Phenomenology of neutrino physics in the Kaluza-Klein theories of low scale gravity

5 Pages·0.11 MB·English

by  A. Ioannisian

1
Phenomenology of neutrino physics in the Kaluza-Klein theories of low
scale gravity
A. N. Ioannisiana∗
aInstituto de Fisica Corpuscular - CSIC - Univ. de Valencia,
1 Edificio Institutos de Paterna - Apartado de Correos 2085,46071 Valencia, Spain
0
0 We discuss the phenomenological consequences of theories which describe sterile neutrinos in large extra di-
2
mensions. We show that the Kaluza-Klein tower of the singlet neutrinos, albeit tiny individual contribution

n in electroweak processes, act cumulatively, giving rise to non-universality of the weak interactions of the light
a neutrinos and to flavour-violating radiative processes. Owing to these non-decoupling effects of th Kaluza–Klein
J neutrinos,we derivestrong constraints on theparameters of thetheory that originates from thenon-observation

4 offlavour-violatinganduniversality-breakingphenomena. Inthistheoryweproposeafour-neutrinomodelwhich
can reconcile the existing data coming from underground experiments in terms of neutrino oscillations, together

1 with the hint from the LSND experiment and a possible neutrino contribution to the hot dark matter of the
v
Universe.
9
3
0
1 Recently, it has been proposed [1] the radical imal model reads
0 possibility that the observed small value of the 2πR
1 gravitational constat at long distance is ascribed d~y N¯ iγµ∂ + iγ ∂ m N
0 to the spreading of the gravitational force in δ Z h (cid:16) µ y~ y~− (cid:17)
/ 0
h largeextraspatialdimensions. Itfollowsthatthe
h
p Standard Model (SM) fields are confined to a 3- + δ(~y) l L Φ˜ξ + H.c. , (1)
p- brane configuration, while the large compactified (cid:16)l=Xe,µ,τ MFδ/2 l (cid:17)i
e dimensions are probed only by gravity and sin- where Φ˜ ( < Φ˜ >= v = 174Gev ) and L are
h glet, under SM gauge group, fields. l
: higgs and lepton doublets, respectively. We have
v In this presentation we examine the phe-
assumed that only one two-component spinor ξ
i nomenological consequences of higher - dimen-
X from the high dimensional spinor N couples to
sional isosinglet neutrinos on collider and lower
r our 3 brane.
a energy experiments.
We cannowexpressthe two-componentspinor
For our phenomenological study we adopt a
ξ and its dirac partner η from high dimensional
variant [2] of the model discussed in Ref. [3] [4].
spinorN intermsofaFourierseriesexpansionas
For definiteness, we consider a model that min-
follows:
imally extends the SM-field content by one sin-
glet Dirac neutrino, N(x,y), which propagates [ξ(x,y), η(x,y)]= (2)
in a [1+(3+δ)]-dimensional Minkowski space. 1 i~n~y
[ξ (x), η (x)] exp .
The y-coordinates are compactified on a circle of (2πR)δ/2 ~n ~n (cid:18) R (cid:19)
radius R by applying the periodic identification: X~n
y y+2πR. SubstitutingintotheEq. (1)andthenperforming
≡
TherelevantpartoftheLagrangianofourmin- the ~y integration yields
ξ¯ (iσ¯µ∂ )ξ +η¯ (iσ¯µ∂ )η (3)
~n µ ~n ~n µ ~n
(cid:26) −
X~n
i~n
∗OnleavefromYerevanPhysicsInstitute,AlikhanyanBr. ξ~n (m+ | |)η−~n+ h¯lLlΦ˜ +H.c.
2,Yerevan375036, Armenia h (cid:16) R l=Xe,µ,τ (cid:17) i(cid:27)
2
where ¯h =h MF , ~n2 δ n2. Owing to the tower of the KK singlet neutri-
l lMP | | ≡ i=1 i
As it is shown in Eq.P(3), there are small nos which acts cumulatively in the loops, sig-
mixings mass terms, h¯v, between any KK state nificant universality-breaking as well as flavour-
l
η and left neutrinos. It was firstly noticed in violating effects are induced in electroweak pro-
~n
