Observation of Beam Spin Asymmetries in the Process e p \rightarrow e π^{+}π^{-}X with CLAS12
T.B. Hayward, C. Dilks, A. Vossen, H. Avakian, S. Adhikari, G. Angelini, M. Arratia, H. Atac, C. Ayerbe Gayoso, N.A. Baltzell, L. Barion, M. Battaglieri, I. Bedlinskiy, F. Benmokhtar, A. Bianconi, A.S. Biselli, M. Bondì, F. Bossù, S. Boiarinov, W.J. Briscoe, W.K. Brooks, D. Bulumulla, V.D. Burkert, D.S. Carman, J.C. Carvajal, A. Celentano, P. Chatagnon, T. Chetry, G. Ciullo, B.A. Clary, P.L. Cole, M. Contalbrigo, G. Costantini, V. Crede, A. D'Angelo, N. Dashyan, R. De Vita, M. Defurne, A. Deur, S. Diehl, C. Djalali, R. Dupre, M. Dugger, H. Egiyan, M. Ehrhart, A. El Alaoui, L. El Fassi, L. Elouadrhiri, S. Fegan, A. Filippi, T.A. Forest, G. Gavalian, G.P. Gilfoyle, F.X. Girod, D.I. Glazier, A.A. Golubenko, R.W. Gothe, Y. Gotra, K.A. Griffioen, M. Guidal, K. Hafidi, H. Hakobyan, M. Hattawy, F. Hauenstein, K. Hicks, A. Hobart, M. Holtrop, D.G. Ireland, E.L. Isupov, H.S. Jo, K. Joo, S. Joosten, D. Keller, M. Khachatryan, A. Khanal, A. Kim, W. Kim, A. Kripko, V. Kubarovsky, S.E. Kuhn, L. Lanza, M. Leali, S. Lee, P. Lenisa, K. Livingston, I.J.D. MacGregor, D. Marchand, N. Markov, L. Marsicano, V. Mascagna, B. McKinnon, Z.E. Meziani, M. Mirazita, V. Mokeev, A Movsisyan, C. Munoz Camacho, P. Nadel-Turonski, P. Naidoo, S. Nanda, K. Neupane, et al. (43 additional authors not shown)
OObservation of Beam Spin Asymmetries in the Process ep → e (cid:48) π + π − X with CLAS12 T.B. Hayward, C. Dilks, A. Vossen, H. Avakian, S. Adhikari, G. Angelini, M. Arratia,
6, 3
H. Atac, C. AyerbeGayoso, N.A. Baltzell, L. Barion, M. Battaglieri,
3, 9
I. Bedlinskiy, F. Benmokhtar, A. Bianconi,
12, 13
A.S. Biselli, M. Bond`ı, F. Boss`u, S. Boiarinov, W.J. Briscoe, W.K. Brooks, D. Bulumulla, V.D. Burkert, D.S. Carman, J.C. Carvajal, A. Celentano, P. Chatagnon, T. Chetry,
19, 20
G. Ciullo,
8, 21
B.A. Clary, P.L. Cole, M. Contalbrigo, G. Costantini,
12, 13
V. Crede, A. D’Angelo,
25, 26
N. Dashyan, R. De Vita, M.Defurne, A. Deur, S. Diehl,
28, 22
C. Djalali, R. Dupre, M. Dugger, H. Egiyan, M. Ehrhart,
30, 18
A. El Alaoui, L. El Fassi, L. Elouadrhiri, S. Fegan, A. Filippi, T.A. Forest, G. Gavalian, G.P. Gilfoyle, F.X. Girod, D.I. Glazier, A.A. Golubenko, R.W. Gothe, Y. Gotra, K.A. Griffioen, M. Guidal, K. Hafidi, H. Hakobyan,
16, 27
M. Hattawy, K. Hicks, A. Hobart, M. Holtrop, D.G. Ireland, E.L. Isupov, H.S. Jo, K. Joo, S. Joosten, D. Keller, M. Khachatryan, A. Khanal, A. Kim, W. Kim, A. Kripko, V. Kubarovsky, S.E. Kuhn, L. Lanza, M. Leali,
12, 13
S. Lee, P. Lenisa,
8, 21
K. Livingston, I.J.D. MacGregor, D. Marchand, N. Markov,
3, 22
L. Marsicano, V. Mascagna,
42, 13, ∗ B. McKinnon, Z.E. Meziani,
30, 7
M. Mirazita, V. Mokeev, A Movsisyan, C. Munoz Camacho, P. Nadel-Turonski, P. Naidoo, S. Nanda, K. Neupane, S. Niccolai, G. Niculescu, T.R. O’Connell, M. Osipenko, M. Paolone,
45, 7
L.L. Pappalardo,
8, 21
R. Paremuzyan,
3, 38
E. Pasyuk, W. Phelps, O. Pogorelko, Y. Prok, B.A. Raue,
4, 3
M. Ripani, J. Ritman, A. Rizzo,
25, 26
P. Rossi,
3, 43
J. Rowley, F. Sabati´e, C. Salgado, A. Schmidt, E.P. Segarra, Y.G. Sharabian, U. Shrestha, O. Soto,
43, 16
N. Sparveris, S. Stepanyan, I.I. Strakovsky, S. Strauch, A. Thornton, N. Tyler, R. Tyson, M. Ungaro, L. Venturelli,
12, 13
