Proposal to Jefferson Lab PAC39 Exclusive Phi Meson Electroproduction with CLAS12

Transcription

1 Proposal to Jefferson Lab PAC39 Exclusive Phi Meson Electroproduction with CLAS2 H. Avakian, J. Ball, 2 A. Biselli, 3 V. Burkert, R. Dupr, 2 L. Elouadrhiri, R. Ent, F. X. Girod,, S. Goloskokov, 4 B. Guegan, 5, 6 M. Guidal, 5, H. S. Jo, 5 K. Joo, 7 P. Kroll, 8 A Marti, 5 H. Moutarde, 2 A. Kubarovsky, 6, V. Kubarovsky,, C. Munoz Camacho, 5 S. Niccolai, 5 K. Park, R. Paremuzyan, 5 S. Procureur, 2 F. Sabatié, 2 N. Saylor, 6, 5 D. Sokhan, 5 S. Stepanyan, P. Stoler, 6, M. Ungaro, 7 E. Voutier, 9 C. Weiss,, D. Weygand, and the CLAS Collaboration Jefferson Lab, Newport News, VA 2366, USA 2 IRFU/SPhN, Saclay, France 3 Fairfield University 4 Joint Institute for Nuclear Research, Dubna, Russia 5 Institut de Physique Nucleaire Orsay, France 6 Rensselaer Polytechnic Institute 7 Department of Physics, University of Connecticut, Storrs, CT 6269, USA 8 Wuppertal University, Wuppertal, Germany 9 LPSC Grenoble, France Spokespersons Spokespersons,Contact persons

2 2 Summary We propose a measurement of exclusive φ meson electroproduction on the proton, ep e + φ + p, at GeV beam energy with the CLAS2 detector. The kinematic range extends in W from 2 5 GeV, Q 2 from 2 GeV 2, and t t min from near zero to 4 GeV 2, the precise limits depending on the specific values of the other variables. The φ will be detected through the K + K and (for the first time) the K S K L mode, which allows for an independent test of the cross section extraction. Differential cross sections and beam spin asymmetries will be measured as functions of the φ KK decay angles, θ and φ, to extract the structure functions σ T, σ L, σ T T, σ LT and σ LT. Exclusive φ electroproduction at Q 2 few GeV 2 is of special significance as a probe of the nucleon s gluon generalized parton distribution (GPD), which represents the nucleon s gluonic form factor and reveals the transverse spatial distribution of gluons in the nucleon. Theoretical calculations including perturbative and non perturbative QCD interactions describe the available exclusive φ cross section data over a wide range of W and Q 2, including the CLAS 6 GeV data, and permit a quantitative analysis in terms of the gluon GPD even at JLab energies. The nucleon s gluonic form factor and the spatial distribution of valence like gluons at x.2.5 will be extracted from the relative t dependence of dσ L /dt and is insensitive to finite size corrections in the QCD process and the uncertainties of the absolute cross section measurements. Exclusive φ electroproduction at energies near threshold, W W th few MeV, may also provide information on potential intrinsic strangeness in the nucleon (correlated s s pairs), which is being discussed in connection with semi inclusive measurements. The objectives of the proposed experiment are to (a) Quantify the approach to the regime of small size configurations at high Q 2 by testing model independent features of the reaction mechanism, such as the Q 2 scaling of cross sections and t slopes, the change of W dependence with Q 2, the L/T ratio obtained from φ KK decays and response functions, and other observables; (b) Extract the nucleon s gluonic size in the valence region from the relative t dependence of dσ L /dt, both model independently (x averaged size) and with information from GPD based model calculations (x dependent size); (c) Explore signatures of a possible intrinsic s s component of the nucleon in exclusive φ production near threshold. FastMC simulations with a realistic cross section parametrization indicate that 6 days of beam time would provide sufficient statistics to address the stated physics objectives. This experiment would run in parallel with the approved CLAS2 DVCS (E2-6-9) and neutral pseudoscalar meson production (π, η, η, E2-6-8) experiments.

3 3 Contents Summary 2 I. Introduction 4 II. Physics Motivation 7 A. Exclusive φ electroproduction and gluon GPD 7 B. Testing the approach to the small size regime C. Gluonic radius of nucleon 2 D. Helicity flip vs. non flip gluon GPD 8 E. Intrinsic strangeness 9 III. Kinematics and Cross Sections 23 A. Kinematics of the reaction ep e p φ 23 B. Cross section parametrization 24 IV. Exclusive φ Detection with CLAS2 28 A. CLAS2 detector 28 B. Particle identification. 29. Electron identification K ± identification φ Detection through K S K L Decay Mode 32 C. Monte Carlo Simulations of Acceptance and Resolution 33 V. Projected Results 36 A. σ L /σ T separation 36 B. Differential Cross Sections and t dependence 4 C. Slopes and t extrapolation 42 VI. Beam time request 44 VII. Exclusive φ production in the context of the JLab 2 GeV program 45 References 46

4 4 I. INTRODUCTION A central goal of the 2 GeV Upgrade of JLab is to explore the internal structure of the nucleon at resolution scales fm, where it can be described in terms of the quark and gluon degrees of freedom of QCD []. Measurements of the inclusive en structure functions will provide detailed information on the valence quarks momentum distribution, including their spin and flavor dependence. Likewise, the form factors of elastic en scattering reveal the spatial size of valence quark configurations in the nucleon and their response to polarization. The valence quarks, however, represent only part of the nucleon s structure at large light front momentum fractions x. It is known from fits to deep inelastic scattering data that the nucleon contains a substantial density of gluons at x >., which carry more than 3% of its total momentum at low scales [2]. Recent results from semi inclusive scattering [3] suggest that the nucleon may also include an intrinsic sea of quark antiquark pairs at large x, as expected from theoretical considerations. These large x gluons and sea quarks are thought to originate from non perturbative correlations in the nucleon wave function and are physically distinct from the small x gluons and sea quarks seen in high energy scattering experiments, which are produced mostly by perturbative QCD radiation. Measuring the properties of the large x gluons and sea quarks is essential to fully understand the nucleon in QCD as an interacting many body system. Of particular interest is the spatial distribution of QCD quarks and gluons in the nucleon. For a relativistic system the proper way to quantify the spatial structure is in terms of the transverse densities of partons (quarks, gluons) in the infinite momentum frame [4 7]. They are obtained as the Fourier transform of the Generalized Parton Distributions (or GPDs), which represent the nucleon form factors for partons with given light front momentum fraction x; see Refs. [8 ] for a review. These concepts have enabled a rich program of quark/gluon imaging of the nucleon, involving a combination of experimental data, dynamical models, and even lattice QCD calculations. The transverse distribution of valence quarks is constrained by the nucleon elastic form factor data (transverse charge densities) and will be measured differentially in x in Deeply virtual Compton scattering (DVCS) at JLab 2 GeV. Very little is known about the transverse spatial distribution of the valence like gluons in the nucleon. One interesting question is how the nucleon s gluonic RMS radius relates to its quark radius, i.e., whether the gluons sit at smaller or larger transverse distances than the valence quarks. This question directly impacts on our understanding of the dynamical origin of large x gluons in the nucleon. For instance, if the large x gluons arise due to correlations of valence quarks one expects a smaller gluonic radius than quark radius, while a picture in which the large x gluons are packaged inside constituent quarks would imply similar radii. Data from high energy experiments at HERA [, 2] and FNAL [3] suggest that the transverse spatial distribution of small x gluons may be narrower than those of quarks; however, nothing is known about the spatial distribution of gluons with x >.. Another interesting question is how the nucleon s gluonic form factor (or gluon GPD) behaves at large t ( GeV 2 ). This describes how the nucleon responds elastically when a large momentum is transferred to its gluon field and again reveals new information on its internal structure.

