[PPT] - Constraints on Non-Standard Neutrino Interactions from Borexino PowerPoint Presentation

SLIDE 1

Constraints on Non-Standard Neutrino Interactions from Borexino Phase-II

Chen Sun

Brown University/ CAS-ITP analysis by S. Agarwalla, A. Formozov, E. Meroni, CS, O. Smirnov, T. Takeuchi internally reviewed by Borexino collaboration

Chen Sun (Brown U./ CAS-ITP) Vector Form NSI at Borexino (UMass Amherst) 04/26/2019 1 / 29

SLIDE 2

Probes of New Physics Complementary to Colliders

γ✿

❈▼❇
✷✶ ❝♠
▲②α
▲❙❙
❙◆❡
❈❡♣❤❡✐❞s
✳✳✳

ν✿

❝♦s♠✐❝
s♦❧❛r
❛t♠
♥❡✉tr♦♥ st❛r
❙✉♣❡r♥♦✈❛❡
❜❡❛♠
r❡❛❝t♦r
✳✳✳
r❛✈✐t❛t✐♦♥❛❧ ✇❛✈❡✿
♣r✐♠♦r❞✐❛❧
t♦♣♦❧♦❣✐❝❛❧ ❞❡❢❡❝ts
♣❤❛s❡ tr❛♥s✐t✐♦♥
❜✐♥❛r② ♠❡r❣❡rs
✳✳✳

Chen Sun (Brown U./ CAS-ITP) Vector Form NSI at Borexino (UMass Amherst) 04/26/2019 2 / 29

SLIDE 3

Probes of New Physics Complementary to Colliders

γ✿

❈▼❇
✷✶ ❝♠
▲②α
▲❙❙
❙◆❡
❈❡♣❤❡✐❞s
✳✳✳

ν✿

❝♦s♠✐❝
s♦❧❛r
❛t♠
♥❡✉tr♦♥ st❛r
❙✉♣❡r♥♦✈❛❡
❜❡❛♠
r❡❛❝t♦r
✳✳✳
r❛✈✐t❛t✐♦♥❛❧ ✇❛✈❡✿
♣r✐♠♦r❞✐❛❧
t♦♣♦❧♦❣✐❝❛❧ ❞❡❢❡❝ts
♣❤❛s❡ tr❛♥s✐t✐♦♥
❜✐♥❛r② ♠❡r❣❡rs
✳✳✳

❙♦❧❛r ν✿

♦♥❡ ♦❢ t❤❡ ♠♦st ✐♥t❡♥s❡ ✭❢r❡❡✮ ν ❜❡❛♠s
❡♥✈✐r♦♥♠❡♥t t❤❛t ✐s ❤❛r❞ t♦ ❛❝❤✐❡✈❡ ♦♥ ❊❛rt❤
✉♥✐q✉❡ ❡♥❡r❣② r❛♥❣❡

Chen Sun (Brown U./ CAS-ITP) Vector Form NSI at Borexino (UMass Amherst) 04/26/2019 2 / 29

SLIDE 4

Probes of New Physics Complementary to Colliders

γ✿

❈▼❇
✷✶ ❝♠
▲②α
▲❙❙
❙◆❡
❈❡♣❤❡✐❞s
✳✳✳

ν✿

❝♦s♠✐❝
s♦❧❛r
❛t♠
♥❡✉tr♦♥ st❛r
❙✉♣❡r♥♦✈❛❡
❜❡❛♠
r❡❛❝t♦r
✳✳✳
r❛✈✐t❛t✐♦♥❛❧ ✇❛✈❡✿
♣r✐♠♦r❞✐❛❧
t♦♣♦❧♦❣✐❝❛❧ ❞❡❢❡❝ts
♣❤❛s❡ tr❛♥s✐t✐♦♥
❜✐♥❛r② ♠❡r❣❡rs
✳✳✳

❙♦❧❛r ν✿

♦♥❡ ♦❢ t❤❡ ♠♦st ✐♥t❡♥s❡ ✭❢r❡❡✮ ν ❜❡❛♠s
❡♥✈✐r♦♥♠❡♥t t❤❛t ✐s ❤❛r❞ t♦ ❛❝❤✐❡✈❡ ♦♥ ❊❛rt❤
✉♥✐q✉❡ ❡♥❡r❣② r❛♥❣❡

Pr♦❜❡s✿

■♥♥❡r ✇♦r❦✐♥❣s ♦❢ t❤❡ ❙✉♥ ✭❤✐❣❤✲ ✈s ❧♦✇✲♠❡t❛❧❧✐❝✐t②✮
❜♦✉♥❞✐♥❣ ♥❡✉tr✐♥♦ ♠❛❣♥❡t✐❝ ♠♦♠❡♥t
r❡❥❡❝t✐♥❣ ν ❢r♦♠ ●❲✶✺✵✾✶✹✱ ●❲✶✺✶✷✷✻✱ ●❲✶✼✵✶✵✹ (1706.10176)
❈♦♥str❛✐♥✐♥❣ ♥❡✇ ♣❤②s✐❝s ♠♦❞❡❧ ✐♥❞❡♣❡♥❞❡♥t❧②

← this talk

Chen Sun (Brown U./ CAS-ITP) Vector Form NSI at Borexino (UMass Amherst) 04/26/2019 2 / 29

SLIDE 5

Vector Interaction in EFT – Standard Model W/ Z

−Lνe

CC = GF

√ 2 [¯ νeγµ(1 − γ5)e] [¯ eγµ(1 − γ5)νe] = 2 √ 2GF [¯ νeLγµνeL] [¯ eLγµeL] −Lναe

NC = GF

√ 2 [¯ να(1 − γ5)να] [¯ eγµ(g νe

V − g νe A γ5)e]

= 2 √ 2GF [¯ ναLγµναL] [g νe

L (¯

eLγµeL) + g νe

R (¯

eRγµeR)] ❝♦♠❜✐♥❡s t♦ −Lναe = 2 √ 2GF [¯ ναLγµναL] [gαL(¯ eLγµeL) + gαR(¯ eRγµeR)] ✇✐t❤ gαL = sin2 θW + 1

