Study of hard and electromagnetic processes at CERN-SPS energies

NA60+ Collaboration††thanks: See Appendix for the list of collaboration
members NA60+ Collaboration

The exploration of the phase diagram of Quantum ChromoDynamics (QCD) is
carried out by studying ultrarelativistic heavy-ion collisions. The energy
range covered by the CERN SPS ($\sqrt{s_{\rm\scriptscriptstyle{NN}}}\sim
6\text{--}17$ GeV) is ideal for the investigation of the region of the phase
diagram corresponding to finite baryochemical potential ($\mu_{\rm B}$), and
has been little explored up to now. We propose in this document a new
experiment, NA60+, that would address several observables which are
fundamental for the understanding of the phase transition from hadronic matter
towards a Quark–Gluon Plasma (QGP) at SPS energies. In particular, we propose
to study, as a function of the collision energy, the production of thermal
dimuons from the created system, from which one would obtain a caloric curve
of the QCD phase diagram that is sensitive to the order of the phase
transition. In addition, the measurement of a $\rho\text{--}{\rm a}_{1}$
mixing contribution would provide conclusive insights into the restoration of
the chiral symmetry of QCD. In parallel, studies of heavy quark and quarkonium
production would also be carried out, addressing the measurement of transport
properties of the QGP and the investigation of the onset of the deconfinement
transition. The document also defines an experimental set-up which couples a
vertex telescope based on monolithic active pixel sensors (MAPS) to a muon
spectrometer with tracking (GEM) and triggering (RPC) detectors within a large
acceptance toroidal magnet. Results of physics performance studies for most
observables accessible to NA60+ are discussed, showing that the results of the
experiment would lead to a significant advance of our understanding of strong
interaction physics. The document has been submitted as an input to the
European Particle Physics Strategy Update 2018–2020
(http://europeanstrategyupdate.web.cern.ch/).

##  1 Introduction and QCD phase diagram

Quantum ChromoDynamics (QCD), the theory of the strong force, has a rich phase
structure. On the one hand, asymptotic freedom allows it to completely define
the degrees of freedom in terms of quarks and gluons, while on the other hand
hadrons become the relevant degrees of freedom when confinement sets in. For a
system in thermodynamic equilibrium, temperature ($T$) and baryochemical
potential ($\mu_{\rm B}$) are intensive parameters that are the same for any
of its subsystems. It is convenient to describe the phase diagram, as shown in
the left panel of Fig. 1, in terms of these intensive parameters both from the
perspective of lattice QCD in which the two are used as independent variables,
and in the application of a grand-canonical ensemble in the analyses of heavy-
ion experiments. Our quantitative understanding of the QCD phase diagram is
largely restricted to the region of low $\mu_{\rm B}$. For $\mu_{\rm B}\sim
0$, lattice QCD provides quantitative results (see Fig. 1-right): a fast
increase of $\epsilon/T^{4}$ ($\epsilon$ = energy density) occurs around a
critical temperature $T_{c}\approx 155\text{~{}MeV}$. In this regime, the
phase transition is a cross-over [1, 2].

The extensive experimental campaigns conducted at the CERN-SPS, BNL-RHIC and
CERN-LHC accelerators have mostly explored so far this region of the phase
diagram at low $\mu_{\rm B}$, showing that a deconfined state of matter is
produced in heavy-ion collisions at high energies, with properties consistent
with the predictions of lattice QCD. Present experiments at RHIC and SPS
started in recent years to address features of the phase diagram structure at
large $\mu_{\rm B}$. For moderate temperatures and high baryon densities the
existence of a first order phase transition with co-existence of a mixed-phase
was suggested. The first order transition line should end with a second order
critical point. The existence of such a critical point and a first-order phase
transition remain to be confirmed in experiments. Evidence for a first order
phase transition can be provided by the measurement of the caloric curve. A
direct measurement of such a curve for the phase transition between a hadron
gas and a QGP can be based on precise temperature measurements as a function
of the centre of mass energy.

Chiral symmetry is spontaneously broken in the hadronic world due to the
formation of quark and gluon condensates. This leads to the generation of the
hadron mass splittings in the light hadron spectrum of
${\sim}0.5\text{~{}GeV}$ for the chiral partners $\pi\text{--}\sigma$ and
$\rho\text{--}\mathrm{a}_{1}$. Lattice QCD calculations for $\mu_{\rm B}=0$
show that at the hadron-QGP phase transition boundary the chiral condensate
steeply decreases around $T_{c}$, indicating the approach to chiral
restoration [3].

Precise measurements of heavy quarkonium states can be used to study the
suppression of such states due to colour screening which is considered a key
signature of a deconfined state. On the other hand, open charm measurements
allow us to extract fundamental transport coefficients from the QGP as well as
improve our understanding of hadronization mechanisms.

We propose a new experiment, NA60+, as a follow-up experiment to NA60 [4, 5]
to address each of these sets of observables through very high precision
measurements in Pb–Pb collisions in the finite $\mu_{\rm B}$ region of the
phase diagram where such measurements either have not been done, or have not
yet reached a level of precision that would allow for meaningful constraints
on theoretical models. In the following section 2, we discuss the NA60+
physics plans and how they will address each of the aforementioned observables
through high precision dimuon and hadronic measurements. In the sections 3 and
4 we detail the requirements to accomplish this programme in terms of
collision energies, integrated luminosities that allow for meaningful
measurements, and proposed detector technologies, respectively. Based on those
requirements, section 5 provides projections for the physics performance for
each of the observables discussed in section 2. This is followed by a brief
overview of other initiatives in terms of present and future
detectors/facilities in section 6 and our conclusions in strong favour of the
NA60+ project in section 7.

Figure 1: The QCD phase diagram (left panel, courtesy of Thomas Ullrich) and
the equation of state $P(T)/T^{4}$ in the limit of vanishing baryon density
[1] measured on the lattice (right panel): the latter is characterized by a
rise in the effective number of active degrees of freedom, indicating the
cross-over transition to a QGP.

##  2 Observables/Measurements

###  2.1 Thermal radiation

####  2.1.1 Chiral symmetry restoration: measurement of
$\mathbf{\rho\text{--}a_{1}}$ chiral mixing

A long-standing question is how chiral symmetry restoration manifests itself
in the hadron spectrum, i. e. what are its observable consequences. The NA60
experiment precisely measured the $\rho$ spectral properties in In–In
collisions at $\sqrt{s_{\mathrm{\scriptscriptstyle NN}}}=17.3\text{~{}GeV}$
[6, 5, 7] to be in agreement with a microscopic many-body model predicting a
very strong broadening with essentially no mass shift [8, 9]. To understand if
the $\rho$ melting is a signal of the restoration of chiral symmetry, and more
in general to understand the changes in the hadron spectrum, a study of the
spectral properties of its chiral partner $\mathrm{a}_{1}$ is fundamental. We
present here our proposal to investigate the $\rho\text{--}\mathrm{a}_{1}$
chiral mixing towards chiral symmetry restoration.

There is no direct coupling of axial states to the dilepton channel, so that
in vacuum the $\mathrm{e}^{+}\mathrm{e}^{-}\to\text{hadrons}$ cross section
has a dip in the $\mathrm{a}_{1}$ mass range [10]. However, in the medium, for
dilepton masses above 1 GeV, 4 pion (and higher) states dominate the free
electromagnetic correlator. Model-independent predictions of chiral symmetry
show that to leading order in temperature one has a pion-induced mixing of
vector ($V$) and axial-vector ($A$) correlators [11]:
$\Pi_{V}(T)=(1-\epsilon)\Pi^{vac}_{V}+\epsilon\Pi^{vac}_{A}$ where $\epsilon$
is the mixing parameter ($\epsilon=T^{2}/6f^{2}_{\pi}$,
$f_{\pi}=93\text{~{}MeV}$, and $\epsilon\sim 0.5$ at chiral symmetry
restoration). The admixture of the $\mathrm{a}_{1}$ resonance, via the axial-
vector correlator, thus entails an enhancement of the dilepton rate for $M\sim
1\text{--}1.4\text{~{}GeV}$. A precision measurement of this enhancement for
$M>1\text{~{}GeV}$ sheds light on the $\rho\text{--}\mathrm{a}_{1}$ chiral
mixing and the approach to chiral symmetry restoration.

To optimize the dilepton signal of interest, the lifetime of matter around
$T_{c}$ should be maximized relative to other contributions: starting out in a
(soft) mixed phase is a key point to enhance the effects related to chiral
restoration. Thus the collision energy should be large enough to produce this
matter, but small enough not to overshoot it producing partonic matter. This
is expected to occur at collision energies somewhat smaller than
$\sqrt{s_{\mathrm{\scriptscriptstyle NN}}}=17\text{~{}GeV}$, close to the
onset of deconfinement, where the QGP yield is negligible. The optimal energy
range of interest can be then established by the medium temperature
measurement, as detailed in section 2.1.2.

