Solar Neutrinos: Theory and Connections to other Neutrino Physics

Transcription

1 Solar Neutrinos: Theory and Connections to other Neutrino Physics This began an effort to combine precise weak-interactions/nuclear microphysics with careful modeling of solar evolution. Ultimately the goal would be 1% predictions of quantities like the core temperature that govern pp-cycle branching ratios. Solar neutrino detection would be the experimental test of the model and its microphysics. Based on Bahcall and Davis History of the Solar Neutrino Problem

2 Hertzsprung-Russell diagram T s, L, R simplest stellar properties Stefan-Boltzmann black-body: L = 4πR 2 σts 4 [ ] [ ] 2 [ L R T = L R T ] 4 one-parameter HR trajectory main sequence of H-burning stars to which sun belongs sun a stellar-evolution test case: M, L, R, T s, age, surface composition

3 The Standard Solar Model assumptions sun burns in hydrostatic equilibrium: gravity balanced by gas pressure gradient (need EOS) energy transported: radiation, convection (convective envelope, radiative core) solar energy generated by H fusion 4p 4 He + 2e + + 2ν e T c K E cm 2keV pp chain, CNO cycle boundary conditions: solar age, L, M, R, today s surface composition H : He : Z needed, where Z denotes metals (A 5) assume t=0 sun homogenized Z from today s surface abundances H+He+Z = 1, He/H adjusted to produce today s L

4 been seen: no spectral distortion, no day-night effects due to the earth s matter effects Solar pp chain There are promising strategies p+p 2 + H+e + - p+p+e 2 H+ for 1920s: probing Eddington distortions: 99.75% 0.25% - recognized 2 3 H+p He + solar energy is nuclear 86% 14%! SNO-III ( 3 He counters), He + He He + 2p 1928: with Gamow a better - NC/CC QM tunneling would separation, allow stellar possibly reactions a lower threshold 1930s: Bethe - describes nuclear! reactions, Low-E pp effective neutrino range detectors theory ppi ppii ppiii Weizacker, Bethe, and Critchfield explored 4p He; Bethe and Critchfield - pp chain in 1938; Bethe - CNO cycle in 1939 pp-chain governs energy production in lower-mass main-sequence stars: three competing cycles -- ppi, ppii, ppiii -- each synthesizing He tagged by three distinctive neutrinos probe of core T He + He Be % 0.11% 7 Be + e - 7 Li + 7 Be + p 8 B+ 7 Li + p 2 4 He 8 B 8 Be * +e + +

5 CNO cycle (p,γ) 13 C 14 N (p,γ) (e +,ν) slowest: control ppi ppii ppiii 13 N 15 O (p,γ) (e +,ν) 12 C 15 N (p,α) Hans identified this as the cycle relevant for hotter MS stars C,N,O catalysts for 4p He competes well with pp chain only at the sun s center: T

6 Standard Solar Model properties over 98% of the sun s energy generated through pp cycle -- ppi dominance dynamic sun 44% luminosity rise over past 4.7 Gy 8 B (ppiii) ν flux doubled over past 0.9 Gy ( T 22 ) large composition gradient in 3 He established significant successes correct depth of convective zone solar acoustic oscillations good agreement with helioseismology probing to depth (more later) as implemented by Bahcall and others, the SSM is 1D and static sun s Li depletion large -- no dynamical convection complicated magnetic phenomena of convective zone beyond SSM

7 Solar neutrinos Hans and others were limited by SSM and cross section uncertainties SSM nuclear cross sections had to be measured at much higher energies, extrapolated to give S(0) in 1959 became apparent solar νs might be measurable: a strong path to the ppii/iii cycles Fowler brought John Bahcall to Caltech to work with Iben and Sears cross section ( barn) S-factor (kev-b) He(!,") 7 Be Holgren & Johnston HO59 PA63 NA69 KR82, RO83a OS84 AL84 HI E (MeV) HO59 PA63 NA69 KR82, RO83a with new SSM results and Cl capture cross sections in hand, Bahcall and Davis proposed Cl in 1964; excavation in 1965; first results in 1968 OS84 AL84 HI88 Carmen Angulo n-tof Winter School 2003

