The measurement of CP violation parameters in the $B_{\mathrm{d,s}}$ meson
mixing have been well established in many b hadron decays. These systems are
very sensitive to any new BSM contribution because the box diagrams that drive
the oscillations and carry CP-violating phases are the neutral entry point for
any new BSM particle. To probe deviations from the SM predictions and test the
BSM models, increased precision on $|V_{ub}|$ and $\gamma$ is required [181].
Considering the sample size collected at FCC-ee, it will be possible to
measure the relevant observables with similar or better precision to previous
experiments [9, 182].

A particular strength of the FCC-ee flavor program will be the ability to make
very sensitive studies of decays containing neutral particles. This
possibility will enable to measure various CP-violating asymmetries such as
time-dependent CP asymmetry in $B^{0}\to\pi^{0}\pi^{0}$ decay or measurement
of CP asymmetry in $B^{-}\to DK^{-}$ (where D indicates a superposition of
$D^{0}$ and $\overline{D}^{0}$) and $B_{s}\to D_{s}^{(*)\pm}K^{\mp}$. Another
benefit of the FCC-ee environment will be the possibility to measure
semileptonic CP-violating asymmetries and determinations of the
$|V_{ub}/V_{cb}|$ performed with $B_{s}^{0}$ mesons and $\Lambda_{b}$ baryons
that are not accessible at current experiments with enough precision.

All these measurements are sensitive to various parameters of the CKM
triangle. It is expected that FCC-ee will provide precise determination of
$|V_{cb}|$, and the semileptonic asymmetries $a^{d}_{sl}$ and $a^{s}_{sl}$
that are key parameters for the CKM. It is expected that first observation of
CP-violation in B mixing will be within reach and the analysis of the BSM
contributions in box mixing processes will provide valuable test of BSM
physics. Assuming the minimum flavor violation scenario, where the new flavor
structures are aligned with the SM Yukawa couplings, the energy scale up to 20
TeV can be probed.

###  8.3 Charged-lepton flavor violating decays

The unprecedented number of Z bosons ($5\times 10^{12}$) and a large sample of
Higgs bosons ($\sim 10^{6}$) expected to be produced at FCC-ee open up a very
rich program of searches for charged-lepton flavor violation (CLFV). In the
following, we review the expected sensitivity coming from a number of
dedicated studies, as well as a few ideas that have not been explored in
detail yet.

####  8.3.1 Higgs boson flavor violating decays to leptons

The present best direct limits on the branching fractions of the
$\mathrm{H}\to e\mu$, $\mathrm{H}\to e\tau$, and $\mathrm{H}\to\mu\tau$ decays
are $6\times 10^{-5}$ [43], $2.2\times 10^{-3}$ [183], and $1.5\times 10^{-3}$
[183] at 95% CL, respectively. Indirect limits from searches for $\mu\to
e\gamma$ conversion by the MEG experiment [184] can be interpreted as indirect
limits on ${\cal B}(H\to e\mu)<10^{-8}$. Present indirect limits from
analogous $\tau\to e\gamma$ or $\tau\to\mu\gamma$ decays on the corresponding
branching fractions of CLFV Higgs boson decays are $\sim 10\%$, i.e. weaker
than the direct limits. While the direct limits will continue improving as
(HL-)LHC accumulates more data, the improvement will be less than an order of
magnitude.

With about one million Higgs bosons produced in association with the Z boson
at FCC-ee, about the same sensitivity in the $e\mu$ channel and about a factor
of two better sensitivity in the other two channels as after full HL-LHC
running can be obtained: $1.2\times 10^{-5}$, $1.6\times 10^{-4}$, and
$1.4\times 10^{-4}$, respectively [185]. In these studies, only the dominant
$\mathrm{Z}(jj)$ decay channel was considered, which is not background-free in
the $\tau$ channels. In addition, the $\tau$ decay is reconstructed only in
the muonic (electronic) channel for the $\mathrm{H}\to e\tau$
($\mathrm{H}\to\mu\tau$) decay, which corresponds to only 17% branching
fraction. Considering other decay channels of the $\tau$ lepton, in
particularly hadronic decay mode, as well as cleaner decay modes of the Z
boson, may result in a further improvement of the FCC-ee sensitivity to these
LFV processes.

####  8.3.2 Z boson charged-lepton flavor violating decays

The improvement compared to the HL-LHC is expected to be significantly better
for the LFV Z boson decays. The most stringent limits on the branching
fractions of the $\mathrm{Z}\to e\mu$, $\mathrm{Z}\to e\tau$, and
$\mathrm{Z}\to\mu\tau$ to date come from the LHC experiments and amount to
$7.5\times 10^{-7}$ [186], $5.0\times 10^{-6}$ [187], and $6.5\times 10^{-6}$
[187] at 95% CL, respectively. The sensitivity is expected to improve to
$10^{-7}$ ($10^{-6}$) level in the $e\mu$ ($\ell\tau$) channels at the HL-LHC.

With $5\times 10^{12}$ Z bosons produced at FCC-ee, the sensitivity to the
branching fractions of the $\mathrm{Z}\to e\tau$ and $\mathrm{Z}\to\mu\tau$
decays is expected to reach $10^{-9}$ level [188], while for the
$\mathrm{Z}\to e\mu$ decay it is expected to be in the range $10^{-10}$ to
$10^{-8}$, depending on to which degree the major background from
$\mathrm{Z}\to\mu\mu$ decays with a muon being misreconstructed as an electron
can be controlled (e.g., using $\mathrm{d}E/\mathrm{d}x$ information) [188].
This corresponds to up to three orders of magnitude improvement achievable at
FCC-ee.

####  8.3.3 Decays of the tau to three muons and to a muon and a photon

The current best limit on ${\cal B}(\tau\to 3\mu)$ comes from Belle [189] and
is $2.1\times 10^{-8}$ at 90% CL. The LHCb experiment set a limit of
$4.6\times 10^{-8}$ using $\tau$ leptons copiously produced in $B$ and $D$
meson decays, based on an integrated luminosity of 3 fb-1 at 7–8 TeV [190].
Given that the upgraded LHCb detector at HL-LHC is expected to record about
100 times that amount of data, and at a higher production cross section at 14
TeV, the sensitivity is expected to improve by only about an order of
magnitude (as in the Belle case, there is sizable background). The CMS
measurement [191] using both heavy-flavor and $\mathrm{W}\to\tau\nu$ channels
based on 36 fb-1 of data at 13 TeV set a limit of $8.0\times 10^{-8}$ at 90%
CL on this branching fraction. With full HL-LHC data set, an improvement by
about an order of magnitude is expected, similar to that in LHCb.

Projected sensitivity from Belle II on this branching fraction will reach
$3.3\times 10^{-10}$ [149]. Given that the number of $\tau$ leptons produced
at Belle II is about 4 times less than in the $\mathrm{Z}\to\tau^{+}\tau^{-}$
at FCC-ee (as shown in Table 7), FCC-ee is expected to reach sensitivity $\sim
10^{-10}$ to this branching fraction [188], which is a few times better than
the expected sensitivity at Belle II.

The sensitivity to the $\tau\to\mu\gamma$ decay branching fraction at FCC-ee
is expected to reach about $2\times 10^{-9}$ [188]. Preliminary studies done
for Belle II expect about 5 times better sensitivity, thanks to the beam
energy constraint that helps eliminating the dominant
$\mathrm{e^{+}e^{-}}\to\tau^{+}\tau^{-}\gamma$ background [192, 149].
Nevertheless, subsequent FCC-ee studies [193] suggested that the $2\times
10^{-9}$ sensitivity may be a conservative estimate, thus bringing FCC-ee and
Belle II sensitivities closer.

A number of other CLFV tau decays can be studied at FCC-ee, similar to what
has been achieved by the B factories. Particle identification, which will be
available in the FCC-ee detectors, should make these measurements highly
competitive with the ultimate precision achievable in Belle II.

