- Email: [email protected]
Bounds on hep neutrinos
24 December 1998
Physics Letters B 444 Ž1998. 387–390
Bounds on hep neutrinos G. Fiorentini
a,b,c
, V. Berezinsky d , S. Degl’Innocenti
e,b
, B. Ricci
a,b
a Dipartimento di Fisica dell’UniÕersita` di Ferrara, Õia Paradiso 12, I-44100 Ferrara, Italy Istituto Nazionale di Fisica Nucleare, Sezione di Ferrara, Õia Paradiso 12, I-44100 Ferrara, Italy c DAPNIAr SPP, CEA Saclay, 91191 Gif-sur-YÕette, France Istituto Nazionale di Fisica Nucleare, Laboratori Nazionali del Gran Sasso, SS. 16 bis, I-67010 Assergi (AQ), Italy e Dipartimento di Fisica dell’UniÕersita` di Pisa, P.zza Torricelli 2, I-56100 Pisa, Italy b
d
Received 20 October 1998 Editor: R. Gatto
Abstract The excess of highest energy solar-neutrino events recently observed by Superkamiokande can be in principle explained by anomalously high hep-neutrino flux Fn Ž hep .. Without using SSM calculations, from the solar luminosity constraint we derive that Fn Ž hep .rS13 cannot exceed the SSM estimate by more than a factor three. If one makes the additional hypothesis that hep neutrino production occurs where the 3 He concentration is at equilibrium, helioseismology gives an upper bound which is Žless then. two times the SSM prediction. We argue that the anomalous hep-neutrino flux of order of that observed by Superkamiokande cannot be explained by astrophysics, but rather by a large production cross-section. q 1998 Elsevier Science B.V. All rights reserved.
1. Introduction In the recent observations of Superkamiokande w1x some excess of high energy solar-neutrino events was detected. This excess is difficult to interpret as distortion of Boron neutrino spectrum due to neutrino oscillations w1,2x. It might indicate w3,4x that the hep neutrino flux, Fn Ž hep ., is significantly larger Žby a factor ; 30. than the SSM prediction FnSS M Ž hep .. Apart from S13 , the zero-energy astrophysical Sfactor of the p q3 He ™ 4 He q eqq n cross-section, the prediction of the hep neutrino flux in the SSM is
rather robust. Bahcall and Krastev w4x estimate this flux as:
Fn Ž hep . s 2.1 Ž 1 q 0.03 .
ž
S13 S13 ,SS M
/
P 10 3 cmy2 sy1
Ž 1. We remark that S13 is not reliably calculated. In SS M the SSM the value S13 s 2.3 P 10y2 0 keV b is used following the most recent calculations by Schiavilla et al w6x, though due to complexity of the calculations Žsee Carlson et al w7x, Schiavilla et al. w6x. the SS M - 1.5, uncertainties are rather large: 0.5 - S13 rS13 according to Ref. w6x. In a short review of the
0370-2693r98r$ - see front matter q 1998 Elsevier Science B.V. All rights reserved. PII: S 0 3 7 0 - 2 6 9 3 Ž 9 8 . 0 1 4 1 7 - 8
G. Fiorentini et al.r Physics Letters B 444 (1998) 387–390
388
calculations w4x, the authors conclude that from the first-principle physics it is difficult to exclude that the cross-section is an order of magnitude larger. The 3% error in Eq. Ž1. accounts for the estimated uncertainties in the solar age, chemical composition, luminosity, radiative opacity, diffusion rate and in all nuclear quantites, except S13 . This small error follows from the fact that Fn Ž hep . depends rather weakly on all astrophysical variables such as temperature T, density r and the chemical composition. Besides, all these quantities, except 3 He abundance, are smooth functions of the radial distance r in the solar region where most of hep-neutrinos are produced, 0.1 - rrR( - 0.2. It is hard to conceive that SSM’s uncertainties in T, r and X can result in a considerable change of Fn Ž hep .. The only exception is 3 He abundance, which radial behaviour is not that smooth. In fact it increases by an order of magnitude when moving from r s 0.1 R( to r s 0.2 R( , so that Fn Ž hep . is sensitive to the 3 He distribution, see Figs. 4.2 and 6.1 of w5x. This abundance is not limited by helioseismic data and in non-standard models it can be, in principle, high in the hep-neutrinos production zone. We have thus analyzed the astrophysical uncertainties in the flux of hep neutrinos in an approach beyond the SSM. In Section 2 we derive an upper limit for Fn Ž hep .rS13 directly from the solarluminosity constraint. In Section 3 we impose the more restrictive assumption of local 3 He equilibrium in the hep-neutrino production zone and use the helioseismic constraints.
