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Nuclear Physics B (Proc. Suppl.) 70 (1999) 129-131

ELSEVIER

Bounds

on sterile neutrino

mixing for cosmologically

interesting

mass

range * H. Nunokawaa “Instituto 46100

, J. T. Peltoniem?

de Fisica

Burjassot,

‘Department ‘Dept.

Corpuscular

Valincia,

of Physics,

de Fisica,

, A. Rossi’

Inst.

- C.S.I.C.,

and J.W.F.Vallea

Departament

de Ffsica Tebrica,

Universitat

de Valbncia

Spain Box 9, 00014

Superior

University

Tecnico,

of Helsinki, Finland

1096 Lisbon Codex,

Portugal

This talk summarizes ouz recent work which studied the impact of resonant Y, ---) u, and fit + B, (Y, is a sterile neutrino) conversions on supernova physics, under the assumption that the mass of the sterile state is in the few eV -cosmologicaIIy significant range.

1.

Y, = l-Y,

Introduction It has been discussed that the resonant

sion (MSW

effect)

some sterile state supernova quences

[l] of electron

into

in the dense media of type-II

could lead to some nontrivial

[2-51.

conver-

neutrinos

We have reanalysed

conse-

the impact

of

such conversion on supernova the mass of the sterile state

physics assuming to be in the cos-

mologically

i.e.

significant

range relevant universe

range,

as dark matter

l-100

component

v, and v,

(and

their

in the

between other flavors.

the system

anti-partners

zero masses and mixings

could naturally

and neglect relevant

appear

of

) with nonthe mixing

The mass spectrum

trinos with the sterile state, cussion,

eV, the

[6]

In what follows we will consider

are the net electron and neutron

ber per baryon,

of neu-

for our dis-

in some models

respectively.

V, should be replaced

system

The resonance

condition

I;- 2 v, = z cos 20 , where dm2 is the mass squared the neutrino

assume 6m2 > 0, i.e., the heavier state is mostly sterile state. In general, nosphere

in the

the density

hand,

the electron

value nearby

v

=

e

where GF is the Fermi

constant,

nosphere

- l), (1) p is the mat-

mN is the nucleon mass and Y, and by

H. Nunokawa

0920-5632/98/%19.00

0 1998

PI1 SO920-5632(98)00404-6

ElsevierScience B.V. All rights

neutriradial

On the other

takes

minimum

due to the effi-

process and then Y, increases

1 (a) the behavior fraction

are schematically

of the matter

From

Fig.

shown.

In Fig.

of the potential

1 (b)

which can

of p and Y, in (a).

1 (b)

we notice that for Sm2 > leave from the neutrinosphere to

version and then v,‘s

are converted.

resonant

con-

The latter

could undergo the transition twice if the values of (t5m2/2E) cos 20 is smaller than the maximum value of V, (see Fig. l(b)). In this work we appropriately take into account the double resonances for the u, -+ va channel.

reserved.

density

Y, above the neutri-

be inferred from the behaviors 0 as neutrinos

~~GFP

given

Y,

the neutrinosphere

cient neutronization

the

as T (the

the outer region, first fiec)sundergo N

*Talk

resonant

for the Y, - v, system is

----&-(Ye- ;Yn)= gq3Y,

ter density,

above

increases.

fraction

we plot the behavior

The effective potential given by,

region decreases

distance from the center)

In Fig. neutrino

E, is

difference,

energy and 8 is the mixing angle. We

p and the electron The active-sterile conversion

by -V,.

is given as

as r increases.

[71. 2.

num-

For anti-neutrino

130

H. Nunokawa et al./Nuclear

Figure

1. In (a) the behavior

Y, above neutrinosphere

Physics B (Proc. Suppl.) 70 (1999) 129-131

of the density p and

are schematically

plot-

V, cx p(3Y, - 1) is

ted and in (b) the potential plotted.

Figure 3.

Impact

of the

conversion

plot of the ratio

versus the case without

In this section signal and heavy

on shock re-heating,

elements

nucleosynthesis

profiles from

Wilson’s

Pi

using

supernova

model.

Kamiokande

and IMB detectors

absence of significant

conversion

favouring the parameter say

Shock

into sterile neutrinos,

conversions.

we discuss the effect of V, -+ V,

and tie -+ 6’s conversions the p and Y,

R of the neu-

behind the shock wave in

the presence of conversions

physics

3.1.

