Experimental Evidence for an Attractive p-φ Interaction

Experimental Evidence for an Attractive p-ϕ Interaction

S. Acharyaet al.^* (ALICE Collaboration)

(Received 16 June 2021; revised 8 September 2021; accepted 14 September 2021; published 20 October 2021) This Letter presents the first experimental evidence of the attractive strong interaction between a proton and a ϕ meson. The result is obtained from two-particle correlations of combined p-ϕ⊕ p-¯ ϕ pairs measured in high-multiplicity ppcollisions at ffiffiffi

ps¼13TeV by the ALICE Collaboration. The spin- averaged scattering length and effective range of thep-ϕinteraction are extracted from the fully corrected correlation function employing the Lednický-Lyuboshits approach. In particular, the imaginary part of the scattering length vanishes within uncertainties, indicating that inelastic processes do not play a prominent role for the p-ϕ interaction. These data demonstrate that the interaction is dominated by elastic p-ϕ scattering. Furthermore, an analysis employing phenomenological Gaussian- and Yukawa-type potentials is conducted. Under the assumption of the latter, the N-ϕ coupling constant is found to be gN-ϕ¼0.140.03ðstatÞ 0.02ðsystÞ. This work provides valuable experimental input to accomplish a self-consistent description of theN-ϕinteraction, which is particularly relevant for the more fundamental studies on partial restoration of chiral symmetry in nuclear medium.

DOI:10.1103/PhysRevLett.127.172301

Quantum chromodynamics (QCD) is the theory of the strong interaction, where the degrees of freedom are represented by colored quarks and gluons. The observable degrees of freedom at low energies, however, are composite hadrons, and their mass is dynamically generated by the interplay between spontaneous and explicit chiral sym- metry breaking. The spontaneous breaking arises from the nonzero vacuum expectation valueh0jqq¯ j0iof the ground state of the QCD Lagrangian, the quark condensateqq. The¯ consideration of the quark mass term leads to the explicit breaking of chiral symmetry. A link between the hadron properties andh0jqq¯ j0iis provided by the QCD sum rule method [1–4], with the hadrons being interpreted as excitations of the qq¯ ground state. Chiral symmetry is expected to be partially restored in a dense and/or hot strongly interacting medium [5]. Consequently, the modi- fication of theqq¯ condensate in the medium is reflected in the spectral shape of its hadronic excitations. This results in a potentially measurable mass shift and/or width broad- ening of the hadrons. From the experimental point of view, the light vector mesons ρ, ω, and ϕ represent the most suitable hadronic probes due to the short lifetime[6,7]. The detection through the dileptonic decay channels (e^þe⁻and

μ^þμ⁻) allows us to infer on the meson properties at the time of their decay[8–12].

In this context, theϕmeson represents an experimentally challenging probe due to the narrow decay width in vacuum, which renders its spectral shape distinguishable from that of the ρ and ω mesons. The KEK-PS E325 Collaboration measured theϕspectral function inp-C and p-Cu reactions and reported a slight mass shift and moderate increase of the width, which was in a model- dependent manner interpreted as an in-medium modifica- tion[13]. The collected data were, however, limited due to the small branching ratio (B≈3×10⁻⁴[14]) of theϕ→ e^þe⁻ decay. Larger data samples were collected by the Spring8-LEPS Collaboration in order to determine theϕ production and absorption cross section in photon-induced reactions by exploiting the decay toK^þK⁻(B≈50%[14]) [15]. TheN-ϕcross section in nuclear matter was found to be much larger than the vacuum cross section, correspond- ing to an in-medium ϕ width of about 110MeV=c². A similar conclusion was reached by other experiments from transparency ratio measurements in photon-induced [16]

and proton-induced reactions[17].

The interpretation of these results is far from trivial due to the lack of model-independent information on theN-ϕ interaction and its complex dynamics. Because of the hidden strangeness content (ss) of the¯ ϕ, the direct coupling to u and d quarks in the nucleon is expected to be suppressed due to the Okubo-Zweig-Iizuka (OZI) rule [18–20]. Indications for a possible OZI rule violation were reported by the HADES Collaboration [10]. In addition, several scenarios allow for a direct interaction of the ϕ

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meson with the nucleon, including a coupling to its strangeness content [21]. An alternative is the QCD van der Waals interaction [22], mediated by multigluon exchange, which has been identified as relevant for the N-(cc) system¯ [23]. Using a phenomenological Yukawa- type potential with adjusted parameters, the QCD van der Waals force is able to form a N-ϕ bound state [24].

