The possibility that non-conventional neutrino oscillations take place in the superstring inspired E sub 6 models is considered. In this context, the influence of leptoquark mediated interactions of the neutrinos with nucleons in the resonant flavor conversion is discussed. It is shown that this effect can be significant for v sub e - v sub tau oscillations if these neutrinos have masses required in the ordinary Mikheyev-Smirnov-Wolfenstein (MSW) effect, and may lead to a solution of the solar neutrino problem even in the absence of vacuum mixings. On the other hand, this model cannot lead to a resonant behavior in the sun if the neutrinos are massless

Roulet, Esteban

English

NASA Technical Reports Server

Fermi National Accelerator Laboratory /
FERMILAB-Pub- 9 i/206-A
August 1991
E6 leptoquarks and the solar neutrino problem
Esteban RouJet
NASA/Fermilab Astrophysics Center
Fermi National Accelerator Laboratory
P.O. Boz 500, Batavia, IL 60510-0500
The possibility that non-conventional neutrino oscillations take place in the
superstring inspired E6 models is considered. In this context, the influence of
leptoquark mediated interactions of the neutrinos with nucleons in the resonant
flavor conversion is discussed. It is shown that this effect can be significant for
u, - v_. oscillations if these neutrinos have the masses required in the ordinary
MSW effect, and may lead to a solution of the solar neutrino problem even in
the absence of vacuum mixings. On the other hand, thismodel cannot lead to a
resonant behaviour in the sun ifthe neutrinos are massless.
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The most plausible explanation of the observed deficit of solar neutrinos is the resonant
conversion in the sun of the v_ to another neutrino flavor, i.e. the so-called Mikheyev-
Smirnov-Wolfenstein (MSW) effect [1,2]. In a recent work [3], I analyzed the possible
matter induced resonant enhancement of the neutrino oscillations caused by flavor changing
v interactions (FCI) rather than by the enhancement of a vacuum mixing. It was shown
that strengths of the FCI of the order of 10 -3 + 10 -1 GF, with neutrino square mass
differences A -- rn_ -- rn_ --. 10 -s + 10 -4 eV 2, can explain the observed deficit of solar
neutrinos in a way very similar to the ordinary MSW effect but even in the absence of
neutrino mixing in vacuum. The required v properties were shown to be achievable in
the minimal supersymmetric standard model in the presence of some R-parity violating
couplings, for which v_ -v,. oscillations can be induced consistently with the various
phenomenological constraints. In ref. [4], the possibility of obtaining a resonant behaviour
in the absence of neutrino masses by means of new flavor diagonal v interactions (FDI)
has been also considered and the general mechanism has been further analyzed in ref. [5].
Given the potential relevance of this scenario, it is interesting to search for other
models where this mechanism may work. In particular, I will analyze the possibility of
obtaining these new v interactions in the superstring inspired E6 models, that are one of
the best motivated low-energy extensions of the standard model (SM). In this context,
the new processes can be due to the interactions of neutrinos with nuclei mediated by
leptoquarks.
In the superstring inspired E8 models [6], the low energy gauge group usually includes
an extra U(1) factor besides the SM group and each generation lies in a 27-dimensional
representation of E6, that contains the ordinary quarks Q = (u,d) T, d", u e, the leptons
L -- (v, e) T, e e and twelve new exotic states: a vector singlet quark D, D e, a vector doublet
ofleptons E, E e (whose scalar counterparts are the usual Higgs doublets) and two neutral
singlets N and v e. In terms of these fields, the superpotential couplings contained in the
27 _ of E8 are (omitting generation indices)
W =_1EQu _ + ,_2E_Le _ + _3E_Qd _ + .L_EECN
+ ,ksDD_N + AsEL_ ,c + (ATDQQ + AsD_uCd_). (1)
+ (_gDeCu _ + ,kloD_LQ + _11D_,¢d _)
The first six terms are responsible of giving masses to the fermions and in particular
the term proportional to _e can give Dirac masses to the neutrinos. Instead, there are
no Majorana mass terms for the ordinary neutrinos (no isospin triplets in the 27 repre-
sentation) nor terms providing large Majorana masses for the neutral singlets, so that the
seesaw mechanism can not be effective. Also, in contrast with the supersymmetric model
with broken R parity, Majorana mass terms for the ordinary neutrinos are not generated
