Active-Sterile Neutrino Mixing In Big Bang NucleosynthesisL. Gilbert1, E. Grohs2, G. Fuller2, C. Ott1

1 Department of Astrophysics, California Institute of Technology, Pasadena, California 91125, USA1 Department of Physics, University of California, San Diego, La Jolla, CA 92093, USA

Sterile Neutrinos

The neutrino sector is perhaps the least well-understood aspect of the Standard Model. Multipleexperiments have detected non-Standard Model be-havior – most notably, the reactor anomaly [?], theMiniBoone anomaly, and the gallium anomaly [?] –suggesting the possibility of one or more additionalneutrino species. However, a sterile neutrino at thesame temperature as the active neutrinos – that is,one with a substantial mixing angle – is not consis-tent with the radiation energy density measurementsof the early universe from Planck and WMAP [?].However, there are numerous mechanisms to createa sterile neutrino that does not conflict with currentcosmological bounds.

For instance, such a neutrino could be producedby Mikheyev-Smirnov-Wolfenstein (MSW) resonantconversion of active neutrinos driven by a net lep-ton number [?]. Since this production mechanismrequires adiabaticity, it would only convert low-energy active neutrinos – resulting in a non-thermalspectrum [?]. These neutrinos would also be non-relativistic at much earlier epochs than a thermalsterile neutrino, and could provide a candidate forcold dark matter [?].

Since the n-p ratio at big bang nucleosynthesis(BBN) depends sensitively on the flux of electronneutrinos [?], any conversion between active andsterile neutrinos would affect primordial elementalabundances. Current primordial deuterium mea-surements have an error bar of <2% [?]. This allowsus to probe the weak interactions at the BBN epochwith precision, as described in Smith et al. [?].

Figure 1: The CMB, as imaged by Planck.

MSW-like Mixing

We use a self-consistent treatment of weak interac-tions and neutrino physics through the weak decou-pling, big bang nucleosynthesis, and photon decou-pling epochs as developed in Grohs et al. [?].We consider a swap between electron neutrinos and

sterile neutrinos only, with some adiabaticity para-mater α that determines the fraction of the energybin that is swapped.This adiabaticity parameter is equal to the Landau-Zeener jump probability, as below:

α = PLZ = 1− e−πγ/2 (1)

H =1V

dV

dt

−1tan 2θ (2)

Lresosc = 4πEν

δm2 sin 2θ(3)

γ = 2πH(~c)Lresosc

= 12

1V

dV

dt

−1 δm2

(~c)Eν

sin2 2θcos 2θ

(4)

In order to evaluate H, we must determine the po-tential seen by an electron neutrino (the potentialseen by a sterile being zero). There are two majorcomponents to this potential; the so-called “thermal"term and the density term.We first consider the density term:

H(νs) = 0 (5)

H(νe) = 3√

22GFnb

ye −13

+ (6)√

2GF

2 (nνe − nν̄e) +nνµ − nν̄µ

+ (nντ − nν̄τ)

η = nbnγ

(7)

Le = 2 (nνe − nν̄e) +nνµ − nν̄µ

+ (nντ − nν̄τ)nγ

(8)

nγ = 2ζ(3)T 3

π2 (9)

nb = 2ζ(3)T 3η

π2 (10)

Ye ≈12

(11)

VD ≈2√

2ζ(3)GFT3

π2

Le + η

4

(12)

MSW-like Mixing

We then consider the thermal term, which is basedon two possible interactions.For electron neutrinos only:

VT = −8√

2GFPn3m2

Z

[〈Ee−〉ne− + 〈Ee+〉ne+] (13)

For a neutrino of any flavor,

VT = −8√

2GFPn3m2

W

[〈Eνα〉nνα + 〈Eν̄α〉nν̄α] (14)

Since 〈Eνα〉nνα ∝ T 4 and ε = Eν/T we can writethis in the form:

V = −rαG2FεT

5 (15)So we can write the total potential as:

V = 2√

2ζ(3)GFT3

π2

Le + 32

Ye −13

η

− rαG2FεT

5

(16)We then apply the MSW resonance condition:

V = δm2 cos 2θ2Eν

(17)

m2eff = δm2 cos 2θ = 2εTV (18)

m2eff = 4

√2ζ(3)GFT

4ε

π2

Le + 32

Ye −13

η

(19)

− 2rαG2Fε

2T 6

To satisfy this condition, the following must be true:

4(ζ(3))2GF

π2m2effrαT

2

Le + 32

Ye −13

η

≥ 1 (20)

We are implementing this swap in the BURST codearchitecture. We intend to compare our results tocurrent limits of BBN parameters.

References

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Contact

Lauren Gilbertlgilbert@caltech.edu