Tensor Polarization t20 of the Deuteron and the ρπrγ Process

Comnun. Theor, Phys. (eijing, China) 35 (2001) pp 455- 458 ;E Internatioual Acadermic PublishersVol. 35. No.。April 15. 2001Tensor Polarization t20 of the Deuteron and the ρπγ Process*YE Tao. CHEN Yan-Bei and CHENG Tan ShengDepartment of Physics, Peking University, Beijing 100871, China(Received May 11, 2000)relativistic wavefunction of the deutcron is used to calculate tbe relativistic impulse appraxination and the contributionof the ptr mesun exchange process. A good agrcenent with cxperimental data is achieved when and only when the pπrcoupling is taken as positive.PACS numbers: 25 30.Bf, 24.70.+8, 27.10.+hKey words: tensor polarization t20; sign of ρπγ coupling constant1 IntroductionIn usual theoretical calculation of elastic ed scatter-The deuteron system is the simplest nucleus whereing, whetber relativistic or nonrelativistic, the sign of Yprrelectron scattering experiments bave provided valuableis simply taken positive.2.3] But until now, the sign of cou-information about the quark structure and strong in-pling constant[4] of the pry process is stil a controversialteraction of nuclear systeun. Since it is a spin-1 n1-problem.5-7|Recently, studies at Jefferson Lab have extended thecleus. where elastic electron scattering can be described bythree deuteron electromagnetic form factors (EMFF): Gcscope of t20 data up toQ2 = 1.8 (GeV/).31 This pro-icharge monopole form factor), Gq (charge quadrupolevides more information for investigating the sign of 9pτγform faxctor) and G M (magnetic dipole form factor). Theand the six-quark cluster effect in t.he deuteron, as sug-diferential cross -section of unpolarized elastic ed scatter-gested in Refs [8]-[10)]. Figure 1 sunmarizes the previousand new data for 2.3.11-1ing is usually written as(((044(1)) (1)IN一( d2/MotwhereA(Q)= GE+ grG唱+ °nGB(Q2)=二n(1 + n)GR,(2)4(Q2) and B(Q2) are the electric and magnetic structurefunctions, η = Q2 /4Mg Mu stands for deuteron mass and0e is the laboratory scattering angle of the electron.It is necessary to measure a spin observable to sepa-rate tbree form factors. In an e-d elastic scattering pro-二5cess, the tensor polarization t2o is one of three observablespwhich describe the relative distribution of the spin of therecoiled deuteron nucleus on the three magnetic substates(b) pTY meson exchangcm: =0, +1. The expression for t2o is given byh1t2o=-v2[x(x+2)+ y/21/[1 +2(x2 +y川]，(3)Fig. 1.y= =(E)1(6),In中国煤化工is calculted audcomparYHCNMHGinorderwiguref(6)=j+(1+ n)tan2(0/2).(4) out the sign of 9pπr'The projet supported in part by National Natural Scicance Foundation under Grant Nos 1697500 and 1983501045YE Tao, CHEN Yan- Bei and CHENG Tan- ShengVol 352 Formalismcorrection Lerms to the order M- 2 .In order tw take into account the quark cluster efect,p(k;k2}=9nN>9opπ-9pNx(1+2r-T1T2the hybrid quark- hadron method is used8-101 in our cal-8mgm3culation. The wavefunction of the deuteron is separatedx(σ: .k1)(σ2xh2).(k x k2)into two parts: the two-nucleon part and the six- quarkx F(k)P(2)+(1→21.(9)cluster part, that is,j(k1,k2)=-irwv9pa>9pNv(1+/)( ψww(r1,r2)，|m1-r2l≥ro，4m2pmn心=( ψeq(2],22; x3,24. s,o)， otherwise .(5x TI r2(σ2. k2)(k; x k2)F, (3F(k2)They are separated in coordinate space, therefore, thex|i-器n(;+*)]+(I→2). (10)EMFF of the deuteron are the sun of the contributionsfrom the two- nucleon and six-quark cluster,wherekI=p(- P1.kx2=p2- P2.Gc=GE~ +GE ,and we introduce k and q such that,Gq=G&N +C,GM=GNN +G%.(6k1=jq-k，ke2=;q+k.and!17|2.1 The Two- Nucleon PartFa(E3)=KB(k3)B=π. p.(11)k2 +m名In the two nucleon part, there are two processes, therelativistic impulse approximation (RIA), which automat-where Kp is the vertex function of the ineson B,ically includes the correction for pair and pion recoil cur-号(2)rents; and tbose from ρπγ meson exchange, to be consid-Kg(k2)=k?+暗B=π. ρ.(12)ered for the deuteron form factors (Figs la and 1b),In the above formulac, 9nNN is the rN N pseudovectorGE~ = cEIa +GE”,coupling constant, 9pπγ the pπγ coupling constant and9pNN and K the pNN vector and tensor coupling con-G%~=GJl^+G&"，stants, n/9pNN = 6.8.18 mr, mp and Inv are the InassesGMN = GRIA + GT.