-proton interactions and onset of deconfinement

A. Aduszkiewicz15, E.V. Andronov21, T. Antici´ c´ 3, V. Babkin19, M. Baszczyk13, S. Bhosale10,

A. Blondel23, M. Bogomilov2, A. Brandin20, A. Bravar23, W. Brylinski´ 17, J. Brzychczyk12,

M. Buryakov19, O. Busygina18, A. Bzdak13, H. Cherif6, M. Cirkovi´ c´ 22, M. Csanad 7,

J. Cybowska17, T. Czopowicz17, A. Damyanova23, N. Davis10, M. Deliyergiyev9, M. Deveaux6,

A. Dmitriev 19, W. Dominik15, P. Dorosz13, J. Dumarchez4, R. Engel5, G.A. Feofilov21, L. Fields24,

Z. Fodor7,16, A. Garibov1, M. Ga´zdzicki6,9, O. Golosov20, M. Golubeva18, K. Grebieszkow17,

F. Guber18, A. Haesler23, S.N. Igolkin21, S. Ilieva2, A. Ivashkin18, S.R. Johnson25, K. Kadija3,

E. Kaptur14, N. Kargin20, E. Kashirin20, M. Kiełbowicz10, V.A. Kireyeu19, V. Klochkov6,

V.I. Kolesnikov19, D. Kolev2, A. Korzenev23, V.N. Kovalenko21, K. Kowalik11, S. Kowalski14,

M. Koziel6, A. Krasnoperov19, W. Kucewicz13, M. Kuich15, A. Kurepin18, D. Larsen12,

A. László7, T.V. Lazareva21, M. Lewicki16, K. Łojek12, B. Łysakowski14, V.V. Lyubushkin19,

M. Mackowiak-Pawłowska´ 17, Z. Majka12, B. Maksiak11, A.I. Malakhov19, D. Manic´ 22,

A. Marchionni24, A. Marcinek10, A.D. Marino25, K. Marton7, H.-J. Mathes5, T. Matulewicz15,

V. Matveev19, G.L. Melkumov19, A.O. Merzlaya12, B. Messerly26, Ł. Mik13, S. Morozov18,20,

S. Mrówczynski´ 9, Y. Nagai25, M. Naskr˛et16, V. Ozvenchuk10, V. Paolone26, M. Pavin4,3,

O. Petukhov18, R. Płaneta12, P. Podlaski15, B.A. Popov19,4, B. Porfy7, M. Posiadała-Zezula15,

D.S. Prokhorova21, D. Pszczel11, S. Puławski14, J. Puzovic´ 22, M. Ravonel23, R. Renfordt6,

E. Richter-W˛as12, D. Röhrich8, E. Rondio11, M. Roth5, B.T. Rumberger25, M. Rumyantsev19,

A. Rustamov1,6, M. Rybczynski9, A. Rybicki10, A. Sadovsky18, K. Schmidt14, I. Selyuzhenkov20,

A.Yu. Seryakov21, P. Seyboth9, M. Słodkowski17, P. Staszel12, G. Stefanek9, J. Stepaniak11,

1 M. Strikhanov20, H. Ströbele6, T. Šuša3, A. Taranenko20, A. Tefelska17, D. Tefelski17,

V. Tereshchenko19, A. Toia6, R. Tsenov2, L. Turko16, R. Ulrich5, M. Unger5, F.F. Valiev21,

D. Vebericˇ 5, V.V. Vechernin21, A. Wickremasinghe26, Z. Włodarczyk9, A. Wojtaszek-Szwarc9,

O. Wyszynski´ 12, L. Zambelli4,1, E.D. Zimmerman25, and R. Zwaska24

1National Nuclear Research Center, Baku, Azerbaijan

2Faculty of Physics, University of Sofia, Sofia, Bulgaria

3Ruder¯ Boškovic´ Institute, Zagreb, Croatia

4LPNHE, University of Paris VI and VII, Paris, France

5Karlsruhe Institute of Technology, Karlsruhe, Germany

6University of Frankfurt, Frankfurt, Germany

7Wigner Research Centre for Physics of the Hungarian Academy of Sciences, Budapest, Hungary

