ЯДЕРНАЯ ФИЗИКА, 2010, том 73, № 4, с. 640-650
ЭЛЕМЕНТАРНЫЕ ЧАСТИЦЫ И ПОЛЯ
SPIN FLIP OF NEUTRINOS WITH MAGNETIC MOMENT IN CORE-COLLAPSE SUPERNOVA
® 2010 O. V. Lychkovskiy1),2)*, S. I. Blinnikov1),3)
Received July 6, 2009
Neutrinos with magnetic moment experience chirality flips while scattering off charged particles. It is known that if neutrino is a Dirac fermion, then such chirality flips lead to the production of sterile right-handed neutrinos inside the core of a star during the stellar collapse, which may facilitate the supernova explosion and modify the supernova neutrino signal. In the present paper we reexamine the production of right-handed neutrinos during the collapse using a dynamical model of the collapse. We refine the estimates of the values of the Dirac magnetic moment which are necessary to substantially alter the supernova dynamics and neutrno signal. It is argued in particular that Super-Kamiokande will be sensitive at least to Dirac = in case of a galactic supernova explosion. Also we briefly discuss the case
of Majorana neutrino magnetic moment. It is pointed out that in the inner supernova core spin flips may quickly equilibrate electron neutrinos with nonelectron antineutrinos if Majorana ^ 10_12^B. This may lead to various consequences for supernova physics.
1. INTRODUCTION
A straightforward way to account for neutrino masses is to introduce three singlet right-handed neutrinos (one per generation) in addition to three left-handed neutrinos of the Standard Model (SM). This allows to generate neutrino masses in the same way as up-quark masses, i.e. through the standard Higgs mechanism. Neutrinos, as quarks and charged leptons, are Dirac fermions in this case. Neutrino—Higgs vertexes are the only tree level vertexes which include right-handed neutrinos. Tiny neutrino masses imply tiny couplings with Higgs, therefore right-handed neutrinos interact extremely weakly with matter. In other words, they appear to be nearly sterile4). In fact, measurements of the invisible Z-boson decay width (see, e.g., [ 1]) and cosmological considerations (see, e.g., [2]) tell us that there are only three active neutrino species, which are veL, v^l, vtL (along with their antiparticles), and therefore right-handed Dirac neutrinos should be nearly sterile in any extension of the SM (with any additional particles and interactions).
^Institute for Theoretical and Experimental Physics, Moscow, Russia.
2)Moscow Institute of Physics and Technology, Dolgoprudny, Russia.
3)IPMU, University of Tokyo, Japan. E-mail: lychkovskiy@itep.ru
4)Not to be confused with sterile left-handed neutrinos, which may constitute additional lepton generations; we do not consider such neutrinos.
Neutrinos may acquire magnetic moments through the loop diagrams. In the minimal extension of the SM (only three right-handed neutrinos added) magnetic moment of the neutrino mass eigenstate vi is proportional to its mass mi and reads (see [3, 4])
Vi
8\/2-
n2
1 eV
(1)
This value seems to be too small to produce any observable effect. However, a number of extensions of the SM exist in which neutrino magnetic moments are orders of magnitude larger (see one of the pioneering papers [5] and a review [6] with further references therein).
Historically a considerable interest to the possibility of large neutrino magnetic moment was caused by a proposition to explain the Solar neutrino deficit through the neutrino spin precession in the magnetic field of the Sun. The idea was first presented in 1971 [7], and elaborated on in a set of papers [8— 12] in 1986—1987. Later, however, the neutrino flavor mixing was established to be a correct solution of the Solar neutrino problem; as for the spin precession hypothesis, neutrino magnetic moment values which it implied were disfavored by the astrophysical constraints (which are discussed below).
Core-collapse supernova was soon realized to be another astrophysical object for which neutrino magnetic moment could be important. In the beginning of the year 1987 Dar proposed a scenario of supernova explosion based on the two-stage vL ^ vR ^ vL transition of Dirac neutrinos, where the first stage
could occur in the supernova core due to the electromagnetic scattering of neutrinos on charged particles, and the second one — in the supernova envelope due to the neutrino spin precession in the magnetic field of the star [13]. The detection of neutrinos from a nearby supernova SN1987A on February 23, 1987 triggered a bunch of papers [14—17] (see also a related paper [18]), which idea was closely related to the Dar's one. Namely, the supernova core was regarded as a source of right-handed sterile neutrinos, vR, as in [13], but the — transition was assumed to occur in the interstellar magnetic field. It was shown that this could lead to the registration of high-energy neutrino events in terrestrial detectors simultaneously with the ordinary supernova neutrino signal. The absence of such events and the estimation of the supernova core cooling rate due to the sterile neutrino emission was used to put stringent bounds on the neutrino magnetic moment (see Table 1 below). Different aspects of the role of neutrino magnetic moment in the supernova explosion and neutrino emission were further investigated in [19— 22]. In particular, it was pointed out in [19, 20] that a resonant — transition could proceed inside a supernova, which could greatly facilitate the explosion through the Dar's mechanism and under certain circumstances to annul the supernova bounds on the neutrino magnetic moment.