2. The solar-luminosity constraint The production rate Qn Ž hep . for the hep neutrinos and the solar-luminosity constraint can be written down as follows 2
Qn Ž hep . s dr4p r n1 Ž r . n 2 Ž r . l13 Ž T Ž r . . ,
H
1 2
where l i j are energy-averaged reaction rates between nucleus i and j,
l i j Ž T . s dEdEX f Ž E,T . f Ž EX ,T . Ž s Õ . i j ,
f Ž E,T . is the normalized Maxwell distribution function, n i is the number density of nuclei with atomic mass number i, Ž s Õ . i j is the reaction rate between nuclei i and j, and the two D correspond respectively to the two values of the heat release: when a 3 He nucleus is produced Ž3 p q ey™ 3 He q n ., and when two 3 He are merged Ž 3 He q3 He ™ 4 He q 2 p .,
D1 s 3m p q m e y m 3 H e y - En ) p p s 6.7 MeV
Ž 5a . D3 s 2 m 3 H e y m 4 H e y 2 m p s 12.9 MeV
li j Ž T . s li j
H
1
2
2
q D2 dr4p r n 3 Ž r . l33 Ž T Ž r . . F L( 2
H
ai j
T
ž /
Ž 6.
To
where generally speaking T0 is an arbitrary temperature scale. We shall fix T0 at the position of maximum of nuclear-energy production in the SSM ŽT0 s 1.336 P 10 7K ., which guarantees that that expansion Ž6. is related to a narrow temperature range. The values of l i j and a i, j Žthis latter rounded to the nearest integer. are given in Table 1. They are calculated using the values of astrophysical S-factors given in Ref. w8x and for T0 s 1.336 P 10 7 K. Note that uncertainties in l i j depend only on cross-sections; in particular l i j A Si j , where Si j are astrophysical factors. From Eq. Ž3., by using the inequality 1r2Ž f 12 q 2. f 2 G f 1 f 2 and the parametrization Ž6. one obtains
Hdr4p r
2
n1 Ž r . n 3 Ž r . l13 Ž T Ž r . .
l13
F
(l
11 l 33
2
Ž 3.
Ž 5b .
The temperature dependence of the reaction rates Ž4. can be parametrized as:
Ž 2.
D1 dr4p r 2 n1 Ž r . l11 Ž T Ž r . .
Ž 4.
H
(D D 1
L( ,
TŽ r.
a
ž / T0
Ž 7.
2
where a s Ž a 11 q a 33 .r2 y a 13 , 2 One can see that the integrand in the lhs of Eq. Ž7. is different from that of Eq. Ž2. only by a factor
G. Fiorentini et al.r Physics Letters B 444 (1998) 387–390 Table 1 Parameters of the reaction rates Ž6.
Putting n 3 Ž r . from this equation into Ž2. and using n1Ž r . s X Ž r . r Ž r .rm p one obtains
li j w cm3 sy1 x
i, j
ai j
Fn Ž hep . s
8.34 10y4 4 4.31 10y4 7 5.88 10y3 5
1,1 1,3 3,3
389
4 8 16
l13 4p D
2
(
l11
1
2 l33 m2p
= dr4p r 2r Ž r .
H
2
X Ž r . T Ž r . rT0
2
.