5 5 Here we propose to measure the nucleon s gluonic form factor and the spatial distribution of valence like gluons through exclusive electroproduction of φ mesons on the proton, γ (Q 2 ) + p φ + p. () At Q 2 few GeV 2 the φ meson is produced in the form of a small size s s pair coupling to the gluon fields in the nucleon ( small size configuration ). This reaction thus provides a clean probe of the nucleon s gluon GPD in the valence region (x.2.5). In recent years theorists made significant progress in developing the QCD based description of exclusive φ electroproduction at Q 2 few GeV 2, implementing perturbative as well as non perturbative QCD interactions [4, 5]. Quantitative predictions for absolute cross sections are available and describe the JLab 6 GeV data (details will be given below). Because of its almost pure s s composition φ production is not affected by scattering from the nucleon s valence quarks or the light quark sea; the latter play a prominent role in the production of other light vector mesons (ρ, ω) and make their GPD based description more challenging. The interesting information on the t dependence of the gluon GPD, which defines the spatial image of gluons in the nucleon, is contained in the relativet dependence of the exclusive φ differential cross sections and thus insensitive to details of the QCD scattering process (coupling, absolute gluon density) and the φ meson distribution amplitude; this information can therefore be reliably extracted from the data at Q 2 few GeV 2. These facts combined make exclusive φ production a unique channel for measuring the nucleon s gluonic size in the valence region. The available data on exclusive φ meson electroproduction (HERA [6, 7], HERMES [8], Cornell [9, 2], NMC [2], CLAS 4/6 GeV [22, 23]) and similar processes indicate that the regime of small size configurations is approached rather gradually as Q 2 increases. Before interpreting the data in terms of a GPD based description one must convince oneself that this description is applicable and quantify eventual finite size corrections. We therefore plan to perform the analysis of exclusive φ electroproduction in two stages: Stage I: Verify the approach to the small size regime by testing model independent features of the reaction mechanism, such as the Q 2 dependence of cross sections and the L/T ratio, the Q 2 independence of the t slopes, the change of W dependence with Q 2 and t. These predictions follow from the general structure of the reaction mechanism in the small size regime and do not depend on the form of the GPDs. Stage II: Extract information on the nucleon s gluonic size in the valence region from the relative t dependence of the differential cross section. This analysis will in parts incorporate information from GPD models, e.g. how the t dependence is correlated with the partonic momentum fractions. Recent results from semi inclusive deep inelastic scattering experiments at HERMES suggest a non zero density of strange quarks and antiquarks in the nucleon at x >.2 [3]. The presence of such an intrinsic strange sea in the nucleon is predicted by phenomenological models of the nucleon based on light front wave functions [24, 25]. Such intrinsic strangeness would in principle enable an alternative mechanism of exclusive φ production

6 near threshold, corresponding to the knockout of a correlated s s pair in the nucleon. The study of this intrinsic strangeness component is rapidly progressing, and quantitative estimates of its role in exclusive φ production are under way. If confirmed by further studies we will incorporate this new mechanism in our analysis. 6

7 7 II. PHYSICS MOTIVATION A. Exclusive φ electroproduction and gluon GPD The basic idea of deep exclusive meson production is that at Q 2 GeV 2 the meson is produced predominantly in configurations of a transverse size much smaller than its natural hadronic size, r R hadron fm (small size configurations, see Fig. ). The production process thus probes the structure of the nucleon locally in transverse space and can be thought of as a local operator inducing transitions between nucleon states, analogous to the well known vector and axial currents. What the exclusive cross sections measure is the nucleon form factor of this local operator as a function of the invariant momentum transfer, t. By choosing mesons with appropriate quantum numbers, one can in this way probe nucleon structure with operators that are not accessible through the usual electroweak currents gluonic structure, transverse spin structure, matter vs. charge distribution, etc. 2 Transverse size r << R had Q hard light Q L, T meson L, T x x 2 GPD N 2 r << R had hard x 2 x s s GPD φ (a) t (b) t FIG. : (a) Exclusive production of light quark mesons (π, η, ρ, ω) at Q 2 GeV 2. The meson is produced in a q q configuration of transverse size r R hadron. The nucleon structure probed in this reaction is summarized in the GPDs. (b) Exclusive φ meson production. The φ is produced as a small size s s pair, coupling to the nucleon s gluon GPD. The gluon GPD represents the nucleon s gluonic form factor and depends on the gluon light front momentum fractions, x and x 2, and the invariant momentum transfer t. Meson production in small size configurations r fm is governed by short range quark/gluon interactions and can be described using methods based on QCD factorization. In the asymptotic regime Q 2 a QCD factorization theorem [26] states that the γ N meson + N amplitude can be calculated as the product of a generalized parton distribution (or GPD) [27 29], describing the amplitude for the emission/absorption of the active quark or gluon by the nucleon; the amplitude of the QCD scattering process; and the distribution amplitude of the meson, describing the conversion of the small size q q pair to the physical meson in the final state (see Fig. a). At momentum transfers Q 2 few GeV 2 this factorized picture is still applicable if non perturbative corrections to the QCD scattering process are included and the small but finite size r of the q q configuration of the meson are taken into account. During the last few years significant progress was made incorporating non perturbative effects within the factorized approximation using the modified hard scattering approach [3], and fully quantitative predictions are now available for the absolute meson production cross sections in most channels [4, 5, 3].

8 8 σ L (γ * p->φp) [nb] 2 GPD model: Goloskokov, Kroll 8 Q 2 = 2 GeV 2 CLAS6 Cornell H/ZEUS W[GeV] FIG. 2: The longitudinal cross section of exclusive φ electroproduction, σ L, as a function of W, as obtained in the modified QCD approach with the gluon GPD model of Refs. [4, 5]. The data are from the HERA H and ZEUS [6, 7], Cornell [2], and CLAS 6 GeV [23] experiments. A unique feature of the φ meson is that its flavor composition does not allow it to couple to the nucleon s valence quarks or light quark sea (ū, d). The small size configurations of the φ meson are almost entirely s s pairs (deviations from ideal mixing are discussed in Sec. II E), and OZI rule violations are suppressed in short distance QCD processes. Exclusive φ production at Q 2 few GeV 2 thus couples mainly to the nucleon s gluon field, and provides a clean probe of the nucleon s gluon GPD even at JLab energies (see Fig. b). A calculation of the exclusive φ cross sections based on the modified hard scattering approach and a simple model of the gluon GPD [4, 5] describe the available cross section data over a wide range of energies, including the CLAS 6 GeV data (see Fig. 2). The gluon GPD describes the form factor for the coupling of two gluons to the nucleon. It depends on the two gluons light cone momentum fractions, x and x 2, and the invariant momentum transfer to the nucleon, t. It is customary to parametrize the individual light cone momentum fractions as x,2 = x ± ξ, (2) and write the gluon GPD in the form H g (x, ξ; t). (3) The light cone momentum transfer to the target x 2 x = 2ξ is kinematically fixed and related to the Bjorken variable, ξ = x B /(2 x B ) (up to /Q 2 corrections), (4) while the average gluon momentum fraction x is integrated over in the factorized amplitude. In the limit t, ξ one has x = x 2 = x, and the gluon GPD reduces to the usual gluon density in the nucleon H g (x, ξ =, t = ) = xg(x). (5) By virtue of the QCD factorization theorem the nucleon s gluon GPD is universal (process independent) and can be connected with the gluon density measured in inclusive

