NA61/SHINE is a ﬁxed target experiment operating at CERN SPS. Its main goals are to search for the critical point of stronglyinteractingmatterandtostudytheonsetofdeconﬁnement. Forthesegoalsascanofthetwodimensionalphase diagram (T-μB) is being performed at the SPS by measurements of hadron production in proton-proton, proton-nucleus and nucleus-nucleus interactions as a function of collision energy. In this paper the status of the search for the critical point of strongly interacting matter by the NA61/SHINE Collaboration is presented including recent results on proton intermittency, strongly intensive ﬂuctuation observables of multiplicity and transverse momentum ﬂuctuations. These measurements are expected to be sensitive to the correlation length and, therefore, have the ability to reveal the existence of the critical point via possible non-monotonic behavior. The new NA61/SHINE results are compared to the model predictions

Aduszkiewicz, A.

Andronov, E.

Andronov, E. V.

Anticic, T.

Baatar, B.

Baszczyk, M.

Bhosale, S.

Blondel, A.

Bogomilov, M.

Brandin, A.

Bravar, A.

Brylinski, W.

Brzychczyk, J.

Bunyatov, S. A.

Busygina, O.

Bzdak, A.

Cherif, H.

Cirkovic, M.

Csanad, M.

Czopowicz, T.

Damyanova, A.

Davis, N.

Deveaux, M.

Dominik, W.

Dorosz, P.

Dumarchez, J.

Engel, R.

Feofilov, G. A.

Fields, L.

Fodor, Z.

Garibov, A.

Gazdzicki, M.

Golosov, O.

Golubeva, M.

Grebieszkow, K.

Guber, F.

Haesler, A.

Igolkin, S. N.

Ilieva, S.

Ivashkin, A.

Johnson, S. R.

Kadija, K.

Kaptur, Emil

Kargin, N.

Kashirin, E.

Kielbowicz, M.

Kireyeu, V. A.

Klochkov, V.

Kolesnikov, V. I.

Kolev, D.

Korzenev, A.

Kovalenko, V. N.

Kowalik, K.

Kowalski, Seweryn

Koziel, M.

Krasnoperov, A.

Kucewicz, W.

Kuich, M.

Kurepin, A.

Larsen, D.

Laszlo, A.

Lazareva, T. V.

Lewicki, M.

Lojek, K.

Lyubushkin, V. V.

Mackowiak-Pawlowska, M.

Majka, Z.

Maksiak, B.

Malakhov, A. I.

Manic, D.

Marchionni, A.

Marcinek, A.

Marino, A. D.

Marton, K.

Mathes, H.-J.

Matulewicz, T.

Matveev, V.

Melkumov, G. L.

Merzlaya, A. O.

Messerly, B.

Mik, L.

Morozov, S.

Mrowczynski, S.

Nagai, Y.

Naskret, M.

Ozvenchuk, V.

Paolone, V.

Pavin, M.

Petukhov, O.

Planeta, R.

Podlaski, P.

Popov, B. A.

Porfy, B.

Posiadala-Zezula, M.

Prokhorova, D. S.

Puzovic, J.

Puławski, Szymon

Rauch, W.

Ravonel, M.

Renfordt, R.

Nuclear Physics A

English

Andronov, Evgeny

Antićić, T.

Bryliński, W.

Brzychczyk, Janusz

Bzdak, Adam

Ćirković, M.

Gaździcki, M.

Kaptur, E.

Kiełbowicz, M.

Kowalski, S.

Larsen, Dag

László, A.

Łojek, Konrad

Łysakowski, B.

Maćkowiak-Pawłowska, M.

Majka, Zbigniew

Manić, D.

Marcinek, Antoni

Merzlaya, Anastasia

Mik, Ł.

Mrówczyński, S.

Naskręt, M.

Płaneta, Roman

Posiadała-Zezula, M.

Puławski, S.

Puzović, J.