H. Voskanyan, E. Voutier, D.P. Watts, K. Wei, X. Wei, M.H. Wood, B. Yale, N. Zachariou, and J. Zhang (The CLAS Collaboration) College of William and Mary, Williamsburg, Virginia 23187-8795 Duke University, Durham, North Carolina 27708-0305 Thomas Jefferson National Accelerator Facility, Newport News, Virginia 23606 Florida International University, Miami, Florida 33199 The George Washington University, Washington, DC 20052 University of California, Riverside, Riverside, California, 92521 Temple University, Philadelphia, PA 19122 INFN, Sezione di Ferrara, 44100 Ferrara, Italy INFN, Sezione di Genova, 16146 Genova, Italy National Research Centre Kurchatov Institute - ITEP, Moscow, 117259, Russia Duquesne University, 600 Forbes Avenue, Pittsburgh, PA 15282 Universit`a degli Studi di Brescia, 25123 Brescia, Italy INFN, Sezione di Pavia, 27100 Pavia, Italy Fairfield University, Fairfield CT 06824 IRFU, CEA, Universit´e Paris-Saclay, F-91191 Gif-sur-Yvette, France Universidad T´ecnica Federico Santa Mar´ıa, Casilla 110-V Valpara´ıso, Chile Old Dominion University, Norfolk, Virginia 23529 Universit´e Paris-Saclay, CNRS/IN2P3, IJCLab, 91405 Orsay, France Mississippi State University, Mississippi State, MS 39762-5167 Ohio University, Athens, Ohio 45701 Universit`a di Ferrara , 44121 Ferrara, Italy University of Connecticut, Storrs, Connecticut 06269 Lamar University, 4400 MLK Blvd, PO Box 10046, Beaumont, Texas 77710 Florida State University, Tallahassee, Florida 32306 INFN, Sezione di Roma Tor Vergata, 00133 Rome, Italy Universit`a di Roma Tor Vergata, 00133 Rome Italy Yerevan Physics Institute, 375036 Yerevan, Armenia II. Physikalisches Institut der Universit¨at Gießen, 35392 Gießen, Germany Arizona State University, Tempe, Arizona 85287 Argonne National Laboratory, Argonne, Illinois 60439 University of York, York YO10 5DD, United Kingdom INFN, Sezione di Torino, 10125 Torino, Italy Idaho State University, Pocatello, Idaho 83209 University of Richmond, Richmond, Virginia 23173 University of Glasgow, Glasgow G12 8QQ, United Kingdom Skobeltsyn Institute of Nuclear Physics, Lomonosov Moscow State University, 119234 Moscow, Russia a r X i v : . [ h e p - e x ] J a n University of South Carolina, Columbia, South Carolina 29208 University of New Hampshire, Durham, New Hampshire 03824-3568 Kyungpook National University, Daegu 41566, Republic of Korea University of Virginia, Charlottesville, Virginia 22901 Massachusetts Institute of Technology, Cambridge, Massachusetts 02139-4307 Universit`a degli Studi dell’Insubria, 22100 Como, Italy INFN, Laboratori Nazionali di Frascati, 00044 Frascati, Italy James Madison University, Harrisonburg, Virginia 22807 New Mexico State University, PO Box 30001, Las Cruces, NM 88003, USA Christopher Newport University, Newport News, Virginia 23606 Institute fur Kernphysik (Juelich), Juelich, Germany Norfolk State University, Norfolk, Virginia 23504 Canisius College, Buffalo, New York 14208-1098 (Dated: January 14, 2021)The observation of beam spin asymmetries in two-pion production in semi-inclusive deep inelasticscattering off an unpolarized proton target is reported for the first time. The data presented herewere taken in the fall of 2018 with the CLAS12 spectrometer using a 10.6 GeV longitudinally spin-polarized electron beam delivered by CEBAF at JLab. The measured asymmetries provide the firstobservation of a signal that can be used to extract the PDF e ( x ) in a collinear framework and thehelicity-dependent two-pion fragmentation function G ⊥ . Keywords: dihadron; beam spin asymmetry; SIDIS; CLAS12; twist-3 PDF; dihadron fragmentation function
Protons and neutrons constitute most of the visiblematter of the universe, however our understanding of howsome of their most important properties, such as massand spin, emerge from the strong interactions of the con-stituent quarks and gluons is still incomplete. Therefore,the study of the internal dynamics of the nucleon is fun-damental to our understanding of the theory of stronginteractions and, by extension, our understanding of thenature of matter itself.Parton distribution functions (PDFs) encode infor-mation about the momentum-dependent distribution ofquarks inside the proton. In the approximation of theparton model, PDFs describe the probability of scatter-ing off a specific parton in the nucleon. Comparably, thenon-perturbative dynamics of hadronization, the processof