9 9 deep inelastic processes. More formally, the gluon GPD is given by the transition matrix element of the twist 2 QCD gluon operator between nucleon states [8 ]. As such it can be computed using non perturbative methods such as in Lattice QCD; first calculations of gluonic structure have recently been reported in the literature [32]. The fact that in high Q 2 exclusive processes one is studying universal structures that are defined in terms of QCD operators distinguishes this field from other processes that can only be described in terms of effective degrees of freedom. The expressions for the differential cross sections of exclusive φ meson in terms of the gluon GPD are given in Refs. [4, 5]; see also Ref. [33]. The longitudinal cross section takes the form dσ L dt = α em Q 2 x 2 B x B [ ( ξ 2 ) H g 2 + terms in E g ], (6) where α em is the QED coupling constant. Here H g denotes the integral or average of the gluon GPD over the momentum fraction x, weighted by the x (and generally Q 2 ) dependent amplitude of the γ L + g φ L + g subprocess. It can be expressed in general form, H g 3πf φ 27 dx H g (x, ξ; t) K(x, ξ, Q 2 ), (7) where f φ = 22 MeV is the φ meson decay constant, and the kernel K represents the amplitude of the γ L + g φ L + g subprocess. In the modified hard scattering approach of Refs. [4, 5] it is given by K(x, ξ, Q 2 ) mod. hard scatt. = dz d 2 r Ψ φ (z, r) α S (µ R ) C(z, x, ξ, Q 2 ) e S(z,r,Q2), (8) where Ψ φ denotes the φ meson light cone wave function, α S the strong coupling constant, C the complex amplitude of the partonic subprocess, and S the Sudakov form factor. The integral runs over the momentum fraction z carried by the s quark in the φ meson (the s quark carries z), and the transverse size r of the s s pair (see Fig. ). Contributions with r fm are strongly suppressed by the Sudakov form factor, ensuring dominance of small size configurations in the integral. Similar expressions are obtained for the subdominant amplitudes involving transverse photon and/or vector meson polarization; see Refs. [4, 5] for details. It is worth noting that in the pure leading twist approximation (r = ) the kernel Eq. (8) of the leading L L amplitude reduces to [33] K(x, ξ, Q 2 ) leading twist = [α S dz Ψ φ(z, r = ) z( z) ] x(ξ x iɛ), (9) and the average of the GPD Eq. (7) becomes, up to an overall factor, just the well known Compton form factor associated with the gluon GPD. This clearly illustrates the connection of the modified hard scattering approach in meson production with the leading twist approximation in DVCS and underscores the universality of the GPDs even in the presence of finite size effects ( higher twist ).

10 R = σ L / σ T (a) γ p φ + p. Cornell Dixon 79 CLAS Santoro 8 HERMES prelim. ZEUS Chekanov 5 H Aaron 9 Parametrization.. Q 2 [GeV 2 ] σ (nb) (b) 3 2 n /(Q +M φ ) Q (GeV ) 2 n = 2.49±.33 FIG. 3: (a) The ratio R = σ L /σ T in exclusive φ production, as measured in experiments at different Q 2 and W. The plot combines data taken at different W. The dashed line shows the empirical parametrization described in Sec. III B, which is used in the simulations of the proposed CLAS2 experiment below. (b) The Q 2 dependence of the unseparated total exclusive φ cross section σ = σ T + ɛσ L measured in the CLAS 6 GeV experiment. The solid line is an empirical fit to in the form /(Q 2 + Mφ 2)n, which gives n 2.5 The terms proportional to the nucleon helicity flip GPD E g in Eq. (6) are suppressed by kinematic factors ξ 2 and t/(4m 2 N ) and can be incorporated in a more detailed analysis using GPD models (see Sec. II D below). B. Testing the approach to the small size regime The transition to the regime of small size configurations in exclusive meson production at high Q 2 has to be understood as a gradual approach, not a sudden change. At any given Q 2 few GeV 2 the amplitude involves a mix of small size (r R hadron ) and hadronic size configurations (r R hadron ); as Q 2 is increased the fraction of small size configuration gradually increases. Before interpreting the exclusive φ data in terms of the gluon GPD we want to verify that the approach to the small size regime indeed takes place and quantify the remaining finite size effects. This can be done by testing certain features of the reaction mechanism that do not depend on the specific form of the GPDs or the QCD scattering process. Specifically, in this experiments we plan the following tests: A) Q 2 scaling of cross sections. A simple first test of the reaction mechanism is provided by the Q 2 dependence of the longitudinal and transverse exclusive φ cross sections, σ L and σ T. In this experiment the L T separation will be performed by analyzing the φ KK decay angular distributions; the formalism is described in detail in Sec. V below. QCD factorization implies that the cross sections at fixed x B scale as σ L /(Q 2 ) 3, σ L /σ T Q 2. ()

11 Perturbative QCD interactions lead to logarithmic corrections to this behavior at large Q 2. At Q 2 few GeV 2, the exponents are sensitive to non perturbative effects, such as the Sudakov form factor implemented in Ref. [4], cf. Eq. (8), so that observed devations can be interpreted quantitatively within this approach and serve to harden the description of finite size corrections. We note that this test is analogous to the verification of Bjorken scaling and the Callan Gross relation in inclusive DIS, which do not depend on the specific form of the parton densities. Figure 3 shows the available data on the ratio R = σ L /σ T, from experiments at various fixed values of W. Little systematic variation of R with W was observed in these experiments. One sees that the observed Q 2 dependence is roughly consistent with Eq. () (which really applies at fixed x B, corresponding to W varying with Q 2 ). The proposed CLAS2 experiment will measure the ratio R over a wide range of Q 2 = 2 8 GeV 2 at various fixed x B and thus enable the first stringent tests of scaling at fixed x B. Figure 3 also shows the Q 2 dependence of the unseparated exclusive φ cross section σ = σ T + ɛσ L as measured in the CLAS 6 GeV experiment [23]. A fit in the form /(Q 2 + Mφ 2)n gives an exponent n = 2.49 ±.33, still below the asymptotic value n = 3. This is in agreement with the modified hard scattering picture of Ref. [4], which predicts non perturbative modifications of the effective Q 2 dependence at Q 2 few GeV 2. The CLAS2 measurements will enable precise tests of the scaling behavior up to Q 2 GeV 2. B) Change of t dependence with Q 2. A more direct test of the approach to the small size regime can be done by studying the change of the t dependence of the exclusive cross section with Q 2. A basic prediction of QCD factorization is that in the limit Q 2 at fixed x B the t dependence of the cross section should become independent of Q 2, and should result only from the t dependence of the GPD. At finite Q 2 few GeV 2 there is generally a contribution to the t slope from the finite size of the vector meson. Thus, one expects the t slope to decrease with Q 2 and eventually become Q 2 independent, reflecting the true t dependence of the gluon GPD. This test was performed in exclusive φ meson production at small x B at HERA, where the cross section was measured over a wide range in Q 2, from zero (photoproduction) to 2 GeV 2. At small x B the invariant momentum transfer is given by the squared transverse momentum of the nucleon and meson in the final state, t = 2 T, and the slope B can directly be interpreted as the transverse area of the interaction region (see Figure 4b). The latter is compounded from the transverse area of the target (the transverse spatial distribution of gluons) and the effective size of the configuration in which the meson is produced. A decrease of B with increasing Q 2 at fixed x B can thus directly be attributed to the shrinkage of the effective size of the meson configurations with increasing Q 2. The data show that the slope decreases by B GeV 2 between Q 2 2 GeV 2 and GeV 2, indicating that the effective size of the s s configurations in the φ indeed decreases with Q 2 (see Figure 4b). HERA measurements also confirmed that the t slopes of different gluon dominated vector channels (J/ψ, φ, ρ ) tend to the same value at large Q 2, proving the universality of the gluon GPD. The CLAS2 data will allow us to perform a similar test of the approach to the small

