Antiproton over proton and K − over K + multiplicity ratios at high z in DIS
M.G. Alexeev, G.D. Alexeev, A. Amoroso, V. Andrieux, V. Anosov, A. Antoshkin, K. Augsten, W. Augustyniak, C.D.R. Azevedo, B. Badelek, F. Balestra, M. Ball, J. Barth, R. Beck, Y. Bedfer, J. Berenguer Antequera, J. Bernhard, M. Bodlak, F. Bradamante, A. Bressan, M. Buechele, V.E. Burtsev, W.-C. Chang, C. Chatterjee, M. Chiosso, A.G. Chumakov, S.-U. Chung, A. Cicuttin, P.M.M. Correia, M.L. Crespo, D. D'Ago, S. Dalla Torre, S.S. Dasgupta, S. Dasgupta, I. Denisenko, O.Yu. Denisov, S.V. Donskov, N. Doshita, Ch. Dreisbach, W. Duennweber, R.R. Dusaev, A. Efremov, P.D. Eversheim, P. Faccioli, M. Faessler, M. Finger, M. Finger jr., H. Fischer, C. Franco, J.M. Friedrich, V. Frolov, F. Gautheron, O.P. Gavrichtchouk, S. Gerassimov, J. Giarra, I. Gnesi, M. Gorzellik, A. Grasso, A. Gridin, M. Grosse Perdekamp, B. Grube, A. Guskov, D. von Harrach, R. Heitz, F. Herrmann, N. Horikawa, N. d'Hose, C.-Y. Hsieh, S. Huber, S. Ishimoto, A. Ivanov, T. Iwata, M. Jandek, T. Jary, R. Joosten, P. Joerg, E. Kabuss, F. Kaspar, A. Kerbizi, B. Ketzer, G.V. Khaustov, Yu.A. Khokhlov, Yu. Kisselev, F. Klein, J.H. Koivuniemi, V.N. Kolosov, K. Kondo, I. Konorov, V.F. Konstantinov, A.M. Kotzinian, O.M. Kouznetsov, A. Koval, Z. Kral, F. Krinner, Y. Kulinich, F. Kunne, K. Kurek, R.P. Kurjata, A. Kveton, K. Lavickova, et al. (99 additional authors not shown)
EEUROPEAN ORGANIZATION FOR NUCLEAR RESEARCH
COMPASS
CERN-EP-version 0.9March 28, 2020
Antiproton over proton and K − over K + multiplicity ratios at high z in DIS The COMPASS Collaboration
Abstract
The ¯p over p multiplicity ratio is measured in deep-inelastic scattering for the first time using (anti-)protons carrying a large fraction of the virtual-photon energy, z > .
5. The data were obtained bythe COMPASS Collaboration using a 160 GeV muon beam impinging on an isoscalar LiD target.The regime of deep-inelastic scattering is ensured by requiring Q > 1 (GeV/ c ) for the photonvirtuality and W > c for the invariant mass of the produced hadronic system. The range inBjorken- x is restricted to 0 . < x < .
40. Protons and antiprotons are identified in the momentumrange 20 ÷
60 GeV/ c . In the whole studied z -region, the ¯p over p multiplicity ratio is found tobe below the lower limit expected from calculations based on leading-order perturbative QuantumChromodynamics (pQCD). Extending our earlier analysis of the K − over K + multiplicity ratio byincluding now events with larger virtual-photon energies, this ratio becomes closer to the expectationof next-to-leading order pQCD. The results of both analyses strengthen our earlier conclusion thatthe phase space available for hadronisation should be taken into account in the pQCD formalism. (to be submitted to PLB) a r X i v : . [ h e p - e x ] M a r he COMPASS Collaboration M.G. Alexeev , G.D. Alexeev , A. Amoroso , V. Andrieux , V. Anosov , A. Antoshkin ,K. Augsten , W. Augustyniak , C.D.R. Azevedo , B. Badełek , F. Balestra , M. Ball , J. Barth ,R. Beck , Y. Bedfer , J. Berenguer Antequera , J. Bernhard , M. Bodlak , F. Bradamante ,A. Bressan , M. Büchele , V. E. Burtsev , W.-C. Chang , C. Chatterjee , M. Chiosso ,A. G. Chumakov , S.-U. Chung A. Cicuttin
P. M. M. Correia , M.L. Crespo , D. D’Ago ,S. Dalla Torre , S.S. Dasgupta , S. Dasgupta , I. Denisenko , O.Yu. Denisov , , S.V. Donskov ,N. Doshita , Ch. Dreisbach , W. Dünnweber d , R. R. Dusaev , A. Efremov , P.D. Eversheim ,P. Faccioli , M. Faessler d , M. Finger , M. Finger jr. , H. Fischer , C. Franco , J.M. Friedrich ,V. Frolov , F. Gautheron , O.P. Gavrichtchouk , S. Gerassimov , J. Giarra , I. Gnesi ,M. Gorzellik , A. Grasso , A. Gridin , M. Grosse Perdekamp , B. Grube , A. Guskov ,D. von Harrach , R. Heitz , F. Herrmann , N. Horikawa , N. d’Hose , C.-Y. Hsieh , S. Huber ,S. Ishimoto , A. Ivanov , T. Iwata , M. Jandek , V. Jary , R. Joosten , P. Jörg , E. Kabuß ,F. Kaspar , A. Kerbizi , B. Ketzer , G.V. Khaustov , Yu.A. Khokhlov ,Yu. Kisselev , F. Klein ,J.H. Koivuniemi , V.N. Kolosov , K. Kondo Horikawa , I. Konorov , V.F. Konstantinov ,A.M. Kotzinian , O.M. Kouznetsov , A. Koval , Z. Kral , F. Krinner , Y. Kulinich , F. Kunne ,K. Kurek , R.P. Kurjata , A. Kveton , K. Lavickova , S. Levorato , Y.-S. Lian , J. Lichtenstadt ,P.-J. Lin , R. Longo , V. E. Lyubovitskij , A. Maggiora , A. Magnon o , N. Makins ,N. Makke , G.K. Mallot , A. Maltsev , S. A. Mamon , B. Marianski , A. Martin , J. Marzec ,J. Matoušek , T. Matsuda , G. Mattson , G.V. Meshcheryakov , M. Meyer , W. Meyer ,Yu.V. Mikhailov , M. Mikhasenko , E. Mitrofanov , N. Mitrofanov , Y. Miyachi , A. Moretti ,A. Nagaytsev , C. Naim , D. Neyret , J. Nový , W.-D. Nowak , G. Nukazuka , A.S. Nunes ,A.G. Olshevsky , M. Ostrick , D. Panzieri , B. Parsamyan , S. Paul , H. Pekeler , J.-C. Peng ,M. Pešek , D.V. Peshekhonov , M. Pešková , N. Pierre , S. Platchkov , J. Pochodzalla ,V.A. Polyakov , J. Pretz , M. Quaresma , C. Quintans , G. Reicherz , C. Riedl , T. Rudnicki ,D.I. Ryabchikov , A. Rybnikov , A. Rychter , V.D. Samoylenko , A. Sandacz , S. Sarkar ,I.A. Savin , G. Sbrizzai , H. Schmieden , A. Selyunin , L. Sinha , M. Slunecka , J. Smolik ,A. Srnka , D. Steffen , M. Stolarski , , O. Subrt , M. Sulc , H. Suzuki , P. Sznajder ,S. Tessaro , F. Tessarotto , , A. Thiel , J. Tomsa , F. Tosello , A. Townsend , V. Tskhay ,S. Uhl , B. I. Vasilishin , A. Vauth , B. M. Veit , J. Veloso , B. Ventura , A. Vidon ,M. Virius , M. Wagner , S. Wallner , K. Zaremba , P. Zavada , M. Zavertyaev , M. Zemko ,E. Zemlyanichkina , Y. Zhao and M. Ziembicki University of Aveiro, Dept. of Physics, 3810-193 Aveiro, Portugal Universität Bochum, Institut für Experimentalphysik, 44780 Bochum, Germany t , u3 Universität Bonn, Helmholtz-Institut für Strahlen- und Kernphysik, 53115 Bonn, Germany t4 Universität Bonn, Physikalisches Institut, 53115 Bonn, Germany t5 Institute of Scientific Instruments of the CAS, 61264 Brno, Czech Republic v6 Matrivani Institute of Experimental Research & Education, Calcutta-700 030, India w7 Joint Institute for Nuclear Research, 141980 Dubna, Moscow region, Russia x8 Universität Freiburg, Physikalisches Institut, 79104 Freiburg, Germany t , u9 CERN, 1211 Geneva 23, Switzerland Technical University in Liberec, 46117 Liberec, Czech Republic v11