2. Contour

trino energy deposition

on supernova

[lo] implies the of Do --) P,, dis-

region right to the curve,

P = 0.5.

re-heating

We first consider the neutrino-conversion on shock re-heating

effect

in the delayed explosion

nario [8]. We estimate

the neutrino

sce-

energy depo-

sition rate at the stalled shock with and without conversion be

and take the ratio which is defined to

R. It is clear that disappearance

fie due to the resonant ile states

will reduce

plot the iso-contour

conversion the rate

2 we

space (6m2, sin2 28).

that if the neutrino

sential for successful rameter

R. In Fig.

for different values of the ra-

tio R in the parameter can conclude

of either V, or into the ster-

supernova

re-heating explosion

region right to the curve, say

We is es-

the pa-

R = 0.5, is

L

100

1

10-3

_I

10-V

10-3

disfavoured.

10-4

10-3

10-3

10-l

sin228

3.2. SN1987A Ve signal Next we consider the impact of ZT~signal on the earth.

10-3

Figure on the observation

It is also clear that the

resonant conversion of tie + P* could induce a reduction of 9, signal in the terrestrial detector. In Fig. 3 we present the contours of the Pi survival probability, properly averaged over the neutrino energy. We conclude that the successful observation of the Do signal from supernova SN1987A in

bility

3.

Contour

plots

of the survival

proba-

P (figures at the curve) for the P, +

Pi

conversion. 3.3. r-process Finally we discuss the impact

of the neutrino

conversion on heavy elements nucleosynthesis, so called r-process in supernova [9]. As discussed in ref. [9] one of the most relevant physical parame-

H. Nunokawa et al./Nuclear

Physics B (Proc. Suppl.)

70 (1999) 129-131

131

ter in the r-process is the electron fraction Y,. To have successful r-process the site must be neutron rich, i.e. Y, < 0.5. The Y, value is mainly determined by the competition between the following two absorption reactions: v, + R. -+p+e-, IT/,+ p --tn+e+.

(3)

In the standard supernova model the latter process is favoured due to the higher average energy of oe guaranteeing the neutron richness. We expect that v, + v, (fie + fis) conversion induce a decrease (increase) of Y, due to the decrease of the first (second) neutrino-absorption reaction in eq. (3). The decrease of Y, implies that the site becomes more neutron rich and the r-process could be enhanced [5] whereas the increase of Y, induces the suppression of the Tdepending on which converprocess. Therefore, sion channel is more efficient the r-process could either be enhanced or suppressed. In Fig. 4 we present the effect of neutrino conversion on the value of Y,. In the region right to the curve Y, = 0.5 the value of Y, is larger than 0.5 and hence the r-process is suppressed. On the other hand, in the region delimited by the curve Y, = 0.4 the value of Y, could be decreased compared to the standard case, leading to the enhancement of r-process. We note that due to non-trivial “feedback” effect the value of Y, is not expected to be smaller than l/3. See ref. [ll] for more discussion 4.

Conclusion

We have studied the impact of the resonant conversion of electron neutrinos into sterile state whose mass is assumed to be in the cosmologically interesting range. We have derived bounds on neutrino parameters from the shock re-heating, SN1987A D, signal as well as r-process and we also found some parameter region where T-process could be enhanced. More detailed discussion on this work is found in ref. [ll]. REFERENCES 1

S. P. Mikheyev and A. Yu. Smirnov, Nucl. Phys. 42 (1986) 913; Sov. Phys.

Sov. J. Usp. 30

sin228 Figure 4. Contour plots for the electron concentration Y, (figures at the curves) in the region relevant for r-process. (1987)

759; L. Wolfenstein, Phys. Rev D17 ibid D20 (1979) 2634. 2 S. P. Mikheyev and A. Yu. Smirnov, Sov. Phys, JETP, 64 (1986) 4; Prog. Part. Nucl. Phys. 23 (1989) 41. 3 G. Raffelt and G. Sigl, Astropart. Phys. 1 (1993) 165. 4 X. Shi and G. Sigl, Phys. Lett. B32S (1994) 360. 5 J. T. Peltoniemi, Proc. Third Tallinn Syposium on Neutrino Physics, Ed. I. Ots, J. LGhmus, P. Helde and L. Palgi (Tartu, 1995) p. 103; hep-ph/9511323; hep-ph/9506228. 6 See for e.g., E. W. Kolb and M. S. Turner, The Early Universe (Addison-Wesley, 1990). 7 J. T. Peltoniemi, D. Tommasini and J. W. F. Valle, Phys. Lett. B298 (1993) 383. 8 J. R. Wilson, Numerical Astrophysics ed. J. M. Centrella, J. M. Leblanc and R. L. Bowers (Boston, Jones and Bartlett), p.422 (1983). 9 Y.-Z. Qian et al., Phys. Rev. Lett.71 (1993) 1965. 10 K. Hirata et. al., Phys. Rev. Lett. 58 (1987) 1490; R. Bionta et. al., Phys. Rev. Lett. 58 (1987) 1494. 11 H. Nunokawa, J. T. Peltoniemi, A. Rossi and J.W.F.Valle, Phys. Rev. D56 (1997) 1704. (1978)

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