12 2 B [GeV -2 ] γ p φ + p dσ/dt exp(b t) Cornell 79/8, W = 2.8 H 9, W = 75 ZEUS 5, W = 75 Area B 2 Q 2 = Q 2 > R 2 hadron (a). Q 2 [GeV 2 ] (b) FIG. 4: (a) The exponential t slope, B, in exclusive φ electroproduction, as a function of Q 2, as measured in the Cornell and HERA experiments. The plot combines data taken at different fixed W (not x B ). (b) Interpretation of the Q 2 dependence of the t slope B. The t slope measures the transverse area of the interaction region, as determined by the effective size of the target and the produced meson. At high Q 2 the meson is predominantly produced in a small size configuration, implying that the slope at fixed x B should decrease and eventually become Q 2 independent. size regime in φ electroproduction at x >.. A new element in our kinematics is that the minimum invariant momentum transfer t min becomes large at large x B, reaching values t min GeV 2, and can no longer be neglected. The variation of t min with Q 2 (at fixed x B ) can induce a change of the effective slope of the cross section in t t t min, which is a purely kinematic effect and not related to any change in the size of the meson configurations. To see the true dynamical shrinkage one must look at the change of the cross section with Q 2 at fixed absolute t, not fixed t t min. This is possible with the statistics and kinematic coverage afforded by CLAS2; the projected results are shown in Fig. 5. It will enable accurate differential measurements of the absolute t dependence at fixed x B and Q 2, allowing us to test the exclusive reaction mechanism in unprecedented detail. C. Gluonic radius of nucleon The gluon GPD, as a function of the invariant momentum transfer t, represents the form factor of gluons with a given light cone momentum fraction in the nucleon. Just as the familiar electromagnetic form factors reveal the spatial distribution of charge and current in the nucleon, this gluonic form factor can used to infer the spatial distribution of gluons in the nucleon. In the parton picture, where the nucleon constituents are specified by their light cone momenta in the longitudinal direction, this spatial representation is constructed in the transverse plane. The transverse Fourier transform of the gluon GPD with diagonal

13 3 CLAS2 dσ L /dt (γ * p->pφ) dσ L /dt nb/gev 2 2 dσ L /dt nb/gev Q 2 =2.5 GeV 2 Q 2 =3.5 GeV 2 Q 2 =4.5 GeV 2 Q 2 =5.5 GeV 2 Q 2 =6.5 GeV 2-3 Q 2 =2.5 GeV 2 Q 2 =3.5 GeV 2 Q 2 =4.5 GeV 2 Q 2 =5.5 GeV 2 Q 2 =6.5 GeV 2 Q 2 =7.5 GeV 2 Q 2 =8.5 GeV t, GeV t, GeV 2 FIG. 5: CLAS2 projected results for the t dependence of the longitudinal differential cross section dσ L /dt of exclusive φ production, in various bins of Q 2 and a fixed bin in x B. It shows the potential of this experiment to study the variation of the t dependence with Q 2 as a test of the reaction mechanism. momentum fractions x = x 2 x, or ξ =, d 2 T xg(x, b) (2π) 2 ei T b H g (x, ξ =, t = 2 T ), () describes the density of gluons with given light cone momentum fraction x in transverse space, with b b measuring the distance from the transverse center of momentum of the nucleon (see Fig. 6b). It is normalized such that its integral over transverse space gives the total density of gluons carrying momentum fraction x, d 2 b xg(x, b) = H g (x, ξ =, t = ) = xg(x). (2) Of particular interest is the normalized distribution ρ g (x, b) g(x, b)/g(x) (3) which satisfies d 2 b ρ(x, b) = for any x and describes the spatial profile of the distribution of gluons at a given x, with the information on the total number of gluons factored out. It can be obtained as the Fourier transform of the normalized gluonic form factor F g (x, t) H g (x, ξ =, t)/h g (x, ξ =, t = ) = H g (x, ξ =, t)/[xg(x)], (4) which satisfies F g (x, t = ) = for all x; namely ρ g (x, b) = d 2 T (2π) 2 ei( T b) F g (x, t = 2 T ). (5)

14 4 Gluonic radius of nucleon b 2 g [fm 2 ] (a) J/ψ, H 5 J/ψ, ZEUS 2 µ + µ - J/ψ, ZEUS 2 e + e - J/ψ, FNAL 82 Fits COMPASS J/ψ CLAS2 φ x (b) gluons changes with b x x FIG. 6: (a) The average squared gluonic transverse radius of the nucleon, b 2 g, as a function of x, as extracted from exclusive J/ψ production experiments at HERA and FNAL [35]. The growth of the nucleon s gluonic size toward small x is consistent with theoretical models ( parton diffusion ). New data at x few 2 are expected from the CERN COMPASS experiment. The CLAS2 experiment would measure the gluonic radius in the region x.2.5 with exclusive φ electroproduction. (b) The transverse spatial distribution of gluons in the nucleon at a given momentum fraction x. The important information on the normalized spatial profile of gluons is contained in the relative t dependence of the GPD. This information in turn is expressed in the relative t dependence of the differential cross section specifically, dσ L /dt and can be extracted from the data with good precision. The point is that the relative t dependence of the cross section is insensitive to the details of the QCD scattering process, such as the scale choice in α s, the shape of the φ meson wave function, and the Sudakov form factor in Eq. (8), as these factors cancel in the ratio [dσ L /dt(t)]/[dσ L /dt(t = )], up to small effects related to the correlation of x and t dependence in the integral over partonic momentum fractions. These details matter only in the absolute cross section. This fortunate circumstance greatly simplifies our analysis. In this experiment we aim only to extract the normalized spatial profile of gluons at large x, Eq. (3), or the normalized gluonic form factor of the nucleon, Eq. (4). While it is an important point of principle that GPD models describe the absolute φ production cross sections in our kinematics, the details of the absolute cross section modeling do not affect our analysis. The transverse spatial distribution of gluons is a fundamental characteristic of the nucleon in QCD. It defines the size and shape of the nucleon s gluon field (more precisely, its leading twist projection) and can be compared to the corresponding characteristics of valence and sea quarks. The spatial profile of gluons changes with their light cone momentum fraction x (see Fig. 6b), a phenomenon which provides interesting information on non perturbative

