一般化King関係式を用いた新しい力の探索
2021/12/08@ 京都大山本 康裕 (NCTS)
Based on 1710.11443, 1911.05345, 2110.13544

Collaborators
Quantum Optics group @ Kyoto UIshiyama

Higomoto

NichiaTakahashi
TakasuOno

SaitoOsaka U

TakanoTanakaMap of phenomenology

Coupling

Interaction strength

Dark matter
Light boson
…

1/17

:

Energy FrontierrSMeitnorF
B-physics
ytisn
Higgs decayet
In…
Cosmic Frontier
EnergyCollider, Flavor, g-2, EDM, Dark matter, Inflation ...

Weakly interacting light boson
Drastically change astrophysical observations.
2005.01515, Fabbrichesi et.al.

Terrestrial experiments

Astrophysical obs.

Some implications in observations.
1508.03339 Kaplinghat et.al.

1512.08108, Giannotti et.al.

2/17

Atomic clock

3/17

Extremely precise atomic spectroscopy.
The relative precision is O(10-15).
(Clock error ~ 410 sec./13By)
The relativistic effect of GPS is O(10-10).
The error of the fine structure constant is O(10-10).

At the frontier with Sr, YbO(10-18) or better.

Experimentally excellent but theoretically poor.
Breakthrough Prize 2022Fundamental Physics
Invention and developmentof the optical lattice clock

H. Katori

J. Ye

Isotope shift and King’s relation
Isotope dependence of spectrum.
Inverse mass diff.

Mass shift

4/17

H. Nagaoka

Nuclear size

Field shift(Electron wave fn) x (Isotope dependence)

Isotope shift of Hg by Nagaoka in 1920s.
(c.f. discovery of neutron by J. Chadwick in 1933)

A linear relation among transitions.

1963, W.H.King

Independent of isotopes

Uncertainties to calculate spectra are suppressed.

Violation of the linear relation
2015, F.Gebert et.al

5/17

1710.11443: K.Mikami, M.Tanaka, Y.Y.

Other higher order contributions.
The linear relation is violated.

1987, Blundell et. al.

Additional fit parameter

Which kinds of non-linearity may appear?

Violation of King’s relation

6/17

Higgs boson
1601.05087: C.Delaunay et.al.
Heavy boson contribution is canceled.
Weakly interacting light boson

1704.05068: J.C.Berengut et.al.

Second order perturbation

1709.00600: V.V. Flambaum et.al.
Yb+

Higher order moment
1710.11443: K.Mikami, M.Tanaka, Y.Y.
1911.05345: M.Tanaka, Y.Y.

1kHz1HzHigher orderBeyond King’s relation

7/17

Non-linearity is observed around 300 Hz of precision.
2004.11383: I.Counts, et. al.

SMNP

What is the origin of this non-linearity?
King’s relation is generalized. 1710.11443: K.Mikami, M.Tanaka, Y.Y.

An additional isotope dependence is canceled.

Result

8/17

2110.13544: K.Ono, Y.Y., et.al.

S0-3P0 transition of neutral Yb
with precision of a few Hz.
1

Additional 2D King plot studies
with Yb+ transitions.
Implication of two higherorder isotope shifts.
First time to study 3D King plot
Further insight to origin of non-linearity
New bound and future prospect to new physics

ContentsIntroduction
Some formulas
Field and particle shift
Generalized King’s relation
2D King’s plot
Review of MIT results
Combined analyses
3D King’s plot
Implication to higher order IS
Upper bounds
Conclusion

Experimental set up
drawn by K. Ono

Field shift
Seltzer moment expansion:

Second order perturbation:

9/17

1969, E. C. Seltzer

Particle shift

10/17

Leading new physics effectSensitive toonly e-n coupling

Heavy

Binding energy
LightCouplinga few keVHeavyHeavyLight

LightMassCancellation of PS

11/17

Heavy mediator expansion is similar to FS.

Same

Keep the linearity

SameNon linearity

Sensitivity to new heavy boson is 1/m4 or worse.
The target is not Higgs but a light particle.

Generalized King’s relation

12/17

Considering only the Seltzer moment,(FS2, PS, … )(Electronic factors : ) x (Isotope dependence)King’s linearity isPrecision of the linearity

Other linearities, e.g., PS induces linearity ofIrreducible formulas to determine the nuclear shape.

Transitions

13/17Yb+ ( [Xe] 4f14 6s1 )α: 2S1/2 – 2D5/2

2004.11383: I.Counts, et. al.

β: 2S1/2 – 2D3/2

Error ~ 300 Hz
Split by the relativistic effect.
Yb ( [Xe] 4f14 6s2 )γ: 1S0 – 3P0
Error ~ 3 Hz

2110.13544: K.Ono, Y.Y., et.al.

(c.f. 1S0 – 1D2 of Yb with 300 Hz by another group.)
4 isotope pairs (168, 170, 172, 174, 176).
3 King’s plots + 3D King’s plot.

2D King relation by Yb+

14/17

α: 2S1/2 – 2D5/2 & β: 2S1/2 – 2D3/2&: SM effects is given by FS2

Remnant

SMNP

NP is excluded by other exps.

2D King’s relation with Yb

15/17

γ: 1S0-3P0 & α / β4.037
Cannot fit the data

Need two or more higher order IS to fit the results.

3D King’s relation

16/17

The linear relation is recovered by an additional source.

Need two or more higher order isotope shifts.
PS fit : excluded by otherexperiments.
FS2 fit : inconsistent with
FS2 + PS hypothesis

Another higher order IS is observed.

Upper bound

17/17

Cancel unknown IS with 3D King relation in FS2 fit.
Assuming that it gives us the correct constraint to h.
Upper bound to PS within the given h.

Future prospectα, β : 1/100 errors(a few Hz level): 1/10 errors
Need accurate numerics.

Current boundFuture prospect

Best bound?

Conclusion
Search for light new boson with isotope shifts.
How can we understand new data with higher order IS?
First attempt of the generalized King relation to data.
New measurement of a few Hz level IS with Yb.
Extract information of higher order IS from data.
New bound and prospect excluding possible BG.

Current boundFuture prospect

Best bound?