2

α = e sin2 θW − 1

2

α = µ, τ gαR = sin2 θW α = e, µ, τ ∼ ❧❛r❣❡r ❝♦✉♣❧✐♥❣ ❢♦r νe✱ ✐♥ ❛❞❞✐t✐♦♥ t♦ t❤❡ Pe→e/Pe→x > 1 ∼ ♠♦r❡ ❡✈❡♥ts ∼ ❜❡tt❡r s❡♥s✐t✐✈✐t② ♦❢ geL t❤❛♥ geR t❤❛♥ gτ✳

Chen Sun (Brown U./ CAS-ITP) Vector Form NSI at Borexino (UMass Amherst) 04/26/2019 3 / 29

SLIDE 6

Vector Interaction in EFT – NSI

−Lναe = 2 √ 2GF [¯ ναLγµναL] [gαL(¯ eLγµeL) + gαR(¯ eRγµeR)] −Lναe

NSI = 2

√ 2GF [¯ ναLγµναL] [εαL(¯ eLγµeL) + εαR(¯ eRγµeR)] ❝♦♠❜✐♥❡s t♦ ❣✐✈❡ gαL → gαL + εαL, gαR → gαR + εαR

Chen Sun (Brown U./ CAS-ITP) Vector Form NSI at Borexino (UMass Amherst) 04/26/2019 4 / 29

SLIDE 7

NSI in Effective Operator Picture

❘❡q✉✐r❡♠❡♥t✿

SU(2)W × U(1)Y ✐♥✈❛r✐❛♥t✱
❝♦♥t❛✐♥s (¯

νLγµνL)(¯ eγµe) ■♥❣r❡❞✐❡♥ts✿ Lα = ναL ℓ−

αL

, H =
φ+

φ0

, e−

R

❲❛②s ♦❢ ❝♦♥tr❛❝t✐♥❣ SU(2) ✐♥❞✐❝❡s✿ 1 : [ · · ]

1

1 · ·

,

3 : [ · · ]

1

1 · ·

, [ ·

· ]

−i

i · ·

, [ ·

· ]

1

−1 · ·

Chen Sun (Brown U./ CAS-ITP)

Vector Form NSI at Borexino (UMass Amherst) 04/26/2019 5 / 29

SLIDE 8

NSI in Effective Operator Picture – cont’d

(¯ ναLγµναL)(¯ eRγµeR) t②♣❡✿ hα(1)

0,R

M2 (¯ LαγµLα)(¯ eRγµeR) (¯ ναLγµναL)(¯ eLγµeL) t②♣❡✿ hα(1)

0,L

M2 (¯ LαγµLα)(¯ LeγµLe) hα(3)

0,L

M2 (¯ LασiγµLα)(¯ LeσiγµLe)

Chen Sun (Brown U./ CAS-ITP) Vector Form NSI at Borexino (UMass Amherst) 04/26/2019 6 / 29

SLIDE 9

NSI in Effective Operator Picture – cont’d

(¯ ναLγµναL)(¯ eRγµeR) t②♣❡✿ hα(1)

0,R

M2 (¯ LαγµLα)(¯ eRγµeR) hα(1)

1,R

M2 (H†H) M2 (¯ LαγµLα)(¯ eRγµeR) hα(2)

1,R

M2 H†σiH M2 (¯ LασiγµLα)(¯ eRγµeR) (¯ ναLγµναL)(¯ eLγµeL) t②♣❡✿ hα(1)

0,L

M2 (¯ LαγµLα)(¯ LeγµLe) hα(1)

1,L

M2 (H†H) M2 (¯ LαγµLα)(¯ LeγµLe) hα(2)

1,L

M2 H†σiH M2 (¯ LασiγµLα)(¯ LeγµLe) hα(3)

0,L

M2 (¯ LασiγµLα)(¯ LeσiγµLe) hα(3)

1,L

M2 (H†H) M2 (¯ LασiγµLα)(¯ LeσiγµLe) hα(4)

1,L

M2 (H†σiH) M2 (¯ LαγµLα)(¯ LeσiγµLe) ǫijk hα(5)

1,L

M2 (H†σiH) M2 (¯ LασjγµLα)(¯ LeσkγµLe)

Chen Sun (Brown U./ CAS-ITP) Vector Form NSI at Borexino (UMass Amherst) 04/26/2019 6 / 29

SLIDE 10

−Lν eff = 2 √ 2GF ( ¯ ναγµPLνα)

εαR (¯

eγµPR e) + εαL(¯ eγµPLe)

,

ν − e −L(1) eff = 2 √ 2GF ( ¯ τγµPLτ)

κτR (¯

eγµPR e) + κτL(¯ eγµPLe)

+ (τ → µ) + (τ → e),

charged lepton scattering −L(2) eff = 2 √ 2GF ( ¯ ντ γµPLνe )

ζτL(¯

eγµPLτ) + h.c.

+ (τ → µ),

LFV −L(3) eff = 2 √ 2GF ( ¯ νe γµPLνe )

ξτL( ¯

τγµPLτ) + ξντ L( ¯ ντ γµPLντ )

+ (τ → µ)

unobservable + 2 √ 2GF ξνe L( ¯ νe γµPLνe )( ¯ νe γµPLνe ),

Chen Sun (Brown U./ CAS-ITP) Vector Form NSI at Borexino (UMass Amherst) 04/26/2019 7 / 29

SLIDE 11

−Lν eff = 2 √ 2GF ( ¯ ναγµPLνα)

εαR (¯

eγµPR e) + εαL(¯ eγµPLe)

,

ν − e −L(1) eff = 2 √ 2GF ( ¯ τγµPLτ)

κτR (¯

eγµPR e) + κτL(¯ eγµPLe)

+ (τ → µ) + (τ → e),

charged lepton scattering −L(2) eff = 2 √ 2GF ( ¯ ντ γµPLνe )

ζτL(¯

eγµPLτ) + h.c.