radiatively, but instead some combinations of couplings may generate Dirac v masses at
one-loop (oc _10_11) or two loops [7]. In order not to violate laboratory and cosmological
bounds one should ensure that the contributions to the neutrino masses are small. Further-
more, to get the tiny masses required for the MSW effect (10 -4 + 10 -2 eV), the couplings
should be even more suppressed. In these theories, the smallness of the neutrino masses
can be more naturally understood if some discrete symmetries (or topological properties
of the compactification manifold) imply the absence of some (or even all) of the Yukawa
couplings generating the 1,, mass terms, and then only the couplings that are left need to
be sufficiently small.
Considering now the remaining terms in eq.(1), it is clear that the couplings in both
brackets cannot be all allowed simultaneously without inducing too fast proton decay, so
that usually one of the brackets is eliminated invoking some symmetry. If the first one is
allowed, the quark D has the quantum numbers of a diquark, while if the second one is
allowed, D is a leptoquark, connecting a lepton with a quark. This last possibility is the
one that will be analyzed in more detail since it could be relevant for the r, oscillations.
In particular, the coupling $ij_D_L.iQ_ (_o = _) induces the following effectiv_
interaction for the neutrinos with the down quarks, mediated by the scalar leptoquarks/_
with
-£ = V/-2Gij_/LT_VjLdT_(1 -- 0's)d, (2!
4 g, (3)
In the presence of these interactions, the v oscillations are governed by the equation
= & 20 + B &c20-A '
B =V C  lVd
, (5)
with
2
where, for simplicity, we have considered only the two-flavor case (a =/_ or r). E is the
neutrino energy, N, is the electron number density while Na is the density of d-quarks, i.e.
Na = Np + 2N,., in terms of the proton and neutron densities (also, s8 = sinS, etc.).
It is of course possible that the v masses and vacuum mixings are such that the
ordinary MSW effect takes place in the absence of leptoquark mediated interactions. This
happens if a2_ _ 10 -2 and A 822/_ _ 10 -v.5 eV 2, in which case the transition is non-
adiabatic, or for 826 _ 0.8 and 10 -s eV 2 _ A _ 10 -4 eV 2, which is the large angle
adiabatic solution (the adiabatic conversion for A _ 10 -4 eV 2 and .s28 _ 10 -2 is disfavored
by Kamiokande results [8]). I want to consider instead the alternative situations discussed
in ref. [3-5], in which some of these conditions are not fulfilled but the flavor conversion is
still efficient due to the presence of the interaction terms in eq. (2). In particular, I will
consider the case in which the neutrinos are massive but their vacuum mixing is negligible
and then discuss the situation in which the neutrino masses are negligible. The first
possibility could be the consequence of the conservation of the individual lepton numbers
by the terms giving rise to the v masses (e.g. by diagonal )_8 couplings), conservation that
could then be violated by the interaction terms involving leptoquarks; while the second
possibility could arise if the mass terms are too suppressed or even absent as a consequence
of discrete symmetries.
As it was shown in ref. [3], to have a sufficient reduction of the solar v, flux in the
absence of vacuum mixing requires that
10-2 G
G,,..(Np + 2N,) _ _ FN. , (6)
and this is satisfied if
_k]]Ak,_l _ 10 -s ( rnbh ,_2100 GeV/ (7)
The strongest experimental constraint in this product of couplings for a = p (v. _ vv
conversion) comes from the upper bound on the branching fraction for the process p _ 3e,
that can proceed through the 1-1oop process /2 _ eT* (the virtual leptoquark running
inside the loop), with the consequent decay 7* _ e+e-. This imposes [7] the bound
AkllA_21 _4x10 -4( mD _2
k300 GeV/ " (s)
Hence, we see that in this model the ve --* vv conversion is not allowed. Instead, for the
ve _ vr conversion the strongest bound arises from the tree-level decay r- --* p°e- and
m_ 2
the corresponding constraint AtllAt31 _ 2 x 10 -2 (100 Gev) [4] is well compatible with
eq. (6). These couplings also induce n _ pep,., what gives an incoherent contribution to
fl-decay processes but leading to less stringent constraints.
The reduction in the ve flux here is very similar to the one in the ordinary MSW
effect, so that there will be a non-adiabatic conversion if eq. (5) holds and the v masses
satisfy [3]
\ GF/ l°-°eV2' (9)
while the large angle adiabatic conversion is not compatible with the bound from T _ pc.
Thus, in this scenario we expect also a large reduction in the rate of the Galium detectors.