Jagiellonian Univeristy Repository

XXVIIth International Conference on Ultrarelativistic Nucleus-Nucleus Collisions(Quark Matter 2018)Search for the critical point by the NA61/SHINE experimentEvgeny Andronov (for the NA61/SHINE Collaboration)Saint Petersburg State University, ul. Ulyanovskaya 1, 198504, Petrodvorets, Saint Petersburg, RussiaAbstractNA61/SHINE is a ﬁxed target experiment operating at CERN SPS. Its main goals are to search for the critical point ofstrongly interacting matter and to study the onset of deconﬁnement. For these goals a scan of the two dimensional phasediagram (T -μB) is being performed at the SPS by measurements of hadron production in proton-proton, proton-nucleusand nucleus-nucleus interactions as a function of collision energy.In this paper the status of the search for the critical point of strongly interacting matter by the NA61/SHINE Col-laboration is presented including recent results on proton intermittency, strongly intensive ﬂuctuation observables ofmultiplicity and transverse momentum ﬂuctuations. These measurements are expected to be sensitive to the correlationlength and, therefore, have the ability to reveal the existence of the critical point via possible non-monotonic behavior.The new NA61/SHINE results are compared to the model predictions.Keywords: critical point, ﬂuctuations, CERN, SPS1. IntroductionThe NA61/SHINE experiment [1] is a multi-purpose ﬁxed target experiment at the Super Proton Syn-chrotron (SPS) of the European Organization for Nuclear Research (CERN). The strong interactions pro-gramme of NA61/SHINE is devoted to the studies of the Quantum Chromodynamics phase structure and,in particular, search for the critical point (CP) [2] of strongly interacting matter. NA61/SHINE is probingdiﬀerent regions of the phase diagram by performing measurements of hadron production in collisions ofprotons and various nuclei (p+p, p+Pb, Be+Be, Ar+Sc, Xe+La, Pb+Pb) in a range of beam momenta (13A- 150/158A GeV/c). It is expected that there will be a non-monotonic dependence of ﬂuctuations of a num-ber of observables on energy and system size in this scan due to the phase transition of strongly interactingmatter and the possible existence of the CP [3]. Some hints of such behaviour have already been observedby the NA49 experiment [4].2. Multiplicity ﬂuctuationsThe study of event-by-event ﬂuctuations is one of the main tools that is applied to search for the criticalpoint. The strength of ﬂuctuations of a given observable can be quantiﬁed by the moments of its distribution.Available online at www.sciencedirect.comNuclear Physics A 982 (2019) 835–8380375-9474/© 2018 Published by Elsevier B.V.www.elsevier.com/locate/nuclphysahttps://doi.org/10.1016/j.nuclphysa.2018.09.019This is an open access article under the CC BY-NC-ND license (http://creativecommons.org/licenses/by-nc-nd/4.0/).In this paper results on multiplicity ﬂuctuations are presented in terms of the scaled variance, ω[N], that isconstructed from the ﬁrst and second moments of the multiplicity distribution as ω[N] = 〈N2〉−〈N〉2〈N〉 , where〈· · ·〉 stands for the averaging over all events. The scaled variance is an intensive quantity which does notdepend on the volume of the system for an ideal Boltzmann gas in the grand canonical ensemble (GCE)or on the number of sources within models of independent sources such as the wounded nucleon model(WNM) [5].One can expect that ω[N] is sensitive to the existence of the CP as within the GCE it is proportionalto the isothermal compressibility that diverges in the vicinity of the CP [6], although this signal may beshadowed by signiﬁcant contribution from volume ﬂuctuations.The NA61/SHINE experiment obtained preliminary results on multiplicity ﬂuctuations for primary nega-tively charged hadrons produced in strong and electromagnetic processes in forward energy selected Be+Be(0-5%) and Ar+Sc (0-0.2%) collisions and in inelastic p+p interactions. The selection of the most cen-tral events in A+A collisions was done using information from the NA61/SHINE forward calorimeter, thePSD. Transverse momenta of all charged hadrons were restricted to 0 < pT < 1.5 GeV/c and rapidities inthe center-of-mass system calculated under the pion mass assumption were restricted to 0 < yπ < ybeam.Moreover, the NA61/SHINE acceptance map [7] was applied. The results for