15 5 dσ /dt (γ * p φ p) [nb / GeV 2 ] 2 - Lukashin, W = 2.3 GeV, Q 2 =.3 GeV 2 Santoro 8, W = 2.5 GeV, Q 2 = 2.5 GeV 2 2 Dipole GPD /(m g - t) 2, 2 mg = GeV t min - t [GeV 2 ] FIG. 7: Differential cross section of exclusive φ electroproduction measured in the CLAS 4 and 6 GeV experiments [22, 23], as a function of t t min. The dashed line is a fit assuming a dipole like t dependence of the GPD with a mass parameter m 2 g = GeV 2, which is supported by theoretical arguments [37] and describes well the t dependence of the FNAL J/ψ data [3]. QCD dynamics in the nucleon s light front wave function. At x < 2 the gluonic size is expected to grow with decreasing x due to diffusion type dynamics (Gribov diffusion). At x >. the change of the gluonic size reflects the dynamics of the gluon fields coupled to the valence quarks and reveals the bound state structure. The spatial profile of gluons also changes with the normalization scale due to DGLAP evolution; this effect is completely calculable and was studied in Ref. [34]. As for practical applications, the transverse spatial distribution of gluons is an essential ingredient in the theory of high energy pp/ pp collisions with hard processes (Tevatron, LHC) [34, 35], and in modeling the initial conditions for small x QCD evolution equations leading to gluon saturation. A measure of the nucleon s average gluonic size at a given x is the average gluonic transverse radius squared, b 2 g d 2 b b 2 ρ g (b, x), (6) which can be obtained from the slope of the normalized gluonic form factor at t = as b 2 g = 4 F g (t = ). (7) t Figure 6a summarizes what is known about the average gluonic radius squared at x < from J/ψ photo/electroproduction experiments at HERA [, 2] and FNAL [3]. In the region 2 < x < new data are expected from the COMPASS experiment [36]. The gluonic radius at x >. is practically unknown. The proposed CLAS2 experiment will measure the gluonic radius in the region x.2.5 through exclusive φ electroproduction, and thus contribute essentially new information to the study of this fascinating landscape. There are encouraging signs that the t dependence of exclusive φ electroproduction at JLab energies is consistent with the extrapolation of the HERA and FNAL data toward larger x (cf. Fig 6a). The t dependence measured in the CLAS 4 and 6 GeV experiments [22, 23] is reasonably well described by a dipole like t dependence of the gluon GPD (i.e., a dipole gluonic form factor) with a mass parameter m 2 g. GeV 2, as was obtained from fitting the t dependence of the FNAL J/ψ data [37] (see Fig. 7). This indicates that exclusive

16 6 CLAS2 dσ/dt (ep->epφ) dσ e /dt nb/gev dσ e /dt nb/gev dipole t-dep. -6 dipole t-dep. -5 exponential t-dep. -7 exponential t-dep t, GeV t, GeV 2 dσ e /dt nb/gev dipole t-dep. exponential t-dep t, GeV 2 dσ e /dt nb/gev dipole t-dep. exponential t-dep t, GeV 2 FIG. 8: CLAS2 projected results for measurement of the t dependence of the differential cross section of exclusive φ electroproduction. Shown is the unseparated electroproduction cross section, σ T +ɛσ L, integrated over the Q 2 and x bins; comparable results are obtained for the separated cross sections (see Fig. 9 below). The measurements will be able to discriminate between exponential and dipole like t dependence of the gluon GPD with good accuracy, and map the t dependence differentially in x B and Q 2. J/ψ production and φ electroproduction probe the same universal gluonic form factor of the nucleon (up to effects related to the change of x and t min ). The extraction of the spatial profile of gluons from the exclusive φ data of the proposed experiment via the Fourier integral Eq. (5) will be done at different levels of complexity. At the simplest level, we can take the square root of the differential cross section (normalized at an arbitrary value of t, e.g., at t = t min ), and infer the t dependence of the average gluon GPD H g, [ / ] /2 dσl H g (t). dt (t) dσl dt (t min) (8) Its spatial Fourier transform corresponds to an average transverse gluonic profile of the

17 7 nucleon in the valence region, with a weigthing determined by the x dependence of the gluon GPD and the hard scattering process. This extraction can be done quasi model independently; the limited average information one obtains in this way would already be new and impact on our understanding of nucleon structure. (The kinematically suppressed contributions from E g are neglected at this level.) At the next level, we aim to detect also signs of the variation of the spatial gluonic profile with x, and/or determine more accurately the x values that give the dominant contribution in H g. This analysis will be done with the help of specific GPD models, which relate the x dependent spatial gluonic profile to the x, ξ and t dependence of the GPD observed in the actual experimental kinematics; e.g. the double distribution model of the GPD employed in Refs. [4, 5, 33]. In this way we can also estimate the contribution of the nucleon helicity flip GPD E g (see Sec. II D below). An essential requirement for nucleon imaging is that the measurements provide accurate information on the t dependence of the differential cross sections at values t t min < GeV2, which define the bulk shape of the spatial distribution, and that they be able to discriminate between different physical scenarios for the behavior of the form factor at larger values t few GeV 2, which determine the gluon profile in the nucleon s center. Figure 8 shows a sample of projected data for the differential cross section in certain x, Q 2 bins. The example here compares a dipole like t dependence with an exponential shape at large t, and shows that the two shapes can be clearly distinguished both at small and at large t. The extraction of transverse spatial images from exclusive data with controlled errors is a complex problem, which has recently been taken up in the literature [38, 39] and is under active consideration. The uncertainty in the transverse spatial image comes from two sources: (a) a theoretical uncertainty resulting from the GPD model implementing the x t correlation and the effect of the skewness ξ; (b) an experimental error resulting from the statistical and systematic errors of the differential cross section data and the incomplete coverage in t. The theoretical uncertainty will be improved by studies validating gluon GPD models and their predictions for the x t dependence, using the data taken in this and other experiments. The propagation of experimental and incompleteness errors into the spatial image can be studied using recently developed methods based on finite bandwidth functions (Shannon Nyquist theorem), which are already being applied to the study of transverse charge densities from elastic form factors [39]. To estimate the magnitude of the expected experimental errors, we have performed a simple study in which we extract the transverse image corresponding to the average gluon GPD H g from the t dependence of dσ L /dt, Eq. (8), using the projected CLAS2 data (see Fig. 9). It is seen that good statistical accuracy can be achieved in the reconstructed spatial image. As explained above, the image thus obtained corresponds to the transverse distribution of gluons at an average value of x in our kinematics. In the next level analysis the correlated x, ξ and t dependence of the GPD will be implemented with the help of GPD parametrizations (e.g. the one of Ref. [4]), which can be tested with experimental data and refined as necessary; corresponding simulations are under way. The projected experimental results for the differential cross sections are described in Sec. V below.

18 8 FIG. 9: Transverse spatial distribution of gluons in the nucleon as extracted from projected CLAS2 exclusive φ data. In this preliminary study the x dependence of the gluon distribution and the influence of skewness ξ were neglected in order to study the error propagation from dσ L /dt into the spatial image. The spatial image may be regarded as the nucleon s transverse gluonic structure at an average value of x in the given kinematics. D. Helicity flip vs. non flip gluon GPD The contribution of the helicity flip gluon GPD E g to the exclusive φ electroproduction cross section is suppressed by kinematic factors of ξ 2 and t/(4m 2 N ). While these factors are numerically small at the low x B and low t end of our kinematics, they become sizable at larger x B (which are accessible at larger Q 2 ). The magnitude of E g is constrained by the condition of positivity of the overall transverse density of gluons [4] but otherwise unknown. Preliminary HERMES results for the transverse target asymmetry A UT in exclusive φ production are consistent with zero, albeit with large errors [4]. The present experiment uses an unpolarized target and will not be able to separate the

