Jagiellonian University Institute of Physics φ meson production in proton-proton collisions in the NA61/SHINE experiment at CERN SPS mgr Antoni Marcinek PhD thesis prepared in the Department of Hot Matter Physics under supervision of Prof. dr hab. Roman Płaneta Kraków, 2016 Oświadczenie Ja niżej podpisany Antoni Marcinek oświadczam, że przedłożona przeze mnie rozprawa doktorska pt. „φ meson production in proton-proton collisions in the NA61/SHINE experiment at CERN SPS” jest oryginalna i przedstawia wyniki badań wykonanych przeze mnie osobiście, pod kierunkiem prof. dr. hab. Romana Płanety. Pracę napisałem samodzielnie. Oświadczam, że moja rozprawa doktorska została opracowana zgodnie z Ustawą o prawie autorskim i prawach pokrewnych z dnia 4 lutego 1994 r. (Dziennik Ustaw 1994 nr 24 poz. 83 wraz z późniejszymi zmianami). Jestem świadom, że niezgodność niniejszego oświadczenia z prawdą ujaw- niona w dowolnym czasie, niezależnie od skutków prawnych wynikających z ww. ustawy, może spowodować unieważnienie stopnia nabytego na podsta- wie tej rozprawy. Kraków, dnia 01.07.2016 Abstract This thesis presents results on φ meson production in p + p collisions at CERN SPS energies. They are derived from data collected by the NA61/ SHINE experiment, by means of invariant mass spectra fits in φ → K+K− decay channel, using the so-called tag-and-probe method to remove bias due to inefficiency of kaon candidates selection with dE/dx. These results include double differential spectra (first for φ mesons at CERN SPS energies) of rapidity y and transverse momentum pT for beam momenta of 158 GeV/c and 80 GeV/c, as well as singly differential spectra of y or pT for beam momentum of 40 GeV/c. Additionally, y spectra integrated over pT were obtained from double differential spectra. Also total φ yields were determined by integration and extrapolation of y spectra and widths of these spectra along with yields at y = 0 were calculated from fits of these distributions with Gaussian functions. Results were compared with world data on φ meson production in p + p collisions showing consistency and superior accuracy. They served also as reference for Pb + Pb data on φ production, confirming and emphasizing earlier findings regarding phenomena in Pb + Pb. Finally, results were also compared with model predictions showing that none of considered models could describe properly all observables. 5 Streszczenie Praca przedstawia wyniki dotyczące produkcji mezonów φ w zderzeniach p + p przy energiach CERN SPS. Są one wyznaczone z danych zebranych przez eksperyment NA61/SHINE, przez dopasowania rozkładów masy nie- zmienniczej w kanale rozpadu φ → K+K−, przy wykorzystaniu tzw. metody tag-and-probe w celu usunięcia strat sygnału ze względu na niewydajność selekcji kaonów przez dE/dx. Wyniki obejmują podwójnie różniczkowe widma (pierwsze dla mezonów φ przy energiach CERN SPS) pospieszności y i pędu poprzecznego pT dla pędów wiązki 158 GeV/c i 80 GeV/c oraz pojedynczo różniczkowe widma y lub pT dla pędu wiązki 40 GeV/c. Dodatkowo, z rozkładów podwójnie róż- niczkowych, otrzymano widma y wycałkowane po pT . Wyznaczono również całkowite krotności φ przez całkowanie i ekstrapolację widm y, a także sze- rokości tych rozkładów i różniczkowe krotności w y = 0 z dopasowań tych widm funkcjami Gaussa. Wyniki porównano z danymi światowymi na temat produkcji mezonów φ w zderzeniach p + p, pokazując ich zgodność i znacznie większą dokład- ność. Posłużyły one także jako dane referencyjne dla danych dotyczących produkcji φ w Pb + Pb, potwierdzając i wzmacniając wcześniejsze wnioski na temat zjawisk w Pb + Pb. W końcu, wyniki zostały również porównane z przewidywaniami modelowymi pokazując, że żaden z rozważanych modeli nie jest w stanie poprawnie opisać wszystkich obserwabli. 6 Contents 1 Introduction 10 1.1 Motivation............................. 10 1.1.1 Constraints on hadron production models....... 10 1.1.2 Reference for Pb + Pb collision data.......... 12 1.2 Phenomena associated with φ mesons.............. 12 1.3 World measurements of φ production.............. 13 1.4 Structure of this thesis...................... 14 2 The NA61/SHINE experiment 15 2.1 Physics programme........................ 15 2.2 Beams............................... 18 2.3 Detector components....................... 21 2.3.1 Beam detectors and the trigger............. 21 2.3.2 Targets.......................... 23 2.3.3 Time Projection Chambers................ 24 2.3.4 Other components.................... 28 3 dE/dx calibration 29 3.1 Energy loss of an ionizing particle................ 29 3.2 Corrections to cluster charges.................. 31 3.2.1 Corrections derived from external information..... 32 3.2.2 Corrections inferred from measured charges...... 