###### Abstract

The search for a novel technology able to detect and reconstruct nuclear and
electron recoil events with the energy of a few keV has become more and more
important now that large regions of high-mass dark matter (DM) candidates have
been excluded. Moreover, a detector sensitive to incoming particle direction
will be crucial in the case of DM discovery to open the possibility of
studying its properties. Gaseous time projection chambers (TPC) with optical
readout are very promising detectors combining the detailed event information
provided by the TPC technique with the high sensitivity and granularity of
latest-generation scientific light sensors. The CYGNO experiment (a CYGNus
module with Optical readout) aims to exploit the optical readout approach of
multiple-GEM structures in large volume TPCs for the study of rare events as
interactions of low-mass DM or solar neutrinos. The combined use of high-
granularity sCMOS cameras and fast light sensors allows the reconstruction of
the 3D direction of the tracks, offering good energy resolution and very high
sensitivity in the few keV energy range, together with a very good particle
identification useful for distinguishing nuclear recoils from electronic
recoils. This experiment is part of the CYGNUS proto-collaboration, which aims
at constructing a network of underground observatories for directional DM
search. A one cubic meter demonstrator is expected to be built in 2022/23
aiming at a larger scale apparatus (30 m3–100 m3) at a later stage.

###### keywords:

dark matter; time projection chamber; optical readout;

###### keywords:

dark matter; time projection chamber; optical readout

1 1 0 Academic Editor: Antonio Ereditato 19 November 2021 12 January 2022
https://doi.org/ The CYGNO Experiment The CYGNO Experiment Fernando Domingues
Amaro 1, Elisabetta Baracchini 2,3, Luigi Benussi 4, Stefano Bianco 4, Cesidio
Capoccia 4, Michele Caponero 4,5, Danilo Santos Cardoso 6, Gianluca Cavoto
7,8, André Cortez 2,3, Igor Abritta Costa 9, Rita Joanna da Cruz Roque 1,
Emiliano Dané 4, Giorgio Dho 2,3, Flaminia Di Giambattista 2,3, Emanuele Di
Marco 7, Giovanni Grilli di Cortona 4, Giulia D’Imperio 7, Francesco
Iacoangeli 7, Herman Pessoa Lima Júnior 6, Guilherme Sebastiao Pinheiro Lopes
9, Amaro da Silva Lopes Júnior 9, Giovanni Maccarrone 4, Rui Daniel Passos
Mano 1, Michela Marafini 10, Robert Renz Marcelo Gregorio 11, David José
Gaspar Marques 2,3, Giovanni Mazzitelli 4, Alasdair Gregor McLean 11, Andrea
Messina 7,8, Cristina Maria Bernardes Monteiro 1, Rafael Antunes Nobrega 9,
Igor Fonseca Pains 9, Emiliano Paoletti 4, Luciano Passamonti 4, Sandro Pelosi
7, Fabrizio Petrucci 12,13, Stefano Piacentini 7,8, Davide Piccolo 4, Daniele
Pierluigi 4, Davide Pinci 7,*, Atul Prajapati 2,3, Francesco Renga 7, Filippo
Rosatelli 4, Alessandro Russo 4, Joaquim Marques Ferreira dos Santos 1,
Giovanna Saviano 4,14, Neil John Curwen Spooner 11, Roberto Tesauro 4, Sandro
Tomassini 4 and Samuele Torelli 2,3 Fernando Domingues Amaro, Elisabetta
Baracchini, Luigi Benussi, Stefano Bianco, Cesidio Capoccia, Michele Caponero,
Danilos Santos Cardoso, Gianluca Cavoto, André Cortez, Igor Abritta Costa ,
Emiliano Dané, Rita Joanna da Cruz Roque, Giorgio Dho, Flaminia Di
Giambattista, Emanuele Di Marco, Giulia D’Imperio, Francesco Iacoangeli,
Herman Pessoa Lima Júnior, Guilherme Sebastiao Pinheiro Lopes, Amaro da Silva
Lopes Júnior , Giovanni Maccarrone, Rui Daniel Passos Mano, Michela Marafini,
Robert Renz Marcelo Gregorio, Giovanni Mazzitelli, Alasdair Gregor McLean,
Andrea Messina, Cristina Maria Bernardes Monteiro, Rafael Antunes Nobrega,
Igor Fonseca Pains, Emiliano Paoletti, Luciano Passamonti, Sandro Pelosi,
Fabrizio Petrucci, Stefano Piacentini, Davide Piccolo, Daniele Pierluigi,
Davide Pinci, Atul Prajapati, Francesco Renga, Filippo Rosatelli, Alessandro
Russo, Joaquim Marques Ferreira dos Santos, Giovanna Saviano, Neil John Curwen
Spooner, Roberto Tesauro, Sandro Tomassini and Samuele Torelli. Amaro, F.D.;
Baracchini, E.; Benussi, L.; Bernardes Monteiro, C.M.; Bianco, S.; Capoccia,
C.; Caponero, M.; Cardoso D.S.; Cavoto, G.; Cortez, A.; et al. Correspondence:
<EMAIL_ADDRESS>
##  1 Introduction

The presence in the universe of large amounts of non-luminous matter (usually
referred to as dark matter (DM)) is nowadays an established, yet still
mysterious, paradigm Bertone et al. (2005). Deciphering its essence is one of
the most compelling tasks for fundamental physics today. Electrically neutral
and very low interacting particles with a mass in the range of few to
thousands of GeV are usually referred to as weakly interacting massive
particles (WIMPs), and represent a well-motivated DM candidate independently
predicted by the extension of the Standard Model of particle physics and the
$\Lambda$-CDM model of cosmology. The measurements of the rotational curve of
our galaxy suggests the presence of a DM halo, through which ordinary,
luminous galactic matter is travelling in its rotation around the galactic
center. This creates a relative motion between an observer on Earth and the
particles in the halo that scientists seek to exploit to detect DM through
their elastic scattering with ordinary matter. In particular, low-energy
(1–100 keV) nuclear recoils (NR) are expected to be the clearest evidence of
WIMP interactions.

Given their rarity, the main experimental challenge of direct DM searches in
the GeV mass region is to discriminate NR from interactions induced by other
particles, which have largely higher rates. The apparent WIMP wind would
create two peculiar effects for an observer on Earth, which can be exploited
for a positive identification of a DM signal. Since, in its rotation around
the Sun, the Earth’s orbital velocity is anti-parallel to the DM wind during
summer and parallel during winter, the observed DM rates inside the detector
are expected to display a seasonal modulation of a few percent. A much more
robust signature is provided by the diurnal directional modulation of the DM
signal. The peak flux, in fact, is expected to come from the direction of
solar motion around the center of our galaxy, which happens to point towards
the Cygnus constellation. Due to the Earth’s rotation around its axis
(oriented at 48∘ with respect to the direction of the apparent DM wind), an
observer on Earth would see the average incoming direction of DM changing by
$\sim$96∘ every 12 sidereal hours. The amplitude of the direction modulation
depends on the relative angle between the laboratory frame and the Earth axis,
with the maximum at 45∘ inclination and no modulation along directions
parallel to the axis.

The determination of the incoming direction of the WIMP can therefore provide
useful information to infer a correlation with an astrophysical source Mayet
et al. (2016) that no source of background can mimic. Directional measurements
can furthermore discriminate between various DM halo models and provide
constraints on WIMP properties, unlike conventional non-directional detectors
Mayet et al. (2016).

While the last few decades have seen enormous advances in direct DM searches,
leading to many orders of magnitude of improvement for masses larger than 10
GeV, the O(GeV) mass range still remains theoretically well-motivated Zurek
(2014); Petraki and Volkas (2013); Hochberg et al. (2015). Despite the great
effort devoted to lowering the threshold for nuclear recoils to include DM
scattering directly from electrons Essig et al. (2012a, b); Agnes et al.
(2018); Crisler et al. (2018); Agnese et al. (2018); Aprile et al. (2020) or
to exploit new signatures such as the Migdal effect Bernabei et al. (2007);
Ibe et al. (2018); Bell et al. (2020); Dolan et al. (2018); Grilli di Cortona
et al. (2020) and photon bremsstrahlung Cavoto et al. (2018), the O(GeV) mass
range is still largely unexplored.

Given the kinematics of elastic scattering, a direct DM detection experiment
achieves its best sensitivity for WIMP masses equal to the target mass nuclei.
The maximum fraction $\epsilon$ of the energy that can be transferred to a
target of mass $m_{T}$ by a WIMP of mass $m_{\chi}$ is in fact given by:

$\epsilon=\frac{4\rho}{\left(\rho+1\right)^{2}}$ (1)

with $\rho=\frac{m_{T}}{m_{\chi}}$. Therefore, low-mass target nuclei, such as
hydrogen and helium, are the best choices to maximise the sensitivity to
O(GeV) WIMP masses.

