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(1)Title. 拡がったクオーク模型におけるハドロン質量. Author(s). 平野, 雅宣; 松田, 康夫. Citation. 北海道教育大学紀要. 第二部. A, 数学・物理学・化学・工学編, 44(1) : 13-22. Issue Date. 1993-07. URL. http://s-ir.sap.hokkyodai.ac.jp/dspace/handle/123456789/6216. Rights. Hokkaido University of Education.

(2) . 北海道教育大学紀要 (第2部A) 第44巻 第1号. 平成5年7月. lof H ido Un iver i i i ‐ Sec I A)Vo l 44 I jouma ty ofEducat t okka s on( onl . . , No. l Ju y ,1993. HADRON MASSSPLITTING1N AN 蔵XTBND猛D QUARK POTENTIAL MODEL ) M[asanobu HIRAN0 and Yasuo M[ATSUDA*. * 〕 Hokka i do Un iver i ion ty ofEducat s ,JAPAN ,Sapporoo02 ,Sapporocampus Hokka inee i l ido Automot i r ng Col ege ve Eng ,Sapporo 062 ,JAPAN. Abstract. Based on an extended constituent quark picture, we haveexamined masses oflowerl y i ng ‐ i ings dueto u d ands quarks we1 had i r t t onsconsisting of “, d,s, c,and あ quarks‐ M[asssP1 e , ,. l ful lyPre電 int ikequark Pi i i r ‐ cture success ctedbythePo onscomPosedofc andる ,andheaVyhad 1obal ly understood. The adequacy of the nonre.ativistic aPpr。xi ion f ( 五nary are g 1nat or or i ~ ””.thePoint l ike Picture case‐ t▽ sd scus sedby comParingi quarksi -. ion か lntroduct The dynamics under l ( 去 r onPhenomenai sthoughtt。be QCD- Butduet。comP1 ying ha ex- i f f i i lyf tto understand d desPi ty ice QCD) idesinlat te 惣ご t cul rect t rom QCD ( eats r , many are di - i i Th i l l h o i i l d l t t t shas g ven rse to a numberof mode s deve rom QCD opedf n e o e n a mo e s e P ‐ for c。nstituent quarks i ing一shed f t r rent quark i sd s rom the cui n . The c。nstituent quark i i lat i 、 Z i i ーassi wh chthe Lagrangeani t se×Pressed‐ The naive constituent quark lr n せま enon d r re s c li ial mode i sg ven by Potent. where. (三 侃“ ); 崩す/3 例” = 飼ば. 1 ‐la ( ). 51 Gev 粥s = 0 ‐. 1-lb ( ). M isthe nucle。n mass‐. )by the baryon The above quを江k mass values are obtainedl. i ma c momentrelations 主犯et. 1- 2a ( ) 3”(△) 粥 = 財/. 1 -2b ( ). ic moment where ”⑦)and”(△)arethe proton al 2肌) ldlamda magnet / ( sin e . Thi l works we l l id i l lythe sconstituentquark mode ty ofthet ia reatment ,buttheval ,esPec 13) ( ・.