Ž 11 . 2
strengthens if Ž T Ž r . rT0 . . Inequality Ž7. further 2 this factor is taken as Ž Tm i nrT0 . , where Tm i n is the minimum temperature in the hep-production zone. In the SSM at the temperature Tm i n s 7 P 10 6 K Žcorresponding to rrR( s 0.3. the probability for a proton to undergo a nuclear reaction during the solar age is as small as 0.1%. Then from Eq. Ž7. one obtains
Fn Ž hep . -
l13
K(
(D D (l 1
3
11 l 33
T0
ž / Tm i n
2
,
Ž 8.
where K( s L( rŽ4p D 2 . and D is the distance between Sun and Earth. Note that the weak inequality Ž7. has turned into a stronger inequality Ž8. due to substitution T Ž r . ™ Tm i n in lhs of Eq. Ž7., while actually one should use T Ž r . ™- T ) . Using the values from Table 1, one obtains numerically
Fn Ž hep . - 6.5
S13
ž / SS M S13
P 10 3 cmy2 sy1 ,
Ž 9.
a factor three larger than in the SSM calculations, Eq. Ž1..
3. Local 3 He equilibrium and helioseismology A more restrictive upper bound can be obtained from helioseismic constraints, with an additional assumption that hep neutrinos are produced in a region where the 3 He concentration is at local equilibrium. This assumption, which is valid for a wide class of stellar models, implies: 1 2
n12 l11T Ž r . s n 23 l 33T Ž r . .
Ž 10 .
In the energy production zone, the equation of state ŽEOS. for the solar interior can be approximated, with an accuracy better than 1% , by the EOS of a fully ionized classical perfect gas: P Ž r . s r Ž r . T Ž r . Ž k Brm p . = 2 XŽ r. q
3 4
YŽ r. q
1 2
ZŽ r . ,
Ž 12.
where P denotes the pressure and k B is the Boltzmann constant. Using Eqs. Ž11. and Ž12. one obtains 1 1 Fn Ž hep . F l 2 4p D 4 Ž kT0 . 2 13
(
=
l11 2 l33
Hdr4p r
2
P2Ž r. .
Ž 13 .
It is known w9x that inverting helioseismic data one can derive the Žisothermal. sound speed squared, u s Prr and r with an accuracy of 1% or better for all rrR( of interest. This implies that also pressure P is known with a comparable accuracy. Since SSMs are in agreement with helioseismology, one can use the SSM-calculated pressure P Ž r . to evaluate the integral in Eq. Ž13.. It gives S13 Fn Ž hep . - 3.5 SS M P 10 3 cmy2 sy1 . Ž 14 . S13
ž /
This upper bound is Žless then. two times the SSM prediction. In fact the agreement is even better. Neglecting Z in Eq. Ž12. and using Y f 1 y X one obtains from Eq. Ž12. XŽ r.T Ž r. s
4mp P Ž r . 5k B r Ž r .
3 y 5
TŽ r.
Ž 15.
The first term on rhs of Eq. Ž15. is determined by helioseismic measurements and thus can be taken as in the SSM. Temperature profile T Ž r . cannot differ from that of the SSM more than by 2 – 3%. Then
390
G. Fiorentini et al.r Physics Letters B 444 (1998) 387–390
w X Ž r .T Ž r .x2 , the only unknown function in the integral Ž11., can differ from the SSM value by a few percent only and so does Fn Ž hep ..
4. Conclusions We have derived an upper limit on Fn Ž hep .rS13 directly from the solar-luminosity constraint. It is only three times the SSM prediction. If one additionally assumes that hep neutrino production occurs in the region where the 3 He concentration is at local equilibrium, helioseismology provides a formal upper bound Žless than. two times the SSM prediction. More realistically, in this case Fn Ž hep .rS13 can be only a few percent higher than in the SSM. Our limits can be violated only in very exotic models of non-stationary sun with non-stationary transport of 3 He in the inner core from outside. This transport should not be accompanied by any noticeable transport of other elements, such as 1 H or 4 He, otherwise the seismically observed sound speed in the inner core will be affected. We doubt that such models can be constructed. In principle, the hep-neutrinos can be resolved in the high precision experiments. We argue that the anomalous hep-neutrino flux of order of that observed by Superkamiokande cannot be explained by astrophysics, but rather by a large production crosssection.
