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Neutrino chirality-flip L R in the sup ernova core Could sterile R 's stimulate the sup ernova explosion?

Dirac neutrino magnetic moment and the dynamics of a supernova explosion
Alexander Okrugin
Yaroslavl State (P. G. Demidov) University, Division of Theoretical Physics

August 20, 2009
14th Lomonosov Conference on Elementary Particle Physics Moscow State University, Moscow In collaboration with A. Kuznetsov and N. Mikheev Based on the paper: JETP Letters 89, 97 (2009) arXiv:0903.2321[hep-ph]
A. Kuznetsov, N. Mikheev, A. Okrugin Neutrino magnetic moment and the sup ernova explosion


Neutrino chirality-flip L R in the sup ernova core Could sterile R 's stimulate the sup ernova explosion?

Outline

1

Neutrino chirality-flip L R in the supernova core Neutrino magnetic moment The rate of the R creation Could sterile R 's stimulate the supernova explosion? Two-step conversion of the neutrino helicity L R L The resonant transition R L

2

A. Kuznetsov, N. Mikheev, A. Okrugin

Neutrino magnetic moment and the sup ernova explosion


Neutrino chirality-flip L R in the sup ernova core Could sterile R 's stimulate the sup ernova explosion?

Neutrino magnetic moment The rate of the R creation

Neutrino magnetic moment

Nonvanishing neutrino magnetic moment leads to chirality-flipping processes L R + , L + R ,

where the left-handed Dirac neutrinos produced in the stellar interior convert into right-handed ones, i.e. sterile with resp ect to the weak interaction, and this can be important e.g. for the stellar energy-loss. How large the neutrino magnetic moment could b e?

A. Kuznetsov, N. Mikheev, A. Okrugin

Neutrino magnetic moment and the sup ernova explosion


Neutrino chirality-flip L R in the sup ernova core Could sterile R 's stimulate the sup ernova explosion?

Neutrino magnetic moment The rate of the R creation

Neutrino magnetic moment

In the standard model with the neutrino mass m , the neutrino magnetic moment is unobservably small (Lee, Shrock, 1977; Fujikawa, Shrock, 1980): µ
(S M )

=

3e GF m 8 2 2



= 3.20 â 10-19

m 1 eV

µB ,

where µB = e/2me is the Bohr magneton. Nontrivial extensions of the standard model such as left-right symmetry can lead to more significant values for the neutrino magnetic moment.

A. Kuznetsov, N. Mikheev, A. Okrugin

Neutrino magnetic moment and the sup ernova explosion


Neutrino chirality-flip L R in the sup ernova core Could sterile R 's stimulate the sup ernova explosion?

Neutrino magnetic moment The rate of the R creation

Neutrino magnetic moment

Several indep endent b ounds were obtained Reactor experiment (Wong e.a., TEXONO Collab., 2007): µ < 0.74 â 10-10 µB ,

Solar neutrino physics (Cisneros, 1971; Voloshin, Vysotsky, Okun, 1986, etc.): µ < 10-10 µB , Early Universe (Fukugita, Yazaki, 1987): µ < 6.2 â 10-11 µB .

Neutrino energy-loss in low-mass red giants (Raffelt, 1990): µ < 3 â 10-12 µB .

A. Kuznetsov, N. Mikheev, A. Okrugin

Neutrino magnetic moment and the sup ernova explosion


Neutrino chirality-flip L R in the sup ernova core Could sterile R 's stimulate the sup ernova explosion?

Neutrino magnetic moment The rate of the R creation

Neutrino chirality-flip L R in the supernova core
Neutrino magnetic moment spin-flipping processes in the supernova core: L R R 's being sterile fly away from the core leaving no enough energy to explain the observed luminosity of the supernova upper bound on the neutrino magnetic moment. SN1987A, R. Barbieri and R. N. Mohapatra (1988): the neutrino spin-flip via both L e- R e- and L p R p processes. From the R luminosity upper limit QR < 1053 erg/s, the upper bound on the neutrino magnetic moment was established : µ < (0.2 - 0.8) â 10-11 µB . However, the essential plasma polarization effects in the photon propagator were not considered comprehensively. An ad ho c photon thermal mass was inserted instead.
A. Kuznetsov, N. Mikheev, A. Okrugin Neutrino magnetic moment and the sup ernova explosion


Neutrino chirality-flip L R in the sup ernova core Could sterile R 's stimulate the sup ernova explosion?

