For the first time, the $K^-/K^+$ multiplicity ratio is measured in deep-inelastic scattering for kaons carrying a large fraction $z$ of the virtual-photon energy. The data were obtained by the COMPASS collaboration using a 160 GeV muon beam and an isoscalar $^6$LiD target. The regime of deep-inelastic scattering is ensured by requiring $Q^2>1$ (GeV/$c)^2$ for the photon virtuality and $W>5$ GeV/$c^2$ for the invariant mass of the produced hadronic system. The Bjorken scaling variable range is $0.010.75$. For very large values of $z$, {\it i.e.} $z>0.8$, the results contradict expectations obtained using the formalism of (next-to-)leading order perturbative quantum chromodynamics. Our studies suggest that, within this formalism, an additional correction may be required to take into account the phase space available for hadronisation.Peer Reviewe

Mamoulis, N

Yiu, ML

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Reverse Nearest Neighbors Search in Ad-hoc Subspaces

K- over K+ multiplicity ratio for kaons produced in DIS with a large fraction of the virtual-photon energy

Nunes, Ana Sofia

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PoS(DIS2018)018K−/K+ multiplicity ratio for kaons produced in DISwith a large fraction of the virtual photon energyA. S. Nunes∗†LIP-LisbonE-mail: Ana.Sofia.Nunes@cern.chFor the first time, the K−/K+ multiplicity ratio is measured in deep-inelastic scattering for kaonscarrying a large fraction z of the virtual-photon energy. The data were obtained by the COMPASScollaboration using a 160 GeV muon beam and an isoscalar 6LiD target. The regime of deep-inelastic scattering is ensured by requiring Q2 > 1 (GeV/c)2 for the photon virtuality and W > 5GeV/c2 for the invariant mass of the produced hadronic system. The Bjorken scaling variablerange is 0.01 < x < 0.40. The z-dependence of the multiplicity ratio is studied for z > 0.75.For very large values of z, i.e. z > 0.8, the results contradict expectations obtained using theformalism of (next-to-)leading order perturbative quantum chromodynamics. Our studies suggestthat, within this formalism, an additional correction may be required to take into account thephase space available for hadronisation.XXVI International Workshop on Deep-Inelastic Scattering and Related Subjects (DIS2018)16-20 April 2018Kobe, Japan∗Speaker.†On behalf of the COMPASS Collaboration.c© Copyright owned by the author(s) under the terms of the Creative CommonsAttribution-NonCommercial-NoDerivatives 4.0 International License (CC BY-NC-ND 4.0). https://pos.sissa.it/PoS(DIS2018)018K−/K+ multiplicity ratio A. S. Nunes1. IntroductionThe strangeness content of nucleons has been a topic of interest since many years, but it hasbeen difficult to measure it experimentally. The difficulty increases for the strange quark polariza-tion (∆s), for which conflicting results have been obtained. When measured in the deep inelasticscattering (DIS) or semi-inclusive DIS (SIDIS) process, the parton distribution functions (PDFs) ortheir convolution with fragmentation functions (FFs) are needed to describe the cross section andasymmetries. For this reason, the knowledge of FFs is relevant to tackle the abovementioned prob-lem. Quark FFs measure, at leading order, the probability of a given quark to give rise to a givenhadron. They are fundamental non-perturbative functions, that are expected to be universal, i.e.independent of the physical process involved. In such context, they become ingredients of globalperturbative QCD fits, i.e. fits that use data taken at different photon virtualities Q2 and assume thevalidity of the DGLAP equations to evolve PDFs and FFs to common values of Q2.SIDIS experiments, such as the ones studied in the COMPASS experiment, give access tofragmentation functions Dhq(z,Q2) by measuring hadron multiplicities Mh,dMh(x,Q2,z)dz≡ d3σhDIS(x,Q2,z)/dxdQ2 dzd2σDIS(x,Q2)/dxdQ2, (1.1)where x is the Bjorken scaling variable, Q is the photon virtuality and z is the fraction of the photonenergy carried by the hadron, using the expressiondMh(x,z,Q2)dzLO=∑q e2q fq(x,Q2)Dhq(z,Q2)∑q e2q fq(x,Q2), (1.2)where fq(x,Q2) are quark distribution functions and eq are the relative electric charges of thequarks, and the sum is over quark flavours.The COMPASS Collaboration has recently published results of multiplicities of charged pi-ons and unidentified charged hadrons [1], multiplicities of charged kaons [2], and also transverse-momentum-dependent multiplicities of charged hadrons, produced in muon-deuteron deep inelasticscattering [3]. While the unidentified charged hadrons and the charged pions are well described byleading order and next to leading order perturbative QCD parametrizations, this is not the case forthe kaon multiplicities, in particular at high values