Acknowledgements We are grateful to J.N. Bahcall, W. Dziembowski, E. Lisi, M. Lissia, M. Spiro and D. Vignaud for interesting discussions. G.F. thanks the DAPNIA of CEA-Saclay for hospitality in a stimulating environment.
References w1x SuperKamiokande Collaboration, Y. Suzuki, in: Y. Suzuki, Y. Totsuka ŽEds.., Neutrino 98, Proceedings of the XVIII International Conference on Neutrino Physics and Astrophysics, Takayama, Japan, 4–9 June 1998, to be published in Nucl. Phys. B ŽProc. Suppl... w2x J.N. Bahcall, P.I. Krastev, A.Yu. Smirnov, hep-phr9807216. w3x R. Escribano, J.M. Frere, ´ A. Gevaert, D. Monderen, hepphr9805238, to appear in Phys. Lett. B Ž1998.. w4x J.N. Bahcall, P.I. Krastev, hep-phr9807525, 1998. w5x J.N. Bahcall, Neutrino Astrophysics, Cambridge University Press, Cambridge, 1989. w6x R. Schiavilla, R.B. Wirings, V.R. Pandharipande, J. Carlson, Phys. Rev. C 45 Ž1992. 2628. w7x J. Carlson, D.O. Riska, R. Schiavilla, R.B. Wiringa, Phys. Rev. C 44 Ž1991. 619. w8x E.G. Adelberger et al., astro-phr9805121, to appear in Rev. Mod. Phys. Ž1998.. w9x W.A. Dziembowski, P. R Goode, A.A. Pamyatnykh, R. Sienkiewicz, Ap. J. 432 Ž1994. 417.
Physics Letters B 444 Ž1998. 387–390
Bounds on hep neutrinos G. Fiorentini
a,b,c
, V. Berezinsky d , S. Degl’Innocenti
e,b
, B. Ricci
a,b
a Dipartimento di Fisica dell’UniÕersita` di Ferrara, Õia Paradiso 12, I-44100 Ferrara, Italy Istituto Nazionale di Fisica Nucleare, Sezione di Ferrara, Õia Paradiso 12, I-44100 Ferrara, Italy c DAPNIAr SPP, CEA Saclay, 91191 Gif-sur-YÕette, France Istituto Nazionale di Fisica Nucleare, Laboratori Nazionali del Gran Sasso, SS. 16 bis, I-67010 Assergi (AQ), Italy e Dipartimento di Fisica dell’UniÕersita` di Pisa, P.zza Torricelli 2, I-56100 Pisa, Italy b
d
Received 20 October 1998 Editor: R. Gatto
Abstract The excess of highest energy solar-neutrino events recently observed by Superkamiokande can be in principle explained by anomalously high hep-neutrino flux Fn Ž hep .. Without using SSM calculations, from the solar luminosity constraint we derive that Fn Ž hep .rS13 cannot exceed the SSM estimate by more than a factor three. If one makes the additional hypothesis that hep neutrino production occurs where the 3 He concentration is at equilibrium, helioseismology gives an upper bound which is Žless then. two times the SSM prediction. We argue that the anomalous hep-neutrino flux of order of that observed by Superkamiokande cannot be explained by astrophysics, but rather by a large production cross-section. q 1998 Elsevier Science B.V. All rights reserved.
