Tev Neutrino Physics at the Large Hadron Collider

0.35 MB·English

by  Zhi-zhong Xing

January 2, 2009 7:16 WSPC/INSTRUCTION FILE TEV
International JournalofModernPhysicsA
(cid:13)c WorldScientificPublishingCompany
9
0
0 TEV NEUTRINO PHYSICS AT THE LARGE HADRON COLLIDER∗
2

n
a
J ZHI-ZHONGXING

2 Institute of High Energy Physics and Theoretical PhysicsCenterfor Science Facilities,
Chinese Academy of Sciences, P.O. Box 918, Beijing100049, China

] [email protected]
h
p
-
IarguethatTeV neutrinophysicsmightbecomeanexcitingfrontierofparticlephysics
p
intheeraoftheLargeHadronCollider(LHC).Theoriginofnon-zerobuttinymassesof
e
h threeknownneutrinosisprobablyrelatedtotheexistenceofsomeheavydegreesoffree-
[ dom, suchas heavy Majorananeutrinos orheavy Higgs bosons,viaaTeV-scaleseesaw
mechanism.Itakeafewexamplestoillustratehowtogetabalancebetweentheoretical

1 naturalnessandexperimentaltestabilityofTeVseesaws.Besidespossiblecollidersigna-
v tures at the LHC, new and non-unitary CP-violating effects are also expected to show
9 upinneutrinooscillationsfortype-I,type-(I+II) andtype-IIIseesawsattheTeVscale.
0
2 Keywords:TeVseesaws;Collidersignatures;Violationofunitarity;Neutrinooscillations.
0
.
1 1. Why TeV Seesaws?
0
9 EnricoFermielaborateda coherenttheoryofthe beta decayandpublished itin La
0 Ricerca Scientifica in December 1933,1 just two months after the Solvay Congress
:
v in October 1933. In this seminal paper, Fermi postulated the existence of a new
i
X forceforthebetadecaybycombiningthreebrand-newconcepts—Pauli’sneutrino
hypothesis, Dirac’s idea about the creation of particles, and Heisenberg’s idea that
r
a the neutron was related to the proton. Today, we have achieved a standard theory
ofelectroweakinteractionsatthe Fermiscale( 100GeV),althoughitisunableto
∼
tell us much about the intrinsic physics of electroweak symmetry breaking and the
origin of non-zero but tiny neutrino masses. We are expecting that the LHC will
soonbringaboutarevolutioninparticlephysicsattheTeVscale( 1000GeV)—a
∼
new energyfrontier thatwe humans haveneverreachedbeforewithin a laboratory.
Can the LHC help solve the puzzle of neutrino mass generation? We do not yet
know the answer to this question. But let us hope so.I personallyforesee that TeV
neutrino physics might become an exciting direction in the era of the LHC.
Among many theoretical and phenomenological ideas towards understanding
2
why the masses of three known neutrinos are so small, the seesaw picture seems
to be mostnaturalandelegant.Its key pointis to ascribethesmallnessofneutrino
massestotheexistenceofsomenewdegreesoffreedomheavierthantheFermiscale,
∗InvitedtalkgivenattheInternationalConferenceonParticlePhysics,AstrophysicsandQuantum
FieldTheory:75YearssinceSolvay,27—29November2008,Singapore.
1
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2 Zhi-zhong Xing
Fig.1. Threetypes ofseesawmechanismstounderstandnon-zerobuttinyneutrinomasses.