the formation of hadrons out of quarks and gluons,are described by fragmentation functions (FFs), whichcan be interpreted in the parton model as the probabilitythat a quark forms a certain hadron. For recent reviews,see Refs. [1–4].In order to access PDFs and FFs, we consider the semi-inclusive deep inelastic scattering (SIDIS) process, wherean electron scatters off a proton target at a high enoughenergy such that this process can be described by thescattering off a single parton in the target [3]. This Letterfocuses on the measurement of beam spin asymmetriesfor the two-pion production process in SIDIS, written e ( (cid:96) ) + p ( P ) → e (cid:48) ( (cid:96) (cid:48) ) + π + ( P ) + π − ( P ) + X, (1)where the quantities in the parentheses denote the respec-tive four-momenta; boldface symbols will indicate thecorresponding three-momenta. Fragmentation into twopions offers more targeted access to the nucleon structureand allows for the observation of more complex phenom-ena in fragmentation than in single-pion production [2]. The first measurement of two-pion beam-spin asymme-tries sensitive to the PDF e ( x ) and to the dihadron FF G ⊥ are reported.Insights into the interaction between gluons andthe struck quark in the nucleon can be gained fromsubleading-twist functions such as e ( x ) [5, 6]. For exam-ple, the x -moment of e ( x ) is proportional to the forceexperienced by a transversely polarized quark in an unpo-larized nucleon immediately after scattering [7, 8]. Likethe other collinear PDFs, it is dependent on the scalingvariable x , which in the parton picture corresponds tothe light-cone momentum fraction carried by the probedquark [3, 5, 9] and can be expressed as x = Q / (2 P µ q µ ).As usual Q = − q µ q µ denotes the scale of the process,where q = (cid:96) − (cid:96) (cid:48) is the four-momentum of the exchangedvirtual photon.A first model-dependent extraction of e ( x ) from single-hadron data has been performed [10], along with an-other extraction from preliminary two-pion data fromCLAS [11, 12]. In SIDIS single-hadron production, e ( x )can only be accessed via beam spin asymmetries withthe inclusion of the transverse momentum dependence(TMD) of the FF. This leads to a convolution of thePDF and FF over the TMD. Furthermore, factorizationin the TMD framework is not yet proven at subleadingtwist [13]. These issues motivate the high-precision mea-surement of two-pion beam spin asymmetries presentedhere.On the hadronization side, FFs describing two-pionproduction depend on M h , the invariant mass of the pionpair and on z , the fraction of the fragmenting quark mo-mentum carried by the pion pair. Dihadron FFs can bedecomposed into partial waves [14, 15], with the corre-sponding associated Legendre polynomials depending onthe decay angle θ of the two-hadron system. This de-pendence is integrated over the CLAS12 acceptance inthe results shown in this Letter and the relevant mean θ values are listed in the supplementary material.The dihadron FF G ⊥ describes the dependence of thetwo-pion production on the helicity of the fragmentingquark. Recently, interest in the possible mechanismbehind G ⊥ led to several model calculations [16, 17].In Ref. [17] interference between different partial wavesleads to a signal with a distinctive dependence on M h ,with a sign change around the ρ mass. It is also inter-esting to note that G ⊥ could be sensitive to QCD vac-uum fluctuations [18] and thus to the strong CP problem.No previous measurement sensitive to G ⊥ exists and theasymmetries given here constitute the first opportunityto study this unique FF.The data presented in this Letter were taken with theCLAS12 spectrometer [19] using a 10.6 GeV longitudi-nally polarized electron beam delivered by CEBAF, inci-dent on a liquid-hydrogen target. The beam polarizationaveraged to 86 . ± .