The CYGNO experiment proposes an innovative approach to the direct DM search
challenge. A high-resolution 3D gaseous time projection chamber (TPC) operated
at atmospheric pressure is employed with low-mass target nuclei, such as
helium and fluorine, to boost the sensitivity to O(GeV) WIMP masses for both
spin- independent (SI) and spin-dependent (SD) couplings. It is also important
to notice that low mass nuclei will result in longer track lengths, easing the
determination of their direction and thus increasing directional sensitivity.
Studies to add a hydrogen-based gas to provide even lighter targets are
ongoing. The topological signature of the recoil event also improves particle
identification and hence rejection of natural radioactivity backgrounds, in
particular electron recoils (ER) produced by photon interactions down to low
energy thresholds. The possibility of operation at atmospheric pressure
guarantees a reasonable volume-to-target-mass ratio, while at the same time
allowing for a reduction in the engineering requirements of the vessel (hence
internal backgrounds). The possibility of a high resolution 3D TPC, such as
the one foreseen by this project, will allow CYGNO to explore new physics
cases including, among others, the elastic scattering of sub-GeV DM Baracchini
et al. (2020) and of solar neutrinos Seguinot et al. (1992); Arpesella et al.
(1996). Moreover, operating at atmospheric pressure would allow a high-mass
target to be exposed without the need of very large volumes.

The results obtained with current prototypes (Section 3) are the basis for the
design of a 1 m3 demonstrator that is the subject of this paper. According to
the performance of this, the collaboration will propose a larger detector for
a competitive experiment. With this program, CYGNO fits in the context of the
wider international CYGNUS effort to establish a galactic directional recoil
observatory that can test the DM hypothesis beyond the neutrino floor and
measure the coherent scattering of neutrinos from the Sun and supernovae
Vahsen et al. (2020).

##  2 The Experimental Approach

The CYGNO experiment goal is to deploy at INFN Gran Sasso Laboratories (LNGS)
a high-resolution TPC with optical readout based on gas electron multipliers
(GEMs) working with a helium/fluorine-based gas mixture at atmospheric
pressure for the study of rare events with energy releases in the range
between hundreds of eV up to tens of keV.

Although challenging, gaseous TPCs constitute a promising approach to
directional DM searches providing a set of crucial features:

  * •

TPCs usually comprise a sensitive volume, filled with gas or liquid, enclosed
between an anode and a cathode generating a suitable electric field in it Marx
and Nygren (1978); Nygren (1974); Atwood et al. (1991). The passage of an
ionising particle produces free electrons and ions that start to drift towards
the above-mentioned electrodes. These are usually segmented and read out to
provide granular information about the charge collection point on the plane.
The third coordinate can be evaluated from the drift time measurement.
Therefore, TPCs are inherently 3D detectors capable of acquiring large
sensitive volumes with a lower amount of readout channels with respect to
other high-precision 3D tracking systems;

  * •

Gaseous detectors can feature very low-energy detection thresholds. A single
electron cluster can be produced with energy releases of the order of few tens
of eV and, in gases, this has a very good chance of reaching the
multiplication region to produce a detectable signal;

  * •

A measurement of the total ionisation indicates the energy released by the
recoil, and (depending on the readout plane granularity) the profile of the
energy deposit along the track can be measured with high precision, providing
excellent background discrimination;

  * •

Depending on the energy and mass of the recoiling particle and on the gas
density, the track itself indicates the axis of the recoil, and the charge
profile along it encodes the track orientation (head-tail), providing an
additional powerful observable for DM searches;

  * •

A large choice of gasses can be employed in TPCs, including light nuclei with
an odd number of nucleons (such as fluorine), which are also sensitive to both
SI and SD interactions in the O(GeV) mass region;

  * •

A room-temperature and atmospheric-pressure detector results in operational
and economical advantages, with no need for cooling or vacuum sealing. These
choices allow for a simpler technology and experiment realization and more
straightforward scaling when compared to cryogenic solutions currently
dominating the DM direct search scene;

  * •

The use of a gaseous target reduces the interaction probability with respect
to denser material (liquid or solid). Nevertheless, TPCs up to 100 m3 of
active volume have already been successfully operated Alme et al. (2010);
Lippmann (2014), showing the feasibility of very large detectors with large
active masses.

###  2.1 The Optical Readout

Gas luminescence is a well-studied and established mechanism: charged
particles traveling in the gas can ionize atoms and molecules but can also
excite them. During the de-excitation processes, photons are emitted. The
amount and spectrum of light produced strongly depends on the gas, on its
density and on the possible presence and strength of an electric field. In
most common gas mixtures, the number of emitted photons per avalanche electron
can vary between $10^{-2}$ and $10^{-1}$ Fraga et al. (2003); Margato et al.
(2013); Baracchini et al. (2020); Monteiro et al. (2012).

The idea of detecting the light produced during the multiplication processes,
proposed many years ago Dominik et al. (1989), has received renewed attention
in recent years. The optical readout approach, in fact, offers several
advantages:

  * •

Highly performing optical sensors are being developed for commercial
applications and can be easily procured;

  * •

Light sensors can be installed outside the sensitive volume, reducing the
interference with high-voltage operation and gas contamination;

  * •

The use of suitable lenses allows the possibility of imaging large O(1) m2
areas with a single sensor while maintaining an O(100) $\mu$m effective pixels
transverse size.

In recent years, an increasing number of tracking detectors have started
employing micro-pattern gaseous detectors (MPGDs). Their major advantages are
their very high achievable granularity and rate capability, together with
mechanical robustness. The production technology for MPGDs nowadays guarantees
very high-quality devices, providing stable and uniform operation. In
particular, GEMs Sauli (1997) have already been used to equip very large areas
with high spacial and time resolution Alme et al. (2010), and have more
recently been employed coupled to pixelised light sensors, showing very good
performances Margato et al. (2004); Marafini et al. (2015); Phan et al.
(2017); Fraga et al. (2003).

Charge coupled devices (CCD) have been widely used in the past as high
granularity light sensors for optical TPC approaches (Fraga et al., 2002; Phan
et al., 2017; Mavrokoridis et al., 2014). CCDs’ main limitation for the study
of rare events in the 1-100 keV energy range is represented by the high level
of readout noise, up to 5 to 10 electrons RMS per pixel. More recently,
cameras based on active pixel sensor (APS) technology developed on
complementary metal-oxide semiconductors (CMOS) have been developed that can
reach tens of millions of pixels with sub-electron readout noise and single
photon sensitivity (usually referred as scientific CMOS (sCMOS).

The CYGNO collaboration proposed the introduction of sCMOS-based optical
devices for GEM readout in 2015 Marafini et al. (2017). The high sensitivity
of this technique resulted in a very good performance in particle detection
not only at the energies of interest for DM searches (as is illustrated in
Section 3), but also for minimum ionising particles from both cosmic rays and
high energy electrons Marafini et al. (2015); Antochi et al. (2018); Marafini
et al. (2018); Pinci et al. (2018); Antochi et al. (2020).

Because the current frame rate available for CCD or sCMOS is still low
compared to the temporal extent of typical TPC signals, such devices can
provide only 2D projection of the recoil track. In order to achieve 3D track
reconstruction, the CYGNO experiment aims at complementing the sCMOS image
information with the signal of a fast light sensor (PMT or SiPM) that can
provide the track profile along the drift direction.

###  2.2 The Gas Mixture

The relative photon yield, defined as the ratio between the number of produced
photons and the total number of secondary electrons produced in the avalanche
process, and in general the overall detector performances, are significantly
dependent on the gas characteristics: ionization statistics, transport
properties (drift velocity and diffusion), electron multiplication and light
production. In the context of optical TPCs for DM searches, CF4 is a
particularly interesting gas because of its well-known property as an
efficient scintillator. Furthermore, the large fluorine content provides
sensitivity to spin-dependent WIMP-proton interactions. It was demonstrated in
previous studies Fraga et al. (2003) that CF4-based mixtures have electro-
luminescence emission spectra with a large peak around 600 nm, where Si-based
sensors (CCD or sCMOS) offer their highest quantum efficiency.

For these reasons, He/CF4 mixtures in different proportions were extensively
studied within the CYGNO project. While the light yield increases for larger
amounts of helium, the detector electrical stability improves for higher CF4
contents. As explained in Baracchini et al. (2020); Campagnola (2018\.
http://cds.cern.ch/record/2313231), the best compromise was found for a
mixture with 60% helium and 40% CF4. The behaviors of the diffusion
coefficients and drift velocity for different electric fields were calculated
with Garfield Veenhof (1993, 1998) and are shown in Figure 1.

Figure 1: Transverse and longitudinal diffusion coefficients for He/CF4 60/40
(left) and electron drift velocity as a function of the drift field (right).

As can be seen from Figure 1, a remarkable additional advantage of the use of
CF4 is the small electron diffusion, which can provide a reduced deterioration
of the track’s original shape.

For this mixture, an average energy loss per single ionization of 42 eV was
estimated. For a minimum ionising particle, 3 ionizations per track millimetre
are expected with about 2 electrons per cluster, resulting in an energy loss
of about 250 eV/mm. An example of an image of a few cosmic rays is shown in
Figure 2: ionization clusters are well-visible along the tracks.

Figure 2: Detail of an image collected with the sCMOS sensor of several tracks
in cosmic rays.

The effective ranges of electron and He-nuclei recoils were simulated,
respectively, with the Geant4 Agostinelli et al. (2003) and Stopping and Range
of Ions in Matter (Srim) software (Visit the http://www.srim.org/ site for
more information, accessed on 18 November 2021). The average 3D ranges (i.e.,
the distance between the production and absorption point) as a function of the
particle kinetic energy are shown in Figure 3:

  * •

He-nuclei recoils have a sub-millimetre range up to energies of 100 keV and
are thus expected to produce bright spots with sizes mainly dominated by
diffusion effects;

  * •

Low-energy (less than 10 keV) electron recoils are, in general, larger then
He-nuclei recoils with the same energy and are expected to produce less
intense spot-like signals. For a kinetic energy of 10 keV, the electron range
becomes longer than 1 mm, and for a few tens of keV, tracks of a few
centimetres are expected.