####  8.3.4 Other measurements with tau leptons

Finally, the large $\tau$ samples expected at FCC-ee, should allow to measure
the $\tau$ lepton lifetime to an absolute precision of 0.04 fs ($10^{-4}$
relative precision) and leptonic branching fractions to an absolute precision
of $3\times 10^{-5}$ ($2\times 10^{-4}$ relative precision) [188]. This would
allow to measure the Fermi constant in $\tau$ decays to a similar or even
higher precision (potentially as good as $10^{-5}$ if the systematic
uncertainties can be kept at the same level as the statistical ones).
Comparing this number with the canonical $G_{F}$ measurement based on the muon
lifetime [2], offers another way of probing new physics possibly responsible
for non-flavor-universal couplings, as shown in Fig. 16 [188].

Figure 16: Branching fraction of $\tau\to e\overline{\nu}_{e}\nu_{\tau}$ vs.
$\tau$ lepton lifetime. The current world averages of the direct measurements
are indicated with the blue ellipse, while the projected FCC-ee accuracy is
given by the yellow ellipse (from Ref. [188]). The red line corresponds to the
prediction based on lepton universality given the present world-average value
$\tau$ lepton mass, which may be further improved by the current and proposed
charm factories in the future.

Another direct test of lepton favor universality can be achieved at FCC-ee by
the precision simultaneous measurement of the branching fractions of the
$\tau\to\mu\overline{\nu}_{\mu}\nu_{\tau}$ and $\tau\to
e\overline{\nu}_{e}\nu_{\tau}$ decays. The present $2\times 10^{-3}$ precision
[2] in these branching fractions is still unchallenged since the LEP times,
where it was possible to control the systematic uncertainties very well. The
FCC-ee will be able to achieve the statistical precision of $\sim 10^{-5}$ in
these branching fraction measurements [193]. Detailed studies are needed to
demonstrate that the systematic uncertainties in the ratio of the two
branching fractions can be kept under control. This might require not just the
experimental improvements, but also full understanding of radiative
corrections to leptonic tau decays. These studies will be continued in the
future, and have a potential to provide most stringent lepton universality
tests achievable.

Several other important measurements in the tau sector, presently dominated by
the LEP data, will be significantly improved at the FCC-ee, e.g., the
measurement of the spectral functions needed to determine the strong coupling
$\alpha_{s}$ and the Cabibbo mixing $V_{us}$ from hadronic tau decays. These
would allow precision tests of QCD at a qualitatively new level of accuracy.

##  9 FCC-hh and FCC-ep physics

Editors: E. Barberis, R. Harris, M. Mangano, M. Selvaggi, and L.-T. Wang

The FCC project begins with an exploration of the precision frontier at FCC-ee
and culminates with the deepest possible probe of the energy frontier at FCC-
hh [7]. A 100 TeV proton-proton collider, within the tunnel built for FCC-ee,
is a pragmatic and familiar plan to attain a machine with the highest
discovery potential. The crucial motivations of FCC-hh are outlined below, but
first we point out that that these two stages of FCC are coherent. FCC-hh
builds on the precision Higgs measurements of FCC-ee, complementing and
extending them. The FCC-hh would be needed to understand the nature of any new
physics indirectly observed at FCC-ee, providing many additional channels for
measurement and discovery and a broad program of physics, resulting from the
many types of partons of varying momentum within colliding protons,
interacting both strongly and weakly.

###  9.1 FCC-hh

The experimental motivation for FCC-hh is the exploration of the energy
frontier. By virtue of the increased collision energy compared to LHC, with
sufficient integrated luminosity [194] FCC-hh can proportionally extend the
mass reach for discovery of many new phenomena. For example, Fig. 17 taken
from Ref. [195] shows the sensitivity to a dijet resonance, typically the
earliest search for new physics conducted at hadron colliders, and
demonstrates that the mass reach of FCC-hh with 30 ab-1 is roughly six times
that of HL-LHC with 3 ab-1. The advantage of energy is realized soon after
turning on FCC-hh, as shown in Fig. 18 by the huge ratio of parton-
luminosities compared to HL-LHC, for final states with large masses for HL-LHC
which are relatively small masses for FCC-hh. With just 10 fb-1 of integrated
luminosity, accumulated during the first year of data taking, the mass reach
for strongly produced objects like a coloron or an excited quark, is already
three times that of HL-LHC with a full 3 ab-1, and well beyond the HL-LHC
total collision energy. A modest additional mass reach beyond the baseline can
be reached by running at higher luminosity. For this phenomena, with 100 ab-1
at FCC-hh, a factor of seven increase in mass reach is achieved over HL-LHC,
fully proportional to the increase in collision energy.

Figure 17: Comparison of the sensitivity of HL-LHC and FCC-hh for models of
new physics. Left: The $5\sigma$ discovery sensitivity for dijet resonances as
a function of integrated luminosity from Ref. [195]. Right: The $5\sigma$
discovery and 95% CL exclusion sensitivities at baseline integrated luminosity
for dijet resonances and for a top squark from Ref. [195, 9, 196, 68]. Figure
18: Ratio of partonic luminosities at 100 and 14 TeV, as a function of
partonic center-of-mass energy $\hat{s}$, for different partonic initial
states. From Ref. [194].

FCC-hh will help to address some of the most important outstanding questions
in particle physics and cosmology, such as the mechanism of electroweak
symmetry breaking and the nature of dark matter. Additional particles are
needed to extend the standard model to answer these questions. The 100 TeV
collision energy of FCC-hh not only increases the sensitive mass range for the
discovery of such new particles, but it is necessary and sufficient to give
clear answers in critical areas. For example, the nature of the Higgs
potential, and whether thermal weakly interacting massive particles (WIMPs)
are the dark matter.

FCC-hh will measure the properties of the Higgs boson with unprecedented
precision. With 30 ab-1 it will produce over 20 billion Higgs particles, and
over 30 million Higgs pairs, more than a hundred times the HL-LHC. This will
allow the measurement of Higgs couplings within $\sim$1% as tabulated in Table
8. The large center-of-mass energy of the FCC-hh will also enable the precise
measurement of the differential cross section of Higgs bosons produced with
large transverse momentum, $p_{\mathrm{T}}$. These measurements could reach a
precision of up to 10%, for $p_{\mathrm{T}}$ values in excess of 1 TeV,
allowing FCC-hh to probe new physics via the presence of higher-dimension
operators within an EFT framework.

FCC-hh will explore the electroweak phase transition (EWPT) that occurred in
the early universe and created the mass of the Higgs boson (for a review see
Ref. [197]). At the FCC-hh the measurement of the Higgs self-coupling
$\delta\lambda/\lambda$ will not be limited by statistics. Depending on the
assumed detector performance and systematic uncertainties, the Higgs self-
coupling will be measured with a precision in the range 3.4–7.8% at 68%
confidence level [198]. For these estimates, the detector performance was
defined by scenarios ranging from established LHC Run 2 (optimistic), to HL-
LHC performance projected using today’s algorithms (pessimistic). The 10$\%$
precision threshold could be achieved already with 3 ab-1, assuming the
expected systematics can be achieved during this early phase of data taking.
The self-coupling is related to the nature of the EWPT, and the possibility in
BSM scenarios that it is strongly of first order, and then may have played a
role in the matter/antimatter asymmetry of the universe. The expected
precision of the FCC-hh measurement of the self-coupling, together with its
discovery reach for new particles in BSM scenarios, have the potential to
conclusively test scenarios leading to a strong first-order EWPT.