A calculation of the dilepton thermal yield with no chiral mixing and full
chiral mixing at $\sqrt{s_{\mathrm{\scriptscriptstyle NN}}}=8.8\text{~{}GeV}$
($\epsilon=1/2$) has been performed within the framework of [12]. The chiral
mixing will fill the dip in the mass range 1–1.4 GeV with a yield increase of
${\sim}30\%$.

####  2.1.2 Hadron–QGP phase transition: measurement of the strongly
interacting matter caloric curve at high $\mu_{\mathbf{\textit{B}}}$

The measurement of a caloric curve provided evidence for a first order phase
transition from the liquid self-bound nuclear ground state to a gas of free
nucleons [13]. We present here the method to perform the first measurement of
a caloric curve for the phase transition between the hadron gas and the QGP.
The temperature measurement, performed as a function of collision energy, is
based on a precise dimuon thermometer.

For dilepton masses above 1.5 GeV, the continuum of overlapping resonances
leads to a flattened spectral density corresponding to a simpler description
in terms of quarks and gluons (hadron-parton duality). Here medium effects on
the electromagnetic spectral function ($\Pi_{\rm EM}$) are parametrically
small, of the order of $(T/M)^{2}$, providing a stable thermometer. With
$\Pi_{\rm EM}\propto M^{2}$, and in non-relativistic approximation, one has
$\mathrm{d}N/\mathrm{d}M\propto M^{3/2}\exp(-M/T_{s})$ [12]. Since mass is by
construction a Lorentz-invariant, the mass spectrum is immune to any motion of
the emitting sources, unlike transverse momentum ($p_{\mathrm{T}}$) spectra.
The parameter $T_{s}$ in the spectral shape of the mass spectrum is therefore
a space-time average of the thermal temperature $T$ over the fireball
evolution. The choice of the mass window, 1.5–2.5 GeV, implies $T\ll M$ and
thus strongly enhances the sensitivity to the early high-$T$ phases of the
evolution. This method has been exploited by NA60 to measure the medium
temperature in In-In collisions at $\sqrt{s_{\mathrm{\scriptscriptstyle
NN}}}=17.3\text{~{}GeV}$. The fit of the mass spectrum gives $T_{s}=205\pm
12\text{~{}MeV}$ [5, 7]. This is above $T_{c}$, thus showing that the QGP is
produced at this collision energy.

The evolution of the initial temperature and $T_{s}$ vs collision energy has
been studied theoretically in [12] in the interval
$\sqrt{s_{\mathrm{\scriptscriptstyle NN}}}=6\text{--}200\text{~{}GeV}$.
However, in this calculation a cross-over transition is assumed. The average
temperature $T_{s}$ from the mass fit is about 30% below the corresponding
initial one at $\sqrt{s_{\mathrm{\scriptscriptstyle NN}}}=200\text{~{}GeV}$.
The two temperatures are both close to the critical temperature below
$\sqrt{s_{\mathrm{\scriptscriptstyle NN}}}=10\text{~{}GeV}$, with their gap
reducing to less than 15%. This is largely due to the (pseudo-)latent heat in
the transition which needs to be burned off in the expansion/cooling. The
collision energy range below $\sqrt{s_{\mathrm{\scriptscriptstyle
NN}}}=10\text{~{}GeV}$ thus appears to be essential to map out the phase-
transition regime at high $\mu_{\rm B}$, with the possible discovery of a
plateau in the caloric curve built with dilepton slopes $T_{s}$. The
experimental programme of NA60+ thus proposes to perform an energy scan in the
interval $\sqrt{s_{\mathrm{\scriptscriptstyle NN}}}=6\text{--}17\text{~{}GeV}$
($E_{\rm lab}=20\text{--}160\text{~{}GeV}/\text{nucleon}$).

####  2.1.3 Thermal dilepton excitation function and fireball lifetime

A precise measurement of the thermal dilepton excitation function—the total
yield of low mass thermal dileptons—is also sensitive to the fireball
lifetime. It was shown in [12] that the integrated thermal excess radiation in
$0.3<M<0.7\text{~{}GeV}$ tracks the total fireball lifetime remarkably well,
within less than 10%. The NA60 measurement in In–In at
$\sqrt{s_{\mathrm{\scriptscriptstyle NN}}}=17.3\text{~{}GeV}$ allowed the
fireball lifetime to be constrained with unprecedented precision: $\tau_{\rm
fb}=7\pm 1~{}\text{fm}/c$ [12]. Thus, low-mass dileptons are an excellent tool
to detect anomalous variations in the fireball lifetime due, for instance, to
the presence of a soft mixed phase: an increase in $\tau_{\rm fb}$ with
identical final-state hadron transverse momentum spectra (i. e. in terms of
radial-flow) would necessarily imply a lifetime extension without extra
collective flow, i. e. a soft phase.

###  2.2 Quarkonium

A suppression of heavy quarkonium states due to a colour screening mechanism
has been considered, from the very beginning of this field, as one of the key
signatures for the formation of a deconfined state [14]. Detailed studies, in
particular for the $\mathrm{J}/\psi$ meson, were first performed at top SPS
energy (centre of mass energy per nucleon–nucleon collision
$\sqrt{s_{\mathrm{\scriptscriptstyle NN}}}=17.3\text{~{}GeV}$) [15]. More
recently, extensive sets of measurements were obtained, for both charmonium
and bottomonium states, at the RHIC ($\sqrt{s_{\mathrm{\scriptscriptstyle
NN}}}$ up to 200 GeV) and LHC ($\sqrt{s_{\mathrm{\scriptscriptstyle NN}}}$ up
to 5.02 TeV) ion colliders [16, 17]. Concerning $\mathrm{J}/\psi$, a
${\sim}30$% suppression of the $\mathrm{J}/\psi$ production that could not be
ascribed to cold nuclear matter effects alone was observed in central Pb–Pb
collisions at the SPS by the NA50/NA60 experiments. The size of such an
“anomalous” suppression is qualitatively consistent with the melting in the
QGP of the $\chi_{\rm c}$ and $\psi\text{(2S)}$ charmonium states, which would
lead to a suppression of the $\mathrm{J}/\psi$ coming from the decay of those
particles.

As of today, heavy quarkonium production in nucleus–nucleus collisions has not
been studied below top SPS energy. NA60+ proposes to carry out a measurement
of $\mathrm{J}/\psi$ production down to a decreased energy of the incident
heavy-ion beam of approximately $E_{\rm lab}=40\text{~{}GeV}/\text{nucleon}$
($\sqrt{s_{\mathrm{\scriptscriptstyle NN}}}=8.8\text{~{}GeV}$). The possible
effects of the formation of a QGP with increasing $\mu_{\rm B}$ on charmonium
states have not been thoroughly investigated by theory. On the one hand, the
initial energy density of the system should decrease when moving to lower
collision energies. Consequently, if the $\mathrm{J}/\psi$ suppression effects
observed at top SPS energy are due to the dissociation of the $\chi_{\rm c}$
and $\psi\text{(2S)}$ states, one should be able to detect the beam energy
threshold for the onset of their suppression. By correlating this information
with the corresponding measurement of the temperature via thermal dimuons, one
could experimentally identify the threshold temperature for the melting of
those charmonium states. In this way a crucial test of the corresponding
lattice QCD predictions can be carried out. On the other hand, the formation
of a baryon-rich QGP may have unexpected, and up to now never investigated,
effects even on directly produced $\mathrm{J}/\psi$, making this measurement
even more appealing.

By moving to lower collision energies, there are also strong indications for
an increase of the size of cold nuclear matter effects on the produced
$\mathrm{c\overline{c}}$ pair. Indeed, by studying $\mathrm{J}/\psi$
production in proton–nucleus collisions at 158 and 400 GeV incident energy
[18], the NA60 experiment discovered a much stronger break-up effect on the
final state $\mathrm{J}/\psi$ at the lower of the two energies. NA60+ proposes
to extend such measurements to even lower energies, with a twofold interest.
First, break-up effects in cold nuclear matter are not related to QGP
formation, therefore they must be corrected for when evaluating any
“anomalous” suppression in nucleus–nucleus collisions. Therefore, such data
would be mandatory for a correct interpretation of nucleus–nucleus results.
Second, the production and propagation of a bound $\mathrm{c\overline{c}}$
state in cold nuclear matter is expected to be sensitive to various QCD-
related phenomena, which include both initial state (nuclear shadowing) and
final state effects (propagation of a colour singlet/octet pre-resonant state
or the final resonance in the nucleus). Past fixed target experiments at
various facilities (SPS, Tevatron, HERA) collected several sets of data, but
the observations still lack a comprehensive interpretation, and new data at
lower collision energy would access up to now unexplored specific kinematic
configurations.