However, the direct N-ϕcoupling is typically not consid- ered in theoretical descriptions of the interaction in vacuum and in medium. OZI-allowed N-ϕ processes can also proceed via the coupling to particle pairs with same quantum numbers, such as K-Λ; K-Σ; K-Λ; K-Σ [25–27]. More importantly, the properties of the ϕ are defined by theϕ-KK¯ coupling[18–20]. Accordingly,KK¯ loops and tadpole diagrams contribute to the self-energy of the ϕ [26–28], linking the ϕ properties to the complex dynamics of the K-N and K-N¯ systems [29]. This was explored by HADES in π-nucleus reactions at beam energies of 1.65 GeV, demonstrating a constant ϕ=K⁻ ratio in different collision systems[30]. Since a strongK⁻ absorption was observed also a strong ϕ absorption is expected. The overall N-ϕ interaction is defined by the interplay of all aforementioned processes. However, the present theoretical and experimental situation is far from being resolved[31]. Indeed, a consistent description of the available photon- and proton-induced data[15–17]is still out of reach[25]. This demonstrates the need for a direct measurement of the two-bodyN-ϕinteraction in vacuum, in order to constrain theoretical models and correctly interpret the data from nuclear collisions.

Recently, detailed measurements of the final-state inter- action were conducted employing two-particle correlations in ultrarelativistic proton-proton (pp) collisions[32–39]. In this Letter, these studies are extended to protons andϕmesons.

The observable is the two-particle correlation functionCðkÞ, defined asCðkÞ ¼N ×ðN_sameðkÞ=N_mixedðkÞ[40]where N_sameandN_mixedare the distributions of the relative momen- tumk¼¹₂×jp₁−p₂jbetween both particles in the pair rest frame (denoted by the ) and a normalization constantN, evaluated from same and mixed events, respectively. The Koonin-Pratt equation CðkÞ ¼R

d³rSðrÞjΨðr!

; k!Þj² [40] relates the observable to the source function SðrÞ and the two-particle wave functionΨð!r

; k!

Þincorporating the final-state interaction, where r is the relative distance between the two particles.

The results reported in this Letter are based on the analysis of a data sample ofppcollisions at ffiffiffi

ps

¼13TeV recorded by ALICE Collaboration[41,42]during the LHC Run 2 (2015–2018). A high-multiplicity trigger relying on the measured signal amplitudes in the V0 detectors[43]is employed to select collisions with on average 30 produced charged particles in the pseudorapidity interval jηj<0.5 [38]. The resulting data sample represents the upper 0.17%

of the charged-particle distribution of all inelastic collisions

with at least one charged particle in the range jηj<1 (referred to as INEL>0)[37]. The event selection follows [32,37]. The reconstructed primary vertex is required to be located within 10cm of the nominal interaction point along the beam direction to assure a uniform detector coverage. Meson-baryon correlation measurements inpp collisions are contaminated by a so-called minijet back- ground, induced by jetlike structures associated with hard parton-parton scatterings [35,44], which influence the event shape [45,46]. Therefore, a selection on the trans- verse sphericityS_T [35,45,46], defined as in Ref. [45], is utilized to reduce the minijet contribution. A total of5× 10⁸events with0.7< S_T <1.0[35]are analyzed. The sub- systems employed in the analysis are the Inner Tracking System[41], the Time Projection Chamber (TPC)[47]and the Time-of-Flight (TOF) detector[48], covering the full azimuthal angle and the pseudorapidity intervaljηj<0.9. The detectors are immersed in a uniform magnetic field of 0.5 T along the beam direction.