1. Introduction In the recent observations of Superkamiokande w1x some excess of high energy solar-neutrino events was detected. This excess is difficult to interpret as distortion of Boron neutrino spectrum due to neutrino oscillations w1,2x. It might indicate w3,4x that the hep neutrino flux, Fn Ž hep ., is significantly larger Žby a factor ; 30. than the SSM prediction FnSS M Ž hep .. Apart from S13 , the zero-energy astrophysical Sfactor of the p q3 He ™ 4 He q eqq n cross-section, the prediction of the hep neutrino flux in the SSM is
rather robust. Bahcall and Krastev w4x estimate this flux as:
Fn Ž hep . s 2.1 Ž 1 q 0.03 .
ž
S13 S13 ,SS M
/
P 10 3 cmy2 sy1
Ž 1. We remark that S13 is not reliably calculated. In SS M the SSM the value S13 s 2.3 P 10y2 0 keV b is used following the most recent calculations by Schiavilla et al w6x, though due to complexity of the calculations Žsee Carlson et al w7x, Schiavilla et al. w6x. the SS M - 1.5, uncertainties are rather large: 0.5 - S13 rS13 according to Ref. w6x. In a short review of the
0370-2693r98r$ - see front matter q 1998 Elsevier Science B.V. All rights reserved. PII: S 0 3 7 0 - 2 6 9 3 Ž 9 8 . 0 1 4 1 7 - 8
G. Fiorentini et al.r Physics Letters B 444 (1998) 387–390
388
calculations w4x, the authors conclude that from the first-principle physics it is difficult to exclude that the cross-section is an order of magnitude larger. The 3% error in Eq. Ž1. accounts for the estimated uncertainties in the solar age, chemical composition, luminosity, radiative opacity, diffusion rate and in all nuclear quantites, except S13 . This small error follows from the fact that Fn Ž hep . depends rather weakly on all astrophysical variables such as temperature T, density r and the chemical composition. Besides, all these quantities, except 3 He abundance, are smooth functions of the radial distance r in the solar region where most of hep-neutrinos are produced, 0.1 - rrR( - 0.2. It is hard to conceive that SSM’s uncertainties in T, r and X can result in a considerable change of Fn Ž hep .. The only exception is 3 He abundance, which radial behaviour is not that smooth. In fact it increases by an order of magnitude when moving from r s 0.1 R( to r s 0.2 R( , so that Fn Ž hep . is sensitive to the 3 He distribution, see Figs. 4.2 and 6.1 of w5x. This abundance is not limited by helioseismic data and in non-standard models it can be, in principle, high in the hep-neutrinos production zone. We have thus analyzed the astrophysical uncertainties in the flux of hep neutrinos in an approach beyond the SSM. In Section 2 we derive an upper limit for Fn Ž hep .rS13 directly from the solarluminosity constraint. In Section 3 we impose the more restrictive assumption of local 3 He equilibrium in the hep-neutrino production zone and use the helioseismic constraints.
2. The solar-luminosity constraint The production rate Qn Ž hep . for the hep neutrinos and the solar-luminosity constraint can be written down as follows 2
Qn Ž hep . s dr4p r n1 Ž r . n 2 Ž r . l13 Ž T Ž r . . ,
H
1 2
where l i j are energy-averaged reaction rates between nucleus i and j,
l i j Ž T . s dEdEX f Ž E,T . f Ž EX ,T . Ž s Õ . i j ,
f Ž E,T . is the normalized Maxwell distribution function, n i is the number density of nuclei with atomic mass number i, Ž s Õ . i j is the reaction rate between nuclei i and j, and the two D correspond respectively to the two values of the heat release: when a 3 He nucleus is produced Ž3 p q ey™ 3 He q n ., and when two 3 He are merged Ž 3 He q3 He ™ 4 He q 2 p .,
D1 s 3m p q m e y m 3 H e y - En ) p p s 6.7 MeV
Ž 5a . D3 s 2 m 3 H e y m 4 H e y 2 m p s 12.9 MeV
li j Ž T . s li j
H
1
2
2
q D2 dr4p r n 3 Ž r . l33 Ž T Ž r . . F L( 2
H
ai j
T
ž /
Ž 6.
