new physics (vector, scalar, dark) nsi’s · 2019. 10. 1. · extra new physics from scalar nsi...
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New Physics
&
(vector, scalar, dark) NSI’s
Shao-Feng Ge
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 .
Shao-Feng Ge @ NEPLES 2019, KIAS, 2019-9-27 New Physics & (vector, scalar, dark) NSI’s
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!
Shao-Feng Ge @ NEPLES 2019, KIAS, 2019-9-27 New Physics & (vector, scalar, dark) NSI’s
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.
Shao-Feng Ge @ NEPLES 2019, KIAS, 2019-9-27 New Physics & (vector, scalar, dark) NSI’s
Neutrino Oscillation in Absence of Mass Term
sin2
(δm2
ijL
4Eν
)→ sin2
(1
2VL
)
Wolfenstein 78’
Shao-Feng Ge @ NEPLES 2019, KIAS, 2019-9-27 New Physics & (vector, scalar, dark) NSI’s
Standard & Non-Standard Interactions
Effective Hamiltonian
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.
Shao-Feng Ge @ NEPLES 2019, KIAS, 2019-9-27 New Physics & (vector, scalar, dark) NSI’s
NSI already appeared in Wolfenstein 78’ Paper
Shao-Feng Ge @ NEPLES 2019, KIAS, 2019-9-27 New Physics & (vector, scalar, dark) NSI’s
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]
Shao-Feng Ge @ NEPLES 2019, KIAS, 2019-9-27 New Physics & (vector, scalar, dark) NSI’s
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 ,
Effective Hamiltonian
H ≈ Eν +(M +MS) (M +MS)
†
2Eν± VSI ,
Shao-Feng Ge @ NEPLES 2019, KIAS, 2019-9-27 New Physics & (vector, scalar, dark) NSI’s
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
Shao-Feng Ge @ NEPLES 2019, KIAS, 2019-9-27 New Physics & (vector, scalar, dark) NSI’s
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.
Shao-Feng Ge @ NEPLES 2019, KIAS, 2019-9-27 New Physics & (vector, scalar, dark) NSI’s
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!
Shao-Feng Ge @ NEPLES 2019, KIAS, 2019-9-27 New Physics & (vector, scalar, dark) NSI’s
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
Shao-Feng Ge @ NEPLES 2019, KIAS, 2019-9-27 New Physics & (vector, scalar, dark) NSI’s
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
Shao-Feng Ge @ NEPLES 2019, KIAS, 2019-9-27 New Physics & (vector, scalar, dark) NSI’s
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
Shao-Feng Ge @ NEPLES 2019, KIAS, 2019-9-27 New Physics & (vector, scalar, dark) NSI’s
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
ν(−pν) ν(−pν)
Shao-Feng Ge @ NEPLES 2019, KIAS, 2019-9-27 New Physics & (vector, scalar, dark) NSI’s
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)
ν(pν) ν(pν)
φ/Vµ φ/Vν
ν(−pν) ν(−pν)
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]
Shao-Feng Ge @ NEPLES 2019, KIAS, 2019-9-27 New Physics & (vector, scalar, dark) NSI’s
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.
Shao-Feng Ge @ NEPLES 2019, KIAS, 2019-9-27 New Physics & (vector, scalar, dark) NSI’s
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.
SFG, Hitoshi Murayama [arXiv:1904.02518]
Shao-Feng Ge @ NEPLES 2019, KIAS, 2019-9-27 New Physics & (vector, scalar, dark) NSI’s
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
SFG, Hitoshi Murayama [arXiv:1904.02518]
Shao-Feng Ge @ NEPLES 2019, KIAS, 2019-9-27 New Physics & (vector, scalar, dark) NSI’s
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!
Shao-Feng Ge @ NEPLES 2019, KIAS, 2019-9-27 New Physics & (vector, scalar, dark) NSI’s
Sign Difference between Neutrino & Anti-Neutrino
Altogether
δΓαβ ∝ 〈0|aα(a†α′ uα′ + bα′ vα′)γµPL(aβ′uβ′ + b†β′vβ′)a†β|0〉
= 〈0|aαa†α′ uα′γµPLaβ′uβ′a†β|0〉 ,
δΓαβ ∝ 〈0|bα(a†α′ uα′ + bα′ vα′)γµPL(aβ′uβ′ + b†β′vβ′)b†β |0〉
= 〈0|bαbα′ vα′γµPLb†β′vβ′b
†β|0〉 .
0 permutation for neutrino vs 1 permutation for anti-neutrino
δΓαβ = +gαeg
∗βe
2m2V
(uαγµPLuβ) 〈e|eγµPLe|e〉 ,
δΓαβ = −gβeg∗αe
2m2V
(vβγµPLvα) 〈e|eγµPLe|e〉 ,
Shao-Feng Ge @ NEPLES 2019, KIAS, 2019-9-27 New Physics & (vector, scalar, dark) NSI’s
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)
✵�✁ ✵�✂ ✁ ✷ ✸ ✂ ✼ ✁✵ ✁✶
❊♥
✥✄☎✆✝
✵�✁
✵�✷
✵�✸
✵�✶
✵�✂
✵�✞
✵�✼
✵�✟
áP ❡❡
ñ✠❋❈❈
✡❋◆❈
❇☛☞✌✍✍✎
❇☛☞✌✏❇✑✎
❇☛☞✌✍✑✍✎
✍✍
❑✒✌✏❇✑✎
✓✔✕☎✖✗✘✔ ✙✽✓✚
❙✛✜☎✕✢✣
❙✤✦
s✗✘✧q★✩
✪ ✫✬✫✭✭✮ s✗✘✧q★✧
✪ ✫✬✯✰
❉♠✧
✧★✪ ✙✹✬✱✮ ✱✬✲✚ ➫ ✰✫
✳✺☎✆
✧
❞✴✻ ✘✗✾✿❀
Psunee =
∣∣∣Uprodei (Uvac
ei )∗∣∣∣2
Guidry & Billings [arXiv:1812.00035]; Maltoni & Smirnov [arXiv:1507.05287]
Shao-Feng Ge @ NEPLES 2019, KIAS, 2019-9-27 New Physics & (vector, scalar, dark) NSI’s