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Mass vs flavour eigenstates in neutrino asymmetries
(or when coherence matters)Gabriela BarenboimUniversity of Valencia & IFIC (UV-CSIC)PPAP2018 Hiroshima University
どうもありがとう
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( )
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What about ξ ?One of the open questions in cosmology is the possibility of admitting a largerelic neutrino-antineutrino asymmetry
The trick is there are no direct observations of the cosmicneutrino background…
CMBBBN
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Two flavors
where the same parameterisation applies to the antineutrino system.
For each momentum p, we write down the one-body reduced density matrices ρ and express them in terms of the function P0 and a “polarization” vector P
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- - --
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- - --𝐁𝐁 = sin 2θ , 0, cos 2θ
electron-positrón energy density
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- - --𝐁𝐁 = sin 2θ , 0, cos 2θ
electron-positrón energy density
self-interaction term
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- - --𝐁𝐁 = sin 2θ , 0, cos 2θ
electron-positrón energy density
self-interaction term
where we are ignoring (so far) the collision term which may or may not be relevant
L~
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- - --𝐁𝐁 = sin 2θ , 0, cos 2θ
electron-positrón energy density
self-interaction term
where we are ignoring (so far) the collision term which may or may not be relevant
L~
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Riess et al (2016) vs CMB fitH0 = 73.24 ± 1.74 km/s/Mpc H0 = 67.8 ± 0.9 km/s/Mpc
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BBN constrains Lα
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BBN constrains Lαthe ratio of neutron-proton number densities (depends on weak interaction rate)
See also‘Mon.Not.Roy.Astron.Soc.445 (2014) no.1,778;JCAP 07,011 (2015)’)
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The change of ‘Lνe’ (or‘ξνe’) can be compensated byΔN from νμ,τ -asymmetries
No practical constraint on LTOT as long as the Lα can be adjusted for a right size of Lνe.
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Neutrino oscillations: In the early universe before BBN,
oscillations mix asymmetries of all neutrino flavors before BBN starts.
[ PLB 708 (2012) 1-5 ]
So, the current bound on θ13 applies to all L’s if LTOT is zero
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There is no reason to expect Lμ=Lτ at late timewhen all mixing angles are non-zero as
indicated at many exps.
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Very simple to decipher !!!The evolution of the three flavor system can be brokendown into three separate two flavor systems
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(i) at T=12 MeV when νμ → ντ oscillations cease to be matter suppresed
(ii) at T=5 MeV only if θ13 is non zero
(iii) at T=2 MeV
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G.B,W.H.Kinney & Wanil Park,PRD ’17 [arXiv:1609.01584]
Lμ & Lτ are different and can be large while Le⋘1 for BBN
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It is valid only if neutrino flavor-mixings are absent.It has been conventional even if flavor-mixings were confirmed
several decades ago. What’s wrong with it?
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ΔN(ξα) is missing off-diagonal contributions!
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ΔN(ξα) is missing off-diagonal contributions!
Asymmetries (Li) in mass basis:Neutrinos free-stream after decoupling at T~2 MeV before BBNstarts. Free-streaming neutrinos are in mass-eigenstates.The late-time asymmetries should be diagonal in mass-basis.
ΔN(ξi) contains all contributions!
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Then,manifestly, diagonalization matrix
Asymmetries in mass-basis (diagonal)
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Then,manifestly,
with sub-% level errors.
well-known neutrino mixing matrixdiagonalization matrix
Asymmetries in flavor-basis (non-diagonal)Asymmetries in mass-basis (diagonal)We numerically confirmed
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Lα vs Li (numerical analysis):Lα can be expressed in terms of Li (diagonal entries of Lm).
BBN constraint:
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Set L1 such that
or
two variables to play with !!!
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Conclusions
A large extra radiation contribution (or ΔN) can arise from neutrino asymmetries without disturbing BBN.
The ΔN coming from neutrino asymmetries should be estimated not from flavor-eigenstates but from mass-eigenstates.
Unfortunately the SIMPLEST version (only one degree of freedom) is not the final answer.
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