###  2.3 Open charm

Heavy-flavour measurements are providing unprecedented insights into the
physics of hot QCD matter at small baryochemical potential, as produced at the
heavy-ion colliders RHIC and LHC. With a focus on the low and intermediate
momentum region, measurements of $p_{\mathrm{T}}$ distributions, compared to
pp collisions, and of azimuthal anisotropies of D mesons are used for example
to extract fundamental transport coefficients of the QGP, such as the heavy-
quark diffusion coefficient (see e. g. Ref. [19]). Measurements of the
strange-charm $\mathrm{D}^{+}_{s}$ meson and of the $\Lambda_{\rm c}$ baryon,
in comparison with $\mathrm{D}^{0}$ and $\mathrm{D}^{+}$ mesons containing
only charm and light quarks, are used to characterize the hadronization
mechanisms of charm quarks and the role of quark recombination [20].

It is of high interest to extend these studies into the region of finite
chemical potential through heavy-ion collisions at lower energies. The charm
diffusion coefficient is predicted to be larger in the hadronic phase at
temperatures approaching the critical temperature $T_{\rm c}\approx
150\text{~{}MeV}$ from below than in the QGP phase at temperatures larger than
$T_{c}$ [21, 22]. It should then be possible to investigate this feature in
Pb–Pb collisions at SPS energies, where the hadronic phase $T<T_{c}$
represents a large part of the space-time evolution of the collisions.
Measurement of $p_{\mathrm{T}}$ distributions and azimuthal anisotropy should
exhibit features induced by a strong collective behaviour. In addition, such
measurements that are sensitive to interactions of charm in the hadronic phase
would be important input also for precision estimates of diffusion
coefficients at collider energies, where a rather extensive hadronic evolution
from $T_{\rm c}$ down to the kinetic freeze-out temperature of $T\sim
100\text{~{}MeV}$ occurs. For what concerns hadronization mechanisms,
recombination effects could lead to a large enhancement of the
$\rm\Lambda_{c}/D$ ratio. The enhancement could be larger at SPS than at RHIC
and LHC energies, because of the larger baryon content of the fireball (the
baryon number of the colliding nuclei is “stopped” in the collision region).

The total production cross section of $\mathrm{c\overline{c}}$ pairs in
hadronic collisions at centre-of-mass energies below 20 GeV has never been
measured with high precision, because the yields at these energies are very
small. The only measurements in nucleus–nucleus collisions at the SPS were
obtained by the NA60 experiment in In–In collisions (using intermediate mass
dimuons, with an uncertainty of about 20%) [5] and by the NA49 experiment in
Pb–Pb collisions (upper limit using reconstructed $\rm D^{0}$ decays) [23]. A
precise measurement of this cross section in p–Pb and Pb–Pb collisions at the
SPS, besides providing the optimal normalization for $\mathrm{J}/\psi$
production, is also predicted to be directly sensitive to chiral symmetry
restoration. The melting of the $\rm\langle\mathrm{\overline{q}q}\rangle$
condensate might also shift the threshold for
$\mathrm{D}\overline{\mathrm{D}}$ production from $2\,m_{\rm D^{0}}\approx
3.73\text{~{}GeV}$ in vacuum to about 3 GeV in the chirally-symmetric medium.
This reduction is predicted to lead to an enhancement of open charm meson
yields by a factor of up to 7, with respect to binary scaling of the
production in pA collisions. Thus, a large enhancement of $\mathrm{D}$ meson
production is regarded as a signature for a chirally-symmetric phase [24].

Finally, measurements of D-meson production in proton–nucleus collisions at
SPS energy can provide constraints to parameterisations of the nuclear
modification of parton distribution functions (PDFs) at $Q^{2}\sim
10\text{--}40\text{~{}GeV}^{2}$ and large Bjorken-$x$ of $x_{\rm Bj}\sim
0.1\text{--}0.3$, depending on $p_{\rm T,c}\sim 0\text{--}3\text{~{}GeV}/c$.
In this kinematic region, which is poorly-constrained by existing data, the
PDFs in large nuclei are expected to change from enhancement (anti-shadowing)
at $x_{\rm Bj}\sim 0.1$ to suppression (“EMC effect”) at $x_{\rm Bj}\sim 0.3$
(see e. g. Ref. [25]). NA60+ could provide precise input via ratios of the
$\mathrm{D}$-meson production cross section in p–Pb or p–U collisions (maximal
nuclear effects) and p–Be collisions (minimal nuclear effects).

##  3 Requirements (statistics, beams, installation)

The experimental programme requires to collect data at different energies
(beam energy scan, BES) in the interval $\sqrt{s_{\mathrm{\scriptscriptstyle
NN}}}\sim 5\text{--}17\text{~{}GeV}$. In order to reach the required precision
for the proposed measurements, the statistics goal at each energy of BES is:

  * $\bullet$

$\geq 5\cdot 10^{7}$ reconstructed thermal muon pairs (factor 100 increase
over NA60 and ${\sim}10^{5}$ over RHIC/LHC experiments);

  * $\bullet$

$\geq 3\cdot 10^{4}$ reconstructed $\mathrm{J}/\psi$;

  * $\bullet$

$\geq 10^{7}$ reconstructed $\mathrm{D}^{0}$.

The proposed physics programme of NA60+ is based on high-intensity lead beams
delivered by the CERN SPS. This facility is continuously running since many
years. Thanks to the new injection scheme it would be able to deliver ion
beams over the required energy interval with intensities exceeding
$10^{7}~{}\text{ions}/\text{s}$ (in 5 s bursts, 15 s inter-bursts). An ion
beam could be delivered to a fixed target experiment while the SPS is used as
ion injector for LHC. Considering the present LHC running conditions with
ions, this means that ions would be available for ${\sim}4$ weeks per year.
Tentatively, data should be collected at $E_{\rm lab}=20$, 30, 40, 80, 120 and
$160\text{~{}GeV}/\text{nucleon}$. Further energy points might be required
depending on the findings. Corresponding periods of proton beams at a few
energy points will be required for reference measurements (like open charm and
Drell-Yan), with intensities of ${\sim}5\cdot
10^{8}~{}\text{protons}/\text{s}$.

The beam intensity dictates that the experiment must be installed underground.
The only existing hall is the ECN3 in the CERN north area. This is presently
under discussion within CERN Physics Beyond Colliders for running after LS3
during LHC Run 4 and Run 5.

##  4 The NA60+ experiment, layout and detectors

A sketch of the NA60+ apparatus is shown in Fig. 2. Muons are measured by a
magnetic spectrometer placed after a hadron absorber. A magnet, which creates
a toroidal field in the plane perpendicular to the beam direction, is placed
in between the muon tracking stations and provides a field integral of 0.75 Tm
at $R=1$ m. While the absorber provides the muon identification, it also
degrades the kinematics of the muons, because of energy loss fluctuations and
multiple scattering. This problem is overcome by measuring particle tracks
also before the hadron absorber with a silicon tracker, which is the key
element for a precision measurement of muons. Muon tracks are then matched to
the tracks measured in the silicon vertex telescope (VT) in coordinate and
momentum space. In addition, the VT provides also the measurement of the
charged-particle multiplicity density, and hadronic decays of open charm. The
apparatus covers the forward rapidity hemisphere, measuring muons in the
pseudo-rapidity interval $1.6<\eta<4.5$. Moreover, the apparatus is designed
to guarantee a good coverage down to low transverse momenta in particular for
dimuons with low mass and low pseudo-rapidity. The set-up will be adapted to
the varying beam energy by scaling the absorbers thickness and moving the
position of the tracking stations in such a way to keep always a good
acceptance close to mid-rapidity.

Figure 2: Geometry of the proposed experimental apparatus.

We foresee two dedicated programmes, one with a proton beam on various nuclear
targets (pA), and one with lead beams on lead targets (Pb–Pb). For the Pb–Pb
running, a segmented Pb target system of 10–15% interaction probability (4 mm
thickness) will be used, whereas for pA collisions, different nuclear targets
(Be, Al, Cu, In, W, Pb and U) with 1 mm thickness will be exposed
simultaneously to the proton beam. The targets will be housed inside a vacuum
box.

In the following subsections we briefly present the detector concept for the
different sub-systems. Detailed performance features and simulations of the
full detector response will be documented in a future Letter of Intent and
Technical Design Reports at a later point.

###  4.1 Detector technology

####  4.1.1 Vertex telescope: pixel detector

The vertex telescope is a spectrometer consisting of 5 silicon pixel tracking
planes immersed in a 1.2 Tm dipole field (see Fig. 2). The tracker will be
based on CMOS Monolithic Active Pixel Sensors (MAPS), which are now reaching
impressive performances, almost ideal in many respects. At present, the state
of the art is the pixel sensor ALPIDE developed for the new ALICE inner
tracker. Based on the $0.18~{}\mu$m CMOS imaging commercial technology by
TowerJazz, this $15\times 30~{}\text{mm}^{2}$ sensor features a pixel size of
$27\times 29~{}\mu\text{m}^{2}$ with a thickness of just $50~{}\mu\text{m}$
[26]. At ${\sim}1$ MHz Pb–Pb interaction rate, the hit flux reaches ${\sim
50}$ MHz/cm2 in the tracking station closest to the interaction point. The
ALPIDE sensor can be operated up to ${\sim}100$ MHz/cm2 but the readout rate
is limited to ${\sim}10$ MHz/cm2.

