Constraining Natural SUSY via the Higgs Coupling and the Muon Anomalous Magnetic Moment Measurements

1.1 MB·

by  Tianjun Li

Constraining Natural SUSY via the Higgs Coupling and
the Muon Anomalous Magnetic Moment Measurements
Tianjun Lia,b1, Shabbar Razaa2, Kechen Wangc3
a State Key Laboratory of Theoretical Physics and Kavli Institute for Theoretical Physics
China (KITPC), Institute of Theoretical Physics, Chinese Academy of Sciences,
6 Beijing, 100190, China
1
0 b School of Physical Electronics, University of Electronic Science and Technology of China,
2
Chengdu, 610054, China
n
a c Center for Future High Energy Physics, Institute of High Energy Physics,
J

2 Chinese Academy of Sciences, Beijing, 100049, China

]
h
p
-
p
e
h Abstract
[

1 We use the Higgs coupling and the muon anomalous magnetic moment measurements to con-
v
strain the parameter space of the natural supersymmetry in the Generalized Minimal Super-
8
7 gravity (GmSUGRA) model. We scan the parameter space of the GmSUGRA model with
1 small electroweak fine-tuning measure (∆ ≤ 100). The parameter space after applying vari-
0 EW
ous sparticle mass bounds, Higgs mass bounds, B-physics bounds, the muon magnetic moment
0
. constraint, and the Higgs coupling constraint from measurements at HL-LHC, ILC, and CEPC,
1
0 is shown in the planes of various interesting model parameters and sparticle masses. Our study
6
indicates that the Higgs coupling and muon anomalous magnetic moment measurements can
1
: constrain the parameter space effectively. It is shown that ∆ ∼ 30, consistence with all con-
v EW
i straints, and having supersymmetric contributions to the muon anomalous magnetic moment
X
within 1σ can be achieved. The precision of k and k measurements at CEPC can bound
r b τ
a m to be above 1.2 TeV and 1.1 TeV respectively. The combination of the Higgs coupling
A
measurement and muon anomalous magnetic moment measurement constrain e˜ mass to be in
R
the range from 0.6 TeV to 2 TeV. The range of both e˜ and ν˜ masses is 0.4 TeV ∼ 1.2 TeV. In
L e
all cases, the χ˜0 mass needs to be small (mostly ≤ 400 GeV). The comparison of bounds in the
1
tanβ −m plane shows that the Higgs coupling measurement is complementary to the direct
A
collider searches for heavy Higgs when constraining the natural SUSY. A few mass spectra in
the typical region of parameter space after applying all constraints are shown as well.
1E-mail: [email protected]
2E-mail: [email protected]
3E-mail: [email protected]
1 Introduction
Supersymmetry (SUSY) is the most promising scenario for new physics beyond the Standard
Model (SM). It not only provides the unification of the SM gauge couplings, but also gives solu-
tion to the gauge hierarchy problem of the SM. Under the assumption of R-parity conservation,
the lightest supersymmetric particle (LSP), such as the lightest neutralino can be a good cold
dark matter candidate.
A SM-like Higgs has been discovered with mass around m ∼ 125 GeV [1, 2] which is a
h
crowningachievementanditcompletestheSM.Thoughm ∼125GeVislittlebitheavy, butit
h
is still consistent with the prediction of the Minimal Supersymmetric Standard Model (MSSM)
of m ≤ 135 GeV [3]. This somewhat heavy Higgs requires the multi-TeV top squarks with
h
small mixing or TeV-scale top squarks with large mixing. Moreover, we have strong constraints
on the parameter space in the Supersymmetric SMs (SSMs) from the SUSY searches at the
Large Hadron Collider (LHC). For example, the gluino mass m should be heavier than about
g˜
1.7 TeV if the first two-generation squark mass m is around the gluino mass m ∼ m , and
q˜ q˜ g˜
heavier than about 1.3 TeV for m (cid:29) m [4, 5]. The heavy SUSY spectrum and relatively
q˜ g˜
heavy Higgs mass raise question about the naturalness of the MSSM. Some of the recent
studies suggest that this problem can be addressed and the naturalness of the MSSM is still
there [6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20]. For instance, in Supernatural MSSM
scenario [21], it was shown that no residual electroweak fine-tuning (EWFT) left in the MSSM
if we employ the No-Scale supergravity boundary conditions [22] and Giudice-Masiero (GM)
mechanism [23] even though one can have relatively heavy spectrum. But one of the major
obstacle for the above Supernatural SUSY studies is the µ-term (higgsino mass parameter),
which is generated by the GM mechanism and then is proportional to the universal gaugino
mass M . The ratio M /µ is of order one but cannot be determined as an exact number.
