Essential Solar Neutrinos

39 Pages·1.6 MB·

by  C. Giunti

C. Giunti & M. Laveder, ESSENTIAL SOLAR NEUTRINOS 1
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C. Giunti & M. Laveder
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- Neutrino Unbound
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C. Giunti & M. Laveder, ESSENTIAL SOLAR NEUTRINOS 2
Contents
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Contents 2
1 Standard Solar Model n 3
2 Solar Neutrino Bibliography 4
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3 Homestake 7
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N
4 Gallium Experiments: SAGE, GALLEX, GNO 8
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5 SAGE: Soviet-American Gallium Experiment i 8
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6 GALLEX: GALLium EXperiment n n 9
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7 GNO: Gallium Neutrino Observatory 9
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8 Kamiokande 10
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9 Super-Kamiokande - 10
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10 SNO: Sudbury Neutrino Observatory t 12
n i
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11 Main characteristics of solar ν data 14
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12 Solar neutrino transitions f 15
r
n
13 Two-neutrino oscillattions in vacuum and matter 16
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u .
14 Fits of current solar neutrino data 21
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15 ν ν ,ν aellowed regions from Ref. [39] 22
e µ τ t
→
.
16 νe νNµ,ντ allowed regions frwom Ref. [86] 23
→
17 ν ν ,ν allowed regions from Ref. [80] 24
e µ τ w
→
18 KamLAND = LMA 25
⇒ w
19 Fits of reactor + solar neutrino data 26
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20 Allowed reactor + solar region from Ref. [88] 27
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21 Allowed reactor + solar region from Ref. [132] 28
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22tAllowed reactor + solar region from Ref. [40] 29
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23 Allowed reactor + solar region from Ref. [79] 30
Bibliography 31
C. Giunti & M. Laveder, ESSENTIAL SOLAR NEUTRINOS 3
1 Standard Solar Model
Current Standard Solar Model (SSM): BP2000 [46, 28] d
pp and CNO cycles: 4p+2e− 4He+2ν +26.731MeV n
e
→
u
U
2 + (cid:0) 2
(pp) p+p ! H+e +(cid:23)e p+e +op ! H+(cid:23)e (pNep)
99.6%XXXXXXXXXXXX(cid:24)(cid:24)(cid:24)(cid:24)(cid:24)(cid:24)(cid:24)(cid:24)b(cid:24)(cid:24)(cid:24)(cid:24) 0.4% ti/
n n
?
u
2 3
H+p ! UHe+(cid:13)
i
g
85% (cid:24)(cid:24)(cid:24)(cid:24)(cid:24)(cid:24)(cid:24)(cid:24)(cid:24)(cid:24)(cid:24)(cid:24)(cid:24)(cid:24)(cid:24)o(cid:24) (cid:24)(cid:24)XXXXXXtX/X-XXXXXXXXXX 2(cid:2)10(cid:0)5%
n i
? . ?
n
3 3 4 3 4 +
He+ He ! He+2p i He+p ! He+e +(cid:23)e
f
r 15%
ppI n? (hep)
t
3 4 7
He+iHe ! Be+(cid:13)
u .
o
(cid:16)P
(cid:16) P
e (cid:16) P
t(cid:16)(cid:16) PP
(cid:16) P
99.87%(cid:16)(cid:16).(cid:16) PPP0.13%
N w
? ?
7 7 (cid:0) 7 7 8
( Be) Be+we ! Li+(cid:23)e Be+p ! B+(cid:13)
w
? ?
/ 7 4 8 8 (cid:3) + 8
/ Li+p ! 2 He B ! Be +e +(cid:23)e ( B)
:
p
ppII
?
t
t 8 (cid:3) 4
Be ! 2 He
h
ppIII
Figure 1: pp cycle.
C. Giunti & M. Laveder, ESSENTIAL SOLAR NEUTRINOS 4
12 13 - 13 13 + 13
C+p ! N+(cid:13) N ! C+e +(cid:23)e ( N)
d
6
(cid:27)- (cid:24) ?
n
15N+p ! 12C+4He CN ? 13C+p ! 14N+(cid:13)
6
(cid:26)(cid:27) (cid:25)
6 u
99:9% U
?
(15O) 15O ! 15N+e+ +(cid:23)e (cid:27) 14N+p ! 15oO+(cid:13) N
6
0:1% b /
i
?
t
15 16 17 14 4
N+p ! O+(cid:13) nO+p ! N+ He n
6 u
U
?
i
16O+p ! 17F+(cid:13) - 17F ! 17O+ge+ +(cid:23)e (17F)