For NA60+ we will pursue, in close synergy with the ALICE experiment, a new
generation of MAPS with almost ideal characteristics: very large area up to
${\sim}14\times 14~{}\text{cm}^{2}$, retaining thickness of 50 $\mu$m or less.
The key idea is to use stitching, a technology that allows an image sensor
that is larger than the field of view of the lithographic equipment to be
fabricated. In this way, sensors of arbitrary size can be manufactured, the
only limit being the size of the wafers. The basic unit might be a sensor of
size $1.5\times 14~{}\text{cm}^{2}$ [27]. A resulting wafer-scale sensor could
be obtained at this stage replicating this sensor chip several times along the
periphery side. Such a matrix amounts to $5000\times 5000$ pixels. The sensor
is meant to be operated in continuous mode, recording frames at
${\sim}5\text{--}10$ MHz rate. The amount of memory buffers and serial data
transmitters, all placed in the periphery, will be determined to match the
required readout band-width.

All tracking stations will be identical, consisting of just few large sensors
leading to a modular, more robust and cheaper layout that allows simple
replacement of non working sensors. A tracking station with few large sensors
where power distribution is totally managed internally will mainly eliminate
the need of a mechanical and electrical support, confining the interconnection
to the outside world to the sensor edges, including the cooling. With a flex
circuit for power distribution the material budget for such tracking stations
might drop to a breakthrough level of 0.1% X0.

####  4.1.2 Muon tracking: GEMs

Gas Electron Multiplier (GEM) foils [28] are structures commonly used as
proportional counters, due to their excellent performance at high particle
rates. Being successfully employed in many experiments, such as COMPASS [29],
LHCb [30] or TOTEM [31], GEMs have become the solution for the upcoming
upgrades of the CMS Muon Endcap [32] or the ALICE TPC [33].

GEM detectors use copper-clad polyimide foil with etched holes for gas
amplification. Thanks to the photo-lithography methods used in the production
process of GEM foils, the size of the amplification region could be reduced to
a sub-millimetre level (typical hole diameter of 50–70 $\mu$m with a pitch of
140 $\mu$m). This allows GEMs to be operated at high particle rates of 1
MHz/cm2 [30] with a very good spatial resolution of
$\mathcal{O}(100~{}\mu\text{m})$ or smaller [29]. A cascade of GEM foils
permits one to attain very high proportional gains without the occurrence of
discharges. Since the development and perfection of the single-mask technique
[34], high-quality large-area GEMs can be produced allowing to cover
substantial detector surfaces at relatively low costs. All that makes the GEM
technology well suited for a high-rate muon tracker to be employed in the
NA60+ spectrometer. Following the schematic layout presented at the beginning
of this section the total active area of the muon tracker is ${\sim}116$ m2,
organized in 4 tracking stations, behind the hadron absorber. We foresee two
modules per station to improve tracking capabilities of the system (position
resolution, background rejection). A single tracking module (chamber) will
employ a triple GEM amplification structure with a short drift gap of
$\mathcal{O}(3~{}\text{mm})$ and strip readout. Due to the raw-material
related constraints on the maximum width of GEM foils (60 cm), we foresee a
single chamber to be a ${\sim}50\times 100$ cm2 rectangle. Taking into account
the active area of the tracker and the dimensions of a single chamber, a total
number of ${\sim}$1500 GEMs will have to be produced (including spares) in
order to assemble more than 450 tracking modules. We propose to use cost-
effective, non-flammable Ar-based gas mixtures with carbon dioxide (CO2) as a
quencher. In order to improve time resolution of the tracking module an
addition of Tetrafluoromethane (CF4) is considered. Both Ar/CO2 and Ar/CO2/CF4
mixtures have been successfully used in currently operated high-rate trackers
(e. g. COMPASS or LHCb) without notable ageing effects.

Because of the large total area of the muon tracker, a pad readout would lead
to an excessively large number of front-end electronics (FEE) channels. The
latter can be reduced by employing 2D strip readout [29]. Given the chamber
dimensions and assuming $200~{}\mu$m spatial resolution, a strip pitch of
$\mathcal{O}(1~{}\text{mm})$ results in almost 900 thousand of FEE channels.
Further improvement of the spatial resolution may be realized by employing a
zigzag strip geometry [35] or utilizing pad readout in the innermost part of
the tracker.

For the readout, we consider using a VFAT chip [36], successfully employed in
TOTEM and ATLAS forward detectors and planned for the CMS GEM chambers, or the
new VMM3 chip [37] developed for the ATLAS New Small Wheel upgrade. Detailed
performance studies will be performed for the final assessment.

####  4.1.3 Muon triggering: RPCs

Resistive Plate Chambers (RPC) were used in LHC experiments for large surface
tracking devices and may represent a viable choice for the muon triggering
system of the NA60+ experiment. In particular, these detectors were adopted
for the ALICE forward muon arm, which had a conceptual structure similar to
the one proposed for NA60+. Following that set-up, one can envisage a system
composed of two stations, each one featuring two RPC planes. This set-up would
allow a trigger condition where one requires three out of four planes fired,
providing the necessary redundancy in case of local inefficiencies in the
detection planes. The single-gap detectors, with Bakelite electrodes, can be
read on both sides with orthogonal strips with a pitch varying from 1 to 4 cm,
following the expected occupancy and the needed spatial resolution. The
detectors could be operated with a FEE which includes an amplification stage,
in order to reduce the charge delivered inside the gas gap, improving both
rate capability ($>100$ Hz/cm2) and detector lifetime. An R&D programme is
ongoing in order to replace the flammable gas mixture used, e. g. in ALICE
with non-flammable and low-GWP gas.

A possible issue that needs investigation is related to the area of the
detection planes, since, presently, the maximum size of Bakelite electrodes
available is about $300\times 180$ cm2. With a transverse size of the detector
of ${\sim}8$ m, the simple arrangement adopted in ALICE (two detectors,
symmetrically positioned with respect to the beam axis) will not be possible,
and some integration studies will be needed in order to devise a practical
solution which ensures sufficient overlaps and avoid dead zones.

####  4.1.4 Muon magnet

A magnet similar to the ACM [38] used by NA60 is needed with larger
dimensions: length of $\sim 3$ m, radius at entrance $0.3<R<1.65$ m, radius at
exit $R=2.95$ m, field $B\cdot R\sim 0.2\text{--}0.25~{}\mathrm{Tm}$. The ACM
was an open toroid with field circling the beam-axis. The windings of the ACM
were arranged in a complicated way, providing an excellent field quality but
making this magnet difficult to build and expensive. We propose a “minimal”
design, easier to build and cheaper, but with a more complex field [39]. This
layout could also be useful for other experiments. The main part consist of a
central cylinder of 0.6 m diameter and 3 m length in the beam direction, build
up out of 8 sectors. The sectors are tangentially displaced with respect to
the cylinder axis in order to cross the current from one segment to another.
The dimensions of the radial conductors are chosen to give little obstruction
for incoming particles. The outer connection of the radial conductors is not
critical. A segment consists out of a single winding, the straight conductors
joined by screws. The idea is to get an easy scalable, meccano-like structure.
This simple concept of minimal amount of windings has to be tested on field
homogeneity and acceptance. For reasons of simplicity and cost efficiency it
is proposed to add segments if the field homogeneity needs to be increased,
instead of adding more outer conductors to the radial ones. Since the total
current remains the same, this will not affect the acceptance. In order to
reduce energy consumption the magnet will be pulsed. To avoid overheating of
the central conductor, coolant has to be flown through it. It can be made
laminated or foreseen of tubes. If the field quality is not satisfying due to
current inhomogeneity, one can try a laminated central conductor with loop for
each lamination.

