new physics (vector, scalar, dark) nsi’s · 2019. 10. 1. · extra new physics from scalar nsi...

New Physics

&

(vector, scalar, dark) NSI’s

Shao-Feng Ge

([email protected])

TDLI & SJTU

2019-9-27

SFG, Stephen J. Parke, Phys.Rev.Lett. 122 (2019) no.21, 211801 [arXiv:1812.08376]

SFG, Hitoshi Murayama [arXiv:1904.02518]

Shao-Feng Ge @ NEPLES 2019, KIAS, 2019-9-27 New Physics & (vector, scalar, dark) NSI’s

Neutrino Oscillation = Mass + Interaction

H =MM†

2Eν± V .


Fierz Transformation for Unifying CC & NC

Using Fierz transformation, the effective Lagrangian becomes

Leffcc =

gαρg∗βσ

2

1

q2V −m2V

(ναγµPLνβ)(ℓσγ

µPLℓρ),

which can account for both charged & neutral currents

The matter potential is defined by not just Lagrangian, but

also external states! When expanding 〈out|S ≡ e−i∫Leffcc |in〉 to

leading order

δΓαβ = −〈ναe|Lcceff |νβe〉 , δΓαβ = −〈ναe|Lcc

eff |νβe〉 ,for neutrino & anti-neutrino modes.Shao-Feng Ge @ NEPLES 2019, KIAS, 2019-9-27 New Physics & (vector, scalar, dark) NSI’s

Forward Scattering & Effective Lagrangian

Standard Model Lagrangian

Lcc =gαρ√2V+µ ναγ

µPLℓρ + h.c .

To be general, let’s keep non-universal couplings gαρ.

The effective Lagrangian for forward scattering withoutmomentum transfer

Leffcc =

gαρg∗βσ

2

1

−m2V

(ναγµPLℓρ)

(ℓσγµPLνβ

),

where 1q2V−m2

V

= 1−m2

V

from the V propagator with vanishing qV.

It seems like effective operator, but not really!


Dispersion Relation & Effective Hamiltonian

Dispersion Relation Only γ0 term survives!

(E±V)2 = ~p2 +MM†

Effective Hamiltonian

H =√

~p2 +MM†±V ≈ |~p|+ MM†

2E±V

Since the leading term is universal, it would not affect neutrinooscillation and hence can be omitted. The neutrino oscillation isdetermined by the effective Hamiltonian

Heff =MM†

2E±V

Note that neutrino oscillation is described by Heff but theanti-neutrino one by H∗

eff . Since the neutrino energy E is a constant,it is equivalent to use 2EH for describing neutrino oscillation.


Neutrino Oscillation in Absence of Mass Term

sin2

(δm2

ijL

4Eν

)→ sin2

(1

2VL

)

Wolfenstein 78’


Standard & Non-Standard Interactions


Heff =MM†

2E±V =

MM†

2E±VSI±VNSI

Standard Interactions

VSI = Vcc

10

0

+ VncI3×3

Non-Standard Interactions

VNSI = Vcc

1 + ǫee ǫeµ ǫeτǫ∗eµ ǫµµ ǫµτǫ∗eτ ǫ∗µτ ǫττ

In the same way as Standard Interactions through vector bosonmediation.


NSI already appeared in Wolfenstein 78’ Paper


Extra New Physics from Scalar NSI

Vector NSI

Leffcc =

gαρg∗βσ

2

1

−m2V

(ναγµPLνβ)(ℓσγ

µPLℓρ),

which is vector-vector type vertex.

Scalar Mediator

−L =1

2m2

φφ2 +

1

2Mαβ νανβ + yαβφνανβ + Yαβφfαfβ + h.c . ,

Due to forward scattering, the effective Lagrangian is

Lseff ∝ yαβYee [να(p3)νβ(p2)] [e(p1)e(p4)] ,

which is a scalar-scalar type vertex ⇒ significantphenomenological consequences.

SFG, Stephen J. Parke, Phys.Rev.Lett. 122 (2019) no.21, 211801 [arXiv:1812.08376]


EOM & Effective Hamiltonian with Scalar NSI

Two-Point Correlation Function

δΓS =yα′β′yee

m2φ

〈να|να′νβ′ |νβ〉〈e|ee|e〉 ,

δΓS =yβ′α′yee

m2φ

〈να|να′νβ′ |νβ〉〈e|ee|e〉 .