of the hadron fractional energy z. In addition,the COMPASS and HERMES results for the ratio of z-integrated kaon multiplicitiesM K+/M K−are not compatible within experimental uncertainties.There was therefore an interest in exploring further the higher values of z, in this case by useof mulplicity ratios, which allow to cancel out many possible sources of systematic uncertainties.In the following sections, the experimental setup is briefly described, after which the method formultiplicity extraction is presented, followed by the obtained results, which are discussed and,finally, a summary is given. This analysis was recently submitted for publication [4].2. Experimental setupThe COMPASS experiment at CERN is presented in detail in Ref. [5] and some of its recentresults and future plans are highlighted in these proceedings [6, 7, 8]. COMPASS is a ground1PoS(DIS2018)018K−/K+ multiplicity ratio A. S. Nuneslevel fixed target experiment at the CERN SPS that uses a terciary muon beam of positive (ornegative) charge, or a secondary hadron beam. The two-stage spectrometer provides large angularand momentum acceptances. The trigger is based on hodoscopes that detect the scattered muonand, optionally, an energy deposit in a calorimeter. Particle identification is ensured by use ofmuon walls, electromagnetic and hadronic calorimeters, and a RICH detector.The analysis described in this contribution refers to data collected in 2006 with a positive muonbeam with 160 GeV/c momentum and with a solid state target of 6LiD. The target was 1.2 meterslong, divided in three cells of 30, 60, and 30 cm long.3. Multiplicity extractionThe process for extraction of multiplicities from data has several steps. First of all, there is adata selection. The spectrometer acceptance and the reconstruction efficiency must be taken intoaccount and corrected for. In addition, the efficiency and the purity of the RICH identificationof kaons are corrected for. Also the decays of diffractively produced vector mesons that producekaons is corrected for. Finally, corrections are applied to account for radiative effects.The initial sample is the data collected by COMPASS in 2006 with a 160 GeV/c positive muonbeam impinging in an isoscalar target of 6LiD. It is required that the tracks of a beam particle andof a scattered muon are reconstructed. Furthermore, the deep inelastic scattering regime is ensuredby requirements of Q2 > 1 GeV/c2 and of the mass of the hadronic final state W > 5 GeV/c2. Toavoid events with badly reconstructed kinematic variables, it is further required that the fraction ofbeam muon energy carried by the virtual photon satisfies y > 0.1. The reconstructed fraction ofthe energy of the virtual photon carried by the kaon is, for the present analysis, restricted to theregion of high values, zrec > 0.75. The momentum of the hadron is restricted to the region wherekaons are well identified by the RICH, i.e. 12 < ph/(GeV/c) < 40. The hadron is required to beidentified as a kaon, in a way that ensures a very pure sample of kaons.The kinematic coverage ofthe final sample with kaon events is depicted in Fig. 1.x 2−10 1−102 )/c(GeV 2Q110Entries 020406080100120140160180200z 0.75 0.8 0.85 0.9 0.95 1 (GeV)ν20304050Entries020406080100120140160180200Figure 1: Kinematic coverage of the final sample of kaon events used in the present analysis: Q2 vs. x (left)and ν vs. z (right) [4].The final sample comprises 64000 charged kaons. For the analysis, we use two bins ofthe Bjorken scaling variable: x < 0.05 and x > 0.05, with 〈Q2〉 = 1.6 (GeV/c2) and 〈Q2〉 =4.8 (GeV/c2), respectively. The following bins limits for the z variable are used: 0.75, 0.80, 0.85,0.90, 0.95 and 1.05.2PoS(DIS2018)018K−/K+ multiplicity ratio A. S. NunesThe way the final sample was obtained and the fact that a ratio of multiplicities is used allowsto simplify many of the corrections applied. The ratio of acceptances of K− and K+ was found tobe constant over z, and the constant obtained from a fit was used as correcting factor for all zrecbins. Moreover, the great purity of the sample allowed a simplified unfolding. As for the vectormeson corrections, they were simulated with the program HEPGEN [9], and it was verified that theφ decay is not important in the high-z region of this analysis. Finally, the electromagnetic radiativeefects cancel out in the multiplicity ratio, because they don’t depend on the charge of the hadron.4. Results and discussionIn Fig. 2, the results for the ratio of multiplicities RK = (dMK−/dz)/(dMK+/dz) are show forthe first bin in x, together with several predictions. Except for the first z bin, all the remaining fourdata points are below the predictions. It should be noted that possible corrections to account forthe vector meson decays or for pion