Neutrino magnetic moment The rate of the R creation

Neutrino chirality-flip L R in the supernova core
Later on, A. Ayala, J. C. D'Olivo and M. Torres (1999) used the formalism of the Thermal Field Theory to take into account the influence of hot dense astrophysical plasma on the photon propagator. The upper bound for the neutrino magnetic moment was improved by them in the factor of 2: µ < (0.1 - 0.4) â 10-11 µB . However, looking at the intermediate analytical results by the authors, we conclude that only the contribution of plasma electrons was taken into account there, while the proton fraction was omitted. Moreover, they took an unrealistic value for the volume V 8 â 1018 cm3 . Thus, the reason existed to reconsider the neutrino spin-flip pro cesses in the sup ernova core more attentively.

A. Kuznetsov, N. Mikheev, A. Okrugin

Neutrino magnetic moment and the sup ernova explosion


Neutrino chirality-flip L R in the sup ernova core Could sterile R 's stimulate the sup ernova explosion?

Neutrino magnetic moment The rate of the R creation

Neutrino chirality-flip L R in the supernova core
How many right-handed neutrinos can b e produced in the sup ernova core? It is necessary to calculate the rate of creation of the right-handed neutrino in the processes L R + , L + R .
L R


J
em

em

Here, J is an electromagnetic current in the general sense, formed by different components of the medium. The technics of calculations is rather standard. The only principal point is to use the photon propagator G (q ) with taking account of the plasma polarization effects.
A. Kuznetsov, N. Mikheev, A. Okrugin Neutrino magnetic moment and the sup ernova explosion


Neutrino chirality-flip L R in the sup ernova core Could sterile R 's stimulate the sup ernova explosion?

Neutrino magnetic moment The rate of the R creation

The rate of the R creation

The rate of creation R (E ) of the right-handed neutrino L R ± was recalculated in our paper (JCAP, 2007). The function R (E ) determines the spectrum of the right-handed neutrino energies, i.e. the number of R 's emitted per 1 MeV of the neutrino energy spectrum, per unit time, from the unit volume of the supernova core:
dnR dE

=

E2 2 2

R (E ) .

A. Kuznetsov, N. Mikheev, A. Okrugin

Neutrino magnetic moment and the sup ernova explosion


Neutrino chirality-flip L R in the sup ernova core Could sterile R 's stimulate the sup ernova explosion?

Neutrino magnetic moment The rate of the R creation

The rate of the R creation

The function R (E ) also determines the spectral density of the right-handed neutrino luminosity (i.e. the right-handed neutrino emissivity) of the supernova core:
dLR dE

=V

dnR dE

E=V

E3 2 2

R (E ) ,

where V is the volume of the area emitting neutrinos.

A. Kuznetsov, N. Mikheev, A. Okrugin

Neutrino magnetic moment and the sup ernova explosion


Neutrino chirality-flip L R in the sup ernova core Could sterile R 's stimulate the sup ernova explosion?

Neutrino magnetic moment The rate of the R creation

The rate of the R creation

The strong domination of the neutrino scattering on protons was found. This effect was missed in previous investigations, where a numb er of created right-handed neutrinos was underestimated essentially. We have obtained a new upper bound on the neutrino magnetic moment from the SN1987A neutrino luminosity: µ < (0.7 - 1.5) â 10-12 µB .

A. Kuznetsov, N. Mikheev, A. Okrugin

Neutrino magnetic moment and the sup ernova explosion


Neutrino chirality-flip L R in the sup ernova core Could sterile R 's stimulate the sup ernova explosion?

Neutrino magnetic moment The rate of the R creation

The energy spectrum of the R luminosity
/dE [erg/(s · MeV)]â10- dL

R

49

2.5 2.0 1.5

1.0

0.5 0

0

100

200
E [MeV]

300

400

The energy spectra of the right-handed neutrino luminosity for the plasma temperatures T = 35 MeV (bold), 25 MeV (dashed), 15 MeV (dash-dotted), 5 MeV (dotted), and for µ = 3 â 10-13 µB .
A. Kuznetsov, N. Mikheev, A. Okrugin Neutrino magnetic moment and the sup ernova explosion


Neutrino chirality-flip L R in the sup ernova core Could sterile R 's stimulate the sup ernova explosion?