[3,4], the four-dimensional Yukawa couplings h¯ cesses involving γ-[5] and Z- boson [6] interac-
l
are naturally suppressed by the volume factor tions. In particular, as has been explicitly shown
MF/MP. recently,[6] we find that the cumulative presence
After diagonalizing the mass matrix these oftheKKstatesleadstoaneffectivetheorywhose
terms give rise to the small admixture of the left Yukawa interactions are mediated by order-unity
neutrinos to the heavy KK states, η′, with the Yukawa couplings of the original Lagrangian be-
~n
mass m2+~n2/R2 fore compactification. In this case, we expect a
p higher-dimensional non-decoupling phenomenon
η′ η +B νl, B h vMF .(4) analogous to the one studied earlier in renormal-
~n ≈ ~n l,~n L l,~n ≈ lM m2+~n2/R2 izable 4-dimensional theories.[7,8] For example,
P
p the effective lepton-flavour-violating vertex Zll′
Applaying to the unitarity condition we arrive
that occurs in µ eee exhibits the dependence:
to the following light states T(Zl′l) ∝ hlhl′→(v2/MF2) k=e,µ,τ (h2kv2)/MW2 ,
i.e.itsstrengthincreaseswiPththefourthpowerof
1
νl (νl + B η′). (5) the higher-dimensional Yukawa couplings. This
light ≈ 1+ ~n|Bl,~n|2 L X~n l,~n ~n shouldbecontrastedwiththerespectivephotonic
p P amplitudeT(γl′l)∝hlhl′v2/MF2,whosestrength
The most striking feature of the higher- increases only quadratically.
dimensional scenario, as it follows from Eq.(5), Basedonthiscumulativenon-decouplingeffect,
is the loss of the lepton universality in the elec- weareabletoderivestronglimitsontheM /h2,
F
troweak processes. forh 1. AsisdisplayedinTable2,thestrongest
≥
It is useful to define the mixing parameters limits are obtained from µ eee and the ab-
→6
sence of µ-to-e conversion in nuclei. Of course,
v2 M4M−2
(sνl)2 B 2 h2 F P the limits presented here contain some degree of
L ≡X~n | l,~n| ≈ l MF2 X~n (m2+ R~n22) uncertainty,whichisinherentinalleffectivenon-
πh2v2 M2 renormalizable theories with a cut-off scale, such
 Ml2 ln(cid:18)mF2 +1(cid:19),δ =2 as MF. Nevertheless, our results are very useful,
≈ SF h2v2 (6) sthinacteotnheeyhainsdtiocaetnecothuentgeernienrimcosidzeel-obfucioldnisntgracionnts-
 δ−δ2 Ml F2 ,δ >2. sidNeroawtiownes wcoitnhcesntterrailteenienuttrhineoms.[i9n,i1m0u]m brane-
In order to evaluate the sumation in the above inspiredscheme in whichall elements requiredto
equation we approximate the sum over the KK explainthe neutrinoanomalies(the LSND/HDM
states by an integral, which has an upper ultra- as well as the solar and atmospheric mass scales)
violet (UV) cutoff at M R, above which string- are generated by the physics of extra dimen-
F
thresholdeffectsareexpectedtobecomemoreim- sions [10]. For definiteness, we will be consid-
portant. ering a model that minimally extends the stan-
AscanbeseenfromTable1,themixings(sνl)2 dard field content by one bulk neutrino, N(x,y)
L
may be constrained by a number of new-physics (with zero high dimensional mass term), singlet
observables induced at the tree level. These ob- under the SM gauge group. This propagates on
servables measure possible non-universality ef- a [1+(3+n)]-dimensionalMinkowskispace with
fects in µ, τ and π decays. In this respect, in δ n.
≥
Table 1 we have defined R =Γ(π eν)/Γ(π After integrating out heavy Kaluza-Klein
π
→ →
µν) and R =B(τ eνν)/B(τ µνν). states, the effective Lagrangianhas the following
τµ
→ →
3
Table 1
Tree level limits on M /TeV from non-universal couplings of the neutrinos to W and Z bosons.
F
h = h = h = h h =0and h =h
e µ τ µ e τ
Observable Lower limit on M /h Lower limit on M /h
F F τ
δ =2 δ >2 δ =2 δ >2