6% and was flipped at 30 Hz to min-imize systematic effects. This analysis uses the ForwardDetector of CLAS12, which contains a tracking subsys-tem consisting of drift chambers in a toroidal magneticfield and high and low-threshold Cherenkov counters toidentify the scattered electron and final state pions, re-spectively. Additional identification is performed for elec-trons with an electromagnetic calorimeter and for pionsby six arrays of plastic scintillation counters.SIDIS events were selected by requiring Q > and the mass of the hadronic final state to be above2 GeV. Exclusive reactions were removed with the condi-tion on the missing mass M X > . X , the unmeasured part of the final state. Con-tributions from events where a photon is radiated fromthe incoming lepton were reduced by placing a conditionof y < .
8, where y = P µ q µ / ( P µ l µ ) is the fractional en-ergy loss of the scattered electron, and by requiring aminimum momentum of 1.25 GeV for each pion. Finally,contributions from the target fragmentation region werereduced by requiring x F > x F denotes Feynman- x and takes a positive value if the out-going hadron moves in the same direction as the incomingelectron, in the struck quark center-of-mass frame.The correlations between quark and gluon fields in thenucleon encoded in e ( x ), as well as the hadronizationprocess described by G ⊥ , are imprinted in the azimuthalangles of the final state hadrons [14, 15, 20]. An observ-able sensitive to these functions can thus be constructedby analyzing beam helicity-dependent azimuthal mod-ulations of the two-pion cross section as described be-low. Figure 1 illustrates the two-pion three-momenta P h = P + P and 2 R = P − P , where P is as-signed to the π + ; the azimuthal angles φ h and φ R ⊥ are FIG. 1. The coordinate system used in this analysis. Theelectron scattering plane is spanned by the incoming and out-going lepton, the dihadron plane is spanned by P and P ,containing also P h , R , and R T , and the q × P h plane con-tains only q and P h . The azimuthal angles φ h and φ R ⊥ aredefined within the plane transverse to q , from the electronscattering plane to, respectively, the q × P h plane and thedihadron plane. See text for details. defined as φ h = ( q × l ) · P h | ( q × l ) · P h | arccos ( q × l ) · ( q × P h ) | q × l | | q × P h | , (2) φ R ⊥ = ( q × l ) · R T | ( q × l ) · R T | arccos ( q × l ) · ( q × R T ) | q × l | | q × R T | , (3)where R T is the component of R perpendicular to P h ,calculated as R T = (cid:16) z P ⊥ − z P ⊥ (cid:17) /z [16].The beam helicity-dependent part of the two-pion crosssection can be written in terms of PDFs and FFs, inte-grating over partonic transverse momenta at subleadingtwist as [14, 15, 20] dσ LU ∝ (4) W λ e sin( φ R ⊥ ) (cid:18) xe ( x ) H (cid:94) ( z, M h ) + 1 z f ( x ) ˜ G (cid:94) ( z, M h ) (cid:19) + . . . . Here, the subscript LU refers to a longitudinally polar-ized beam and an unpolarized target, λ e is the electronhelicity and W is a kinematic proportionality factor ap-propriate for the LU term and dependent on x and y ,and is interpreted as the depolarization of the exchangedvirtual photon [14, 15, 20]. The additional terms are lin-early independent of the sin( φ R ⊥ ) term shown here andcan therefore be extracted independently. Eq. (4) omitsthe sum over quark flavors.The dihadron FF H (cid:94) that e ( x ) is multiplied by issensitive to the transverse polarization of the outgoingquark and has been extracted from e + e − data [21, 22].The second term contains the twist-3 dihadron FF ˜ G (cid:94) ,which is significantly smaller than H (cid:94) in model calcu-lations [23], but remains unmeasured. The two contri-butions can be disentangled in a combined fit includingtarget spin asymmetries [12]. - FIG. 2. The measured A sin ( φ R ⊥ ) LU asymmetry vs. x . The thin,black bars indicate statistical uncertainties and the verticalextent of the wide, gray bars indicates