+ (τ → µ),

LFV −L(3) eff = 2 √ 2GF ( ¯ νe γµPLνe )

ξτL( ¯

τγµPLτ) + ξντ L( ¯ ντ γµPLντ )

+ (τ → µ)

unobservable + 2 √ 2GF ξνe L( ¯ νe γµPLνe )( ¯ νe γµPLνe ), where the dimensionless parameters such as εαR(L), καR(L) etc. are to be identified as follows (α = e, µ, τ; β = µ, τ): 2 √ 2GF εαR = 1 M2

hα(1)

0,R + Shα(1) 1,R + Thα(2) 1,R + · · ·

,

2 √ 2GF καR = 1 M2

hα(1)

0,R + Shα(1) 1,R − Thα(2) 1,R + · · ·

,

2 √ 2GF εβL = 1 M2

(hβ(1)

0,L − hβ(2) 0,L ) + S(hβ(1) 1,L − hβ(2) 1,L ) + T(hβ(3) 1,L − hβ(4) 1,L ) + · · ·

,

2 √ 2GF εeL = 2 M2

he(1)

0,L + She(1) 1,L + · · ·

,

2 √ 2GF κβL = 1 M2

(hβ(1)

0,L + hβ(2) 0,L ) + S(hβ(1) 1,L + hβ(2) 1,L ) − T(hβ(3) 1,L + hβ(4) 1,L ) + · · ·

,

2 √ 2GF κeL = 1 M2

he(1)

0,L + She(1) 1,L − The(2) 1,L + · · ·

,

2 √ 2GF ζβL = 2 M2

hβ(2)

0,L + Shβ(2) 1,L + iThβ(5) 1,L + · · ·

,

2 √ 2GF ξβL = 1 M2

(hβ(1)

0,L − hβ(2) 0,L ) + S(hβ(1) 1,L − hβ(2) 1,L ) − T(hβ(3) 1,L − hβ(4) 1,L ) + · · ·

2

√ 2GF ξνβ L = 1 M2

(hβ(1)

0,L + hβ(2) 0,L ) + S(hβ(1) 1,L + hβ(2) 1,L ) + T(hβ(3) 1,L + hβ(4) 1,L ) + · · ·

2

√ 2GF ξνe L = 1 M2

he(1)

0,L + She(1) 1,L + The(2) 1,L + · · ·

c.f. hep-ph/0111137

Chen Sun (Brown U./ CAS-ITP) Vector Form NSI at Borexino (UMass Amherst) 04/26/2019 7 / 29

SLIDE 12

where the dimensionless parameters such as εαR(L), καR(L) etc. are to be identified as follows (α = e, µ, τ; β = µ, τ): 2 √ 2GF εαR = 1 M2

hα(1)

0,R + Shα(1) 1,R + Thα(2) 1,R + · · ·

,

2 √ 2GF καR = 1 M2

hα(1)

0,R + Shα(1) 1,R − Thα(2) 1,R + · · ·

,

2 √ 2GF εβL = 1 M2

(hβ(1)

0,L − hβ(2) 0,L ) + S(hβ(1) 1,L − hβ(2) 1,L ) + T(hβ(3) 1,L − hβ(4) 1,L ) + · · ·

,

2 √ 2GF εeL = 2 M2

he(1)

0,L + She(1) 1,L + · · ·

,

2 √ 2GF κβL = 1 M2

(hβ(1)

0,L + hβ(2) 0,L ) + S(hβ(1) 1,L + hβ(2) 1,L ) − T(hβ(3) 1,L + hβ(4) 1,L ) + · · ·

,

2 √ 2GF κeL = 1 M2

he(1)

0,L + She(1) 1,L − The(2) 1,L + · · ·

,

2 √ 2GF ζβL = 2 M2

hβ(2)

0,L + Shβ(2) 1,L + iThβ(5) 1,L + · · ·

,

2 √ 2GF ξβL = 1 M2

(hβ(1)

0,L − hβ(2) 0,L ) + S(hβ(1) 1,L − hβ(2) 1,L ) − T(hβ(3) 1,L − hβ(4) 1,L ) + · · ·

2

√ 2GF ξνβ L = 1 M2

(hβ(1)

0,L + hβ(2) 0,L ) + S(hβ(1) 1,L + hβ(2) 1,L ) + T(hβ(3) 1,L + hβ(4) 1,L ) + · · ·

2

√ 2GF ξνe L = 1 M2

he(1)

0,L + She(1) 1,L + The(2) 1,L + · · ·

c.f. hep-ph/0111137

For other types of NSI e.g. scalar, light mediator induced, c.f. Tatsu Takeuchi’s talk tomorrow For realizing model building and light mediators, c.f. Bhaskar Dutta’s talk yesterday

Chen Sun (Brown U./ CAS-ITP) Vector Form NSI at Borexino (UMass Amherst) 04/26/2019 7 / 29

SLIDE 13

Constraints on εα

νµ ❈❍❆❘▼ ■■ ✭str♦♥❣✮ ντ ▲❊P νe ▲❙◆❉ ¯ νe ❚❊❳❖◆❖ c.f. Muhammed Deniz’s talk ❲❡ ✇✐❧❧ ❢♦❝✉s ♦♥ ε ❢♦r νe ❛♥❞ ντ✳

Chen Sun (Brown U./ CAS-ITP) Vector Form NSI at Borexino (UMass Amherst) 04/26/2019 8 / 29

SLIDE 14

How NSI manifests at Borexino

R ∼ NeΦν σν

❉❡t❡❝t✐♦♥

dσ dTe ✱ ❞♦♠✐♥❛♥t ❡✛❡❝t

Pr♦♣❛❣❛t✐♦♥

Pee ∼ Φν ✱ s♠❛❧❧ ❡✛❡❝t

Pr♦❞✉❝t✐♦♥

γe → eν¯ ν✱ ✐rr❡❧❡✈❛♥t Eν ≪ 50 keV

Chen Sun (Brown U./ CAS-ITP) Vector Form NSI at Borexino (UMass Amherst) 04/26/2019 9 / 29

SLIDE 15

How NSI manifests at Borexino – Detection

dσα(E, T) dT = 2 π G 2

Fme

g 2

αL + g 2 αR

1 − T

E 2 − gαLgαR meT E 2

,

✇✐t❤ t❤❡ r❡❝♦✐❧ ❦✐♥❡t✐❝ ❡♥❡r❣② 0 ≤ T ≤ Tmax = E 1 + me 2E .

