The Continuous Electron Beam Accelerator Facility (CEBAF) is by its high current and precision an excellent tool in studying hadronic structure. The experiment approved for 1996 aims at the separation of the longitudinal and transverse cross– sections and the K+ form–factor measurement in the reaction p(e, e’ K+)Λ/Σ. Kinematic conditions and trigger modelling have been computed for the two–arm spectrometer with a programme which optimizes the experimental conditions taking into account the expected cross–section and the spectrometer acceptance.Posebno prikladan uređaj za proučavanje hadronske strukture je Pogon akceleratora za neprekidan elektronski snop (CEBAF) u S.A.D. zbog njegove snažne struje i točnosti. Za 1996. je odobreno mjerenje kojim treba odrediti omjer uzdužnih i poprečnih udarnih presjeka i utvrditi faktor oblika K+ putem reakcije p(e, e’ K+)Λ/Σ. Izračunali smo kinematičke uvjete i okidne modele za par okretnih spektrometara, s programom koji optimizira eksperimentalne uvjete, uzimajući u obzir očekivane udarne presjeke i prihvatnost (akceptancije) spektrometra

Angelescu, Tatiana

Baker, Oliver K.

Mihul, Alexandru

Niculescu, Gabriel

Niculescu, Ioana

Teodorescu, Liliana

English

HRČAK - Portal of Croatian Scientific and Professional Journals

ISSN1330–0016CODENFIZBE7MODELLING KAON ELECTROPRODUCTION ON PROTONS AND LIGHTNUCLEITATIANA ANGELESCU, OLIVER K. BAKERa, ALEXANDRU MIHUL, GABRIELNICULESCUa, IOANA NICULESCUa and LILIANA TEODORESCUFaculty of Physics, Bucharest University, PO Box Mg12, RomaniaaHampton University, Hampton, VA 23668, U.S.A.Received 24 January 1996UDC 539.17.02PACS 25.80.NvThe Continuous Electron Beam Accelerator Facility (CEBAF) is by its high currentand precision an excellent tool in studying hadronic structure. The experimentapproved for 1996 aims at the separation of the longitudinal and transverse cross–sections and the K+ form–factor measurement in the reaction p(e, e’ K+)Λ/Σ.Kinematic conditions and trigger modelling have been computed for the two–armspectrometer with a programme which optimizes the experimental conditions takinginto account the expected cross–section and the spectrometer acceptance.1. IntroductionElectroproduction is an efficient tool for studying particle structure. Quantumelectrodynamics has been proved to be valid for leptons up to a very high order,and electromagnetic interaction can be treated in the one–photon approximation(OPA) due to the small value of the coupling constant α.Using these well established assumptions, we can write the differential cross–section for scattering of unpolarized electrons in an unpolarized target [1]. It hasfour components which can be separated using suitable experimental configurations:FIZIKA B 5 (1996) 2, 113–124 113angelescu et al.: modelling kaon electroproduction . . .dσdt= σU + ǫσL + ǫ cos(2φ) σTT +[ǫ(ǫ+ 1)2]1/2cosφ σLT (1)where φ is the angle between the scattering and production planes, t is the four–momentum transfer from the virtual photon to the kaon and ǫ is the polarizationof the virtual photon.The kaon cross–section components are related to the virtual photon helicityamplitudes:1. σU is the cross–section for transverse unpolarized virtual photons and canbe compared with unpolarized real photon cross–section for very small four–momentum transfer values.2. σL is the cross–section for longitudinally polarized photons and is an attributeof the virtual photons only. The longitudinal virtual photons having zerohelicity are able to produce pions or kaons moving along their direction. Ifdominated by the kaon–pole contribution, σL can provide a value of the kaonform–factor by using the Chew–Low extrapolation method.3. σTT describes the modification in the cross–section if the transverse photonsare partially polarized.4. σLT is the result of the interference between longitudinal and transversecomponents.For zero four–momentum transfer, i.e. for real photons, ǫ vanishes and thevirtual cross–section becomes the photoproduction cross–section.The separation of the four