There is both complementarity and synergy between FCC-hh and FCC-ee in Higgs
physics. First, FCC-ee provides the absolute and most precise measurement of
the Higgs coupling to the Z boson and of the total Higgs width, as well as of
the largest rate decays. It has the greatest sensitivity to elusive SM
hadronic decays, such as $\mathrm{H}\to gg$ and
$\mathrm{H}\to\mbox{$c\overline{c}$}$, and others within some BSM scenarios
[118, 116]. Then, following the FCC-ee, the FCC-hh provides the most precision
for the rare SM decays $\mathrm{H}\to\mu\mu$, $\gamma\gamma$,
$\mathrm{Z}\,\gamma$, as well as the ttH coupling and the important Higgs
self-coupling. The critical synergy between the two colliders is that FCC-ee
input is essential to reduce the parametric systematics of the aforementioned
FCC-hh measurements. For example, Table 8 shows that for the rare SM decays
$\mathrm{H}\to\mu\mu$, $\gamma\gamma$, $\mathrm{Z}\,\gamma$, FCC-hh measures
precisely the ratio (R) of branching fractions ($\mathcal{B}$) in each channel
($xx$) relative to the branching fraction into four leptons,
$\mathcal{B}(\mathrm{H}\to xx)/\mathcal{B}(\mathrm{H}\to 4l$). The absolute
determination of the branching fractions for these rare SM decays then relies
on the precise measurement of $\mathcal{B}(\mathrm{H}\to 4l)$ at FCC-ee.
Similarly, the extraction of ttH comes from the measurement of the ratio
ttH/ttZ at FCC-hh and the precision measurement of ttZ at FCC-ee with
$\sqrt{s}=365$ GeV. This joint measurement of ttH by FCC-hh facilitated by
FCC-ee, in turns allows a precision extraction of the Higgs self-coupling,
$\lambda$, from HH production at FCC-hh. This is because the box and triangle
diagrams for HH production involve the top quark in the loop, which interfere
and enter with different powers of the ttH coupling. Precise measurements of
the ttZ coupling at FCC-ee allow us to avoid theoretical uncertainties in that
coupling when extracting both ttH and the crucial Higgs self-coupling from
measurements at FCC-hh.

One of the central open questions in the Standard Model is the origin of the
electroweak scale. Any potential underlying mechanism would have to explain
the vast difference between the EW scale and other fundamental scales, such as
the Planck scale. Many solutions of this so-called hierarchy problem point to
the presence of new physics not too far beyond the TeV scale. Such new physics
will continue to be a main physics target at the HL-LHC. FCC-hh will
significantly enhance the reach, and provide a much more stringent test of
these ideas. In the unlikely case that a discovery is not made, the FCC-hh
would force a dramatic rethinking, and significantly alter the direction of
the quest for an explanation of the weak scale.

Table 8:  Target precision for the parameters relative to the measurement of various Higgs decays and ratios thereof [7], and of the Higgs self-coupling $\lambda$ with 30 ab-1 at FCC-hh [198]. Notice that Lagrangian couplings have a precision that is typically half that of what is shown here, since all rates and branching ratios depend quadratically on the couplings. The range given for $\lambda$’s precision refers to the three scenarios mentioned in the text. Observable | Parameter | Precision | Precision
---|---|---|---
|  | (stat) | (stat+syst+lumi)
$\mu=\sigma$(H)$\times\mathcal{B}$(H$\to\gamma\gamma$) | $\delta\mu/\mu$ | 0.1% | 1.45%
$\mu=\sigma$(H)$\times\mathcal{B}$(H$\to\mu\mu$) | $\delta\mu/\mu$ | 0.28% | 1.22%
$\mu=\sigma$(H)$\times\mathcal{B}$(H$\to 4\mu$) | $\delta\mu/\mu$ | 0.18% | 1.85%
$\mu=\sigma$(H)$\times\mathcal{B}$(H$\to\gamma\mu\mu$) | $\delta\mu/\mu$ | 0.55% | 1.61%
$R=\mathcal{B}$(H$\to\mu\mu)/\mathcal{B}$(H$\to 4\mu$) | $\delta R/R$ | 0.33% | 1.3%
$R=\mathcal{B}$(H$\to\gamma\gamma)/\mathcal{B}$(H$\to 2e2\mu$) | $\delta R/R$ | 0.17% | 0.8%
$R=\mathcal{B}$(H$\to\gamma\gamma)/\mathcal{B}$(H$\to 2\mu$) | $\delta R/R$ | 0.29% | 1.38%
$R=\mathcal{B}$(H$\to\mu\mu\gamma)/\mathcal{B}$(H$\to\mu\mu$) | $\delta R/R$ | 0.58% | 1.82%
$R=\sigma$(tt̄H)$\times\mathcal{B}$(H$\to$ bb̄)/$\sigma$(tt̄Z)$\times\mathcal{B}$(Z$\to$ bb̄) | $\delta R/R$ | 1.05% | 1.9%
$\mathcal{B}$(H$\to$ invisible) |  $\mathcal{B}$@95%CL | $1\times 10^{-4}$ | $2.5\times 10^{-4}$
HH production | $\delta\lambda/\lambda$ | 3.0–5.6% | 3.4–7.8%

Thermal WIMPs are an important class of models of dark mater (DM) that could
explain the large scale structure of the universe. Their mass is somewhere
between a GeV and $10^{2}$ TeV. Any discovery or exclusion by the many planned
direct or indirect detection experiments, in underground and/or space-based
facilities, would require confirmation and detailed study by accelerator-based
measurements to be conclusive, and these experiments do not cover all the
possibilities. The LHC and prior accelerators covered a fraction of the mass
range for thermal WIMPs. Also, dark matter searches for a broad range of
models, in particular Higgs to invisible decays, can cover and in some cases
go beyond the sensitivity of direct detection experiments past the neutrino
floor. A 100 TeV FCC-hh facility is necessary to test several of the most
compelling benchmark scenarios [7]. In particular, in the simplest and most
predictive scenario, DM is part of an electroweak multiplet and it interacts
with the SM through the weak interaction. The obvious examples of this class
are an electroweak doublet or a Majorana electroweak triplet. These are the
Higgsino and wino in the context of SUSY, although they can be perfect dark
matter candidates without SUSY. FCC-hh energies are required to cover these
cases. For example, wino DM has a thermal relic mass of 2.8 TeV, and only the
FCC-hh is sensitive to masses this high. Further, many other weakly-
interacting DM models would _only_ be discovered at FCC-hh, such as for
example, “Higgsinos”, “bino-winos”, and “co-annihilated singlets”, which
contain two DM particles with different interaction strengths and masses.

Within the discovery reach of the FCC-hh for BSM, there is also the
possibility of detecting signs of lepton flavor violation, e.g., through the
production of leptoquark (LQ) particles coupling to leptons and quarks of
different generation. These LQ models can explain the anomalies currently
observed by flavor experiments (e.g., LHCb and muon $g-2$). Both the FCC-hh
and the FCC-ep will significantly extend the reach of the LHC and HL-LHC, and
explore LQ masses in the multi-TeV range [7].

###  9.2 FCC-ep

A FCC-ep [199] machine will realize Deep Inelastic Scattering with
unprecedented kinematic reach, allowing for the high precision study of the
strong coupling constant $\alpha_{S}$, and the the parton distribution
functions (PDFs) in the proton for all individual quarks and the gluon. High-
precision determinations of the proton parton densities in the mid-$Q^{2}$
range are, first, critical to warrant the calculation of the corresponding p-p
cross sections for W, Z, and Higgs bosons and top quarks at FCC-hh, with
reduced theoretical uncertainties. Second, measurements of PDFs at high
$Q^{2}$ (up to $10^{6}$ GeV2) will improve the precision of jet production
cross sections at the FCC-hh, at the highest energies, improving the
sensitivity to possible new contact interactions, or quark-substructure. Last
but not least, measurements of the PDFs for $x$ down to $10^{-7}$, where gluon
saturation and deviations from DGLAP QCD evolution equations can be tested.
Beyond QCD studies, the FCC-ep machine will enable unique measurements of EW
parameters, such as the effective weak mixing angle, and of the Wtb vertex in
single top quark production, e.g., the measurement of the CKM matrix element
$V_{tb}$ with a precision $<1\%$.