The proton candidates are selected following the methods used in Ref.[32]. The particle identification (PID) is con- ducted employing the TPC and TOF detectors by determining the deviationn_σ between the signal hypothesis for a proton and the measurement, normalized by the detector resolution σ. Contributions from secondary particles stemming from weak decays or the interaction of primary particles with the detector material are extracted using Monte Carlo (MC) template fits to the measured distribution of the distance of closest approach (DCA) of the track to the primary vertex [32]. This results in a proton purity of 99%, with a primary fraction of 82%[33]. Theϕmeson is reconstructed from its hadronic decay to charged kaonsϕ→K^þK⁻as in Refs.[49– 51]. Charged kaons are identified with a transverse momen- tum ofp_T >0.15GeV=candjηj<0.8. For momentap <

0.4GeV=cthe PID selection provided by the TPC is used, while for larger momenta the information of TPC and TOF is combined. A selection on the DCA of the track to the primary vertex in both the beam direction (jDCA_zj<0.8cm) and transverse plane (jDCA_xyj<0.4cm) is employed to increase the fraction of kaons fromϕdecays. The purity of the kaon sample is>90%forp_T <1.25GeV=c. TheK^þK⁻ invari- ant mass is calculated combining two oppositely charged kaons assuming their nominal masses[14]. Theϕcandidates are selected within a window of 8MeV=c² around the nominalϕmass, resulting in a total number of5.8×10⁶with a purity of 66%.

A total of4.17×10⁴ p-ϕand3.61×10⁴p-¯ ϕpairs with k<200MeV=c contribute to the N_same distribution of the respective correlation function. As they are com- patible within uncertainties, both correlation functions are combined. In the following, p-ϕ refers to p-ϕ⊕

¯

p-ϕ. The correlation function is normalized within k∈½800;1000MeV=c, where all the contributions to the correlation function are expected to be flat. The data are unfolded for the finite momentum resolution of the detector

[52], which modifies the correlation function by 0.7% at lowk. The measuredp-ϕcorrelation function is shown in Fig.1. Thekvalue of the data points is determined by the averagehkiof theN_same distribution in the corresponding interval. In the region150< k<600MeV=ca rise in the correlation function attributed to residual minijet back- ground is visible. Therefore, any conclusion on the genuine p-ϕ interaction demands a treatment of the contributions due to residual correlations from the underlying event topology (minijets and energy-momentum conservation), weak decays feeding to the particles of interest (feed-down) and misidentifications [32].

The experimental p-ϕ correlation function C_expðkÞ is decomposed as

C_expðkÞ ¼M×C_bkgðkÞ×½λp-ϕ×C_p-ϕðkÞþλflat×C_flatðkÞ þλ_p-ðK^þK⁻Þ×C_p-ðK^þ_K⁻_ÞðkÞ; ð1Þ where M is a normalization constant, C_bkgðkÞ is the nonfemtoscopic background, C_p-ϕðkÞ the genuine p-ϕ correlation function,C_flatðkÞ≈1considers the effect from weak decays and single particle misidentification and C_p-ðK^þ_K⁻_ÞðkÞ is the contribution from combinatorial K^þK⁻ background. Correlations are summed for indepen- dent pairs and multiplied when considering different effects acting on the same pair. The parametersλi, summarized in Table I, are obtained in a data-driven way from single- particle properties[32]. As the purity of the ϕcandidates depends on p_T, it is evaluated for those entering the correlation function, and found to be 57%.

The combinatorialK^þK⁻ background, referred to asp- (K^þK⁻), significantly contributes to the measured corre- lation function. Its shape is extracted from the sidebands of the K^þK⁻ invariant mass selection and mainly driven by

p-K^þ and p-K⁻ interactions. The sideband intervals are chosen as0.995–1.011GeV=c²and1.028–1.044GeV=c² to avoid threshold effects and have comparable kinematic properties as the ϕ candidates. The resulting correlation function is parametrized with a double Gaussian and a quadratic polynomial. Finally, a residualϕamount of 8.6%

in the sidebands is considered, which arises from the tail of the ϕ resonance extending into the sideband intervals.

This results in a 7% contribution to the experimental C_p-ðKþK⁻ÞðkÞ, which is absorbed by a renormalization of the λ parameters. Since the p-(K^þK⁻) contribution is obtained from data, the corresponding residual minijet background and energy-momentum conservation effects are accounted for. The resultingC_p-ðK^þ_K⁻_ÞðkÞ is depicted by the green band in Fig.1.

The nonfemtoscopic backgroundC_bkgðkÞ in Eq.(1) is multiplied to the genuine p-ϕ and flat contributions.

