.fdocuments.net/reader036/viewer/2022081516/56649eb35503460f94bba99a/html5/thumbnails/25.jpg)
(ii) Intermediate mass scale neutrino case MMmmm
i
dominant contribution to the process is from the “s-type” diagram because the neutrino propagator is kinematically entirely on-shell
![Page 26: Probing Majorana Neutrinos (in Rare Decays of Mesons) 11/17/2011 - DBD11 C. S. Kim arXiv:1005.4282 (PRD82,053010,2010) G. Cvetic, C. Dib, S.K. Kang, C.S.](https://reader036.fdocuments.net/reader036/viewer/2022081516/56649eb35503460f94bba99a/html5/thumbnails/26.jpg)
Effective amplitude at meson level:
If we neglect charged lepton masses;
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Br for as function of mN, with lepton mixings divided out
( , )K e
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(iii) Heavy neutrino case M
mmi
In this case, both contributions of “s-type” and “t-type” diagrams are rather comparable.
neutrino propagators reduce to -1/(mN)2
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Present bounds on PMNS for MN > 100 GeV [Nardi etal, PLB327,319]:
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• It is hard to avoid the TeV-scale physics to contrib-ute
to flavor-changing effects in general whatever it is,– SUSY, extra dimensions, TeV seesaw, techni-
color, Higgsless, little Higgs
(c) Probing Majorana Neutrinos at LHC
• In accelerator-based experiments, neutrinos in the final
state are undetectable by the detectors, leading to the “missing energy”. So it is desirable to look for charged leptons in the final state.
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NlN
NNl ji
Uimp
mpU
22
transition rates are proportional to
production resonant for )()(
heavy for
light for
23
4
23
1
2
21
2121
Nm
fNiN
antonly relevm
UU
mUUm
NN
n
i i
ilil
iiililll
Basic process we consider
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Testability at the LHC
Two necessary conditions to test at the LHC:
-- Masses of heavy Majorana n’s must be less than TeV -- Light-heavy neutrino mixing (i.e., MD/MR) must be large enough.
LHC signatures of heavy Majorana ’s are essentially decoupled from masses and mixing parameters of light Majorana ’s.
Non-unitarity of the light neutrino flavor mixing ma-trix might lead to observable effects.
( ) / (100 1 )D M m E m O GeV TeV
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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
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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
N can be produced on reso-nance
dominant channel
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Some Results
Cross sections are generally smaller for larger masses of heavy
Majorana neutrinos. [ Han, Zhang (hep-ph/0904064) ]
Tevatron LHC
Signal & background cross sections (in fb) as a function of the
heavy Majorana neutrino mass (in GeV) : [ Del Aguila et al (hep-ph/0906198) ]
*Background could be much larger by soft-piling up !!
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4. Concluding Remarks
Knowing that neutrinos are Dirac or Majorana is THE MOST
important to go beyond the SM. We have discussed three possible ways to probe Majo-
rana neutrinos, and three possible mass ranges for rare me-son decays. Hoping that probing Majorana neutrinos via meson’s
rare decays and collider signature would become more and more relevant in forthcoming future.