1/2 1/2
This problem was addressed in the M-theory inspired Next to MSSM (NMSSM) [24]. Another
issue, related to the Higgs sector, is the scrutiny of the properties of the SM-like Higgs boson
predicted by the SM, such as its decay width, the Higgs couplings to the SM particles, and its
spin and CP properties. This has already triggered new studies, experimental and as well as
theoretical [25, 26, 27]. Any deviations in the predicted properties of a SM-like Higgs boson
may hint towards the physics Beyond the SM (BSM). Moreover, besides the LHC, new e+e−
colliders have been proposed such as the International Linear Collider (ILC) and Circular
Electron Positron Collider (CEPC) where these Higgs properties can be studied with high
precisions. Apart from looking for physics at high energy colliders, one can also get glimpses of
the BSM physics by using low energy precision measurements such as the measurements of the
muon magnetic moment (g − 2) . To address the (g − 2) anomaly between experiment and
µ µ
1
theory, new direct measurements of the muon magnetic moment with fourfold improvement
in accuracy have been proposed at Fermilab by the E989 experiment as well as Japan Proton
AcceleratorResearchComplex[28,29]. FirstresultsfromE989areexpectedaround2017/2018.
These measurements will firmly establish or constrain the new physics effects. Spurred by these
developments, new studies have been done in order to explore this opportunity (For some latest
studies, see Ref. [30, 31, 32, 33, 34, 35, 36, 37, 38, 39]).
In this paper, we try to study the parameter space of General Minimal Supergravity (Gm-
SUGRA)[40,41]byimposingnaturalness, Higgscouplingprecisionmeasurementandthemuon
(g − 2) measurement as constraints. Besides these constraints, we also demand that the pa-
rameter space is consistent with Higgs mass bounds, SUSY particle mass bounds and B physics
constraints. By concerning the naturalness of GmSUGRA, we will be probing the parameter
space with low µ values. In this scenario one can expect to have light higgsinos as the LSPs.
But bino, wino or mixed DM may also be possible in some regions of parameter space. In
addition to it, one can constrain the stop quark mass ranges [42]. One can also probe the
BSM physics by studying the Higgs couplings such as hbb,hττ,htt,hWW,hZZ as functions of
pseudo-scalar mass m . We will show that these precision measurements can constrain m
A A
effectively. Stop quark masses can also be constrained by hgg coupling while hγγ can constrain
not only stop quark but also chargino masses. On the other hand, it is a well-known fact
that if SUSY provides solution to the muon (g −2) discrepancy, sleptons and elctroweakinos
µ
(charginos, bino, wino, and/or higgsinos) should be light [43]. In this study we see that if
some parameters, such as m , cannot be constrained by the naturalness constraint, they can
A
be constrained by Higgs coupling precision measurements. Moreover, some parameters, such
as stops and electroweakions, can be restricted by more than one constraints. We hope that
the ongoing and future experiments will be able to probe the BSM physics and shed light on
new avenues of physics.
In this paper, we restrict our solutions to ∆ ≤ 100 which is a measure of Electroweak
EW
Fine-Tuning (EWFT) and will be discussed later. We find that the minimal value of ∆
EW
for a point satisfying Higgs mass bounds, SUSY particle mass bounds and B-physics bounds
(which we call basic constraints) is about 8 with µ ∼ 0.1 TeV, but it jumps to 20 after the
application of the (g−2) bounds and Higgs coupling precision measurement bounds with µ ∼
µ
0.140 TeV. The minimal light stop quark mass consistent with all the constraints is found to be
around 0.7 TeV. The pseudo-scalar mass m can be constrained by using the hbb (hττ) Higgs
A
coupling precision measurements at the LHC-HL, ILC and CEPC in the mass bounds of, 0.4
(0.5) TeV, 1.1 (0.9) TeV and 1.2 (1.1) TeV, respectively. On the other hand, hgg coupling can
constrain the light stop quark mass upto 0.5 TeV but by combining with (g −2) constraint,
µ
2
it rises to 0.7 TeV as mentioned above. The deviations in hWW and hZZ are very small
and beyond the sensitivity of the collider measurements. We also notice in our present scans,
solutions that satisfy the basic constraints and the CEPC Higgs coupling constraint can have
∆ ∼ 30-40 and contributions to (g − 2) within 1σ of ∆a measurement. Slepton and
EW µ µ
electroweakino sectors are also constrained by the combination of constraints. For instance,
m and m are constrained to the mass ranges [0.5,2] TeV and [0.3,1.2] TeV, respectively.
