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Electron antineutrinos from the sun with random magnetic fields
ELSEVIER
PROCEEDINGS SUPPLEMENTS
Nuclear Physics B (Proc. Suppl.) 87 (2000) 212-214
www.elsevier.nl/locate/npe
Electron Antineutrinos from the Sun with Random Magnetic Fields A.A.Bykov a, V.Yu.Popov a, D.D.SokolofP and A.I.Rez b, V.B.Semikoz b aDepartment of Physics, Moscow State University, Moscow, 119899, Russia bInstitute of Terrestrial Magnetism, Ionosphere and Radio Wave Propagation of the Russian Academy of Sciences, IZMIRAN, Troitsk, Moscow Region, 142092, Russia The magnetic field in the solar convective zone has a random small-scale component with a r.m.s, value substantially exceeding the strength of a regular large-scale field. In the presence of a neutrino transition magnetic moment we find an effective production of electron antineutrinos in the Sun even for small neutrino mixing through the cascade conversions in the random magnetic field that would be a signature of the Majorana nature of neutrino if ~ a were registered. Basing on the present SK bound on electron antineutrinos we also estimated the corresponding excluded area in the plane Am ~, sin 2 20.
1. The mean magnetic field is accompanied by a
small scale random magnetic field. This random magnetic field is not directly traced by sunspots or other tracers of solar activity. It propagates through the convective zone and photosphere, drastically decreasing in the strength value while increasing its scale. According to the available understanding of solar dynamo, the strength of the random magnetic field inside the convective zone is larger than the mean field strength. A direct observational estimation of the ratio between this strengths is not available, the ratio of order 50 - 100 however does not seem impossible. At least, the ratio between the mean magnetic field strength and the fluctuation at the solar surface is estimated as 50 (see e.g. [1]). This is the main reason why we consider here an analogue to the R S F P scenario [2], an aperiodic spin-flavour conversion (ASFC), based on the presence of random magnetic fields in the solar convective zone [3],[4]. It turns out that the ASFC is an additional probable way to describe the solar neutrino deficit in different energy regions, especially if current and future experiments were to detect electron antineutrinos from the Sun leading to conclusion that neutrinos are Majorana particles. The word "aperiodic" simply reflects the exponential behaviour of conversion
probabilities in noisy media (cf. [5],[6]). As well as for the RSFP mechanism, all argnments for and against the ASFC mechanism with random magnetic fields remain those recently summarized and commented by Akhmedov (see [2] and references therein). But contrary to the case of regular magnetic fields we find out that one of the signatures of random magnetic field in the Sun is the prediction of a wider allowed region for neutrino mixing angle in the presence of Pc from the Sun, including the case of small mixing angles. At the stage of numerical simulation of the random magnetic field we generate the set of random numbers with a given r.m.s, value and for each realization of random magnetic fields along each of neutrino rays solve the Cauchy problem for the (4 x 4) SchrSdinger equation, then we calculate the dynamical probabilities Paa(t), and average them in transversal plane, i.e., obtain the mean arithmetic probabilities as functions of mixing parameters sin 2 20 , 5 [3]. We argue that being additive functions of the area of the convective zone layer (or, in the same way, of the number of rays) these probabilities become self-averaged with increasing area. 2.
In
0920-5632/00/$ - see front matter © 2000 ElsevierScienceB.V. All rights reserved." PII S0920-5632(00)00670-8
order
to
find
the
regions
213
A.A. Bykov et al./Nuclear Physics B (Proc. Suppl.) 87 (2000) 212-214
in the (Am2,sin220) plane excluded from nonobservation of PeR in SK, it is necessary to compute and plot the isolines of the ratio @o/~SsSM. As antineutrinos were not detected in the SK experiment, one should claim that the antineutrino flux is smaller than the SK background ~ . (E > 8.3 MeV) < 6 x 104 cm-2s -1 [7]. Dividing this inequality by the SSM boron neutrino flux with energies E > Eth = 8.3 MeV, ~SBSM(E > 8.3 MeV) = 1.7 x 106 cm-2s -1 we find the bound on the allowed (Am 2, sin 2 28) region:
DATA/SSM br.m.s. =50 kG. -3 10
I
-4
l0
10-5 Gallex (Sage)--~ -6
~ . (E > 8.3 MeV) 'I~SSM(E > 8.3) < 0.035.