components of the cross–section can provide valuableinformation about the photoproduction with real and virtual photons. The advan-tage of the virtual–photon reaction is the fact that the polarization is preciselyknown and can be varied in large limits by choosing different kinematical configu-ration. The separation of the four cross–sections does not involve model–dependentmethods. This is the most important advantage of the experiment proposed atCEBAF by our group and described in Ref. 2.This paper presents a programme performing the kinematical computations,the counting rate and trigger efficiency evaluations depending on the experimentalpossibilities of the project in reaching the proposed goal. The program takes intoaccount the two–arm spectrometer acceptances, neglecting multiple scattering anddetector resolution. A Monte–Carlo simulation of the missing mass distribution inkaon electroproduction on deuterium shows the possible degree of Λ/Σ separationdue to the Fermi motion inside the deuterium nucleus.The cross–sections used in counting rate evaluations were based on the previousexperimental data obtained by other groups and extrapolated for our kinematicconfigurations. We did not use theoretical predictions for the cross–sections because114 FIZIKA B 5 (1996) 2, 113–124angelescu et al.: modelling kaon electroproduction . . .many models involve parameters (coupling constants, form–factors) obtained by theauthors using the same experimental data.The program can be used for computing background diagram contributions. ForΛ and Σ channels separation, the missing mass distribution can be modelled takinginto account radiative corrections or spectator distributions in other light nuclei.2. Modelling two–arm spectrometer for K+electroproductionThe study of kaon electroproduction on protons and deuterons at CEBAF HMS–SOS facility benefits from some characteristic which lead to much more completeand reliable results than those obtained in the previous experiments [3–5]:1. The first and most important new contribution of the experiment should bethe separation of the transverse and longitudinal cross–section by varying thepolarization ǫ in a large range (0.28 ≤ ǫ ≤ 0.86) in the same experiment.2. The electron–four momentum transfer Q2 range extends from 0.5 (GeV/c)2up to 2.0 (GeV/c)2. Using the Chew–Low extrapolation technique for thelongitudinal cross–section, one should be able obtain a Q2 dependence ofthe kaon form–factor for a large range and thus test different theoreticalpredictions.3. The ratio of the cross–section for K+Λ and K+Σ0 channels in the Bjorkenvariable range 0.2 ≤ x ≤ 0.5 could give an answer about the strangenesscontent of the proton as predicted by Nachtmann [6].4. The measurement of the out of plane kaon electroproduction for −10◦ ≤ φ ≤10◦, with a precision of 0.06◦, would lead to the separation of σLT and σTTfor t in the range 0.11 to 0.50 (GeV/c)2.5. The uncertainty of kinematic parameter values is expected to be about 1%and the uncertainty on the cross–section less than 5%. In this way the errorsof the separated cross–sections are smaller than those obtained in previousexperiments.2.1. Phase–space limitations for the CEBAF two–arm spectrometerThe limitations imposed by the experimental conditions define the range ofvariation for the variables: Q2, W , t, ǫ. The proposal [2] gives the experimentalconditions which define the kinematical limits:1. The scattered electron angle can vary from 14.5◦ to 61.4◦.2. The produced kaon can be detected between 13.5◦ and 23.6◦.FIZIKA B 5 (1996) 2, 113–124 115angelescu et al.: modelling kaon electroproduction . . .3. The electron momentum can be varied between 0.7 and 2.4 GeV/c with a20% acceptance.4. The kaon momentum can be varied between 1.0 and 1.7 GeV/c with a 40%acceptance.The K+ electroproduction starts with a threshold value for the invariant massof the KΛ system, W :Wmin = mΛ +mK = 1.61 GeV. (2)This limitation will fix the minimum energy of the virtual photon ν:νmin =W 2min +Q2 −M22M, (3)where M is the proton