8University of Bergen, Bergen, Norway

9Jan Kochanowski University in Kielce, Poland

10Institute of Nuclear Physics, Polish Academy of Sciences, Cracow, Poland

11National Centre for Nuclear Research, Warsaw, Poland

12Jagiellonian University, Cracow, Poland

13AGH - University of Science and Technology, Cracow, Poland

14University of Silesia, Katowice, Poland

15University of Warsaw, Warsaw, Poland

16University of Wrocław, Wrocław, Poland

17Warsaw University of Technology, Warsaw, Poland

2 18Institute for Nuclear Research, Moscow, Russia

19Joint Institute for Nuclear Research, Dubna, Russia

20National Research Nuclear University (Moscow Engineering Physics Institute), Moscow, Russia

21St. Petersburg State University, St. Petersburg, Russia

22University of Belgrade, Belgrade, Serbia

23University of Geneva, Geneva, Switzerland

24Fermilab, Batavia, USA

25University of Colorado, Boulder, USA

26University of Pittsburgh, Pittsburgh, USA

3 Strongly interacting matter at very high densities is expected to be in a state of quasi-free

quarks and gluons - the quark-gluon plasma. Such form of matter likely existed in the first

moments after the Big Bang. This hypothesis motivates experimental and theoretical studies

of phases and transitions of strongly interacting matter. In particular, the study of high en-

ergy collisions between two atomic nuclei offers the possibility to address these issues in well

controlled laboratory experiments, which are now conducted at the European Laboratory

for Particle Physics (CERN, the SPS and LHC accelerators) as well as at the Brookhaven

National Laboratory (the RHIC accelerator). The study of the transition to the quark-gluon

plasma in high energy nuclear collisions by varying collision energy and nuclear mass num-

ber is the main focus of the NA61/SHINE experiment at the CERN SPS. This paper reports

new results on proton-proton interactions which uncover similarities, and at the same time

confirm with increased precision previously known qualitative differences, with results on

-lead collisions - the latter showing evidence for the transition to the quark-gluon plasma

at the low SPS energies. Recent results on p+p interactions serve as an important reference with respect to which new phenomena are searched for in strongly interacting matter cre-

ated in collisions of heavy nuclei. NA61/SHINE results presented here allow to study the

question whether effects related to the phase transition are also present to some degree in

proton-proton collisions already at SPS energies. Interestingly, results on proton-proton in-

teractions with high particle multiplicity at the CERN LHC in fact suggest the creation of

strongly interacting matter in this class of collisions. The NA61/SHINE results demonstrate

clearly that understanding particle production in proton-proton interactions, and, in general

4 in collisions of small atomic nuclei, is an essential objective of heavy-ion physics today.

One of the important issues of contemporary physics is the understanding of strong interactions

and, in particular, the study of the properties of strongly interacting matter in equilibrium. What

are the phases of this matter and what do the transitions between them look like? At sufficiently

high energy densities one expects a transition from the phase in which quarks and gluons are

confined in hadrons to the quark-gluon plasma - a state of quasi-free quarks and gluons. These

questions motivate broad experimental and theoretical efforts since about 50 years. The study of

high energy collisions between two atomic nuclei offers the unique possibility to address these

issues in well controlled laboratory experiments. Rich experimental results on central Pb+Pb and

Au+Au collisions from experiments at the Alternating Gradient Synchrotron (BNL), the Super

Proton Synchrotron (CERN), the Relativistic Heavy Ion Collider (BNL) and the Large Hadron

Collider (CERN) lead to two main observations:

(i) The data from the lowest to the highest collision energies indicate that a system of strongly

interacting particles close to, at least local, equilibrium is created. At freeze-out the system

occupies a volume which is much larger than the volume of an individual hadron. These

findings are based on the failure of the Wounded Nucleon Model 1 - the simplest proxy for

microscopic dynamical models - and the success of statistical 2 and hydrodynamical models 3.

Thus, one concludes that strongly interacting matter is created in heavy-ion collisions.