(3) . 14. M脳髄ー ATSUDA RANoand Yasuo M[ nobu HI. } as ion has not been e i i tabl lat ivi lnat t s shed2 s c approxi non こ re , 2-2 6 〉 =1 〈p2/飼美 . ‐. 1‐3 ) (. 帆r 1- 2 )arisesfrom theassumptionthatthe quark anomalous maをPietic moment enotethatEq ‐( i ike const tuent quark model lbased on this assumption a point‐l l la mode bl i igi ‐ e snegl ,and ca l ike ヒ メ i t tuentquark aspoint li ‐ Another aspectofthi econs sthatthe naivetreatmentofロ s mode コ ron l ia lextensionofquarksi i i l i f f 【 lal sfarsn erthantheobserevedhad t runsi cu esasthespat ntod ) ikethe charge radius3 fm)l extension(~l ‐. l ike but extended ln th hat the constituent quarks are not poi i l i nt ‐ t n ne t c e we assu・ s ar fect i i i but ions f ve i i th cont t r anomalous chromomagnetic moment r rom the es wi ent . The ef k d l i i l i k i i ht h l i h t t dt t n ‐ u a r mo e s Hami l ianofconstituent quarksi o e n o n w e v e a ton ere an p q sg lat i 3 ) re ‐ et mesons are d i ‐ 2 et baryons and 35 ons for L = 0 pl pl scussedin S ,56 , SU( ‐ ln S3 d i i d l i i d t t t f i l i d L u a t t n u n l 4 = s a n c o s e ngs are scus e meson nesp q rk parameters exam ne ‐ nS, f ine spl i ings of s‐wave mesons are t t ing these parameters, in S5 termined are de 「 per ‐ Us , hy i i▽ lat i ionoftheadequacyofnon i ‐ capproxl thdata st i r e scuss ctedandcompared wi predi ‐ Thed lare giveninS 6 ions o fconstituent quarks and other aspects ofthe present mode ・nat ‐. l ian i ton S2 Constituent Quark EH; ve Hami ect ‐ tem,should be l i fect ive Hami to副 VV an forthe constituent quark sys e assu工ne thatthe ef f f h h h d i i tf t di k fextendedquar parameters w c are eren rom evaluesofnaive lnso expresse n ter quark ones .. A. } in thecenter of mass i l ian4 bed by a Hami i ton meson,for example scr , , s de. ln syste. 2‐1 ) (. 2十 U 互の =J 粥テ+ 〆 +J弼茅F つが + にγ. ◎ 「ヨ { +≠デキ} )ルト 矛十等 十等 矛) ナーテ(鯵 デ 冬・ .誓[ %… -¥ 『 伽 ,方 @が I. 2‐2 ( ). 随 ー8 ” 十 煮 物{;¥ キー 趨 麹 T 跨 メ. ] } ) が( γ. (五nate ive momentuヱn and coor Where p and γ are the relat ‐. Here モヱのれ stands for dle ,. i ion of the spin- ial l i 1ator potent hami l ian bound by the osc scuss ton . There has been d ) and 5 ) and i t dependence o ] ; f fthe cor i川ng force s Lorentz prope貴y6 concerning the shape ,( 7 ) lar i ion atlarge distances i鱈ble since the vacuum po zat ti ) s negl others - ▽Ve assu工ne thati ) reduces s i l lnes ial ining potent : t ] ly6 s of spin‐ sma e conf pn dependent forces oft great . The‐. 4) (1.

(4) . 15. HADRON MASS SPLITTINGIN AN E×TENDED QUARK POTENTIAL MODEL ) he confining interactioni dependent forces due to t s confirlnedinlattice gaugetheory8 .. The. ▽o (= 1 十 #ざ ) sthe one gluon exchange contribution between Zandゾ constituents whereg i G Ei i 3 tぬin & andquark mass breakingbo ) rePresentsacolorgyroma鱒1 et cfactor eassumeSU( ‐ - Wr i ic l ions t “偽. Th s ar e takes ▽oGE into account as Pe貴urbat - The 2ヒ stands for the quark- iquark ann ihi lat ioncont ibut ionin a quark‐antiquark system‐ lfthesystem isquarkomu 1n, ant r 1. 2+ び 品 =2 同房F浮 十 Kγ. 2‐ 3 ( ). forthel ing orderintheP/粥 expans ion ead , we have 亙,. 2十 ″ 伽 + 易 十 Kγ. 2 ‐4 ( ). ine l f we def th a constant , wi 1. 1. ~= 1- β )創 粥 T T 扉 m = で 粥 =(. 2‐5a ) (. 1 - )虻 K =(. 2‐5b ( ). ion ion transformat i latat ad. 2-6 ) ( leaves f z ive constant t ln, exceptf or an addi 。inthesaユne for ,. . . . 頓r i fythe Hami l ia l mode l to山an( 2-7 )to be せlatofthe naive constituent quark Potent eident ‐ Comment 2‐4 2-7 )transformation: )-( s onthe( 1 ipl i ings are unchanged by the ( 2-4 2‐7 format ion ince they are ( ) Mul t t t )t )-( et spl rans ,s inalto K/m wh i iant chi sinvar proport ‐. 2 2 2 The parameter 洲だ) may depend on f 2 1-び lavor ( ) F )( ,mther 野/溺) . We may ,p /創 =( ‐ expect. ~○for heavy quarks since heavy quarks1ocate close to each otherand have1ess. loud ef fect fl > c . l. ivist ic aPproxi ion wi > ofor ordinary quarks,then the noni l l relat rnat. have someva l id i ty ‐. 3 ( ). Thespin and orbi talanき犯lar momentum operators areinvariant‐. S3. S‐wave hadrons composed of u d and s quarks , ,. lnthi ion ful lyreexaminetheSU( 3 lat ionsPfor乙 ; 0 )re ssect ‐pl etbaryonand ,wesucces ,56 k 35 l d i di h l k l l -pet meson erve nt e Point ‐ike quar mode rom 伍eextended quar mode ‐ ,f. 5) (1.