C_bkgðkÞ ¼C_baselineðkÞ þC_minijetðkÞ is dominated by residual minijet contributions C_minijetðkÞ obtained from

PYTHIA8 [53] generated events, which yield a consistent description of such background[54,55]. However, further correlations at large k due to energy-momentum conser- vation effects are not properly reproduced byPYTHIA8[56].

Therefore, an additionalC_baselineðkÞfunction, described by a second order polynomial, is considered.

The data are then fitted with a background model [Eq.(1) withC_p-ϕðkÞ ¼1] withink∈½200;800MeV=c, which accounts for all contributions besides the genuine p-ϕ interaction. Theλparameters and the shape of the minijet andp-ðK^þK⁻Þ background are fixed in the fit. Only the normalization constant and baseline parameters are free.

The resultingC_bkgðkÞis shown by the red band in Fig.1 and the mean value of the normalization constant is M¼0.96. Accordingly, the total background is obtained as the blue band in Fig.1, which accurately reproduces the enhancement between 200 and1000MeV=c.

The genuine p-ϕ contribution C_p-ϕðkÞ, is extracted from Eq. (1) by subtracting the obtained background contributions from the experimental correlation and is shown in Fig. 2. For k>200MeV=c, it is flat and consistent with unity within uncertainties. At low k a pronounced enhancement with a significance of4.7−6.6σ with respect to the unity becomes apparent, which evi- dences the attractive nature of the p-ϕ interaction. The systematic uncertainties of the data and the background description are assessed by varying simultaneously the

0 200 400 600 800 1000

) c

* (MeV/

k 0.95

1 1.05 1.1 1.15 1.2 1.25 1.3 1.35 1.4

*)k(expC

= 13 TeV s ALICE pp

0.17% INEL > 0)

− High-mult. (0

< 1.0 ST

0.7 <

φ

−

⊕p φ

− p

Background model

Cbkg

⋅ M

K

−K

Cp

FIG. 1. The experimentalp-ϕcorrelation functionC_expðkÞand various contributions as described in Eq.(1). Statistical (bars) and systematic uncertainties (boxes) are shown separately. The width of the dark (light) shaded bands depicts the statistical (total) uncertainty.

TABLE I. Weight parameters of the individual components of thep-ϕcorrelation function.

Pair Weightλ(%)

p-ϕ 46.3

p-ðK^þK⁻Þ 43.3

Flat 10.4

selection criteria of protons and kaons as well as the lower limit of the sphericity. These variations are chosen such that any combination leads to a maximum change of20%of N_same within k<200MeV=c in order to retain the statistical significance. Systematic uncertainties associated with the background description are evaluated by varying the fit ranges and the order of the polynomial assumed for C_baselineðkÞ. Uncertainties related to the unfolding are accounted for according to Ref. [38]. This results in a relative systematic uncertainty at lowkof 2.8%.

In correlation measurements, the detected pairs are emitted in the final state of the scattering processes. The correlation function of the sample is then sensitive to elastic and inelastic channels produced in the collision [58].

Inelastic channels opening below threshold act as an effective increase of the correlation function. The relevant channels for the p-ϕ system, Λ-K and Σ-K are located substantially below threshold. Channels appearing above threshold lead to a cusp structure inCðkÞin the vicinity of the threshold. Because of the large uncertainties and the broad bin width, no such structures are observed at the opening of the Λ-K (k¼221.6MeV=c) and Σ-K (k¼357.4 MeV=c) thresholds.

In order to interpret the measured genuinep-ϕcorrela- tion one has to consider that the p-ϕinteraction features one isospin and two spin configurations. Since the latter cannot be disentangled, spin-averaged results are pre- sented. The strong p-ϕ interaction is modeled employing the Lednický-Lyuboshits approach[57]. Coupled channel effects are incorporated via an imaginary contribution to the scattering length. For large values ofd₀, the term∝d₀=r₀ that corrects the asymptotic wave function for small sources has an impact on the modeled correlation function [34].

Additionally, in line with studies of charmonium states [23,59], phenomenological potentials are employed to

model the p-ϕ interaction [24], including Yukawa- type, V_YukawaðrÞ ¼−A×r⁻¹×e^−α×r, and Gaussian-type V_GaussianðrÞ ¼−V_eff×e^−μ×r2 potentials. The correlation functions based on these potentials are obtained with the correlation analysis tool using the Schrödinger equation (CATS)[60].