Chen Sun (Brown U./ CAS-ITP) Vector Form NSI at Borexino (UMass Amherst) 04/26/2019 10 / 29

SLIDE 16

How NSI manifests at Borexino – Detection

dσα(E, T) dT = 2 π G 2

Fme

g 2

αL + g 2 αR

1 − T

E 2 − gαLgαR meT E 2

,

gαL → gαL + εαL ❧❡❛❞s t♦ ❛ s❤✐❢t ✐♥ ♥♦r♠❛❧✐③❛t✐♦♥✳ gαR → gαR + εαR ❧❡❛❞s t♦ ❛ s❤✐❢t ✐♥ T ❞❡♣❡♥❞❡♥❝❡✱ ✐✳❡✳ s♣❡❝tr✉♠ ❞✐st♦rt✐♦♥✳

Chen Sun (Brown U./ CAS-ITP) Vector Form NSI at Borexino (UMass Amherst) 04/26/2019 10 / 29

SLIDE 17

How NSI manifests at Borexino – Detection

dσα(E, T) dT = 2 π G 2

Fme

g 2

αL + g 2 αR

1 − T

E 2 − gαLgαR meT E 2

,

gαL → gαL + εαL ❧❡❛❞s t♦ ❛ s❤✐❢t ✐♥ ♥♦r♠❛❧✐③❛t✐♦♥✳ gαR → gαR + εαR ❧❡❛❞s t♦ ❛ s❤✐❢t ✐♥ T ❞❡♣❡♥❞❡♥❝❡✱ ✐✳❡✳ s♣❡❝tr✉♠ ❞✐st♦rt✐♦♥✳ ✶✷✵✼✳✸✹✾✷

♣♦s✐t✐✈❡ ❝♦rr❡❧❛t✐♦♥ ✭♣❛rt✐❛❧

❝❛♥❝❡❧❧❛t✐♦♥✮ ✐♥ εL ❛♥❞ εR σ ∼ g 2

αLTmax − g 2 αRE(1 − Tmax

E )3 − gαLgαR T 2

max

E 2 me

str♦♥❣❡r ❝♦rr❡❧❛t✐♦♥ ❞✉❡ t♦ 85Kr

❜❛❝❦❣r♦✉♥❞ εR ❝❤❛♥❣❡ s❤❛♣❡ ∼ 85Kr ❝♦♠♣❡♥s❛t❡ t❤❡ s❤❛♣❡ ∼ εL ❝♦♠♣❡♥s❛t❡ t❤❡ ♥♦r♠❛❧✐③❛t✐♦♥

Chen Sun (Brown U./ CAS-ITP) Vector Form NSI at Borexino (UMass Amherst) 04/26/2019 10 / 29

SLIDE 18

How NSI manifests at Borexino

R ∼ NeΦν σν

❉❡t❡❝t✐♦♥

dσ dTe ✱ ❞♦♠✐♥❛♥t ❡✛❡❝t

Pr♦♣❛❣❛t✐♦♥

Pee ∼ Φν ✱ s♠❛❧❧ ❡✛❡❝t

Pr♦❞✉❝t✐♦♥

γe → eν¯ ν✱ ✐rr❡❧❡✈❛♥t Eν ≪ 50 keV

Chen Sun (Brown U./ CAS-ITP) Vector Form NSI at Borexino (UMass Amherst) 04/26/2019 11 / 29

SLIDE 19

How NSI manifests at Borexino – Propagation

❊✳❖✳▼✳✿ i d dx νe νµ ντ

= H
νe

νµ ντ

H ✐s ♥♦t ❞✐❛❣♦♥❛❧✱ ❜✴❝ ♣r♦♣❛❣❛t❡ ✐♥ ♠❛ss ❡✐❣❡♥st❛t❡s✳

H = 1 2E U

r♦t✳ ❜❛❝❦

  δm2

21

m2

31

 

♣r♦♣❛❣❛t❡ ❛s eiδm2/2E

U†

f →m

+ √ 2GFNe(x) 1

νe,νµ,τ s❝❛tt❡r ❛t

❞✐✛✳ r❛t❡✱ r❡❢r❛❝t✐♦♥

Chen Sun (Brown U./ CAS-ITP) Vector Form NSI at Borexino (UMass Amherst) 04/26/2019 12 / 29

SLIDE 20

How NSI manifests at Borexino – Propagation

❊✳❖✳▼✳✿ i d dx νe νµ ντ

= H
νe

νµ ντ

H ✐s ♥♦t ❞✐❛❣♦♥❛❧✱ ❜✴❝ ♣r♦♣❛❣❛t❡ ✐♥ ♠❛ss ❡✐❣❡♥st❛t❡s✳

H = 1 2E U

r♦t✳ ❜❛❝❦

  δm2

21

m2

31

 

♣r♦♣❛❣❛t❡ ❛s eiδm2/2E

U†

f →m

+ √ 2GFNe(x)   1 + εV

e

εV

τ

 

νe,νµ,τ s❝❛tt❡r ❛t

❞✐✛✳ r❛t❡✱ r❡❢r❛❝t✐♦♥

εV = εL + εR

Chen Sun (Brown U./ CAS-ITP) Vector Form NSI at Borexino (UMass Amherst) 04/26/2019 12 / 29

SLIDE 21

How NSI manifests at Borexino – Propagation

❊✳❖✳▼✳✿ i d dx νe νµ ντ

= H
νe

νµ ντ

H ✐s ♥♦t ❞✐❛❣♦♥❛❧✱ ❜✴❝ ♣r♦♣❛❣❛t❡ ✐♥ ♠❛ss ❡✐❣❡♥st❛t❡s✳

H = 1 2E U   δm2

21

m2

31

  U† + (1 − εV

τ sin2 θ23 + εV e )

√ 2GFNe(x) 1

εV = εL + εR

◆♦t❡ t❤❛t ε s❤♦✇s ✉♣ ✐♥ ♣r♦♣❛❣❛t✐♦♥ ♦♥❧② ♦♥ t♦♣ ♦❢ ▼❙❲ ❡✛❡❝t✳

Chen Sun (Brown U./ CAS-ITP) Vector Form NSI at Borexino (UMass Amherst) 04/26/2019 12 / 29

SLIDE 22

H = 1 2E U   δm2

21

m2

31

  U† + (1 − εV

τ sin2 θ23 + εV e )

√ 2GFNe(x) 1

◆♦t❡ t❤❛t ε s❤♦✇s ✉♣ ✐♥ ♣r♦♣❛❣❛t✐♦♥ ♦♥❧② ♦♥ t♦♣ ♦❢ ▼❙❲ ❡✛❡❝t✳

❚❤❡r❡❢♦r❡✱ ✇❡ ♥❡❡❞ t♦ ❧♦♦❦ ❛t ✇❤❡r❡ ▼❙❲ ✐s t❤❡ str♦♥❣❡st✳

Chen Sun (Brown U./ CAS-ITP) Vector Form NSI at Borexino (UMass Amherst) 04/26/2019 13 / 29