mass.The Q2 value is limited by the electron scattering angle and the beam energy.The minimum scattering angle (14.5◦) leads to the minimum Q2 valueQ2min = Ee(Ee − ν) sin2(θmin/2), (4)where Ee is the beam energy.The minimum four–momentum transfer from the virtual photon to the kaon,tmin, depends on W , Q2 and Ee. Its dependence on Q2 and the kaon momentum pKfor W = 1.84 GeV and Ee = 4 GeV is given in Fig. 1. The Chew–Low extrapolationof the longitudinal cross–section depends on the minimum four–momentum transfertmin. In order to obtain smaller tmin values, we need higher W values. Especiallyfor high Q2, W is limited by the angular range of the kaon–arm spectrometer.Fig. 1. Dependence of tmin on kaon laboratory momentum for different Q2 values.116 FIZIKA B 5 (1996) 2, 113–124angelescu et al.: modelling kaon electroproduction . . .To obtain high Q2 values, we are constrained to work near the threshold (W ≈1.7 GeV) for small beam energy.The Bjorken variable x is limited to a short–range of values, 0.2 ≤ x ≤ 0.5,not interesting for deep inelastic scattering studies. However, measurements of theKΛ and KΣ0 cross–sections with high precision extend the possibility to check thestrangeness content of the proton given by the theoretical models [6].Fig. 2. Dependence of σU and σL on t according to Williams and Cotanch model[7].As one of the most important goals of this experiment is the trans-verse/longitudinal cross–section separation. We show in Fig. 2 the dependenceof σU , σL on t and a set of measurements proposed in this experiment.2.2. Kaon electroproduction cross–sectionsTable 1 gives the kinematical settings chosen in the experiment for the transverselongitudinal cross–section separation in the kaon electroproduction on nucleon:e + p → e′ +K+ + Λ(Σ0), (5)e + n → e′ +K+ +Σ−. (6)At these values for W , all other strange particle production channels are closed(for example K+K−N). The pion rejection achieved will be 103 using time–of–flightand Cherenkov counter in the kaon–arm spectrometer (SOS) [2]. In the electronFIZIKA B 5 (1996) 2, 113–124 117angelescu et al.: modelling kaon electroproduction . . .spectrometer arm (HMS) the pion rejection will be about 500. Therefore, the back-ground in the two–arm coincidence experiment will be due to the reactions (aa)and (aaa) with different kinematical configurations accepted by the spectrometerduring the resolution time of the coincidence scheme.TABLE 1.Kinematical configurations for cross–section t dependence.Kine. Q2 Ee E′e θe θγ W pK ǫ t(GeV/c)2 GeV GeV deg. deg. GeV GeV/c (GeV/c)2t1b 0.65 3.5 1.70 19.03 16.31 1.90 1.40 0.75 0.228t2b 0.50 3.5 1.70 16.68 14.57 1.94 1.43 0.75 0.169t3b 0.35 3.5 1.69 13.96 12.41 1.98 1.46 0.76 0.121t4b 0.75 3.5 1.46 22.10 14.33 1.99 1.66 0.67 0.214Counting rate evaluation in the two–spectrometer arm should start with thekaon cross–sections of the reaction investigated. We chose as imput the data ob-tained by Bebek [4], as the most recent and reliable. dσCMS/dΩK has been extrap-olated to the kinematical settings used in our experiment (W , Q2, t), by using theextrapolation law [4]:W (W 2 −M2)(Q2 + a)pCMSKe2.1tdσCMSdΩK= const., (7)with a = 2.67 for Λ production, and a = 0.79 for Σ0 production.For evaluating the counting rate we used the following cross–sections:2.2.1. Kaon electroproduction cross–sectionThe laboratory system cross–section for reactions (5) and (6) is given by:σ(e, e’, K) =d3σdE′edΩedΩK= ΓdσCMSdΩKd(cos θCMS)d(cos θ), (8)whereΓ =α/4π2E′(W 2 −M2)EMQ2(1− ǫ)(9)is the virtual photon flux, and dσCMS/dΩK is the extrapolated cross–section ac-cording to Ref. 4. In computing the cross–section for reaction (6), we made theassumption:σ(γvn ⇒ K+Σ−) = σ(γvp ⇒ K+Σ0), (10)which is supported by the experimental data of Bebek [4].The cross–section given by Eq. (8) was used to evaluate the coincidence countingrate.118 FIZIKA B 5 (1996) 2, 113–124angelescu et al.: modelling kaon electroproduction . . .2.2.2. Cross–section for elastic electron scattering on nucleonThe elastic electron scattering on