10 (1)
For strong magnetic fields, the forbidden parameter regions arising from (1) appear in different areas over 6, sin z 2/9 depending on the kind of magnetic fields (regular and random). In general, the influence of random magnetic fields is more pronounced as compared to the regular ones of the same strength. Here we illustrate only the random magnetic field case. The more intensive the r.m.s, field v ~ is in the convective zone, the more effective spin-flavour conversions lead to the production of the right-handed PeR, OuR antineutrinos. In Figs. 1,2 we present the allowed parameter regions which reconcile four solar neutrino experiments along with the SK bound on PeR. One can see that without the latter bound there exist two commonly adopted parameter regions, the small mixing and the large mixing ones, currently allowed or excluded depending on the value of the r.m.s, magnetic field parameters. Here we demonstrate the allowed case only, when the region excluded by the SK bound is well below the two parameter regions of interest. Our resuits, however, show that there exists a strong dependence not only on the r.m.s, magnetic field strength but on its correlation length also [3]. 3. We develop a model of neutrino spin-fiavour conversions in random magnetic fields of the solar convective zone supposing consistently with modern MHD models of solar magnetic fields that random fields are naturally much higher than largescale magnetic fields created and supported continuously from the small-scale random ones [1].
SK bound on
l0
-7
168
10-9
!
~0"5
10"4
10"3
1(12
1(}1
100
sin2(2 O) Figure 1. Putting together all experiments: the isolines with dashed bands represent the DATA/SSM ratio equal respectively to 0.368 + 0.026 (SK), 0.5094-0.059, 0.504+0.085 (GALLEX + SAGE), and 0.274 4- 0.027 (Homestake). The random field brm, = 50 kG. There follows that if neutrinos have a large transition magnetic moment their dynamics in the Sun is governed by random magnetic fields that first, lead to aperiodic and rather nonresonant neutrino spin-flavor conversions, and second, inevitably lead to production of electronantineutrinos for low energy or large mass difference conditions [3]. If antineutrinos PeR were found with a positive signal in the Borexino experiment[8] or, in other words, if a small-mixing MSW solution to SNP falls, this would be a strong argument in favour of a magnetic field scenario with ASFC in the presence of a large neutrino
A.A. Bykov et al./Nuclear Physics B (Proc. Suppl.) 87 (2000) 212-214
214
trum profiles for different scenarios would be a crucial test in favour of the very mechanism providing the solution to SNP.
DATA/SSM br.m.s.=100 kG. -3
I
l0
The authors thank Sergio Pastor, Emilio Torrente, Jose Valle for fruitful discussions. This work has been supported by RFBR grant 97-0216501 and by INTAS grant 96-0659 of the European Union.
-4
l0
-
l 0 "5 _
REFERENCES
Gallex (Sagc)-.~
1. E.N. Parker, Astrophys. J. 408 (1993) 707; E.N. Parker, Cosmological Magnetic Fields, Oxford University Press, Oxford, 1979; S.I. Vainstein, A.M. Bykov, I.M. Toptygin, Turbulence, Current Sheets and Shocks in Cosmic Plasma, Gordon and Breach, 1993. 2. E.Kh. Akhmedov, The neutrino magnetic moment and time variations of the solar neutrino flux, Preprint IC/97/49. 3. A.A. Bykov, A.Yu. Popov, A.I. Rez, V.B. Semikoz, and D.D. Sokoloff, Phys. Rev. D 59
SK bound on ant -7
lO
-
16 8 -
10-9 -
(1999) 063001. 161°10 5 -
10-4
10-3
10-2
1() 1
100
sin2(20)
Figure 2. Putting together all experiments: the isolines with dashed bands represent the DATA/SSM ratio equal respectively to 0.368 + 0.026 (SK), 0.509=t:0.059, 0.504±0.085 (GALLEX + SAGE), and 0.274 :t= 0.027 (Homestake). The random field brms = 100 kG. transition moment, # ,~ 10-Xl/JB for the same small mixing angle. The search of bounds on /~ at the level # ~ 10-1Z#B in low energy v e-scattering, currently planned in laboratory experiments, would be crucial for the model considered here. We would like to emphasize the importance of future low-energy neutrino experiments (BOREXINO, HELLAZ) which will be sensitive both to check the MSW scenario and the PeRproduction through ASFP. As it was shown in a recent work[9] a different slope of energy spec-
4. V.B. Semikoz and E. Torrente-Lujan, Nucl. Phys. B 556 (1999) 353. 5. A. Nicolaidis, Phys.Lett. B 262 (1991) 303. 6. K. Enqvist, A.I. Rez, V.B. Semikoz, Nucl. Phys. B 436 (1995) 49. 7. G. Fiorentini, M. Moretti, and F.L. Villante, hep-ph/9707097. 8. J.B. Benziger et al., Status Report of Borexino Project: The Counting Test Facility and its Results. A proposal for participation in the Borexino Solar Neutrino Experiment, Princeton, October 1996. Talk presented by P.A. Eisenstein at Baksan International School "Particles and Cosmology" (April 1997). 9. S. Pastor, V.B. Semikoz, J.W.F. Valle, Phys.Lett. B 423 (1998) 118.