##  5 Physics performances

###  5.1 Thermal dileptons: caloric curve, $\rho\text{--}\mathrm{a}_{1}$
chiral mixing, excitation function

Detailed performance studies were carried out for 5% most central Pb–Pb
collisions at $\sqrt{s_{\mathrm{\scriptscriptstyle NN}}}=6.3$, 8.8 and 17.3
GeV. The differential spectra of thermal $\mu^{+}\mu^{-}$ pairs,
$\mathrm{d}^{3}N/(\mathrm{d}M\mathrm{d}p_{\mathrm{T}}\mathrm{d}y)$, are based
on the in-medium $\rho$, $\omega$ and $4\pi$ spectral functions, QGP and the
expanding thermal fireball model of [12]. The generator is based on the model
calculation which assumes either no $\rho\text{--}\mathrm{a}_{1}$ chiral
mixing or full chiral mixing ($\epsilon=1/2$) in the mass region
$1<M<1.5\text{~{}GeV}$. For the performance of the temperature measurement,
thermal dileptons were generated without chiral mixing. The hadron cocktail
generator for the 2-body decays of $\eta$, $\omega$, and $\phi$ and the Dalitz
decays $\eta\to\gamma\mu^{+}\mu^{-}$ and $\omega\to\pi^{0}\mu^{+}\mu^{-}$ is
based on the NA60 generator and on the statistical model of [40]. The Drell-
Yan process and open-charm production are simulated with the Pythia event
generator.

We present the results for a sample of $2\cdot 10^{7}$ reconstructed pairs in
central collisions at each energy, corresponding to a total sample of
${\sim}5\cdot 10^{7}$ integrated in centrality at each energy. The left panel
of Fig. 3 shows the signal reconstructed mass spectra (black) for
$\sqrt{s_{\mathrm{\scriptscriptstyle NN}}}=8.8\text{~{}GeV}$ after subtraction
of the combinatorial background due to pion and kaon decays as well as fake
matches. The latter arise from incorrect matches of a muon track to a track
reconstructed in the VT. The combinatorial background is subtracted assuming a
0.5% systematic uncertainty (shown as a yellow band). For what concerns
minimum bias collisions, the progress in statistics over NA60 is a factor
${\sim}100$, retaining a similar background ratio and a better mass
resolution. At a ${\sim}1$ MHz interaction rate, this statistics can be
collected in a ${\sim}30$ days run. The figure shows all the expected signal
components. For $M<1\text{~{}GeV}$, the thermal radiation yield is dominated
by the in-medium $\rho$. The $\omega$ and $\phi$ peaks are well resolved with
a resolution of ${\sim}10\text{~{}MeV}$ at the $\omega$ mass. The thermal
spectrum is measurable up to 2.5–3 GeV. The open charm yield becomes totally
negligible at low energy. The Drell-Yan yield will be measured in dedicated pA
runs (see also section 5.3). The thermal spectra are obtained after (i)
subtraction of the hadronic cocktail for $M<1\text{~{}GeV}$ of $\phi$,
$\omega$ and $\eta$ decays into $\mu^{+}\mu^{-}$ and the $\omega$, $\eta$
Dalitz decays and (ii) subtraction of Drell-Yan and open charm muon pairs for
$M>1\text{~{}GeV}$. After acceptance correction the spectra are fit with
$\mathrm{d}N/\mathrm{d}M\propto M^{3/2}\exp(-M/T_{s})$ in the interval
$M=1.5\text{--}2.5\text{~{}GeV}$. This is shown in the right panel of Fig. 3.

The resulting temperatures are compared to the theoretical model used as an
input in the left panel of Fig. 4. At low energies, the temperatures can be
measured with a combined statistical and systematic uncertainty of just a few
MeV, thus showing that the experiment has a strong sensitivity to a possible
flattening of the caloric curve. The acceptance corrected mass spectrum at
$\sqrt{s_{\mathrm{\scriptscriptstyle NN}}}=8.8\text{~{}GeV}$, based on the
assumption of no chiral mixing, is compared to the expectation in case of full
chiral mixing in the right panel of Fig. 4. As shown, the statistical and
systematic uncertainty provide a very good sensitivity to an increase of the
yield due to chiral mixing of ${\sim}20\text{--}30\%$.

Figure 3: (Left) expected signal sample in 5% most central Pb–Pb collision at
$\sqrt{s_{\mathrm{\scriptscriptstyle NN}}}=8.8\text{~{}GeV}$ after subtraction
of combinatorial and fake match background. (Right) acceptance corrected
thermal spectra at three different beam energies obtained after subtraction of
open charm, Drell-Yan and hadronic cocktail below 1 GeV. Figure 4: (Left)
medium temperature evolution vs $\sqrt{s_{\mathrm{\scriptscriptstyle NN}}}$ in
central Pb–Pb collisions. $T_{\rm initial}$ (magenta) and $T_{\rm slope}$
(red) are theoretical estimates for the initial medium temperature and the
temperature from dilepton spectra respectively, using [12] and a coarse
graining approach in UrQMD [41, 42]. Blue triangles are the expected
performance from NA60+ (CBM performance is also shown). The only existing
measurements at present are from NA60 In–In [5, 7] and from HADES Au–Au [43].
(Right) NA60+ projection for the acceptance corrected thermal dimuon mass
spectrum at $\sqrt{s_{\mathrm{\scriptscriptstyle NN}}}=8.8\text{~{}GeV}$ in
case of no chiral mixing compared to the theoretical expectation (green line).
The black line above 1 GeV is the expectation from full chiral mixing [12].

Finally the performance for the dilepton excitation function, i. e. the total
thermal yield measurement in the mass range 0.3–0.7 GeV, is compared to the
lifetime estimate of [12] in Fig. 5. The uncertainty is dominated by the
systematic error from background subtraction. The measurement at low energies
provides very good sensitivity to possible anomalies in the fireball lifetime.

Figure 5: Performance for thermal dilepton yield measurement for the fireball
lifetime measurement.

###  5.2 Open charm measurements: hadronic decays of mesons/baryons

Open charm hadrons can be fully reconstructed with the NA60+ apparatus via
their decays into two or three charged hadrons. In particular, the following
decays could enable the measurement of non-strange and strange D mesons as
well as $\Lambda_{\rm c}$ baryons: $\mathrm{D}^{0}\to{\rm K}^{-}\pi^{+}$,
$\mathrm{D}^{+}\to{\rm K}^{-}\pi^{+}\pi^{+}$,
${\mathrm{D}^{+}_{s}\to\phi\pi^{+}\to{\rm K}^{+}{\rm K}^{-}\pi^{+}}$,
$\Lambda_{\rm c}^{+}\to{\rm pK^{-}}\pi^{+}$ and their charge conjugates. The
decay particles (pions, kaons and protons) are detected by reconstructing
their tracks in the silicon-pixel detectors of the VT. D-meson and
$\Lambda_{\rm c}$ candidates are built combining pairs or triplets of tracks
with the proper charge signs. The huge combinatorial background can be reduced
via geometrical selections on the displaced decay-vertex topology, exploiting
the fact that the mean proper decay lengths $c\tau$ of open charm hadrons are
of about 60–310 $\mu$m, and therefore their decay vertices are typically
displaced by a few hundred $\mu$m from the interaction vertex. Among the
measurements proposed by NA60+, open-charm hadron studies are those that
impose the strongest constraints on the design of the VT detectors, which
should provide good resolution on the track parameters in order to allow us to
separate the secondary tracks produced in open-charm hadron decays from the
primary ones originating from the interaction point.

The benchmark studies were carried out for the measurement of
$\mathrm{D}^{0}\to{\rm K}^{-}\pi^{+}$ in the 5% most central Pb–Pb collisions
at two different beam energies: 158 and $60\text{~{}GeV}/\text{nucleon}$,
corresponding to $\sqrt{s_{\mathrm{\scriptscriptstyle NN}}}=17.3$ and 10.6
GeV, respectively. The $\mathrm{D}^{0}$ and $\overline{\mathrm{D}^{0}}$ mesons
were simulated with $p_{\mathrm{T}}$ and rapidity distributions obtained with
the Powheg-Box event generator [44] for the hard-scattering and Pythia 6 for
the parton shower and hadronization. The combinatorial background was
estimated by simulating pions, kaons and protons with multiplicity,
$p_{\mathrm{T}}$ and rapidity distributions taken from the parameterisations
published by the NA49 collaboration in Refs. [45, 46]. The number of particles
per event at $\sqrt{s_{\mathrm{\scriptscriptstyle NN}}}=17.3\text{~{}GeV}$ is
about 1200, which produce about 350k background candidates per event, out of
which about 8000 have an invariant mass within 60 MeV from the
$\mathrm{D}^{0}$-meson mass (1.865 GeV). The yield per event at
$\sqrt{s_{\mathrm{\scriptscriptstyle NN}}}=17.3\text{~{}GeV}$, estimated
assuming $\sigma_{\mathrm{c\overline{c}}}=5~{}\mu$b (based on [47, 48] and
Powheg) and $f({\rm c}\to\mathrm{D}^{0})\sim 0.55$, is about 0.006. The
signal-to-background ratio is therefore about $7\cdot 10^{-7}$ and needs to be
enhanced with the kinematical and geometrical selections.