8 !( 8 B) /!( 8 B) SSM Cl, Ga, Kamioka experiments: φ(pp) φ SSM (pp) φ( 7 Be) 0 φ( 8 B) 0.43 φ SSM ( 8 B) Using reaction T-dependences Monte Carlo SSMs TC SSM Low Z Low Opacity WIMPs Large S 11 Dar-Shaviv Model Combined Fit 90% C.L. 95% C.L. 99% C.L. SSM 90% C.L. T C Power Law Hata et al !( 7 Be) /!( 7 Be) SSM φ( 8 B) T 22 c φ( 7 Be) φ( 8 B) T 10 c colder sun warmer sun so a contradiction

9 Neutrino oscillations (vacuum) flavor states ν e > ν L > m L ν µ > ν H > m H mass states assume that these bases are not coincident, do an experiment: v e > = cos θ ν L > + sin θ ν H > v µ > = sin θ ν L > + cos θ ν H > νe k > = ν k (x = 0, t = 0) > E 2 = k 2 + m 2 i ν k (x ct, t) > = e ikx [ e ielt cos θ ν L > +e ie H t sin θ ν H > ] ( ) δm < ν µ ν k (t) > 2 = sin 2 2θ sin 2 2 4E t, δm 2 = m 2 H m 2 L ν μ appearance downstream vacuum oscillations

10 Bethe and the MSW mechanism (1987) d ν k (0) >= a e (0) ν e > +a µ (0) ν µ > solar matter generates a flavor asymmetry d a) b) e e,n e d d d Z 0 W - d d e e,n e e explicitly ρ e dependent i d [ ] ae (x) = 1 dx a µ (x) 4E [ δm 2 cos 2θ + 2E 2G F ρ e (x) δm 2 sin 2θ δm 2 sin 2θ 2E 2G F ρ e (x) + δm 2 cos 2θ m 2 ν e = 4E 2G F ρ e (x) makes the electron neutrino heavier at high densi Matter effects on oscillations first discussed by Wolfenstein ] [ ae (x) a µ (x) In 1987 Mikheyev and Smirnov numerically integrated equation large regions of sin 2 2θ - δm 2 plane yielded large suppressions of solar ν flux e ] Bethe: pointed out level crossing at ρ e (x) = ρ c = δm 2 cos 2θ/2E 2G F

11 Solar Core (x) /2 H> e> Solar Surface (x) v H> > m i 2 2E L> > L> e> (x c ) 0

12 Think in terms of local mass (instantaneous) eigenstates: ν(x) >= a H (x) ν H (x) > +a L (x) ν L (x) > i d [ ] ah (x) = 1 [ ] m 2 H (x) iα(x) dx a L (x) 4E iα(x) m 2 L (x) Observe: mass splitting at ρ c small: avoided level crossing ν H ν e in large density limit if vacuum angle is small, ν H ν μ in vaccum Thus there is a local matter angle θ(x) which rotates from π/2 to the vacuum value θ as ρ e (x) goes from infinity 0

13 α(x) must be dρ(x)/dx: so small if density change gentle if small (everywhere), ignore relative to diagonal elements integrate Bethe: P adiab ν e = cos 2θ v cos 2θ i path independent this led Hans to predict a solar neutrino solution with δm ev 2 can generalize: most nonadiabatic region is very near crossing point beat frequency lowest period largest best chance to see dρ/dx derivative at ρ c governs nonadiabatic behavior: Landau-Zener P LZ ν e = cos 2θ v cos 2θ i (1 2P hop ) P hop = e πγ c/2 γ c = sin2 2θ cos 2θ δm 2 2E 1 1 ρ c dρ dx

14 so γ c >> 1 slowly varying density P hop 0 adiabatic crossing allows strong ν e ν μ conversion and γ c << 1 sharply varying density P hop 1 nonadiabatic crossing hops to lower level: no flavor conversion so two conditions necessary for strong flavor conversion a level crossing must occur (θ i π/2) the crossing must be adiabatic

15 0.08 (r)/ (0) sin 2 2 = r c nonadiabatic m 2 /E=10-6 ev 2 /MeV r (units of r )

16 r (units of r ) 1.0 (r)/ (0) r c r (units of r )

17 10-4 no level crossing m 2 /E (ev 2 /MeV) 10-6 γ<<1 Flavor conversion here pp 7 Be 8 B nonadiabatic sin 2 2 v

18 10-4 no level crossing m 2 /E (ev 2 /MeV) 10-6 nonadiabatic pp 7 Be Low solution 8 B sin 2 2 v

19 10-4 no level crossing pp 7 Be Small angle solution m 2 /E (ev 2 /MeV) B nonadiabatic sin 2 2 v