In BSM physics, leptoquark searches are a particularly strong aspect of the
FCC-ep program [7]. Contact interactions and a lepton/quark substructure, up
to scales in the 100 TeV range can also be tested with at a FCC-ep machine.

Last but not least, and in analogy to the LHC, the hadron collider complex
opens the door to a varied and diverse physics program, ranging from the study
of heavy ion collisions [9, 200], to flavor physics, to the use of the
injector complex for fixed-target experiments [201].

##  10 Instrumentation

Editors: M. Aleksa, F. Bedeschi, P. Giacomelli, E. Perez, J. Qian, and S.
Seidel

Two complementary detector design concepts have been proposed in the FCC-ee
Conceptual Design Report (CDR) [6], the “CLIC-like Detector” (CLD) [202] and
the “International Detector for Electron-positron Accelerator” (IDEA) [203].
The concepts are evolution of the detectors for the past and current colliders
incorporating the latest results from years of R&D as well as the newest
technologies. They are the conceptual realizations of the detector
requirements discussed in Ref. [204] and serve as bases for further studies.

Figure 19: Schematics of the two detector concepts proposed in the FCC-ee
Conceptual Design Report: (a) CLD and (b) IDEA.

As illustrated in Fig. 19, the CLD detector features a silicon pixel vertex
detector, a silicon tracker, followed by a highly granular calorimeters (a
silicon-tungsten ECAL and a scintillator-steel HCAL) surrounded by a 2T
superconducting solenoid and muon chambers interleaved with steel return
yokes. The IDEA detector comprises a silicon vertex detector, a large-volume
extremely-light drift chamber surrounded by a layer of silicon detector, a
thin low-mass superconducting solenoid, a preshower detector, a dual-readout
fiber calorimeter and muon chambers within the magnet return yoke. These
detectors are designed to operate at bunch crossings from a minimum of 20 ns
at the Z pole running to a maximum 7 $\mu$s at the highest energy,
$\sqrt{s}=365\,{\rm GeV}$. Recently, work has started on a third detector
concept [205], comprising a silicon vertex detector, a light tracker (drift
chamber or full Si are being studied), a thin low-mass superconducting
solenoid, a noble-liquid based ECAL, a scintillator-iron HCAL and a muon
tagger.

All these detector concepts are still under evolution and still being
optimized. There is ample room for further innovative concepts. Currently up
to four interaction points are foreseen for the FCC-ee. This section
summarizes the major subsystems and their expected performances and highlights
areas for further R&D and optimizations.

###  10.1 Tracking and Vertexing

The innermost subsystem [206] of an FCC-ee experiment must provide excellent
efficiency for tracking down to about 120 mrad, for charged particles of
transverse momentum as low as 100 MeV. A tracking volume of relatively large
radius, with minimum mass and stable structure, will be needed to ensure that
systematic uncertainties do not exceed the statistical uncertainties that will
be achieved by the anticipated large data sets. The minimum tracking detector
radius is limited by the detector solenoid strength, which must be restricted
to 2T [207] for the Z pole running to avoid blow-up of low-emittance beams
crossing at 30 mrad. For a pixel pitch of $25\,\mu$m, an occupancy below
$10^{-3}$ for cluster multiplicities of 5 (with safety factor 3) may be
possible. The attainable impact parameter resolution for individual tracks is
$2\oplus 10/(p_{\rm T}\sin^{1/2}\theta)~{}\mu$m [208]. The intended momentum
resolution is $\Delta(1/p_{\rm T})\sim 2\times 10^{-5}\oplus 1\times
10^{-3}/(p_{\rm T}\sin^{1/2}\theta)$. The physics goals for the tracker imply
a material budget for the innermost layer of $0.2\%\,X_{0}$ or better, with
the budget for the entire vertex detector limited to less than $1\%\,X_{0}$
and individual hit resolution on the order of $3\,\mu$m. This has direct
implications for the power budget and cooling mechanism of the tracker.

Tracking in the CLD concept adapts the CLIC design [209], extending to radius
2.1 m and introducing CO2 evaporative cooling. This all-silicon concept uses
three double layers of silicon pixel sensors plus three double disks for the
vertexing system, three double layers of short strip sensors plus seven double
disks for the inner tracking volume, and three double strip layers plus four
double disks for the outer tracking volume. The vertex detector implements
$25\times 25\,\mu{\rm m}^{2}$ pixels of effective thickness $50\,\mu$m. The
thickness per layer is being further optimized, current designs achieve $\sim
0.5\%\,X_{0}$ per layer [210] but monolithic architectures are being studied
to significantly reduce this value.

A variety of silicon technologies should be mature for consideration in the
FCC-ee design. Low-mass and low-power MAPS is being explored for large area
coverage. Its commercial CMOS processes allow full circuitry inside the pixel
cell with high resistivity wafers permitting operation in fully or partially
depletion mode. HVCMOS devices [211] embed NMOS and PMOS transistors in a
single deep n-well that acts as a charge collection electrode; the substrate
can be biased with a high negative voltage for depletion around the well.
Looking ahead to the needs of FCC-hh, which require substantial R&D, driven by
radiation hardness as well as fast readout and timing requirements, depleted
MAPS (DMAPS) sensors use high resistivity substrate which, under reverse bias,
allows signal charge to be collected through drift. Some of its concepts have
already been incorporated into ASICs such as the MALTA/Monopix chip [212].

Alternatives to DMAPS include those with split charge amplification and
readout sectors: DEPFET and FPCCD. Another potential direction uses
heterogeneous vertical integration; a number of variations on the silicon-on-
insulator (SoI) technology [213] are being pursued.

Associated mechanical technologies are also in development, including for
example self-supported curved circuits that conform to small radii and
minimize material overlaps. Connections between this type of material and
sensors have been demonstrated with aluminum wedge wirebonding. Other
interconnect technologies, such as anisotropic conductive film, are under
study; these can also permit realization of serial powering with its
accompanying reduction of services material. Microchannel cooling [214]
embedded in silicon, and microvascular networks [215] in carbon, hold promise
as low-Z structurally stable options. An ideal configuration might ultimately
integrate support, electronics, and routing in a single ladder.

Hybrid technologies, for which the sensor and the readout are optimized
separately and then brought together, provide a different approach. Research
on low gain avalanche detectors (LGADs) [216] aims for a timing resolution of
a couple of tens of picoseconds. Silicon sensors of the 3D geometry are
achieving superior radiation hardness and, through their geometry, are
intrinsically fast. Parallel research on ASICs is proceeding.

The IDEA concept includes a silicon vertex detector [217] surrounded by a
drift chamber, enclosed in a silicon wrapper. The vertex detector implements
monolithic active pixel sensor (MAPS) technology with fully depleted high-
resistivity substrates, on-pixel sparsification, and data-driven time-stamped
readout. The silicon wrapper encapsulates the drift chamber in both the barrel
and disk regions. The drift chamber [218] is designed to provide an efficient
tracking, a high precision momentum measurement and an excellent particle
identification. The distinctive element of the chamber is its high
transparency, in terms of radiation lengths, obtained thanks to the novel
approach for the wiring and assembly procedures adopted for the MEG2 drift
chamber [219]. Indeed, the total amount of material in radial direction,
towards the barrel calorimeter is of the order of $0.016\,X_{0}$ and
approximately $0.05\,X_{0}$ in the forward and backward directions, including
the end-plates instrumented with front-end electronics. The chamber is a
unique volume, high granularity, all stereo, low mass cylindrical drift
chamber, co-axial to the solenoid field filled with helium based gas mixture.
The minimization of the amount of material in the end-plates is obtained
thanks to an innovative system of tie-rods, which redirects the wire tension
stress to the outer end-plate rim, where a cylindrical carbon fibre support
structure bearing the total load is attached. The gas volume is enclosed by
two thin carbon fibre domes, whose profile is suitably shaped in order to
minimize the stress on the inner cylindrical wall, allowing for free
deformations under gas pressure variations, without affecting the wire
tension. The choice of an extremely light gas mixture allows for the
exploitation of the counting techniques for particle identification with a
$\mathrm{d}N/\mathrm{d}x$ resolution below 3% (a factor 2 better than
$\mathrm{d}E/\mathrm{d}x$) [220] and of the cluster timing to improve the
spatial resolution under $100\,\mu$m.