The neutrino magnetic moment could also play a role in the cooling of stars through the plasmon decay in two neutrinos. This was first pointed out as early as 1963 [23]; in this work first astrophysical bound on ¡iv was derived from the cooling rate of the Sun. Later cooling of different types of stars, He burning stars (see, e.g, [24]), white dwarfs (see, e.g., [25]) and red giants (see, e.g., [26]) in particular, was studied to put bounds on the neutrino magnetic moment.
The neutrino magnetic moment should slightly change the neutrino—electron scattering cross section. This fact underlies the laboratory experiments which search for the neutrino magnetic moment. GEMMA [27, 28], Borexino [29] and MUNU [30] experiments currently provide the best limits. The most relevant limits on the neutrino magnetic moment are summarized in Table 1 below.
In the present paper we calculate the supernova core luminosity in right-handed Dirac neutrinos up to 250 ms after the core bounce. We use a dynamical supernova model in contrast with all previous studies [13—17, 31—33]5). Also we use an accurate expression for the spin-flip rate [31, 35] in contrast with the early studies [13—17] and with [32, 33]. We implement our result to refine the estimate of
the energy injected in the supernova envelope in the Dar's scenario. Also we calculate the expected number of high-energy neutrino events in a water Cherenkov detector for a galactic supernova explosion. The above-mentioned advantages of the present study allow us to substantially diminish some of the uncertainties which existed previously.
Although the main subject of the paper is neutrino spin flip due to the Dirac magnetic moment, we also briefly comment upon the case of Majorana magnetic moment. We point out that in this case spin flips may effectively convert electron neutrinos to nonelectron antineutrinos inside the inner supernova core. This may lead to various consequences for supernova physics.
2. RIGHT-HANDED DIRAC NEUTRINO EMISSION FROM SUPERNOVA CORE
Although numerous studies have failed to reproduce an explosion of a core-collapse supernova, there exists a commonly accepted general picture of the collapse, see, e.g., review [36]. When the mass of the iron core of a massive star reaches the Chandrasekhar limit, the infall phase of the collapse starts. The core contracts due to the gravitational attraction. Some fraction of electrons is converted to electron neutrinos through the inverse beta processes. When the density of the inner part of the core reaches the nuclear density value, x 1014 g/cm3, the infalling matter of the outer core bounces from it. A shock wave is created; it propagates outwards increasing the temperature up to tens of MeV and dissociating heavy nuclei into nucleons.
When the densities and temperatures reach extreme values, a fraction of left-handed neutrinos experience spin flips in collisions with charged particles [13]. After the bounce, mainly protons, neutrons and leptons constitute the core, therefore spin flips on electrons and protons play the major role:
vl + e ^ vr + e, vL + p ^ vr + p.
(2)
During a short period of time in the end of the infall (few milliseconds), when the density is high, but the temperature is low, a coherent spin-flip scattering on nuclei may dominate [17]. We believe that its contribution to the total (integrated over hundreds of milliseconds after bounce) right-handed neutrino output is relatively small. Therefore we do not take it into account in the present work.
The rate of the emission of right-handed neutrinos from a supernova core reads
5)In a recent paper [34] dynamical supernova models are employed too.
dN,
vr
dEdt
3 ftOEPHAfl OH3HKA tom 73 № 4 2010
T, MeV
M/MSun
Fig. 1. Temperature inside the supernova core. This figure and Figs. 2—4 are obtained with the aid of the open-code program "Boom" [38]. The mass coordinate on this figure and on Figs. 2—5 is measured in the Sun mass units.
= J <Pr^(E,ne(r,t),nv(r,t),T(r,t)).
Here, dnVR/dEdt is a spin-flip rate, i.e. the number of right-handed neutrinos with energy E emitted per unit energy interval per unit time from unit volume of supernova matter with temperature T(r,t), electron and neutrino number densities ne (r,t) and nv (r,t) correspondingly. The integration is performed over the volume of the supernova core. Note that in the first hundreds of millis
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