Figure 3: Average 3D distance between the production and absorption point for
electron- and He-nucleus recoils as a function of their kinetic energy in a
He/CF4 (60/40) gas mixture.

Measurements with other mixtures are also being carried out, including, in
particular, the possible use of small amount of hydrocarbons (e.g., C4H10 or
CH4) to add protons as low mass targets. Additionally, alternative gases with
reduced global warming power gases (e.g., HFO) are being tested.

##  3 Experimental Results with Lemon Prototype

The experimental results obtained with the prototype named the Long Elliptical
MOdule (Lemon) represents the most comprehensive example currently available
of the performance achievable with the CYGNO approach. The Lemon detector,
shown in the schematic of Figure 4, is composed of:

  * •

A gas sensitive volume of 7 litres contained in a 20 cm long cylindrical field
cage (FC) with an elliptical base with 24 cm and 20 cm axes [A];

  * •

A 24 $\times$ 20 cm2 stack of 3 GEMs as the amplification stage facing the
sCMOS camera [D], optically coupled through a 50 cm long (see Equation (2))
black bellow [C] to protect the optics from external light, with the bottom
electrode of the last GEM used as the anode;

  * •

A mesh-based semitransparent cathode closing the volume on the opposite side,
behind which a PMT [B] is placed.

A more detailed description of this prototype can be found in Ref. Costa et
al. (2019); Antochi et al. (2020).

Figure 4: The Lemon prototype Antochi et al. (2021). The elliptical sensitive
volume (A), the fast photo-multiplier (B), the optical bellow (C) and the
sCMOS-based camera (D) are indicated.

Lemon standard operating conditions were based on the following sets:

  * •

An He/CF4 (60/40) gas mixture flux of 200 cc/min;

  * •

An electric drift field within the sensitive volume ED = 0.5 kV/cm;

  * •

An electric transfer field in the 2 mm gaps between the GEMs ETransf = 2.5
kV/cm;

  * •

A voltage difference across the two sides of each GEM VGEM = 460 V;

According to results presented in Campagnola (2018\.
http://cds.cern.ch/record/2313231), in this configuration, an electron
multiplication of about 1.5$\times 10^{6}$ is expected.

As anticipated in Section 2.1, high-quality cameras are a crucial ingredient
for the experiment results. As a result, an ORCA Flash 4.0 camera (for more
details visit www.hamamatsu.com) was selected to equip Lemon. This device is
based on a 1.33 $\times$ 1.33 cm2 sCMOS sensor, subdivided in 2048 $\times$
2048 pixels with an active area of 6.5 $\times$ 6.5 $\mu$m2 each, with a
quantum efficiency of 70% at 600 nm and a readout noise of 1.4 electrons RMS.
The response and noise level of this sensor were tested with a calibrated
light source Marafini et al. (2015). A response of 0.9 counts/photon was
measured together with a RMS fluctuation of the pedestal of 1.3 photons/pixel.

In order to image the large GEM surface, the camera is equipped with a
Schneider lens with a 25.6 mm focal length $f$ and a 0.95 aperture $a$. Since
at a distance $d$ the lens provides a de-magnification of

$\delta=\frac{f}{d-f}$ (2)

the camera optical system is placed at $d$ = 52.6 cm distance from the GEMs in
order to image a 26 $\times$ 26 cm2 area. The solid angle covered by the
sensor, which in turn determines the geometrical acceptance of photons, is
given by

$\Omega=\frac{1}{\left(4(1/\delta+1)\times a\right)^{2}}$

resulting in $1.6\times 10^{-4}$ for the Lemon layout.

In order to complement the 2D track projection recorded by the sCMOS with the
track trajectory along the drift direction, the arrival time profile of the
primary electrons could be extracted from the signal induced on the third GEM
bottom electrode. Nonetheless, this is expected (and explicitly shown in
Antochi et al. (2018)) to suffer from considerable noise (typically due to
jitter on the high voltage supply line) that could prevent signal detection at
the low energies at play. To overcome this limitation, a light track time
profile was concurrently readout by a Photonics XP3392 Photo Multiplier Tube
(PMT), each with a 5 ns rise-time, a maximum QE of 12% for 420 nm and a 76 mm
square-window, providing sensitivity to a single photon and significantly
reduced noise with respect to the GEM electric signal.

The performances of Lemon has been tested in recent years at the INFN
Laboratori Nazionali di Frascati (LNF) overground laboratory by means of
radioactive sources (${}^{55}\textrm{Fe}$, AmBe), high-energy (450 MeV)
electrons from a beam at the Beam Test Facility (BTF, B.Buonomo et al. (2016);
P.Valente et al. (2016)) and cosmic rays, and are summarised in the following.

###  3.1 Operation Stability

The performance and long-term stability of Lemon was tested for a month long
run, during which the detector was exposed to environmental radioactivity,
cosmic rays and a ${}^{55}\textrm{Fe}$ source Baracchini et al. (2020). During
the whole period, all currents drawn by the high-voltage channels supplying
the electrodes of the GEM stack were monitored and recorded to identify sudden
and large increases that could indicate discharges or other electrostatic
issues. During the test, two different kinds of electrostatic instabilities
were observed:

  * •

Hot-spots appearing on the GEM surface. While in some cases these would fade
out with time, sometimes they started to slowly grow up to tens of nA (on a
time scale of minutes). These are very likely due to self-sustaining micro-
discharges happening in one or a few GEM holes;

  * •

High charge density due to very high ionizing particles or charge accumulation
on electrode imperfections can suddenly discharge across GEM holes. In these
events, a sudden increase in the drawn current is recorded with a voltage
restoring on the electrodes through $10~{}\Omega$ protection resistors on a
time basis of a few seconds. Even if these events are less frequent than hot
spots, they can be dangerous for the GEM structure and the energy released in
the discharge can, in principle, damage it.

An automatic recovery procedure was implemented, triggered by the raising of
the GEM currents, which was able to recover both hot-spots and discharges by
lowering and gradually restoring the GEM voltage operating conditions in a few
minutes.

An average of 16 such instabilities per day were observed and the total dead
time introduced by the recovering procedures was less than 4$\%$. A detailed
analysis of the time interval between two consecutive phenomena did not show
any correlation between two subsequent events, nor any increase of their
rates. This study demonstrated that the detector operation looked very safe
and stable, and the obtained performance is considered to be satisfactory.
Different gas proportions were tested, and a lower amount of CF4 resulted in a
less stable electrostatic configuration.

###  3.2 Light Yield and Energy Resolution

The light production was evaluated by analysing the response of sCMOS and PMT
to interactions in a gas of 5.9 keV X-rays produced by a ${}^{55}\textrm{Fe}$
source. The sCMOS images were acquired in a free-running mode (i.e., without
using any trigger signal) with an exposure of 100 ms. The sCMOS pixels’
pedestal noise was extracted from an average of 100 images acquired in the
absence of any light signal and subtracted from each image before the
analysis. An elementary clustering algorithm based on the nearest neighbor-
cluster (NNC) is applied to 4 $\times$ 4 rebinned images to select
${}^{55}\textrm{Fe}$ induced energy deposits.

Figure 5 shows, on the left, the light spectrum of the ${}^{55}\textrm{Fe}$
events reconstructed from the sCMOS images, and on the right, the integral of
the charge signal measured by the PMT.

Figure 5: Distribution of the light content of the ${}^{55}\textrm{Fe}$ events
reconstructed from the sCMOS images (left), and distribution of the charge
measured by the PMT signals (right).

The average light yields were evaluated from a Polya fit Blum et al. (2008) to
the two distributions, resulting in an average of 514 $\pm$ 63 photons per keV
detected by the sCMOS camera (in agreement with results obtained with lower
VGEM and ETransf Costa et al. (2019)), with an RMS energy resolution of 12%
and an average of (12.0 $\pm$ 0.2) pC per keV together with an RMS energy
resolution of 16% by the PMT charge signal.

The energy resolutions are mainly due to the Poisson’s fluctuations of the
numbers of primary electrons (8%) and of the gain of the first GEM. The latter
term can be simply evaluated to be about 10% by supposing an exponential
distribution for it Pinci (2006\. http://cds.cern.ch/record/1005178), with an
average value of 100.

###  3.3 Detection Efficiency

The detection efficiency along the whole 7 litre sensitive volume was studied
acquiring sCMOS images by changing the electric field strength within the
field cage (drift field) and the position of a collimated ${}^{55}\textrm{Fe}$
source in order to vary the X-ray interaction distance to the amplification
region. Figure 6 shows, on the left, the number of reconstructed
${}^{55}\textrm{Fe}$ spots in the sCMOS images with the algorithm illustrated
in Section 3.2 as a function of drift field (ED), normalized to the value
obtained for ED = 600 V/cm. For ED larger than 300 V/cm, a plateau is found,
suggesting a full detection efficiency. The right panel of Figure 6 shows the
dependence of the number of reconstructed spots normalised to its average
value on the source distance from the GEM amplification plane, as measured
with an ED of 600 V/cm. A constant behavior is found in all tested positions,
indicating a stable detection efficiency that is not dependent on the
interaction point distance from the GEM.