such as heavy Majorana neutrinos or heavy Higgs bosons. Three typical seesaw
mechanismsareillustratedinFig.1,andsomeothervariationsorcombinationsare
possible. The energy scale where a seesaw mechanism works is crucial, because it
is relevant to whether this mechanism is theoretically natural and experimentally
testable.BetweenFermiandPlanckscales,theremightexisttwootherfundamental
scales: one is the scale of a grand unified theory (GUT) at which strong, weak and
electromagnetic forces can be unified, and the other is the TeV scale at which
the unnatural gauge hierarchy problem of the standard model (SM) can be solved
or at least softened by new physics. Many theorists argue that the conventional
seesaw scenarios are natural because their scales (i.e., the masses of heavy degrees
offreedom)areclosetotheGUTscale.IftheTeVscaleisreallyafundamentalscale,
may we arguethat the TeV seesawsare natural?In other words,we arereasonably
motivated to speculate that possible new physics existing at the TeV scale and
responsible for the electroweak symmetry breaking might also be responsible for
3
the origin of neutrino masses. It is interesting and meaningful in this sense to
investigate and balance the “naturalness” and “testability” of TeV seesaws at the
energy frontier set by the LHC.
2. Naturalness and Testability
As shownin Fig.1,the type-I seesawmechanismgivesa naturalexplanationofthe
smallness of neutrino masses by introducing three heavy right-handed Majorana
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TeVNeutrino Physics at the Large Hadron Collider 3
neutrinos,whilethetype-IIseesawmechanismistoextendtheSMbyincludingone
SU(2) Higgstriplet.Onemayingeneralcombinethetwomechanismsbyassuming
L
theexistenceofboththeHiggstripletandright-handedMajorananeutrinos,leading
to a “hybrid” seesaw scenario which will be referred to as the type-(I+II) seesaw
mechanism. The gauge-invariantneutrino mass terms in such a type-(I+II) seesaw
model can be written as
1 1
= l Y H˜N + NcM N + l Y ∆iσ lc +h.c., (1)
−Lmass L ν R 2 R R R 2 L ∆ 2 L
where M is the mass matrix of right-handed Majorana neutrinos, and
R
H− √2 H0
∆ − (2)
≡ √2 H−− H−
(cid:18) − (cid:19)
denotes the SU(2) Higgs triplet. After spontaneous gauge symmetry breaking,
L
we obtain the neutrino mass matrices M = Y v/√2 and M = Y v , where
D ν L ∆ ∆
H v/√2 and ∆ v correspond to the vacuum expectation values of the
h i ≡ h i ≡ ∆
neutral components of H and ∆. Then Eq. (1) can be rewritten as
1 M M νc
′ = (ν Nc) L D L +h.c.. (3)
−Lmass 2 L R MT M N
(cid:18) D R(cid:19)(cid:18) R(cid:19)
The 6 6neutrino massmatrixinEq.(3)is symmetricandcanbe diagonalizedby
×
the following unitary transformation:
† ∗
V R M M V R M 0
L D = ν , (4)
(cid:18)S U(cid:19) (cid:18)MDT MR(cid:19)(cid:18)S U(cid:19) 0 MN!
c
whereM =Diag m ,m ,m withm beingthemassescofthreelightneutrinosν
ν { 1 2 3} i i
and M = Diag M ,M ,M with M being the masses of three heavy neutrinos
N { 1 2 3} i
N .NotcethatV†V +S†S =VV†+RR† =1holdsasaconsequenceoftheunitarity
i
of thcis transformation. Hence V, the flavor mixing matrix of three light neutrinos,
must be non-unitary if R and S are non-zero.
2.1. Type-I seesaw
The type-I seesawscenariocan be obtainedfrom Eqs.(1)—(4) by switching off the
Higgs triplet. In this case, M = 0 and R S M /M hold, leading to the
L ∼ ∼ D R
approximate seesaw formula
M VM VT M M−1MT . (5)
ν ≡ ν ≈ − D R D
The deviation of V from unitarity is measured by RR†/2 and has been neglected
c
in this expression. Let us consider two interesting possibilities:
(1)M (102)GeVandM (1015)GeVtogetM (10−2)eV.Inthis
D ∼O R ∼O ν ∼O
conventional and natural case, R S (10−13) holds. Hence the non-unitarity
∼ ∼ O
of V is only at the (10−26) level, too small to be observed.