###  10.2 Calorimetry

There have been considerable R&D on calorimeter technologies over the past
several decades, primarily driven by the physics needs of future
$\mathrm{e^{+}e^{-}}$ colliders. Hadronic final states with two or more jets,
either produced directly in the collisions or indirectly from the decays of W,
Z, or H bosons, are expected to dominate the production. Therefore precise
measurements of jet energies are critical for any physics program. One
benchmark of particular interest is the performance in separating the hadronic
$\mathrm{W}\to\mbox{$q\overline{q}$}^{\prime}$ and
$\mathrm{Z}\to\mbox{$q\overline{q}$}$ decays through the measurement of the
dijet invariant mass. Given the mass difference of $\sim 12\%$ between the W
and Z boson, a dijet mass resolution of 3–4% or better is needed to adequately
distinguish between the two decays. This sets a requirement of jet energy
resolution of $\sim 30\%/\sqrt{E}$, approximately a factor of two better than
those of the current and past calorimeters.

Fluctuations in electromagnetic (EM) and non-EM energy deposits from hadronic
showers and non-uniform detector responses to these deposits are the dominant
sources affecting the jet energy resolution. Different technologies have been
pursued to mitigate their impacts as discussed in Ref. [221]. Particle-flow
(PF) and dual-readout (DR) sampling calorimeters, respectively incorporated in
the CLD and IDEA detector concepts, are currently the two leading approaches.
The PF method aims to identify and reconstruct all visible particles in an
event while the DR method targets the separate measurements of the EM and non-
EM energy deposits event by event.

Prototypes of PF calorimeters with different absorbing materials and readout
techniques have been tested with beams by the CALICE collaboration [222]. The
CLD calorimetry design calls for a silicon-tungsten ECAL with a transverse
segmentation of $5\times 5\,{\rm mm}^{2}$ and a longitudinal segmentation of
40 identical layers with a total depth of $22X_{0}$, and a scintillator-steel
HCAL with a transverse segmentation of $30\times 30\,{\rm mm}^{2}$ and 44
longitudinal layers for a total depth of $5.5\lambda_{I}$. This segmentation
is deemed adequate to resolve energy deposits from nearby particles in jets. A
PF-based calorimeter is being constructed for the Phase-2 upgrade of the CMS
endcap calorimeter [223].

A fiber dual-readout calorimeter [224] is proposed for IDEA. The calorimeter
will read out both scintillation light (S) produced primarily by hadrons (non-
EM component) and Cherenkov light (C) emitted mostly by relativistic electrons
(EM component). This technology has been developed by the RD52/DREAM
collaboration [225, 226, 227]. The proposed calorimeter for IDEA is 2 m deep,
corresponds to approximately $7\lambda_{I}$. It combines ECAL and HCAL
functionalities in one uniform system and consists of a total of ${\cal
O}(10^{8})$ fibers.

Fine segmentation is a common feature for both PF and DR approaches, resulting
in a far larger number of channels compared with traditional calorimeters.
Silicon multiplier (SiPM) [228, 229] readout is a key component of both
calorimeter designs. SiPMs with their high efficiencies, large gains, wide
dynamic ranges along with their compact nature and cost effectiveness make
them the ideal choice for calorimetry applications. However, the large number
of readout channels will require robust monitoring and calibration system of
detector responses.

CALICE and RD52/DREAM collaborations have demonstrated that both designs can
achieve a jet energy resolution of 3–4% for jets expected from
$\mathrm{W/Z}\to\mbox{$q\overline{q}$}$ decays [222, 227]. However, the EM
energy resolution is expected to be $\sim 15\%/\sqrt{E}$ for PF and $\sim
10\%/\sqrt{E}$ for DR, largely because of the small sampling fractions. These
resolutions are significantly worse than those of crystal ECALs [230, 231]. It
has been proposed that the combination of a DR crystal ECAL with a DR fiber
HCAL can potentially maintain or even improve the jet energy resolution while
attaining the EM resolution of $<3\%/\sqrt{E}$ expected from a crystal ECAL
[232]. A consortium of US teams is leading this R&D.

Highly granular noble-liquid sampling calorimetry was proposed for a possible
FCC-hh experiment [7, 233, 234]. It has been shown that, on top of its
intrinsic excellent electromagnetic energy resolution, noble-liquid
calorimetry can be optimized in terms of granularity to allow for 4D imaging,
machine learning or, in combination with the tracker measurements, particle-
flow reconstruction.

Recently, a highly granular noble-liquid sampling calorimeter was also
proposed as an electromagnetic calorimeter of an FCC-ee experiment [235]. It
consists of a cylindrical stack of lead/steel absorbers, readout electrodes
and active liquid Argon (LAr) gaps with an inner radius of 2.1 m, compatible
with a thin 2 T solenoid integrated in the same cryostat. Tungsten absorbers
or liquid krypton (LKr) as active material are interesting options due to the
resulting smaller radiation length and smaller Molière radius. The granularity
of each longitudinal compartment can be optimized according to the needs of
particle-flow reconstruction and particle ID. Currently, a granularity of
$\Delta\theta\times\Delta\varphi=2.5\,\mathrm{mrad}\times 8.2\,\mathrm{mrad}$
($5.4\,\mathrm{mm}\times 17.7\,\mathrm{mm}$) is foreseen in the first
calorimeter compartment to optimize the $\pi^{0}$ rejection. Single-particle
simulations of electrons and photons have resulted in a stochastic term of 8.2
% [233, 234] for the standalone electromagnetic energy resolution. Exploiting
the full 4D imaging information, it was demonstrated that a deep-neural-
network analysis can achieve a single-$\pi^{-}$ resolution stochastic term of
37 % ($B=4$ T) for such a highly granular noble-liquid calorimeter
complemented with a scintillator-iron HCAL. It should be noted that this
remarkable result relies on the calorimeter measurement alone, the planned PF
reconstruction combined with the tracker will further substantially improve
the hadronic resolution. R&D on such a noble-liquid calorimeter is supported
by the CERN EP R&D program [236].

The calorimeter performance could be further enhanced with the time-stamping
of the energy deposits. This is particularly true for the fiber DR calorimeter
that lacks adequate longitudinal segmentation. A resolution of 1 ns or better
could offer valuable information for the reconstruction of the longitudinal
shower profiles and, for the FCC-hh, have the additional benefits of
mitigating pileup impacts.

###  10.3 Muon detection

Compared with hadron colliders, muon detection at $\mathrm{e^{+}e^{-}}$
machines poses less of a challenge thanks to the relative cleanness of the
$\mathrm{e^{+}e^{-}}$ collisions. Muon detectors at LEP and other past
$\mathrm{e^{+}e^{-}}$ colliders were primarily aimed at tagging muons while
relying on the inner tracking detectors for their momentum measurements. The
CLD detector concept envisions 6–7 layers of Resistive Plate Chambers (RPCs)
[237, 238] embedded in a steel return yoke to tag muons with a position
precision of ${\cal O}(2-3\,{\rm mm})$, sufficient for matching with the
tracks reconstructed in the inner tracking detector and therefore tagging
muons. On the other hand, the IDEA concept proposes to use the new $\mu{\rm
RWELL}$ technology [239, 240] with a spatial resolution of ${\cal
O}(100\,\mu{\rm m})$ to provide a standalone muon momentum measurement along
the line of the L3 [241], ATLAS [242], and CMS [243] detector designs. The
more precise spatial resolution could be an interesting tool also for studying
long-lived particles, LLPs. A detailed summary of the muon detector options
can be found in Ref. [244].

