Solar Neutrinos II: New Physics

Solar Neutrinos II: New Physics Helioseismology Matter-enhanced neutrino oscillations SNO and Super-Kamiokande Wick Haxton, UC Berkeley and LBL SSI 2010, August 2-10

Cl/Ga/Kamioka measured the three major solar ν fluxes and found they were difficult to reconcile with the SSM!( 8 B) /!( 8 B) SSM 1.0 0.8 0.6 0.4 0.2 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 0.0 0.0 0.2 0.4 0.6 0.8 1.0!( 7 Be) /!( 7 Be) SSM Hata et al. Castellani et al. (and Heeger and Robertson )

Under the assumption that the experiments were measuring EC line sources and continuous β-decay sources with allowed shapes φ(pp) 9.9φ SSM (pp) φ( 7 Be) 0 φ( 8 B) 0.43φ SSM ( 8 B) Steady-state models where the fluxes are largely controlled by the average temperature of the core cannot produce this pattern φ( 8 B) φ(pp) T 23 << φssm ( 8 B) φ SSM (pp) T < T SSM cooler Sun φ( 7 Be) φ( 8 B) T 12 << φssm ( 7 Be) φ SSM ( 8 B) T > T SSM hotter Sun so the pattern is contradictory

In parallel, a second precise probe of the solar interior was being developed: helioseismology, the measurement and analysis of Doppler shifts of photospheric absorption lines. Amplitudes 30m and velocities 0.1m/s. Turbulence within Sun s convective zone acts as a random driver of sound waves propagating through the gas Specific frequencies are enhanced as standing waves -- normal modes whose frequencies depend on solar physics n=14 l=20 m=16 p-mode (acoustic)

How does this probe the SSM? For a spherical star p(r), ρ(r), T(r), s(r), φ gravity (r), ɛ nuclear energy (r) Introduce adiabatic indices describing power-law behavior of p, T with ρ ( ) ( ) logp logt Γ 1 Γ 3 1 logρ logρ Define a total derivative D Dt t Write down the equations for motion: ρ D v continuity: Dt = p ρ φ gravitational potential: 2 φ =4πGρ energy conservation: s + v where F is the energy flux. Static interior solution SSM s Dρ Dt + ρ v =0 1 Dp p Dt Γ 1 Dρ 1 ρ Dt = Γ 3 1 (ρɛ p F ) (internal energy corrected for any work done due to volume change)

Now look for a variation around the SSM solution ρ( r, t) =ρ 0 (r)+ρ ( r, t) where displacements are small, δ( r), v = t δ( r) Plug into the stellar evolution equations (see Balantekin, WH nucl-th9903038) try normal mode solution ρ ( r, t) ρ (r)y lm (θ, φ)e iωt introduce the adiabatic sound speed c, p = 1 Γ 1 ρc 2 and the field Ψ(r) =c 2 ρ δ r and one finds that the equations reduce to a Schroedinger-like form

d 2 Ψ(r) dr 2 + 1 c 2 [ω 2 ω 2co l(l + 1)c2 r 2 (1 N 2 ω 2 )] Ψ(r) 0 ω 2 eff>0 propagating ω 2 eff<0 damped an eigenvalue problem, governed by two frequencies ( Gm(r) 1 dlog p the bouyancy frequency N(r) = r Γ 1 dr acoustic cutoff frequency propagating modes are those where one does not see a change in the density over a wavelength p-modes: surface modes, different modes propagate to different depths depending on l dlog ρ dr vanishes in the convective zone, constant in radiative zone ω co = c 2H ) 1 2 dh dr where H 1 = 1 ρ N =0, ω > ω co, ω > l(l + 1)c2 r 2 dρ dr

the turning-point defined by ω 2 ωco 2 l(l + 1) = c(r)2 r 2 so large-l acoustic modes (p-modes) less penetrating similar arguments for the gravity modes, those that propagate in the radiative zone, controlled by the bouyancy frequency ( ω < N guarantees propagation at sufficiently small r): difficult to see, because the surface is in the forbidden region

sound speed c(r) derived from mode inversion, compared to SSM Bahcall: agreement at 0.2% over 80% of Sun a more severe test than the νs

The neutrino flux discrepancy -- the fact it was not compatible with any adjustment of T in steady-state solar models --combined with the SSM success in helioseismology made a new-physics solution more credible Another development that changed viewpoints was a theoretical step, the recognition that solar matter could enhance ν oscillations

Vacuum flavor oscillations: mass and weak eigenstates flavor states ν e > ν L > m L ν µ > ν H > m H mass states Noncoincident bases oscillations down stream: 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 (some cheating here: wave packets)