O
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4 Zhi-zhong Xing
(2) M (102) GeV and M (103) GeV to get M (10−2) eV. In
D ∼ O R ∼ O ν ∼ O
thisunnaturalcase,asignificant“structuralcancellation”hastobe imposedonthe
textures of M and M . Because of R S (0.1), the non-unitarity of V can
D R ∼ ∼ O
reach the percent level and may lead to some observable effects.
Now let us discuss how to realize the above “structural cancellation” for the
type-I seesaw mechanism at the TeV scale. Taking the flavor basis of M = M ,
R N
one may easily show that M in Eq. (5) vanishes if
ν
c
y1 y2 y3 3 y2
M = m αy αy αy and i = 0 (6)
D  1 2 3 M
βy βy βy i=1 i
1 2 3 X
 
4
simultaneouslyhold. Tiny neutrino massescanbe generatedfromtiny corrections
to the texture of M in Eq. (6). For example, M′ = M ǫX with M given
D D D − D D
above and ǫ being a small dimensionless parameter (i.e., ǫ 1) will yield
| |≪
M′ M′M−1M′T ǫ M M−1XT +X M−1MT , (7)
ν ≈ − D R D ≈ D R D D R D
from which M′ (10−2) eV can be ob(cid:0)tained by adjusting the size(cid:1)of ǫ. We learn
ν ∼O
the following lessons from this simple exercise:
Two necessary conditions must be satisfiedin order to test a type-I seesaw
•
modelattheLHC:(a)M areof (1)TeVorsmaller;and(b)the strength
i O
oflight-heavyneutrinomixing (i.e.,M /M )arelargeenough.Otherwise,
D R
it would be impossible to produce and detect N at the LHC.
i
The collider signatures of N are essentially decoupled from the mass and
• i
mixing parameters of three light neutrinos ν . For instance, the small pa-
i
rameter ǫ in Eq. (7) has nothing to do with the ratio M /M .
D R
The non-unitarity of V might lead to some observable effects in neutrino
•
oscillations and other lepton-flavor/number-violating processes, provided
M /M . (0.1) holds. More discussions will be given later.
D R O
The clean LHC signatures of heavy Majorana neutrinos are the ∆L = 2
• like-sign dilepton events,5 such as pp W∗±W∗± µ±µ±jj (a collider
→ →
analoguetotheneutrinolessdouble-betadecay)andpp W∗± µ±N
i
→ → →
µ±µ±jj (a dominant channel due to the resonant production of N ).
i
Some naive numerical calculations of possible LHC events for a single heavy Majo-
6
rananeutrinohavebeendone inthe literature, but they only servefor illustration
becausesucha minimalversionofthe type-I seesawscenarioisactually unrealistic.
2.2. Type-II seesaw
Thetype-IIseesawscenariocanbeobtainedfromEqs.(1)—(4)byswitchingoffthe
right-handed Majorana neutrinos and taking account of a simple potential of the
Higgs doublet and triplet:
= µ2H†H +λ H†H 2+ 1M2Tr ∆†∆ λ M HTiσ ∆H +h.c. . (8)
V − 2 ∆ − ∆ ∆ 2
(cid:0) (cid:1) (cid:0) (cid:1) (cid:2) (cid:3)
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TeVNeutrino Physics at the Large Hadron Collider 5
Whenthe neutralcomponentsofH and∆acquiretheirvacuumexpectationvalues
v and v respectively, the electroweak gauge symmetry is spontaneously broken.