e˜R e˜L
But to have contributions within 1σ of ∆a , we need m and m in mass ranges [0.8,1.3]
µ e˜R e˜L
TeV and [0.4,0.5] TeV, receptively. For sneutrinos, the allowed mass ranges are more or less
in the same ranges as m . In electroweakino sector, the lightest neutralino, is confined in the
e˜L
mass range of 0.03 TeV to 0.5 TeV. In our present scans, this ranges shrinks to even a smaller
strip of 0.03 TeV to 0.3 TeV if we demand contributions within 1σ of ∆a . On the other hand,
µ
charginos can be as light as 0.1 TeV and the maximal allowed range is about 0.7 TeV. But
for contributions better than 1σ of ∆a , we need chargino in the mass range [0.16,0.22] TeV.
µ
Although we have not imposed relic density constraint, but we do indicate regions of parameter
space where the correct relic density can be achieved by the LSP neutralino annihilation and
coannihilation mechanisms. For example, we show that there can be A resonance and stau-
neutralino coannihilation channels consistent with all the relevant constraints. We also note
that the LSP neutralino can be higgsino, bino, wino or mixed DM. Furthermore, we indicate
the large mass gap in light stop and the LSP neutralino masses and comment on the possible
detection of our solutions in the boosted stop scenario at the CEPC-SPPC [44]. Finally, we
display four benchmark points as examples of our solutions.
The rest the of paper is organized as follows. In Section 2, we show the definition of the
EWFT measure ∆ and the theoretical expressions for the Higgs couplings and the muon
EW
anomalous magnetic moment in the GmSUGRA model. In Section 3, we give the phenomeno-
logical constraints and the scanning procedure. In Section 4, we apply the constraints to the
parameter space and discuss the numerical results. We conclude in Section 5.
2 The GmSUGRA in the MSSM
It was shown in [40, 41] that EWSUSY can be realized in the GmSUGRA model. In this
scenario, the sleptons and charginos, bino, wino, and/or higgsinos are within one TeV while
squarks and/or gluinos can be in several TeV mass ranges [45]. In GmSUGRA, the GUT
gauge group is SU(5) and the Higgs field for the GUT symmetry breaking is in the SU(5)
adjoint representation [40, 41]. Since Φ can couple to the gauge field kinetic terms via high-
dimensional operators, the gauge coupling relation and gaugino mass relation at the GUT
scale will be modified after acquires a Vacuum Expectation Value (VEV). The gauge coupling
3
relation and gaugino mass relation at the GUT scale are
(cid:18) (cid:19)
1 1 1 1
− = k − , (1)
α α α α
2 3 1 3
(cid:18) (cid:19)
M M M M
2 3 1 3
− = k − , (2)
α α α α
2 3 1 3
where k is the index and equal to 5/3 in the simple GmSUGRA. We obtain a simple gaugino
mass relation
5
M −M = (M −M ) , (3)
2 3 1 3
3
by assuming gauge coupling unification at the GUT scale (α = α = α ). The universal
1 2 3
gaugino mass relation M = M = M in the mSUGRA, is just a special case of this general
1 2 3
Eq. 3. Choosing M and M to be free input parameters, which vary around several hundred
1 2
GeV for the EWSUSY, we get M from Eq. (3)
3
5 3
M = M − M , (4)
3 1 2
2 2
which could be as large as several TeV or as small as several hundred GeV, depending on
specific values of M and M . The general SSB scalar masses at the GUT scale are given in
1 2
Ref. [41]. Taking the slepton masses as free parameters, we obtain the following squark masses
in the SU(5) model with an adjoint Higgs field
5 1
m2 = (mU)2 + m2 , (5)
Q˜i 6 0 6 E˜ic
5 2
m2 = (mU)2 − m2 , (6)
U˜c 3 0 3 E˜c
i i
5 2
m2 = (mU)2 − m2 , (7)
D˜ic 3 0 3 L˜i
where m , m , m , m , and m represent the scalar masses of the left-handed squark dou-
Q˜ U˜c D˜c L˜ E˜c
blets, right-handedup-typesquarks, right-handeddown-typesquarks, left-handedsleptons, and
right-handed sleptons, respectively, while mU is the universal scalar mass, as in the mSUGRA.