LIP, 1649-003 Lisbon, Portugal y12
Universität Mainz, Institut für Kernphysik, 55099 Mainz, Germany t13
University of Miyazaki, Miyazaki 889-2192, Japan z14
Lebedev Physical Institute, 119991 Moscow, Russia Technische Universität München, Physik Dept., 85748 Garching, Germany t , d16 Nagoya University, 464 Nagoya, Japan z7 Charles University, Faculty of Mathematics and Physics, 12116 Prague, Czech Republic v18
Czech Technical University in Prague, 16636 Prague, Czech Republic v19
State Scientific Center Institute for High Energy Physics of National Research Center ‘KurchatovInstitute’, 142281 Protvino, Russia IRFU, CEA, Université Paris-Saclay, 91191 Gif-sur-Yvette, France u21
Academia Sinica, Institute of Physics, Taipei 11529, Taiwan aa22
Tel Aviv University, School of Physics and Astronomy, 69978 Tel Aviv, Israel ab23
University of Trieste, Dept. of Physics, 34127 Trieste, Italy Trieste Section of INFN, 34127 Trieste, Italy University of Turin, Dept. of Physics, 10125 Turin, Italy Torino Section of INFN, 10125 Turin, Italy Tomsk Polytechnic University, 634050 Tomsk, Russia ac28
University of Illinois at Urbana-Champaign, Dept. of Physics, Urbana, IL 61801-3080, USA ad29
National Centre for Nuclear Research, 02-093 Warsaw, Poland ae30
University of Warsaw, Faculty of Physics, 02-093 Warsaw, Poland ae31
Warsaw University of Technology, Institute of Radioelectronics, 00-665 Warsaw, Poland ae32
Yamagata University, Yamagata 992-8510, Japan z Corresponding authors a Also at Dept. of Physics, Pusan National University, Busan 609-735, Republic of Korea b Also at Physics Dept., Brookhaven National Laboratory, Upton, NY 11973, USA c Also at Abdus Salam ICTP, 34151 Trieste, Italy d e Supported by the DFG Research Training Group Programmes 1102 and 2044 (Germany) f Also at Chubu University, Kasugai, Aichi 487-8501, Japan g Also at Dept. of Physics, National Central University, 300 Jhongda Road, Jhongli 32001, Taiwan h Also at KEK, 1-1 Oho, Tsukuba, Ibaraki 305-0801, Japan i Present address: Universität Bonn, Physikalisches Institut, 53115 Bonn, Germany j Also at Moscow Institute of Physics and Technology, Moscow Region, 141700, Russia k Also at Yerevan Physics Institute, Alikhanian Br. Street, Yerevan, Armenia, 0036 l Also at Dept. of Physics, National Kaohsiung Normal University, Kaohsiung County 824, Taiwan m Supported by ANR, France with P2IO LabEx (ANR-10-LBX-0038) in the framework “Investisse-ments d’Avenir” (ANR-11-IDEX-003-01) n Also at Institut für Theoretische Physik, Universität Tübingen, 72076 Tübingen, Germany o Retired p Present address: Brookhaven National Laboratory, Brookhaven, USA q Also at University of Eastern Piedmont, 15100 Alessandria, Italy r Present address: Universität Hamburg, 20146 Hamburg, Germany s Present address: RWTH Aachen University, III. Physikalisches Institut, 52056 Aachen, Germany t Supported by BMBF - Bundesministerium für Bildung und Forschung (Germany) u Supported by FP7, HadronPhysics3, Grant 283286 (European Union) v Supported by MEYS, Grant LM20150581 (Czech Republic) w Supported by B. Sen fund (India) x Supported by CERN-RFBR Grant 12-02-91500 y Supported by FCT, Grants CERN/FIS-PAR/0007/2017 and CERN/FIS-PAR/0022/2019 (Portugal) z Supported by MEXT and JSPS, Grants 18002006, 20540299, 18540281 and 26247032, the Daikoand Yamada Foundations (Japan) aa Supported by the Ministry of Science and Technology (Taiwan) ab Supported by the Israel Academy of Sciences and Humanities (Israel) c Supported by the Russian Federation program “Nauka” (Contract No. 0.1764.GZB.2017) (Russia) ad Supported by the National Science Foundation, Grant no. PHY-1506416 (USA) ae Supported by NCN, Grant 2017/26/M/ST2/00498 (Poland)
Within the standard approach of perturbative Quantum Chromodynamics (pQCD), hadron productionfrom an active quark in a deep-inelastic scattering process (DIS) is effectively described by non-pertur-bative objects called fragmentation functions (FFs). These functions presently cannot be predicted bytheory, but their scale evolution is described by the DGLAP equations [1]. For a given negative four-momentum transfer squared Q , in leading order (LO) pQCD the FF D hq ( z , Q ) represents the probabilitydensity that a hadron h is produced in the fragmentation of a quark with flavour q. The produced hadroncarries a fraction z of the virtual-photon energy ν , where the latter is defined in the laboratory frame.The cleanest way to access FFs consists in studying single-inclusive hadron production in lepton annihi-lation, e + + e − → h + X, where the remaining final state X is not analysed. However, only informationabout D hq + D h¯q is accessible there and only limited flavour separation is possible. Additional input, likesemi-inclusive measurements of deep-inelastic lepton-nucleon scattering (SIDIS), is required to fullyunderstand quark fragmentation into