SLIDE 23

H = 1 2E U   δm2

21

m2

31

  U† + (1 − εV

τ sin2 θ23 + εV e )

√ 2GFNe(x) 1

◆♦t❡ t❤❛t ε s❤♦✇s ✉♣ ✐♥ ♣r♦♣❛❣❛t✐♦♥ ♦♥❧② ♦♥ t♦♣ ♦❢ ▼❙❲ ❡✛❡❝t✳

❚❤❡r❡❢♦r❡✱ ✇❡ ♥❡❡❞ t♦ ❧♦♦❦ ❛t ✇❤❡r❡ ▼❙❲ ✐s t❤❡ str♦♥❣❡st✳

U = 1 c23 s23 −s23 c23

R23

  c13 s13e−iδ 1 −s13eiδ c13  

R13
c12

s12 −s12 c12 1

R12

≈ R23R12 ,

Chen Sun (Brown U./ CAS-ITP) Vector Form NSI at Borexino (UMass Amherst) 04/26/2019 13 / 29

SLIDE 24

H = 1 2E U   δm2

21

m2

31

  U† + (1 − εV

τ sin2 θ23 + εV e )

√ 2GFNe(x) 1

◆♦t❡ t❤❛t ε s❤♦✇s ✉♣ ✐♥ ♣r♦♣❛❣❛t✐♦♥ ♦♥❧② ♦♥ t♦♣ ♦❢ ▼❙❲ ❡✛❡❝t✳

❚❤❡r❡❢♦r❡✱ ✇❡ ♥❡❡❞ t♦ ❧♦♦❦ ❛t ✇❤❡r❡ ▼❙❲ ✐s t❤❡ str♦♥❣❡st✳

U = 1 c23 s23 −s23 c23

R23

  c13 s13e−iδ 1 −s13eiδ c13  

R13
c12

s12 −s12 c12 1

R12

≈ R23R12 , R†

23HR23

≈ 1 2E R12 δm2

21

δm2

31

R†

12 +

√ 2GF Ne(x) R†

23

  1 + εV

e

εV

τ

 R23 = 1 2E   δm2

21s2 12

δm2

21s12c12

δm2

21s12c12

δm2

21c2 12

δm2

31

  + √ 2GF Ne(x) 1 + εV

e − εV τ s2 23

O(ǫ) O(ǫ) O(ǫ)

Chen Sun (Brown U./ CAS-ITP)

Vector Form NSI at Borexino (UMass Amherst) 04/26/2019 13 / 29

SLIDE 25

H = 1 2E U   δm2

21

m2

31

  U† + (1 − εV

τ sin2 θ23 + εV e )

√ 2GFNe(x) 1

◆♦t❡ t❤❛t ε s❤♦✇s ✉♣ ✐♥ ♣r♦♣❛❣❛t✐♦♥ ♦♥❧② ♦♥ t♦♣ ♦❢ ▼❙❲ ❡✛❡❝t✳

❚❤❡r❡❢♦r❡✱ ✇❡ ♥❡❡❞ t♦ ❧♦♦❦ ❛t ✇❤❡r❡ ▼❙❲ ✐s t❤❡ str♦♥❣❡st✳ ◆❡❡❞ ❛ ❢✉rt❤❡r ✶✷ r♦t❛t✐♦♥ R12(φ) ♦♥ t♦♣ ♦❢ t❤❡ ✈❛❝✉✉♠ R12✳ ❘❡s♦♥❛♥❝❡ ❝♦♥✈❡rs✐♦♥✿ θ12 + φ = π/4✱ ✭❧❡✈❡❧ ❝r♦ss✐♥❣ ✐❢ θ12 = 0✳✮

Chen Sun (Brown U./ CAS-ITP) Vector Form NSI at Borexino (UMass Amherst) 04/26/2019 13 / 29

SLIDE 26

H = 1 2E U   δm2

21

m2

31

  U† + (1 − εV

τ sin2 θ23 + εV e )

√ 2GFNe(x) 1

◆♦t❡ t❤❛t ε s❤♦✇s ✉♣ ✐♥ ♣r♦♣❛❣❛t✐♦♥ ♦♥❧② ♦♥ t♦♣ ♦❢ ▼❙❲ ❡✛❡❝t✳

❚❤❡r❡❢♦r❡✱ ✇❡ ♥❡❡❞ t♦ ❧♦♦❦ ❛t ✇❤❡r❡ ▼❙❲ ✐s t❤❡ str♦♥❣❡st✳ ◆❡❡❞ ❛ ❢✉rt❤❡r ✶✷ r♦t❛t✐♦♥ R12(φ) ♦♥ t♦♣ ♦❢ t❤❡ ✈❛❝✉✉♠ R12✳ ❘❡s♦♥❛♥❝❡ ❝♦♥✈❡rs✐♦♥✿ θ12 + φ = π/4✱ ✭❧❡✈❡❧ ❝r♦ss✐♥❣ ✐❢ θ12 = 0✳✮ Eres(x) = δm2

21 cos 2θ12

(1 − εV

τ s2 23 + εV e )2

√ 2GFNe(x) E ⊙

res(0) ≈

2 MeV (1 − εV

τ s2 23 + εV e )

❢♦r Eν ∼ MeV✱

r❡❧❡✈❛♥t ✐❢ ε ∼ O(1)

E ⊕

res(0) ≈

30 MeV (1 − εV

τ s2 23 + εV e )

♥♦t r❡❧❡✈❛♥t

Chen Sun (Brown U./ CAS-ITP) Vector Form NSI at Borexino (UMass Amherst) 04/26/2019 13 / 29

SLIDE 27

How NSI manifests at Borexino – Propagation

Energy [MeV] 1 10

ee

P 0.2 0.3 0.4 0.5 0.6 0.7 0.8

pp Be

7

pep B

8

Vacuum-LMA MSW-LMA

. 5 − . 5 ' = 1.0 ε Chen Sun (Brown U./ CAS-ITP) Vector Form NSI at Borexino (UMass Amherst) 04/26/2019 14 / 29