(7of π, ρ and nucleon. We take the same values for theparameters of the ρπ) meson exclange proces; as thoseFor simplicity, we use an approximate formula,16used in sulving the wavefunetions.19| In addition, we takewhich can give satisfactory results when Q2 < 3 (GeV/c)2.0.56 for the absolute value of 9ptr. 4The formulae are listed below:For GRT, we cannot use the frrnula given by GariGBIA = GEsDc + (2Gms - GEes)D2O，and Hyuga directly, since we take a different vector partof exchange current operator. 17] However, the mnethod canGB^ = GrsDq + (2Gws - Gxs)D2O，still be used here with ninor adjustment, since our currentGRA = Gres唱+ GmsDM ,(8operator is still local. Consider the first part of Eq. (10),where GEs and GMs are the isoscalar electric and mag-if we combine the two terms [1 - (/4m品)号+ i川andFx(k3) to form F-(k), and a second part with 1 replacednetic form factors of the nucleon,by 2, it can be proved that tbe fllwing manipulativns17|Ggs(Q?)=(1 +Q2/M2)2 'are still valid. Therefore, we can get the formof FBT for-mula if the following substitution is made,Gxs(Q)=0.88(1 + Q2/M3)2'Jp°7→jpT7= I dx R(x)F(k2--q2 - akx)M。= 3.8 fm-'.中国煤化工，(13)For the pρπγ meson excbange charge operator, we useYHCNMHGbe usual nonrelativistic formulal17,18] and for the ex-We use a wavefunction solved from thr Grosschange current operator, we introduce local relativistic equation'19.20] in a one-boson- exchange (OBE) tmodel, inXo.↓Tensor Polarization t2o of the Deuteron and the ρπr ProcessI57whirl the folowiul forn of the πNN coupling is uscd,1M9()=dr j(r)Y 1小1(2,) j(r).91[\x*+(1-2)--129，(14)(例|p(r)w)= 0(川”()。2Mwhen λ = 1. the coupling is pure pseudoscalar: while(1(r)|) = (r)y4(r).λ = 0. pure psedovector.3 Result and Summary2.2 Six-Quark Cluster PartUsing the above frmulas we have calculated the tensorThe contributions frum the six-quark clusters to thepolarization l20. Figures 2 and 3 show that the resul:s areform factors. G GQ GXi, can be written in termns of sensitive to the match point ro and πNN uixing parame-redured matrix elements between single particle states.9lter入. When we take 9pπγ >0,r0=0.65 and λ= 0.1, theresults agree well with experimental data. The six -qarkG=°”(1(212/2151/2/2p + Drob)cluster efet improves the agreernent of our resiu!ts withexperitmental data, especially the tendency il lhigh Q2.一21:/z1iMg"|1p1/2)SDproh.017- (!l)]|d/2)Dprobl”=0.650.5---. =0.60、18MZ.0-V Sprob DPpeub员-0.;4.5 +(四一周)(, SDprob- 2.0101.03√2SDoo]l2“(GeV c;'QFig.2 The variation of t20 calculation results with rov6.Md(λ= 0.4). 'The cxpcrinental data are taken from Refs 3].(2Sprab _ Pprob/2)19-13).√VSprobDprobI 07-- λ-0.2SDprob)5-一λ-1.4-- A.06r下。00 .920吕-10.3.) Dprob-1.0-- (√5+√2)(lps/2| rM11/2)); SDpob](15) .-1.5-whereSprob= | u2dr， Dprob= w?dr,中国煤化工SDrrob = Spub + Dprob,DHCNMHGFig. 3 The variation of t2o calculation resuls with λC(0)=fdr j(ryY>M(Y)(r),(ro = 0.65 fm). The experimental data are tiaken fromRefs [3; [9]-[13].458YE Tao, CHEN Y'an Bei iand CHFNG Ta-ShengVol. 35一-儿>1.=065 fiFigure 4 shows that the t20 calculation rsults do not!07 .... <0 '。=0.65 fnagree apparently with experimenial data if Yorr Is taken-- 9. >0r-0as negative. whether the quark cluster efect is taken into-- <0τ 0account or llot.Froru the abuove results, we reach the conclusion thatthe tensor polarizatin l20 of deuteron is a good observ-able to discriminate the sign of 9axn. especially its new-1.01-data. A positive 9ρτ~ is arceptable. More experimental-15 +data may help to confirmn this conclusion.Acknowledgement1;.013 2We are grateful lo Prof. YANG Li-Ming for many use-Q° (GeVie)'ful discussions.Fig. 4 t20 calculation results with difcrent sigu of 9pπvThe experimental data are taken from Refs |3], [9)-|13].References[9] TS. (heng and L.S. Kislinger, Phys. Rev. C35 (1987)1432.1] M.I Haftel, L. Mathelitsch and F.K. Zingl, Phys. Rev.[10] LC. Lu and TS. Cheng, Phys. Lett. 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