Equation of Motion

νβ

[i∂µγ

µ +

(Mβα +

neyeYαβ

m2φ

)]να = 0 ,


H ≈ Eν +(M +MS) (M +MS)

†

2Eν± VSI ,


Mass Scale & Unphysical CP Phases in Oscillation

The effective mass term is a combination

MM† → (M+MS)(M+MS)† = MM† +MM†

S +MSM† +MSM

†S

The absolute neutrino mass can enter neutrino oscillation!

MM†S +MSM

†

The unphysical CP phases can also enter neutrino oscillation!

M ≡ RνDνR†ν & Rν ≡ PνUνQν

The Majorana rephasing matrice Qν = {e iδM1/2, 1, e iδM3/2} can

be absorbed, QνDνQ†ν = Dν while the unphysical rephasing

matrix Pν ≡ {e iα, e iβ, e iγ} can not be simply rotated away now:

M → M = UνDνU†ν , MS → MS = P†

νMSPν


Parametrization & Constant Density Subtraction

Use characteristic scale ∆m2a to parametrize scalar NSI

MS ≡√

∆m2a

ηee η∗µe η∗τeηµe ηµµ η∗τµητe ητµ ηττ

,

where ∆m2a ≡ ∆m2

31 = 2.7× 10−3 eV2.

We first need input for M which is not directly measured.

However, the one directly measured from terrestial experiments isalways a combination, M+ MS(ρs ≈ 3g/cm3). It is then necessaryto first substract a constant term:

M → M + MSρ− ρsρs

where M = UνDνU†ν is reconstructed in terms of the measured

mixing matrix while MS is the scalar NSI @ typical constantsubtraction density ρs.


Density Subtraction for Reactor Anti-Neutrinos

Since the reactor anti-neutrino experiments (Daya Bay & JUNO)are the most precise ones, we do substraction according to them:

0

0.02

0.04

0.06

0.08

0.1

0.12

0.14

1 2 3 4 5 6 7 8

DayaBay(a)

1-P

ee

Eν [MeV]

SIηee = 0.1ηµµ = 0.1ηττ = 0.1

0

0.02

0.04

0.06

0.08

0.1

0.12

0.14

1 2 3 4 5 6 7 8 0

0.02

0.04

0.06

0.08

0.1

0.12

0.14

1 2 3 4 5 6 7 8

DayaBay [subtracted](b)

1-P

ee

Eν [MeV]

SIηee = 0.1ηµµ = 0.1ηττ = 0.1

0

0.02

0.04

0.06

0.08

0.1

0.12

0.14

1 2 3 4 5 6 7 8

M → M + MSρ− ρsρs

Then no constraint on scalar NSI from reactor experiments!


Scalar NSI @ Accelerator Neutrino: TNT2K

0

0.01

0.02

0.03

0.04

0.05

0.06

0.07

0.08

300 400 500 600 700 800 900 1000

νT2K(a)

Pµe

Eν [MeV]

SIηee = 0.1ηµµ = 0.1ηττ = 0.1

0

0.01

0.02

0.03

0.04

0.05

0.06

0.07

0.08

300 400 500 600 700 800 900 1000 0

0.01

0.02

0.03

0.04

0.05

0.06

0.07

0.08

20 25 30 35 40 45 50 55 60

µSK(b)

Pµe

Eν [MeV]

SIηee = 0.1ηµµ = 0.1ηττ = 0.1

0

0.01

0.02

0.03

0.04

0.05

0.06

0.07

0.08

20 25 30 35 40 45 50 55 60

0

0.01

0.02

0.03

0.04

0.05

0.06

0.07

0.08

1 1.5 2 2.5 3 3.5 4

DUNU [nu](c)

Pµe

Eν [MeV]

SIηee = 0.1ηµµ = 0.1ηττ = 0.1

0

0.01

0.02

0.03

0.04

0.05

0.06

0.07

0.08

1 1.5 2 2.5 3 3.5 4 0

0.01

0.02

0.03

0.04

0.05

0.06

0.07

0.08

1 1.5 2 2.5 3

DUNU [NU](d)

Pµe

Eν [MeV]

SIηee = 0.1ηµµ = 0.1ηττ = 0.1

0

0.01

0.02

0.03

0.04

0.05

0.06

0.07

0.08

1 1.5 2 2.5 3


Scalar NSI @ Solar Neutrino Oscillation

Neutrino energy (MeV)

pp

13N

15O

17F

pep

7B

e

7B

eB

hep

8

ClGa Super-K

0.1 0.2 0.5 1.0 2.0 5.0 10.0 20.0

Spectrum of

solar neutrinos

102

104

106

108

1010

1012

Flu

x a

t 1 A

U (

cm

-2 s

-1)