Figure 6: $\mathrm{D}^{0}$-meson statistical significance (normalized to the
square root of the number of events) and signal-over-background ratio as a
function of the selection efficiency for the 5% most central Pb–Pb collisions
at $\sqrt{s_{\mathrm{\scriptscriptstyle NN}}}=17.3\text{~{}GeV}$. The signal
and the background yields are evaluated in a $2\sigma$ invariant-mass region
around the $\mathrm{D}^{0}$ peak.

Several selection sets were tested, and for each of them the signal-selection
efficiency, the statistical significance of the signal ($S/\sqrt{S+B}$) and
the signal-to-background ratio ($S/B$) were computed. In Fig. 6, the
significance per event and the $S/B$ at $\sqrt{s_{\mathrm{\scriptscriptstyle
NN}}}=17.3\text{~{}GeV}$ are shown as a function of the efficiency for two
different configurations of the VT detectors, namely the one based on hybrid
pixel sensors with $10~{}\mu$m spatial resolution and the one based on
Monolithic Active Pixels (MAPS) which feature a better spatial resolution
($5~{}\mu$m) and a reduced material budget. The performance is substantially
better with the MAPS detector, which provides a better resolution on the decay
track momentum, on the decay vertex position (10–15 $\mu$m in the plane
transverse to the beam line with MAPS vs. 30–40 $\mu$m with hybrid pixels) and
therefore on the $\mathrm{D}^{0}$ invariant mass (10 MeV vs. 24 MeV). In the
left panel of Fig. 7, we show a projection for the invariant-mass distribution
of $\mathrm{D}^{0}$ candidates in $5\cdot 10^{9}$ central Pb–Pb collisions at
$\sqrt{s_{\mathrm{\scriptscriptstyle NN}}}=17.3\text{~{}GeV}$, corresponding
to a sample of $10^{11}$ minimum bias (MB) collisions which can be collected
in one month of data taking at 150 kHz of acquisition rate. The MAPS detector
would enable a measurement of the $\mathrm{D}^{0}$-meson yield in central
Pb–Pb collision with a statistical precision much better than 1%, which would
allow also for studies in $p_{\mathrm{T}}$ and $y$ intervals and for the
determination of the elliptic flow coefficient $v_{2}$ of D mesons with
percent level statistical uncertainty. In the right panel of Fig. 7, the
projected performance for the 5% most central Pb–Pb collisions at
$\sqrt{s_{\mathrm{\scriptscriptstyle NN}}}=10.6\text{~{}GeV}$ is shown for the
case of MAPS detectors. For this performance study we assumed
$\sigma_{\mathrm{c\overline{c}}}=0.5~{}\mu$b and the combinatorial background
was simulated based on interpolation of NA49 measurements at 40 and
$80\text{~{}GeV}/\text{nucleon}$ incident energy. It demonstrates that the
integrated $\mathrm{D}^{0}$-meson cross section can be measured with
statistical precision better than 1% at collision energies at which the charm
cross section is poorly known experimentally.

Figure 7: Projection for invariant-mass distribution of $\mathrm{D}^{0}$
candidates in $5\cdot 10^{9}$ central Pb–Pb collisions at beam energies of 160
(left) and 60 (right) $\text{~{}GeV}/\text{nucleon}$ for the case of the VT
detector based on MAPS with 5 $\mu$m spatial resolution.

The excellent performance obtained for the two-body decays of $\mathrm{D}^{0}$
mesons suggests that open-charm measurements will also be feasible for three-
body decay channels. This opens the possibility to measure the production
yield of strange D mesons and of $\Lambda_{\rm c}$ baryons.

###  5.3 $\mathrm{J}/\psi$ suppression: onset of deconfinement

Among the measurements proposed by NA60+, quarkonium studies require the
highest integrated luminosity $L_{\rm int}$, due to the small production cross
section at low incident beam energy. On the other hand, past SPS experiments
(NA50/NA60) showed that the background levels in the dimuon invariant mass
spectrum in the $\mathrm{J}/\psi$ region are also very small (${<}5\%$) [49].
In addition, the NA60 experiment was able to perform a very accurate
measurement of the centrality dependence of the suppression by collecting
${\sim}3\cdot 10^{4}$ $\mathrm{J}/\psi$ in In–In collisions at
$158\text{~{}GeV}/\text{nucleon}$ incident energy, i. e.
$\sqrt{s_{\mathrm{\scriptscriptstyle NN}}}=17.3\text{~{}GeV}$. In order to
assess the possibility of a measurement with similar accuracy at lower
incident energy, we have calculated the interaction rate needed in order to
collect $3\cdot 10^{4}$ $\mathrm{J}/\psi$ in a 30-day long Pb–Pb data taking
period with NA60+. We have assumed (i) SPS burst structure similar to the one
at top SPS energy, (ii) realistic values for the acceptance of the apparatus
in the rapidity region $|y|<0.5$ and (iii) a suppression of the
$\mathrm{J}/\psi$ leading to a $2/3$ reduction of the expected yields.
Assuming a target thickness of 4 mm, we have also evaluated the corresponding
beam intensity needed to collect the desired statistics. The result, shown in
Fig. 8, shows that a large $\mathrm{J}/\psi$ sample can be collected while
keeping the interaction rate below 1 MHz, corresponding to a beam intensity of
about $10^{7}$ Pb ions/s.

Figure 8: Interaction rate and beam intensity needed to collect a sample of
$3\cdot$104 $\mathrm{J}/\psi$ in Pb–Pb collisions at various energies.

At SPS energies, it is well known that the break-up of the $\mathrm{J}/\psi$
in cold nuclear matter plays an important role in determining the final
observed yields in nucleus–nucleus collisions. Therefore, data taking with pA
collisions are mandatory to calibrate such an effect. We assumed to have 7
nuclear targets as mentioned in section 4 and 15 days of data taking at a beam
intensity of $3\cdot 10^{8}~{}\text{protons}/\text{s}$. In the left panel of
Fig. 9, the expected cross sections as a function of the mass number A are
shown, for an incident beam energy $E_{\rm lab}=50\text{~{}GeV}$, or
$\sqrt{s_{\mathrm{\scriptscriptstyle NN}}}=9.8\text{~{}GeV}$, and in the
hypothesis of a dissociation cross section
$\sigma_{\mathrm{J}/\psi\text{--}\rm N}=4.3$ mb. Such results are necessary in
order to (i) evaluate the $\mathrm{J}/\psi$ production cross section
$\sigma_{\rm pp\rightarrow\mathrm{J}/\psi\rm X}$, needed for
$R_{\mathrm{AA}}$, (ii) extrapolate break-up effects to the geometrical
conditions of Pb–Pb results. These procedures were well tested in past SPS
experiments [50].

Figure 9: (Left) $\mathrm{J}/\psi$ cross section normalized to the mass number
A for pA collisions at $E_{\rm lab}=50\text{~{}GeV}$. The results of a fit
using the parameterisation
$\sigma^{\mathrm{J}/\psi}_{\text{pA}}=\sigma^{\mathrm{J}/\psi}_{\rm pp}\cdot
A^{\alpha}$ are shown. (Right) The nuclear modification factor for
$\mathrm{J}/\psi$ production in Pb–Pb collisions at $E_{\rm
lab}=50\text{~{}GeV}$ as a function of $N_{\mathrm{part}}$, compared with
expectations from cold nuclear matter effects, obtained from the pA results
and shown as a blue band.

Finally, the right panel of Fig. 9 shows the results of a simulation of the
$\mathrm{J}/\psi$ $R_{\mathrm{AA}}$ as a function of the number of participant
nucleons, $N_{\mathrm{part}}$, assuming that for $N_{\mathrm{part}}\lesssim
50$ the suppression is entirely due to cold nuclear matter effects, while for
more central events an extra-suppression reaching 20% sets in. The simulation
assumes 30 days of Pb–Pb collisions at $E_{\rm lab}=50\text{~{}GeV}$, with an
SPS beam intensity of $8.5\cdot 10^{6}~{}\text{Pb ions}/\text{s}$. The
uncertainties shown for $R_{\mathrm{AA}}$ in the right panel of Fig. 9
include, in addition to the statistical uncertainty on the $\mathrm{J}/\psi$,
conservatively evaluated assuming a 20% background level, those on the
evaluation of the centrality variables (Glauber model) and on the $\rm pp$
cross section, calculated from the pA results displayed in the left panel of
Fig. 9. One can clearly see that a precise evaluation of a relatively small
anomalous $\mathrm{J}/\psi$ suppression is within reach down to low $E_{\rm
lab}$.

Corresponding studies for the detection of the
$\psi\text{(2S)}\rightarrow\mu^{+}\mu^{-}$ and $\chi_{\rm
c}\rightarrow\mu^{+}\mu^{-}\gamma$ decays are ongoing and are expected to
nicely complement the physics programme of NA60+ in the charmonium sector.