Be+Be and Ar+Sc collisionswere not corrected for detector ineﬃciencies and trigger biases as simulations have shown that their ef-fect estimated using the GEANT3 package does not exceed 5%. However, the trigger bias modiﬁes resultssigniﬁcantly for p+p interactions and, therefore, requires corrections described precisely in Ref. [8]. Thestatistical uncertainties were determined using the sub-sample method. Analysis of the systematic uncer-tainties is not ﬁnished but they are estimated to be smaller than 5%.The results for the dependence of multiplicity ﬂuctuations on the mean number of wounded nucleons,〈W〉, are shown in Figure 1. A dotted line indicates the lower limit for ω[N] for A+A collisions within theWNM that is deﬁned by the measurement for p+p interactions. One can see that these model predictionsare violated in Ar+Sc collisions. However, the scaled variance obtained for Ar+Sc collisions is consistentwith the statistical model, where ω[N] ≈ 0.9 for large volume systems [9]. Comparison with the EPOS1.99model predictions [10], in turn, shows a signiﬁcant discrepancy in Be+Be collisions. The observed rapidchange of ω[N] when moving from lighter (p+p, Be+Be) to heavier (Ar+Sc) colliding systems can beinterpreted as the beginning of creation of large clusters of strongly interacting matter, e.g. as predicted inpercolation models [11, 12].Fig. 1. Dependence of ω[N] for negatively charged hadrons on the mean number of wounded nucleons 〈W〉 measured by theNA61/SHINE experiment (ﬁlled symbols) in comparison to the EPOS1.99 model predictions (open symbols).E. Andronov / Nuclear Physics A 982 (2019) 835–8388363. PT − N ﬂuctuation measurementsIn order to minimize the inﬂuence of volume ﬂuctuations strongly intensive observables are used insearch for the critical point [13, 14]:Δ[PT ,N] = 1〈N〉ω[pT ][〈N〉ω[PT ] − 〈PT 〉ω[N]], (1)Σ[PT ,N] = 1〈N〉ω[pT ][〈N〉ω[PT ] + 〈PT 〉ω[N] − 2(〈PTN〉 − 〈PT 〉〈N〉)], (2)where PT =∑Ni=1 pTi and ω[pT ] is the scaled variance of the inclusive pT spectrum.In recent measurements by the NA61/SHINE collaboration of the strongly intensive quantities Δ[PT ,N]and Σ[PT ,N] in p+p, Be+Be and Ar+Sc collisions no anomaly attributable to the CP was observed [15].The analysis was extended to studies of the pseudorapidity dependence of strongly intensive observables inorder to probe diﬀerent values of baryochemical potential [16].In this paper new results were obtained for Be+Be collisions at 150A GeV/c selected for the smallest 8%of forward energies. Fluctuations were studied in 9 pseudorapidity intervals deﬁned in the laboratory refer-ence frame. The forward edge of the intervals was ﬁxed at 5.2 units of pseudorapidity, with the backwardedge changing from 3 up to 4.6 units. The choice of lower bounds was motivated by the small azimuthalangle acceptance at smaller pseudorapidities. The upper bound was introduced in order to suppress possiblequasi-diﬀractive or electromagnetic eﬀects which become important at larger pseudorapidities. All the otheranalysis details are identical to the methods described in the previous section.Figure 2 shows preliminary results for the dependence of Δ[PT ,N] and Σ[PT ,N] on the width of thepseudorapidity interval and comparisons to the EPOS1.99 model [10] predictions. Both quantities changemonotonously for the data in contrast to the EPOS1.99 results for Δ[PT ,N] which show a minimum forintermediate width and lie signiﬁcantly above the measurements. Another observation is that for smallerwindows these quantities approach unity (independent particle production limit) as the number of particlesin the interval gets small. Moreover, the inequalitiesΔ[PT ,N] < 1 and Σ[PT ,N] ≥ 1, previously observed forall studied systems at all collision energies [15], also hold when modifying the width of the pseudorapiditywindow of the measurement. In general, no traces of the possible critical point of strongly interacting matterare visible.window width0 0.5 1 1.5 2 2.5]N, T[PΔ0.40.60.811.2++h-hNA61/SHINE preliminary GeV/cABe, 0-8%, 1509Be+7NA61/SHINE, GeV/cABe, 0-8%, 1509Be+7EPOS1.99,window width0 0.5 1 1.5 2 2.5]N, T[PΣ0.9511.051.1 ++h-hNA61/SHINE preliminary GeV/cABe, 0-8%, 1509Be+7NA61/SHINE, GeV/cABe, 0-8%, 1509Be+7EPOS1.99,Fig. 2. Dependence of Δ[PT ,N] (left) and Σ[PT ,N] (right) on the width of the pseudorapidity window. Red squares are preliminaryNA61/SHINE