∆
The minimum of is achieved at v = µ/(λ 2λ2 )1/2 and v =λ v2/M , where
V − ∆ ∆ ∆ ∆
λ has been assumed to be real. Note that v may modify the SM masses of W±
∆ ∆
andZ0insuchawaythatρ M2 /(M2cos2θ )=(v2+2v2)/(v2+4v2)holds.By
using current experimental ≡dataWon theZρ-paraWmeter,2 we g∆et κ √2 ∆v /v <0.01
≡ ∆
andv <2.5GeV.GivenM v,anapproximateseesawformulaturnsouttobe
∆ ∆ ≫
v2
M M = Y v λ Y , (9)
ν ≡ L ∆ ∆ ≈ ∆ ∆M
∆
as shown in Fig. 1. Note that the last term of Eq. (8) violates both L and B L,
−
andthusthesmallnessofλ isnaturallyallowedaccordingto’tHooft’snaturalness
∆
7
criterion (i.e., setting λ = 0 will increase the symmetry of the theory). Given
∆
M (1) TeV, for example, the seesaw works to generate M (10−2) eV
∆ ∼ O ν ∼ O
providedλ Y (10−12)holds.TheneutrinomixingmatrixV isexactlyunitary
∆ ∆ ∼O
in the type-II seesaw mechanism, simply because the heavy degrees of freedom do
not mix with the light ones.
There are totally seven physical Higgs bosons in this model: doubly-charged
H++ and H−−, singly-chargedH+ and H−, neutral A0 (CP-odd), and neutral h0
and H0 (CP-even), where h0 is the SM-like Higgs boson. Except for M2 2µ2,
h0 ≈
we get a quasi-degenerate mass spectrum for other scalars: M2 = M2 M2 ,
H±± ∆ ≈ H0
M2 =M2(1+κ2),andM2 =M2(1+2κ2).Asaconsequence,thedecaychannels
H± ∆ A0 ∆
H±± W±H± and H±± H±H± are kinematically forbidden. The production
→ →
of H±± at the LHC is mainly through qq¯ γ∗,Z∗ H++H−− and qq¯′ W∗
→ → → →
H±±H∓ processes, which do not depend on the small Yukawa couplings.
The typical collider signatures in this seesaw scenario are the lepton-number-
violatingH±± l±l± decays8aswellasH+ l+ν andH− l−ν decays.9Their
→ α β → α → α
branching ratios
(M ) 2
(2 δ )(M ) 2 | L αβ|
(H±± l±l±)= − αβ | L αβ| , (H+ l+ν)= Xβ (10)
B → α β (M ) 2 B → α (M ) 2
| L ρσ| | L ρσ|
ρ,σ ρ,σ
X X
are closely related to the masses, flavor mixing angles and CP-violating phases of
three light neutrinos, because M = VM VT holds. Some numerical analyses of
L ν
such decay modes together with the LHC signatures of H±± and H± bosons have
been done by a number of authors (see, ec.g., Refs. 8 and 9).
2.3. Type-(I+II) seesaw
A type-(I+II) seesaw mechanism can be achieved by combining the neutrino mass
terms in Eq. (1) with the Higgs potential in Eq. (8). The seesaw formula is
M VM VT M M M−1MT (11)
ν ≡ ν ≈ L− D R D
c
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6 Zhi-zhong Xing
in the leading-order approximation, where the small deviation of V from unitarity
hasbeenomittedandtheexpressionofM canbefoundinEq.(9).Hencethetype-I
L
andtype-IIseesawscanberegardedastwoextremecasesofthetype-(I+II)seesaw.
NotethattwomasstermsinEq.(11)arepossiblycomparableinmagnitude.Ifboth
ofthem aresmall,their contributionsto M shouldessentiallybe constructive;but
ν
if bothofthem arelarge,their contributionsto M mustbe destructive.The latter
ν
case unnaturally requires a significant cancellation between two big quantities in
order to obtain a small quantity, but it is interesting in the sense that it may give
10
rise to observable collider signatures of heavy Majorana neutrinos.