(ii) Several basic hadron production properties rapidly change their dependence on collision energy

in a common, narrow energy interval, 7-12 GeV 4–6. This behaviour indicates 7 the beginning

5 of the creation of a quark-gluon plasma with increasing collision energy. It is referred to as

the onset of deconfinement. Models which do not assume the onset of deconfinement cannot

reproduce the data, for a review see Ref. 6.

Proton-proton interactions played a special role in these two discoveries. It was commonly assumed

that neither of the two effects is present in these interactions and thus experimental results on

p+p interactions served as an important reference with respect to which new physics in heavy-ion

collisions was searched for. Strong, qualitative deviations of data on heavy-ion collisions from the

p+p reference as well as the agreement of measurements in heavy-ion collisions with predictions of

models assuming creation of strongly interacting matter and its phase transition to a quark-gluon

plasma at intermediate SPS collision energies are convincing arguments for the two discoveries.

The most popular models of p+p interactions are qualitatively different from the most popular

models of heavy-ion collisions. The former are resonance-string models 8 in which hydrodynamic

expansion of the matter is replaced by exiciting resonances and/or stretching a string between

colour charges of quarks and/or di-quarks. The assumption of statistical hadronization of matter

is replaced by dynamical modelling of resonance and/or string decays as well as quark/gluon

fragmentation into hadrons. Since the early days the different modelling of p+p interactions and

heavy-ion collisions was supported by qualitative disagreement of the p+p data with predictions

of statistical and hydrodynamical models - large particle multiplicity fluctuations and a power-law

9 shape of transverse momentum spectra at high pT . On the other hand, the different modelling

has been questioned by striking agreement of the p+p data with other predictions of statistical and

hydrodynamical models - mean multiplicities of hadrons follow a pattern predicted by statistical

6 models and transverse mass spectra at low and intermediate pT are close to statistical approach expectations 2, 10. Moreover, recent LHC data on the azimuthal angle distribution of charged particles in high multiplicity p+p interactions 8, 11 show anisotropies up to now observed only in heavy-ion collisions and attributed to the hydrodynamical expansion of matter 12. This suggests that the first discovery of heavy-ion physics - the creation of strongly interacting matter - may also extend to p+p interactions at LHC energies at sufficiently high multiplicity.

This paper addresses the relation between the second discovery of heavy-ion physics - the discovery of the onset of deconfinement - and data on p+p interactions. New experimental insight is possible thanks to recent results on p+p interactions from NA61/SHINE at the CERN SPS 13, 14. The data cover the energy range in which experimental effects attributed to the onset of deconfinement in heavy-ion collisions are located. Furthermore, recent data on p+p interactions at LHC energies allow to establish the collision energy dependence of bulk hadron production properties in the energy range in which the quark gluon plasma is likely to be created in heavy-ion collisions. The new p+p data uncover qualitative similarities between the collision energy dependence measured for p+p interactions and for heavy-ion collisions. At the same time qualitative differences between the p+p and heavy-ion results observed previously are confirmed with higher precision and significance by the NA61/SHINE p+p measurements.

The recent NA61/SHINE measurements of spectra of π± ,K±, p and p¯ produce in p+p interactions 13 allow to significantly extend and improve the world data on the K+/π+ ratio 15, 16 and the inverse slope parameter T of transverse mass spectra of 17.

7 The energy dependence of the K+/π+ ratio at mid-rapidity and in the full phase-space for

inelastic p+p interactions is shown in Fig. 1 top-left and top-right, respectively. The results for

heavy-ion collisions are plotted for comparison. The new NA61/SHINE data on p+p interactions

at the CERN SPS energies are shown together with the world data 15, 16, 18–20. Data on the mid-

rapidity ratio (the top-left plot) cover the range from the low SPS energy to the LHC energies. For

comparison the mid-rapidity plot includes also p+p data of other experiments on the full phase-space √ ratio. The p+p data on the full phase-space ratio (the top-right plot) extends only to sNN ≈ 50 GeV, whereas the heavy-ion data reach 200 GeV. The energy dependence of the mid-rapidity and full

phase-space ratio in inelastic p+p interactions is similar. This seems to be also true for heavy-ion

collisions. The collision energy dependence of the K+/π+ ratio in heavy-ion collisions shows the

so-called horn structure. Following a fast rise the ratio passes through a maximum in the SPS range

and then settles to a plateau value at higher energies. The K+/π+ ratio at SPS energies was shown

to be a good measure of the strangeness to entropy ratio 6 which is different in the confined phase