The particle-emitting source is extracted from studies of p-p and p-Λ pairs [33], which demonstrated that by accounting for the effect of strong resonances feeding to the particle pair of interest, a common source for both pairs is found. The primordial source depends on the transverse massm_Tof the particle pair and is obtained by evaluating the core radius at thehmTi ¼1.66GeV=c²of the p-ϕpairs.

The strong decays feeding to protons are explicitly consid- ered[33], while for the ϕ a 100% primordial fraction is assumed[14]. The resulting source function is parametrized by a Gaussian profile withr_eff ¼ ð1.080.05Þfm.

The interaction parameters are extracted by fitting the genuinep-ϕcorrelation functionC_p-ϕðkÞwith the respec- tive model withink<200MeV=c. The systematic uncer- tainties of the procedure are assessed by varying the upper limit of the fit range by30MeV=cand the source radius within its uncertainties.

The real and imaginary parts of the scattering length obtained from the Lednický-Lyuboshits fit are ℜðf₀Þ ¼ 0.850.34ðstatÞ 0.14ðsystÞfm and ℑðf₀Þ ¼0.16 0.10ðstatÞ 0.09ðsystÞ fm. The resulting effective range isd₀¼7.851.54ðstatÞ 0.26ðsystÞfm.ℜðf₀Þdeviates by2.3σfrom zero, indicating the attractiveness of thep-ϕ interaction in the approximate vacuum of pp collisions.

Notably, ℑðf₀Þ vanishes within uncertainties, indicating that inelastic processes do not play a prominent role in the interaction. Instead, the elasticp-ϕ interaction appears to be dominant in vacuum. The scattering length is larger than values found in literature: a recent analysis of data recorded with the CLAS experiment reports jf₀j ¼ ð0.063 0.010Þfm [61]; a value of around f₀¼0.15fm is con- sistent with LEPS measurements of the ϕ cross section [62,63]; studies of an effective Lagrangian combining chiral SU(3) dynamics with vector meson dominance obtain f₀¼ ð−0.01þi0.08Þ fm [64]; and a QCD sum rule analysis finds f₀¼ ð−0.150.02Þfm [65]. The obtained scattering lengths are rather model dependent since the data refer to the properties of theϕmeson inside a nucleus and not to a two-body system as in this work. This underlines the importance of direct measurements of the two-bodyN-ϕinteraction to provide constraints for theo- retical models.

Finally, the data are employed to constrain the param- eters of phenomenological Gaussian- and Yukawa-type potentials. As the imaginary contribution of the scattering length is consistent with zero, only real values are used for the parameters. The fits yield a comparable degree of consistency as the fit with the Lednický-Lyuboshits approach. The resulting values for the Gaussian-type

0 50 100 150 200 250 300 350 400

) c

* (MeV/

k 1

1.1 1.2 1.3 1.4 1.5

*)k(φ−pC

φ

−

⊕p φ

− p

-Lyuboshits model y

Lednick = 13 TeV s ALICE pp

0.17% INEL > 0)

− High-mult. (0

< 1.0 S 0.7 <

0.26 (syst.) fm

± 1.54 (stat.)

± = 7.85 d

0.14 (syst.) fm

± 0.34 (stat.)

± ) = 0.85 f ℜ(

0.09 (syst.) fm

± 0.10 (stat.)

± ) = 0.16 f ℑ(

FIG. 2. The genuine p-ϕ correlation function C_p-ϕðkÞ with statistical (bars) and systematic uncertainties (boxes). The red band depicts the results from the fit employing the Lednický- Lyuboshits approach[57]. The width corresponds to one standard deviation of the uncertainty of the fit.

potential are V_eff ¼2.50.9ðstatÞ 1.4ðsystÞMeV and μ¼0.140.06ðstatÞ0.09ðsystÞfm⁻², indicating a much shallower strong interaction potential than lattice QCD results for the N-J=ψ strong interaction [66]. For the Yukawa-type potential the fit yields A¼0.021 0.009ðstatÞ 0.006ðsystÞ and α¼65.938.0ðstatÞ 17.5ðsystÞMeV. Predictions of possibleN-ϕbound states employing the same kind of potential with modified parameters (α¼600MeV and A¼1.25) [24] are there- fore incompatible with this measurement. The N-ϕ coupling constant under the assumption of a Yukawa- type potential (g_N-ϕ¼ ffiffiffiffi

pA

) is g_N-ϕ¼0.140.03ðstatÞ 0.02ðsystÞ. In conclusion, this Letter presents the first correlation-based measurement of the p-ϕ interaction.