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Figure 2: CNO cycle. /
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n i
.
Luminosity = (2.400 0.005) 1039MeVs−1
⊙ n
L ± ×
Radius i ⊙ = 6.961 1010cm
Rf ×
Mass r = (1.989 0.003) 1033g
⊙
Mn ± ×
Astronomical Unit 1a.u. = 1.496 1013cm
t
×
Solar Constant K i/4π(1a.u.)2 = 8.534 1011MeVcm−2s−1
u ⊙ ≡.L⊙ ×
o
Table 1: Fundamental characteristics of the Sun and Sun-Earth system [101]. One astronomical unit is the mean sun-earth
e
distance. The solar constant K is the meatn solar photon flux on the Earth.
⊙
.
N w
w
Luminosity Constraint [33]: α Φ = K (r = pp,pep,hep,7Be,8B,13N,15O,17F) (1)
r r ⊙
Xr
w
2 Solar Neutrino Bibliography
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Books: [p153, 30]
Revitews: [70, 163, 136]
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Bhahcall’s Standard Solar Models: [29, 41, 47, 44, 45, 34, 46, 28]
Detection cross sections: [30, 37, 32, 28, 143, 69, 138, 20]
C. Giunti & M. Laveder, ESSENTIAL SOLAR NEUTRINOS 5
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n n
u
(a) Figure from Ref. [70]. U (b) Figure from Ref. [28].
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Figure 3: Energy spectra of neutrino fluxes from the pp and CNO chains, as predicgted by the Standard Solar Model. For
continuous sources, the differential flux is in cm−2s−1 MeV−1. For the lines, the flux is in cm−2s−1. The percentages in
Fig. 3(b) indicate the uncertainties on the values of the fluxes. -
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Figutre 4: Differential fraction df/dR of produced neutrinos as a function of radius R, normalized to the solar radius R .
Fhigure from Ref. [70]. ⊙
C. Giunti & M. Laveder, ESSENTIAL SOLAR NEUTRINOS 6
E Emax α
Source r Reaction h ir r r
(MeV) (MeV) (MeV)
pp p+p d+e+ +ν 0.2668 0.423 0.03 13.09d87
e
→ ±
pep p+e− +p d+ν 1.445 1.445 11.9193
→ e n
hep 3He+p 4He+e+ +ν 9.628 18.778 3.7370
e
→
u
0.3855 0.3855
7Be e− +7Be 7Li+ν 12.6008 U
→ e 0.8631 0.8631
o
8B 8B 8Be∗ +e+ +ν 6.735 0.036 15 6.6305 N
e
→ ± ∼
13N 13N 13C+e+ +νe 0.7063 b1.1982 0.0003 3.4/577
→ ± i
15O 15O 15N+e+ +ν 0.9964 1.7317 0.0005 t21.5706
e
→ n ± n
17F 17F 17O+e+ +ν 0.9977 1.7364 0.0003 2.363
e
→ ± u
U
Table 2: Sources of solar neutrinos [30, 37, 32, 31]. For each reaction r, hEir is the aiverage neutrino energy, Ermax is the
maximum neutrino energy and α is the average thermal energy released together wgith a neutrino from the source r [33],
r
that enters in the luminosity constraint (1).
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Source r (cFmlu−x2sΦ−r1) n (10h−σ4C4lcimr 2) .i(SSNC(rUl)) (10h−σ4G4acimr 2) (SSNG(rUa))
n
pp 5.95 1010(i1 0.01) – – 0.117 0.003 69.7
f
× r± ±
pep 1.40 108(1 0.015) 0.n16 0.22 2.04+0.35 2.8
×t ± −0.14
i
hep u9.3×103 .390 0.04 714−+121248 0.1
o
7Be 4.77 109(1 0.10) 0.024 1.15 0.717+0.050 34.2
e × ± −0.021
t
8B 5.05 106 1+0.20 114 11 5.76 240+77 12.1
× −.0.16 ± −36
N (cid:0)w (cid:1)
13N 5.48 108 1+0.21 0.017 0.09 0.604+0.036 3.4
× −0.17 −0.018
(cid:0) (cid:1)
15O 4.80 w108 1+0.25 0.068 0.001 0.33 1.137+0.136 5.5
× −0.19 ± −0.057
(cid:0) (cid:1)
17F 5.63 106(1 0.25) 0.069 0.0 1.139+0.137 0.1
w × ± −0.057
Total 6.54 1010 7.6+1.3 128+9
/ × −1.1 −7
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Table 3: BP2000 Standard Solar Model [46] neutrino fluxes, average neutrino cross sections [30, 37, 32] and BP2000 SSM
p
predictions for the neutrino capture rates [46] in the chlorine (Cl) Homestake experiment and in the gallium (Ga) GALLEX,
SAGE and GNO experiments.
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C. Giunti & M. Laveder, ESSENTIAL SOLAR NEUTRINOS 7
3 Homestake
radiochemical experiment [29, 77] d
νe +37 Cl 37 Ar+e− [150, 19] n (2)
→
Homestake Gold Mine (Lead, South Dakota, USA)
u
U
1478 m deep, 4200 m.w.e. = Φ 4m−2day−1
µ
⇒ ≃ o
N
steel tank, 6.1 m diameter, 14.6 m long (6 105 liters)
b× /
i
615 tons of tetrachloroethylene (C Cl ), 2.16 1030 atoms of 37Cl (133ttons)
2 4
×
n n
energy threshold: ECl = 0.814MeV = 8B, 7Be, pep, hep
th ⇒ u
U
data taking: 1970–1994, 108 extractions [75] – historyi: [36, 35]
g