measurements for 0-8% Be+Be collisions at 150A GeV/c. Blue band represents the EPOS1.99 model predictions.E. Andronov / Nuclear Physics A 982 (2019) 835–838 8374. Proton density ﬂuctuations: intermittencyIn the grand canonical ensemble the correlation length diverges at the critical point and the systembecomes scale invariant [17]. In a pure critical system, intermittency in transverse momentum space can berevealed by the scaling of the Second Scaled Factorial Moments of protons as a function of bin size [18].For that purpose, a region of transverse momentum space is partitioned into M×M equal-size bins and thesemoments are deﬁned as:F2(M) =〈 1M2∑M2i=1 ni(ni − 1)〉〈 1M2∑M2i=1 ni〉2 (3)where ni is the number of particles in the i-th bin. If the system exhibits critical ﬂuctuations, F2(M) isexpected to scale with M, for large values of M, as a power-law F2(M) ∼ M2φ2 , where φ2 is the intermittencyindex.An intermittency analysis was performed for NA61/SHINE data on Be+Be collisions (0-10%) at 150AGeV/c beam momentum. No signiﬁcant intermittency eﬀect was observed, with an upper limit for protonsobeying critical ﬂuctuations being of the order of 0.3%. This limit was estimated based on the CriticalMonte Carlo model predictions [19]. For more details see Ref. [20].5. AcknowledgmentsThis work is supported by the Russian Science Foundation under grant 17-72-20045.References[1] N. Abgrall, et al., NA61/SHINE facility at the CERN SPS: beams and detector system, JINST 9 (2014) P06005.[2] Z. Fodor, S. Katz, Critical point of QCD at ﬁnite T and mu, lattice results for physical quark masses, JHEP 0404 (2004) 050.[3] M. A. Stephanov, K. Rajagopal, E. V. Shuryak, Event-by-event ﬂuctuations in heavy ion collisions and the QCD critical point,Phys.Rev. D60 (1999) 114028.[4] K. Grebieszkow for the NA49 Collab., Search for the critical point of strongly interacting matter in NA49, Nucl. Phys. A830(2009) 547C.[5] A. Bialas, M. Bleszynski, W. Czyz, Multiplicity Distributions in Nucleus-Nucleus Collisions at High-Energies, Nucl. Phys. B111(1976) 461.[6] M. Mukherjee, et al., Estimation of the isothermal compressibility from event-by-event multiplicity ﬂuctuation studies, EPJ WebConf. 171 (2017) 14010.[7] T. Czopowicz, NA61/SHINE acceptance map, https://edms.cern.ch/document/1237791/1.[8] A. Aduszkiewicz, et al., Multiplicity and transverse momentum ﬂuctuations in inelastic proton-proton interactions at the CERNSuper Proton Synchrotron, Eur. Phys. J. C76 (11) (2015) 635.[9] V. V. Begun, M. Gazdzicki, M. I. Gorenstein, M. Hauer, V. P. Konchakovski, B. Lungwitz, Multiplicity ﬂuctuations in relativisticnuclear collisions: Statistical model versus experimental data, Phys. Rev. C76 (2007) 024902.[10] T. Pierog, K. Werner, EPOS Model and Ultra High Energy Cosmic Rays, Nucl.Phys.Proc.Suppl. 196 (2009) 102–105.[11] T. Celik, F. Karsch, H. Satz, A percolation approach to strongly interacting matter, Phys. Lett. 97B (1980) 128–130.[12] M. Braun, C. Pajares, A Probabilistic model of interacting strings, Nucl. Phys. B390 (1993) 542–558.[13] M. Gorenstein, M. Gazdzicki, Strongly Intensive Quantities, Phys. Rev. C84 (2011) 014904. doi:10.1103/PhysRevC.84.014904.[14] M. Gazdzicki, M. Gorenstein, M. Mackowiak-Pawlowska, On Normalization of Strongly Intensive Quantities, Phys. Rev. C88(2013) 024907.[15] E. Andronov, Transverse momentum and multiplicity ﬂuctuations in Ar+Sc collisions at the CERN SPS from NA61/SHINE,Acta Phys. Polon. Supp. 10 (2017) 449–453.[16] J. Brewer, S. Mukherjee, K. Rajagopal, Y. Yin, Searching for the QCD critical point via the rapidity dependence of cumulants.arXiv:1804.10215.[17] H. Satz, Intermittency and Critical Behavior, Nucl.Phys. B326 (1989) 613–618.[18] A. Bialas, R. Peschanski, Moments of rapidity distributions as a measure of short-range ﬂuctuations in high-energy collisions,Nuclear Physics B 273 (3) (1986) 703 – 718.[19] N. Antoniou, Y. Contoyiannis, F. Diakonos, A. Karanikas, C. Ktorides, Pion production from a critical QCD phase, Nucl.Phys.A693 (2001) 799–824. arXiv:hep-ph/0012164, doi:10.1016/S0375-9474(01)00921-6.[20] N. Davis, et al., Intermittency analysis of proton density as a probe for the critical point of strongly interacting matter inNA61/SHINE, poster at the Quark Matter 2018, 14-19 May 2018, Venice, Italy (2018).E. Andronov / Nuclear Physics A 982 (2019) 835–838838