hadrons. In the case of the SIDIS cross section, fragmentationfunctions are convoluted with parton distribution functions (PDFs). As these are rather well known,fragmentation functions for q and ¯q can be accessed separately and full flavour separation is possiblein principle. As a result, fragmentation functions obtained using only e + e − data differ in some casessignificantly from those that were determined by additionally taking into account data from SIDIS orother processes, see Refs. [2–7].Recently, the HERMES and COMPASS Collaborations have published several papers concerning uniden-tified hadron, pion and kaon multiplicities in SIDIS, see Refs. [8–11]. In the most recent COMPASSarticle [12] it was shown that for kaons at high z the K − over K + multiplicity ratio R K falls belowthe lower limit predicted by pQCD. From the measured ν -dependence it was concluded that in experi-ments with similar or lower centre-of-mass energy than in COMPASS an insufficient description of thedata by pQCD may affect the high- z region. This kinematic region is important in many respects, as e . g . transverse-momentum-dependent azimuthal asymmetries are quite pronounced there [13]. Hencethe above described phenomenon should be better understood in order to avoid possible bias when ex-tracting fragmentation functions and/or transverse-momentum-dependent PDFs and FFs by applying thenaive pQCD formalism to SIDIS data in the high- z region.In order to provide more experimental input for further phenomenological studies, we present here forthe first time the COMPASS results on the ¯p over p multiplicity ratio R p at high z , i . e . z > .
5, whichare obtained from SIDIS data taken on an isoscalar target. In addition we present new results on R K ,obtained in a ν -range extended with respect to Ref. [12], which became attainable by improving the kaonidentification procedure. Note that when measuring a multiplicity ratio, several systematic uncertaintiescancel in both theory and experiment. Thus a multiplicity ratio can be considered as one of the mostrobust observables presently available when analysing SIDIS data.This Letter is organised as follows. In Section 2, pQCD-based predictions for R p and R K are discussed.Experimental set-up and data selection are described in Section 3. The analysis method is presented inSection 4, followed by the discussion of systematic uncertainties in Section 5. The results are presentedand discussed in Section 6. Hadrons of type h produced in the final state of DIS are commonly characterised by their relative abun-dance. The hadron multiplicity M h is defined as ratio of the SIDIS cross section for hadron type h andthe cross section for an inclusive measurement of the deep-inelastic scattering process (DIS):d M h ( x , Q , z ) d z = d σ h ( x , Q , z ) / d x d Q d z d σ DIS ( x , Q ) / d x d Q . (1)Here, x denotes the Bjorken scaling variable. The cross sections σ DIS and σ h can be composed usingthe standard factorisation approach of pQCD [14, 15]. In the following, the LO pQCD expressions forthe cross section calculations will be used. In the LO approximation for the multiplicity, where the sumover parton species a = q , ¯q is weighted by the square of the electric charge e a of the quark expressed inunits of the elementary charge, only simple products of PDFs f a ( x , Q ) and FFs D h a ( z , Q ) are involvedinstead of the aforementioned convolutions:d M h ( x , Q , z ) d z = ∑ a e a f a ( x , Q ) D h a ( z , Q ) ∑ a e a f a ( x , Q ) . (2)For a deuteron target, the ¯p over p multiplicity ratio in LO pQCD reads as follows: R p ( x , Q , z ) = d M ¯p ( x , Q , z ) / d z d M p ( x , Q , z ) / d z = . ( ¯u + ¯d ) D fav + ( + + + ) D unf . ( u + d ) D fav + ( + + + ) D unf . (3)Here, u, ¯u, d, ¯d, s, ¯s denote the PDFs in the proton for corresponding quark flavours. Their dependenceson x and Q are omitted for brevity. The symbols D fav ( D unf ) denote favoured (unfavoured) fragmentationfunctions and their dependence on z and Q are also omitted for brevity. Presently, proton FFs and theirratios are not well known at high z as their extraction is based on e + e − annihilation data only [2].Following Refs. [2] and [16] it is assumed that D pu = D pd = D fav . In addition, the existing data do notallow to distinguish between different functions D unf for different quark flavours. In the large- z region,the ratios D unf / D fav are expected to be small . Neglecting D unf in Eq. (3) leads to the following lowerlimit for R p in LO pQCD R p > ¯u + ¯du + d , (4)which depends only upon rather well known PDFs, and is independent on the assumption that D pu = D pd = D fav . It is interesting to notice that the value of the lower limit predicted by LO pQCD is the samefor both protons and kaons, see Ref. [12]. However, one expects R K > R p as in the case of kaons thestrange quark FFs ( D K − s , D K + ¯s ) are of the favoured type, contrary to the proton case. The expected valueof R K / R p is about 1.10 when using FFs from Ref. [5] and the MSTW08LO PDF set from Ref. [17],where the strange-quark contribution is suppressed with respect to the light-quark sea. It can be aslarge as 1.15 if strange quarks are not suppressed with respect to the light-quark sea as suggested by theinterpretation of some LHC measurements [18,19]. On the other hand, newer kaon FFs that are availableonly at NLO [6] suggest that the ratio of D K + ¯s / D K + u is about 1.5 times smaller than originally obtained inRef. [5]. In this case, R K / R p is reduced back to about 1.10. Therefore, R K / R p = . ± .