misidentification as kaon further decreses the values of RKobtained from the data, thereby increasing the tension between data and predictions.corrz0.8 0.85 0.9 0.95  KR00.10.20.30.40.50.62)c=1.6 (GeV/2Q=0.03,  xLO DSSLEPTO MCLO LOWER LIMITNLO DEHSS=0strNLO DEHSS, DFigure 2: (Left) Final results obtained for the ratio of multiplicities of K− over K+, RK , for the bin with x<0.05. The ratio is shown as a function of the variable zcorr = zdatarec -(zMCrec −zMCgen ), that is, a correction is appliedto the values of z obtained from the data that is equal to the difference obtained in Monte Carlo simulationsbetween the generated and the reconstructed values of that variable. The curves represent the predictionsfor the ratio RK obtained from the leading order DSS parametrization, from a simulation using the LEPTOgenerator, together with the leading order lower limit, and from the next to leading order parametrizationDEHSS, both without and with the constraint of Dstr = 0 [4].It should also be noted that the behaviour of RK is similar for both the x bins considered, beingwell fitted by a functional form of type ∝ (1− z)β , β = 0.71±0.03. Furthermore, the ratio of theresults obtained from the two x bins is constant over z, as can be seen in Fig. 3.In Fig. 4, the results for the ratio of multiplicities RK is shown as a function of the energy ofthe virtual photon ν , in five bins of zrec. Also the leading order lower limit and the next to leadingorder parametrization of DEHSS, assuming Dstr = 0, are shown. The ratio is seen to be below thepredictions, most noticeably for low ν and for higher z. This is in agreement with the observationfrom the LSS group ("the largest discrepancy between pQCD expectations and experimental resultsis observed in the region of large z and small y, i.e. small ν" [10].)It should be noted that high values of z of a given kaon correspond to a reduction of thephase space available for the formation of other particles. Therefore, the missing mass, MX ≈3PoS(DIS2018)018K−/K+ multiplicity ratio A. S. Nunescorrz0.8 0.85 0.9 0.95  KR00.10.20.30.40.50.6 2)c=1.6 (GeV/〉2Q〈=0.030, 〉x〈2)c=4.8 (GeV/〉2Q〈=0.094, 〉x〈corrz0.8 0.85 0.9 0.95KD11.21.41.61.82Figure 3: Final results obtained for the ratio of multiplicities of K− over K+, RK , for the two two bins of x.In the inset, the ratio DK of the results of the two x bins is also shown [4]. (GeV)  ν20 30 40 50  KR00.20.40.6 <0.80recz0.75<LO LOWER LIMIT=0strNLO DEHSS, D (GeV)  ν20 30 40 50  KR00.20.40.6 <0.85recz0.80< (GeV)  ν20 30 40 50  KR00.20.40.6 <0.90recz0.85< (GeV)  ν20 30 40 50  KR00.20.40.6 <0.95recz0.90< (GeV)  ν20 30 40 50  KR00.20.40.6 <1.05recz0.95<Figure 4: RK(ν) in 5 bins of z, together with the lower limit prediction at leading order and the next toleading order DEHSS parametrization for Dstr [4].√M2p+2Mpν(1− z)−Q2(1− z2), seems a natural variable to study the observed effect and, in-deed, there is a smooth increasing trend of RK as a function of MX , as can be seen in Fig. 5.5. SummaryFor the first time, the ratio of multiplicities of charged kaons produced in deep inelastic scat-tering was measured in the region of high z. This ratio is particularly useful because it doesn’tdepend on most of the possible sources of systematic uncertainties. The results are at contrast tothe expectations from QCD leading order and next to leading order parametrizations as well asfrom limits at the leading order approximation. The disagreement is larger at larger values of zand lower values of ν , the energy of the virtual photon. The beforementioned ratio of multiplicitiesexhibits a smooth trend as a function of the missing mass MX ≈√M2p+2MPν(1− z)−Q2(1− z2),which may be an indication that, within the perturbative QCD framework, a correction might beincluded in order to take into account the phase space available for the hadronisation of the targetremnants.4PoS(DIS2018)018K−/K+ multiplicity ratio A. S. Nunes)2c(GeV/ XM2 2.5 3 3.5 4 4.5  KR00.20.40.6<0.80recz0.75<<0.85recz0.85<<0.90recz0.85<<0.95recz0.90<<1.05recz0.95<Figure 5: Ratio RK as a function of the missing mass, defined as MX ≈√M2p+2Mpν(1− z)−Q2(1− z2) [4].AcknowledgementsThis work was financed by FCT project CERN/FIS-PAR/0007/2017.References[1] C. Adolph et al. (COMPASS Collaboration), Phys. Lett. B764 (2017) 001.[2] C. Adolph et al. (COMPASS Collaboration), Phys. Lett. B767 (2017) 133.[3] M. Aghasyan et al. (COMPASS Collaboration), Phys. Rev. D97 (2018) 032006.[4] R. Akhunzyanov et al. (COMPASS Collaboration), arXiv:1802.00584.[5] P. Abbon et al. (COMPASS Collaboration), Nucl. Instr. Meth. A577 (2007) 455.[6] B. Parsamyan, these proceedings.[7] M. Chiosso, these proceedings.[8] B. Badełek, these proceedings.[9] A. Sandacz, P. Sznajder, arXiv:1207.0333.[10] LSS group, private communication.5