##  6 Competition with present and future measurements

Several proposals have been put forward to investigate experimentally the QCD
phase diagram at high $\mu_{\rm B}$ in the next decade. Since thermal dilepton
radiation, open charm and quarkonia are produced by rare processes, high
precision measurements require very large interaction rates and operation in
fixed target mode. Moreover, the $\mu_{\rm B}$ interval accessible by a single
experiment should be as wide as possible. The combination of these two key
aspects is such that the physics programme described in this document can be
uniquely pursued at the CERN SPS. Although other facilities for the study of
ultra-relativistic heavy-ion collisions in the high-$\mu_{\rm B}$ domain are
being built (FAIR, NICA) they are either lacking the necessary interaction
rate (NICA) or reach too low energy (SIS100 at FAIR) to address all the
physics topics addressed by NA60+. Similarly, the beam energy scan programme
at RHIC (BES-II) covers the same energy range as the CERN SPS, but with
interaction rates lower by orders of magnitude. It should be noted that NA60+
and CBM with their high-interaction rates but different collision energies
would nicely complement each other in mapping out, e. g. the caloric curve.

##  7 Conclusions

The exploration of the high-$\mu_{\rm B}$ region of the QCD phase diagram
represents one of the main directions in the evolution of the field of
ultrarelativistic heavy-ion collisions. This document, submitted to the
European Strategy for Particle Physics, summarizes the status of the NA60+
project, which aims at performing a comprehensive measurement, in the energy
range accessible to the CERN SPS, of hard and electromagnetic processes, with
unprecedented accuracy. The addressed observables include the production of
thermal muon pairs from the QGP phase, the investigation of the modifications
of the vector meson spectral functions as well as the study of charmonia and
open charm mesons/baryons. Preliminary physics performance studies discussed
in this document show that a set-up which makes use of existing advanced
detection techniques would be able to carry out the proposed physics
programme, provided that the experiment can profit of high-intensity ion beams
as those that can be delivered in the ECN3 experimental hall.

## Acknowledgements

We would like to thank F. Bergsma and P. A. G. Giudici (both CERN) for their
contribution on the study of the toroidal magnet.

## References

  * [1] S. Borsanyi et al., “Full result for the QCD equation of state with $2+1$ flavors,” Phys. Lett. B730 (2014) 99, arXiv:1309.5258 [hep-lat].
  * [2] C. Ratti, “Lattice QCD and heavy ion collisions: a review of recent progress,” Rept. Prog. Phys. 81 (2018) 084301, arXiv:1804.07810 [hep-lat].
  * [3] Wuppertal-Budapest Collaboration, S. Borsanyi et al., “Is there still any $T_{c}$ mystery in lattice QCD? Results with physical masses in the continuum limit III,” JHEP 09 (2010) 073, arXiv:1005.3508 [hep-lat].
  * [4] NA60 Collaboration, A. Baldit et al., “Study of prompt dimuon and charm production with proton and heavy ion beams at the CERN SPS: Proposal,”. http://cds.cern.ch/record/430343.
  * [5] NA60 Collaboration, R. Arnaldi et al., “Evidence for the production of thermal-like muon pairs with masses above 1 GeV$/c^{2}$ in 158 AGeV Indium–Indium Collisions,” Eur. Phys. J. C59 (2009) 607, arXiv:0810.3204 [nucl-ex].
  * [6] NA60 Collaboration, R. Arnaldi et al., “First measurement of the rho spectral function in high-energy nuclear collisions,” Phys. Rev. Lett. 96 (2006) 162302, arXiv:nucl-ex/0605007 [nucl-ex].
  * [7] NA60 Collaboration, H. J. Specht, “Thermal Dileptons from Hot and Dense Strongly Interacting Matter,” AIP Conf. Proc. 1322 (2010) 1, arXiv:1011.0615 [nucl-ex].
  * [8] R. Rapp and J. Wambach, “Low mass dileptons at the CERN SPS: Evidence for chiral restoration?,” Eur. Phys. J. A6 (1999) 415, arXiv:hep-ph/9907502 [hep-ph].
  * [9] H. van Hees and R. Rapp, “Dilepton Radiation at the CERN Super Proton Synchrotron,” Nucl. Phys. A806 (2008) 339, arXiv:0711.3444 [hep-ph].
  * [10] Particle Data Group, M. Tanabashi, et al., “Review of Particle Physics,” Phys. Rev. D98 (2018) 030001.
  * [11] M. Dey et al., “Mixing of vector and axial mesons at finite temperature: an indication towards chiral symmetry restoration,” Phys. Lett. B252 (1990) 620.
  * [12] R. Rapp and H. van Hees, “Thermal dileptons as fireball thermometer and chronometer,” Phys. Lett. B753 (2016) 586.
  * [13] J. Pochodzalla et al., “Probing the nuclear liquid–gas phase transition,” Phys. Rev. Lett. 75 (1995) 1040.
  * [14] T. Matsui and H. Satz, “$\mathrm{J}/\psi$ Suppression by Quark-Gluon Plasma Formation,” Phys. Lett. B178 (1986) 416.
  * [15] NA50 Collaboration, B. Alessandro et al., “A new measurement of $\mathrm{J}/\psi$ suppression in Pb–Pb collisions at 158 GeV per nucleon,” Eur. Phys. J. C39 (2005) 335, arXiv:hep-ex/0412036 [hep-ex].
  * [16] PHENIX Collaboration, A. Adare et al., “$\mathrm{J}/\psi$ suppression at forward rapidity in Au+Au collisions at $\sqrt{s_{\rm NN}}=200$ GeV,” Phys. Rev. C84 (2011) 054912, arXiv:1103.6269 [nucl-ex].
  * [17] ALICE Collaboration, J. Adam et al., “$\mathrm{J}/\psi$ suppression at forward rapidity in Pb–Pb collisions at $\sqrt{s_{\rm NN}}=5.02$ TeV,” Phys. Lett. B766 (2017) 212, arXiv:1606.08197 [nucl-ex].
  * [18] NA60 Collaboration, R. Arnaldi et al., “$\mathrm{J}/\psi$ production in proton–nucleus collisions at 158 and 400 GeV,” Phys. Lett. B706 (2012) 263, arXiv:1004.5523 [nucl-ex].
  * [19] A. Beraudo et al., “Extraction of Heavy-Flavor Transport Coefficients in QCD Matter,” Nucl. Phys. A979 (2018) 21, arXiv:1803.03824 [nucl-th].
  * [20] S. Plumari, V. Minissale, S. K. Das, G. Coci, and V. Greco, “Charmed Hadrons from Coalescence plus Fragmentation in relativistic nucleus–nucleus collisions at RHIC and LHC,” Eur. Phys. J. C78 (2018) 348, arXiv:1712.00730 [hep-ph].
  * [21] M. He, R. J. Fries, and R. Rapp, “Thermal Relaxation of Charm in Hadronic Matter,” Phys. Lett. B701 (2011) 445, arXiv:1103.6279 [nucl-th].
  * [22] F. Scardina, S. K. Das, V. Minissale, S. Plumari, and V. Greco, “Estimating the charm quark diffusion coefficient and thermalization time from D meson spectra at energies available at the BNL Relativistic Heavy Ion Collider and the CERN Large Hadron Collider,” Phys. Rev. C96 (2017) 044905, arXiv:1707.05452 [nucl-th].
  * [23] NA49 Collaboration, C. Alt et al., “Upper limit of D0 production in central Pb–Pb collisions at 158 AGeV,” Phys. Rev. C73 (2006) 034910, arXiv:nucl-ex/0507031 [nucl-ex].
  * [24] B. Friman, C. Hohne, J. Knoll, S. Leupold, J. Randrup, R. Rapp, and P. Senger, “The CBM physics book: Compressed baryonic matter in laboratory experiments,” Lect. Notes Phys. 814 (2011) 1.
  * [25] K. J. Eskola, P. Paakkinen, H. Paukkunen, and C. A. Salgado, “EPPS16: Nuclear parton distributions with LHC data,” Eur. Phys. J. C77 (2017) 163, arXiv:1612.05741 [hep-ph].
  * [26] G. Aglieri Rinella et al., “The ALPIDE pixel sensor chip for the upgrade of the ALICE Inner Tracking System,” Nucl. Instrum. Meth. A845 (2017) 583. Proceedings of the Vienna Conference on Instrumentation 2016.
  * [27] ALICE Collaboration, “Expression of Interest for an ALICE ITS Upgrade in LS3,”. https://cds.cern.ch/record/2644611/files/ITS3%20EoI.5.pdf.
  * [28] F. Sauli, “GEM: A new concept for electron amplification in gas detectors,” Nucl. Instrum. Meth. A386 (1997) 531.
  * [29] Altunbas, C. and others, “Construction, test and commissioning of the triple-GEM tracking detectors for COMPASS,” Nucl. Instrum. Meth. A490 (2002) 177.
  * [30] G. Bencivenni et al., “A triple GEM detector with pad readout for high rate charged particle triggering,” Nucl. Instrum. Meth. A488 (2002) 493.
  * [31] M. Bagliesi et al., “The TOTEM T2 telescope based on triple-GEM chambers,” Nucl. Instrum. Meth. A617 (2010) 134.
  * [32] D. Abbaneo et al., “Upgrade of the CMS muon system with triple-GEM detectors,” JINST 9 (2014) C10036.
  * [33] ALICE Collaboration, “Upgrade of the ALICE Time Projection Chamber,” Tech. Rep. CERN-LHCC-2013-020. ALICE-TDR-016, CERN, Geneva, 2013.  https://cds.cern.ch/record/1622286.
  * [34] M. Villa et al., “Progress on large area GEMs,” Nucl. Instrum. Meth. A628 (2011) 182. VCI 2010.
  * [35] A. Zhang et al., “A GEM readout with radial zigzag strips and linear charge-sharing response,” Nucl. Instrum. Meth. A887 (2018) 184.
  * [36] P. Aspell, G. Anelli, P. Chalmet, J. Kaplon, K. Kloukinas, H. Mugnier, and W. Snoeys, “VFAT2: A front-end system on chip providing fast trigger information, digitized data storage and formatting for the charge sensitive readout of multi-channel silicon and gas particle detectors,”. http://cds.cern.ch/record/1069906.
  * [37] ATLAS Collaboration, G. Iakovidis, “VMM3, an ASIC for Micropattern Detectors,” Tech. Rep. ATL-MUON-PROC-2018-003, CERN, Geneva, 2018\.  http://cds.cern.ch/record/2309951.
  * [38] L. Anderson et al., “A high resolution spectrometer for the study of high mass muon pairs produced by intense hadron beams,” Nuclear Instruments and Methods in Physics Research 223 (1984) 26.
  * [39] F. Bergsma and P. Giudici, “A general-purpose toroidal spectrometer magnet—conceptual study for the NA60+ proposal,”.
  * [40] F. Becattini, J. Manninen, and M. Gazdzicki, “Energy and system size dependence of chemical freeze-out in relativistic nuclear collisions,” Phys. Rev. C73 (2006) 044905, arXiv:hep-ph/0511092 [hep-ph].
  * [41] S. Endres, H. van Hees, J. Weil, and M. Bleicher, “Dilepton production and reaction dynamics in heavy-ion collisions at SIS energies from coarse-grained transport simulations,” Phys. Rev. C92 (2015) 014911.
  * [42] T. Galatyuk, “Future facilities for high $\mu_{\rm b}$ physics,” to be published in Quark Matter 2018 conference proceedings .
  * [43] HADES Collaboration, S. Harabasz et al., “Multi-differential pattern of low-mass e+e- excess from $\sqrt{s_{\rm NN}}=2.4$ GeV Au–Au collisions with HADES,” to be published in Quark Matter 2018 conference proceedings .
  * [44] S. Alioli, P. Nason, C. Oleari, and E. Re, “A general framework for implementing NLO calculations in shower Monte Carlo programs: the POWHEG BOX,” JHEP 06 (2010) 043, arXiv:1002.2581 [hep-ph].
  * [45] NA49 Collaboration, S. V. Afanasiev et al., “Energy dependence of pion and kaon production in central Pb+Pb collisions,” Phys. Rev. C66 (2002) 054902, arXiv:nucl-ex/0205002 [nucl-ex].
  * [46] NA49 Collaboration, C. Alt et al., “Energy and centrality dependence of anti-p and p production and the anti-Lambda/anti-p ratio in Pb+Pb collisions between 20 AGeV and 158 AGeV,” Phys. Rev. C73 (2006) 044910.
  * [47] C. Lourenco and H. K. Wohri, “Heavy flavour hadro-production from fixed-target to collider energies,” Phys. Rept. 433 (2006) 127, arXiv:hep-ph/0609101 [hep-ph].
  * [48] Hard Probe Collaboration, R. Vogt, “The A dependence of open charm and bottom production,” Int. J. Mod. Phys. E12 (2003) 211, arXiv:hep-ph/0111271 [hep-ph].
  * [49] NA60 Collaboration, R. Arnaldi et al., “$\mathrm{J}/\psi$ production in indium-indium collisions at 158 GeV/nucleon,” Phys. Rev. Lett. 99 (2007) 132302.
  * [50] NA50 Collaboration, B. Alessandro et al., “Charmonia and Drell-Yan production in proton–nucleus collisions at the CERN SPS,” Phys. Lett. B553 (2003) 167.