05 appears asa reasonable expectation based on the LO pQCD formalism.The present analysis is performed in two x -bins, below and above x = .
05. The average values of x and Q are (cid:104) x (cid:105) = . (cid:104) Q (cid:105) = 2.4 (GeV/ c ) in the first x -bin and (cid:104) x (cid:105) = . (cid:104) Q (cid:105) = 9.8 (GeV/ c ) in thesecond one. Based on Eq. (4) and the MSTW08LO PDF set, the expected lower limits on R p in these two x -bins are 0.51 and 0.28. These values are about 10% higher if newer PDF sets as in Refs. [18, 19] areused instead. Due to the above mentioned lack of reliable proton FFs at NLO, presently no predictionscan be made for the lower limit of R p at higher perturbative order.We also evaluate R p with the LEPTO Monte Carlo event generator [20] (version 6.5), with the resultthat the LUND string fragmentation model [21] used in LEPTO is incapable to model R p correctly. Forexample, for z ≈ . R p ≈
1, which is definitely not supported by the data as it will beshown below. On the other hand, for z > .
85 the predicted value of R p falls below the naive LO pQCDlower limit. This is possible as in the LUND model the mechanism of string hadronisation does not only For kaons, this expectation is indeed confirmed in pQCD fits already at moderate values of z , see e . g . Ref. [6]. depend on quark and hadron types and on z , as in the pQCD formalism, but also on the type of the targetnucleon and on x , see Ref. [22] for more details.Due to different lower momentum limits for particle identification at COMPASS, 18 GeV/ c for protonsand 9 GeV/ c for kaons, the observed x and Q distributions are slightly different for pions and kaons. Asa result, the lower limit on R K is about 0.47, which is obtained for (cid:104) x (cid:105) = .
03 and (cid:104) Q (cid:105) = 1.6 (GeV/ c ) .The LO pQCD predictions for the lower limit on R K are ν independent, because they depend on PDFs inthe same way as given in Eq. (4) for the proton case. However, in our earlier measurement [12] a clear ν dependence was observed. With higher values of ν accessible in the current measurement, we expect theresults to be in better agreement with the expectation of (N)LO pQCD. We also note that the NLO lowerlimit for R K turns out to be 10 ÷
15% smaller than the LO pQCD lower limit given above, see Ref. [12].Some phenomenological models [23–25] are able to accommodate R K below the pQCD limits presentedabove, but the predicted effect is too small to explain our earlier published results [12]. There are alsoimportant theoretical efforts ongoing to improve the formalism (higher-order corrections, treatment ofheavy quarks etc. ), see e . g . Refs. [26–31], which however do not affect the interpretation of the datashown in Ref. [12] and in the present paper.
The present analysis is based on COMPASS data taken in 2006. The 160 GeV/ c µ + beam delivered bythe M2 beam line of the CERN SPS had a momentum spread of about 5%. The beam was naturallypolarised, but the polarisation is not affecting this analysis since we integrate over azimuthal angle andtransverse momentum of the produced hadrons. The LiD target has a total length of 120 cm, whichcorresponds to about half of a hadron interaction length. It is considered to be isoscalar, and the 0.2%excess of neutrons over protons due to the presence of additional material in the target ( He and Li) isneglected. The target was longitudinally polarised, but in the present analysis the data are averaged overthe target polarisation, which leads to a remaining average target polarisation below 1%.The COMPASS two-stage spectrometer has a polar-angle acceptance of ±
180 mrad, and it is capable ofdetecting charged particles with momenta as low as 0.5 GeV/ c . However, in this analysis typical particlemomenta are above 20 GeV/ c . The ring-imaging Cherenkov detector (RICH) was used to identify pions,kaons and protons. Its radiator volume was filled with C F leading to a threshold for pion, kaon andproton identification of about 3 GeV/ c , 9 GeV/ c and 18 GeV/ c respectively. Two trigger types are usedin the analysis. The “inclusive” trigger is based on a signal from a combination of hodoscope signalscaused by the scattered muon. The “semi-inclusive” trigger requires an energy deposition in one of thehadron calorimeters. The experimental set-up is described in more detail in Ref. [32].The data selection criteria are kept similar to those used in the recently published analyses [10, 12]whenever possible. In order to formally ensure the applicability of the pQCD formalism, the DIS regionis selected by requiring Q > c ) and W > c for the invariant mass of the producedhadronic system. The fraction of the incoming muon energy carried by the virtual photon, y , is keptlarger than 0.1 to avoid the region with degraded momentum resolution.For the proton multiplicity analysis, the constraint x > .
01 is used in order to make the kinematiccoverage more similar to that of our earlier kaon studies [12]. In the present analysis, we study protonscarrying a large fraction z of the virtual-photon energy, z > .
5. In order to ensure efficient protonidentification by the RICH, only events with proton momentum above 20 GeV/ c are used, i . e . c above the RICH proton threshold. The upper limit for proton identification is set to 60 GeV/ c . Purity andefficiency of the proton selection are optimised by imposing appropriate constraints on the likelihoodsof proton, kaon, pion and background hypotheses that are calculated by the RICH particle-identificationsoftware [33].In our earlier studies of R K [12], kaons with momenta between 12 GeV/ c and 40 GeV/ c were analysedfor z > .
75. By the improvements in the RICH particle-identification software described in Section 4,the momentum range extends now up to 55 GeV/ c , which leads to a significant extension of the available ν range. All other kaon selection criteria remain unchanged with respect to the earlier analysis. The proton (kaon) multiplicities M p ( K ) ( x , Q , z ) are determined from the proton (kaon) yields N p ( K ) normalised by the number of DIS events, N DIS , and corrected by the acceptance A p ( K ) ( x , Q , z ) :d M p ( K ) ( x , Q , z ) d z = N DIS ( x , Q ) d N p ( K ) ( x , Q , z ) d z A p ( K ) ( x , Q , z ) . (5)As in our earlier kaon analysis [12], we use “semi-inclusive” triggers. This is possible because a bias-freedetermination of N DIS is not needed, as the latter cancels in R p and R K . The total number of protons andanti-protons used in the analysis is about 50 000. In addition to about 64 000 kaons analysed in Ref. [12],there are about 13 000 kaons more in the newly explored kinematic range. Note that the kinematic rangefor protons is wider than that for kaons.As it was mentioned in Section 2, the proton analysis is performed in two x -bins, below and above x = .