Figure 6: Behavior of the normalized number of ${}^{55}\textrm{Fe}$ spots as a
function of the drift electric field (left) and event depth in the sensitive
volume (right).

###  3.4 Track Absolute Distance along the Drift Direction

The possibility to determine the absolute $z$ position of the energy deposit
exploiting the electron drift was studied with 450 MeV electrons from the LNF-
BTF facility Antochi et al. (2020). The transverse diffusion in the drift gap
can, in fact, be used to extract the drift length and thus infer the absolute
z distance at which the track occurred. Seven millimetre-long track segments
were used to evaluate the detector performance for small energy releases.

As described in Antochi et al. (2021), the light profile transverse to the
track direction possesses a Gaussian shape with the total light $L$ being
proportional to $\sigma\times$ A (where $\sigma$ is the RMS and A is the
amplitude of the Gaussian). Because of the attachment effect in gas Anderson
et al. (1992), the probability for an electron to reach the GEM stack
decreases exponentially with a mean free path $\lambda$ (and thus
$L=L_{0}e^{-z/\lambda}$). Since $\sigma$ is expected to increase as $\sqrt{z}$
because of diffusion in gas, the ratio $\eta$, defined as $\sigma$/A, is
expected, at a first order approximation, to grow quadratically with the drift
distance Antochi et al. (2020).

Similarly, longitudinal electron diffusion modifies the electron time of
arrival on the GEM and thus the time structure of the signal recorded by the
PMT. Additionally, in this case, the ratio $\eta_{PMT}=\sigma_{PMT}/A_{PMT}$
is expected to increase with z.

Figure 7 shows the dependence of $\eta$ and $\eta_{PMT}$ as a function of z
with a superimposed quadratic fit.

Figure 7: Dependence of $\eta$ on the left and $\eta_{PMT}$ on the right as a
function of the track distance from the GEM (see text for details).

The inset shows the distribution of the ratio between the RMS and the average
values of the spectra of $\eta$ obtained at the various $z$. These observables
can be, therefore, used to evaluate the absolute $z$ with about 15$\%$
uncertainty over a 20 cm length Antochi et al. (2020). These features will
allow the fiducial signal volume to be selected, therefore rejecting
background signals coming from the radioactivity of TPC materials, like the
cathode or GEMs.

###  3.5 Detection and Identification of Nuclear and Electron Recoils

Thanks to the detailed information provided by the high granularity optical
sensor, track properties like the shape, the length and width, and light
density, among others, can efficiently be exploited to identify and separate
ER which are surely due to background sources from NR which are possible
candidates of DM signals.

To quantify these features within the CYGNO experimental approach, a track
reconstruction and identification algorithm was developed for the analysis of
the sCMOS images called iDBSCAN Baracchini et al. (2020) and based on an
adapted version of the well-known Density-Based Spatial Clustering of
Applications with Noise (DBSCAN) Ester et al. (1996). The reconstructed
clusters were used as seeds for a superclustering algorithm based on Geodesic
Active Contours (Gac Caselles et al. (1997); P. Marquez-Neila and L. Baumela
and L. Alvarez (2014)), which gathers together sub-clusters of the energy
deposits belonging to a single track. The Gac, exploiting the number of
photons in each pixel as a third dimension to the phase space of the points
considered, separately identifies clusters displaying different intensity
(i.e., energy deposition patterns) which are, therefore, likely belonging to
different classes of particles interactions.

The performance of the algorithm was studied using 5.9 keV energy deposits
from 55Fe and NR produced by an AmBe source Baracchini et al. (2020). The 59
keV photons produced by AmBe were nearly completely shielded by a lead shield
built around the detector. Data were taken overground at LNF and were,
therefore, highly contaminated by cosmic ray particle interactions.

In order to select a pure sample of nuclear recoil candidates produced by the
interaction of the neutrons originating from the source and to identify
various sources of backgrounds, several cluster shape observables were
exploited. Among these, the  _slimness_ ($\xi$) was used to mainly distinguish
cosmic rays and the light _density_ ($\delta$) to discriminate electron from
nuclear recoils. The slimness is defined as the ratio of the Gaussian width of
the track in the transverse direction over the projected path length. The
density is the ratio of the total number of photons detected by all the pixels
gathered in the cluster over the total number of pixels.

As shown in Figure 8, by simply exploiting a selection on $\delta$, an ER
background rejection in the energy region around 5.9 keVee of 96.5$\%$
(99.2$\%$) was found together with 50$\%$ (40$\%$) NR efficiency Baracchini et
al. (2020).

Figure 8: Detection efficiency for nuclear recoils ($\epsilon^{total}_{s}$) as
a function of their detected energy for electron recoils efficiency of 4%
(squares) and 1% (circles).

While this cut-based approach is minimalist and could be improved by more
sophisticated analyses combining several topological variables as well as the
information from PMT waveforms, it shows that a rejection factor larger than
102 for electron recoils at $E=5.9\,\textrm{keV}$ can be obtained with a gas
detector at atmospheric pressure while retaining a high fraction of NR event
signals.

##  4 The CYGNO Experiment Roadmap and Synergies

The CYGNO project will be developed through a staged approach to optimise the
apparatus and improve its performance while better mitigating any unexpected
cost.

This roadmap, comprises:

  * •

PHASE_0: the installation, in 2022, of a large prototype (50 litres of
sensitive volume) underground at the INFN-Laboratori Nazionali del Gran Sasso
(LNGS) to study its performance in a low background environment and validate
MC simulation;

  * •

PHASE_1: testing, in 2024–2026, of the scalability of the experimental
approach on a O(1) m3 detector while studying and minimising the radioactivity
background due to apparatus material;

  * •

PHASE_2: depending on the results of the previous phases, a larger scale
experiment (30–100 m3) will be proposed to explore the 1–10 GeV WIMP mass
region with high sensitivity for both SI and SD couplings and the possibility
of performing the first measurement of low-energy solar neutrinos. In both
cases the _directionality capabilities_ of the CYGNO approach will allow not
only detection of the interactions, but will also provide useful information
for astrophysical studies of incoming particles.

The roadmap details and synergies with other projects are outlined in the
following sections.

###  4.1 CYGNO PHASE_0: the LIME Prototype

The Long Imaging ModulE (Lime, shown in Figure 9), is the larger prototype
foreseen to conclude the R&D phase of the project. It was conceived to have
the same drift length (50 cm) of the final demonstrator (Section 4.2) and the
same readout scheme based on triple 33 $\times$ 33 cm2 thin GEMs (stretched on
a plexiglass frame to reduce radioactivity) imaged by a single sCMOS sensor
and 4 small PMT symmetrically placed around the sensor at a distance of about
15 cm from it and 25 cm apart from the GEM surface.

The PHASE_1 demonstrator will be based on readout modules having the LIME
dimensions and layout. For this reason, its successful assembly and operation
will be paramount to substantiate the efforts and confirm the scientific and
technological choices towards the 1 m3 detector.

The new Hamamtsu ORCA-Fusion Camera was employed
(https://www.hamamatsu.com/eu/en/product/type/C14440-20UP/index.html, accessed
on 18 November 2021) with improved performance with respect to the Orca Flash
in terms of reduced noise (0.7 versus 1.4 electrons per pixel), a larger
number of pixels (2304 $\times$ 2304 versus 2048 $\times$ 2048) and a larger
sensitivity spectrum with a maximum quantum efficiency at 600 nm of 80$\%$
versus 70%. The choice of 4 PMT resides in the possibility of better
reconstructing the track position and inclination through the center of
gravity of the light signal from the 4 sides.

The gas volume is enclosed in a 10 mm thick plexiglass box that provides gas
tightness. The field cage is composed by square copper rings, with a rounded
shape to avoid discharges, at a 16 mm pitch.

In its underground installation, LIME will be equipped with the same DAQ
system and gas system envisaged for the realisation of PHASE_1, which is
currently undergoing testing.

Figure 9: Pictures of the LIME detector. Left: front view of the field cage
with the copper cathode visible at the end. Right: field cage copper rings in
the gas vessel.

A response of about 650 ph/keV was measured that has to be compared with 514
ph/keV obtained with Lemon (see Section 3.2) thanks to the larger sensitivity
of the Orca Fusion camera. The low sensor noise (about 1 photon/pixel) will
allow operation with an effective energy threshold of hundreds of eV. The
energy resolution on the 55Fe peak is measured to be 14$\%$ across the whole
50 cm drift length, with full efficiency in the full 50 litres volume.
Furthermore, LIME has already been operated for one entire month, with its
currents continuously monitored and logged, showing comparable stability to
Lemon (see Section 3.1).

The installation at LNGS, completed with the PHASE_1 auxiliary systems, will
allow:

  * •

The detector performance in low radioactivity and a low pile-up configuration
to be tested;

  * •

The real radioactive background present in the site to be characterized, and
then the GEANT4 simulation to be validated.

###  4.2 CYGNO PHASE_1: the O(1) m3 Demonstrator

Having optimised and assessed all technological aspects with LIME underground
tests, the project will move to PHASE_1, with the aim of studying and
minimising material radioactivity effects on a real experiment scale,
therefore evaluating its sensitivities.

The exact PHASE_1 detector size will depend on the available underground site,
which is still under discussion; regardless, a 1 m3 active volume will be
discussed in this paper, schematically shown in Figure 10, with the
consideration that the foreseen layout and auxiliary system can be directly
and easily adapted to the definitive detector dimensions.