PROCEEDINGS SUPPLEMENTS
Nuclear Physics B (Proc. Suppl.) 87 (2000) 212-214
www.elsevier.nl/locate/npe
Electron Antineutrinos from the Sun with Random Magnetic Fields A.A.Bykov a, V.Yu.Popov a, D.D.SokolofP and A.I.Rez b, V.B.Semikoz b aDepartment of Physics, Moscow State University, Moscow, 119899, Russia bInstitute of Terrestrial Magnetism, Ionosphere and Radio Wave Propagation of the Russian Academy of Sciences, IZMIRAN, Troitsk, Moscow Region, 142092, Russia The magnetic field in the solar convective zone has a random small-scale component with a r.m.s, value substantially exceeding the strength of a regular large-scale field. In the presence of a neutrino transition magnetic moment we find an effective production of electron antineutrinos in the Sun even for small neutrino mixing through the cascade conversions in the random magnetic field that would be a signature of the Majorana nature of neutrino if ~ a were registered. Basing on the present SK bound on electron antineutrinos we also estimated the corresponding excluded area in the plane Am ~, sin 2 20.
1. The mean magnetic field is accompanied by a
small scale random magnetic field. This random magnetic field is not directly traced by sunspots or other tracers of solar activity. It propagates through the convective zone and photosphere, drastically decreasing in the strength value while increasing its scale. According to the available understanding of solar dynamo, the strength of the random magnetic field inside the convective zone is larger than the mean field strength. A direct observational estimation of the ratio between this strengths is not available, the ratio of order 50 - 100 however does not seem impossible. At least, the ratio between the mean magnetic field strength and the fluctuation at the solar surface is estimated as 50 (see e.g. [1]). This is the main reason why we consider here an analogue to the R S F P scenario [2], an aperiodic spin-flavour conversion (ASFC), based on the presence of random magnetic fields in the solar convective zone [3],[4]. It turns out that the ASFC is an additional probable way to describe the solar neutrino deficit in different energy regions, especially if current and future experiments were to detect electron antineutrinos from the Sun leading to conclusion that neutrinos are Majorana particles. The word "aperiodic" simply reflects the exponential behaviour of conversion
probabilities in noisy media (cf. [5],[6]). As well as for the RSFP mechanism, all argnments for and against the ASFC mechanism with random magnetic fields remain those recently summarized and commented by Akhmedov (see [2] and references therein). But contrary to the case of regular magnetic fields we find out that one of the signatures of random magnetic field in the Sun is the prediction of a wider allowed region for neutrino mixing angle in the presence of Pc from the Sun, including the case of small mixing angles. At the stage of numerical simulation of the random magnetic field we generate the set of random numbers with a given r.m.s, value and for each realization of random magnetic fields along each of neutrino rays solve the Cauchy problem for the (4 x 4) SchrSdinger equation, then we calculate the dynamical probabilities Paa(t), and average them in transversal plane, i.e., obtain the mean arithmetic probabilities as functions of mixing parameters sin 2 20 , 5 [3]. We argue that being additive functions of the area of the convective zone layer (or, in the same way, of the number of rays) these probabilities become self-averaged with increasing area. 2.
In
0920-5632/00/$ - see front matter © 2000 ElsevierScienceB.V. All rights reserved." PII S0920-5632(00)00670-8
order
to
find
the
regions
213
A.A. Bykov et al./Nuclear Physics B (Proc. Suppl.) 87 (2000) 212-214
in the (Am2,sin220) plane excluded from nonobservation of PeR in SK, it is necessary to compute and plot the isolines of the ratio @o/~SsSM. As antineutrinos were not detected in the SK experiment, one should claim that the antineutrino flux is smaller than the SK background ~ . (E > 8.3 MeV) < 6 x 104 cm-2s -1 [7]. Dividing this inequality by the SSM boron neutrino flux with energies E > Eth = 8.3 MeV, ~SBSM(E > 8.3 MeV) = 1.7 x 106 cm-2s -1 we find the bound on the allowed (Am 2, sin 2 28) region:
DATA/SSM br.m.s. =50 kG. -3 10
I
-4
l0
10-5 Gallex (Sage)--~ -6
~ . (E > 8.3 MeV) 'I~SSM(E > 8.3) < 0.035.