05. In each x -bin, nine bins are used in the reconstructed z variable z rec , with the bin limits 0.50,0.55, 0.60, 0.65, 0.70, 0.75, 0.80, 0.85, 0.90 and 1.10. In addition, for events in the first x -bin the dataare separated in four bins of proton momentum p h , with the bin limits 20 GeV/ c , 30 GeV/ c , 40 GeV/ c ,50 GeV/ c and 60 GeV/ c . This 2-dimensional binning allows implicit studies of the ν -dependence of R p . For the second x -bin, the anti-proton statistics is too limited to perform the analysis in the additionaldimension of (anti-)proton momentum. For kaons the present analysis is only performed for x < . z -bins with bin limits 0.75, 0.80, 0.85, 0.90, 0.95 and 1.05, and three momentum bins with binlimits 40 GeV/ c , 45 GeV/ c , 50 GeV/ c and 55 GeV/ c .In order to determine the multiplicity ratio R p from the raw yield of ¯p and p, only a few correction factorshave to be taken into account. First, the correction related to RICH efficiencies is applied. From ananalysis of Λ and Λ decays into an (anti-)proton-pion pair it was concluded that the RICH efficiencyfor p is charge-symmetric within a precision of about 1%. The proton selection, which was improvedwith respect to our earlier papers, ensures that the contamination from π and K can be safely neglected.Upper limits to such a possible contamination are taken into account in the systematic uncertainty. Theacceptance correction factors A p for p and ¯p are determined using Monte Carlo simulations. The sameunfolding method is used as in Ref. [12], i . e . , in a given ( x , Q ) bin we calculate the ratio of the numberof reconstructed events to that of generated ones. Note that in order to count generated (reconstructed)events, generated (reconstructed) variables are used. As for z unfolding, we present the results as afunction of z corr , which denotes the value of z reconstructed in the experiment, corrected by the averagedifference between the generated and reconstructed values of z rec , where the latter are determined byMonte Carlo simulations. The average acceptance ratio for the first x -bin is A ¯p / A p = . ± . x -bin. The systematic uncertainty related to theacceptance ratio is discussed in the next section. It is also verified by using the DJANGOH MonteCarlo generator [34] that in the COMPASS kinematics the radiative correction for positive and negativeparticles is of the same value within uncertainties, thus it cancels in the ratio.Compared to the above proton analysis and the kaon analysis presented in Ref. [12], the raw K ± yieldsare obtained in a different way, which is described below. After that, the present analysis follows closelythe same procedure as in the case of the proton analysis and the one from Ref. [12]. With respect to theproton analysis described above it is in addition verified using simulations that the contamination fromdiffractive vector meson decays ( e . g . φ → K + K − ) and charm meson decays is negligible. p L / K L E n t r i e s ) c < 40 (GeV/ h p ) < c
35 (GeV/ p K
53 54 55 56 (mrad) corr
NNring q E n t r i e s ) c < 40 (GeV/ h p ) < c
35 (GeV/ p K Fig. 1:
Left panel: RICH likelihood ratio of K over π hypotheses for tracks with momenta between 35 GeV/ c and 40 GeV/ c where the separation between K and π is not obvious. In order to select kaons, the constraint L K / L π > . π and K is visible. In the proton analysis and in the kaon analysis from Ref. [12], the raw yields are obtained directlyby counting the number of events that fulfil certain criteria of RICH particle identification. However,by improving the RICH particle-identification software a better separation between π and K can beachieved at higher momenta. For the present analysis, the polar angle θ of the Cherenkov photon rings iscorrected by a Neural Networks (NN) parametrisation, which intends to improve the internal descriptionof the RICH sub-structure with respect to what was known during the original data production andthe reconstruction. This correction depends upon various track parameters like position and angle at theRICH entrance, momentum of the particle etc . and is applied on an event-by-event basis. In the left panelof Fig. 1, we recall from our earlier analysis [12] the likelihood ratio for the K/ π hypothesis in the highestmomentum bin, where the separation was most challenging. In order to optimise the uncertainties of R K ,a lower limit of 1.5 had to be used there. Using in the present analysis the NN method, the separationof kaons and pions is improved considerably as illustrated in the right panel of Fig. 1, where the θ distribution after the NN correction is shown for the same events as in the left panel. A much betterseparation of the two particle species is clearly visible, which allows us to extend the analysis to highermomenta up to 55 GeV.In order to obtain the raw kaon yield, the spectra as the one shown in the right panel of Fig. 1 are fittedin each z and p h bin using the functional form described below. It turns out that a single Gaussian todescribe the kaon peak and two Gaussians for the pion peak are sufficient to obtain the raw kaon yield.The fit is performed simultaneously in all z and p h bins. This procedure is a source of non-negligiblesystematic uncertainties, especially at higher z and higher momenta. The systematic uncertainty relatedto this extraction is described in Section 5. This section is split into two parts. In the first part, studies of systematic effects for the proton resultsare described. This is a rather standard analysis that benefits from the significant knowledge acquiredwith the previously published COMPASS analyses [9, 10, 12]. In the second part, the kaon results aredescribed. As for the first time in COMPASS a new method is used to estimate the kaon yield, detailedstudies are performed to verify the reliability of the results. Additionally, standard studies as done for R K in Ref. [12] are also performed. .1 Systematic uncertainties for R p R p i) The COMPASS data taking was divided into periods, mainly depending upon the schedule of the SPSaccelerator. A typical data period took about one week, and in between two periods interventions to theCOMPASS spectrometer could happen. The whole 2006 data taking took about half a year. Therefore,it is verified that the values for R p obtained from different data periods agree with one another.ii) As in Ref. [12], and contrary to standard multiplicity analyses [9–11], two trigger types are used inthis analysis, with or without the requirement of energy deposit in the calorimeters. It is verified thatthese two trigger types give consistent values for R p . This