Report series ISSN 0284 - 2769 of SE9900247 THE SVEDBERG LABORATORY and \ DEPARTMENT OF RADIATION SCIENCES UPPSALA UNIVERSITY Box 533, S-75121 Uppsala, Sweden http://www.tsl.uu.se/ TSL/ISV-99-0204 February 1999 Charm and Strange Quark Contributions to the Proton Structure Kristel Torokoff1 Dept. of Radiation Sciences, Uppsala University, Box 535, S-751 21 Uppsala, Sweden Abstract: The possibility to have charm and strange quarks as quantum mechanical fluc- tuations in the proton wave function is investigated based on a model for non-perturbative QCD dynamics. Both hadron and parton basis are examined. A scheme for energy fluctu- ations is constructed and compared with explicit energy-momentum conservation. Resulting momentum distributions for charniand_strange quarks in the proton are derived at the start- ing scale Qo f°r the perturbative QCD evolution. Kinematical constraints are found to be important when comparing to the "intrinsic charm" model. Master of Science Thesis Linkoping University Supervisor: Gunnar Ingelman, Uppsala University 1 kuldsepp@tsl .uu.se 30-37 Contents 1 Introduction 1 2 Standard Model 3 2.1 Introductory QCD 4 2.2 Light-cone variables 5 3 Experiments 7 3.1 The HERA machine 7 3.2 Deep Inelastic Scattering 8 4 Theory 11 4.1 The Parton model 11 4.2 The structure functions 12 4.3 Perturbative QCD corrections 13 4.4 The DGLAP equations 14 5 The Edin-Ingelman Model 15 6 Heavy Quarks in the Proton Wave Function 19 6.1 Extrinsic charm 19 6.2 Intrinsic charm 20 6.3 Hadronisation 22 6.4 The El-model applied to heavy quarks 23 6.4.1 The hadron basis 24 6.4.2 The parton basis 25 7 Energy Fluctuation in Hadron Basis 25 7.1 Kinematics 26 7.2 Detailed description of the method 28 7.3 Constraints 29 8 Energy Fluctuation in Parton Basis 30 8.1 Kinematics 30 8.2 Constraints 31 9 Energy Conservation in Hadron Basis 31 9.1 Kinematics 31 9.2 Constraints 33 10 Energy Conservation in Parton Basis 33 10.1 Kinematics 33 10.2 Constraints 34 11 The Momentum Fraction x and Bjorken Scaling Variable XB 34 11.1 General definition of x and XB 34 11.2 The relationship of x and XB in the methods 35 12 Overview of the Methods 36 12.1 The method with energy fluctuation 36 12.2 The method with energy conservation 37 13 Results on Charm 37 13.1 Internal model quantities 37 13.2 Charm quark momentum distributions 39 14 Discussion 41 14.1 The credibility of the methods 41 14.2 The capability of the methods 43 15 Strangeness 44 16 Results on Strange Quarks 45 16.1 Internal model quantities 45 16.2 Strange quark momentum distributions 45 16.3 Discussion 46 17 Conclusions 47 "I ca'n't believe that}" said Alice. "Ca'n't you?" the Queen said in a pitying tone. "Try again: draw a long breath, and shut your eyes." Alice laughed. "There is no use trying," she said, "one ca'n't believe impossible things." "I daresay you haven't had much practice," said the Queen. Why, sometimes I've believed as many as six impossible things before breakfast." Lewis Carroll 1 Introduction The first experimental evidence that the proton has an internal structure was obtained in 1969 at Stanford Linear Accelerator Center (SLAC) [1]. Since then many high energy physics experiments have been performed and shown that the proton is a bound state of quarks. The valence quarks (two up and one down quark) give the proton its characteristic quantum numbers. A new theory of strong interactions, Quantum ChromoDynamics (QCD), has been developed, where the interaction between quarks is mediated by the field quanta called gluons. The proton, once thought to be a simple pointlike particle is found to have a complex internal structure. As a quantum mechanical particle, the proton may fluctuate in any way as long as its quantum numbers are conserved. Described in a hadron basis the proton may fluctuate into a baryon (a three quark bound state) and a meson (a bound state of a quark and an anti-quark), in parton basis additional quark anti-quark pairs are considered. The life-time of a fluctuation is given by the Heisenberg uncertainty relation, At ~ -^. Thus, the smaller the mass of the fluctuation, the longer the life-time and thereby the larger the probability of having such a fluctuation. In general these probability amplitudes are unknown. Naturally the fluctuations into light particles should be dominant due to the low mass, but in principle there may also exist fluctuations into heavy particles, even including charm. The problem is rather how to describe these fluctuations. All these fluctuations are part of the total proton wave function. Unfortunately this wave function is largely unknown. It cannot be derived from first principles because of the complex non-perturbative internal dynamics of the proton. Experiments