systematic uncertain-ties. See text for further discussion. When the dependence on transverse momenta is in-cluded, the cross section depends on φ h and the dihadronFF G ⊥ appears, which describes the helicity dependenceof the two-pion production: dσ LU ∝ Cλ e sin( φ h − φ R ⊥ ) I (cid:2) f G ⊥ (cid:3) + . . . , (5)where C is the corresponding kinematic depolarizationfactor and additional terms in the cross section are againlinearly independent from the given one. As G ⊥ is aTMD FF, it appears in Eq. (5) in a convolution, denotedby I , over the transverse momentum dependences of thePDF and FF [14, 15, 24].The individual terms can be extracted from Eqs. (4)and (5) by forming the beam spin asymmetry A LU fromthe two-pion yields N ± , produced from the scattering ofan electron with helicity ± , written A LU = 1 P beam N + ( φ h , φ R ⊥ ) − N − ( φ h , φ R ⊥ ) N + ( φ h , φ R ⊥ ) + N − ( φ h , φ R ⊥ ) = (6) A sin ( φ h − φ R ⊥ ) LU sin( φ h − φ R ⊥ ) + A sin ( φ R ⊥ ) LU sin( φ R ⊥ ) , and fitting for the resulting azimuthal modulation am-plitudes where P beam is the beam polarization. The am-plitudes in Eq. (6) were extracted from the data usingan unbinned maximum likelihood fit that includes addi-tional modulations beyond the two listed here, from thecross section partial waves up to (cid:96) = 2; see Ref. [15] fordetails. A binned χ -minimization fit with 8 × φ h and φ R ⊥ was also performed and is in very goodagreement with the unbinned fit with a mean reduced χ of 1.05. The resulting asymmetries are corrected for theratio of the depolarization factors W ( x, y ) and C ( x, y ) inEqs. (4) and (5) to the respective factor A ( x, y ) of theunpolarized cross section. - - - FIG. 3. The measured A sin( φ h − φ R ⊥ ) LU asymmetry vs. M h . Thethin, black bars indicate statistical uncertainties and the ver-tical extent of the wide, gray bars indicates systematic uncer-tainties. See text for further discussion. ● ● ● ● ● ●■ ■ ■ ■ ■ ■ - - - FIG. 4. The measured A sin( φ h − φ R ⊥ ) LU asymmetry vs. P ⊥ h . Thedata have been split into two bins of M h above and below0.63 GeV. Asymmetries for lower values of M h are shown inred squares and the blue circles show the values for higher M h . The thin, solid bars indicate statistical uncertaintiesand the vertical extent of the wide bars indicates systematicuncertainties. See text for further discussion. Figure 2 shows the result for A sin ( φ R ⊥ ) LU vs. x and in-tegrated over the other relevant variables. A significantsignal is observed that is relatively flat throughout thevalence quark region. The PDF e ( x ) is confirmed tobe nonzero and its general shape can be observed be-cause the asymmetry presented here is proportional to e ( x ) H (cid:94) ( z, M h ) and H (cid:94) ( z, M h ) is well-constrained [12].The function e ( x ) can be extracted point-by-point fromthese data with further theoretical development.In Figs. 3-5 results for A sin( φ h − φ R ⊥ ) LU , sensitive to G ⊥ ,are shown vs. M h , P ⊥ h and z and integrated over the othervariables. The quantity P ⊥ h , the transverse momentumof the final-state pion pair with respect to q , accesses theconvolution of the TMD of the PDF and dihadron FF. ■ ■ ■ ■ ■ ■● ● ● ● ● ● - - - FIG. 5. The measured A sin( φ h − φ R ⊥ ) LU asymmetry vs. z . Thedata have been split into two bins of M h above and below0.63 GeV. Asymmetries for lower values of M h are shown inred squares and the blue circles show the values for higher M h . The thin, solid bars indicate statistical uncertaintiesand the vertical extent of the wide bars indicates systematicuncertainties. See text for further discussion. In particular, a dependence on M h with a sign changearound the ρ mass is seen. This behavior is consistentwith model calculations [17] and originates from the realpart of the interference of s and p wave dihadrons.Inspired by the sign change in M h , the data were fur-ther split into events with M h < .