Search for the critical point by the NA61/SHINE experiment

Łysakowski, Bartosz

Repozytorium Uniwersytetu Śląskiego RE-BUŚ

             Title: Search for the critical point by the NA61/SHINE experiment  Author: E. Andronov, A. Aduszkiewicz, Emil Kaptur, Seweryn Kowalski, Bartosz Łysakowski, Szymon Puławski, Katarzyna Schmidt i in.  Citation style: Andronov E., Aduszkiewicz A., Kaptur Emil, Kowalski Seweryn, Łysakowski Bartosz, Puławski Szymon, Schmidt Katarzyna i in. (2019). Search for the critical point by the NA61/SHINE experiment. „Nuclear Physics A” (Vol. 982 (2019), s. 835-838), doi: 10.1016/j.nuclphysa.2018.09.019 XXVIIth International Conference on Ultrarelativistic Nucleus-Nucleus Collisions(Quark Matter 2018)Search for the critical point by the NA61/SHINE experimentEvgeny Andronov (for the NA61/SHINE Collaboration)Saint Petersburg State University, ul. Ulyanovskaya 1, 198504, Petrodvorets, Saint Petersburg, RussiaAbstractNA61/SHINE is a fixed target experiment operating at CERN SPS. Its main goals are to search for the critical point ofstrongly interacting matter and to study the onset of deconfinement. For these goals a scan of the two dimensional phasediagram (T -μB) is being performed at the SPS by measurements of hadron production in proton-proton, proton-nucleusand nucleus-nucleus interactions as a function of collision energy.In this paper the status of the search for the critical point of strongly interacting matter by the NA61/SHINE Col-laboration is presented including recent results on proton intermittency, strongly intensive fluctuation observables ofmultiplicity and transverse momentum fluctuations. These measurements are expected to be sensitive to the correlationlength and, therefore, have the ability to reveal the existence of the critical point via possible non-monotonic behavior.The new NA61/SHINE results are compared to the model predictions.Keywords: critical point, fluctuations, CERN, SPS1. IntroductionThe NA61/SHINE experiment [1] is a multi-purpose fixed target experiment at the Super Proton Syn-chrotron (SPS) of the European Organization for Nuclear Research (CERN). The strong interactions pro-gramme of NA61/SHINE is devoted to the studies of the Quantum Chromodynamics phase structure and,in particular, search for the critical point (CP) [2] of strongly interacting matter. NA61/SHINE is probingdifferent regions of the phase diagram by performing measurements of hadron production in collisions ofprotons and various nuclei (p+p, p+Pb, Be+Be, Ar+Sc, Xe+La, Pb+Pb) in a range of beam momenta (13A- 150/158A GeV/c). It is expected that there will be a non-monotonic dependence of fluctuations of a num-ber of observables on energy and system size in this scan due to the phase transition of strongly interactingmatter and the possible existence of the CP [3]. Some hints of such behaviour have already been observedby the NA49 experiment [4].2. Multiplicity fluctuationsThe study of event-by-event fluctuations is one of the main tools that is applied to search for the criticalpoint. The strength of fluctuations of a given observable can be quantified by the moments of its distribution.Available online at www.sciencedirect.comNuclear Physics A 982 (2019) 835–8380375-9474/© 2018 Published by Elsevier B.V.www.elsevier.com/locate/nuclphysahttps://doi.org/10.1016/j.nuclphysa.2018.09.019This is an open access article under the CC BY-NC-ND license (http://creativecommons.org/licenses/by-nc-nd/4.0/).In this paper results on multiplicity fluctuations are presented in terms of the scaled variance, ω[N], that isconstructed from the first and second moments of the multiplicity distribution as ω[N] = 〈N2〉−〈N〉2〈N〉 , where〈· · ·〉 stands for the averaging over all events. The scaled variance is an intensive quantity which does notdepend on the volume