The active volume of the detector will be contained in a gas volume vessel
(GVES) realized with PMMA to lower the material intrinsic radioactivity,
reduce the gas contamination, and ensure the electrical isolation from the
cathode and field cage. The GVES will contain 2 field cages, 500 mm long, with
2 back-to-back TPCs separated by a central aluminised mylar cathode following
the DRIFT example Daw et al. (2012); Battat et al. (2017, 2015). This foil is
expected to minimise backgrounds induced from recoils by the decay chain of
radon.

Figure 10: CYGNO PHASE_1 Detector Layout.

Each of the 2 end-caps will have an active area of 1 m2 surface, readout by a
matrix of $3\times 3$ modules of $33\times 33$ cm2 area. Furthermore, each one
will be equipped with a stack of 3 GEMS, 1 sCMOS and 4 PMT, identical to the
LIME prototype (see 4.1).

The GEMs will be assembled adapting the technique discussed in Akl et al.
(2015). The mechanical rigidity will be provided by the outer frame that will
be anchored to the GVES. The assembled GEM stack will be inserted into the
GVES through vertical slits, which will allow an easy substitution of a single
GEM foil in case of damage.

The high-voltage system has been conceived with the assumption of independent
lines for each electrode of the GEM foils in order to ensure the safe and
reliable operation of the detector modules.

The DAQ system will be able to collect synchronized data from cameras and
photodetectors and to handle the following specifications:

  * •

Camera exposure from 0.2 to 1 second (1 to 5 Hz frame rate);

  * •

10 MB of data per picture (5 MP, 16 bits/pixel);

  * •

12-bit digitization of photodetector waveforms at $\sim 250$ MS/s in $\lesssim
1~{}\mu$s windows.

Fast responses provided by the PMT will be exploited to trigger the
acquisition of sCMOS sensors. Different possible trigger scheme are under
evaluation along with the possibility of running either in trigger or trigger-
less mode.

The acquisition will be distributed through a redundant system of machines to
ensure the system stability. To acquire fast photodetectors, digitization
boards are considered. In this scenario, the bottleneck for the acquisition
would be the throughput to the disk, typically limited to O(200 MB/s), and
some preselection of the images by a farm of CPUs would be needed.

####  4.2.1 PHASE_1 Shielding Scheme and Material Budget

A Geant4 based Monte Carlo simulation of the whole apparatus, shown in Figure
10, has been developed to study detector backgrounds and to optimise the
choice of shielding and materials.

The effect of the diffused environmental gamma rays and neutron flux was
studied. Different configurations of external passive shielding with layers of
copper, lead and water were studied with the goal of having less than 104
photons/year interacting in the target gas between 1 keV and 20 keV. The
choice of this benchmark is backed up by indication from measurements Riffard
et al. (2016); Phan et al. (2016) and simulations within the CYGNUS
collaboration Vahsen et al. (2020) showing that a TPC with 3D readout can
reach a 105 gamma/year rejection factor at O(keV).

While the use of lead can significantly reduce the overall setup dimensions,
the simulation showed that this configuration would require archaeological
lead in order not to induce additional background from the shielding,
therefore largely raising the cost of this layer. A cost-benefit optimisation
of the shielding materials and thicknesses was hence developed, identifying 2
m of water + 5 cm of copper as the optimal configuration. This shielding
provides an attenuation by a factor of 10-7 for external photons and 5
$\times$ 10-5 for external neutrons, reducing the number of expected electron
recoils in the active volume below 103 cpy (with O(1) cpy nuclear recoils) in
the range 1-20 keV.

For the evaluation of the backgrounds generated by detector components, the
natural photon radioactivity of the parts expected to give the largest
contributions was measured with high-purity Germanium detectors thanks to the
support of LNGS Special Techniques Service. Results are reported in Table 1.

Table 1: Measured activity of the internal detector components expected to
produce the largest backgrounds in the active volume. The isotopes in
parentheses indicate the activity from that particular part of the decay
chain. Upper limits are given at the 90% confidence level.

Component |  238U (234mPa) | 238U (226Ra) | 235U |  232Th (228Ra) |  232Th (228Th) |  40K
---|---|---|---|---|---|---
Camera body [Bq/pc] | 7 | 1.8 | 0.4 | 2.1 | 2.1 | 1.9
Camera lens [Bq/pc] | 0.9 | 0.41 | 0.031 | 0.08 | 0.08 | 11
GEM foil [Bq/$m^{2}$] | <0.104 | 0.004 | <0.002 | <0.004 | <0.002 | <0.045
Acrylic [Bq/kg] |  | 0.003 |  | 0.005 | 0.004 | 0.035

Regarding the GEMs (made of kapton foils, copper clad on each side), the major
source of background is found to come from the frames rather than the foils
themselves. For this reason, in the LIME prototype of PHASE_0, the triple
$33\times 33$ cm2 GEMs were mounted and stretched on low-radioactivity acrylic
frames, with the same technique foreseen to be applied to the PHASE_1
detector.

For what concerns the sCMOS optical system, a large 40K contamination was
observed in the lens glass. A high-purity synthetic fused silica (Suprasil®)
was selected as an alternative material for the fabrication of the lens, for
an expected $\sim$104 reduction of the contribution from this item. An overall
activity of less than 50 mBq/kg was found in recent measurements performed on
a sample at LNGS, confirming the very good properties of this material.

sCMOS cameras have not been employed yet in DM searches, and therefore their
intrinsic radioactivity has never been studied or optimised in this context.
For this reason, an extensive program working in close contact with sCMOS
camera producer companies and with LNGS Services to assess this aspect within
our experimental approach has started. Gamma spectroscopy of several sCMOS
cameras as a whole was performed, including models from companies other than
Hamamatsu, and verified that all display similar activities in the O(10)
Bq/piece. The measured activities of the Hamamatsu Orca Fusion are shown in
Table 1. A camera was disassembled in 20 different pieces, which are currently
under measurement in order to pinpoint the components introducing the largest
radioactivity contamination and possibly replace them by cleaner options.
Given the very large sCMOS activity, in the PHASE_1 design, they are foreseen
to be shielded by the 5 cm copper layer on all sides, except for the one
facing the GEMs.

Starting from these considerations, a background evaluation for a 1 m3 PHASE_1
detector was developed that includes the external gamma and neutron flux
contribution with the copper and water shielding discussed above and the
radioactivity contribution of the main internal components. For the latter,
the values measured at LNGS for the GEMs, camera lens, camera body and acrylic
for the gas vessel and data from the literature for the Cu of the cathode and
the field cage rings Castel et al. (2019) were employed. This study showed
that O(103) nuclear recoils and O($10^{6}$) electron recoils per year are
expected in the sensitive volume, with energy in the 0-20 keV range. It must
be noticed that the alphas produced by the GEMs represent the largest
contribution to the total NR rate and are absorbed in the gas within 5 cm from
them. As described in Section 3.4, by exploiting the effect of diffusion in
gas, the track absolute distance from the GEM can be evaluated with a
resolution better than 20%. Therefore, this NR background is expected to be
reduced to zero with a suitable selection on the drift distance without a
significant reduction of the detector fiducial volume. Apart from the current
lens, the largest amount of electron recoils is produced by the sCMOS cameras,
and, at a second order, by the GEMs.

This study represents the current evaluation of the expected backgrounds for a
1 m3 detector. Therefore it is the starting point for the optimisation and
assessment of the background level, which will be further minimised by the
detailed study of the GEM, sCMOS and optics materials.

###  4.3 CYGNO PHASE_2

A CYGNO detector with a volume of the order of several tens of cubic meters
would be able to generate a significant contribution to the search and study
of DM in the mass region below 10 GeV, both for SI and SD coupling. In case of
appearance of signals or evidence of interactions not due to ordinary matter,
the information provided by a directional detector (interaction position,
incoming particle direction and energy) will be fundamental to positively
confirm the galactic origin of the detected signal as DM and determine its
properties.

Such a detector could furthermore provide the first directional measurement of
solar neutrinos from the pp chain, possibly extending to lower energies the
Borexino measurement, as will be illustrated in Section 5.3.

As an example, Figure 11 shows how a 30 m3 sensitive volume apparatus with all
its shields (for a total volume of 2$\times 10^{3}$ m3) would fit into the
LNGS experimental Hall C.

Figure 11: CYGNO PHASE_2 possible setup.

The development of such a detector in terms of intrinsic background
minimisation, performance and costs would, of course, require an improved
scalable design, materials and readout. The possible improvements include, but
are not limited to, the following:

  * •

The development of custom sCMOS sensors, with features focused on CYGNO
requirements: low noise, high sensitivity and reduced intrinsic radioactivity
together with a lower production cost;

  * •

The design and realisation of low-radioactivity lenses with fixed focus and
large aperture;

  * •

The reduction of the intrinsic detector material radioactivity, with the
lesson learned after the results obtained with PHASE_1;

  * •

The development of innovative gas mixtures for optical readout (illustrated in
the following sub-sections) to boost the tracking performances and improve
sensitivity for low energy releases.

###  4.4 Hydrogen Rich Gas Mixtures

The presence of low-mass nuclei as targets in the gas mixture improves
detector performance mostly in the low DM mass region:

  * •

Momentum transfer is more efficient, as shown in Equation (1);

  * •

Longer lengths of light nuclear recoils in gas produces tracks which are more
easy to detect and with a clearer direction.