0
In the Electroweak SUSY (EWSUSY), m and m are both within 1 TeV, resulting in light
L˜ E˜c
sleptons. Especially, in the limit mU (cid:29) m , we have the approximated relations for squark
0 L˜/E˜c
masses: 2m2 ∼ m2 ∼ m2 . In addition, the Higgs soft masses m and m , and the trilinear
Q˜ U˜c D˜c H˜u H˜d
soft terms A , A and A can all be free parameters from the GmSUGRA [41, 45].
U D E
2.1 The Electroweak Fine-Tuning
GmSUGRA model offers solution to the Electroweak Fine-Tuning (EWFT) problem [46]. We
use ISAJET 7.85 [47] to calculate the fine-tuning conditions at the EW scale M . The Z
EW
4
boson mass M , after including the one-loop effective potential contributions to the tree-level
Z
MSSM Higgs potential, is given by
m2 m2 +Σd −(m2 +Σu) tan2β
Z = Hd d Hu u −µ2, (8)
2 tan2β −1
where Σu and Σd denote the corrections to the scalar potential coming from the one-loop
u d
effective potential defined in [20] while m and m are the Higgs soft masses. tanβ ≡
Hu Hd
(cid:104)H (cid:105)/(cid:104)H (cid:105) is the ratio of the Higgs VEVs. The largest contribution to Σu comes from top
u d u
squarks (t˜ ): Σu ∼ 3yt2 × m2 log(m ), where y is the top Yukawa coupling and Q =
√ 1,2 u 16π2 t˜1,2 t˜1,2/Q2 t
m m [48]. On the other hand, m2 and Σd terms are suppresed by tan2β. This allows one
t˜1 t˜2 Hd d
to have large m2 and hence large m2 values without agrivate fine-tuning problem [48]. We
H A
d
discuss it more in the later part of the paper. All the parameters in Eq. (8) are defined at the
electroweak scale M . In order to measure the EWFT condition we follow [20] and use the
EW
definitions
C ≡ |m2 /(tan2β −1)|,C ≡ |−m2 (tan2 −1)|,C ≡ |−µ2|, (9)
Hd Hd Hu Hu µ
with each C less than some characteristic value of order M2. Here, k labels the SM and
Σu,d(k) Z
u,d
SUSY particles that contribute to the one-loop Higgs potential. For the fine-tuning measure,
we define
∆ ≡ max(C )/(M2/2). (10)
EW k Z
Note that ∆ only depends on the weak-scale parameters of the SUSY models, and then
EW
is fixed by the particle spectra. Hence, it is independent of how the SUSY particle masses
arise. The lower values of ∆ corresponds to less fine tuning, for example, ∆ = 10 implies
EW EW
∆−1 = 10% fine tuning. In addition to ∆ , ISAJET also calculates ∆ , which is a measure
EW EW HS
of fine-tuning at the High Scale (HS) like the GUT scale in our case [20]. The HS fine tuning
measure ∆ is given as follows
HS
∆ ≡ max(B )/(M2/2). (11)
HS i Z
For definition of B and more details, see Ref. [20].
i
2.2 Higgs Couplings
Inthissubsection, weshowthetheoreticalexpressionsoftheHiggscouplingsintheGmSUGRA
model. Their deviations from the SM Higgs couplings are parametrized by the ratio k ≡
i
5
gSUSY/gSM, where i = W,Z,b,τ,t,g,γ. Here gSM is the SM Higgs couplings, while gSUSY is the
hii hii hii hii
SUSY Higgs couplings.
In general, the Higgs couplings to W and Z gauge bosons mainly depend on the angle β and
the mixing angle α between the SM-like Higgs boson and the heavier CP-even Higgs boson.