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Figure5: Resultsofthe108individualsolarneutrinoobservationsmadewiththeHomestakechlorinedetector. Theproduction
:
rate of 37Ar shown has already had all known sources of nonsolar 37Ar production subtracted from it. The errors shown for
p
individual measurements are statistical errors only and are significantly non-Gaussian for results near zero. The error shown
for the cumulative result is the combination of the statistical and systematic errors in quadrature. Figure from Ref. [75].
t
t
h Rexp = 2.56 0.16 0.16SNU = 2.56 0.23SNU [75] (3)
Cl ± ± ±
RSSM = 7.6+1.3SNU [46, 28] (4)
Cl −1.1
C. Giunti & M. Laveder, ESSENTIAL SOLAR NEUTRINOS 8
4 Gallium Experiments: SAGE, GALLEX, GNO
radiochemical experiments d
νe +71Ga 71Ge+e− [125] n (5)
→
threshold: EGa = 0.233MeV = all ν fluxes (pp, 7Be, 8B, pep, hep, 13N, 15O, 17F)
th ⇒ u
U
SAGE + GALLEX + GNO = Rexp = 72.4 4.7SNU (6)
⇒ Ga ±
o
Standard Solar Model = RSSM = 128+9SNU [46, 28] N (7)
⇒ Ga −7
b /
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5 SAGE: Soviet-American Gallium Experiment
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n n
Baksan Neutrino Observatory, northern Caucasus, 3.5 km from entrance of horizontal adit
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U
50 tons of metallic 71Ga, 2000 m deep, 4700 m.w.e. = Φ i2.6m−2day−1
µ
⇒ g≃