20

21

22

23

24

25

26

0 0.2 0.4 0.6 0.8 1

Log

10

(ne

cm

-3)

Neutrino

production

8B pp7Be

R/R

ne

= 1.475 x 1026 e-10.54(R/R )

Solar electron

number density

0.2

0.3

0.4

0.5

0.6

0.7

0.1 1 10

pp

Be7pep

(a)

B8

Pee

Eν [MeV]

SIεee = 1εµµ = 1εττ = 1

Borexino17 0.2

0.3

0.4

0.5

0.6

0.7

0.1 1 10 0.2

0.3

0.4

0.5

0.6

0.7

0.1 1 10

pp Be7

pep

(b)

B8P

ee

Eν [MeV]

∆m221 = 7.5x10-5eV2

4.7x10-5eV2

Borexino17

0.2

0.3

0.4

0.5

0.6

0.7

0.1 1 10 0.2

0.3

0.4

0.5

0.6

0.7

0.1 1 10

pp Be7

pep

(b)

B8P

ee

Eν [MeV]

ηee = -0.05ηµµ = -0.05ηττ = -0.05ηee = -0.16

0.2

0.3

0.4

0.5

0.6

0.7

0.1 1 10

Psunee =

∣∣∣Uprodei (Uvac

ei )∗∣∣∣2


Fitting the Borexino 2017 Data

0

2

4

6

8

-0.2 -0.15 -0.1 -0.05 0 0.05 0.1 0.15 0.2

δχ2

η Elements

ηeeηµµηττ

0

2

4

6

8

-0.2 -0.15 -0.1 -0.05 0 0.05 0.1 0.15 0.2


Light Dark Matter SFG, Hitoshi Murayama [arXiv:1904.02518]

The DM mass can span almost 100 orders

For light bosonic DM

−L =1

2m2

φφ2 +

1

2Mαβ νανβ + yαβφνανβ + h.c . ,

leading to forward scattering

ν(pν)

φ/Vµ φ/Vν

ν(pν)

ν(−pν) ν(−pν)

ν(pν) ν(pν)

φ/Vµ φ/Vν



Effective Mass Correction from Dark Matter

The forward scattering with the DM background

ν(pν)

φ/Vµ φ/Vν

ν(pν)


ν(pν) ν(pν)

φ/Vµ φ/Vν


modifies the neutrino kinetic term

iδΓαβ =iρφ(vφ)

m2φ

∑

j

yαjy∗jβ

[p/ν + p/φ +mν

p2φ + 2pν · pφ+

p/ν − p/φ +mν

p2φ − 2pν · pφ

]

with pφ ∼ mφ(1, vφ), the correction

δΓαβ ≈∑

j

yαjy∗jβ

ρχm2

φEν

γ0

appears as dark potential. SFG, Hitoshi Murayama [arXiv:1904.02518]


Dark NSI SFG, Hitoshi Murayama [arXiv:1904.02518]

The dark potential

δΓαβ ≈∑

j

yαjy∗jβ

ρχm2

φEν

γ0

is a correction to the Hamiltonian, same as the matter potential.

Due to 1/Eν dependence, the dark potential is promoted to masscorrection

H =M2

2Eν− 1

Eν

∑

j

yαjy∗jβ

ρχm2

φ

≡ M2 + δM2

2Eν

which is totally different from the scalar NSI.

With mass term correction, any neutrino oscillation cannotsee the original variables. Neutrino oscillation can happeneven if the original mass term M2 vanishes.


Dark NSI & Faked CP

With just 3% of dark NSI

0.01

0.02

0.03

0.04

0.05

0.06

0.07

0.01 0.02 0.03 0.04 0.05 0.06 0.07 0.08 0.09 0.1

T2(H)K

Eν,—ν = 500 MeV

P— µ

— e

Pµe

ηee = 0.03ηµµ = 0.03ηττ = 0.03

SIηeµ = 0.03ηeτ = 0.03ηµτ = 0.03

0.01

0.02

0.03

0.04

0.05

0.06

0.07

0.01 0.02 0.03 0.04 0.05 0.06 0.07 0.08 0.09 0.1 0

0.01

0.02

0.03

0.04

0.02 0.04 0.06 0.08 0.1 0.12 0.14

DUNE

Eν,—ν = 2 GeV

P— µ

— ePµe

ηee = 0.03ηµµ = 0.03ηττ = 0.03

SIηeµ = 0.03ηeτ = 0.03ηµτ = 0.03

0

0.01

0.02

0.03

0.04

0.02 0.04 0.06 0.08 0.1 0.12 0.14

The biprobability contour can totally change.