From the reference [49], in the decoupling limit of m (cid:29) m , we can have the relation
A Z
(cid:18)m2 sin4β(cid:19) (cid:18) m2 2 (cid:19)
cos(α+β) ∼ O Z ∼ O − Z . (12)
2m2 m2 tanβ
A A
(cid:16) (cid:17)
m2
Here we have terminated the above expression upto the order O Z and used the identity
m2
A
sin4β ≈ − 4 for large tanβ.
tanβ
Since cos(α+β) ≈ 0 when m (cid:29) m , we then have
A Z
1 (cid:18)m4 2 (cid:19)
sin(α+β) ≈ 1− cos2(α+β) ∼ 1−O Z . (13)
2 m4 tan2β
A
Following the reference [50], in the MSSM the Higgs couplings to W and Z gauge bosons
are given as gSUSY = gSM sin(α + β), where V = W, Z. Therefore, these deviations can be
hVV hVV
expressed as
gSUSY (cid:18)m4 2 (cid:19)
k ≡ hVV = sin(α+β) ∼ 1−O Z , for V = W,Z. (14)
V gSM m4 tan2β
hVV A
The deviations of the Higgs couplings to fermions (b,τ,t) are given in [50] as
(cid:26) (cid:27)
cos(α+β) δf
b
k = sin(α+β)− tanβ −∆ cotβ +(tanβ +cotβ)
b b
1+∆ f
b b
(cid:26) (cid:27)
cos(α+β) δf
τ
k = sin(α+β)− tanβ −∆ cotβ +(tanβ +cotβ)
τ τ
1+∆ f
τ τ
(cid:26) (cid:27)
cos(α+β) ∆f
k = sin(α+β)+ (1+∆ )cotβ −(1+cot2β) t (15)
t t
1+∆ f
t t
Plugging in the above expressions of sin(α+β) and cos(α+β) and terminating the expres-
(cid:16) (cid:17)
m2
sions upto the order O Z , finally we can get
m2
A
(cid:18)m4 2 (cid:19) (cid:18)m2 2 (cid:19) (cid:18) m2 (cid:19)
k ∼ 1−O Z +O Z tanβ ∼ 1+O 2 Z , (16)
b,τ m4 tan2β m2 tanβ m2
A A A
(cid:18)m4 2 (cid:19) (cid:18)m2 2 (cid:19) (cid:18)m2 2 (cid:19)
k ∼ 1−O Z −O Z cotβ ∼ 1−O Z . (17)
t m4 tan2β m2 tanβ m2 tan2β
A A A
Furthermore, in the MSSM the deviation in the effective Higgs couplings to gluons are
dominantly induced by the stop loop contribution, which can be approximately expressed as
6
[51, 52, 53]
(cid:34) (cid:35)
m2 1 1 X2
k ≈ 1+ t + − t , (18)
g 4 m2 m2 m2 m2
t˜1 t˜2 t˜1 t˜2
where X =| A −µ/tanβ | is the stop mixing parameter.
t t
The effective Higgs couplings to photons are much more complicated. In the SM, it is
dominated by the W boson loop contribution, while in the MSSM, k gets contributions from
γ
all charged particles, including charged Higgs, stops and charginos.
2.3 The anomalous magnetic moment of the muon
The theoretical value of the anomalous muon magnetic moment a = (g − 2) /2 within the
µ µ
SM can be calculated to within sub-parts-per-million precision [54]. A comparison between the
theoretical calculation and the experimental measurement of a may reveal, though indirectly,
µ
traces for the physics beyond the SM. The discrepancy can be quantifized as follows [55]
∆a ≡ a (exp)−a (SM) = (28.7±8.0)×10−10 . (19)
µ µ µ
Moreover, using [56] for contributions of the hadronic vacuum polarization, and [57] for the
hadronic light-by-light contribution, the discrepancy can be calculated as ∆a = (26.1±8.0)×
µ
10−10. Either way, a has a ∼ 3σ deviation from its SM value, providing a possible hint of new
µ
physics.
SUSY can address this discrepancy. At the EW scale, the main contributions to ∆a come
µ
from the neutralino-slepton and chargino-sneutrino loops and are given as
M µtanβ
∆aSUSY ∼ i , (20)
µ m4
SUSY
where M (i = 1, 2) are the weak scale gaugino masses, µ is the higgsino mass parameter,
i
tanβ ≡ (cid:104)H (cid:105)/(cid:104)H (cid:105), and m is the sparticle mass circulating in the loop. For a review of the
u d SUSY
constraints on ∆a given by SUSY collider searches, see [58].