SLIDE 28

How NSI manifests at Borexino

R ∼ NeΦν σν

❉❡t❡❝t✐♦♥

dσ dTe ✱ ❞♦♠✐♥❛♥t ❡✛❡❝t

Pr♦♣❛❣❛t✐♦♥

Pee ∼ Φν ✱ s♠❛❧❧ ❡✛❡❝t

Pr♦❞✉❝t✐♦♥

γe → eν¯ ν✱ ✐rr❡❧❡✈❛♥t Eν ≪ 50 keV

Chen Sun (Brown U./ CAS-ITP) Vector Form NSI at Borexino (UMass Amherst) 04/26/2019 15 / 29

SLIDE 29

How NSI manifests at Borexino

R ∼ NeΦν σν

❉❡t❡❝t✐♦♥

dσ dTe ✱ ❞♦♠✐♥❛♥t ❡✛❡❝t

Pr♦♣❛❣❛t✐♦♥

Pee ∼ Φν ✱ s♠❛❧❧ ❡✛❡❝t

Pr♦❞✉❝t✐♦♥

γe → eν¯ ν✱ ✐rr❡❧❡✈❛♥t Eν ≪ 50 keV

Chen Sun (Brown U./ CAS-ITP) Vector Form NSI at Borexino (UMass Amherst) 04/26/2019 15 / 29

SLIDE 30

Chen Sun (Brown U./ CAS-ITP) Vector Form NSI at Borexino (UMass Amherst) 04/26/2019 16 / 29

SLIDE 31

Borexino Timeline

P❤❛s❡ ■✿ ✵✺✴✶✻✴✷✵✵✼ ✲ ✵✺✴✵✽✴✷✵✶✵✱ ✼✹✵✳✼ ❧✐✈❡ ❞❛②s✱ ②✐❡❧❞✐♥❣ ✶✺✸✳✻ t♦♥·

②❡❛r ♦❢ ✜❞✉❝✐❛❧ ❡①♣♦s✉r❡

▲♦✇❡st ❡♥❡r❣② t❤r❡s❤♦❧❞ 8❇ ♥❡✉tr✐♥♦ ❞❡t❡❝t✐♦♥
Phys. Rev. D82, 033006 (2010)
❋✐rst Pr❡❝✐s✐♦♥ ▼❡❛s✉r❡♠❡♥t ♦❢ 7❇❡ ❙♦❧❛r ◆❡✉tr✐♥♦ ❋❧✉①
Phys. Rev. Lett. 107, 141302 (2011)
❋✐rst ❞✐r❡❝t ❞❡t❡❝t✐♦♥ ♦❢ pep s♦❧❛r ♥❡✉tr✐♥♦s
Phys. Rev. Lett. 108, 051302 (2012)
❋♦❧❧♦✇✐♥❣ P❤❛s❡ ■✱ s❝✐♥t✐❧❧❛t♦r ♣✉r✐✜❝❛t✐♦♥ ✇❛s ❝♦♥❞✉❝t❡❞✳
s✐❣♥✐✜❝❛♥t r❡❞✉❝t✐♦♥ ♦❢ r❛❞✐♦❛❝t✐✈❡ ❝♦♥t❛♠✐♥❛♥ts
❯r❛♥✐✉♠✲✷✸✽ < 9.4 × 10−20
❚❤♦r✐✉♠✲✷✸✷ < 5.7 × 10−19
85❑r r❡❞✉❝❡❞ ❜② ∼ 4.6
210❇✐ r❡❞✉❝❡❞ ❜② ∼ 2.3
P❤❛s❡ ■■✿ ✷✵✶✶✲✱ ✇✐❞❡r r❛♥❣❡ ❡♥❡r❣② r❛♥❣❡✱ 0.19MeV < T < 2.93MeV
❋✐rst r❡❛❧t✐♠❡ ❞❡t❡❝t✐♦♥ ♦❢ pp s♦❧❛r ♥❡✉tr✐♥♦s

Nature 512, 383-386 (2014)

■♠♣r♦✈❡❞ ♠❡❛s✉r❡♠❡♥t ♦❢ 8❇ ♥❡✉tr✐♥♦ ✇✐t❤ P❤❛s❡ ■ ❛♥❞ P❤❛s❡ ■■ ❞❛t❛

1709.00756

t❤✐s ❛♥❛❧②s✐s✿ ✶✷✴✶✹✴✷✵✶✶ ✕ ✵✺✴✷✶✴✷✵✶✻✱ ✶✷✾✶✳✺✶ ❞❛②s × ✼✶✳✸ t ✭✷✺✷✳✶ t♦♥·

②❡❛rs✮ ♦❢ ✜❞✉❝✐❛❧ ❡①♣♦s✉r❡

Chen Sun (Brown U./ CAS-ITP) Vector Form NSI at Borexino (UMass Amherst) 04/26/2019 17 / 29

SLIDE 32

Solar ν Source

♣♣ ❝❤❛✐♥✿ ♣♣✲ν✱ ♣❡♣✲ν✱ 7❇❡✲ν✱

8❇✲ν

❈◆❖ ❝②❝❧❡✿ ❈◆❖✲ν
♠❛♥②✲❜♦❞② ❞❡❝❛②✴ ❢✉s✐♦♥ ⇒

❝♦♥t✐♥✉♦✉s s♣❡❝tr✉♠✿ pp✱ 8❇✱ ❈◆❖

t✇♦ ❜♦❞② ♣r♦❝❡ss ⇒

♠♦♥♦❝❤r♦♠❛t✐❝ s♣❡❝tr✉♠✿ 7❇❡✱ ♣❡♣

c.f. Strigari’s talk yesterday Chen Sun (Brown U./ CAS-ITP) Vector Form NSI at Borexino (UMass Amherst) 04/26/2019 18 / 29

SLIDE 33

Electron response to 7Be ν

7❇❡ s♦❧❛r ♥❡✉tr✐♥♦s ❛r❡ ♣r♦❞✉❝❡❞ ✈✐❛ ❑✲s❤❡❧❧ e− ❝❛♣t✉r❡ 7Be + e− →

7Li + νe (89.6%)