Letme brieflydescribeatype-(I+II)seesawmodelandcommentonitspossible
12
LHC signatures. First, we assume that both M and M are of (1) TeV. Then
i ∆ O
theproductionofH±± andH± bosonsattheLHCisguaranteed,andtheirlepton-
number-violating signatures will probe the Higgs triplet sector of the type-(I+II)
11
seesaw mechanism. On the other hand, (M /M ). (0.1) is possible as a re-
O D R O
sultof (M ) (1)TeVand (M ). (v),suchthatappreciablesignaturesof
O R ∼O O D O
N canbeachievedattheLHC.Second,thesmallmassscaleofM impliesthatthe
i ν
relation (M ) (M M−1MT) must hold. In other words, it is the significant
O L ∼ O D R D
butincomplete cancellationbetweenM andM M−1MT termsthatresultsinthe
L D R D
non-vanishing but tiny masses for three light neutrinos. We admit that dangerous
radiative corrections to two mass terms of M require a delicate fine-tuning of the
ν
12
afore-mentioned cancellation. But this scenario allows us to reconstruct M via
L
the excellent approximation M = VM VT +RM RT RM RT, such that the
L ν N ≈ N
elements of the Yukawa coupling matrix Y read
∆
c c c
(M ) 3 R R M
L αβ αi βi i
(Y ) = , (12)
∆ αβ v ≈ v
∆ i=1 ∆
X
where the subscripts α and β run over e, µ and τ. This result implies that the
leptonic decays of H±± and H± bosons depend on both R and M , which actually
i
determine the production and decays of N . Thus we have established an interest-
i
ing correlation between the singly- or doubly-charged Higgs bosons and the heavy
Majorana neutrinos. To observe the correlative signatures of H±, H±± and N at
i
the LHC will serve for a direct test of this type-(I+II) seesaw model.
Toillustrate,hereIfocusontheminimaltype-(I+II)seesawmodelwithasingle
13
heavyMajorananeutrino, whereRcanbeparametrizedintermsofthreerotation
14
angles θ and three phase angles δ (for i=1,2,3). In this case, we have
i4 i4
ω σ(pp→µ+µ+W−X)|N1 σN s214+s224+s234 ,
1 ≡ σ(pp µ+µ+H−X) ≈ σ · 4
→ |H++ H
ω σ(pp→µ+µ+W−X)|N1 σN s214+s224+s234 (13)
2 ≡ σ(pp µ+µ+H−−X) ≈ σ · 4
→ |H++ pair
for s sinθ . (0.1), where σ σ(pp l+N X)/R 2, σ σ(pp
H++iH4 −≡X) anid4 σ O σ(pp H+N+H≡−−X) →are tαhre1e red|ucαe1d| crosHs s≡ections.1→2
pair ≡ →
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TeVNeutrino Physics at the Large Hadron Collider 7
Fig.2. Correlativesignatures ofN1 andH±± attheLHCwithaluminosityof300fb−1.
Fig. 2 illustrates the numerical results of ω and ω changing with M at the LHC
1 2 1
with an integrated luminosity of 300 fb−1, just to give one a ball-park feeling of
possible collider signatures of N and H±± and their correlation in our model.
1
3. Unitarity Violation
It is worth emphasizing that the charged-current interactions of light and heavy
Majorana neutrinos are not completely independent in either the type-I seesaw or
the type-(I+II) seesaw.The standardcharged-currentinteractions of ν and N are
i i
ν N
g 1 1
= (e µ τ) Vγµ ν W−+(e µ τ) Rγµ N W− +h.c.,(14)
−Lcc √2 L  2 µ L  2 µ 
ν N
 3 L 3 L 
     
whereV isjustthelightneutrinomixingmatrixresponsibleforneutrinooscillations,
and R describes the strength of charged-current interactions between (e,µ,τ) and
(N ,N ,N ). Since V and R belong to the same unitary transformation done in
1 2 3
Eq. (4), they must be correlated with each other and their correlation signifies an
important relationship between neutrino physics and collider physics.