33 3.3 Track dE/dx............................ 34 3.4 Known problems......................... 35 4 Analysis methodology 38 4.1 Goal definition.......................... 38 4.2 Invariant mass method...................... 39 4.3 Data selection........................... 40 4.3.1 The data — experimental and Monte Carlo...... 40 4.3.2 Cuts............................ 42 7 4.4 Signal extraction......................... 46 4.4.1 Phase space binning................... 46 4.4.2 Single invariant mass spectrum............. 48 4.4.3 Tag-and-probe method.................. 52 4.4.4 Fitting strategy...................... 54 4.5 Corrections............................ 58 4.5.1 Overview......................... 58 4.5.2 Correction for off-target interactions.......... 60 4.5.3 Correction due to integration cut-off.......... 62 4.5.4 Monte Carlo correction.................. 65 4.6 Systematic studies and optimizations.............. 78 4.6.1 Background distortions.................. 79 4.6.2 Resolution model study................. 83 4.6.3 Signal parametrization discussion............ 87 4.6.4 Systematic uncertainties due to constraints on signal shape parameters..................... 90 4.6.5 Tag-and-probe systematics................ 92 4.6.6 Systematic uncertainties related to event & track qual- ity cuts.......................... 95 4.6.7 Monte Carlo correction averaging............ 99 4.6.8 Summary of uncertainties................ 110 5 Results and their discussion 113 5.1 Methods for derived results................... 113 5.1.1 Primary vs derived results................ 113 5.1.2 Spectral functions and parameters............ 114 5.1.3 Summation and extrapolation of spectra........ 116 5.2 Double differential analysis.................... 116 5.2.1 Analysis binnings..................... 117 5.2.2 Double differential spectra................ 117 5.2.3 Rapidity spectra..................... 119 5.2.4 Transverse mass spectra at midrapidity......... 121 5.2.5 Comparison with NA49 transverse mass spectrum... 122 5.3 Single differential analysis.................... 123 5.4 These results as reference for Pb + Pb............. 125 5.4.1 Width of rapidity spectra................ 125 5.4.2 Multiplicity ratios..................... 126 5.5 Comparison with world data and models............ 128 5.5.1 World data........................ 128 5.5.2 Models........................... 129 8 6 Summary and conclusions 131 Acknowledgements 133 A Basic definitions 134 A.1 Conventions used in this work.................. 134 A.2 Kinematic variables........................ 135 B Phase space of kaons from φ 137 C Tag-and-probe with variable ε 140 C.1 Derivation of formulas for Nt and Np .............. 140 C.2 ε+ and ε− distribution properties................ 141 C.3 Bias of the tag-and-probe method................ 142 Bibliography 144 9 Chapter 1 Introduction 1.1 Motivation Motivation of study of φ meson production in proton-proton collisions is twofold. First, it is useful in itself to constrain hadron production models. Second, it may serve as reference for lead-lead measurements at the same energies to infer about strangeness-related phenomena in heavy ion collisions. 1.1.1 Constraints on hadron production models The matter which surrounds us is built of atoms, which are in turn built of nuclei and electrons. Atomic nuclei are built of neutrons and protons, which are hadrons — particles built of quarks and gluons. Hadrons are divided into two groups: mesons having even number of valence quarks (in most cases two) and baryons with odd number of valence quarks (in most cases three). The valence quarks are those which contribute to quantum numbers of hadrons in contrast to sea quarks that are virtual — they are continuously created in quark-antiquark (qq¯) pairs from gluons and instantly annihilated still within hadrons. The theory which describes how hadrons, and therefore the surrounding matter, are bound together by the so-called strong interactions of quarks and gluons, mediated by gluons, is quantum chromodynamics (QCD). The problem of this theory is, that actually little can be directly calcu- lated from its equations. The standard technique of quantum mechanics or quantum field theory, the perturbation theory, is applicable only in the high energy or high momentum transfer domain, where the strong interaction be- comes relatively weak (what is called asymptotic freedom of QCD). In terms of experimental observables it corresponds to high transverse momenta — the so-called hard regime. However, the bulk of hadron production in nu- 10 Table 1.1: Properties of the φ meson relevant for the analysis. Numbers are taken from Ref. [7]. BR() stands for branching ratio for the decay channel in parentheses. mass [MeV] width [MeV] BR(φ → K+K−) [%] 1019.461 ± 0.019 4.266 ± 0.031 48.9 ± 0.5 clear collisions, as well as many