The collaboration is studying the effect of the addition of a small percentage
of iC4H10 (1–5%) to the He/CF4 gas mixture. First results demonstrate that,
even if the number of photons collected per keV released decreases up to a
factor of 3 (with a 5% addition), light signals are still clear and well-
visible. Studies on this and other hydrogen rich mixtures are still going-on
and represent a very promising opportunity to lower the effective DM mass
threshold.

###  4.5 INITIUM: an Innovative Negative Ion Time Projection Chamber for
Underground Dark Matter Searches

The challenging goal of INITIUM is to develop negative ion drift (NID)
operation within the CYGNO optical approach.

Negative ion drift is a peculiar modification of conventional TPCs (NI-TPC)
that involves the addition to the gas of a highly electronegative dopant
Martoff et al. (2000); Ohnuki et al. (2001). In this configuration, primary
electrons produced by an ionizing particle along its track in the gas are
captured at very short distances <10-100 $\upmu$m by electronegative
molecules, creating negative ions. These anions drift to the anode, where
their additional electron is stripped and gives rise to a standard electron
avalanche. Since anions’ mobility depends on mass, the difference in the time
of arrival of different anions effectively provides a measurement of the
position of the event along the drift direction. Full 3D detector
fiducialization can be obtained by exploiting this information (as achieved in
the DRIFT experiment) and background-free operation over 1 m3 Battat et al.
(2017). Thanks to these two features, NI-TPC readout planes can image a larger
volume than conventional TPC approaches, resulting in lower backgrounds and
costs per unit mass.

The SF6 compound has been recently demonstrated to work very well as a
negative ion gas between 20 and 100 Torr, including the possibility of high
gains and fiducialization via minority charge carriers Phan et al. (2017);
Ikeda et al. (2020); Lightfoot et al. (2007). Compared to the high-vapour
pressure, low flash point and low explosive mixture in air of the CS2 employed
by DRIFT, SF6 has the substantial advantages of much safer handling, combined
with easy radon purification and re-circulation, while at the same time
increasing the target fluorine mass. The studies proved, for the first time,
the feasibility of NID at nearly atmospheric pressure (0.8 atm) with
He/CF4/SF6 at 360/240/10 Torr with triple thin GEMs and charge pixel readout
(Timepix) Baracchini et al. (2018).

The goal of INITIUM is to develop a scintillating He/CF4/SF6-based gas mixture
at atmospheric pressure with a low content of SF6 for NID with optical
readout. If NID can be achieved within the optical approach, tracking could be
improved by the possibility of reconstructing the track shape along the drift
direction by sampling the recorded light at a kHz frame rate. At the moment,
such a high rate can be met only by cameras with low resolution and high
noise, which are not yet suited for low-energy rare event searches.
Nonetheless, given the fast development of the sCMOS technology, progress in
short time is possible, which could open the door to this possibility.

##  5 CYGNO Scientific Goals and Expected Physics Performances

A discussion about the expected sensitivity of CYGNO PHASE 1 to WIMP searches
and the tools developed to evaluate it (Section 5.1) is presented in the next
sections together with an overview of the experiment potentialities towards
additional directional searches.

###  5.1 WIMP-like DM Searches at Low Masses through Nuclear Recoil Signature

A statistical analysis based on the Bayesian approach to evaluate the
sensitivity of the CYGNO PHASE_2 30 m3 experiment to WIMP searches in the
presence of background was performed. Details on the used method are described
in the Appendix.

The CYGNO approach allows the measurement of both the energy and the direction
of the track simultaneously, and both of these will be combined to evaluate
the number of detected events for the final analysis. Nonetheless, since the
angular distribution discriminating power is significantly stronger than the
energy spectrum shape, this sensitivity study focuses only on the former for
the sake of simplicity. In addition, the background angular distribution can
reasonably be assumed to be isotropic in galactic coordinates, while its
energy spectrum will highly depend on the exact materials and shielding
employed in the experiment; it is therefore difficult to predict with
precision at this stage of the project development.

However, the energy threshold plays an important role in the determination of
the signal angular distribution together with the target nuclei. Moreover,
while the electrons’ kinetic energy ($\,\textrm{eV}_{ee}$ ) is very
efficiently translated into ionization in gas, an important part of slow NR
kinetic energy ($\,\textrm{eV}_{nr}$ ) is loss in scatterings with other
nuclei. The fraction of $\,\textrm{eV}_{nr}$ effectively producing ionization
is usually referred to as the quenching factor (QF).

In this sensitivity study, two energy thresholds were assumed: a conservative
1 $\,\textrm{keV}_{ee}$, backed up by the published results Costa et al.
(2019), and a realistic value of 0.5 $\,\textrm{keV}_{ee}$, extrapolated from
the improved performances obtained with the PHASE_0 LIME prototype (see
Section 4.1). In order to translate this into nuclear recoil energy, a SRIM
simulation was developed to evaluate the QFs for the elements in our gas
mixture, including hydrogen, given the discussion in Section 4.4. The QFs for
H, He, C and F in He/CF4 60/40 at 1 atm as a function of the nuclear recoil
energy E[$\,\textrm{keV}_{nr}$ ] were evaluated and found to be in the range
10%-30% for $\,\textrm{keV}_{ee}$ =100 eV and 60%-90% for
$\,\textrm{keV}_{ee}$ =100 keV. These result in effective energy thresholds of
1.4 (0.8) $\,\textrm{keV}_{r}$ for H, 2.1 (1.2) $\,\textrm{keV}_{r}$ for He,
3.1 (1.8) $\,\textrm{keV}_{r}$ for C and 3.8 (2.2) $\,\textrm{keV}_{r}$ for F
for a 1 (0.5) $\,\textrm{keV}_{r}$ energy deposit.

The signal angular distributions were hence calculated with these effective
thresholds in galactic coordinates, starting from Lewin and Smith (1996);
Gondolo (2002); Baxter et al. (2021) and neglecting the motion of the Earth,
as it was shown to have secondary relevance on the angular distribution.
Possible shapes of a DM signal nuclear recoil distribution are shown in 2D
galactic coordinates in Figure 12, where the expected anisotropic nature is
clearly visible. The final shape of the distribution strongly depends on three
elements: the DM mass, the element hit and the energy threshold. With the
chosen settings for the analysis, the angular distributions tend to be
strongly peaked at low masses and more spread out at heavier masses, where the
angular regions strongly suppressed by kinematics are less evident.

Figure 12: Two examples of the angular distribution of recoils due to DM in
Galactic coordinates, obtained by Monte Carlo simulations. Top: helium recoils
induced by 10 GeV/c2 DM. Bottom: fluorine recoils induced by 100 GeV/c2 DM.

In order to establish the credible interval (CI) of the sensitivity limits,
experiments are simulated by extracting events according to the expected
measured angular distributions discussed so far, adding detector effects.
Since CYGNO’s approach directional capabilities are still under evaluation,
for this study, an angular resolution of $30^{\circ}$ in the whole detectable
range is assumed, as from literature Nakamura et al. (2012) and from the
CYGNUS simulation Vahsen et al. (2020), with full head-tail recognition down
to the 1 keVee energy threshold.

A simple flat distribution of the number of expected signal events between 0
and 1000 is used, given that articulated signal prior probabilities cannot be
assumed without risking biases, because the actual cross-section of DM with
protons is unknown. Indeed, events per year is a non-negative defined
variable, and due to current limits in the DM community, it is hardly
believable that more than 1000 events per year would be produced in the CYGNO
detector.

The number of expected background events for CYGNO PHASE_2 cannot easily be
predicted at this stage of the project, since it will depend on the outcome of
PHASE_0 and PHASE_1 and the possible improvements discussed in Sections
4.3–4.5. For this reason, different possible background scenarios are
simulated, with 100, 1000 and 10,000 events per year. For these, a Poissonian
prior is used. Measurements with PHASE_1 and simulations informed from these
results will, in the future, allow a better estimate of the background yield.

For each scenario, the actual number of events is randomly extracted from this
Poissonian distribution and a direction is assigned to each, randomly sampling
the background angular distribution. After applying a Gaussian smearing to
account for the resolution, a histogram representing the measured event
direction in galactic coordinates is filled, with its binning reflecting the
angular resolution. In the hypothesis of only background, no events for the
WIMP-induced signal recoils are added. In order to avoid suffering from any
underfluctuation of the background (as undersampling), 500 data samples are
simulated, and the average result is taken as the final value.

The likelihood of the detected events to be the sum of background plus signal
(see Section A for details) is evaluated on each data sample. From these, the
posterior probability at 90%CI of the number of WIMP-induced recoil is
computed and averaged to obtain the final result.

In order to translate this into a limit in the cross-section versus mass
parameters space, it is important to take into account that, because the
target is a mixture of different elements, both the kinematics of the expected
DM-nucleus interactions and the expected rate calculation influence the
probability of each element to be detected differently as a function of the DM
mass. This is shown on Figure 13 for a 1 keVee energy threshold. The region of
the DM velocity distribution accessible to detection is limited at lower
values by the energy threshold and at higher values by the local escape
velocity (here taken as 544 km/s Smith et al. (2007)). For low DM masses, the
detection of a nuclear recoil is strongly susceptible to the experiment energy
threshold. Because of their light masses, hydrogen and helium detection
dominate the early part of the figure, and the rising probabilities of carbon
and fluorine reflect their different thresholds. At higher DM masses, when the
window is quite large, the A2 cross section enhancement (where A is the atomic
number) dominates, making fluorine the most probable detectable element.
Figure 13 also displays the minimum detectable DM mass by each element with a
1 (0.5) keVee energy threshold; that is, 0.5 (0.3) GeV/c2 for H, 1.0 (0.7)
GeV/c2 for He, 1.9 (1.4) GeV/c2 for C and 2.5 (1.9) GeV/c2 for F recoils.