µ
7
3 Phenomenological Constraints and Scanning Proce-
dure
We use the ISAJET 7.85 package [47] to perform random scans. The Higgs coupling ratios k
i
are also calculated by this package. We scan over the parameter space given below
0GeV ≤ mU ≤ 9000GeV,
0
100GeV ≤ M ≤ 2000GeV,
1
100GeV ≤ M ≤ 2100GeV,
2
100GeV ≤ m ≤ 1200GeV,
L˜
100GeV ≤ m ≤ 1200GeV,
E˜c
100GeV ≤ µ ≤ 1500GeV,
0GeV ≤ m ≤ 9500GeV,
A
−16000GeV ≤ A = A ≤ 18000GeV,
U D
−6000GeV ≤ A ≤ 6000GeV,
E
2 ≤ tanβ ≤ 60. (21)
When scanning the parameter space, we consider µ > 0 and use m = 173.3 GeV [59].
t
We use mD¯R(M ) = 2.83 GeV as it is hard-coded into ISAJET. We employ the Metropolis-
b Z
Hastings algorithm as described in [60] during our scanning. In rest of the paper, we will use
the notations A , A , A for A , A , and A , respectively.
t b τ U D E
After collecting the data, we apply the following constraints.
(I) Basic constraints:
(a) The Radiative Electroweak Symmetry Breaking (REWSB).
(b) One of the neutralinos is the LSP.
(c) Sparticle masses.
We employ the LEP2 bounds on sparticle masses
m ,m ≥ 100GeV,
t˜1 ˜b1
m ≥ 105GeV,
τ˜1
m ≥ 103GeV. (22)
χ˜±
1
We also apply the following bounds from the LHC
1.7TeV ≤ m (for m ∼ m ) [4, 5],
g˜ g˜ q˜
1.3TeV ≤ m (for m (cid:28) m ) [4, 5],
g˜ g˜ q˜
300GeV ≤ m [50]. (23)
A
8
(d) Higgs mass.
We use the following Higgs mass bound from the LHC
123GeV ≤ m ≤ 127GeV[1, 2]. (24)
h
(e) B-physics.
We use the IsaTools package [61, 62] and implement the following B-physics constraints
1.6×10−9 ≤ BR(B → µ+µ−) ≤ 4.2×10−9 (2σ) [63] , (25)
s
2.99×10−4 ≤ BR(b → sγ) ≤ 3.87×10−4 (2σ) [64] , (26)
0.70×10−4 ≤ BR(B → τν ) ≤ 1.5×10−4 (2σ) [64] . (27)
u τ
(f) Fine-tuning.
In this paper, since we consider the natural SUSY, therefore, the following constraint for
fine-tuning measure ∆ is applied.
EW
∆ ≤ 100. (28)
EW
(II) Muon anomalous magnetic moment constraint
Wealsoapplythefollowingboundsforthemuonanomalousmagneticmomentmeasurement
4.7×10−10 ≤ ∆a ≤ 52.7×10−10 (3σ) [54]. (29)
µ
(III) Higgs coupling constraints
The discovery of the SM-like Higgs boson with mass around 125 GeV provides the op-
portunity to extract the new physics indrectly by measuring the Higgs couplings (and other
properties) precisely at a “Higgs factory”. For this study, we mainly consider two proposed
future e+e− colliders which are able to produce a large number of Higgs events: the Interna-
tional Linear Collier (ILC) and the Circular Electron-Positron Collider (CEPC). As a linear
e+e− collider, the ILC is designed to adopt the polarized beams technology and can reach a
√
high center of mass energy s = 500 GeV [65]. The CEPC, however, so far is focusing on
√
s = 240 GeV. Its proposed intergrated luminisity is 5ab−1 over a running time of 10 years
with 2 Interaction Points (IP) [66, 67]. Furthermore, the CEPC is designed to be upgraded to
a 100 TeV Super Proton-Proton Collider (SPPC) finally.
Besides ILC and CEPC, we also consider the Higgs coupling measurements at the High-
Luminosity LHC (HL-LHC) and the e+e− mode of the CERN Future Circular Collider which
has 4 IP (FCC-ee (4 IP)). We use the precisions at CEPC (2 IP) from the Table 3.12 of [66].
The precisions at HL-LHC are given by the Table 3 of [68], while the precisions at the ILC
9