The correlation function reflects the pattern of an attractive interaction. The scattering parameters, extracted with the Lednický-Lyuboshits approach, are ℜðf₀Þ ¼0.85 0.34ðstatÞ 0.14ðsystÞfm, ℑðf₀Þ ¼0.160.10ðstatÞ 0.09ðsystÞfm, and d₀¼7.851.54ðstatÞ0.26ðsystÞfm.

Remarkably, the imaginary contribution to the scattering length vanishes, indicating that inelastic processes do not play a prominent role. Instead, the interaction is domi- nated by the elasticp-ϕdynamics. Under the assumption of a Yukawa-type potential for the N-ϕ interaction, the value of the coupling constant is extracted as g_N-ϕ¼0.140.03ðstatÞ 0.02ðsystÞ.

These results seem to contradict the interpretation of the ϕproduction off nuclear targets in terms of large absorption cross-sections but more data are needed to extract the precise value of the imaginary part of the scattering length and the here reported results should serve as an input for more advanced modelings in medium. The upcoming Run 3 and Run 4 data taking at the LHC will allow to significantly improve the precision of the extracted inter- action parameters. This measurement demonstrates for the first time that thep-ϕinteraction in vacuum is attractive and dominated by elastic scattering. It provides valuable exper- imental input on theN-ϕinteraction, which is fundamental to reach a self-consistent description of the interaction as required for the correct interpretation of data from nuclear collisions.

The ALICE Collaboration is grateful to P. Gubler and N.

Kaiser for valuable discussions. The ALICE Collaboration would like to thank all its engineers and technicians for their invaluable contributions to the construction of the experiment and the CERN accelerator teams for the out- standing performance of the LHC complex. The ALICE Collaboration gratefully acknowledges the resources and support provided by all Grid centres and the Worldwide LHC Computing Grid (WLCG) Collaboration. The ALICE Collaboration acknowledges the following funding agen- cies for their support in building and running the ALICE detector: A. I. Alikhanyan National Science Laboratory (Yerevan Physics Institute) Foundation (ANSL), State

Committee of Science and World Federation of Scientists (WFS), Armenia; Austrian Academy of Sciences, Austrian Science Fund (FWF): [M 2467-N36]

and Nationalstiftung für Forschung, Technologie und Entwicklung, Austria; Ministry of Communications and High Technologies, National Nuclear Research Center, Azerbaijan; Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq), Financiadora de Estudos e Projetos (Finep), Fundação de Amparo `a Pesquisa do Estado de São Paulo (FAPESP) and Universidade Federal do Rio Grande do Sul (UFRGS), Brazil; Ministry of Education of China (MOEC), Ministry of Science & Technology of China (MSTC) and National Natural Science Foundation of China (NSFC), China;

Ministry of Science and Education and Croatian Science Foundation, Croatia; Centro de Aplicaciones Tecnológicas y Desarrollo Nuclear (CEADEN), Cubaenergía, Cuba;

Ministry of Education, Youth and Sports of the Czech Republic, Czech Republic; The Danish Council for Independent Research | Natural Sciences, the VILLUM FONDEN and Danish National Research Foundation (DNRF), Denmark; Helsinki Institute of Physics (HIP), Finland; Commissariat `a l’Energie Atomique (CEA) and Institut National de Physique Nucl´eaire et de Physique des Particules (IN2P3) and Centre National de la Recherche Scientifique (CNRS), France; Bundesministerium für Bildung und Forschung (BMBF) and GSI Helmholtzzentrum für Schwerionenforschung GmbH, Germany; General Secretariat for Research and Technology, Ministry of Education, Research and Religions, Greece; National Research, Development and Innovation Office, Hungary; Department of Atomic Energy Government of India (DAE), Department of Science and Technology, Government of India (DST), University Grants Commission, Government of India (UGC) and Council of Scientific and Industrial Research (CSIR), India; Indonesian Institute of Science, Indonesia; Istituto Nazionale di Fisica Nucleare (INFN), Italy; Institute for Innovative Science and Technology, Nagasaki Institute of Applied Science (IIST), Japanese Ministry of Education, Culture, Sports, Science and Technology (MEXT) and Japan Society for the Promotion of Science (JSPS) KAKENHI, Japan; Consejo Nacional de Ciencia (CONACYT) y Tecnología, through Fondo de Cooperación Internacional en Ciencia y Tecnología (FONCICYT) and Dirección General de Asuntos del Personal Academico (DGAPA), Mexico; Nederlandse Organisatie voor Wetenschappelijk Onderzoek (NWO), Netherlands; The Research Council of Norway, Norway;