###  10.4 Particle identification

Particle identification (PID) capabilities are essential for the flavor
physics program, can aid the searches for LLPs, and are also beneficial to
other physics through for example the improvement of the jet flavor tagging.
Candidate PID techniques [245] include measurements of ionization energy
($\mathrm{d}E/\mathrm{d}x$), time-of-flight (TOF), and the Cherenkov radiation
ring (RICH). While a RICH detector is conceivable for a special flavor-
oriented collider detector, $\mathrm{d}E/\mathrm{d}x$ and TOF measurements are
the most practical options for a general purpose FCC-ee detector.

The $\mathrm{d}E/\mathrm{d}x$ measurement is a long-established technique for
PID in a tracking detector for charged particles with momenta $\lesssim
10\,{\rm GeV}$. The performance of this traditional method, however, suffers
from Landau fluctuations. An alternative method of counting the number of
clusters, $\mathrm{d}N/\mathrm{d}x$, giving rise to the ionization can
significantly improve the PID performance [220]. The drift chamber for the
IDEA detector concept is well suited for PID using both the
$\mathrm{d}E/\mathrm{d}x$ and cluster counting methods. A three-sigma
separation between $\pi$-$K$ is expected for charged particles with momenta up
to $\sim$30 GeV except for a narrow “blind region” around 1 GeV that can be
covered with a minimal TOF detector [246].

TOF is an effective PID method for charged particles with momenta up to a few
GeV for a collider detector in which the flight distance is limited to $\sim
2\,{\rm m}$. Though a TOF detector is not incorporated explicitly in the
current detector concepts, the advancement in SiPMs and semiconductor tracking
detectors with good timing resolutions has made a TOF detector an attractive
addition to extend physics reach, as exemplified by the MIP timing layer in
CMS [247] and HGTD detector in ATLAS [248] for the HL-LHC upgrade. Both ATLAS
and CMS timing detectors are expected to achieve a time resolution of ${\cal
O}(30\,{\rm ps})$. With further R&D, a timing resolution of ${\cal O}(10\,{\rm
ps})$ could be within the reach at the time-scale of the FCC-ee, significantly
improving the PID performance.

Apart from the identifications of SM particles, both $\mathrm{d}E/\mathrm{d}x$
and TOF techniques can improve the detectors’ capabilities in tagging heavy
long-lived particles predicted in many SM extensions. A compact TOF timing
layer similar to those being constructed for the ATLAS and CMS upgrades but
with improved time resolution will be particularly attractive for the FCC-ee.
The physics potential of such a detector remains to be explored [249].

###  10.5 Luminosity monitoring

The FCC-ee Z physics program calls for a precision of $10^{-4}$ on the
absolute luminosity measurement and of $5\times 10^{-5}$ on the relative
measurement between the energy points of the Z-lineshape scan [6]. These
requirements are more stringent than those achieved previously, but more
importantly for a much more challenging environment. At $\mathrm{e^{+}e^{-}}$
colliders, the luminosity is traditionally determined from the rate of the
small-angle Bhabha scattering, $\mathrm{e^{+}e^{-}}\to\mathrm{e^{+}e^{-}}$,
due to its large cross section that can be calculated precisely. The Bhabha
events are detected in a dedicated monitor, often called the luminosity
calorimeter or LumiCal, covering small angles in the forward-backward regions.

Unlike LEP detectors, the forward-backward region, often referred to as the
machine-detector interface (MDI) region [23], of a FCC-ee detector is crowded
with crossing beam pipes, the quadrupoles and compensating solenoids. It
necessitates the integration of the LumiCal into the MDI design which
positions the LumiCal at approximately 1 m away from the interaction point.
The design faces significant engineering and operational challenges as
discussed in Ref. [250]. For example, the steep angular dependence of the
Bhabha scattering cross section imposes a precision of ${\cal O}(1\mu{\rm
rad})$ on the geometrical acceptance, correspond to a precision of ${\cal
O}(1\,\mu{\rm m})$ on the radial dimension of the LumiCal. Inspired by the
second-generation of LEP LumiCals, a compact finely segmented sandwich
calorimeter of tungsten-silicon (W-Si) layers is proposed for the FCC-ee. The
OPAL collaboration showed that an experimental precision as low as $3.4\times
10^{-4}$ can be achieved with this design [251]. However, it will be
considerably more difficult for the FCC-ee to achieve the required precision
as the LumiCal will be deep inside the detector volume about 2.5 times closer
to the IP than those at LEP.

The large angle $\mathrm{e^{+}e^{-}}\to\gamma\gamma$ production offers an
alternative process for the luminosity determination. Despite of a cross
section several orders of magnitude smaller than the Bhabha process, this
process should be statistically sufficient to reach the required precision and
enjoys entirely different sources of systematic uncertainties.

###  10.6 Online, computing, and software

The online, offline, and software requirements [252, 253, 254] for the FCC-ee
are dominated by those of the Z pole running with a physics event rate of
$\sim 200$ kHz. However, the data throughput rate, storage and CPU resource
needs will be similar to those of the HL-LHC, in operation long before the
FCC-ee. While there might be unique challenges specific to the FCC-ee and its
detector designs, the requirements are not expected to be too different from
those for the HL-LHC. Thus, the successful operation of the HL-LHC is the best
R&D for the FCC-ee. It is reasonable to expect that the models developed for
and tested at the HL-LHC will serve as starting points for the FCC-ee, refined
with experiences gained and improved with technological developments and
targeted R&D since.

A “triggerless” DAQ system will likely be the preferred choice at the FCC-ee.
A software-based online trigger provides a flexibility that cannot be matched
by traditional multilevel hardware-based filtering systems. The triggerless
system is already being implemented by the LHCb experiment for the LHC Run 3
[255].

For what relates to software requirements, also in this case the developments
and solutions that will be done and put in place for the HL-LHC will be very
beneficial to the FCC-ee. FCC is currently fully committed in implementing its
software around Key4hep [254], a software ecosystem which aims to become the
common “Turnkey Software Stack” for future experiments. Key4hep is being
actively developed and is expected to cover most, if not all, the needs of
future colliders. It mostly builds on the experience and cumulative knowledge
of the LHC, taking naturally advantage of the continuous ongoing developments
required to meet the needs of the HL-LHC. Key4hep also aims to include
software products emerging from R&D programs, such as the AIDA series [256],
addressing software aspects of interest for larger communities, such as the
Pandora SDK for pattern recognition [257].

###  10.7 FCC-hh

The high energy and high luminosity of the FCC-hh impose stringent criteria on
its detector design. The detector must be able to measure multi-TeV jets,
leptons and photons from heavy resonances with masses up to ${\cal O}(50\,{\rm
TeV})$ in a harsh collision environment with the projected average value of
1000 $pp$ collisions per bunch-crossing. The significant higher level of
radiation compared with the HL-LHC —a factor of 20 to 30 higher radiation is
expected— will severely constrain technological choices for detector
subsystems. A more detailed discussion of these challenges can be found in the
FCC-hh conceptual design report [7]. The report also presents one reference
detector design without specific choices for subsystem technologies. These
designs serve as concrete examples to facilitate identifications of areas
where dedicated R&D efforts are needed.

##  11 Executive Summary

It is rare that a single investment can open up an entire wide-ranging physics
program, allowing an unprecedented investigation into the building blocks and
forces of our Universe, and thousands of impactful measurements to be made.
The discovery of the Higgs boson marks the opening of a new era of
exploration, for which the FCC program (the electron-positron collider FCC-ee,
followed by the proton collider FCC-hh) is the most effective answer, with its
complementarity and synergy with other domains of particle physics. It enables
precision studies of the electroweak and strong forces, and extends our
knowledge of potential new high energy physics coupling to the Higgs, the W/Z
bosons, the heavy quarks and leptons and even neutrinos. The reach for the
discovery of new particles is considerably extended both towards weaker
couplings and higher masses.