give merely limited information because only one parton is probed at a time. In this way the wave function can be partially represented by momentum distributions of partons, i.e. quarks and gluons in the proton. These distributions provide the probabilities of scattering on a certain quark or gluon. They are conventionally obtained by fitting parametrisations to experimental data. A model to derive these distributions from non-perturbative dynamics was presented by Edin and Ingelman [3]. The El-model is based on quantum mechanical fluctuations. The valence parton distributions were derived from partonic fluctuations in the proton while the additional partons were assumed to originate from hadronic fluctuations of the proton. For a long time it was a common belief that only the massless or approximately massless partons (gluons, up and down quarks) may be part of the proton wave function. Heavy quarks were treated as "extrinsic", i.e. generated by large-momentum processes described by perturbative QCD. The conventional mechanism for charm production is the photon-gluon- fusion (PGF) process photon + gluon -> charm + anticharm. However there are experimental data which are in conflict with the predictions of the PGF model. Contrary to expectations, charm quarks have been found to also carry larger fractions of the proton's momentum [10], and charmed particles have been observed closer to the proton beam direction [11]. These data indicate an additional source of charm production. This has led to a model with "intrinsic" heavy quarks in the proton [9]. The model has been studied for over 15 years, but has still not been neither confirmed nor ruled out. As a further investigation of this problem, this thesis develops the El-model to be applicable also for heavy quark fluctuations in the proton. This includes a careful analysis of suitable quantum mechanical bases and treatment of energy fluctuations. The report is organised as follows. In Section 2 background material in terms of the Standard Model and the strong interaction are reviewed based on books such as those in [2]. The natural units are used throughout this thesis, i.e. c = h = I. The internal structure of the proton is best studied in deep inelastic electron-proton scattering experiments, as discussed in Section 3, and with theoretical aspects treated in Section 4. The El-model is described in Section 5. In Section 6 alternative descriptions of charm and strange quarks in the proton are discussed. The new approaches derived from the El-model are described and applied to charmed fluctuations in Sections 7 to 10 and to strange fluctuations in Section 15. A detailed treatment of the momentum fraction x is given in Section 11. The methods are summarised and compared in block diagrams in Section 12. The resulting charm momentum distributions are presented in Section 13, followed by a critical discussion of methods and results in Section 14. Similarly, the case of strangeness is discussed in 16. Finally, Section 17 gives a concluding discussion. 2 Standard Model The Standard Model (SM) is the theoretical framework which describes the elementary parti- cles and their interactions as known today. The theory is mathematically self-consistent but has 19 parameters that must be determined from data. Yet, no experimental result in conflict with the model has been found. In SM the fundamental particles are the leptons and the quarks. Up to the present limits of resolution, ~ 10~18m, they are known to be structureless. They can be arranged into three generations of increasing mass, as shown in Table 1. Flavour Mass Electric Flavour Mass Electric Flavour Mass Electric GeV charge GeV charge GeV charge u ~ 0.005 2/3 c ~ 1.4 2/3 t ~170 2/3 d ~0.01 -1/3 s ~0.2 -1/3 b ~4.7 -1/3 e 0.000511 -1 0.106 -1 T 1.7771 -1 9 < 7 x 10~ 0 < 0.0003 0 Vr <0.03 0 Table 1: The elementary particles in Standard Model The six types of quarks, the flavours, are called up, down, charm, strange, top and bottom. In addition to the electric charge they also carry colour, which is the charge of the strong interaction. There are three different colour charges, conventionally labelled as red, green and blue. Each charged lepton, i.e. electron, muon and taon, has a neutrino associated with it. For each of these particles there exists a corresponding anti-particle with opposite sign of many quantum numbers. The fundamental interactions in the SM are shortly summarised in Table 2. Interaction Field Basic coupling Couplings Range 2 quanta Quarks Leptons atQ 0 2^y Y^ Electromagnetic (EM) photon 7 A A a « 10~2 oo ± /d /e 18 Weak Z°,W oew ~ ID 10- m Strong gluons g a « 1 10-15m Table 2: The fundamental interactions and some of their properties.