result is expected as for the lowest protonenergy analysed (20 GeV) calorimeter efficiencies are already close to 100%.iii) The key correction factor that has to be applied to the raw value of R p is the acceptance differencebetween p and ¯p. The COMPASS spectrometer is charge symmetric at the level of 1%. However, protonsand anti-protons interact differently with the target material as they do not have the same re-interactionlength in the long solid-state COMPASS LiD target. Therefore, as already mentioned in Sect. 4, theacceptance for ¯p is about 10% lower than that for p, with an estimated uncertainty of about 3%.iv) More complex methods of unfolding the acceptance were tested in Ref. [12], as well as in the presentanalysis. They are giving very similar results when compared to the selected method, but their resultingcovariance matrix has large off-diagonal elements. On the contrary, for the selected method the resultsin each bin and their statistical uncertainties can be considered to be independent from each other.v) A correction factor has to be taken into account because of possibly different RICH reconstructionefficiencies for p and ¯p. While the correction factor is found to be one, the systematic studies suggestthat its uncertainty is about 5%. This uncertainty on R p is by 2% larger than that found for R K , mostlydue to the higher mass of the proton compared to that of the kaon, which leads to less photons per ringin the RICH in most of the phase space region covered. On top of that, some performed tests are limitedin precision due to the small statistics, especially for anti-protons at larger momenta and/or larger valuesof z .vi) As in previous studies, the stability of R p is tested on data using several variables that are definedin the spectrometer coordinate system. A clear instability is seen in the dependence of R p upon theazimuthal angle measured in the laboratory frame, as it was the case in our earlier analysis of R K . InRef. [12], this asymmetry led to a systematic uncertainty of up to 12% in both x -bins. In this analysis,for data binned in x and z , the systematic uncertainty amounts up to 5% for the 1st x -bin and up to 11%in the 2nd x -bin. For data binned in z and p h , it can be up to 15% for high momenta. Thus in a significantpart of the phase space this systematic uncertainty is the dominant one.The total systematic uncertainty of R p is obtained by adding in quadrature the above discussed contri-butions. The relative systematic uncertainty is found to range between 6% and 16%. The correlationbetween systematic uncertainties in various z and p h -bins is about 0.7–0.8, as in Ref. [12]. R K Most studies of systematic effects for kaon results follow closely the ones from Ref. [12], which are alsodescribed above for protons. The systematic uncertainty related to the acceptance ratio and the RICHefficiency ratio for the two kaon charges is taken as in Ref. [12], i . e .
2% and 3%, respectively. Theuncertainty related to the azimuthal-angle distribution of hadrons in the spectrometer is studied using thesame method as in our previous paper and the resulting relative uncertainty ranges between 4% and 12%.Compared to the analysis presented in Ref. [12], a new type of systematic uncertainty has to be studied,which is related to the new method of extracting the raw kaon yields from RICH data.First, it is verified that the results obtained with the new method do agree with those previously pub-lished [12]. Various combinations of functional forms are used in the fit, e . g . the main results are ob-0 tained using a Gaussian functional form to fit the polar-angle distribution of the kaon and two Gaussianfunctions for the one of the pion. In the systematic studies, we use a single or two Gaussian function(s)for each particle type. With three Gaussian functions to describe the polar-angle distribution of photonsin the RICH detector, there are nine free parameters in every single z and hadron momentum bin, andfor each of the two hadron charges. The fit in certain bins (at large z and large momentum) results invery large uncertainties on the obtained values of R K . In order to improve accuracy, studies are per-formed to determine which parameters can be kept common for the two charges and across various z and momentum bins. For example, the pion and kaon Cherenkov opening angles depend only on theparticle momenta but not on z . Indeed, it is confirmed in the fit that this angle is independent on z withinuncertainties. Altogether, the initial 450 free parameters in the fit are reduced by about a factor of three.The systematic uncertainty of the final results on R K is evaluated by performing several fits, in which thenumber of free parameters is reduced by releasing certain constraints.As a systematic uncertainty, half of the difference between maximum and minimum value of R K obtainedin these studies is taken. The resulting relative uncertainty of the kaon yield is found to range between4% and 25%. The total systematic uncertainty of R K is found to range between 7% and 28% of the R K value, and correspondingly between 0.4 and 1.1 of the statistical uncertainty on R K . As in previousanalyses, the correlation between systematic uncertainties in various z and p h -bins is about 0.7–0.8. Wenote that a fit of all data simultaneously may introduce correlations between R K values in different z and p h -bins. These correlations are found to be below 5% and hence neglected. In Fig. 2 and Table 1, the results on the anti-proton over proton multiplicity ratio R p are presented as afunction of the variable z corr for the two x -bins used in this analysis. The measured z -dependence of R p can be fitted in both x -bins by simple functional forms, e . g . ∝ ( − z ) β . The obtained β value for thisfit, β = . ± .
04, agrees within uncertainties well with β = . ± .
03 obtained from the fit to R K inRef. [12]. Presently, it is not clear if this observed agreement between kaons and protons is accidentalor not. A “double ratio” D p = R p ( x < . ) / R p ( x > . ) , is shown in the insert of the figure. It maybe considered constant within uncertainties over the full measured z -range, with an average value of D p = . ± . stat . ± . syst . .The most important observation is that with the increase of z the measured value of R p is increasinglyundershooting the LO pQCD expectation, which is 0.51 and 0.28 calculated for the average kinematicsof the data in the 1st and 2nd x -bin, respectively. It is remarkable that R p falls below the LO pQCDprediction over the whole measured z range, which starts in this analysis from z > .