The FCC program starts with the construction of a 90 km tunnel near CERN. The
first stage is a high luminosity $\mathrm{e^{+}e^{-}}$ collider based on well
established technologies with center-of-mass energies running from the Z boson
mass, with the highest possible luminosity, allowing collection of $5\times
10^{12}$ Z bosons in a few years, through the WW threshold, to Higgs
production in association with a Z, and up to top-quark pair production.

The FCC-ee run plan will give unprecedented measurements of Higgs couplings,
the electroweak and flavor parameters, the top mass and the strong coupling
constant, with ample discovery potential for light feebly interacting
particles in BSM models addressing the origin of dark matter, neutrino masses,
and of the EW scale. Record-setting control of the beam energy will allow
measurements of boson masses to extreme precision. The development of new
magnets will then allow a 100 TeV proton-proton collider complementing the
FCC-ee for precision studies of Higgs phenomena beyond the statistical reach
of lepton colliders, including Higgs pair production and the associated study
of the Higgs potential. The contents of the proton can be further elucidated
over many orders-of-magnitude in parton momentum fraction and energy scale
with a subsequent electron-proton collider (FCC-ep). A heavy ion run can yield
truly hard probes to explore the only fundamental non-Abelian quantum field
theory (QCD) whose collective properties can be studied in the lab. It is a
bold vision of a breathtaking scientific menu, bringing us ever closer to a
true knowledge of the fundamental structure of the universe.

The program will allow measuring the Higgs boson mass to a few MeV, and its
width to the percent level (40 keV). The Higgs branching fractions times
production cross section will be measured with a precision at the percent
level, reaching 0.3% for the H $\to b\overline{b}$ decay in the ZH production
mode. Most of the Higgs boson couplings determined at the HL-LHC with a number
of assumptions will be measured in an absolute and model-independent manner at
FCC-ee, and significantly improved to reach a precision better than 1%, down
to the per mil level for the HZZ coupling. All but the couplings to the first
generation and the Higgs self-coupling (which will be eventually measured to
better than 5% precision) will be measured to that precision over the full
program. With precision center-of-mass energy control, FCC-ee offers also the
unique opportunity to probe the electron Yukawa coupling through resonant
$\mathrm{e^{+}e^{-}}\to$ H production.

Precision measurements of electroweak observables such as forward-backward
asymmetries at the Z pole, the W mass, and the top mass, will accurately test
the closure of the Standard Model. Projected conservative reductions of
uncertainties range from a factor of 90 ($\Gamma_{Z}$) or more, to a factor of
10 ($\sigma_{\text{had}}^{0}$). Studies above $t\overline{t}$ production
threshold will reduce the uncertainty on the top mass by an order of magnitude
compared to the HL-LHC reach.

All such ultra precise measurements will be able to indirectly discover new
particles coupling to the Higgs and/or electroweak bosons up to scales of
$\Lambda\approx 7$ and 50 TeV, respectively.

The program greatly extends our reach for observation of new weakly coupled or
high mass particles. For example, FCC-ee is unique in its sensitivity to
axion-like particles with masses in the range $\sim$1–100 GeV and SM couplings
down to $10^{-7}$, and to heavy neutral leptons directly, all the way down to
the seesaw limit for masses below the Z mass, or, indirectly from precision Z
and $\tau$ measurements up to 1000 TeV masses for mixing $U^{2}$ down to
$10^{-5}$, giving a finite chance of a great step in our understanding of
neutrino mass generation and of the origin of the baryon asymmetry of the
universe. FCC-hh will extend the reach for heavy particles beyond that of LHC
typically by a factor of six, up to masses of several tens of TeV, matching
with direct measurements the indirect sensitivity to new phenomena obtained
with precision FCC-ee measurements and, among other results, largely probing
weakly interacting massive particle scenarios of thermal relic dark matter.

Current results from flavor experiments may indicate the first hints of new
physics. FCC-ee Z-pole running will increase samples well beyond those
ultimately expected from BELLE-II by factors of 20 for B mesons containing
light quarks, and allow precision studies of mesons containing charm and
strange quarks. Extremely large $\tau$ data samples will also be provided.
Many $\tau$ properties are still dominated by LEP measurements, and large
improvements are guaranteed. Important examples are tests of lepton
universality, where 1–3 orders of magnitude are possible via precise
measurements of $\tau$ lifetime and leptonic branching fractions, and searches
for lepton flavor violation, where enhancements as large as three orders of
magnitude are expected.

The study of FCC physics is in its infancy, just 10 years old, and the above
precision estimates are often very conservative. By design, in addition to
high luminosity, FCC-ee provides superb experimental conditions. Beam-induced
backgrounds are small and easily filtered out, the beam spot is tiny, and a
beam pipe radius of 10 mm is being designed. Operation without trigger should
be possible. The center-of-mass energy calibration will be at the ppm level,
possibly better, based on the resonant depolarization of the beams. These
experimental conditions promise huge leaps in sensitivity in the search for
new phenomena, and in precision for measurements sensitive to new physics in
loops or by mixing. This is especially true in the Z run, where the
statistical uncertainty reduction by a factor 500 and sometimes greater,
challenges equally: (i) the ingenuity and technological savvy of experimenters
to imagine and design detectors, and (ii) the skill of theorists to organize
the program of calculations; both with the aim of improving accuracy and
sensitivity to match the available statistical uncertainty. Working groups are
being formed to answer the challenge, several of which are led by US
scientists.

Finally, the FCC program builds on the large stable international community
that has for more than 30 years been working at CERN on the LEP and LHC
programs, the pioneering work on intense electron beams for VEPP-4M,
DA$\Phi$NE, the SLAC and KEK B-factories, and the present SuperKEKB. CERN’s
stable funding structure, robust international participation and long-term
commitment to the delivery of ambitious projects, together with CERN
unparalleled infrastructure, give unique strength to this far-sighted project.
The U.S. has an opportunity to be a leader in this exciting, multifaceted
physics program, continuing our contributions to humanity’s exploration of
fundamental physics.

##  12 Acknowledgments

We acknowledge support from the following funding agencies: DOE and NSF (USA),
Istituto Nazionale di Fiscia Nucleare (Italy)

The work by UNM was made possible by support from the U.S. Department of
Energy grant DE-SC0020255 and the National Science Foundation grant number
1906674. U. Maryland is supported by DOE grant DESC0010072. U. Mass Amherst is
supported by DOE grant DE-SC0010004

Research supported by the Fermi National Accelerator Laboratory, managed and
operated by Fermi Research Alliance, LLC under Contract No. DE-AC02-07CH11359
with the U.S. Department of Energy

The work of Jorge de Blas has been supported by the FEDER/Junta de Andalucía
project grant P18-FRJ-3735.

J. Gluza has been supported in part by the Polish National Science Center
(NCN) under grant 2020/37/B/ST2/02371.

For Spain we must acknowledge: ”MCIN/AEI/10.13039/501100011033 (Spain)”

A. Pich is supported by MCIN/AEI/10.13039/501100011033, Grant No.
PID2020-114473GB-I00, Generalitat Valenciana, Grant No. Prometeo/2021/071,

The work of S.Heinemeyer is supported in part by the grant
PID2019-110058GB-C21 funded by “ERDF A way of making Europe” and by
MCIN/AEI/10.13039/501100011033, and in part by the grant CEX2020-001007-S
funded by MCIN/AEI/10.13039/501100011033.

S.A. acknowledges support from the Swiss National Science Foundation (project
grant number 200020/175502).

This work has been partially supported by the from the European Union’s
Horizon 2020 research and innovation programme under grant agreement No
951754.