(hadrons) and the QGP (quarks, anti-quarks and gluons). The collision energy dependence of the

K+/π+ ratio in inelastic p+p interactions is different from the one in heavy-ion collisions. First of

all, the ratio is smaller in p+p interactions than in Pb+Pb and Au+Au collisions and does not show

the horn structure. The suppression factor decreases with increasing energy, at LHC it is only about

0.9. Starting from the threshold energy the ratio steeply increases to reach a plateau at the CERN

SPS energies. The plateau is followed by a weak increase towards the LHC energies. Notably

the beginning of the plateau in p+p interactions coincides with the horn maximum in heavy-ion

collisions.

8 Fig. 1. Energy dependence of the K+/π+ ratio in inelastic p+p interactions as well as

central Pb+Pb and Au+Au collisions at mid-rapidity (top-left) and in the full phase-space

(top-right). Energy dependence of the inverse slope parameter T of transverse mass spec-

tra at mid-rapidity for K− (bottom-left) and K+ (bottom-right) mesons.

〉 0) p+p Pb+PbAu+Au ≈ +

π SPS NA61/SHINE

(y 〈 WORLD(p+p) + /

π AGS 〉 /

+

+ SPS NA49

K RHIC 0.2 K 0.2 〈

0.1 0.1 p+p Pb+Pb Au+Au SPS(NA61 p+p) WORLD(p+p, 4π) AGS SPS(NA49) RHIC LHC(ALICE) 0 0 1 102 104 1 10 102

sNN (GeV) sNN (GeV)

- 400 K 400 K+ y ≈ 0 y ≈ 0 T (MeV) T (MeV)

200 200 Pb+Pb Au+Au p+p Pb+Pb Au+Au p+p SPS(NA61 p+p) SPS(NA61 p+p) WORLD(p+p) WORLD(p+p) AGS AGS SPS(NA49) SPS(NA49) RHIC RHIC LHC(ALICE) LHC(ALICE) 1 102 104 1 102 104

sNN (GeV) sNN (GeV)

The NA61/SHINE results for inelastic p+p interactions are compared with the world data on p+p interactions as

well as central Pb+Pb and Au+Au collisions 17, 19, 21, 22.

9 The energy dependence of the inverse slope parameter of transverse mass spectra of K+ and K−

mesons produced at mid-rapidity in inelastic p+p interactions is presented in Fig. 2 bottom-left and

bottom-right, respectively. The NA61/SHINE data 13 are compared to the world data for p+p and

heavy-ion collisions 17, 18, 20, 21. The collision energy dependence of the T parameter in heavy-ion

collisions shows the so-called step structure. Following a fast rise the T parameter passes through a

stationary region (or even a weak minimum for K−), which starts at the low SPS energies, and then

(above the top SPS energy) enters a domain of a steady increase. The increase continues up to the

top LHC energy. The collision energy dependence of the T parameter in inelastic p+p interactions

is surprisingly similar to the one for central Pb+Pb and Au+Au collisions. The main difference is

that the T parameter in p+p interactions is significantly smaller than for heavy-ion collisions. It

seems that the plateau region is broader in p+p interactions than in central heavy-ion collisions.

In Fig. 2 the results on p+p interactions presented in Fig. 1 are compared with predictions of a

resonance-string model, UrQMD 23. The model does not reproduce the collision energy dependence

of neither the K+/π+ ratio nor the inverse slope parameter of transverse mass spectra of charged

kaons. To estimate the transition energy between a fast rise at low energies and a slower increase

at high energies two straight lines were fitted to the p+p data (see Fig. 2). The low energy line was constrained by the threshold energy for production. The fitted transition energy is

8.3 ± 0.6 GeV, 7.70 ± 0.14 GeV, 6.5 ± 0.5 GeV and 7.9 ± 0.2 GeV, for the K+/π+, hK+i/hπ+i

ratios and T(K−), T(K+), respectively. They are close to each other and close to the energy of the

onset of deconfinement, ≈ 8 GeV, established by the results from central Pb+Pb collisions (see

Fig. 1).