of the system for an ideal Boltzmann gas in the grand canonical ensemble (GCE)or on the number of sources within models of independent sources such as the wounded nucleon model(WNM) [5].One can expect that ω[N] is sensitive to the existence of the CP as within the GCE it is proportionalto the isothermal compressibility that diverges in the vicinity of the CP [6], although this signal may beshadowed by significant contribution from volume fluctuations.The NA61/SHINE experiment obtained preliminary results on multiplicity fluctuations for primary nega-tively charged hadrons produced in strong and electromagnetic processes in forward energy selected Be+Be(0-5%) and Ar+Sc (0-0.2%) collisions and in inelastic p+p interactions. The selection of the most cen-tral events in A+A collisions was done using information from the NA61/SHINE forward calorimeter, thePSD. Transverse momenta of all charged hadrons were restricted to 0 < pT < 1.5 GeV/c and rapidities inthe center-of-mass system calculated under the pion mass assumption were restricted to 0 < yπ < ybeam.Moreover, the NA61/SHINE acceptance map [7] was applied. The results for Be+Be and Ar+Sc collisionswere not corrected for detector inefficiencies and trigger biases as simulations have shown that their ef-fect estimated using the GEANT3 package does not exceed 5%. However, the trigger bias modifies resultssignificantly for p+p interactions and, therefore, requires corrections described precisely in Ref. [8]. Thestatistical uncertainties were determined using the sub-sample method. Analysis of the systematic uncer-tainties is not finished but they are estimated to be smaller than 5%.The results for the dependence of multiplicity fluctuations on the mean number of wounded nucleons,〈W〉, are shown in Figure 1. A dotted line indicates the lower limit for ω[N] for A+A collisions within theWNM that is defined by the measurement for p+p interactions. One can see that these model predictionsare violated in Ar+Sc collisions. However, the scaled variance obtained for Ar+Sc collisions is consistentwith the statistical model, where ω[N] ≈ 0.9 for large volume systems [9]. Comparison with the EPOS1.99model predictions [10], in turn, shows a significant discrepancy in Be+Be collisions. The observed rapidchange of ω[N] when moving from lighter (p+p, Be+Be) to heavier (Ar+Sc) colliding systems can beinterpreted as the beginning of creation of large clusters of strongly interacting matter, e.g. as predicted inpercolation models [11, 12].Fig. 1. Dependence of ω[N] for negatively charged hadrons on the mean number of wounded nucleons 〈W〉 measured by theNA61/SHINE experiment (filled symbols) in comparison to the EPOS1.99 model predictions (open symbols).E. Andronov / Nuclear Physics A 982 (2019) 835–8388363. PT − N fluctuation measurementsIn order to minimize the influence of volume fluctuations strongly intensive observables are used insearch for the critical point [13, 14]:Δ[PT ,N] = 1〈N〉ω[pT ][〈N〉ω[PT ] − 〈PT 〉ω[N]], (1)Σ[PT ,N] = 1〈N〉ω[pT ][〈N〉ω[PT ] + 〈PT 〉ω[N] − 2(〈PTN〉 − 〈PT 〉〈N〉)], (2)where PT =∑Ni=1 pTi and ω[pT ] is the scaled variance of the inclusive pT spectrum.In recent measurements by the NA61/SHINE collaboration of the strongly intensive quantities Δ[PT ,N]and Σ[PT ,N] in p+p, Be+Be and Ar+Sc collisions no anomaly attributable to the CP was observed [15].The analysis was extended to studies of the pseudorapidity dependence of strongly intensive observables inorder to probe different values of baryochemical potential [16].In this paper new results were obtained for Be+Be collisions at 150A GeV/c selected for the smallest 8%of forward energies. Fluctuations were studied in 9 pseudorapidity intervals defined in the laboratory refer-ence frame. The forward edge of the intervals was fixed at 5.2 units of pseudorapidity, with