5. This effect wasobserved for R K only for z > .
8. In Fig. 3, the comparison of R p with R K calculated using data inRef. [10] and from Ref. [12] shows that over the whole measured phase space R p falls significantlybelow R K . As mentioned above, the x and Q distributions from the two analyses are different, whichcan change the results by about 5-10%. We hence avoid to quote precise results on the R p / R K ratiohere. As discussed in Section 2, the lower limit for R p and R K in LO pQCD is the same. For theratio itself, a small difference of the order of 10% is expected due to the presence of favoured strange-quark fragmentation in the kaon case. The two effects, i . e . different x and Q distributions and favouredstrange quark fragmentation in the case of kaons, act in opposite directions. Thus in naive LO pQCDone would expect the proton and kaon data points shown in Fig. 3 to agree within better than 5%, whichis clearly not the case. This indicates that the additional correction to the pQCD formalism we suggestedin Ref. [12], which takes into account the phase space available for hadronisation, depends on the massof the produced hadron.One of the striking features of the observed disagreement between the expectation of (N)LO pQCD andthe results on R K obtained in Ref. [12] was the observed strong dependence of R K on the virtual-photon1 corr z p R -bin x st LO lower limit, 1 ) c =2.4 (GeV/ æ Q Æ =0.023, æ x Æ -bin x nd LO lower limit, 2 ) c =9.8 (GeV/ æ Q Æ =0.10, æ x Æ ISOSCALAR TARGET corr z p D Fig. 2:
Results on R p as a function of z corr for the two x -bins. The insert shows the double ratio D p defined asthe ratio of R p in the first x -bin over R p in the second x -bin. Statistical uncertainties are shown by error bars andsystematic uncertainties by shaded bands at the bottom. The lines indicate the lower limit on R p predicted by LOpQCD using the PDF set from Ref. [17]. The relative uncertainty of the limit is below 4% in both x -bins. energy ν , with values of R K closer to the pQCD prediction for higher ν . Our present results on R p doconfirm a similar dependence for the proton case. These results as well as the prediction of LO pQCDare shown in Fig. 4 and in Table 2. Much higher energies than those available in COMPASS seem tobe required to eventually reach in the high- z region the lower limit of R p predicted by LO pQCD. Wemention that the lower limit of R p does not directly depend on ν . The ν -dependence of the pQCD lowerlimit seen in Fig. 4 is related to different mean values of x and Q for different values of ν .In Ref. [12] it was found that the z and ν dependences, which are both unexpected in pQCD, can becombined in the dependence on only one observable, which is the missing mass in the final state thatis approximately given by M X = (cid:113) M + M p ν ( − z ) − Q ( − z ) . In Fig. 5 the antiproton over pro-ton multiplicity ratio R p is shown as a function of the missing mass, and indeed a smooth trend withoverlapping points at different values of z is observed.The strong ν dependence of R K discussed above, as originally seen in Ref. [12], was also the inspirationto extend the covered ν range by improving the RICH K- π separation. In this way, kaon identificationup to 55 GeV/ c was achieved instead of 40 GeV/ c previously, which allows us to extend the covered ν range in every z bin. In Fig. 6, the obtained results of R K in bins of z as a function of ν in the extendedmomentum range are compared to the ones published in Ref. [12], as well as to the NLO pQCD lowerlimit for R K . The results confirm that the compatibility with pQCD expectations is better at higher ν .They also suggest that with increasing values of ν the growth of the ratio R K becomes smaller. Theseresults are also given in Table 3.For completeness, in Fig. 7 the values of R K in the extended momentum range are compared to ourearlier results [12] as a function of missing mass. The smooth growth with M X is still seen over the fullkinematically accessible range. Now there is larger overlap in M X between different z -bins, i . e . one canfind M X regions where in four different z bins at very different values of ν the results on R K are found to2 corr z i R ISOSCALAR TARGET present analysis p R (2017) 133 PLB K R (2018) 390 PLB K R Fig. 3:
Results on R p and R K as a function of z corr for the first x -bin, x < .
05. The ratio R p falls below R K in thewhole measured phase space. The kaon data come from Refs. [10, 12]. Statistical uncertainties are shown by errorbars, systematic uncertainties by the bands at the bottom. be consistent with one another. In this article the ¯p over p multiplicity ratio R p , obtained from semi-inclusive measurements of deep-inelastic lepton-nucleon scattering at z -values above 0.5, is presented for the first time. In the wholestudied z -region the ratio R p is observed to be below the lower limit predicted by LO pQCD. It is foundto be significantly smaller than the K − over K + multiplicity ratio R K as presented in our previous letter,while in naive LO pQCD both ratios are expected to be very similar. A strong dependence on the virtual-photon energy ν is observed, which is also not expected by LO pQCD but was already seen for the ratio R K in our earlier analysis. In this article, the analysis of R K is extended to larger values of ν up to 70GeV. The obtained results suggest that for high ν values there is an indication for saturation of R K at orabove the value predicted by NLO pQCD. The present studies provide further support that the additionalcorrection to the pQCD formalism suggested in our previous paper, which takes into account the phasespace available for hadronisation, depends on the mass of the produced hadron. Acknowledgements
We gratefully acknowledge the support of the CERN management and staff and the skill and effort ofthe technicians of our collaborating institutes. This work was made possible by the financial support ofour funding agencies.3 (GeV) n p R <0.55 rec z ISOSCALAR TARGET
LO lower limit (GeV) n p R <0.70 rec z (GeV) n p R <0.85 rec z (GeV) n p R <0.60 rec z (GeV) n p R <0.75 rec z (GeV) n p R <0.90 rec z (GeV) n p R <0.65 rec z (GeV) n p R <0.80 rec z (GeV) n p R <1.10 rec z Fig. 4:
Results on R p as a function of ν in nine bins of z rec for the first x -bin, x < .
05. Statistical uncertainties areshown by error bars, systematic uncertainties by the shaded bands at the bottom. The curves represent the lowerlimits for R p calculated in LO pQCD using [17] PDF set. The shaded bands around the LO lower limits indicatestheir uncertainty. References [1] V.N. Gribov and L.N. Lipatov, Sov. J. Nucl. Phys. (1972) 438; L.N. Lipatov, ibid. (1975) 95;G. Altarelli and G. Parisi, Nucl. Phys. B (1977) 298; Yu.L. Dokshitzer, Sov. Phys. JETP (1977) 641.[2] M. Hirai, S. Kumano, T.-H. Nagai and K. Sudoh, Phys. Rev. D (2007) 094009.[3] M. Hirai, H. Kawamura, S. Kumano and K. Saito, Prog. Theor. Exp. Phys. (2016) 113B04.[4] N. Sato et al. , Phys. Rev. D (2016) 114004.[5] D. de Florian, R. Sassot and M. Stratmann, Phys. Rev. D (2007) 114010.[6] D. de Florian et al. , Phys. Rev. D (2017) 094019.[7] NNPDF Collaboration, V. Bertone et al. , Eur. Phys. J. C (2017) 516.[8] HERMES Collaboration, A. Airapetian et al. , Phys. Rev. D (2013) 074029.[9] COMPASS Collaboration, C. Adolph et al. , Phys. Lett. B (2017) 1.[10] COMPASS Collaboration, C. Adolph et al. , Phys. Lett. B (2017) 133.4 ) /c (GeV X M p R <0.55 rec z rec z rec z rec z rec z rec z rec z rec z rec z ISOSCALAR TARGET
Fig. 5:
Results on R p as a function of missing mass M X for the first x -bin, x < .