It has been shown that V and R share nine rotation angles (θ , θ and θ for
i4 i5 i6
14
i=1, 2 and 3) and nine phase angles (δ , δ and δ for i=1, 2 and 3). To see
i4 i5 i6
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8 Zhi-zhong Xing
this point clearly, let me decompose V into V =AV , where
0
c c sˆ∗ c sˆ∗
12 13 12 13 13
V = sˆ c c sˆ sˆ∗ c c sˆ∗ sˆ sˆ∗ c sˆ∗ (15)
0 − 12 23− 12 13 23 12 23− 12 13 23 13 23
sˆ sˆ c sˆ c c sˆ sˆ∗ sˆ c c c
12 23− 12 13 23 − 12 23− 12 13 23 13 23
 
with c cosθ and sˆ eiδij sinθ is just the standard parametrization of the
ij ≡ ij ij ≡ ij
3 3unitaryneutrinomixingmatrix(uptosomeproperphaserearrangements).2,15
×
BecauseofVV† =AA† =1 RR†,itisobviousthatV V inthelimitofA 1
− → 0 →
(or equivalently, R 0). Considering the fact that the non-unitarity of V must
→
be a small effect (at most at the percent level as constrained by current neutrino
16
oscillation data and precision electroweak data ), we expect s . (0.1) (for
ij O
14
i=1,2,3 and j =4,5,6) to hold. Then we obtain
1 s2 +s2 +s2 0 0
2 14 15 16
A=1 sˆ sˆ∗ +sˆ sˆ∗ +sˆ sˆ∗ 1 s2 +s2 +s2 0 ,
− 14 2(cid:0)4 15 25 16(cid:1)26 2 24 25 26 
sˆ sˆ∗ +sˆ sˆ∗ +sˆ sˆ∗ sˆ sˆ∗ +sˆ sˆ∗ +sˆ sˆ∗ 1 s2 +s2 +s2
14 34 15 35 16 36 24 3(cid:0)4 25 35 26(cid:1)36 2 34 35 36
 
sˆ∗14 sˆ∗15 sˆ∗16 (cid:0) (cid:1)
R =0+ sˆ∗ sˆ∗ sˆ∗ (16)
 24 25 26
sˆ∗ sˆ∗ sˆ∗
34 35 36
 
as two excellent approximations. A striking consequence of the non-unitarity of
V is the loss of universality for the Jarlskog invariants of CP violation,17 Jij
αβ ≡
Im(V V V∗ V∗), where the Greek indices run over (e,µ,τ) and the Latin indices
αi βj αj βi
run over (1,2,3). For example, the extra CP-violating phases of V are possible to
give rise to a significant asymmetry between ν ν and ν ν oscillations.
µ → τ µ → τ
14
Theprobabilityofν ν oscillationsinvacuum,definedasP ,isgivenby
α → β αβ
V 2 V 2+2 Re V V V∗ V∗ cos∆ 2 Jij sin∆
| αi| | βi| αi βj αj βi ij − αβ ij
i i<j i<j
P = X X (cid:0) (cid:1) X , (17)
αβ VV† VV†
αα ββ
where∆ ∆m2 L/(2E)with∆(cid:0)m2 (cid:1)m2(cid:0) m2,(cid:1)Ebeingtheneutrinobeamenergy
ij ≡ ij ij ≡ i− j
andLbeingthebaselinelength.IfV isexactlyunitary(i.e.,A=1andV =V ),the
0
denominatorofEq.(17)willbecomeunityandtheconventionalformulaofP will
αβ
be reproduced. It has been observed in Refs. 14 and 18 that ν ν and ν ν
µ → τ µ → τ
oscillations may serve as a good tool to probe possible signatures of CP violation
induced by the non-unitarity of V. To illustrate this point, we consider a short-
or medium-baseline neutrino oscillation experiment with sin∆ sin∆
| 13| ∼ | 23| ≫
sin∆ , in which the terrestrial matter effects are expected to be insignificant
| 12|
or negligibly small. Then the dominant CP-conserving and CP-violating terms of
P(ν ν ) and P(ν ν ) can simply be obtained from Eq. (17):
µ → τ µ → τ
∆
P(ν ν ) sin22θ sin2 23 2 J23 +J13 sin∆ ,
µ → τ ≈ 23 2 − µτ µτ 23