To
where generally speaking T0 is an arbitrary temperature scale. We shall fix T0 at the position of maximum of nuclear-energy production in the SSM ŽT0 s 1.336 P 10 7K ., which guarantees that that expansion Ž6. is related to a narrow temperature range. The values of l i j and a i, j Žthis latter rounded to the nearest integer. are given in Table 1. They are calculated using the values of astrophysical S-factors given in Ref. w8x and for T0 s 1.336 P 10 7 K. Note that uncertainties in l i j depend only on cross-sections; in particular l i j A Si j , where Si j are astrophysical factors. From Eq. Ž3., by using the inequality 1r2Ž f 12 q 2. f 2 G f 1 f 2 and the parametrization Ž6. one obtains
Hdr4p r
2
n1 Ž r . n 3 Ž r . l13 Ž T Ž r . .
l13
F
(l
11 l 33
2
Ž 3.
Ž 5b .
The temperature dependence of the reaction rates Ž4. can be parametrized as:
Ž 2.
D1 dr4p r 2 n1 Ž r . l11 Ž T Ž r . .
Ž 4.
H
(D D 1
L( ,
TŽ r.
a
ž / T0
Ž 7.
2
where a s Ž a 11 q a 33 .r2 y a 13 , 2 One can see that the integrand in the lhs of Eq. Ž7. is different from that of Eq. Ž2. only by a factor
G. Fiorentini et al.r Physics Letters B 444 (1998) 387–390 Table 1 Parameters of the reaction rates Ž6.
Putting n 3 Ž r . from this equation into Ž2. and using n1Ž r . s X Ž r . r Ž r .rm p one obtains
li j w cm3 sy1 x
i, j
ai j
Fn Ž hep . s
8.34 10y4 4 4.31 10y4 7 5.88 10y3 5
1,1 1,3 3,3
389
4 8 16
l13 4p D
2
(
l11
1
2 l33 m2p
= dr4p r 2r Ž r .
H
2
X Ž r . T Ž r . rT0
2
.
Ž 11 . 2
strengthens if Ž T Ž r . rT0 . . Inequality Ž7. further 2 this factor is taken as Ž Tm i nrT0 . , where Tm i n is the minimum temperature in the hep-production zone. In the SSM at the temperature Tm i n s 7 P 10 6 K Žcorresponding to rrR( s 0.3. the probability for a proton to undergo a nuclear reaction during the solar age is as small as 0.1%. Then from Eq. Ž7. one obtains
Fn Ž hep . -
l13
K(
(D D (l 1
3
11 l 33
T0
ž / Tm i n
2
,
Ž 8.
where K( s L( rŽ4p D 2 . and D is the distance between Sun and Earth. Note that the weak inequality Ž7. has turned into a stronger inequality Ž8. due to substitution T Ž r . ™ Tm i n in lhs of Eq. Ž7., while actually one should use T Ž r . ™- T ) . Using the values from Table 1, one obtains numerically
Fn Ž hep . - 6.5
S13
ž / SS M S13
P 10 3 cmy2 sy1 ,
Ž 9.
a factor three larger than in the SSM calculations, Eq. Ž1..
3. Local 3 He equilibrium and helioseismology A more restrictive upper bound can be obtained from helioseismic constraints, with an additional assumption that hep neutrinos are produced in a region where the 3 He concentration is at local equilibrium. This assumption, which is valid for a wide class of stellar models, implies: 1 2
n12 l11T Ž r . s n 23 l 33T Ž r . .
Ž 10 .
In the energy production zone, the equation of state ŽEOS. for the solar interior can be approximated, with an accuracy better than 1% , by the EOS of a fully ionized classical perfect gas: P Ž r . s r Ž r . T Ž r . Ž k Brm p . = 2 XŽ r. q
3 4
YŽ r. q
1 2
ZŽ r . ,
Ž 12.
where P denotes the pressure and k B is the Boltzmann constant. Using Eqs. Ž11. and Ž12. one obtains 1 1 Fn Ž hep . F l 2 4p D 4 Ž kT0 . 2 13
(
=
l11 2 l33
Hdr4p r
2
P2Ž r. .