Let us note that improved constraints on the branching Br(r --_ pc) from future r factories
and also ep collisions at HERA (looking for ep --_ _'X) may be able to further test the
allowed window of solutions.
Turning now to the case in which the masses are negligible (A << 10 -s eV 2), in order
that the neutrinos find a resonance in their way through the matter it is necessary that
the effects of the v, charged current interactions be compensated now by the leptoquark
mediated interactions. Hence, at some point the diagonal entries of the matrix in eq. (4)
should become equal, i.e.
(G,-._ - G,,)(1 + 2Y.)-- GF. (10)
For solar neutrinos, since the value of Yn - Nn/Ne is small (--,0.5 in the center and
,-- 0.15 in the surface of the sun [9]), the factor (1 _- 2Yn) changes very little in the v
path. Furthermore, this smooth behaviour makes the resonance broad, leading to a flavor
conversion that is largely adiabatic. This leads to too much v, conversion unless the peak
of the resonance is close to the center or to the surface of the sun, so that there is only
partial resonance crossing. Hence, the appropriate reduction of the v, flux requires very
specific values of the effective couplings [4,5]. (In a supernova, Y, changes significantly
and this mechanism may lead to a resonant behaviour in a thin layer along the v path.)
As was shown in ref. [5], deep-lnelastic v-q scattering constraints preclude the possi-
bility of achieving the large couplings Gvv or G_ required for the v, --_ vv conversion in
the sun by interactions with dn quarks. The coupling Go, is further constrained in this
model since it would induce an effective V-A type NC coupling of electrons with u-quarks,
so that atomic parity violation and polarized eD scattering constrain IG,., I to be below
the level of ,-- IO-1GF . No strong model-independent bounds apply to, the coupling G,_
4
involved in the v_ --_ v_- conversion, but in the E8 model the strongest effect induced by the
leptoquarks mediating the v_d -_ v_d scattering is their contribution to the r decay chan-
nel r- -* p-v, lr-v. Since the effective coupling for the leptoquark mediated decay needs
to be G_ _ GF/2 (from eq. (10)), the corresponding branching fractions are affected by
more than 50 %, in clear contradiction with their experimental agreement with the SM
predictions at the few percent level. Hence, no resonance for massless neutrinos can occur
in the sun in this model. An important difference between this model and the broken R
parity model is that the exchanged particle is always an isosinglet. The constraint on G_T
from r-decays does not apply when an isodoublet is exchanged, as was considered in refs.
[4,5]. Let us note also that a previous attempt [10] to obtain a resonant behaviour for
massless neutrinos in an E6 model, but where the non-universal neutrino NC interactions
were due to the mixing of the ordinary neutrinos with heavy isosinglets, also led to neg-
ative results. Hence, these mechanisms may only be of some relevance in stellar objects
like neutron stars, where the much smaller relative electron density may be compensated
by means of a much weaker FDI of the neutrinos with quarks.
We conclude then that, if the neutrino masses are such that they lead to a resonant
behaviour in the propagation of the solar neutrinos, the leptoquark mediated interactions
may affect significantly the v, -_ vT conversion and can lead to a solution to the solar
neutrino problem even in the absence of vacuum mixings. Instead, the experimental con-
straints exclude the possibility that in this model a resonant conversion in the sun takes
place for massless neutrinos.
This work was supported in part by the DOE and by the NASA (grant # NAGW-
1340) at Fermilab.
5
[8]-
[9]-
[lO]-
[1]- L. Wolfenstein, Phys. Rev. D17, 2369 (1978);
S.P. Mikheyev and A.Yu. Smirnov, Yad. Fir. 42, 1441 (1985) [Soy. J. Nucl. Phys.
42,913(1985)].
[2]- For a recent review see T.K. Kuo and J. Pantaleone, Rev. Mod. Phys. 61,937 (1989).
[3]- E. Roulet, Phys. Rev. D in press.
[4]- M.M. Guzzo, A. Masiero and S. Petcov, Phys. Lett. B260, 154 (1991).
[5]- V. Barger, R.J.N. Phillips and K. Whisnant, preprint MAD/PH/648 (1991)
[6]- For a review see J.L Hewett and T.G. Rizzo, Phys. Rep. 183, 195 (1989).
[7]- B.A. Campbell, J. Ellis, M. Gaillard and D. Nanopoulos, Int. J. of Mod. Phys. A2,
831(1987).
K.S. Hirata et al.,Phys. Rev. Lett. 65, 1297 (1990); ibid. 1301.
J. Bahcall and R.K. Ulrich, Rev. Mod. Phys. 60, 298 (1988).
J.W.F. Valle,Phys. Lett. 199B, 432 (1987).


E sub 6 leptoquarks and the solar neutrino problem

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