Neutrino magnetic moment The rate of the R creation

Bounds On The Neutrino Magnetic Moment From The SN Neutrino Luminosity
Uniform ball model for th SN core: µ < (0.7 - 1.5) â 10-12 µB . The recent model of the O-Ne-Mg core collapse SN: µ < 2.4 â 10-12 µB (H.-Th. Janka with collaborators, 2009). ¯ Earlier µ < 2 ¯ µ < 1 ¯ µ < 1 ¯ models of the .7 â 10-12 µB .2 â 10-12 µB .1 â 10-12 µB SN explosion: (R. Buras et al., 2006); (J. A. Pons et al., 1999); (W. Keil and H.-Th. Janka, 1995).

(See poster: A. Kuznetsov, N. Mikheev, A. Okrugin. Reexamination Of A Bound On The Dirac Neutrino Magnetic Moment From The Supernova Neutrino Luminosity.)
A. Kuznetsov, N. Mikheev, A. Okrugin Neutrino magnetic moment and the sup ernova explosion


Neutrino chirality-flip L R in the sup ernova core Could sterile R 's stimulate the sup ernova explosion?

Two-step conversion of the neutrino helicity L R L The resonant transition R L

Could sterile R 's stimulate the supernova explosion?
We will show that the obtained R luminosity is large enough to influence essentially on the supernova explosion dynamics. In a mo delling of the supernova explosion, two main problems arise. The mechanism of the damp ed shock wave stimulation has not been developed completely yet.

0
A. Kuznetsov, N. Mikheev, A. Okrugin Neutrino magnetic moment and the sup ernova explosion


Neutrino chirality-flip L R in the sup ernova core Could sterile R 's stimulate the sup ernova explosion?

Two-step conversion of the neutrino helicity L R L The resonant transition R L

Could sterile R 's stimulate the supernova explosion?
We will show that the obtained R luminosity is large enough to influence essentially on the supernova explosion dynamics. In a mo delling of the sup ernova explosion, two main problems arise. The mechanism of the damp ed shock wave stimulation has not been developed completely yet. Even in the case of the "successful" theoretical supernova explosion, the energy release turns out to be essentialy less than the observed kinetic energy of the envelope 1051 erg (FOE problem).

A. Kuznetsov, N. Mikheev, A. Okrugin

Neutrino magnetic moment and the sup ernova explosion


Neutrino chirality-flip L R in the sup ernova core Could sterile R 's stimulate the sup ernova explosion?

Two-step conversion of the neutrino helicity L R L The resonant transition R L

Could sterile R 's stimulate the supernova explosion?

It is necessary for the self-consistent description of the explosion dynamics, that the neutrino flux, outgoing from the supernova core, could transfer by some mechanism the energy 1051 erg to the supernova envelope. In fact, the known mechanisms do not fill the deficit (several) â 1050 erg.

A. Kuznetsov, N. Mikheev, A. Okrugin

Neutrino magnetic moment and the sup ernova explosion


Neutrino chirality-flip L R in the sup ernova core Could sterile R 's stimulate the sup ernova explosion?

Two-step conversion of the neutrino helicity L R L The resonant transition R L

Two-step conversion of the neutrino helicity L R L
The mechanism first proposed by A. Dar, 1987, with the neutrino magnetic moment being not too small. A part of left-handed electron neutrinos e produced in the collapsing supernova core could convert into right-handed neutrinos due to the interaction of the neutrino magnetic moment with plasma electrons and protons. These eR 's (sterile to the weak interaction), freely escape from the central part of the supernova, if the neutrino magnetic moment is not too large, µ < 10-11 µB .

A. Kuznetsov, N. Mikheev, A. Okrugin

Neutrino magnetic moment and the sup ernova explosion


Neutrino chirality-flip L R in the sup ernova core Could sterile R 's stimulate the sup ernova explosion?