20 10-4 no level crossing pp 7 Be 8 B Large angle solution m 2 /E (ev 2 /MeV) nonadiabatic this is the solution matching SNO and SuperK results + Ga/Cl/KII tan 2 θ v sin 2 2 v

21 e m 2 eff e e g/cm 3 density vacuum

22 10-1 Maltoni et al. "m 2 31 [ev2 ] sin 2! 13

23 Art s talk: SNO and SuperK, KamLAND, K2K, MINOS,... What do we know about masses? m 12 2 (8 ± 1) 10-5 ev 2 m 2 m 2 m 23 2 (2.2 ± 0.8) 10-3 ev 2 ν e ν µ ν τ WMAP + LSSS m i < 1 ev m 3 2 solar~ ev 2 atmospheric ~ ev 2 atmospheric m 2 2 m 2 1 Degenerate or hierarchical schemes allowed within this constraint m 2 2 m solar~ ev 2?? ~ ev 2 m Mohapatra et al., APS study FIG. 3: Neutrino masses and mixings as indicated by the cur

24 !"!!"#$%&'( )&*&'+,$-$#,.!!# /! #$ "! " # = "!# "!$ #!# "!$ #!$! $% #!# " #$ "!# # #$ #!$! $% "!# " #$ #!# # #$ #!$! $% # #$ "!$ "!! $&!" # " $ #!# # #$ "!# " #$ #!$! $% "!# # #$ #!# " #$ #!$! $% " #$ "!$! $& #" $ =! " #$ # #$ "!$ #!$! $%! "!# #!# #!# "!#! "! " # # #$ " #$ #!$! $% "!$ " $ -$)(,01"%&2 "! 3&,-00"-%-'2",(4-% %",#4$,.! #$ %& '()!!$ *.!+!!# $*

25 Neutrino mass may be the first signature of physics at the GUT scale ψ R m D ψ L + h.c. ψc L m L ψ L + ψ R c m Rψ R neither allowed in the minimal standard model ( ) 0 md m light m D m ν = m D ( m D ) R m R a natural explanation of the suppression (m D /m R ) of light ν masses relative to the Dirac scale (m D ) of other SM fermions 60 Λ using m ev 50 MSSM m U(1) D m top 180 GeV 40 m R GeV Mohaptra et al. APS study α i 1 30 SU(2) 20 SU(3) µ (GeV)

26 Great program of future physics has been mapped out determining the absolute scale of neutrino mass: near-term ββ exps. and cosmological tests should reach 50 mev; future efforts to 10 mev measuring the unknown mixing angle θ 13 in reactor or LB off-axis exps. demonstrating that Majorana masses exist in ββ decay distinguishing between the inverted and normal hierarchies in LB or next-generation atmospheric ν studies of subdominant oscillations seeing the effects of the Dirac CP phase in LB exps. once the masses and mixing angles are known, do the nuclear physics to high precision to constrain the Majorana phases in ββ decay includes future solar, supernova experiments to do astro-ν physics

27 Hans s CNO cycle and solar/stellar evolution while CNO cycle is a minor contributor to solar energy, CNO νs are measurable; test core metalicity crucial to solar opacity and SSM key SSM assumption: homogeneity on entering the main sequence current zero-age SSM metals today s solar surface abundances tested in helioseismology: depth of the convective zone sensitive to Z CNO elements also control very early evolution of core: out-ofequilibrium burning keeps core convective for almost 100 My recent improvements in modeling solar atmosphere (3D) have revised surface Z downward by 30%! destroys previous SSM helioseismology concordance and alters other SSM properties

28 Recent precise measurement of the controlling CNO cycle reaction S(0) measured in the Gamow peak, lower by 50%: 1.61± 0.08 kev-b delays point at which CNO cycle will take over from pp chain in hydrogen-burning stars 14 N(p,γ) Lemut et al. (LUNA) lowers CNO ν flux

29 solar-like stars within globular clusters important to formation history of the host galaxy GCs are a standard ruler for the age of the universe post first light new S(0) delays onset of CNO cycle and its steep T 17 dependence: slows evolution along main sequence and onto subsequent RG and He-burning (AGB) tracks, with variable star clocks effect is estimated to be an increase in the ages of the oldest such stars of 0.8 Gy Hans would be delighted by LUNA s exquisite measurement and by its effects on his 67-year-old theory of MS stellar evolution. He would be intrigued by the consequences.