EDM Limit Calculator

maintained by the Fan Group
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Frequency Resolution Calculator

beam type
(e.g. ACME EDM)
$$\delta f=\frac{1}{2\pi\tau\sqrt{\dot{N}T_\mathrm{DAQ}}}$$
s
/s
day

$\rightarrow\delta f$ = 0 $\mu$Hz

trap type
(e.g. JILA EDM III, Optical Dipole Trap)
$$\delta f=\frac{1}{2\pi\tau\sqrt{f_\mathrm{rep}N_\mathrm{shot}T_\mathrm{DAQ}}}$$
s
Hz
day

$\rightarrow\delta f$ = 0 $\mu$Hz

trap type ($\small{f_\mathrm{rep}=1/\tau}$)
(e.g. JILA EDM I&II)
$$\delta f=\frac{1}{2\pi\sqrt{\tau N_\mathrm{shot}T_\mathrm{DAQ}}}$$
s
day

$\rightarrow\delta f$ = 0 $\mu$Hz

New Physics Mass-Scale Calculator [AAA2022]

Since electron EDM ($d_e$), MQM ($M$), and NSM ($S$) originate from various underlying couplings and depend on different sets of fundamental parameters, a direct and fully consistent comparison of the experimental sensitivities is intrinsically not possible.

The representation here therefore is a "best-effort" projection onto a single effective axis. In general, these observables probe complementary regions of parameter space and should be interpreted carefully.

frequency resolution $\delta f:~$

$\mu$Hz
$\mathcal{E}_{\rm eff}$: GV/cm $~~~~~~~~~~~~~~~~~\rightarrow d_e =~$ 0$~e\cdot{\rm cm}$
$\boldsymbol{M_\textrm{NP} \textrm{(1-loop)} = }$0$~\boldsymbol{\mathrm{TeV}}$
$\boldsymbol{M_\textrm{NP} \textrm{(2-loop)} = }$0$~\boldsymbol{\mathrm{TeV}}$
$W_M$: $\times10^{33}~$ Hz/$e\cdot\rm{cm}^2~$ $\rightarrow M =~$ 0$~e\cdot{\rm cm}^2$
$~~~M/\tilde{d}_q:$ $\times10^{-10}e\cdot\rm{cm}$ $ \rightarrow\tilde{d}_q= $ 0$~\mathrm{cm}$
$~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~\boldsymbol{M_\textrm{NP} \textrm{(1-loop)} = }$ 0$~\boldsymbol{\mathrm{TeV}}$
$~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~\boldsymbol{M_\textrm{NP} \textrm{(2-loop)} = }$ 0$~\boldsymbol{\mathrm{TeV}}$
$W_S$: a.u. $~~~~~~~~~~~~~~~~~~\rightarrow S =~$ 0$~e\cdot{\rm fm}^3$
$~~~S/\tilde{d}_q:$ $e\cdot\rm{fm}^2~$ $~~~~~~\rightarrow \tilde{d}_q= $ 0$~\mathrm{cm}$
$~~~~~~~~~~~~~~~\small{(\approx 400\times S/g\tilde{g}_1)}$$~~~~~~~~~~~~~~\boldsymbol{M_\textrm{NP} \textrm{(1-loop)} = }$ 0$~\boldsymbol{\mathrm{TeV}}$
$~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~\boldsymbol{M_\textrm{NP} \textrm{(2-loop)} = }$ 0$~\boldsymbol{\mathrm{TeV}}$
New physics mass-scale figure


Details about Conversion from $\delta f$ to $M_\mathrm{NP}$ [AAA2022]

$\large\delta f = \frac{2}{h}\left(d_e\mathcal{E}_\textrm{eff} + \beta_{M}MW_M + \beta_{S}SW_S\right)$

$\delta f$: frequency resolution

$d_e$: electron electric dipole moment (EDM)
$\mathcal{E}_\textrm{eff}$: effective electric field
$\beta_{M}=\frac{2J+1}{2}\frac{\left(\begin{matrix}J&2&J\\-\Omega&0&\Omega\end{matrix}\right)}{\left(\begin{matrix}I&2&I\\-I&0&I\end{matrix}\right)}\left\{\begin{matrix}J&I&F\\I&J&2\end{matrix}\right\}\simeq0.1$ : MQM alignment factor [SPT2014]
$M$: nuclear magnetic quadrupole moment (MQM)
$W_M$: MQM sensitivity parameter
$\beta_{S}=(2J+1)\frac{\left(\begin{matrix}J&1&J\\-\Omega&0&\Omega\end{matrix}\right)}{\left(\begin{matrix}I&1&I\\-I&0&I\end{matrix}\right)}\left\{\begin{matrix}J&I&F\\I&J&1\end{matrix}\right\}\simeq0.7$: NSM alignment factor
$S$: nuclear Schiff moment (NSM)
$W_S$: NSM sensitivity parameter


conversion from $d_e$ to new physics

For the electron EDM ($d_e$), $$d_e=\frac{e\hbar}{c}\left(\frac{g^2}{16\pi^2}\right)^\ell\frac{m_e}{M_\mathrm{NP}^2}\sin\phi_\mathrm{CP}$$
$g=0.6$: weak coupling constant
$m_{e}$: electron's mass
$\phi_\mathrm{CP}$: CP-violating phase (assumed to be $\sin\phi_\mathrm{CP}=$0.7)
$\ell$: # of loops
$M_\mathrm{NP}$: new physics mass-scale

conversion from $M$ and $S$ to new physics

For MQM ($M$) and NSM ($S$), we first convert to quark chromo-EDMs $\tilde{d}_{q}$, for example,