the backwardedge changing from 3 up to 4.6 units. The choice of lower bounds was motivated by the small azimuthalangle acceptance at smaller pseudorapidities. The upper bound was introduced in order to suppress possiblequasi-diffractive or electromagnetic effects which become important at larger pseudorapidities. All the otheranalysis details are identical to the methods described in the previous section.Figure 2 shows preliminary results for the dependence of Δ[PT ,N] and Σ[PT ,N] on the width of thepseudorapidity interval and comparisons to the EPOS1.99 model [10] predictions. Both quantities changemonotonously for the data in contrast to the EPOS1.99 results for Δ[PT ,N] which show a minimum forintermediate width and lie significantly above the measurements. Another observation is that for smallerwindows these quantities approach unity (independent particle production limit) as the number of particlesin the interval gets small. Moreover, the inequalitiesΔ[PT ,N] < 1 and Σ[PT ,N] ≥ 1, previously observed forall studied systems at all collision energies [15], also hold when modifying the width of the pseudorapiditywindow of the measurement. In general, no traces of the possible critical point of strongly interacting matterare visible.window width0 0.5 1 1.5 2 2.5]N, T[PΔ0.40.60.811.2++h-hNA61/SHINE preliminary GeV/cABe, 0-8%, 1509Be+7NA61/SHINE, GeV/cABe, 0-8%, 1509Be+7EPOS1.99,window width0 0.5 1 1.5 2 2.5]N, T[PΣ0.9511.051.1 ++h-hNA61/SHINE preliminary GeV/cABe, 0-8%, 1509Be+7NA61/SHINE, GeV/cABe, 0-8%, 1509Be+7EPOS1.99,Fig. 2. Dependence of Δ[PT ,N] (left) and Σ[PT ,N] (right) on the width of the pseudorapidity window. Red squares are preliminaryNA61/SHINE measurements for 0-8% Be+Be collisions at 150A GeV/c. Blue band represents the EPOS1.99 model predictions.E. Andronov / Nuclear Physics A 982 (2019) 835–838 8374. Proton density fluctuations: intermittencyIn the grand canonical ensemble the correlation length diverges at the critical point and the systembecomes scale invariant [17]. In a pure critical system, intermittency in transverse momentum space can berevealed by the scaling of the Second Scaled Factorial Moments of protons as a function of bin size [18].For that purpose, a region of transverse momentum space is partitioned into M×M equal-size bins and thesemoments are defined as:F2(M) =〈 1M2∑M2i=1 ni(ni − 1)〉〈 1M2∑M2i=1 ni〉2 (3)where ni is the number of particles in the i-th bin. If the system exhibits critical fluctuations, F2(M) isexpected to scale with M, for large values of M, as a power-law F2(M) ∼ M2φ2 , where φ2 is the intermittencyindex.An intermittency analysis was performed for NA61/SHINE data on Be+Be collisions (0-10%) at 150AGeV/c beam momentum. No significant intermittency effect was observed, with an upper limit for protonsobeying critical fluctuations being of the order of 0.3%. This limit was estimated based on the CriticalMonte Carlo model predictions [19]. For more details see Ref. [20].5. AcknowledgmentsThis work is supported by the Russian Science Foundation under grant 17-72-20045.References[1] N. Abgrall, et al., NA61/SHINE facility at the CERN SPS: beams and detector system, JINST 9 (2014) P06005.[2] Z. Fodor, S. Katz, Critical point of QCD at finite T and mu, lattice results for physical quark masses, JHEP 0404 (2004) 050.[3] M. A. Stephanov, K. Rajagopal, E. V. Shuryak, Event-by-event fluctuations in heavy ion collisions and the QCD critical point,Phys.Rev. D60 (1999) 114028.[4] K. Grebieszkow for the NA49 Collab., Search for the critical point of strongly interacting matter in NA49, Nucl. Phys. A830(2009) 547C.[5] A. Bialas, M. Bleszynski, W. 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Search for the critical point by the NA61/SHINE experiment

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