FR9804607 La Physique a HERA W. Krasny LPNHE, Paris 6/7 NEXT PAGE(S) left BLANK Physics at HERA Selected Topics M.W. Krasny L.P.N.II.K I\2P:5 CNKS, Universities Paris VI ef. VII 4, pi. Jussieu, TM IMC 75252 Paris (!cflcx (J5. I'ranee Abstract: In these lectures I discuss recent results obtained by the two experiments HI and ZI'UJS at the first electron proton collider - IIKKA. In particular, I concentrate on results which are of importance (or our understanding of the nature of the strong interactions. In the week coupling limit of the strong interactions i.e. in the processes involv- ing short distances, the perturbative Quantum Chromodynamics can be confronted with the IIKRA data in a new regime;. What is however more challenging is the unique possibility of IIKR.A to map the transition from the regime ol the short distance phenomena., which are controlled by the perl.urba.tive QCI), to the large distance phenomena, where perturbative Q( !l) can not be applied. 324 1 Introduction The ep collider HERA, in which 27.6 GeV electrons collide with 820 GeV protons, opens several new research domains. The two colliding beam experiments HI and ZEUS have been taking and analyzing the electron-proton scattering data at ener- gies up to y/s = 300 GeV since 1992. In 1995 the HERMES experiment became operational and is presently investigating the scattering of polarized electrons on polarized stationary targets of helium, deuterium and hydrogen. The HERA-B experiment has been approved recently to measure the CP-violating decays of B- mesons produced by HERA protons scattered off a stationary tungsten target. The future program at HERA which is presently being discussed includes the scattering of electrons on nuclei, both in the fixed target mode and in the colliding mode as well as a possible program of scattering of polarized electrons on polarized protons in the colliding mode. In my lectures I shall focus on the ongoing research program using the two collider detector HI and ZEUS. Two kinematical variables x and Q2 specify the kinematics of electron-proton scattering at fixed CM energy \fs. They can be calculated from 4-momenta of the incoming electron, k, of the scattered electron, k , and incoming proton P as: Q2 = ~{k'-kf (1) X = 2P(k' - k) (2) The momentum transfered squared, Q2, defines the resolution power of the virtual boson exchanged between the electron and the proton in the plane transverse to their momenta. The photon of virtuality Q2 resolves the structure of the target at distances of d f» \— The Bjorken variable x has a very simple interpretation in the reference system in which the proton moves with large momentum (infinite momentum frame). It can be interpreted [1] as the momentum fraction of the proton carried by a charged parton on which the electron scatters elastically. This interpretation is valid in the Bjorken limit [2] for Q2 values much larger than a typical scale of the hadronic masses. In addition the variable x can be related [3] to the longitudinal localization of the interaction volume where the electron couples to the charged parton, / « K At HERA, owing to large y/s and the wide angular acceptance of both HI [4] and ZEUS [5] detectors, the electron-proton scattering processes can be studied in a vast range of x and Q2 variables, extending over 10 orders of magnitude. This unique feature of the HERA experiments enables us to study both the photo-production (Q2 = 10~5 — 10~2) processes and the deep inelastic scattering (DIS) processes, where the resolution power of the virtual photon reaches the distances of 10~17m. In the DIS regime of electron-proton scattering (Q2 > 2 GeV2) HERA experiments cover 4 orders of magnitude in x and, as shown in Fig. 1, extend significantly the measurement domain of the previous DIS experiments. For the first time the domain of low x in DIS regime can be explored, where the longitudinal localization of the interaction volume is 1000 times larger than the size of the proton. HERA can thus be considered as a dedicated machine for exploring the transition region between the 325 10 C4 O III ZEUS Data 10 10 10 i. i L l l 1.1 10" Figure I: The kinematical domains covcnnl by the deep inelastic Icpton nuck-on scatU'ring experiments short distance and long distance strong interactions and for verifying I lie validity of the perturbative QCI) in this transition region. Several important experimental results have been obtained from the analysis of the data collected over the first three years of IIIOHA operation. For these lectures I selected predominantly those corresponding to the DIS processes. In chapter 2 I shall try to summarize what we have learned so far from the measurements of the proton structure1 function /''j at 11FRA and discuss their Q(!