19 9 contributions of H g of E g using polarization observables. In the present analysis we plan to estimate the effect of E g using GPD models constrained by the positivity condition; quantitative estimates using the double distribution model are presently being prepared. We also plan to minimize the contribution of E g by measurements at the low x B and low t end of our kinematics; once the reaction mechanism is better understood we can use the lower Q 2 data from this region to extract the transverse nucleon image. We note that the ratio E g /H g could in principle be constrained by future experiments with a transversely polarized target. E. Intrinsic strangeness Exclusive electroproduction of φ mesons near threshold may also be sensitive to the nucleon s intrinsic strangeness content. This term refers to s s pairs in the nucleon s light front wave function in which both the s and s carry substantial momentum fraction x >.. The presence of such pairs was predicted on the basis of the light front description of hadron structure in QCD, where they appear as the result of interactions involving several valence quarks in the nucleon, q val q val q val q val + s s (pair correlations) [24, 25]. As such they are physically distinct from the small x ss pairs that appear due to perturbative QCD radiation emitted by a single valence quark (gluon splitting, or DGLAP evolution). The properties of the intrinsic sea of the nucleon are presently a topic of great interest and are being investigated using theoretical models and a combination of inclusive and semi inclusive deep inelastic scattering data [42]. The results of the HERMES semi inclusive kaon production experiment [3] show hints of a non zero intrinsic strangeness at x >. (see Fig. ); the main source of error in this analysis are the uncertainties associated with the treatment of quark fragmentation into kaons. More direct evidence for a strange sea at large x comes from the NuTeV neutrino DIS experiment at Fermilab [43]. The presence of an intrinsic strange sea could provide an alternative mechanism for exclusive φ electroproduction near threshold W W th few MeV [44]. General considerations based on the light front picture suggest that an exclusive φ in this kinematics could be produced by knocking out a correlated s s pair in the nucleon wave function. In this process the momentum fractions of the s and s would be added to give the total longitudinal momentum transfer to the nucleon, x s + x s = ξ >.2, (9) producing large values of ξ much more effectively than scattering from an individual s or s that remains in the nucleon, where the momentum fractions of the initial and final parton would be subtracted. In the GPD representation such pair knockout contributions correspond to the Efremov Radyushkin Brodsky Lepage (or ERBL) region, where the GPD describes the distribution amplitude for emission of a quark antiquark pair by the nucleon. It is important to stress that this putative new mechanism is naturally contained in the general framework of the GPD description and would manifest itself simply as an enhanced ERBL contribution in the strange quark GPDs; it would not be an additional mechanism requiring a separate description.

20 2 x(s+s ).3 HERMES BHPS (µ=.5 GeV) BHPS (µ=.3 GeV).2 "Intrinsic strangeness" s QCD s φ. GPD (a) - x (b) FIG. : (a) Strange sea quark distribution ρ(s + s) extracted from the HERMES semi inclusive kaon production data [3]. The curves show a fit of the intrinsic strangeness component at x >. based on the model of Ref. [24] (from Ref. [42]). (b) s s pair knockout contribution to exclusive φ meson production. In the GPD representation this process is expected to be dominated by the ERBL region, where the GPD describes the distribution amplitude for emission of a q q pair. Work on a quantitative estimate of the intrinsic strangeness contribution to exclusive φ production in our kinematics is in progress. We plan to incorporate the results of these studies for our analysis as they become available. The question of a possible quark exchange mechanism in exclusive φ electroproduction at high Q 2 may also be connected with observations made in recent precise measurements of φ photoproduction near threshold. The LEPS data [45] show a drop in the extrapolated differential cross section dσ/dt(t = ) in the region W = GeV, indicative of a non diffractive exchange mechanism; at larger W the data show the typical diffractive rise (see Fig. a). It should be stressed that near threshold t min becomes large (t min,th =.5 GeV 2 in photoproduction) and results in a purely kinematic suppression of the differential cross section in the physical region t < t min ; to see the true dynamical dependence on W one must extrapolate to the unphysical point t =, which relies on the measured t slopes and thus fraught with some uncertainty [46]. The preliminary CLAS 6 φ photoproduction data agree with the LEPS data near threshold and extend to higher energies. They show a similar behavior near threshold (see Fig. b; this plot is for fixed CM scattering angle and not corrected for t min ). The CLAS 6 GeV data show that the non uniform W dependence near threshold is found equally in φ s reconstructed from K + K and K L K S decays, making it unlikely that it is due to kaons produced through excitation and decay of nucleon resonances. While our experiment concerns hard electroproduction of φ, these observations in photoproduction offer useful suggestions for the interpretation of our projected results. If a

21 2 dσ/dt (t = ) [nb/gev 2 ] (a) Photoproduction γ p φ + p 3 2 LEPS 5 LAMP2 82 DESY Threshold W [GeV] (b) d!/dt!"µb/gev 2 #! ".85 < cos# # c.m. <.95 Charged-mode, w/o $(52) cut Neutral-mode S (GeV) FIG. : (a) Exclusive φ photoproduction differential cross section dσ/dt as function of W, as measured in several experiments. Shown are the values extrapolated to the unphysical point t =, where the suppression due to t min is removed. The extrapolation to t = was performed using the t slopes measured in the respective experiments. (b) Preliminary CLAS 6 GeV photoproduction data (CMU analysis). Shown is the differential cross section at a fixed CM scattering angle as a function of W = s, for exclusive φ s reconstructed from the K + K (blue) and K L K S decays. non diffractive exchange mechanism were confirmed in photoproduction near threshold, it should also leave a trace in electroproduction at Q 2 few GeV 2, where it gets resolved into its QCD quark constituents precisely the conjectured small size s s pairs in the nucleon s light front wave function. In this sense hard φ electroproduction near threshold, may help to solve the φ photoproduction puzzle. The photoproduction data also show that this mechanism (if at all) should be prominent only at energies close to threshold, W W th few MeV, and that over most of our W range a diffractive energy dependence prevails, consistent with dominance of the gluon GPD in the small size regime. A quark exchange contribution to φ electroproduction near threshold could in principle also result from the small uū and d d components of the φ wave function ( non ideal mixing ). The magnitude of this effect can be estimated using information on the SU(3) flavor composition of the φ and ω obtained from a variety of sources such as hadron mass formulas [47], B decays [48], etc. The φ and ω flavor wave functions are given by ω = cos δ uū + d d 2 + sin δ s s (2) φ = sin δ uū + d d 2 + cos δ s s (2) where δ 3.7 deg [47] measures the deviation from ideal mixing. Neglecting phase space effects, this would imply a ratio of φ to ω production cross sections (the so called Lipkin ratio) of R φ/ω = tan 2 δ = 4 3. (22)

22 22 The observed φ/ω cross section ratio near the φ threshold is at least an order of magnitude larger in photoproduction (see Ref. [49] for a recent analysis); a similar order of magnitude is seen in the CLAS 6 GeV electroproduction data [23]. We therefore conclude that φ production through uū and d d exchange is negligible in our kinematics, and that a quark exchange mechanism near threshold (if any) proceeds mainly through the s s component.

23 23 III. KINEMATICS AND CROSS SECTIONS A. Kinematics of the reaction ep e p φ In this section we briefly introduce the kinematic variables and cross section decomposition in exclusive φ meson electroproduction; the φ KK decay and its analysis is discussed in Sec. V A. The kinematic variables of the process e(k) + p(p) e (k ) + p (p ) + φ(v) (23) are defined as follows. The four momenta of the incident and outgoing leptons are denoted by k and k, and the four-momentum of the virtual photon q is defined as q k k. In the laboratory system, θ is the scattering angle between the incident and outgoing leptons, and E and E are the energies of the leptons. The photon virtuality is then given by Q 2 q 2 = (k k ) 2 4 E E sin 2 θ 2 >. (24) The four momenta of the incident and outgoing protons are denoted by p and p. The energy of the virtual photon in the laboratory frame is ν = pq m N = E E, (25) where m N is the nucleon mass. The Bjorken scaling variable x B is defined as x B = Q2 2pq = The squared invariant mass of the photon proton system is given by Q2 2m N ν. (26) s W 2 = (p + q) 2 = m 2 N + 2m N ν Q 2. (27) The invariant momentum transfer to the proton is defined as t (q v) 2 = (p p ) 2 (28) where v is the four momentum of the produced φ meson. The kinematical boundaries for t for given W (or x B ) and Q 2 correspond to scattering angles of and π in the center of mass (CM) frame and are given by t min, max = t(θ CM =, π) = 2(m 2 N E CM E CM ± P CM P CM), (29) where P CM, P CM and E CM, E CM are the CM momenta and nucleon energies in the initial and final state P CM λ/2 (W 2, m 2 N, Q2 ), 2W (3) P CM λ/2 (W 2, m 2 N, m2 φ ), 2W (3) E CM PCM 2 + m2 N, (32) E CM P 2 CM + m2 N, (33) λ(x, y, z) x 2 + y 2 + z 2 2xy 2xz 2yz. (34)