## Appendix: NA60+ Collaboration

M. Agnellotorinodisat&F. Antinoripadova&H. Appelshäuserfrankfurt&R.
Arnalditorino&R. Bailhachefrankfurt&L. Barioglioutorinotorino&S.
Beoleutorinotorino&A. Beraudotorino A. Bianchiutorinotorino&L.
Bianchiutorinotorino&E. Bottautorinotorino&E. Brunatorino&S.
Bufalinodisattorino&E. Casulacagliariucagliari&F. Catalanodisattorino&S.
Chattopadhyaysaha&A. Chauvincagliari&C. Cicalocagliari&M. Concasdettorino&P.
Cortesepiemontetorino&T. Dahmsclustertumeditor&A. Dainesepadova&A. Dassaha&D.
Dassaha&D. Dassaha&I. Dassaha&L. Das Bosesaha&A. De Falcocagliari&N. De
Marcotorino&S. Delsantoutorinotorino&A. Dreesstonybrook&L. Fabbiettitum&P.
Fecchiodisattorino&A. Ferrettiutorinotorino&A. Feliciellotorino&M.
Gagliardiutorinotorino&P. Gasiktum&F. Geurtsrice&P. Giubilatopadovaupadova&V.
Grecocatania&F. Grosadisattorino&H. Hansenlyon&J. Kleintorino&W. Lirice&M.P.
Lombardolfn M. Maserautorinotorino&A. Masonicagliari&L.
Michelettiutorinotorino&L. Musacern&M. Narditorino&H. Onishitohoku&C.
Oppedisanotorino&B. Paulcagliariucagliari&S. Plumariucatania&F. Prinotorino&M.
Puccioutorinotorino&L. Ramellopiemontetorino&R. Rapptamu&I.
Ravasengadisattorino&A. Rossipadovaupadova&P. Roysaha&E.
Scomparintorinoeditor&S. Siddhantacagliari&R. Shahoyancern&T. Sinhasaha&M.
Sittapiemontetorino&H. Spechtheidelberg&S. Trogoloutorinotorino&R.
Turrisipadova&A. Uraslyon&G. Usaicagliariucagliarieditorcontact&E.
Vercellinutorinotorino&J. Wiechulafrankfurt

### Notes

editorEditors

contactE-mail<EMAIL_ADDRESS>

### Collaboration Institutes

lyonUniversité de Lyon, Université Lyon 1, CNRS/IN2P3, IPN-Lyon, Villeurbanne,
Lyon, France

frankfurtInstitut für Kernphysik, Johann Wolfgang Goethe-Universität
Frankfurt, Frankfurt, Germany

heidelbergPhysikalisches Institut, Ruprecht-Karls-Universität Heidelberg,
Heidelberg, Germany

clusterExcellence Cluster ‘Universe’, Technische Universität München, Munich,
Germany

tumPhysik Department, Technische Universität München, Munich, Germany

sahaSaha Institute of Nuclear Physics, Homi Bhabha National Institute,
Kolkata, India

cagliariINFN, Sezione di Cagliari, Cagliari, Italy

ucagliariDipartimento di Fisica dell’Università di Cagliari, Cagliari, Italy

cataniaINFN, Laboratori Nazionali del Sud, Catania, Italy

ucataniaDipartimento di Fisica e Astronomia dell’Università di Catania,
Catania, Italy

lfnINFN, Laboratori Nazionali di Frascati, Frascati, Italy

padovaINFN, Sezione di Padova, Padova, Italy

upadovaDipartimento di Fisica e Astronomia dell’Università di Padova, Padova
Italy

torinoINFN, Sezione di Torino, Turin, Italy

detDipartimento DET del Politecnico di Torino, Turin, Italy

disatDipartimento DISAT del Politecnico di Torino, Turin, Italy

utorinoDipartimento di Fisica dell Università di Torino, Turin, Italy

piemonteDipartimento di Scienze e Innovazione Tecnologica dell’Università del
Piemonte Orientale, Alessandria, Italy

tohokuResearch Center for Electron Photon Science (ELPH), Tohoku University,
Sendai, Japan

cernEuropean Organization for Nuclear Research (CERN), Geneva, Switzerland

riceDepartment of Physics and Astronomy, Rice University, Houston, Texas, USA

stonybrookDepartment of Physics and Astronomy, Stony Brook University, SUNY,
Stony Brook, New York, USA

tamuCyclotron Institute and Department of Physics and Astronomy, Texas A&M
University, College Station, Texas, USA