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Supporters of U.S. involvement in a future FCC program

Brad Abbott University of Oklahoma
Kaustubh Agashe University of Maryland
Nural Akchurin Texas Tech University
W. Altmannshofer University of California Santa Cruz
Giorgio Apollinari Fermi National Accelerator Laboratory
Artur Apresyan Fermi National Accelerator Lab.
Howard Baer University of Oklahoma
Ela Barberis Northeastern University
Lothar A. T. Bauerdick Fermi National Accelerator Laboratory
Michael Begel Brookhaven National Laboratory
Alberto Belloni University of Maryland
Sergey Belomestnykh Fermilab
Jeffrey Berryhill Fermi National Accelerator Laboratory
Kenneth Bloom University of Nebraska Lincoln
Adi Bornheim California Institute of Technology
Dimitri Bourilkov University of Florida
Antonio Boveia Ohio State University
Gustaaf Brooijmans Columbia University
Elizabeth Brost Brookhaven National Laboratory
Quentin Buat University of Washington
John Mark Butler Boston University
Yunhai Cai SLAC National Accelerator Laboratory
Anadi Canepa Fermi National Accelerator Laboratory
Marcela Carena Fermilab/UChicago
Cari Cesarotti Harvard University
Zackaria Chacko University of Maryland
Maria Chamizo Llatas Brookhaven National Laboratory
Sanha Cheong SLAC National Accelerator Laboratory
Frank Chlebana Fermi National Accelerator Laboratory
Dan Claes University of Nebraska Lincoln
Raymond Co University of Minnesota
Lucien Cremaldi University of Mississippi
Tiesheng Dai University of Michigan
Mariarosaria D’Alfonso Massachusetts Inst. of Technology
Sridhara Dasu University of Wisconsin Madison
Sally Dawson Brookhaven National Laboratory
Andre Luiz De Gouvea Northwestern University
Regina Demina University of Rochester
Dmitri Denisov Brookhaven National Laboratory
Bogdan Dobrescu Fermi National Accelerator Laboratory
Javier Mauricio Duarte Univ. of California San Diego
Kevin Frank Einsweiler Lawrence Berkeley National Laboratory
Sarah Eno University of Maryland
Robin Erbacher University of California Davis
Jan Eysermans Massachusetts Inst. of Technology
JiJi Fan Brown University
Abhijith Gandrakota Fermi National Accelerator Laboratory
Yongsheng Gao California State University, Fresno
Yuri Gershtein Rutgers State Univ. of New Jersey
Tony Gherghetta University of Minnesota
Matthew Gignac University of California,Santa Cruz
Frank Golf University of Nebraska Lincoln
Dorival Gonçalves Oklahoma State University
Julia Lynne Gonski Columbia University
Paul Grannis Stony Brook University
Heather Gray, University of California Berkeley/LBNL
Lindsey Gray Fermi National Accelerator Laboratory
Phillip Gutierrez University of Oklahoma
Joe Haley Oklahoma State University
Tao Han University of Pittsburgh
Mike Hance UC Santa Cruz
Phillip Harris Massachusetts Inst. of Technology
Robert M. Harris Fermi National Accelerator Laboratory
Nicole Michelle Hartman SLAC National Accelerator Laboratory
Kenichi Hatakeyama Baylor University
Hannah Elizabeth Herde SLAC National Accelerator Laboratory
Christian Herwig Fermi National Accelerator Laboratory
Mike Hildreth Notre Dame University
James Hirschauer Fermi National Accelerator Laboratory
John Hobbs Stony Brook University
Julie Hogan Bethel University
Sungwoo Hong University of Chicago
Anson Hook University of Maryland
John Huth Harvard University
Andreas Werner Jung Purdue University
Keti Kaadze Kansas State University
Michael Kagan SLAC National Accelerator Laboratory
Boris Kayser Fermi National Accelerator Laboratory
Doojin Kim Texas A&M University
Boaz Klima Fermi National Accelerator Laboratory
Markus Klute MIT/KIT
Kyoungchul Kong University of Kansas
Ashutosh Kotwal Duke University
Ilya Kravchenko University of Nebraska-Lincoln
Eric Christian Lancon Brookhaven National Laboratory
Greg Landsberg Brown University
Katharine Leney Southern Methodist University
Zoltan Ligeti Lawrence Berkeley National Laboratory
Don Lincoln Fermi National Accelerator Laboratory
Zhen Liu University of Minnesota
Henry Lubatti University of Washington
Joseph Lykken Fermi National Accelerator Laboratory
Yang Ma University of Pittsburgh
Christopher Madrid Fermi National Accelerator Laboratory
Jeremy Mans University of Minnesota
Verena Ingrid Martinez Outschoorn University of Massachusetts
Simone Michele Mazza University of California, Santa Cruz
Petra Merkel Fermi National Accelerator Laboratory
Corrinne Mills University of Illinois at Chicago
Rabindra Mohapatra University of Maryland
Benjamin Nachman LBNL
Sergei Nagaitsev Fermilab/U.Chicago
Steve Nahn Fermi National Accelerator Laboratory
Christopher Neu University of Virginia
Mark Neubauer Univ. Illinois at Urbana Champaign
David Neuffer Fermi National Accelerator Laboratory
Harvey Newman California Institute of Technology
Jennifer Ngadiuba Fermi National Accelerator Laboratory
Jason Nielsen University of California,Santa Cruz
Yuri Nosochkov SLAC National Accelerator Laboratory
Radek Novotny University of New Mexico
Isobel Ojalvo Princeton University
Yasar Onel University of Iowa
Toyoko Orimoto Northeastern University
Jennifer Ott University of California,Santa Cruz
Chris Palmer University of Maryland
Vaia Papadimitriou Fermi National Accelerator Laboratory
John Parsons Columbia University
Christoph Paus Massachusetts Inst. of Technology
Michael Peskin SLAC National Accelerator Laboratory
Marc-André Pleier Brookhaven National Laboratory
Mason Proffitt University of Washington
Jianming Qian University of Michigan
Chris Quigg Fermi National Accelerator Laboratory
Salvatore Rappoccio The State University of New York SUNY
Tor Raubenheimer SLAC / Stanford University
Laura Reina Florida State University
Thomas Rizzo SLAC National Accelerator Laboratory
Jennifer Roloff Brookhaven National Laboratory
David Saltzberg University of California, Los Angeles
David Sanders University of Mississippi
Deepak Sathyan University of Maryland
Todd Satogata Jefferson Lab
Bruce Andrew Schumm University of California,Santa Cruz
Thomas Andrew Schartz University of Michigan
Ariel Gustavo Schwartzman SLAC National Accelerator Laboratory
Reinhard Schwienhorst Michigan State University
Andrea Sciandra University of California, Santa Cruz (US)
Sally Seidel University of New Mexico (US)
Andrei Seryi Jefferson Lab
Elizabeth Sexton-Kennedy Fermi National Accelerator Laboratory
Vladimir Shiltsev Fermi National Accelerator Laboratory
Mel Shochet University of Chicago
Louise Skinnari Northeastern University
Maria Spiropulu California Institute of Technology
Giordon Holtsberg Stark University of California,Santa Cruz
Kevin Stenson University of Colorado Boulder
James Strait Fermi National Accelerator Lab.
Nadja Strobbe University of Minnesota
John Stupak University of Oklahoma
Shufang Su University of Arizona
Indara Suarez Boston University
Raman Sundrum University of Maryland, College Park
Anyes Taffard University of California Irvine
Rafael Teixeira De Lima SLAC National Accelerator Laboratory
Evelyn Jean Thomson University of Pennsylvania
Alessandro Tricoli Brookhaven National Laboratory
Dmitri Tsybychev Stony Brook University
Carlos E.M. Wagner University of Chicago and Argonne National Laboratory
LianTao Wang University of Chicago
Bennie Ward Baylor University
Gordon Watts University of Washington
James Wells University of Michigan, Ann Arbor
Stephane Willocq University of Massachusetts
Darien Wood Northeastern University
Frank Wuerthwein UC San Diego
Si Xie California Institute of Technology
Zijun Xu SLAC National Accelerator Laboratory
Hongtao Yang Lawrence Berkeley National Laboratory
Charlie Young SLAC National Accelerator Laboratory
Jinlong Zhang Argonne National Laboratory
Bing Zhou University of Michigan, Ann Arbor
Junjie Zhu University of Michigan, Ann Arbor