24 24 The photon polarization parameter, determining the ratio of fluxes of logitudinally and transversely polarized virtual photons, is given by where ɛ = y Q2 4E 2 y + y2 +, (35) Q2 2 4E 2 y pq qk = ν E denotes the fractional electron energy loss. The cross section of the reaction ep e p φ for an unpolarized proton has the structure (36) d 4 σ dq 2 dx B dtdφ =Γ(Q2, x B, E) 2π [ dσt dt + ɛdσ L dt + ɛdσ T T dt cos 2φ + ɛ(ɛ + ) dσ LT dt cos φ + λ 2ɛ( ɛ) dσ LT dt ] sin φ, (37) where dσ T /dt, dσ L /dt, dσ T T /dt, dσ LT /dt and dσ LT /dt are structure functions, λ is the beam polarization. The angle φ between the leptonic plane and the hadronic plane is defined according to the Trento convention. The cross section integrated over φ is [ d 3 σ = Γ(Q 2 dσt, x dq 2 B, E) dx B dt dt (Q2, x B, t) + ɛ dσ ] L dt (Q2, x B, t), (38) The virtual photon flux in the Hand convention is defined as Γ α 8π Q 2 x B m 2 N E2 x 3 B ɛ. (39) The differential cross section at Q 2, x B and t is then related to the number of observed events in an interval Q 2 W t by d 3 σ dq 2 dx B dt = N Q 2 x B t L Br Acc (4) where N is the number of measured events, L the integrated luminosity, Acc the acceptance, and Br the branching ratio for the decay used to detect the φ meson. B. Cross section parametrization In order to simulate the proposed measurements we have developed an empirical parametrization of the exclusive φ electroproduction cross section, which reflects the basic kinematic dependences and permits a numerical estimate of the cross sections in the the region Q 2 > GeV 2 and W W th few GeV. It describes the presently available data from fixed target experiments with energies W few GeV (CLAS, Cornell, HERMES, NMC) and from the HERA collider experiments with W 2 GeV (see Table I for a summary).

25 25 The parametrization has a smooth limiting behavior for Q 2 and can be used in numerical simulations without restrictions; however, it is not meant to be accurate for photoproduction at W few GeV, and no photoproduction data were used in the fit. It is limited to values of t in the forward peak, i.e., t W 2, or scattering angles θ CM π. Furthermore, while the parametrization describes the HERA cross section data and has a sensible limiting behavior for W, it is not inteded to reflect fine details of the Regge like behavior at high W. The parametrization was cosntricted by fitting data on the transverse cross section σ T (W, Q 2 ) and the ratio R = σ L (W, Q 2 )/σ T (W, Q 2 ); the differential cross sections and their t dependence were then parametrized according to different physical models for the t dependence (exponential, dipole) [5]. The transverse cross section is parametrized as σ T (W, Q 2 ) = The longitudinal cross section is parametrized as c T (W ), (4) ( + Q 2 /m 2 φ )ν T ν T = 3. (independent of W (42) ( c T (W ) = α W ) th 2 α2 ( ) α3 W nb (43) W 2 GeV W th = m N + m φ =.96 GeV (44) α = 4, (45) α 2 =., (46) α 3 =.32. (47) σ L (W, Q 2 ) = R(W, Q 2 ) σ T (W, Q 2 ) (48) R(W, Q 2 ) = c RQ 2, (49) m 2 φ c R =.4 (independent of W ) (5) A comparison with the available cross section data is shown in Fig. 2. Experiment W [GeV] Q 2 [GeV 2 ] Comments CLAS Lukashin [22] CLAS Santoro 8 [23] Cornell Dixon 79 [9] 3.2 Cornell Cassel 8 [2] HERMES prelim. [8] NMC Arneodo 94 [2] µ beam, nuclear targets ZEUS Chekanov 5 [6] H Aaron 9 [7] TABLE I: Summary of exclusive φ production experiments.

26 26 R = σ L / σ T (a) γ p φ + p. Cornell Dixon 79 CLAS Santoro 8 HERMES prelim. ZEUS Chekanov 5 H Aaron 9 Parametrization.. Q 2 [GeV 2 ] σ T [nb] (b). H 9, W=75 ZEUS 5, W=75 HERMES prelim., W=5. Cornell 8, W=2.8 CLAS 8, W=2.5 Parametrization γ p φ + p.. Q 2 [GeV 2 ] γ p φ + p Q 2 = 2.5 GeV 2 ZEUS 5 HERMES prelim. H 9 σ T [nb] (c) Cornell 8 CLAS 8 Parametrization W [GeV] FIG. 2: (a) Ratio R = σ L /σ T as function of Q 2, combining measurements at different W. (b) Transverse cross section σ T as function of Q 2, for measurements at different W. (c) Transverse cross section σ T as function of W, at Q 2 = 2.5 GeV 2. The curves represents the parametrization of Eqs. (4) (5). The differential cross section is given by the general expression dσ L,T = σ L,T F (t) dt F int (5) F () =, (52) F int tmin t max dt F (t), (53) where different physical models are considered for the function F (t) implementing the t dependence.. Exponential t dependence F (t) = e Bt (54) F int = e Bt min /B (55)

27 27 The exponential slope B is parametrized as a function of W : B(W ) = B + 4α ln W GeV (56) B = 2.2 GeV 2, (57) α =.24. (58) 2. Power like t dependence (dipole at amplitude level): F (t) = F int = m 8 g (m 2 g t) 4 (59) m 8 g 3(m 2 g t min ) 3 (6) The mass parameter at W few GeV is chosen as m 2 g =. GeV 2. (6)

28 28 IV. EXCLUSIVE φ DETECTION WITH CLAS2 The current plan is to run the experiment with only the standard baseline CLAS2 equipment. Our simulations indicate that about 6 days of beam on target will be sufficient to carry out the proposed experiment. The requested beam time is therefore 6 days. This is less beam time than for the other experiments such as DVCS and π, η electroproduction which are approved to run under all of the same conditions. The φ meson is near the K K theshold, and its primary modes of decay are φ K + K (49%) and φ KS K L (34%). In this experiment we will measure both channels. For the leading K + K channel we will detect the K + and K, or detect either kaon and reconstruct the other by the missing mass technique. For the KS K L channel we will measure the decay of the KS into π+ and π pair (69%) and identify the KS from their invariant mass. The KL is reconstructed from the missing mass of the epk S. A. CLAS2 detector This experiment will use the CLAS2 spectrometer in its standard configuration, as illustrated in Fig. 3. The standard cryogenic hydrogen target will be used with electron beam energies of GeV at a nominal luminosity of 35 cm 2 s. Details of the CLAS2 magnet and detector design can be found in the CLAS2 technical design report. FIG. 3: The CLAS2 spectrometer. The subsystems are referred to in the text as needed.