data taking: 1990 – 2001, 92 runs [1, 2-, 5, 6, 7]
o
/
detector test: 51Cr Source (R = 0.95t+0.11+0.06) [3, 4]
n i−0.10−0.05
.
n
i
f
400 r
n
t
i L+K peaks
u . K peak only
300
o
)
U
N e
S t d
e ( . ne
Ne rat 200 w mbi
r o
u c
pt s
a w n
C u
r
100 All
w L
K
/
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:
p 1990 1991 1992 1993 1994 1995 1996 1997 1998 1999 2000 2001
Mean extraction time
t
t
Fhigure 6: Capture rate for all SAGE extractions as a function of time. Error bars are statistical with 68% confidence. The
combined result of all runs in the L peak, the K peak, and both L and K peaks is shown on the right side. The last 3 runs
are still counting and their results are preliminary. Figure from Ref. [7].
RSAGE = 70.8+5.3+3.7SNU = 70.8+6.5SNU [7] (8)
Ga −5.2−3.2 −6.1
C. Giunti & M. Laveder, ESSENTIAL SOLAR NEUTRINOS 9
6 GALLEX: GALLium EXperiment
Gran Sasso Underground Laboratory, Italy, overhead shielding: 3300 m.w.e. d
30.3 tons of gallium in 101 tons of gallium chloride (GaCl -HCl) soluntion
3
data taking: May 1991 – Jan 1997, 65 runs [21, 22, 23, 25, 105, 108]
u
U
detector tests: 51Cr Source (R = 0.93 0.08) [24, 106], 71As Test [107]
o
± N
RGALLEX = 77.5 6.2+4.3SNU = 77.5+7.6SNU [108] (9)
Ga ± −4.7 −7.8b /
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7 GNO: Gallium Neutrino Observatonry n
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successor of GALLEX, GNOU30: 30.3 tons of gallium
i
g
data taking: May 1998 – Jan 2000, 19 runs [18]

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RGNO = 65.8+10.2+3.4SNU = 65.8+10.7/SNU [18] (10)
Ga −9.6 −3.6 −10.2
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Figuret7: GNO and GALLEX single run results. Error bars are statistical only. Open dots represent group mean values; the
boldtsquarerepresentstheglobalresultofGALLEX;theboldsoliddotrepresentstheglobalresultofGNOandGallex. Figure
fhrom Ref. [18].
GALLEX + GNO = RGALLEX+GNO = 74.1 5.4+4.0SNU = 74.1+6.7SNU [18] (11)
⇒ Ga ± −4.2 −6.8
C. Giunti & M. Laveder, ESSENTIAL SOLAR NEUTRINOS 10
8 Kamiokande
real-time water Cherenkov detector ν +e− ν +e− [117, 15d9]
→
Sensitive to ν , ν , ν , but σ(ν ) 6σ(ν ) n
e µ τ e µ,τ
≃
Kamioka mine (200 km west of Tokyo), 1000 m underground, 2u700 m.w.e.
U
3000 tons of water, 680 tons fiducial volume, 948 PMTs
o
N
threshold: EKam 6.75MeV = 8B, hep
th ≃ ⇒ b /
i
t
data taking: Jan 1987 – Feb 1995 (2079 days) [110, 111, 112, 114, 113, 94]
n n
ΦKam = 2.82+0.25 0.27 106cm−2s−1 = 2.82 0.37 106cm−u2s−1 [94] (12)
νe −0.24 ± × U ± ×
Standard Solar Model = Φ8B = 5.05+1.01 106cm−2is−1 [46, 28] (13)
⇒ νe −0.81 × g

-
9 Super-Kamiokande o
/
t
successor of Kamiokande, 50nktons of water, 22.5 kitons fiducial volume, 11146 PMTs
.
n
tihreshold: EKam 4.75MeV = 8B, hep
th ≃ f ⇒
r
n
data taking: 1996 – 2001 (1496 days) [95, 96, 97, 92, 91, 93]
t
i
ΦSK = 2.u348 0.025+0.071 10.6cm−2s−1 = 2.348+0.075 106cm−2s−1 [93] (14)
νe ± −0.061 ×o −0.066 ×
e
t
N w Event/day/kton/binw0.2.5
0.2
w
0.15
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0.1
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p 0.05
t
0
t -1 -0.8 -0.6 -0.4 -0.2 0 0.2 0.4 0.6 0.8 1
cos ΘSun
h
Figure 8: Super-Kamiokande cosθ distribution. The points represent observed data. The histogram shows the best-fit
sun
signal (shaded) plus background. The horizontal dashed line shows the estimated background. Figure from Ref. [155].