63 GeV and M h > .
63 GeV to investigate the dependence on z and on P ⊥ h .The dependence on P ⊥ h is of special interest, since herefor the first time results are shown that are sensitive toa TMD fragmentation into two pions. It is a commonassumption that the transverse momentum dependenceof the PDFs and FFs is Gaussian [3]; the data are con-sistent with this assumption but with an indication fordifferent widths in the two mass regions. One interpreta-tion is that for M h > .
63 GeV, vector mesons make upa significant fraction of the hadron pairs, which changesthe transverse momentum spectrum. This interpretationwould also be relevant in single-hadron production. Fi-nally, the dependence of the asymmetry on z , shown inFig. 5, is relatively flat for both M h bins with the excep-tion of z < . M h bin, where the asym-metry is smaller and may change sign at the lowest z value.Systematic effects on these measurements have beenstudied using a Monte Carlo simulation based on thePEPSI generator [25] and a GEANT4-based simulationof the detector [26, 27] that was tuned to match theCLAS12 data. The systematic uncertainties are dom-inated by contributions from baryonic decays from thetarget fragmentation region, bin migration effects, and ascale uncertainty stemming from the uncertainty on thebeam polarization. Baryonic contributions from the tar-get fragmentation region are dependent on z , reachingup to 6% at the lowest z but falling steeply to about 1% at z of 0.755. Bin migration effects are only signifi-cant for A sin( φ h − φ R ⊥ ) LU , which changes rapidly around the ρ mass. In this region, systematic uncertainties from binmigration reach up to 10% of the asymmetry. The beampolarization scale uncertainty is 3.0%.Several additional sources of systematic uncertaintieshave been studied but found to be negligible. Contri-butions include particle identification, radiative effects,accidental coincidences and the photoproduction of elec-trons that are misidentified as the scattered electron.Eqs. (4) and (5) show the beam-spin dependent partof the cross section, however, the asymmetries A LU arenormalized by the beam-spin independent cross section σ UU . The unknown relative strength of the partial wavescontributing to σ UU , along with their non-orthogonalitywithin the experimental acceptance, leads to an effectiveshift in the extracted asymmetries. The size of this effecthas been estimated elsewhere [28], but a precise system-atic assignment requires a more thorough understandingof the unpolarized fragmentation function than is cur-rently available. The supplementary materia containsestimates of the effect on A LU based on Monte Carlostudies, however these estimates are based on an assump-tion of the size of the yet unknown σ UU modulation am-plitudes and are therefore not included in the presentedsystematic uncertainties.In summary, this Letter reports the first significantbeam spin asymmetries observed in two-pion productionin SIDIS. The data indicate a non-zero signal for theazimuthal modulation sensitive to the subleading-twistPDF e ( x ) and, with further theoretical development, willenable a point-by-point extraction of this quantity. Ad-ditionally, the first measurement sensitive to G ⊥ , thehelicity-dependent dihadron FF is reported. Figures 2–5 show the main results, and all asymmetry measure-ments are included in the CLAS Physics Database [29].Future work will concentrate on a measurement of thepartial wave decomposition of σ LU and σ UU , which willaddress the uncertainty discussed above but is also inter-esting in its own right in order to gain further insight intohadronization phenomena as well. The beam spin asym-metry modulated by sin( φ h ), which has been a byprod-uct of the extraction presented here, will be a topic offuture studies. It can be thought of as the equivalent tothe Collins FF for two pions [18] and, in the ρ mass re-gion, can be used to test predictions by the Artru modelabout the relative size of Collins asymmetries of vectorand scalar mesons [30].We acknowledge the outstanding efforts of the staff ofthe Accelerator and the Physics Divisions at JeffersonLab in making this experiment possible. This work wassupported in part by the U.S. Department of Energy, theNational Science Foundation (NSF), the Italian IstitutoNazionale di Fisica Nucleare (INFN), the French Cen-tre National de la Recherche Scientifique (CNRS), theFrench Commissariat pour l (cid:48) Energie Atomique, the UKScience and Technology Facilities Council, the NationalResearch Foundation (NRF) of Korea, the Helmholtz-Forschungsakademie Hessen f¨ur FAIR (HFHF) and theMinistry of Science and Higher Education of the Rus-sian Federation. 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