(5) . . 16. Masanobu 日I A Noand Yasuo MATS t 冗 ) RF ~. S‐wave 56 et baryon -pl. i l in αs lat i to雄an i For せl t order, 10 l u r e vi st c hami ef rs , we have a1. i Andthef s rst order massformulai. . ] 蒸 篭 矛十鯵 デ + 著 誉} -÷; キ ー ユ . (H) 3‐2a ( ). . . . 物 辺2+ 翻れ勉 盛 1 > ≠ に ÷ < ≠一 , γも. ) (細c 2d 3‐ ( ). メニ テ 〈 創 始・ 1≠ ) 2 o> where 小 ois an eigenstate of. 2+ U 2 脇 十 髪 十 比γ. (淵). i ight mas t(刃, β, β, β)becomeasl Thusthe massformulaforthee stedin ‐ e sesof 故e56 P1 2 i Tabl )sym met ng SU ( ryfor 鉱e % and α quarks j o 口 el . ,assu. l Tab el. -★×. &( 1 -★). 紡( ). N. ^ = V. 1. B. リム. 1. I← ^ ” V . ▲. 穿. ハ ム. T I. l. r. 〆. I. 4. △. l. 1. ・. QU. Q. .. -co ゑ 7 2 7 2. . 身. 十¥. +甚). -4&2十12& ー6. 0. 0. 2 ,1 郷 鈷 2 . { 7 2 7 2 7 2 S I-2 1 ““ れs. 4&-2. ÷ 諾 +8&ー4. 2+8g ー4 -4gれ カ. 4g s-2. を 2+8&-4. 4&-2. & ““. 2 4g 。 十12& ー6. I E2 翻 然 211 硲. 霜. 心 S S. 6) (1. お +8&一4 4&-2 o. 、o. 4&-2 を 2+8&-4 2g ‐6 4軽 十1. 1 6. 一. すg遜s 0. 1 6. 冊. Tggs o. 8 手g遜s 8. すg鮎偽 0.