Figure 13: Relative probability of nuclear recoils being detected, given that
a recoil was detected, as a function of the DM mass for the SI (top) and SD
(bottom) couplings. An energy threshold of 1 keVee was used, and the quenching
factor corrections are included.

Figure 14 shows in the top part the expected SI limits for a 30 m3 CYGNO
PHASE_2 experiment for a 3-year exposure with different background scenarios
and a 1 keV energy threshold. The possible regions explored with an operating
threshold of 0.5 keV are shown in the bottom of Figure 14, together with the
results that can be reached with a hydrogen-rich gas mixture with 2$\%$
isobutane content, as discussed in Section 4.4.

Figure 14: Spin-independent sensitivity for WIMP-nucleon cross-section for 30
m3 CYGNO detector for 3 years of exposure with different background level
assumptions and an operative threshold of 1 keV (top plot) and 0.5 keV (bottom
plot). The dashed curves correspond to a HeCF4 60/40 detector with Nbkg = 100
(black), 1000 (red) and 10,000 (dark green). The dotted curves show the
sensitivity for a HeCF4:isobutane 58/40/2 mixture. Current bounds from Xenon1T
(violet) Aprile et al. (2018), Xenon1T S2 analysis (blue) Aprile et al.
(2019), DarkSide (cyan) Agnes et al. (2018), CRESST III (orange) Mancuso et
al. (2020) and CDMSLite (green) Agnese et al. (2018) are also shown. The
densely dotted curves show the future expected limits of SuperCDMS Ge (green)
Agnese et al. (2017) and CRESST (orange) Willers et al. (2017). The light gray
regions denote DM hints by DAMA Savage et al. (2009), while the different gray
curves show the neutrino background levels for different targets Bœhm et al.
(2019).

The shape of the limit reflects the different nuclear composition of the gas
mixture. The lower detectable DM mass obviously corresponds to the one
obtainable with the 0.5 keVee energy threshold and helium quenching factor
(hydrogen in the hypothesis of the addition of a small fraction of isobutane).
There is a kink on the curve at around 0.9 GeV/c2 corresponding to the
transition from hydrogen-dominated to helium-dominated recoils, and at 3
GeV/c2, from helium- to fluorine-dominated recoils. The carbon percentage on
the total gas mixture (8%) is too low to produce a visible effect on the
curve.

Figure 14 shows how all the scenarios considered in this sensitivity
evaluation will be able to probe regions in WIMP masses versus cross-section
planes not yet explored, therefore significantly contributing to future DM
searches for low WIMP masses. While it is true that the expected reach of
future SuperCDMS Agnese et al. (2017), CRESST Willers et al. (2017), Darkside
low-mass Aalseth et al. and NEWS-G experiments may be able to cover these
regions, all of these will be realised through modes of operation that
strongly reduce (if not even completely give up) tools for background
discrimination. Each of these approaches implies, therefore, very strict (and
not yet demonstrated) requirements on the detector materials’ radio-purity and
the capability to strongly rely on a precise estimate of the expected
backgrounds. As a consequence, any observed signal in this region by these
experiments will be difficult to interpret unambiguously as a DM signal.
CYGNO’s potential of establishing the galactic origin of the detected signal
through directional correlation with the Cygnus constellation would therefore
constitute a compelling and decisive test to experiment claim in this region,
being the only existing approach able to provide a positive identification of
a DM signal. CYGNO PHASE_2 realisation would moreover establish the grounds
for the development of a multi-site network of modules for a ton-scale CYGNUS
project that, through directionality, could perform a precise study of WIMP
properties and DM astronomy.

In addition, thanks to the high flourine content, CYGNO PHASE_2 is expected to
also be significantly sensitive to SD couplings and be able to explore regions
not yet excluded by the PICO experiment in the low background scenario, as
shown on the top in Figure 15. The PICO experiment, which possesses the
strongest sensitivity among all the existing and planned experiments exploring
SD coupling, is based, however, on an energy threshold approach. This implies
that signal observation does not allow the measurement of the energy of the
detected nuclear recoil and could not, therefore, be translated into a
constraint in the masses versus coupling parameter space. Hence, also in this
context, a confirmation of the galactic origin of the detected signal would be
necessary to establish the properties of the detected WIMP. Moreover, the
possibility, now under study, of running with a threshold of 0.5 keV and
adding a small amount (2%) of isobutane to the gas mixture would allow DM
masses even lower than what is expected for the upgrade of PICO to be reached.

The estimated sensitivities presented in Figures 14 and 15 demonstrate how
CYGNO PHASE_2 realisation would therefore constitute a very important and
compelling step towards the observation and study of a DM signal in the low
WIMP mass region for both SI and SD couplings.

Figure 15: Spin-dependent sensitivity for WIMP–proton cross sections for 30 m3
CYGNO detector for 3 years of exposure with different background level
assumptions and an operative threshold of 1 keV (top plot) and 0.5 keV (bottom
plot). The dashed curves correspond to Nbkg = 100 (black), 1000 (red) and
10,000 (dark green). The dotted curves show the sensitivity for a
HeCF4:isobutane 58/40/2 mixture. Current bounds from PICO (purple) Amole et
al. (2019), DRIFT (orange) Battat et al. (2017), and NEWAGE (cyan) Yakabe et
al. (2020) are also shown. The allowed region by DAMA is denoted by the light
green band Savage et al. (2004). The light gray dotted line representing the
neutrino floor for C3F8 is also taken from PICO Amole et al. (2019).

###  5.2 Directional Searches for MeV Dark Matter Produced by Supernovae
through Nuclear Recoil

While WIMPs still remain highly motivated DM candidates, they are not the only
paradigm that can explain the DM presence. Core-collapse supernovae (SN) can
reach core temperatures in excess of 30 MeV for O(10) seconds, allowing them
to produce vast thermal fluxes of particles with masses O(100) MeV at
relativistic speeds DeRocco et al. (2019). This makes them an ideal
astrophysical source for sub-GeV dark matter. The DM candidates emerging from
this scenario considered in DeRocco et al. (2019) are dark fermions, but this
is not the only possible realisation of such a mechanism. Those particles end
up diffusively trapped near the proto-neutron star that forms from the SN
core. The dark fermions that do eventually escape are produced with a velocity
distribution approximately Maxwell–Boltzmann with semirelativistic velocities
(v $\sim$ 1, to be compared to classical WIMPs with v $\sim 10^{-3}$ ),
exhibiting a roughly order-one spread in velocities. This will result in a
time-spreading effect during their propagation to Earth of up to 105 years for
an average galactic SN, creating an overlap in time of various SN. Given the
high SN concentration in the galactic center, the emission of > 100 SN is
expected to be overlapping in a diffuse flux at Earth at any given time. This
resembles the diffuse flux of SN neutrinos comprising the neutrino floor at
energies larger than 10 GeV WIMP masses.

Thanks to the large dark fermion momentum, such particles, even of masses of
O(10 MeV), would cause, in a detector on Earth, a measurable nuclear recoil of
O(keV) to be very hard to distinguish from the one induced by a classic WIMP
of the galactic halo by an experiment measuring only the energy deposited in
the active volume. Nonetheless, the expected diffuse flux will be strongly
peaked towards the galactic center due to the large presence of SN in this
region compared to extragalactic sources. Thanks to this high degree of
anisotropy, a directional detector is a crucial tool to discriminate MeV SN-
produced DM with respect to classical WIMP scenarios. It has in fact recently
been shown that a directional approach with realistic experimental
performances could distinguish the two scenarios with few detected signal
events, while a non-directional detector typically needs a one to two times
order of magnitude more signal yield Baracchini et al. (2020). While this
study was performed under the assumption of the absence of background in the
detected events, a full estimation of CYGNO sensitivity to this DM candidate
scenario with the tools discussed developed for the WIMP physics case in
Section 5.1 is under development.

###  5.3 Solar Neutrino Detection through Both Nuclear and Electron Recoil
Signature

Solar neutrinos are a well-known background to DM searches. They can interact
in the active volume of the detector either via elastic scattering on the
electrons (producing an electron recoil) or coherent scattering on the nuclei
(producing a nuclear recoil).

Since most current DM experiments possess ER/NR discrimination, typically only
the coherent scattering on nuclei is viewed as an irreducible source
background, determining the so-called “neutrino floor”. Directionality has
been extensively recognised as the preeminent tool to identify and
discriminate NR induced by solar neutrinos from WIMP signal events Mayet et
al. (2016); Vahsen et al. (2020); Billard et al. (2014). While a ton-scale
experiment is needed to start detecting these events Vahsen et al. (2020), due
to the low cross-section, new physics in the neutrino sector (described in
terms of new mediators between neutrinos and electrons and/or quarks or in
terms of non-standard effective interactions) can increase the rate at low
energies Bœhm et al. (2019); Bertuzzo et al. (2017). This is particularly true
for DM masses below 10 GeV, if a new scalar mediator is assumed, where the
neutrino floor can be raised by several orders of magnitude, making this
accessible to CYGNO PHASE_2.