7Li∗(0.48) + νe

(10.4%) ②✐❡❧❞✐♥❣ ♠♦♥♦✲❡♥❡r❣❡t✐❝ ν ♦❢ 0.862 MeV ❛♥❞ 0.384 MeV✳

dRν dT = NeΦν

dE dλν

dE dσe dT Pee(E) +

c2

23

dσµ dT + s2

23

dστ dT

(1 − Pee(E))
,

Tmax = E/(1 + me/2E) = 0.665 MeV ❛♥❞ 0.231 MeV

Energy [keV]

100 200 300 400 500 600 700 800 Enents / (day x 100 tons x 1 keV) 0.02 0.04 0.06 0.08 0.1 0.12 0.14 0.16

SI = 0.1

L e

ε 0.1 − =

L e

ε = 0.1

R e

ε 0.1 − =

R e

ε Chen Sun (Brown U./ CAS-ITP) Vector Form NSI at Borexino (UMass Amherst) 04/26/2019 19 / 29

SLIDE 34

Integrated Effect of NSI

R/L e

ε

0.2 − 0.15 − 0.1 − 0.05 − 0.05 0.1 0.15 0.2 SM

〉

Be

7

σ 〈 / 〉

Be

7

σ 〈

0.6 0.8 1 1.2 1.4 1.6 1.8

R e

ε

L e

ε

R e

ε

Chen Sun (Brown U./ CAS-ITP) Vector Form NSI at Borexino (UMass Amherst) 04/26/2019 20 / 29

SLIDE 35

Backgrounds at Borexino

Chen Sun (Brown U./ CAS-ITP) Vector Form NSI at Borexino (UMass Amherst) 04/26/2019 21 / 29

SLIDE 36

Backgrounds at Borexino

▲✐q✉✐❞ s❝✐♥t✐❧❧❛t♦r ❤❛s ✐s♦tr♦♣✐❝

❧✐❣❤t ❡♠✐ss✐♦♥

♥♦ ❞✐r❡❝t✐♦♥❛❧ ✐♥❢♦r♠❛t✐♦♥✱
❧♦✇ ❡♥❡r❣② s❡♥s✐t✐✈✐t② ✭∼ ✺✵

t✐♠❡s ❧❛r❣❡r ②✐❡❧❞ t❤❛♥ ❲❛t❡r ❈❤❡r❡♥❦♦✈✮ 1308.0443

♥❡❡❞ t♦ ❞✐st✐♥❣✉✐s❤ ν ✐♥❞✉❝❡❞

❡✈❡♥ts ❢r♦♠ β ♦r γ ✐♥❞✉❝❡❞ ❡✈❡♥ts

Chen Sun (Brown U./ CAS-ITP) Vector Form NSI at Borexino (UMass Amherst) 04/26/2019 21 / 29

SLIDE 37

Backgrounds at Borexino

▲✐q✉✐❞ s❝✐♥t✐❧❧❛t♦r ❤❛s ✐s♦tr♦♣✐❝

❧✐❣❤t ❡♠✐ss✐♦♥

♥♦ ❞✐r❡❝t✐♦♥❛❧ ✐♥❢♦r♠❛t✐♦♥✱
❧♦✇ ❡♥❡r❣② s❡♥s✐t✐✈✐t② ✭∼ ✺✵

t✐♠❡s ❧❛r❣❡r ②✐❡❧❞ t❤❛♥ ❲❛t❡r ❈❤❡r❡♥❦♦✈✮ 1308.0443

♥❡❡❞ t♦ ❞✐st✐♥❣✉✐s❤ ν ✐♥❞✉❝❡❞

❡✈❡♥ts ❢r♦♠ β ♦r γ ✐♥❞✉❝❡❞ ❡✈❡♥ts

❚❛❣❣❛❜❧❡ ❇● ✭❡✈❡♥t✲❜②✲❡✈❡♥t ❝✉t✮
r❛❞✐♦❛❝t✐✈❡ ❞❡❝❛②s ❢r♦♠ ❞❡❧❛②❡❞ ❝♦✐♥❝✐❞❡♥❝❡✱
♠✉♦♥ ❡✈❡♥ts ❛♥❞ t❤♦s❡ ❢♦❧❧♦✇✐♥❣
❝✉t ♦✛ s♦♠❡ ❡①♣♦s✉r❡ r❡❣✐♦♥ ✭r❡♠♦✈❡ ❞❡t❡❝t♦r r❡❣✐♦♥ ❢♦r ❛ t✐♠❡ ✐♥t❡r✈❛❧✮
❡✳❣✳ ❝♦s♠✐❝ µ + 12C → µ + 11C + n ❧❡❛❞s t♦ 11C✱ ✭❝♦✐♥❝✐❞❡♥❝❡ ❜❡t✇❡❡♥ µ ❛♥❞ ♥✮

11C → 11B + e+ + n ❤❛s τ ∼ 29.4 min ✭❝r♦♣ ♦✉t ❛ ❜❛❧❧ ♦❢ ✶ ♠ ❢♦r ✷ ❤rs✮

▼❛❥♦r✐t② ✐s r❡❝♦♥str✉❝t❡❞ t❤r♦✉❣❤ ✜tt✐♥❣
85Kr → 85Rb + e− + ¯

νe (Q = 0.687 MeV, t1/2 ≈ 10.8 yrs)

210Bi → 210Po + e− + ¯

νe (Q = 1.161 MeV, t1/2 ≈ 5 d)

210Po → 205Pb + 4He

(Q = 5.3 MeV, t1/2 ≈ 138 d)

Chen Sun (Brown U./ CAS-ITP) Vector Form NSI at Borexino (UMass Amherst) 04/26/2019 21 / 29

SLIDE 38

Fitting w/o NSI

7❇❡ ✢✉①✿ ✻✪ ✉♥❝❡rt❛✐♥t② ✭s❛♠❡ ❢♦r ▲❩ ❛♥❞ ❍❩✱ st❛♥❞❛r❞ ❛♥❛❧②s✐s ✇✴♦ ◆❙■

❧❡❛❞s t♦ ∼ 2.7% 1707.09279✮ ❇❛❝❦❣r♦✉♥❞ r❡❧❛t❡❞ ✇✐t❤♦✉t ◆❙■✿

Chen Sun (Brown U./ CAS-ITP) Vector Form NSI at Borexino (UMass Amherst) 04/26/2019 22 / 29