Can slightly generalize this yielding vacuum mν 2 matrix

solar matter generates a flavor asymmetry a) b) e e,n e e e Z 0 W - e,n e e modifies forward scattering amplitude explicitly dependent on solar electron density makes the electron neutrino heavier at high density

inserting this into mass matrix generates the 2-flavor MSW equation or equivalently the mν 2 matrix s diagonal elements vanish at a critical density

Alternately this in terms of local mass eigenstates observe: mass splittings small at ρc: avoided level crossing at high density if vacuum θ small, in vacuum thus there is a local mixing angle θ(x) that rotates from as

(x) /2 H> e> (x) v H> > m i 2 2E L> > L> e> (x c ) 0

it must be that if derivative gentle (change in density small over one local oscillation length) we can ignore: matrix then diagonal, easy to integrate most adiabatic behavior is near the crossing point: small splitting large local oscillation length can see density gradient derivative at governs nonadiabatic behavior (Landau Zener) so

0.08 (r)/ (0) 0.07 0.06 0.05 sin 2 2 = 0.005 r c nonadiabatic m 2 /E=10-6 ev 2 /MeV 0.32 0.34 0.36 r (units of r ) (r)/ (0) 1.0 0.8 0.6 0.4 0.2 0.0 r c 0.0 0.2 0.4 0.6 0.8 1.0 r (units of r ) we can do this problem analytically

ϒc >> 1 adiabatic, so strong flavor conversion ϒc << 1 nonadiabatic, little flavor conversion so two conditions for strong flavor conversion: sufficient density to create a level crossing adiabatic crossing of that critical density MSW mechanism is about passing through a level crossing

Survival Probability Survival Probability 1.0 0.8 0.6 0.4 0.2 0.0 1.0 - - 0.8 0.6 0.4 0.2 0.0-20 - 10 0 10 20 R Mathematica HW problem a) vacuum oscillations θ=15 R from -20 to +20 R in units of b) matter oscillations add normalize so that crossing occurs at R = 0 note ν e ρ e (R) 1 2 π 4E cos 2θ δm 2 sin 2 2θ arctan ar ρ e (R) 0 as R So is produced as a heavy eigenstate, then propagates toward the vacuum, where it is the light eigenstate

10-4 solving the solar neutrino problem m 2 /E (ev 2 /MeV) 10-6 no level crossing!<<1 nonadiabatic Flavor conversion here pp 7 Be 8 B 10-8 10-4 10-2 1 sin 2 2 v Monday, July 6, 2009

10-4 no level crossing m 2 /E (ev 2 /MeV) 10-6 nonadiabatic pp 7 Be Low solution 8 B 10-8 10-4 10-2 1 sin 2 2 v Monday, July 6, 2009

10-4 no level crossing pp 7 Be Small angle solution m 2 /E (ev 2 /MeV) 10-6 8 B nonadiabatic 10-8 10-4 10-2 1 sin 2 2 v Monday, July 6, 2009

10-4 no level crossing pp 7 Be 8 B Large angle solution m 2 /E (ev 2 /MeV) 10-6 10-8 nonadiabatic this is the solution matching SNO and SuperK results + Ga/Cl/KII tan 2! v 10-4 10-2 1 sin 2 2 v Monday, July 6, 2009

1.0 distinctive energy-dependent suppression 0.8 P(E ) 0.6 0.4 Borexino Super-Kamiokande and SNO sin 2 2 = 0.006 0.2 sin 2 2 = 0.6 0.0 5 10 E (MeV)

Neutrino oscillations had been one of the early suggestions for solving the solar neutrino puzzle (Pontecorvo) -- but the apparent need for nearly complete mixing of three neutrino species to produce the needed factorof-three reduction in the Cl counting rate seemed a stretch. The known quark mixing angles are small. The MSW mechanism provided a means for suppressing the flux even if the mixing angle were small; and the energy-dependent reductions that the data seemed to demand.!( 8 B) /!( 8 B) SSM 1.0 0.8 0.6 0.4 0.2 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 0.0 0.0 0.2 0.4 0.6 0.8 1.0!( 7 Be) /!( 7 Be) SSM By the mid-1980s planning was underway for two next-generation experiments to resolve the solar neutrino puzzle, Super-Kamiokande and SNO

SK increase in fiducial volume (from 0.68 to 22 ktons) provided the potential to see spectrum distortions or day-night matter effects -- reconstructed from spectrum of scattered electrons in ν e (ν x )+e ν e(ν x)+e

BC501312+C, "#$%%%&'()&*+,-&./00&.12+0&-+3405 678&$ '9&:5;<&&''78&=>?2 "1@2+0A& F?-! -/2 *1->C1G/>1?2

SKI (1996 ), SKII (2002 ), SKIII (2006 ), SKIV (2008 ) φ( 8 B) = [ 2.38 ± 0.05(stat) +0.16 0.15 (sys)] 10 6 cm 2 s 1 SKII δ(day/night) = 6.3 ± 4.2(stat) ± 3.7(sys)% Ratio of SKII observed to SSM energy spectrum. Purple: 1σ level of energy-correlated systematic errors.