Dark NSI @ Low Energy Exps

0

0.02

0.04

0.06

0.08

0.1

0.12

0.14

1 2 3 4 5 6 7 8

DayaBay(a)

1-P

ee

Eν [MeV]

SIηee = 0.01

ηµµ = 0.01

ηττ = 0.01

0

0.02

0.04

0.06

0.08

0.1

0.12

0.14

1 2 3 4 5 6 7 8 0

0.2

0.4

0.6

0.8

1

1 2 3 4 5 6 7 8

JUNO (b)

1-P

ee

Eν [MeV]

SIηee = 0.01

ηµµ = 0.01

ηττ = 0.01 0

0.2

0.4

0.6

0.8

1

1 2 3 4 5 6 7 8

0

0.2

0.4

0.6

0.8

1

0.1 1 10

ppBe7

pep

(a)

B8

dark NSI [with subtraction]

Pee

Eν [MeV]

SIηee = 0.01ηµµ = 0.01ηττ = 0.01

ηeµ = −0.016data

0

0.2

0.4

0.6

0.8

1

0.1 1 10 0

2

4

6

8

10

12

14

16

−0.04 −0.02 0 0.02 0.04

Borexino17+SK−IV

(b)4σ

3 σ

2σ

1σ

δχ2

η Elements

ηeeηµµηττηeµηeτηµτ

0

2

4

6

8

10

12

14

16

−0.04 −0.02 0 0.02 0.04



Summary

Neutrino oscillation = Mass + InteractionMass → vacuum mixing & oscillationInteraction → matter effect

Both are importantYukawa coupling → MassGauge coupling → Interaction

Crossing & Hybrid of the two → scalar NSIAppears as NSI, but contribute as mass term correction.The effect of scalar NSI is not suppressed by neutrino energy.Can completely disguise the original oscillation parameters.Neutrino mass scale & unphysical CP phases can enter oscillation.Matter density variation can help to identify scalar NSI;

Dark NSI – Scalar NSI is not alone!

H =(M +MS)(M +MS)

† + δM2

2Eν+ VSI + VNSI

The scalar or dark NSI can fake the neutrino mass term!Shao-Feng Ge @ NEPLES 2019, KIAS, 2019-9-27 New Physics & (vector, scalar, dark) NSI’s

Thank You!


MSW Effect

Take 2-neutrino oscillation as an example

1

2E

cos θ sin θ− sin θ cos θ

m2

1

m22

cos θ − sin θsin θ cos θ

+

Vcc 0

0 0

The lagrangian can be described by effective matter term

Hvaceff =

1

2E

cos θ sin θ

− sin θ cos θ

m2

1

m22

cos θ − sin θ

sin θ cos θ

Resonance if Vcc∆m2 > 0

sin 2θ =sin 2θ√

sin2 2θ + (cos 2θ − 2EV/∆m2)2

∆m2 = ∆m2√

sin2 2θ + (cos 2θ − 2EV/∆m2)2

Energy modulation: H → 2EHShao-Feng Ge @ NEPLES 2019, KIAS, 2019-9-27 New Physics & (vector, scalar, dark) NSI’s

Adiabatic Evolution of Solar Neutrinos

Neutrino energy (MeV)

pp

13N

15O

17Fpep

7B

e

7B

e

B

hep

8

ClGa Super-K

0.1 0.2 0.5 1.0 2.0 5.0 10.0 20.0

Spectrum of

solar neutrinos

102

104

106

108

1010

1012

Flu

x a

t 1 A

U (

cm

-2 s

-1)

20

21

22

23

24

25

26

0 0.2 0.4 0.6 0.8 1

Log

10

(ne c

m-3

)

Neutrino

production

8B pp7Be

R/R

ne

= 1.475 x 1026 e-10.54(R/R )

Solar electron

number density

m2

νµ

νe

MSW

resonanceSurface

of Sun

neR

m21

m22

ne

νe

νµ

Center

of Sunvac

∆m2

∆m2

(ne)

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❑✒✌✏❇✑✎

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❙✛✜☎✕✢✣

❙✤✦

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✪ ✫✬✫✭✭✮ s✗✘✧q★✧

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❉♠✧

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✳✺☎✆

✧

❞✴✻ ✘✗✾✿❀

Psunee =

∣∣∣Uprodei (Uvac

ei )∗∣∣∣2

Guidry & Billings [arXiv:1812.00035]; Maltoni & Smirnov [arXiv:1507.05287]


new physics (vector, scalar, dark) nsi’s · 2019. 10. 1. · extra new physics from scalar nsi...

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