SLIDE 39

Fitting w/ NSI

▼✉❧t✐✲✈❛r✐❛t❡ ✜tt✐♥❣ ♣❛r❛♠❡t❡rs✿

❧✐❣❤t ②✐❡❧❞ ✭❡♥❡r❣② s❝❛❧❡✮
❡♥❡r❣② r❡s♦❧✉t✐♦♥
210P♦ ν ❝❡♥tr❛❧ ❛♥❞ ✇✐❞t❤
11❈ ν st❛rt✐♥❣ ♣♦s✐t✐♦♥
♦t❤❡r ❜❛❝❦❣r♦✉♥❞

♣❛r❛♠❡t❡rs ✐♥ t❤❡ ❞❡t❡❝t♦r ♠♦❞❡❧ ✭85Kr✱ 210Bi ❡t❝✳✮

ε′s

Chen Sun (Brown U./ CAS-ITP) Vector Form NSI at Borexino (UMass Amherst) 04/26/2019 23 / 29

SLIDE 40

Chen Sun (Brown U./ CAS-ITP) Vector Form NSI at Borexino (UMass Amherst) 04/26/2019 24 / 29

SLIDE 41

❍❩✲❙❙▼ ▲❩✲❙❙▼ P❤❛s❡ ■ 1207.3492

❧♦❜❛❧ 0711.0698

εR

e

❬❄❄❄✱ ❄❄❄ ❪ ❬❄❄❄✱ ❄❄❄ ❪ ❬−0.21✱ +0.16 ❪ ❬0.004✱ +0.151 ❪ εL

e

❬???✱ ??? ❪ ❬???✱ ??? ❪ ❬−0.046✱ +0.053 ❪ ❬−0.03✱ +0.08 ❪ εR

τ

❬???✱ ??? ❪ ❬???✱ ??? ❪ ❬−0.98✱ +0.73 ❪ ❬−0.3✱ +0.4 ❪ εL

τ

❬???✱ ??? ❪ ❬???✱ ??? ❪ ❬−0.23✱ +0.87 ❪ ❬−0.5✱ +0.2 ❪

Chen Sun (Brown U./ CAS-ITP) Vector Form NSI at Borexino (UMass Amherst) 04/26/2019 25 / 29

SLIDE 42

Preliminary Results

Chen Sun (Brown U./ CAS-ITP) Vector Form NSI at Borexino (UMass Amherst) 04/26/2019 26 / 29

SLIDE 43

Preliminary Results

εL − 85Kr − εR ❝♦rr❡❧❛t✐♦♥
♦rt❤♦❣♦♥❛❧ t♦ ❚❊❳❖◆❖

❛s νe ✈✳s✳ ¯ νe

❤✉❣❡ ✐♠♣r♦✈❡♠❡♥t ♦✈❡r

▲❙◆❉

Chen Sun (Brown U./ CAS-ITP) Vector Form NSI at Borexino (UMass Amherst) 04/26/2019 26 / 29

SLIDE 44

Preliminary Results

Chen Sun (Brown U./ CAS-ITP) Vector Form NSI at Borexino (UMass Amherst) 04/26/2019 27 / 29

SLIDE 45

Preliminary Results

❝♦✈❡rs ❞✐✛❡r❡♥t r❡❣✐♦♥

❝♦♠♣❛r❡❞ t♦ ▲❊P

s❡❝♦♥❞ ♠✐♥✐♠✉♠ ❞✉❡ t♦

gτL → −gτL ❛♣♣r♦①✐♠❛t❡ s②♠♠❡tr②✱ ✐✳❡✳ ετL = 0✱ ♦r −2gτL✳

Chen Sun (Brown U./ CAS-ITP) Vector Form NSI at Borexino (UMass Amherst) 04/26/2019 27 / 29

SLIDE 46

Weak mixing angle

gαL = sin2 θW + 1

2

α = e sin2 θW − 1

2

α = µ, τ gαR = sin2 θW α = e, µ, τ

❙♣❡❝✐✜❝ ❞✐r❡❝t✐♦♥ ✐♥ εL − εR ♣❧❛♥❡
s✐♠✐❧❛r ❡✛❡❝t ❢♦r ❜♦t❤ νe ❛♥❞ ντ✳

sin2 θW =????±???? ✭st❛t✰s②st✮ , t❤✐s ✇♦r❦ sin2 θW = 0.251 ± 0.031 (st❛t) ± 0.024 (s②st) . ❚❊❳❖◆❖ sin2 θW = 0.2324 ± 0.0058 (st❛t) ± 0.0059 (s②st) . ❈❍❆❘▼ ■■

Chen Sun (Brown U./ CAS-ITP) Vector Form NSI at Borexino (UMass Amherst) 04/26/2019 28 / 29

SLIDE 47

Summary

❙❡❛r❝❤✐♥❣ ❢♦r ♥❡✇ ♣❤②s✐❝s ✐♥ t❤❡ ♣r❡s❡♥❝❡ ♦❢ ν − e ◆❙■
◆❙■ ♣❤❡♥♦♠❡♥♦❧♦❣②
♣r♦♣❛❣❛t✐♦♥✿ ◆❙■ ❝❤❛♥❣❡s t❤❡ 7❇❡ ♥❡✉tr✐♥♦ ✢✉① ❝♦♠♣♦♥❡♥t✱ νe r❡❧❛t✐✈❡ t♦

♥♦♥✲νµ,τ

❞❡t❡❝t✐♦♥✿ ◆❙■ ❝❤❛♥❣❡s t❤❡ r❡❝♦✐❧ ❡❧❡❝tr♦♥ s♣❡❝tr✉♠
❇❛❝❦❣r♦✉♥❞
❡✈❡♥t✲❜②✲❡✈❡♥t ❝✉t
✏s♣❛❝❡✲t✐♠❡✑ ❝✉t
♠✉❧t✐✲✈❛r✐❛t❡ ✜t
❘❡s✉❧t ♦❢ ε ❝♦♥str❛✐♥ts✱ ❛♥❞ ✉♥❞❡rst❛♥❞✐♥❣ ♦❢ ❝♦rr❡❧❛t✐♦♥s
εeR ✲ 85Kr
εeR − εeL
sin2 θW

Chen Sun (Brown U./ CAS-ITP) Vector Form NSI at Borexino (UMass Amherst) 04/26/2019 29 / 29