(6) . . HADRON MASS SPLITTINGIN AN E×TENDED QUARK POTENTIAL MODEL. 17. Then 2(』 * - 』) - gs 粥れ 2ガ *+ お ー 34 g” 粥s. 3ー4) (. 参 三 分 = 針・- 昔 祷}. ㈹. 2 2N 十2g -( 34 十 』 ド ー サ d{ 考 - 肴 }. (『. 2 (4 - “}-(』*- メ ド - 誉 偽d{ 貴 - 蓄 }. 瀞). 2 ば *- β* )‐(β*- 〃- )= ÷ ”{ 考 - 肴 }. (淵). (Z* - β)=(β* 一. 三). 3-9) (. hepa貴ic l i wheret enamesstandforthe r masses ‐ Then f hef i ighthands torderof β 癌,ther id 3-6 3-7 rs 3‐8 ) ) )arezero (篤 ofEqs , ort ‐( ‐ ,( ,and( 9 ) i They are Ge l d h l l l M i ok b t 1 ゴ ロes 3-9 ‐ ann ave equa spac ng r ( u o re a ons , an )i s a relation ‐ Eq .. independentof 雛 and 1 fせl 3-7 3-9 )~( ) are expressedin terms of 例,they are ofthe e relations hold and Eqs ‐( int l i ike quark pred ions sa 1 α 1 e for ththe po ln wi ‐ ct ‐ The para]meter free relation. f i ied t l ssa s ‐ S‐wave Me ヱ≠ sons(. の. ou i こ rf rst order massformulai s. 財-脇. {★ 鶴十〆. ] ★}. Tab ー t( 1≠0 e 2 S‐wave35 ionsin 仇etabl ‐ e )meson massformulas i i t pl s earetobe mul ;expres edby pl thetop ofeachco l r tandf i i u i m皿 wherenandss t ort er ( おpec vequark mas ses ‐. &+ ( ÷★) α ^ = V I l. K*. ^ ” V. P. T . ▲. K. -÷d m. -“). ’ -〆 [サ. +¥. +封]. 1. ふ ”“. -4&2+4& 冊2. 0. 0. 1. 1 7 2 S. 2gれ-1. 2g s-1. ー4g i 疑g s. 1. ↓ ““. 4 ÷察+ ー &. ふ. 2&-1. ー. 7 2 S. (17). ” 2g ‘-ー. 影禽.

(7) . M[ A ATS sm) R ! I N0and Yasuo M[ asanobu 日I. 18. ’ ’- エ ーメ ]+x {街 き+ 塾 r 十 葛 轡 } ‐キーら . 1 0 3 - ) (. ’ b i lartoα i d i【 i df 1 assformula l where α, . Thenthe ,る,and c as nthe aryonα ,わ,and ご are e ne sn S-Wave me son masses can be expressed asin Table2 ‐. Thus weobtai nthe relation. K* - ” β一ガ. 2(』 * - ぎ) 冊 2ぶ * + β 一 34. S4 Values of Quark. 粥 粥s. 3‐11 ) (. ic moments Masses and Anomalous Chromo ‐magnet. 7 f h f 3-8 3‐3 ) ionsin Eqs ) 一( Asseenf rom thes‐waveexpress ‐( ,ぎsand 伽 senterint e orm o ′ l i d h t i f n oma o u s ‐ f h i n a r mo ma e c c o 鱒l the ratio, g/雛‐ To obtain urt er n ormaton on masses a Th f l f P 乙> i k ma s n e s o r i me s o s o r mu a t e ‐ wa v e ft h t t we x n e am r n u a s n s u e t c o n e q so . mome 、 ,. oisnow &- 爾 すん {鯵 矛 加 -★} ]守 る&{ M 細十頭4粥 一 身-. 十峯 デLm 泰i 鰯 十 泰. 鞠 十 煮曇毎 朝 ,. 4 ‐ 1 ( ). where 7 もisthestandard tensor operator,上毛1≠。 〉 = ルグコ ヂ。 >,and. 4‐2 ( ) 1 0 ) ) , inesp1 i ings are4 t t i iesforthe p-statef coα1 i t lnon1yl sted quant. 3 3 P, ー P o. 4-3a ) (. and. 4‐3b ( ) l ヒ n to be lnthe present mode i venfor quarkoniu] ,they are g. ‘; 2 d e 尺ro. 4g - ・ - 号 g2. 各 a ). 4g 一 1 + 3g2 4g - ・ 十 号 g2. R ド ヒ 3. 4-4b ( ). 4g -I一 ÷ g2. l 国u iwm, and bot tomo ( 五nary lm i st s the 乙 = l or e31 ch depend omy on g whi ‐ Tabl ,charmon ’ l k di i i d i d di ios i ththe r 尺 rat states wi ‐ ,the gs for or nary, c, an ら quar s are eterm ne n prncpe d d i hb d ら n に a a s ) t n n e s a ma s sr a Not ingthatthereare afew p‐waveor山na s w r o a me o n s g ly l . 7 IP states of cご and も f 廿 l hed l b l i texpe i t n s rom 品 t n i m e sr a e ea s s e b l s w r n o a s a e r me n a g g a y , , G d 例。 = 4 ー 1 6 1 k l ; n e v a l d dろ : 粥 ぢ i a e s ma s sv u T h t for 房 andろ‐ quar ecommonyc e c an . . c. 8) (1.