10 (1)
For strong magnetic fields, the forbidden parameter regions arising from (1) appear in different areas over 6, sin z 2/9 depending on the kind of magnetic fields (regular and random). In general, the influence of random magnetic fields is more pronounced as compared to the regular ones of the same strength. Here we illustrate only the random magnetic field case. The more intensive the r.m.s, field v ~ is in the convective zone, the more effective spin-flavour conversions lead to the production of the right-handed PeR, OuR antineutrinos. In Figs. 1,2 we present the allowed parameter regions which reconcile four solar neutrino experiments along with the SK bound on PeR. One can see that without the latter bound there exist two commonly adopted parameter regions, the small mixing and the large mixing ones, currently allowed or excluded depending on the value of the r.m.s, magnetic field parameters. Here we demonstrate the allowed case only, when the region excluded by the SK bound is well below the two parameter regions of interest. Our resuits, however, show that there exists a strong dependence not only on the r.m.s, magnetic field strength but on its correlation length also [3]. 3. We develop a model of neutrino spin-fiavour conversions in random magnetic fields of the solar convective zone supposing consistently with modern MHD models of solar magnetic fields that random fields are naturally much higher than largescale magnetic fields created and supported continuously from the small-scale random ones [1].
SK bound on
l0
-7
168
10-9
!
~0"5
10"4
10"3
1(12
1(}1
100
sin2(2 O) Figure 1. Putting together all experiments: the isolines with dashed bands represent the DATA/SSM ratio equal respectively to 0.368 + 0.026 (SK), 0.5094-0.059, 0.504+0.085 (GALLEX + SAGE), and 0.274 4- 0.027 (Homestake). The random field brm, = 50 kG. There follows that if neutrinos have a large transition magnetic moment their dynamics in the Sun is governed by random magnetic fields that first, lead to aperiodic and rather nonresonant neutrino spin-flavor conversions, and second, inevitably lead to production of electronantineutrinos for low energy or large mass difference conditions [3]. If antineutrinos PeR were found with a positive signal in the Borexino experiment[8] or, in other words, if a small-mixing MSW solution to SNP falls, this would be a strong argument in favour of a magnetic field scenario with ASFC in the presence of a large neutrino
A.A. Bykov et al./Nuclear Physics B (Proc. Suppl.) 87 (2000) 212-214
214
trum profiles for different scenarios would be a crucial test in favour of the very mechanism providing the solution to SNP.
DATA/SSM br.m.s.=100 kG. -3
I
l0
The authors thank Sergio Pastor, Emilio Torrente, Jose Valle for fruitful discussions. This work has been supported by RFBR grant 97-0216501 and by INTAS grant 96-0659 of the European Union.
-4
l0
-
l 0 "5 _
REFERENCES
Gallex (Sagc)-.~
1. E.N. Parker, Astrophys. J. 408 (1993) 707; E.N. Parker, Cosmological Magnetic Fields, Oxford University Press, Oxford, 1979; S.I. Vainstein, A.M. Bykov, I.M. Toptygin, Turbulence, Current Sheets and Shocks in Cosmic Plasma, Gordon and Breach, 1993. 2. E.Kh. Akhmedov, The neutrino magnetic moment and time variations of the solar neutrino flux, Preprint IC/97/49. 3. A.A. Bykov, A.Yu. Popov, A.I. Rez, V.B. Semikoz, and D.D. Sokoloff, Phys. Rev. D 59
SK bound on ant -7
lO
-
16 8 -
10-9 -
(1999) 063001. 161°10 5 -
10-4
10-3
10-2
1() 1
100
sin2(20)
Figure 2. Putting together all experiments: the isolines with dashed bands represent the DATA/SSM ratio equal respectively to 0.368 + 0.026 (SK), 0.509=t:0.059, 0.504±0.085 (GALLEX + SAGE), and 0.274 :t= 0.027 (Homestake). The random field brms = 100 kG. transition moment, # ,~ 10-Xl/JB for the same small mixing angle. The search of bounds on /~ at the level # ~ 10-1Z#B in low energy v e-scattering, currently planned in laboratory experiments, would be crucial for the model considered here. We would like to emphasize the importance of future low-energy neutrino experiments (BOREXINO, HELLAZ) which will be sensitive both to check the MSW scenario and the PeRproduction through ASFP. As it was shown in a recent work[9] a different slope of energy spec-
4. V.B. Semikoz and E. Torrente-Lujan, Nucl. Phys. B 556 (1999) 353. 5. A. Nicolaidis, Phys.Lett. B 262 (1991) 303. 6. K. Enqvist, A.I. Rez, V.B. Semikoz, Nucl. Phys. B 436 (1995) 49. 7. G. Fiorentini, M. Moretti, and F.L. Villante, hep-ph/9707097. 8. J.B. Benziger et al., Status Report of Borexino Project: The Counting Test Facility and its Results. A proposal for participation in the Borexino Solar Neutrino Experiment, Princeton, October 1996. Talk presented by P.A. Eisenstein at Baksan International School "Particles and Cosmology" (April 1997). 9. S. Pastor, V.B. Semikoz, J.W.F. Valle, Phys.Lett. B 423 (1998) 118.