10 The similarity of the UrQMD model results and the measurements suggest that the step is likely due to a transition from resonance dominated to string dominated particle production mechanism. Thus the step cannot be considered a unique feature of the onset of deconfinement although, of course, it is consistent with it.

Results on multiplicity fluctuations allow to significantly limit the spectrum of model ap- proaches to p+p interactions and heavy-ion collisions 24. For this reason the energy dependence of the scaled variance of multiplicity fluctuations for inelastic p+p interactions and heavy-ion collisions 14 is presented in Fig. 3. The scaled variance ω[N] is shown separately for negatively (left) and positively (right) charged hadrons in the largest common acceptance of the p+p and heavy-ion data 14. The acceptance is determined for each energy independently. The results for negatively and positively charged hadrons are influenced significantly less by decays of resonances than the results for all charged hadrons 25. For heavy-ion collisions ω[N] is weakly, if at all, dependent on collision energy. Moreover in the full SPS energy range it remains below one - the value of the scaled variance for the Poisson distribution. One concludes that the collision energy dependence of

ω[N] in inelastic p+p interactions is qualitatively different. A monotonic increase with increasing energy is observed. The scaled variance crosses unity at intermediate SPS energies. At the top SPS energy it is larger than one. As in the case of heavy-ion collisions, the results for negatively and positively charged hadrons are similar.

The results on inelastic p+p interactions presented here are puzzling. On one hand, multiplicity

fluctuations are in qualitative disagreement with predictions of statistical models. This provides an

11 additional argument in favour of the old paradigm of different physics in heavy-ion collisions and

inelastic p+p interactions. On the other hand, the unexpected qualitative similarity of the collision

energy dependence of the T parameter in p+p interactions and heavy-ion collisions uncovered in

this paper suggests that this feature may not be a unique signature of the onset of deconfinement,

or alternatively, effects related to the onset of deconfinement are present in p+p interactions at the

CERN SPS energies. This asks for a unified approach in which both reactions could be interpreted.

Such an approach would make it possible to clarify whether the onset of deconfinement is, or is not,

a universal feature of both small and large colliding systems.

In summary, new results of NA61/SHINE on the collision energy dependence of the K+/π+

ratio and the inverse slope parameter of kaon mT spectra in inelastic p+p interactions are presented

together with the compilation of the world data. The p+p data are compared with the corresponding

results on central Pb+Pb and Au+Au collisions. The comparison uncovers similarities between the

collision energy dependence in p+p interactions and central heavy ion collisions, namely a rapid √ change at the same energy range ( sNN). At the same time they confirm with higher significance

previously reported qualitative difference in multiplicity fluctuations.

Clearly, understanding particle production in inelastic p+p interactions, and, in general in

collisions of small atomic nuclei, is one of the key objectives of heavy-ion physics today.

Acknowledgements We would like to thank the CERN PH, BE and EN Departments for the strong support

of NA61. This work was supported by the Hungarian Scientific Research Fund (grants OTKA 68506 and

71989), the János Bolyai Research Scholarship of the Hungarian Academy of Sciences, the Polish Ministry

12 of Science and Higher Education (grants 667/N-CERN/2010/0, NN 202 48 4339 and NN 202 23 1837), the

Polish National Center for Science (grants 2011/03/N/ST2/03691, 2012/04/M/ST2/00816 and 2013/11/N/

ST2/03879), the Foundation for Polish Science — MPD program, co-financed by the European Union within the European Regional Development Fund, the Federal Agency of Education of the Ministry of Education and Science of the Russian Federation (SPbSU research grant 11.38.193.2014), the Russian Academy of