nucleons has been computed using the relation[8]:σ(e, e′) =dσdΩe= σMottG2E +Q24M2G2M1 +Q24M2+Q22M2G2M tan(θ/2), (11)where GE and GM are the elastic and magnetic form–factors of the target (protonor neutron) and σMott is the Mott cross–section:σMott =α2 cos2 θ/24E2e sin4 θ/2E′eEe. (12)The cross–section computed with the relation (11) has been used in evaluatingelectron–arm counting rate and consequently the background coincidence events.2.2.3. Kaon–arm integrated cross–sectionWe integrated the (e, e’, K) cross–section expressed as a function of W and Q2for all K+ momentum values accepted by the kaon–arm spectrometer at a givenangle:σ(e,K) =∫dW 2∫Γ′dσCMSdΩKd(cos θCMS)d(cos θ)dQ2, (13)whereΓ′ =α16π2W 2 −M2E21M2Q2(1− ǫ), (14)Wmin = MA +MK , (15)Wmax = s1/2−Me, (16)Q2min = 0, (17)andQ2max = 4(EeE′e)GSMS . (18)GSMS is the general center of mass (e, N) system.This integrated cross–section will give the counting rate in the kaon arm foraccidental coincidences.FIZIKA B 5 (1996) 2, 113–124 119angelescu et al.: modelling kaon electroproduction . . .2.3. Counting rates2.3.1. Coincidence counting rateThis counting rate is determined by true coincidence between the scatteredelectron and the K+ in reactions (5) and (6). We evaluated it using the σ(e, e’,K+) given by (ab).The coincidence rate is:Rc = σ(e, e′,K+) exp(−LmK/pKτK)∆Ee∆Ωe∆ΩKnentt, (19)where, ne = I/qe, I is the beam intensity, nt the density of nuclei in the target, tthe target length, ∆Ee the energy acceptance in the electron–arm, ∆Ωe the angularacceptance in the electron–arm and ∆ΩK is the angular acceptance in the kaon–arm.The exponential term define the probability that the kaon does not decay beforedetection.2.3.2. Electron–arm counting rateThe electron–arm counting rate is evaluated using the elastic electron scatteringcross–section given by Eq. (8). It has been computed separately for protons andneutrons according to the relation:Re =dσdΩenentt∆Ωe. (20)2.3.3. Kaon–arm counting rateThe kaon–arm counting rate has been evaluated according to the proceduredescribed in (2.2.3) with σ(e, K) given by Eq. (13):RK = σ(e,K+) exp(−LMK/pKτK)∆ΩKnentt. (21)Using these rates, we computed the ratio of accident and true events for a givenresolution time (τres) in the coincidence scheme:AT=τresReRKfRc. (22)f is the duty factor (f = 1 for CEBAF). The ratio A/T is an important character-istic of the experiment: it defines the efficiency of the triggering system.3. Results and facilities of the programThe program for the computation of kinematics, cross–sections and countingrates starts with the reactions (5) and (6) and combines the cross–section data120 FIZIKA B 5 (1996) 2, 113–124angelescu et al.: modelling kaon electroproduction . . .to obtain rates for reactions on nuclei without taking into account the nuclearinteractione +AZN → e′ +K+ +X. (23)We applied the model for deuterium where the binding energy is small. Table2 shows the computed rates for the kinematical settings shown in Table 1 for deu-terium electroproduction. It is seen that, except for small Q2 values where A/T isstill high, we can reduce the accidental events to less than 10%.TABLE 2.Counting rates for cross–section t dependence.Kine. I Rc(e, e’, K) Re(e, e’) RK(e, K) A/T(µA) s−1 103 s−1 103 s−1 τrez = 2 nst1b 30 0.693 19.60 0.739 0.042t2b 30 1.126 48.99 0.821 0.070t3b 30 1.970 153.75 0.910 0.142t4b 30 0.430 8.30 0.919 0.035Fig. 3. Dependence of counting rates on Q2 for W = 1.84 GeV and Ee = 3.2 GeV.Using the computed values of the coincidence counting rate and the accidentalon true events ratio, we can optimize the experimental conditions with respect tothe kinematical variables. As an example, we show in Fig. 3 the dependence of therates on Q2 for W = 1.84 GeV at the beam energy of 3.2 GeV. Figure 4 shows therate dependence on W for the same beam energy and for Q2 = 2.0 (GeV/c)2. WeFIZIKA B 5 (1996) 2, 113–124 121angelescu et al.: modelling kaon electroproduction . . .can see a steep decrease of the coincidence rate with Q2, as expected. The ratioA/T does not vary