$K^-/K^+$ multiplicity ratio for kaons produced in DIS with a large fraction of the virtual photon energy

Given an object q, modeled by a multidimensional point, a reverse nearest neighbors (RNN) query returns the set of objects in the database that have q as their nearest neighbor. In this paper, we study an interesting generalization of the RNN query, where not all dimensions are considered, but only an ad-hoc subset thereof. The rationale is that (i) the dimensionality might be too high for the result of a regular RNN query to be useful, (ii) missing values may implicitly define a meaningful subspace for RNN retrieval, and (iii) analysts may be interested in the query results only for a set of (ad-hoc) problem dimensions (i.e., object attributes). We consider a suitable storage scheme and develop appropriate algorithms for projected RNN queries, without relying on multidimensional indexes. Our methods are experimentally evaluated with real and synthetic data. © 2006 IEEE.link_to_subscribed_fulltex

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Reverse nearest neighbors search in ad-hoc subspaces

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$K^-/K^+$ multiplicity ratio for kaons produced in DIS with a large fraction of the virtual photon energy

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K−/K+K^-/K^+K−/K+ multiplicity ratio for kaons produced in DIS with a large fraction of the virtual photon energy

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$K^-/K^+$ multiplicity ratio for kaons produced in DIS with a large fraction of the virtual photon energy