05. For clarity only statisticaluncertainties are shown.
20 40 60 (GeV) n K R <0.80 rec z LO LOWER LIMITNLO LOWER LIMIT
20 40 60 (GeV) n K R <0.85 rec z
20 40 60 (GeV) n K R <0.90 rec z
20 40 60 (GeV) n K R <0.95 rec z
20 40 60 (GeV) n K R <1.05 rec z ISOSCALAR TARGET this analysis K R (2018) 390 PLB K R Fig. 6:
The K − over K + multiplicity ratio as a function of ν in five bins of z obtained in this analysis (blue) and inRef. [12] (red). The errors bars represent statistical uncertainties. The systematic uncertainties of the data pointsare indicated by the shaded band at the bottom of each panel. The shaded bands around the (N)LO lower limitsindicate their uncertainties. ) c (GeV/ X M K R <0.80 rec z rec z rec z rec z rec z ISOSCALAR TARGET
Fig. 7:
The K − over K + multiplicity ratio presented as a function of M X for this analysis (full symbols) and forthe analysis in Ref. [12] (open symbols), see text for details. For clarity only statistical uncertainties are shown. [11] COMPASS Collaboration, M. Aghasyan et al. , Phys. Rev. D (2018) 032006.[12] COMPASS Collaboration, R. Akhunzyanov et al. , Phys. Lett. B (2018) 390.[13] M. Anselmino et al. , Phys. Rev. D (2005) 074006.[14] W. Furmanski and R. Petronzio, Z. Phys. C (1982) 293.[15] D. de Florian, M. Stratmann and W. Vogelsang, Phys. Rev. D (1998) 5811.[16] R. Jakob, P. J. Mulders and J. Rodrigues, Nucl. Phys. A (1997) 937.[17] A. D. Martin, W. J. Stirling, R. S. Thorne and G. Watt, Eur. Phys. J. C (2009) 653.[18] L. A. Harland-Lang, A. D. Martin, P. Motylinski and R. S. Thorne, Eur. Phys. J. C (2015) 204.[19] NNPDF Collaboration, R. D. Ball et al. , J. High En. Phys. (2015) 040.[20] G. Ingelman, A. Edin and J. Rathsman, Comput. Phys. Commun. (1997) 108.[21] T. Sjöstrand, LU-TP-95-20, CERN-TH-7112-93-REV, hep-ph/9508391.[22] A. Kotzinian, Eur. Phys. J. C (2005) 211.[23] J. V. Guerrero et al. , J. High En. Phys. (2015) 169.[24] E. Christova and E. Leader, Phys. Rev. D (2016) 096001.[25] J. V. Guerrero and A. Accardi, Phys. Rev. D (2018) 114012.[26] D. P. Anderle, F. Ringer and W. Vogelsang, Phys. Rev. D (2013) 034014.[27] D. P. Anderle, M. Stratmann and F. Ringer, Phys. Rev. D (2015) 114017.[28] D. P. Anderle, T. Kaufmann, M. Stratmann and F. Ringer, Phys. Rev. D (2017) 054003.[29] M. Epele, C. G. Canal and R. Sassot, Phys. Rev. D (2016) 034037.[30] M. Epele, C. G. Canal and R. Sassot, Phys. Lett. B (2019) 102.[31] A. Accardi and A. Signori, Phys. Lett. B (2019) 134993.[32] COMPASS Collaboration, P. Abbon et al. , Nucl. Instr. and Meth. A (2007) 455.[33] P. Abbon et al. , Nucl. Instr. and Meth. A (2011) 26.[34] E. C. Aschenauer et al. , Phys. Rev. D (2013) 114025; H. Spiesberger, HERACLES and DJAN-6 Table 1:
Extracted values of R p with statistical and systematic uncertainties, bin limits of z ( z min , z max ) , and averagevalues of x , Q , z rec and z corr in the first (upper part) and second (lower part) x -bin. bin x Q (GeV/ c ) z min z max z rec z corr R p ± δ R p , stat . ± δ R p , syst . . ± . ± . . ± . ± . . ± . ± . . ± . ± . . ± . ± . . ± . ± . . ± . ± . . ± . ± . . ± . ± . . ± . ± . . ± . ± . . ± . ± . . ± . ± . . ± . ± . . ± . ± . . ± . ± . . ± . ± . . ± . ± . Table 2:
Extracted values of R p with statistical and systematic uncertainties, bin range of proton momenta ( p rg (GeV/ c )), bin range in z ( z rg ) , and average values of x , Q , z rec and z corr in the first x -bin. bin x Q (GeV/ c ) p rg (GeV/ c ) z rg z rec z corr R p ± δ R p , stat . ± δ R p , syst .
1a 0.022 1.9 20–30 0.50–0.55 0.524 0.524 0 . ± . ± . . ± . ± . . ± . ± . . ± . ± . . ± . ± . . ± . ± . . ± . ± . . ± . ± . . ± . ± . . ± . ± . . ± . ± . . ± . ± . . ± . ± . . ± . ± . . ± . ± . . ± . ± . . ± . ± . . ± . ± . . ± . ± . . ± . ± . . ± . ± . . ± . ± . . ± . ± . . ± . ± . . ± . ± . . ± . ± . . ± . ± . . ± . ± . . ± . ± . . ± . ± . . ± . ± . . ± . ± . . ± . ± . . ± . ± . Table 3:
Extracted values of R K with statistical and systematic uncertainties, bin range of kaon momenta ( p rg (GeV/ c )), bin range in z ( z rg ) , and average values of x , Q , z rec and z corr . bin x Q (GeV/ c ) p rg (GeV/ c ) z rg z rec z corr R K ± δ R K , stat . ± δ R K , syst .
1g 0.021 2.1 40–45 0.75–0.80 0.774 0.774 0 . ± . ± . . ± . ± . . ± . ± . . ± . ± . . ± . ± . . ± . ± . . ± . ± . . ± . ± . . ± . ± . . ± . ± . . ± . ± . . ± . ± . . ± . ± . . ± . ± . . ± . ± ..