Ž 13 .
It is known w9x that inverting helioseismic data one can derive the Žisothermal. sound speed squared, u s Prr and r with an accuracy of 1% or better for all rrR( of interest. This implies that also pressure P is known with a comparable accuracy. Since SSMs are in agreement with helioseismology, one can use the SSM-calculated pressure P Ž r . to evaluate the integral in Eq. Ž13.. It gives S13 Fn Ž hep . - 3.5 SS M P 10 3 cmy2 sy1 . Ž 14 . S13
ž /
This upper bound is Žless then. two times the SSM prediction. In fact the agreement is even better. Neglecting Z in Eq. Ž12. and using Y f 1 y X one obtains from Eq. Ž12. XŽ r.T Ž r. s
4mp P Ž r . 5k B r Ž r .
3 y 5
TŽ r.
Ž 15.
The first term on rhs of Eq. Ž15. is determined by helioseismic measurements and thus can be taken as in the SSM. Temperature profile T Ž r . cannot differ from that of the SSM more than by 2 – 3%. Then
390
G. Fiorentini et al.r Physics Letters B 444 (1998) 387–390
w X Ž r .T Ž r .x2 , the only unknown function in the integral Ž11., can differ from the SSM value by a few percent only and so does Fn Ž hep ..
4. Conclusions We have derived an upper limit on Fn Ž hep .rS13 directly from the solar-luminosity constraint. It is only three times the SSM prediction. If one additionally assumes that hep neutrino production occurs in the region where the 3 He concentration is at local equilibrium, helioseismology provides a formal upper bound Žless than. two times the SSM prediction. More realistically, in this case Fn Ž hep .rS13 can be only a few percent higher than in the SSM. Our limits can be violated only in very exotic models of non-stationary sun with non-stationary transport of 3 He in the inner core from outside. This transport should not be accompanied by any noticeable transport of other elements, such as 1 H or 4 He, otherwise the seismically observed sound speed in the inner core will be affected. We doubt that such models can be constructed. In principle, the hep-neutrinos can be resolved in the high precision experiments. We argue that the anomalous hep-neutrino flux of order of that observed by Superkamiokande cannot be explained by astrophysics, but rather by a large production crosssection.
Acknowledgements We are grateful to J.N. Bahcall, W. Dziembowski, E. Lisi, M. Lissia, M. Spiro and D. Vignaud for interesting discussions. G.F. thanks the DAPNIA of CEA-Saclay for hospitality in a stimulating environment.
References w1x SuperKamiokande Collaboration, Y. Suzuki, in: Y. Suzuki, Y. Totsuka ŽEds.., Neutrino 98, Proceedings of the XVIII International Conference on Neutrino Physics and Astrophysics, Takayama, Japan, 4–9 June 1998, to be published in Nucl. Phys. B ŽProc. Suppl... w2x J.N. Bahcall, P.I. Krastev, A.Yu. Smirnov, hep-phr9807216. w3x R. Escribano, J.M. Frere, ´ A. Gevaert, D. Monderen, hepphr9805238, to appear in Phys. Lett. B Ž1998.. w4x J.N. Bahcall, P.I. Krastev, hep-phr9807525, 1998. w5x J.N. Bahcall, Neutrino Astrophysics, Cambridge University Press, Cambridge, 1989. w6x R. Schiavilla, R.B. Wirings, V.R. Pandharipande, J. Carlson, Phys. Rev. C 45 Ž1992. 2628. w7x J. Carlson, D.O. Riska, R. Schiavilla, R.B. Wiringa, Phys. Rev. C 44 Ž1991. 619. w8x E.G. Adelberger et al., astro-phr9805121, to appear in Rev. Mod. Phys. Ž1998.. w9x W.A. Dziembowski, P. R Goode, A.A. Pamyatnykh, R. Sienkiewicz, Ap. J. 432 Ž1994. 417.