29 Q 2 vs W Q 2 vs x B Q 2 vs -t FIG. 4: a) Kinematical coverage for φ production as a function of Q 2 and W integrated over t. b) Kinematical coverage for φ production as a function of Q 2 and x B integrated over t. c) Kinematical coverage for φ production as a function of Q 2 and t integrated over W. We have run extensive Monte Carlo simulations of the experiment using the simulation code FastMC. Further details regarding the simulation are described in Subsection C below. The cross sections used in the simulation are those described in Sec. III above. The resulting accepted distributions of φ production as a function of Q 2 vs. W and Q 2 vs. x B and Q 2 vs. t is shown in Fig. 4. In the following sections we discuss the particle identification and particle distributions on which this is based. B. Particle identification.. Electron identification. The distribution of accepted electrons as a function of angle and momentum in the laboratory system is shown in Fig. 5. The physical minimum angle for detection of electrons at forward angles is constrained by physical obstructions such that θ e 5 The two primary

30 3 components of CLAS2 which will be used for electron identification are the High Threshold Cerenkov Counter (HTCC) and electromagnetic calorimeter (EC). The HTCC will have a pion detection threshold of > 4.9 GeV/c. However, the efficiency for detecting charged pions begins to rise slowly, so that the HTCC will dominate the electron PID even at higher momenta. Additional electron hadron separation will be made using the sampling fraction distributions in the EC. A new pre-shower calorimeter (see Fig. 3) will be placed just upstream to further improve our ability to identify electrons e vs p e FIG. 5: Accepted electron angular distribution vs. momentum p e 2. K ± identification. Fig. 6 shows a simulation of the distribution of kaons detected as a function of angle and kaon momentum p K (note the log scale). Also shown is the distribution Q 2 vs. p K and t vs. p K. The distributions are rather broad. The kaon momentum ranges from less that GeV/c to about 6 GeV/c. The K ± mesons will be identified using a combination of several techniques, starting with time-of flight (TOF). The TOF resolution for CLAS2 is expected to be considerably better that for CLAS6- σ t 8 ps vs. 5 ps for CLAS6. This is illustrated in Fig. 7, which shows the difference in time for detection of K + mesons and other contaminants. The most prolific contaminant will be charged pions, mostly originating from the decay of ρ mesons. A separation of -σ occurs at p 5.5 GeV/c, 2-σ at 3.8 GeV/c, and 3-σ at 3. GeV/c. For high momentum an important resource will be the low threshold Cherenkov detector- LTCC. This will be used in CLAS2 primarily as a pion detector. The LTCC has a π ± threshold momentum of about 2.5 GeV/c so the efficiency for pion detection should be quite high above 3 GeV/c, while the threshold for the K ± momentum is almost 9 GeV/c and need not be considered.

31 2/6/ degrees vs p of K + GeV FIG. 6: FIG. 3: Angular distribution of the detected K + mesons corresponding the decay of the φ with the requirement that K +,p and e are detected. Left: Accepted kaon angle θ K vs. momentum p K distribution in the lab frame. Rightupper: Accepted kaon distribution vs. p K and Q 2. Right-lower: Accepted kaon distribution vs. p K and t. The distributions are obtained for the simulation corresponding to a pure exponential cross section with t slope parameter B = 2.2 GeV 2. In the mode in which only one kaon is detected, after vetoing the pions, the missing mass of detected particles will be constructed and a further cut made around the kaon mass. Finally, the φ will be reconstructed from the missing mass ep e p X. The remaining background will be estimated from projecting the higher invariant mass background. At smaller momentum the TOF resolution should be sufficient. The GENEV Monte Carlo generator was used to simulate the rejection of the background using the TOF system. Fig. 8 shows the missing mass distribution for the reaction ep e p X produced by FastMC with the events generated by GENEV. The ρ, ω and φ resonances are visible in the figure. The background under the φ peak is very high. However after the TOF cuts and a cut on the missing mass around the K (Fig. 8b) the distribution becomes very clean (Fig. 8c). The combined missing mass distribution for the charged and neutral kaon mode (see discussion below) is shown in Fig. 8d. The cleanest situation for minimizing pion background is to detect both the K + and K pair. Nearly all the remaining misidentified background is then eliminated by exclusivity cuts requiring conservation of energy and all components of momentum. An additional resource for separating particle ID is the RICH detector. One sector will be installed as part of the initial operation of CLAS2. The RICH has been shown to be quite effective in separating K ± and π ± in the momentum region planned for this experiment. We plan to use the RICH to separate K ± and π ± distributions, which will then provide us with in-situ background information underlying the φ mass. A remaining background under the φ comes from the kaons in the final state of Lambdas, mainly (52), as well as Sigmas and Cascades. As of this writing, we have not yet modeled this background, but are currently beginning the process of inserting this into the generator.

32 32 FIG. 7: Difference in time of flight for various pairs of particles vs. the momentum of the particles. The number of standard deviations in the expected resolution of 8 ps is indicated by horizontal lines. 3. φ Detection through K S K L Decay Mode The φ-meson can be detected from the neutral mode φ K S K L. The K S decays to a pair of charged pions: K S π + π, which occurs in 69% of K S decays. In this case the K S can be reconstructed from the detected pion s invariant mass and the K L reconstructed from the missing mass of epk S (Fig. 9). The background from other meson decays, for example ρ π + π, ω π + π π and so on can be suppressed by cuts that sort out the masses of K S and K L as shown on Fig. 9. The missing mass of ep e p K S X from events generated by GENEV is shown in Fig. 9a.The background under the φ peak is very significant. The π + π invariant mass without any cuts is presented in panel (b) in red. The K S signal is very week. However after applying the cut on missing K L, the background under K S peak (blue) is almost gone. The missing mass distribution in the reaction ep e p π + π X without any cuts is shown in panel (c) in red. After the applying the K S cut (panel b) the K S signal becomes visible. The final missing mass distribution is shown in panel (d). The ratio of signal to background is good enough to extract the φ signal. This technique was intensively investigated in CLAS6 data.

33 33 FIG. 8: (a) Missing mass to e p in the reaction ep e p X without cuts; (b) Missing mass of ep e p K + X after TOF cuts; (c) Missing mass to e p in the reaction ep e p X with cut shown on figure (b); (d) Missing mass to e p in the reaction ep e p X with cuts for both φ to K S K L and K + K decay modes). C. Monte Carlo Simulations of Acceptance and Resolution The CLAS2 Fast-MC program was used for the simulation. The plots correspond to 6 days beam time at the CLAS2 luminosity L = 35 cm 2 s. The reaction ep e p φ was simulated with two decay modes of φ-meson; φ K + K and φ K S K L. The particles required to be detected were the e, p and K + or K for the charged decay mode or π + and π for the neutral mode. The missing K (K + ) or K L is assumed to be constructed from the missing mass of the ep e p K + X, ep e p K X, or

34 34 FIG. 9: (a) Missing mass in the reaction ep e p X for events generated by GENEV without any cuts; (b) The π + π invariant mass in the reaction ep e p π + π X without cuts (red) and with cut on missing K L (blue); (c) Missing mass in the reaction ep e p π + π X without cuts ( red) and with K S cut (blue); (d) Missing mass to e p in the reaction ep e p X with cuts shown in (b) and (c). ep e p π + π X. Because the acceptance and event rates are rather high, the coincidence of all the final state particles e, p, K +, and K was investigated as well. The missing mass distributions in the reaction ep e p K + X for different K + momenta is presented in Fig. 2. The distributions were fit by Gaussian function and it s sigma is shown in FIg. 22a. The resolution is increasing from 6 MeV at p K -momentum GeV up to 23 MeV at p K -momentum 5 GeV. The missing mass distribution in the reaction ep e p K S X for different K S momenta is presented in Fig. 2. The sigma of this distribution is shown in Fig. 22b as a function of K S momentum. It varies from 8 MeV up to 8 MeV with increasing momentum from to 5 GeV. The missing mass resolution in the reaction ep e p X as a function of the K + momen-