1− ΓΓSM(µ(µ→eνeνν)ν) 8.9 ln1/2 MmF 3√.5δSδ1/22 6.3 ln1/2 MmF 2√.5δSδ1/22
1− ΓΓSM(Z(Z→→ννν)ν) 5.9 ln1/2 MmF 2√.4δS−δ1/22 4.8 ln1/2 MmF 1√.9δS−δ1/22
1 Rπ→ − 18.7 ln1/2 MF 7.5S−δ1/2
− RSM − − m √δ 2
π −1/2
1 Rτµ 5.7 ln1/2 MF 2.3Sδ
− RSM − − m √δ 2
τµ −
Table 2
One-loop-levellimits on M /h2.
F
h = h = h =h 1
e µ τ
Observable Lower limit on M /h≥2 [TeV]
F
δ =2 δ =3 δ =6
Br(µ eγ) 75 43 33
→
Br(µ eee) 250 230 200
48 → 48
Br(µ Ti e Ti) 380 320 300
22 22
→
form The Majorana part of the neutrino masses is
then expected to be
eff = SM + h¯lLlΦ˜ξ0 + H.c. , (7)
L L (cid:16) l=Xe,µ,τ (cid:17) v2 M 2n/δ−4/δ
F
mll′ fll′ (9)
where ξ0 is the zero mode of the Kaluza-Klein ∼ MF (cid:18)MP(cid:19)
states and now
The neutrino mass matrix takes in the basis
n
h¯ = MF δ h . (8) (νe,νµ,ντ,νs ) (νs =ξ0) the form
l l
(cid:18)MP(cid:19)
Imnatotredrermtaossascccaoluenmt for th1eeVLSoNrDsoo,rwheocthdoaorske Mν = (cid:18)mMllTl′′ M0l(cid:19) . (10)
ν
δ =6 and n=4, giving∼h¯ 10−10h .
l ∼ l Here M =h¯ v. Note that the m entry in eq. 10
Now we turn to the Majorana masses for neu- l l s
has been omitted since the bulk sector where the
trinos. These are crucial in order to generate
sterile neutrino ν lives is eight–dimensional.
the mass splittings required in neutrino oscilla- s
In the limit that Dirac mass terms (M ) are
tion interpretations of the solar and atmospheric l
neutrinoanomaliesfound inundergroundexperi- much bigger than Majorana mass terms (mll′),
two of the neutrinos are massless and other two
ments. AsshowninRef.[3]theneutrinosmayget
form Dirac state with a mass
small Majorana masses via interactions with dis-
tant branes where fermion number is maximally
broken. mν ≡mLSND/HDM =qMe2+Mµ2+Mτ2 (11)
4
This state is identified by two angles θ and ϕ crucial to account for the hint coming from the
defined as LSNDexperiment,andmayalsocontributetothe
hot dark matter of the Universe. Apart from the
M M
e µ
sinθ = , tanϕ= . (12) mass of the Quasi–Dirac state [12], one has the
m M
ν τ splittings between its components, as well as the
The entries mll′ only arise due to the break- masses of two light active states. The splittings
ing lepton number on distant branes. In the case between the heavystates and that characterizing
δ = 6 and n = 4 they are suppressed compared the lighter neutrinos will be associated with the
to the Dirac mass terms by the factor v fll′. explanations of the atmospheric and solar neu-
MF hl
These terms give masses to the lowest-lying neu- trino anomalies, respectively. The atmospheric
trinos and also responsible for splitting Dirac neutrino deficit is ascribed to the νµ to νs os-
state to twoMajoranastates. Forsuitable values cilations. The solar neutrino problem could be
of the parameters, these are in the right range solved via MSW small or large angle νe to ντ so-
to have a solutionfor solarand atmosphericneu- lutions. This reproduces exactly the phenomeno-
trino deficit. More especifically, from the latest logicalfeaturesofthemodelproposedinref.[13],
fits one needs [11] providingacompletescenarioforthepresentneu-
trino anomalies.
∆m2 3.5 10−3eV2 (13)
atm ≃ ×
inordertoaccountforthefull setofatmospheric
neutrino data. Acknowledgements: It is pleasure to thanks
On the other hand the latest globalanalysis of the organizers for organizing a very interest-
solar neutrino data characterized by the best-fit ing workshop. This work was supported by
points [11] Spanish DGICYT under grants PB98-0693 and
SAB/1998-0136 (A.I.) and by the European
∆m2 3.6 10−5eV2 (14)
LMA ≃ × Union TMR network ERBFMRXCT960090.
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