Science and the Russian Foundation for Basic Research (grants 08-02-00018, 09-02-00664 and 12-02-

91503-CERN), the Ministry of Education, Culture, Sports, Science and Technology, Japan, Grant-in-Aid for

Scientific Research (grants 18071005, 19034011, 19740162, 20740160 and 20039012), the German Research

Foundation (grant GA 1480/2-2), the EU-funded Marie Curie Outgoing Fellowship, Grant PIOF-GA-2013-

624803, the Bulgarian Nuclear Regulatory Agency and the Joint Institute for Nuclear Research, Dubna

(bilateral contract No. 4418-1-15/17), Ministry of Education and Science of the Republic of Serbia (grant

OI171002), Swiss Nationalfonds Foundation (grant 200020117913/1) and ETH Research Grant TH-01 07-3.

1. Bialas, A., Bleszynski, M. & Czyz, W. Multiplicity Distributions in Nucleus-Nucleus Collisions

at High-Energies. Nucl. Phys. B111, 461 (1976).

2. Becattini, F. An Introduction to the Statistical Hadronization Model. In International School

on Quark-Gluon Plasma and Heavy Ion Collisions: past, present, future Villa Gualino, Torino,

Italy, December 8-14, 2008 (2009). 0901.3643.

3. Florkowski, W. Phenomenology of Ultra-Relativistic Heavy-Ion Collisions (2010).

4. Afanasiev, S. et al. Energy dependence of and kaon production in central Pb + Pb collisions.

Phys. Rev. C66, 054902 (2002).

13 5. Alt, C. et al. Pion and kaon production in central Pb + Pb collisions at 20-A and 30-A-GeV:

Evidence for the onset of deconfinement. Phys. Rev. C77, 024903 (2008).

6. Gazdzicki, M., Gorenstein, M. & Seyboth, P. Onset of deconfinement in nucleus-nucleus

collisions: Review for pedestrians and experts. Acta Phys.Polon. B42, 307–351 (2011).

1006.1765.

7. Gazdzicki, M. & Gorenstein, M. On the Early Stage of Nucleus–Nucleus Collisions. Acta Phys.

Pol. B30, 2705 (1999).

8. Andersson, B., Gustafson, G., Ingelman, G. & Sjostrand, T. Parton Fragmentation and String

Dynamics. Phys. Rept. 97, 31–145 (1983).

9. Begun, V. V., Gazdzicki, M. & Gorenstein, M. I. Power Law in Micro-Canonical Ensemble

with Scaling Volume Fluctuations. Phys. Rev. C78, 024904 (2008). 0804.0075.

10. Hagedorn, R. Statistical thermodynamics of strong interactions at high-energies. Nuovo Cim.

Suppl. 3, 147–186 (1965).

11. Chatrchyan, S. et al. Observation of long-range near-side angular correlations in proton-lead

collisions at the LHC. Phys.Lett. B718, 795–814 (2013). 1210.5482.

12. Bozek, P. & Broniowski, W. Theory of pp/pA/small systems. PoS LHCP2016, 116 (2016).

13. Aduszkiewicz, A. et al. Measurements of π± ,K± , p and p¯ spectra in proton-proton interactions

at 20, 31, 40, 80 and 158 GeV/c with the NA61/SHINE spectrometer at the CERN SPS.

European Physical Journal C77, 671 (2017). 1705.02467.

14 14. Aduszkiewicz, A. et al. Multiplicity and transverse momentum fluctuations in inelastic pro-

ton–proton interactions at the CERN . Eur. Phys. J. C76, 635 (2016).

1510.00163.

15. Gazdzicki, M. & Roehrich, D. Pion multiplicity in nuclear collisions. Z.Phys. C65, 215 (1995).

16. Gazdzicki, M. & Rohrich, D. Strangeness in nuclear collisions. Z.Phys. C71, 55–64 (1996).

hep-ex/9607004.

17. Kliemant, M., Lungwitz, B. & Gazdzicki, M. Energy dependence of transverse mass spectra of

kaons produced in p + p and p + anti-p interactions: A Compilation. Phys.Rev. C69, 044903

(2004). hep-ex/0308002.