$~~~~~~~~M(^{173}\mathrm{Yb})\simeq0.6\times10^{-10}\tilde{d}_q~e\cdot\mathrm{cm}$ [MSF2019]
$~~~~~~~~S(^{225}\mathrm{Ra})\simeq5\times10^{3}\tilde{d}_q~e\cdot\mathrm{fm}^2$ [SAV1997]
$~~~~~~~~S(^{229}\mathrm{Th})\simeq1\times10^{4}\tilde{d}_q~e\cdot\mathrm{fm}^2$ [F2019]


and then use the following formula to estimate the mass scale of new physics
$$\tilde{d}_{q}=\frac{\hbar}{c}\left(\frac{g^2}{16\pi^2}\right)^\ell\frac{m_{q}}{M_\mathrm{NP}^2}\sin\phi_\mathrm{CP}$$
$g=1.2$: strong coupling constant
$m_{q}$: quark's mass (we use down quark)

Parameters of Molecules

Electron Electric Dipole Moment $d_e$

molecule science state Eeff (GV/cm) intrinsic coherence
time $\tau$ (s)		 Parity interval (MHz) E-field for
polarization (V/cm)
232ThO 3Δ1, J=1 78 0.005 0.36 ~0.2
180HfF+ 3Δ1, J=1 23 2.1 0.7 ~0.4
232ThF+ 3Δ1, J=1 35 ∞ 5.3 ~1.5
88SrOH 2Σ+(010), N=0 2 ~1 10 ~5
138BaF 2Σ+, N=0 10 ∞ 12,000 ~10,000
174YbF 2Σ+, N=0 26 ∞ 14,000 ~10,000
174YbOH 2Σ+(010), N=0 23 ~1 10 ~5
226RaF 2Σ+, N=0 52 ∞ 11,000 ~10,000
226RaOH 2Σ+(010), N=0 52 ~1 10 ~5
184WC 3Δ1, J=1 36 ∞ 1 ~0.5
197Au208Pb 2Π1/2, J=1/2 39 ∞ 1,000 ~500

Nuclear Magnetic Quadrupole Moment $M$

molecule science state nuclear spin $I$ $W_M~(10^{33}$Hz/$e\cdot\mathrm{cm}^2$) $M/\tilde{d}_q$ ($10^{-10}e\cdot\mathrm{cm}$) intrinsic coherence
time $\tau$ (s)		 Parity interval (MHz) E-field for
polarization (V/cm)
229ThO 3Δ1, J=1 5/2 1.7 [SPT2014] 0.2 [SPT2014] 0.005 0.36 ~0.2
177HfF+ 3Δ1, J=1 7/2 0.5 [SPT2017] 0.4 [SPT2017] 2.1 0.7 ~0.4
229ThF+ 3Δ1, J=1 5/2 1.1 [LF2019] 0.4 [LF2019] ∞ 5.3 ~1.5
137BaF 2Σ+, N=0 7/2 0.38 [DHE2020] 0.01 [FDK2014] ∞ 12,000 ~10,000
173YbF 2Σ+, N=0 5/2 1.1 [DHE2020] 0.6 [MSF2019] ∞ 14,000 ~10,000
173YbOH 2Σ+(010), N=0 5/2 1.1 [DHE2020] 0.6 [MSF2019] ~1 10 ~5
181TaO+ 3Δ1, J=1 7/2 0.45 [F2017] 0.3 [FDK2014] ∞ 10 ~5
175LuOH+ 2Σ+(010), N=0 7/2 1.3 [MSF2020] 0.7 [MSF2020] ~1 10 ~5

Nuclear Schiff Moment $S$

molecule science state nuclear spin $I$ $W_S$ (a.u.) $S/\tilde{d}_q$ ($e\cdot\mathrm{fm}^2$) $\small{(\approx 400\times S/g\tilde{g}_1)}$ intrinsic coherence
time $\tau$ (s)		 Parity interval (MHz) E-field for
polarization (V/cm)
199Hg - 1/2 2 [GCL2016]
(effective at 10 kV/cm)		 10 [BDE2010] ∞ - -
153Eu3+:YSO - 5/2 33 [RV2023], 55,000 [FNR2025] 240 [S2024], 19,000 [FD2020] ∞ - naturally
polarized
161DyO X($\Omega=8$) 5/2 7,400 [CZC2024] ~20,000 [FD2020] ∞ $\ll$1 $\ll$1
205TlF 1Σ+, N=0 1/2 33,000 [CZC2024] 10 [GTK2020][FD2020] ∞ 13,000 ~10,000
223FrAg 1Σ+, N=0 3/2 29,000 [CZC2024] ~8,000 [FD2020] ∞ 1,300 ~600
225Ra - 1/2 50 [PDK2015]
(effective at 75 kV/cm)		 5,000 [FD2020] ∞ - -
225RaOH 2Σ+(010), N=0 1/2 23,000 [CZC2024] 5,000 [FD2020] ~1 10 ~5
225RaOCH3 2Σ+, |K|=1 1/2 23,000 [CZC2024] 5,000 [FD2020] $\gg$1 $\ll$1 $\ll$1
225RaOH+ 1Σ+(010), N=0 1/2 48,000 [CZC2024] 5,000 [FD2020] ~1 10 ~5
227ThO 3Δ1, J=1 1/2 25,000 [CZC2024] ~10,000 [FD2020] [F2019] 0.005 0.36 ~0.2
227ThF+ 3Δ1, J=1 1/2 38,000 [CZC2024] ~10,000 [FD2020] [F2019] ∞ 5.3 ~1.5
229ThF+ 3Δ1, J=1 5/2 38,000 [CZC2024] ~10,000 [FD2020] [F2019] ∞ 5.3 ~1.5