P(ν ν ) sin22θ sin2 ∆23 + 2(cid:0)J23 +J13(cid:1)sin∆ , (18)
µ → τ ≈ 23 2 µτ µτ 23
(cid:0) (cid:1)
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TeVNeutrino Physics at the Large Hadron Collider 9
wherethegoodapproximation∆ ∆ hasbeenusedinviewoftheexperimental
13 ≈ 23
fact ∆m2 ∆m2 ∆m2 , and the sub-leading and CP-conserving “zero-
| 13| ≈ |16 23| ≫ | 12|
distance” effect has been omitted. For simplicity, I take V to be the exactly
0
tri-bimaximal mixing pattern19 (i.e., θ = arctan(1/√2), θ = 0 and θ = π/4
12 13 23
14
as well as δ =δ =δ =0) and then arrive at
12 13 23
6
2 J23 +J13 s s sin(δ δ ) . (19)
µτ µτ ≈ 2l 3l 2l− 3l
l=4
(cid:0) (cid:1) X
Givens s (0.1)and(δ δ ) (1)(forl=4,5,6),thisnon-trivialCP-
2l ∼ 3l ∼O 2l− 3l ∼O
violating quantity can reach the percent level. A numerical illustration of the CP-
violatingasymmetrybetweenν ν andν ν oscillationshasbeenpresented
µ → τ µ → τ
in Ref. 14, from which one can see that it is possible to measure this asymmetry in
the range L/E (100 400) km/GeV if the experimental sensitivity is 1%. A
∼ ··· ≤
neutrino factory with the beam energy E being above m 1.78 GeV may have a
τ ≈ 18
good chance to explore the non-unitary effect of CP violation.
Whenalong-baselineneutrinooscillationexperimentisconcerned,however,the
terrestrial matter effects must be taken into account because they might fake the
20
genuine CP-violating signals. As for ν ν and ν ν oscillations discussed
µ → τ µ → τ
21
above, the dominant matter effect results from the neutral-current interactions
and modifies the CP-violating quantity of Eq. (18) in the following way:
6
2 J23 +J13 = s s [sin(δ δ )+A Lcos(δ δ )] , (20)
µτ µτ ⇒ 2l 3l 2l− 3l NC 2l− 3l
l=4
(cid:0) (cid:1) X
where A = G N /√2 with N being the background density of neutrons, and
NC F n n
L is the baseline length. It is easy to find A L (1) for L 4 103 km.
NC ∼O ∼ ×
4. Concluding Remarks
WehopethattheLHCmightopenanewwindowforustounderstandtheoriginof
neutrino massesand the dynamics of lepton number violation.To be more specific,
a TeV seesaw might work (naturalness?) and its heavy degrees of freedom might
show up at the LHC (testability?). A bridge between collider physics and neutrino
physics is highly anticipated and, if it exists, will lead to rich phenomenology.
Acknowledgments
I am greatly indebted to A.H. Chan, C.H. Oh and K.K. Phua for warm hospitality
during my visiting stay in Singapore. I am also grateful to W. Chao, Z. Si and S.
Zhou for enjoyable collaboration. This work is supported in part by the National
NaturalScience Foundationof China under grantNo. 10425522and No. 10875131.
References
1. E.Fermi,La Ricerca Scientifica 4 (II), 491 (1933). Thefirst version of thispaperwas
rejected byNature because it was considered too abstract.
January 2, 2009 7:16 WSPC/INSTRUCTION FILE TEV
10 Zhi-zhong Xing
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