Two-step conversion of the neutrino helicity L R L The resonant transition R L

Two-step conversion of the neutrino helicity L R L

In the supernova envelope, a part of these neutrinos can flip back to eL 's due to the interaction of the neutrino magnetic moment with a magnetic field, which could achieve the critical value Be = m2 /e 4.41 â 1013 G. e These eL 's being absorbed in b eta-pro cesses, e n e- p, can transfer an additional energy to the supernova envelope.

A. Kuznetsov, N. Mikheev, A. Okrugin

Neutrino magnetic moment and the sup ernova explosion


Neutrino chirality-flip L R in the sup ernova core Could sterile R 's stimulate the sup ernova explosion?

Two-step conversion of the neutrino helicity L R L The resonant transition R L

The equation of the neutrino helicity evolution
The equation of the helicity evolution of the neutrino with a magnetic moment in an external uniform magnetic field (Voloshin, Okun, 1986) i
t

R L

^ = E0 +

0 µ B



µ B CL

R L

,

µ is the neutrino magnetic moment, B is the transverse component of the magnetic field, CL is the additional energy of eL in medium: CL =
3 F G 2 mN

Ye + 4 Y 3

e

-

1 3

.

n

e,p,

e

/mN = nB is the nucleon density, Ye = ne /nB = np /nB , Ye = ne /nB , are the densities of electrons, protons and neutrinos.
Neutrino magnetic moment and the sup ernova explosion

A. Kuznetsov, N. Mikheev, A. Okrugin


Neutrino chirality-flip L R in the sup ernova core Could sterile R 's stimulate the sup ernova explosion?

Two-step conversion of the neutrino helicity L R L The resonant transition R L

The resonant transition R

L

The additional energy of left-handed neutrinos CL deserves a special analysis CL =
3 F G 2 mN

Ye + 4 Y 3

e

-

1 3

.

The possibility exists for this value to be zero just in the region of the supernova envelope between the neutrinosphere and the sho ck-wave stagnation area, R < R < Rs . And this is the condition of the resonant transition R L . The neutrino density Ye in the supernova envelope can be neglected, and the condition of the resonance takes the form Ye = 1/3.

A. Kuznetsov, N. Mikheev, A. Okrugin

Neutrino magnetic moment and the sup ernova explosion


Neutrino chirality-flip L R in the sup ernova core Could sterile R 's stimulate the sup ernova explosion?

Two-step conversion of the neutrino helicity L R L The resonant transition R L

The resonant transition R

L

The values Ye in the supernova envelope, typical for the collapsing matter, are: Ye 0.4­0.5. The shock wave causes the nuclei dissociation and makes the substance to be more transparent for neutrinos. This leads to the so-called "short" neutrino outburst and consequently to the significiant matter deleptonization in this region. A typical dip arises in the radial distribution of the value Ye , where Ye may fall down to the value 0.1, see e.g. Bethe (1990); Buras et al. (2005).

A. Kuznetsov, N. Mikheev, A. Okrugin

Neutrino magnetic moment and the sup ernova explosion


Neutrino chirality-flip L R in the sup ernova core Could sterile R 's stimulate the sup ernova explosion?

Two-step conversion of the neutrino helicity L R L The resonant transition R L

The dependence Ye (r)
0.5 Ye 0.4 0.3 0.2 0.1 10 100 r [km] 1000

The dependence Ye (r) about 0.1 to 0.2 s after the shock formation, with the typical dip caused by the "short" neutrino outburst, see e.g. Buras et al. (2005). The dashed line corresponds to the value Ye = 1/3.
A. Kuznetsov, N. Mikheev, A. Okrugin Neutrino magnetic moment and the sup ernova explosion


Neutrino chirality-flip L R in the sup ernova core Could sterile R 's stimulate the sup ernova explosion?

Two-step conversion of the neutrino helicity L R L The resonant transition R L

The resonant transition R

L

A point necessarily exists where Ye = 1/3. Only one such point appears, with dYe /dr > 0. The condition Ye = 1/3 is the necessary but not the sufficient one for the resonant conversion R L . The adiabatic condition: the diagonal element CL should not exceed the nondiagonal element µ B , when the shift is made from the resonance point at the distance oscillations length. This leads to the condition (Voloshin, 1988): µ B
dCL dr 1/2 3 F dYe G 2 mN dr 1/2

.