Commission on Science and Technology for Sustainable Development in the South (COMSATS), Pakistan;

Pontificia Universidad Católica del Perú, Peru; Ministry of Education and Science, National Science Centre and WUT ID-UB, Poland; Korea Institute of Science and Technology Information and National Research

Foundation of Korea (NRF), Republic of Korea; Ministry of Education and Scientific Research, Institute of Atomic Physics and Ministry of Research and Innovation and Institute of Atomic Physics, Romania; Joint Institute for Nuclear Research (JINR), Ministry of Education and Science of the Russian Federation, National Research Centre Kurchatov Institute, Russian Science Foundation and Russian Foundation for Basic Research, Russia;

Ministry of Education, Science, Research and Sport of the Slovak Republic, Slovakia; National Research Foundation of South Africa, South Africa; Swedish Research Council (VR) and Knut & Alice Wallenberg Foundation (KAW), Sweden; European Organization for Nuclear Research, Switzerland; Suranaree University of Technology (SUT), National Science and Technology Development Agency (NSDTA) and Office of the Higher Education Commission under NRU project of Thailand, Thailand; Turkish Energy, Nuclear and Mineral Research Agency (TENMAK), Turkey; National Academy of Sciences of Ukraine, Ukraine; Science and Technology Facilities Council (STFC), United Kingdom;

National Science Foundation of the United States of America (NSF) and United States Department of Energy, Office of Nuclear Physics (DOE NP), USA.

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R. Langoy,¹³² K. Lapidus,³⁵P. Larionov,⁵³E. Laudi,³⁵L. Lautner,^35,108 R. Lavicka,³⁸T. Lazareva,¹¹⁵R. Lea,24a,24b,59,142

J. Lee,¹³⁶J. Lehrbach,⁴⁰R. C. Lemmon,⁹⁷I. León Monzón,¹²²E. D. Lesser,¹⁹M. Lettrich,^35,108P. L´evai,¹⁴⁷X. Li,¹¹X. L. Li,⁷ J. Lien,¹³²R. Lietava,¹¹³ B. Lim,¹⁷S. H. Lim,¹⁷V. Lindenstruth,⁴⁰A. Lindner,⁴⁹C. Lippmann,¹¹⁰ A. Liu,¹⁹J. Liu,¹³⁰ I. M. Lofnes,²¹V. Loginov,⁹⁶C. Loizides,⁹⁹P. Loncar,³⁶ J. A. Lopez,¹⁰⁷ X. Lopez,¹³⁷ E. López Torres,⁸ J. R. Luhder,¹⁴⁶ M. Lunardon,^28a,28bG. Luparello,⁶²Y. G. Ma,⁴¹A. Maevskaya,⁶⁵M. Mager,³⁵T. Mahmoud,⁴⁴A. Maire,¹³⁹M. Malaev,¹⁰¹

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P. F. T. Matuoka,¹²³A. Matyja,¹²⁰C. Mayer,¹²⁰A. L. Mazuecos,³⁵ F. Mazzaschi,^25a,25bM. Mazzilli,³⁵M. A. Mazzoni,⁶⁰ J. E. Mdhluli,¹³⁴ A. F. Mechler,⁷⁰ F. Meddi,^22a,22b Y. Melikyan,⁶⁵A. Menchaca-Rocha,⁷³E. Meninno,30a,30b,116