D1(*$#6&1(1E))-= #:;777)*<'$(=>?>&@ 2!)*"A 2 B*C*?/"./)D"EFG/ ;< B!"#$%&'()*%+'" vacuum region matter-enhanced region : ;&-2(#5.-"&82$3(5282-# <+&2%$3#.7&37$##25.-/= >32-3.#.42&#"&$%%&! '%$4"53? Low-energy turnup predicted is potentially a 10% effect, detectable with proper attention to energycorrelated systematic errors, and with a reduced threshold A$BCD;0<,B0! @27".%&2%27#5"-&2-25/+ F#6G'H= &'%#($#)''#*(+#,'#-.)(/! @27".%&$-/%2&52%$#.42&#"&#02&1(- $&''()#*(+,'-.,-/*/0/*1 H&IJ&K&L(JL$*! :$(;,<$=>?;$<@$!!"#$%&'%()! *$+,-./0#! 12$3"-$%&'%()&4$5.$#."-! 1627#5(8&9.3#"5#."-& Year!"#$% &'%()*+ (%$,-'$% "#$%, &'()(*+), 0(-+), G$(; @//4106*-. $(8A0+3+7..BC$DDD.E(8F*)9467.2+3+2 "#$% &'()(*+),!(-+), "#$%%.'()(*+), /(-+), &'%()*+."(%$"-/0 "#$%%% &'()(*+),!(-+),!0(!+),!"#$%&'()**+,-*./ 01 2//3*)**41&-(5$-61&()*78!942//3!

Sudbury Neutrino Observatory Suggested by Herb Chen in mid-1980s: replacement of the ordinary water in a Cerenkov detector with heavy water Provides three complementary detection channels reaction detected 1) ν x + e ν x + e scattered electron 2) ν e + D p + p + e produced electron 3) ν x + D p + n + ν x produced neutron 1) isolated from the forward-peaking of the scattering: energy shared among outgoing leptons -- sensitive to ν e s, reduced sensitive to ν µ,τ s 2) detected by the scattered electron, hard spectrum with E e E ν 1.44 MeV, as GT strength concentrated near threshold; angular distribution 1 1/3 cos θ ; only sensitive to ν e s

3) detected by capture of the produce neutron: total cross section measured; sensitive equal to νs of any flavor

Detection of electrons weakly correlated with direction, and especial of neutrons, placed exception requirements on background reduction cavity at exceptional depth of 2 kilometers to reduce muons construction under cleanroom conditions: tiny quantities of dust in 12-story cavity would have produced neutrons above the expected solar rate, 8/day Experiment proceeded in three phases, depending on the neutral current detection scheme capture on deuterium d(n, γ) producing a 6.25 MeV γ Phase I capture on 2 tons of dissolved salt: 35 Cl(n, γ) 8.6 MeV energy release Phase II capture in 3 He proportional counters Phase III Recent low-energy re-analysis of Phases I and II, reaching to electron kinetic energies of 3.5 MeV

s -1 ) 6 cm -2 (10! µ" 8 7 6 5 4 3 2 1 SNO! ES SNO! CC SNO! NC! SSM 0 0 1 2 3 4 5 6! e 6 (10-2 cm -1 s ) Figure 2: Flux of 8 B solar neutrinos is divided into ν µ /ν τ and ν e flavors by the SNO analysis. The diagonal bands show the total 8 B flux as predicted by the SSM (dashed lines) and that measured with the NC reaction in SNO (solid band). The widths of these bands represent the ±1σ errors. The bands intersect in a single region for φ(ν e ) and φ(ν µ /ν τ ), indicating that the combined flux results are consistent with neutrino flavor transformation assuming no distortion in the 8 B neutrino energy spectrum.

SNO thus definitively resolved the solar neutrino problem The detector is dismantled, making space for SNO+, but the analysis continues. The best-fit combined-analysis two-flavor parameters are δm 2 12 =7.59 +0.20 0.21 10 5 ev 2 θ 12 = 34.06 +1.16 0.84 degrees The SSM was found to be consistent with the measurements ( ) φ( 8 B) = 5.046 +0.169 0.152 (stat)+0.107 0.123 (syst) 10 6 cm 2 s 1 BPS08(OP; GS) 5.95 10 6 cm 2 s 1 BPS08(OP; AGS) 4.72 10 6 cm 2 s 1 ``I was called right after the[sno] announcement was made by someone from the New York Times and asked how I felt. Without thinking I said `I feel like dancing I'm so happy.'... It was like a person who had been sentenced for some heinous crime, and then a DNA test is made and it s found that he isn t guilty. That s exactly the way I felt. JNB