Concerning ER induced by neutrino-electron elastic scattering, classical DM
experiments measuring only the deposited energy in the detector have no means
to discriminate them from ER caused by other sources, and hence treat them as
background. A detector exhibiting directional capabilities like CYGNO can
actually transform these events into a signal. From the ER direction and the
Sun position, the angle between the incoming neutrino and the scattered
electron can in fact be inferred, providing an unambiguous signal
identification just like with the one in directional WIMP searches. Ton-scale
gaseous TPC have already been proposed in the past Seguinot et al. (1992);
Arpesella et al. (1996) to perform solar neutrino spectroscopy. CYGNO’s
CF4-based gas mixture appears very attractive in this sense Arpesella et al.
(1996) because it possesses a significative electron density (1.05 $\times$
1021 cm-3) with a low $Z$ nuclei, a feature that maximises the number of
targets while minimising multiple scattering.

About 1 event/m3 per year is expected at atmospheric pressure for an ER energy
threshold of 20 keV coming from the $pp$ chain, making this an extremely
interesting physics case for the CYGNO PHASE_2 experiment. Due to the larger
multiple scattering suffered by low-energy electrons with respect to nuclei,
ER direction determination is more complex than with NR tracks. First results
from a dedicated algorithm developed within the collaboration, inspired from
X-ray polarimetry Soffitta et al. (2013), shows that 30∘ 2D angular resolution
with sense recognition larger than 80$\%$ from the sCMOS images analysis can
be achieved at 20 keV in a 1 m3 detector, improving at higher energies. Figure
16 displays the angular distribution for ER induced by Solar neutrinos for 20
keV and 100 keV energy thresholds with a 30∘ $\times$ 30∘ angular resolution.
Since background events will be isotropically distributed, this shows how,
even with the limited angular resolution assumed, directionality provides an
extremely effective means for a high-precision solar neutrino measurement.
Moreover, the 20 keV energy threshold assumed for the ER translates to about
an 80 keV threshold on the incoming neutrino, opening a new window of
opportunity on the pp Sun process down to low energy, unreachable to
conventional neutrino detectors Seguinot et al. (1992).

Figure 16: Angular distribution for electron recoils induced by solar
neutrinos for 20 keV and 100 keV energy thresholds with a 30∘ $\times$ 30∘
angular resolution, shown on the right in log scale.

##  6 Conclusions

In this paper, the case for directional DM searches with gaseous TPC optically
read out through the combination of sCMOS images and PMT signals is presented.
The performances achieved with a 7-litre prototype based on this approach show
the possibility of a O(keVnr) detection threshold with 102 ER/NR
discrimination at 5.9 keVee. The CYGNO experiment will develop through a
staged approach. The underground installation at LNGS of a 50 litre prototype
(PHASE_0) is foreseen for the first quarter of 2022, followed by a O(1) m3
experiment (PHASE_1). PHASE_0 will allow validation of MC simulation and test
CYGNO performance in an underground environment. PHASE_1 will be realised to
control and minimize the backgrounds from internal materials towards the
scalability to larger volume. From the results of these phases, a large-scale
experiment (30–100 m3) will be proposed to explore the 1-10 GeV WIMP mass
region with high sensitivity to both SI and SD coupling and directionality. A
preliminary sensitivity reach to WIMP searches was hence evaluated for PHASE_2
with different background assumptions, reflecting realistic performance
improvements. This study demonstrates that PHASE_2 would bring a significant
contribution to WIMP searches, not only by probing parameter spaces unexplored
so far, but also being the only approach able to confirm and study any future
DM claim by other experiments in this region for both SI and SD couplings.
Additional compelling physics cases which are accessible thanks to directional
capabilities have also been discussed, for which detailed studies are being
carried out.

This project has received funds under the European Union’s Horizon 2020
research and innovation programme from the European Research Council (ERC)
grant agreement No 818744 and is supported by the Italian Ministry of
Education, University and Research through the project PRIN: Progetti di
Ricerca di Rilevante Interesse Nazionale “Zero Radioactivity in Future
experiment” (Prot. 2017T54J9J).

###### Acknowledgements.

The authors want to thank the General Services and Mechanical Workshops of
Laboratori Nazionali di Frascati and Laboratori Nazionali del Gran Sasso for
their precious work and L. Leonzi (LNGS) for technical support. yes

##  Appendix A Statistical Analysis for the Sensitivity Limit Evaluation

The estimation of the expected limits of the CYGNO experiment was performed
applying a Bayesian-based method. In principle, this approach allows the
probability of any model to be calculated given a certain amount of
information (data) related to it. This methodology is rarely used in this
field, even though it is recently gaining ground Roszkowski et al. (2009);
Trotta et al. (2007); Strege et al. (2012); Arina (2014); Bringmann et al.
(2017); Liem et al. (2016); Messina et al. (2020).

Every model and parameter which is of interest to the specific analysis, as
well as experimental data, are all considered connected to a probability
distribution and, as such, follow the rules of probability. Exploiting Bayes’
theorem, it is possible to find a relation between them and infer a final
probability, called posterior, for the desired quantity. In the case of the
CYGNO experiment, one is interested in knowing, given a certain number of
observed events per year, the probability that some of them are produced by
DM-nucleus interactions. Those can be events of background ($\mu_{b}$) or of
signal ($\mu_{s}$), which are strictly connected to the cross-section of WIMP
DM particles with protons. Bayes’ theorem can be expressed as follows:

$p(\mu,\boldsymbol{\theta}|\boldsymbol{D},H)=\frac{p(\boldsymbol{D}|\mu,\boldsymbol{\theta},H)\pi(\mu,\boldsymbol{\theta}|H)}{\int_{\Omega}\int_{0}^{\infty}p(\boldsymbol{D}|\mu,\boldsymbol{\theta},H)\pi(\mu,\boldsymbol{\theta}|H)d\mu
d\boldsymbol{\theta}}$ (3)

with $p(\boldsymbol{D}|\mu_{s},\boldsymbol{\theta},H)$ representing the
likelihood function $L(\mu_{s},\boldsymbol{\theta})$.

In Equation (3), the following notation is used:

  * •

$p(\mu|\boldsymbol{D})$—posterior probability function for the paramenter
$\mu$, given $\boldsymbol{D}$;

  * •

$\pi(\mu)$—prior probability of a parameter. This includes the expectations of
the parameters as well as constraints and knowledge previously obtained from
other experiments;

  * •

$\mu$—free and of interest parameter representing the expected events due to
WIMP-induced recoil ($\mu_{s}$) or background ($\mu_{b}$), given a certain
WIMP mass (the analysis performs a raster scan);

  * •

$\boldsymbol{\theta}$—vector of nuisance parameters, necessary to describe
theoretical assumptions and experimental conditions that can affect the
results. They can be not completely known and may depend on prior probability
distributions. For example, when $\mu=\mu_{s}$, $\mu_{b}$, the events expected
from the background becomes a nuisance parameter;

  * •

$\boldsymbol{D}$—data set. Can be made of actual experimental data or
simulated data;

  * •

$H$—hypothesis under test. It can be the hypothesis of pure background,
$H_{0}$, or the one where both background and signal are present, $H_{1}$;

  * •

$\Omega$—nuisance parameters space.

The likelihood function used to obtain the results shown in Section 5.1 is
defined as:

$p(\boldsymbol{D}|\mu_{s},\mu_{b},H_{1})=(\mu_{b}+\mu_{s})^{N_{evt}}e^{-(\mu_{b}+\mu_{s})}\prod_{i=1}^{N_{\text{bins}}}\left[\left(\frac{\mu_{b}}{\mu_{b}+\mu_{s}}P_{i,b}+\frac{\mu_{s}}{\mu_{b}+\mu_{s}}P_{i,s}\right)^{n_{i}}\frac{1}{n_{i}!}\right]$
(4)

with:

  * •

$N_{evt}$—total number of events of the data sample;

  * •

$i$—index representing the bin of the histogram in the 2D angular galactic
coordinates;

  * •

$n_{i}$—number of events occurring in the i-th bin;

  * •

$\mu$—the expected events due to WIMP-induced recoil ($\mu_{s}$) or background
($\mu_{b}$), given a certain WIMP mass;

  * •

$P_{i,x}$—the probability of single event to end up in the i-th bin, according
to x model (background or signal).

The $P_{i,x}$ marginalized probability includes the effects due to the
theoretical angular distribution, the migration from one bin to another caused
by resolution effects, and which element recoils. Being in the context of
estimating the limits of the CYGNO experiment when data results are consistent
with a pure background hypothesis, once the posterior probability of the
parameter $\mu_{s}$ is evaluated, it is possible to compute the upper bound as
the 90% credible interval (C.I.). This is defined as follows:

$\mu_{s}(90\%CI):\int_{0}^{\mu_{s}(90\%CI)}p(\mu_{s}|\boldsymbol{D},H_{1})d\mu_{s}=0.9$
(5)

where $p(\mu_{s}|\boldsymbol{D},H_{1})$ is the posterior probability
marginalised over the nuisance parameters. This value represents the limit
under which the true value of $\mu_{s}$ is, with a 90% probability.

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