A. S. Menon,¹²⁷M. Meres,¹³S. Mhlanga,^74,126 Y. Miake,¹³⁶ L. Micheletti,^25a,25b,61 L. C. Migliorin,¹³⁸D. L. Mihaylov,¹⁰⁸ K. Mikhaylov,^77,95A. N. Mishra,¹⁴⁷D. Miśkowiec,¹¹⁰A. Modak,^4a,4bA. P. Mohanty,⁶⁴B. Mohanty,⁸⁹M. Mohisin Khan,¹⁶ Z. Moravcova,⁹²C. Mordasini,¹⁰⁸D. A. Moreira De Godoy,¹⁴⁶L. A. P. Moreno,⁴⁶I. Morozov,⁶⁵A. Morsch,³⁵T. Mrnjavac,³⁵

V. Muccifora,⁵³E. Mudnic,³⁶D. Mühlheim,¹⁴⁶ S. Muhuri,¹⁴³ J. D. Mulligan,⁸²A. Mulliri,^23a,23b M. G. Munhoz,¹²³ R. H. Munzer,⁷⁰H. Murakami,¹³⁵S. Murray,¹²⁶L. Musa,³⁵J. Musinsky,⁶⁶C. J. Myers,¹²⁷J. W. Myrcha,¹⁴⁴B. Naik,^50,134 R. Nair,⁸⁸B. K. Nandi,⁵⁰R. Nania,⁵⁵E. Nappi,⁵⁴M. U. Naru,¹⁴A. F. Nassirpour,⁸³A. Nath,¹⁰⁷C. Nattrass,¹³³A. Neagu,²⁰ L. Nellen,⁷¹S. V. Nesbo,³⁷G. Neskovic,⁴⁰D. Nesterov,¹¹⁵B. S. Nielsen,⁹²S. Nikolaev,⁹¹S. Nikulin,⁹¹V. Nikulin,¹⁰¹ F. Noferini,⁵⁵S. Noh,¹²P. Nomokonov,⁷⁷J. Norman,¹³⁰N. Novitzky,¹³⁶ P. Nowakowski,¹⁴⁴ A. Nyanin,⁹¹ J. Nystrand,²¹ M. Ogino,⁸⁵A. Ohlson,⁸³V. A. Okorokov,⁹⁶J. Oleniacz,¹⁴⁴A. C. Oliveira Da Silva,¹³³M. H. Oliver,¹⁴⁸A. Onnerstad,¹²⁸ C. Oppedisano,⁶¹A. Ortiz Velasquez,⁷¹T. Osako,⁴⁷A. Oskarsson,⁸³J. Otwinowski,¹²⁰ K. Oyama,⁸⁵Y. Pachmayer,¹⁰⁷ S. Padhan,⁵⁰D. Pagano,^59,142G. Paić,⁷¹A. Palasciano,⁵⁴J. Pan,¹⁴⁵S. Panebianco,¹⁴⁰P. Pareek,¹⁴³J. Park,⁶³J. E. Parkkila,¹²⁸

S. P. Pathak,¹²⁷ R. N. Patra,^35,104B. Paul,^23a,23bJ. Pazzini,^59,142 H. Pei,⁷ T. Peitzmann,⁶⁴X. Peng,⁷ L. G. Pereira,⁷² H. Pereira Da Costa,¹⁴⁰D. Peresunko,⁹¹G. M. Perez,⁸S. Perrin,¹⁴⁰Y. Pestov,⁵V. Petráček,³⁸M. Petrovici,⁴⁹R. P. Pezzi,^72,117 S. Piano,⁶²M. Pikna,¹³P. Pillot,¹¹⁷O. Pinazza,^35,55L. Pinsky,¹²⁷C. Pinto,^27a,27bS. Pisano,⁵³M. Płoskoń,⁸²M. Planinic,¹⁰² F. Pliquett,⁷⁰M. G. Poghosyan,⁹⁹B. Polichtchouk,⁹⁴S. Politano,³¹N. Poljak,¹⁰² A. Pop,⁴⁹S. Porteboeuf-Houssais,¹³⁷ J. Porter,⁸²V. Pozdniakov,⁷⁷S. K. Prasad,^4a,4bR. Preghenella,⁵⁵F. Prino,⁶¹C. A. Pruneau,¹⁴⁵I. Pshenichnov,⁶⁵M. Puccio,³⁵