very much with W and is flat beyond W = 1.7 GeV. Accordingto this behaviour, the kinematic configurations in the experiment have been chosenat about the same value of W (1.84 GeV), for Q2 as large as possible. For higherenergies, the kinematics would permit better separation in ǫ.Fig. 4. Dependence of counting rates on W for Q2 = 2 (GeV/c)2 and Ee = 3.2GeV.TABLE 3.Kinematical settings for the d(e, e’ K+)Λ,Σ0,Σ− experiment.Kine. Q2 Ee E′e θe θγ W ν ǫ x(GeV/c)2 GeV GeV deg. deg. GeV GeV1.a 0.50 2.40 0.80 29.56 13.04 1.84 1.60 0.54 0.171.b 0.50 3.20 1.57 18.25 16.31 1.84 1.60 0.76 0.171.c 0.50 4.00 2.39 13.16 18.10 1.84 1.60 0.86 0.172.a 1.00 2.40 0.61 49.20 12.76 1.81 1.80 0.36 0.302.b 1.00 3.20 1.38 27.69 18.08 1.81 1.80 0.66 0.302.c 1.00 4.00 2.19 19.48 20.77 1.81 1.80 0.80 0.303.a 1.50 2.40 0.61 61.37 12.98 1.69 1.85 0.28 0.433.b 1.50 3.20 1.34 34.39 19.91 1.69 1.85 0.61 0.433.c 1.50 4.00 2.23 23.42 23.56 1.69 1.85 0.78 0.434.a 2.00 3.20 0.79 53.14 13.03 1.69 1.84 0.34 0.444.b 2.00 3.50 1.09 42.51 15.33 1.69 1.84 0.46 0.444.c 2.00 4.00 1.59 32.67 17.90 1.69 1.84 0.60 0.44122 FIZIKA B 5 (1996) 2, 113–124angelescu et al.: modelling kaon electroproduction . . .TABLE 4.Coincidence and single rates for the d(e, e’ K+)Λ,Σ0,Σ− experiment.Kine. I Rc(e, e’, K) Re(e, e’) RK(e, K) A/T(µA) 10−2 s−1 103 s−1 103 s−1 (ns)1.a 10 6.50 5.30 1.33 0.111.b 10 19.1 24.0 1.22 0.151.c 10 38.0 56.5 1.19 0.172.a 20 2.14 0.40 3.32 0.062.b 20 7.20 2.78 2.70 0.102.c 20 15.4 7.50 2.10 0.123.a 30 0.56 0.09 2.34 0.043.b 30 1.94 0.70 1.90 0.073.c 30 4.10 1.97 1.70 0.084.a 30 0.94 0.06 8.52 0.054.b 30 1.44 0.12 7.45 0.064.c 30 2.47 0.28 6.36 0.074. ConclusionsPreliminary computations for the experimental study of kaon electroproductionhave been performed in order to optimize the kinematical set–ups and evaluatethe countings rates, statistical errors, background contributions and the runningtime for each set–up. The program has been used in run–plan evaluations for theexperiment accepted to be performed at CEBAF in 1996 [2].References1) J. Martino, An Introduction to Electron–Scattering Hadronic Physics with MultiGeVElectrons, Les Houches 6–15 Febr. 1990, New York 1991;2) O. K. Baker et al., Longitudinal/Transverse Cross–Section Separation in p(e, e’,K)Λ(Σ) for 0.5 ≤ Q2 ≤ 2.0 (GeV/c)2, CEBAF Proposal E 93–018, 1993;3) G. N. Brown et al., Phys. Rev. Lett. 28 (1972) 1086;4) C. J. Bebek, C. N. Brown, P. Bucksbaum, M. Herzliner, S. D. Holmes, C. A. Lichten-stein, F. M. Pipkin, S. W. Raither and L. K. Sisterson, Phys. Rev. D15 (1977) 594; C.J. Bebek, C. N. Brown, R. V. Kline, F. M. Pipkin, S. W. Raither, L. K. Hanson, D.Larson and A. Silverman, Phys. Rev. D15 (1977) 3082;5) P. Brauel, T. Canzler, D. Cords, R. Feist, G. Grindhammer, M. Helm, W. D. Kollmann,H. Krehbiel and M. Schadlich, Phys Lett. B69 (1977) 253; P. Brauel,T. Canzler, D.Cords, R. Feist, G. Grindhammer, M. Helm, W. D. Kollmann, H. Krehbiel and M.Schadlich, Z. Physik C, Particles and Fields 3 (1979) 101;6) O. Nachtmann, Nucl. Phys. B74 (1974) 422;7) R. Williams, private communications (1993);8) J. W. Lightbody and J. S. O’Connell, Comp. Phys. May/June (1988) 57.FIZIKA B 5 (1996) 2, 113–124 123angelescu et al.: modelling kaon electroproduction . . .MODEL ZA ELEKTROTVORBU KAONA NA PROTONIMA I LAKIMJEZGRAMAPosebno prikladan uredaj za proučavanje hadronske strukture je Pogon akcelera-tora za neprekidan elektronski snop (CEBAF) u S.A.D. zbog njegove snažne strujei točnosti. Za 1996. je odobreno mjerenje kojim treba odrediti omjer uzdužnihi poprečnih udarnih presjeka i utvrditi faktor oblika K+ putem reakcije p(e, e’K+)Λ/Σ. Izračunali smo kinematičke uvjete i okidne modele za par okretnih spek-trometara, s programom koji optimizira eksperimentalne uvjete, uzimajući u obziročekivane udarne presjeke i prihvatnost (akceptancije) spektrometra.124 FIZIKA B 5 (1996) 2, 113–124

Model za elektrotvorbu kaona na protonima i lakim jezgrama

Abstract

Similar works

Full text

Available Versions

HRČAK - Portal of Croatian Scientific and Professional Journals