A. Kuznetsov, N. Mikheev, A. Okrugin

Neutrino magnetic moment and the sup ernova explosion


Neutrino chirality-flip L R in the sup ernova core Could sterile R 's stimulate the sup ernova explosion?

Two-step conversion of the neutrino helicity L R L The resonant transition R L

The resonant transition R

L

The magnetic field value, providing the realization of the resonance condition: B


2.6 â 1012 G

10-12 µB µ

1010 g·cm-3

1/2

d Ye dr

â 108 cm

1/2

.

where the typical values for and dYe /dr in the considered area are taken.

A. Kuznetsov, N. Mikheev, A. Okrugin

Neutrino magnetic moment and the sup ernova explosion


Neutrino chirality-flip L R in the sup ernova core Could sterile R 's stimulate the sup ernova explosion?

Two-step conversion of the neutrino helicity L R L The resonant transition R L

The resonant transition R

L

Thus, the Dar scenario of the two-step conversion of the neutrino helicity, L R L , can b e realized, if the value of the neutrino magnetic moment is in the interval 10-13 µB < µ < 10-12 µB , and under the condition that the magnetic field of the scale (1012 Â 1013 ) G exists in the region R < R < Rs . During the shock wave stagnation time t 0.2­0.4 sec the additional energy can be injected into this region, of the order of E LR t 1051 erg ,

which is just enough for the problem solution.
A. Kuznetsov, N. Mikheev, A. Okrugin Neutrino magnetic moment and the sup ernova explosion


Neutrino chirality-flip L R in the sup ernova core Could sterile R 's stimulate the sup ernova explosion?

Two-step conversion of the neutrino helicity L R L The resonant transition R L

Conclusions
We have analysed quantitatively the two-step conversion of the neutrino helicity, L R L , under the supernova conditions.

A. Kuznetsov, N. Mikheev, A. Okrugin

Neutrino magnetic moment and the sup ernova explosion


Neutrino chirality-flip L R in the sup ernova core Could sterile R 's stimulate the sup ernova explosion?

Two-step conversion of the neutrino helicity L R L The resonant transition R L

Conclusions
We have analysed quantitatively the two-step conversion of the neutrino helicity, L R L , under the supernova conditions. This process could provide an additional energy 1051 erg to be injected into the region between the neutrinosphere and the shock-wave stagnation area, R < R < Rs , during the typical stagnation time of the order of some tenths of a second.

A. Kuznetsov, N. Mikheev, A. Okrugin

Neutrino magnetic moment and the sup ernova explosion


Neutrino chirality-flip L R in the sup ernova core Could sterile R 's stimulate the sup ernova explosion?

Two-step conversion of the neutrino helicity L R L The resonant transition R L

Conclusions
We have analysed quantitatively the two-step conversion of the neutrino helicity, L R L , under the supernova conditions. This process could provide an additional energy 1051 erg to be injected into the region between the neutrinosphere and the shock-wave stagnation area, R < R < Rs , during the typical stagnation time of the order of some tenths of a second. This energy could be sufficient for stumulation of the damp ed sho ck wave.

A. Kuznetsov, N. Mikheev, A. Okrugin

Neutrino magnetic moment and the sup ernova explosion


Neutrino chirality-flip L R in the sup ernova core Could sterile R 's stimulate the sup ernova explosion?

Two-step conversion of the neutrino helicity L R L The resonant transition R L

Conclusions
We have analysed quantitatively the two-step conversion of the neutrino helicity, L R L , under the supernova conditions. This process could provide an additional energy 1051 erg to be injected into the region between the neutrinosphere and the shock-wave stagnation area, R < R < Rs , during the typical stagnation time of the order of some tenths of a second. This energy could be sufficient for stumulation of the damp ed sho ck wave. The conditions for the realization of this scenario appear to be not very rigid. The Dirac neutrino magnetic moment should belong to the interval 10-13 µB < µ < 10-12 µB , and the magnetic field (1012 Â 1013 ) G should exist in the region R < R < Rs .
A. Kuznetsov, N. Mikheev, A. Okrugin Neutrino magnetic moment and the sup ernova explosion