18. Arsene, I. et al. Centrality dependent particle production at y=0 and y 1 in Au + Au collisions

at s(NN)**(1/2) = 200-GeV. Phys.Rev. C72, 014908 (2005). nucl-ex/0503010.

√ 19. Aamodt, K. et al. Production of , kaons and in pp collisions at s = 900 GeV

with ALICE at the LHC. Eur.Phys.J. C71, 1655 (2011). 1101.4110.

√ 20. Abelev, B. et al. Pion, Kaon, and Proton Production in Central Pb–Pb Collisions at sNN = 2.76

TeV. Phys.Rev.Lett. 109, 252301 (2012). 1208.1974.

21. Abelev, B. et al. Systematic Measurements of Identified Particle Spectra in pp,d+ Au and

Au+Au Collisions from STAR. Phys.Rev. C79, 034909 (2009). 0808.2041.

15 22. Abelev, B. B. et al. Production of charged pions, kaons and protons at large transverse √ momenta in pp and Pb–Pb collisions at sNN =2.76 TeV. Phys.Lett. B736, 196–207 (2014).

1401.1250.

23. Bleicher, M. et al. Relativistic hadron hadron collisions in the ultrarelativistic quantum

molecular dynamics model. J.Phys. G25, 1859–1896 (1999). hep-ph/9909407.

24. Konchakovski, V. P., Hauer, M., Gorenstein, M. I. & Bratkovskaya, E. L. Particle Number

Fluctuations and Correlations in Nucleus-Nucleus Collisions. J. Phys. G36, 125106 (2009).

0906.3229.

25. Begun, V. V. et al. Multiplicity fluctuations in relativistic nuclear collisions: Statistical model

versus experimental data. Phys. Rev. C76, 024902 (2007). nucl-th/0611075.

26. Alt, C. et al. Energy Dependence of Multiplicity Fluctuations in Heavy Ion Collisions at the

CERN SPS. Phys. Rev. C78, 034914 (2008).

16 Fig. 2. Energy dependence of the K+/π+ ratio in inelastic p+p interactions at mid-rapidity

(top-left) and in the full phase-space (top-right). Energy dependence of the inverse slope pa-

rameter T of transverse mass spectra at mid-rapidity for K− (bottom-left) and K+ (bottom-

right) mesons. 〉

0) + ≈ π

〈 (y / + 〉

π + / + K K 〈 0.1 0.1

p+p p+p SPS(NA61 p+p) SPS(NA61 p+p) RHIC WORLD(p+p) LHC(ALICE) UrQMD 3.4 UrQMD 3.4 Fit Fit 0 0 1 102 104 1 102 104

sNN (GeV) sNN (GeV)

K- K+ y ≈ 0 y ≈ 0 T (MeV) T (MeV)

200 200

p+p p+p SPS(NA61 p+p) SPS(NA61 p+p) 100 RHIC 100 RHIC LHC(ALICE) LHC(ALICE) ISR ISR UrQMD 3.4 UrQMD 3.4 Fit Fit 1 102 104 1 102 104

sNN (GeV) sNN (GeV)

The data are compared with predictions of the resonance-string model, UrQMD 23, and fitted by two straight lines.

Only statistical uncertainties are shown.

17 Fig. 3. Collision energy dependence of the scaled variance of the multiplicity distribution of charged hadrons for inelastic p+p interactions and most central Pb+Pb collisions.

-- + [N] h [N] NA49--B acceptance h ω ω p+p (NA61/SHINE) 1.2 1.2 Pb+Pb 1% (NA49)

1 1

0.8 0.8

5 10 15 20 5 10 15 20

sNN (GeV) sNN (GeV)

Collision energy dependence of the scaled variance of the multiplicity distribution of negatively (left) and positively

(right) charged hadrons for inelastic p+p interactions 14 measured by NA61/SHINE and and the 1% most central

Pb+Pb collisions 26 from NA49 in the common acceptance (NA49-(B) 14). Statistical uncertainties are smaller than a symbol size, systematic uncertainties are shown by shaded bands.

18