|) fit. In chapter ."5 I shall point out few IIFHA-specific issues related to the measurement of the coupling constant of the strong interactions, (\s. The discussion of the hadroiiic energy flow as a function of the photon virfuality Q1 is presented in chapter 1. Finally, I shall discuss in chapter 5 the diffractive processes giving rise to the "rapidity ga.p events". In particular I shall summarize what we have learned so far on the nature of the Pomeron. 326 2 The structure function F>2 2.1 Measurement of F2 2 The proton structure function F2{x^Q ) is determined from the measured inclusive differential cross section da/dxdQ2. There are several important differences in the procedure and in the systematic accuracy of the differential cross section measured at HERA with respect to earlier measurements made by the fixed target experi- ments. The event kinematics is reconstructed at HERA not only from the scattered electron angle and energy but also redundantly from the measured hadroriic energy flow. This provides a valuable cross check of the systematic uncertainty of the mea- surement. The calorimetric measurement of the scattered electron energy give rise to worse resolution and larger energy scale error than in the fixed target experiments. In these experiments the outgoing electrons (muons) were measured in the magnetic spectrometers. On the other hand, owing to the colliding mode, the event topology at HERA can be more easily resolved. Note, that in the fixed target experiments all particles are emitted in a small size cone around the incoming lepton direction. One of the most important limitations of HERA experiments in extending the mea- surement domain towards higher y = Q2/sx, where the exchange of longitudinally polarized photons largely contribute to the electron-proton scattering cross section, originates from a poor experimental means to control the background due to photo- production. On the other hand the radiative corrections, which for several fixed target experiments have to be unfolded from the experimental data, can be better controlled at HERA. The structure function F2 is derived from the measured differential cross section according to the following formula: The corrections bpL stands for the unmeasured fraction of the differential cross sec- tion due to photoabsorbtion of longitudinal photons. This correction has to be calculated using the perturbative QCD. The corrections 8zo reflects the contribu- 2 tion of the Zo exchange to the ep scattering ( in the Q domain discussed here mostly via the interference term). The corrections 6r is the radiative correction dominated by the the processes of the real photon emission by the incoming (outgoing) electron. 2.2 F2 in the parton model and in QCD In the quark-parton model [1], [2] the structure function F2 can be interpreted as the charge weighted momentum density (measured in the units of the proton momentum) of quarks and anti-quarks: 2 3 2 2 F2(x, Q ) = Ee *(9(s, Q ) + q(x, Q )), (4) 327 where g(g(x,, Q)Q2) and q(,q(x, Q)Q2) are the pprobabilitie s of rinding a qquar k (anti-quark(q)) in the interaction volumvolume of the transverse size of the order of —j= and longitudinal size of the order of j. 2 The perturbative QCD can not predict both the x and the Q shape of the F2. Nevertheless, in the large Q2 and large x region it predicts an evolution of partonic densities as a function of Q2 once they are specified at any chosen Q2 value. These predictions can be formulated in terms of the DGLAP equations (for the derivation of the DGLAP equations see the lectures given by Eric Pilon [6]). The DGLAP equations are derived under assumption that the most dominant terms in the series describing the scattering amplitude (~ a™\gn(Q2) - Leading Log Approximation and ~ o^lg""1^2) - Next to Leading Log Approximation ) are retained. The form of these equations is the following: Q2 Mx^)_ = a^p_ £ ^ (^ Q2) pMy) + ^ Q2) p 2 2 ^(g qi{y,Q )Pgq{x/y)+gM )Pgg(X/y)), where qi(x,Q2) is the density of quarks carrying flavor "i", qNS(x,Q2) is a non- singlet combination of the quark densities, g(x, Q2) describes the gluon density and Np stands for the number of quark flavors. The Q2 dependence of-the renormalized coupling constant as follows from the solution of the renormalisation group equation [7], [8] which in the Leading Log Approximation (LLA) reads: (6) (33 - 2iVF) In § whereas in the Next to Leading Log Approximation (NLLA): In In TT . In the DGLAP equations an arbitrary renormalization mass scale \i has been chosen to be the momentum transfer y/Q7. A is the only parameter of the theory, which fixes the strength of the interactions at a scale fi0.