(8) . HADRON MASS SPLITTINGIN AN E×TENDED QUARK POTENTIAL MODEL. I9. iosofP‐wavespi Tab l ings r l t t i tat tabl e 3 尺 rat eIP ldbる sl r l E おarenot巴 s shed l ore ;forcごa 1s ,t ,and 尺,i l i re abl e せl an R3 . SL J. るわ. 3P 2. 3P ,. 3F 。. 1320 ) の(. 1260 ) α .(. 983 ) 命(. x2( ) 3555. ×.( 3510 ). ヱ0( 3415 ). xウ ) 9915 2(. ヱわ 9890 ) 1(. xb 986の. 2. 4. IP .. R. e×P .. ろ 0 21±0 11 1232 ) .( . - 1 1 48±0 ×( )} 0 01 3525 ‐ . 2 ) 066±004 ×( 9895 )1 ‐ .. 6. 8. R3 l mode. exp .. l mode. 0 45 .. 3 9±0 5 ‐ ‐. 4 1 ‐. 0 48 .. 4 6士0 13 . ‐. 3 9 .. 0 65 .. 2 9±0 3 ‐ ‐. 3 3 .. 10. m(Gev). F ig.1 Anoma lousc l立omomagne i ins t t瓦aga tquark mas cmomen tehロロned官om sm‐ Thedataarede p‐wavef inespl i i i ium‐ t t tomon ngsofchamコon u u 〔 nandbot. 4 6 - 4‐7 Gev,correspondtoァ”(not 免) h ion doesnotusethe magmet ic moment ‐ ,ast e determinat l i 1 i f Th l t i i l lot re a on or m n ma couP ng‐ ese g va ues are p ted against 粥 instead of 況 in Fig ‐1 ‐ The curve characteristic ofthese pointsf i t tedby . . 4‐ 5 ( ). 1+ 堺. 21and 4 ; 6 60 Gev th α = 1 wi 4-5 uesfor7 ) 2a l ーdsquarksareobtaninedby Eq ‐ ‐ ‐ Theg val ‐( , ’ The valuesforquark massesa i T h d ら h に nd gs ar tedin Table4 恒 h el α a n s n e ma a v e ≦ 海 e w s c . ‐ , ‐ ies are pr large experimental unce 〕 naint i 1y 1215 M[ ed ctedto beapp l oxi l エ ー ate ev and1238 M【 ev , ‐. 9) (1.

(9) . . 20. M[ ATS狐) A asanobu 日限第Noand Yasuo M[ i I P r t c moment sg l Tab o 】 mo 】 ma ter ousc ミ 鵜esand anomal を頭e e 4 Quark parame s ;ma . 猟 = 粥/g int l ike ‐ po. l extended mode. quark f lavor. ) mas s(Gev. 免(Gev ). 2.15. 0.726. 0‐337. 2‐07. 1.06. 0‐51. 2-00. 1.52. 0‐76. 1.40. 4‐70. - -3.36. 1‐00. ミ5. g ふ ▲ . ふ 1 1 ユ ー ▲ .. 入り チレ. ぴ 。. 120.O. 120‐O. ) mas s(Gev 0‐337 0.51 1.52 4.7 120‐O. i S‐Wave ord inary and a charm‐ )quark containing mes。ns (ant. lavorsyrnmet Thef )i and ろ s bamy broken, so we treat more 宝y a]mong “, d, g and c ( ly i r lychar ons madeof“,d,andsPreVious exact nned 立lesonsthanthatdoneforhad ‐ VVetake , inthe center of a masssystem,. 5- 1 ) ( 2-1 l ) teadofEq he mlperturbed nonrelativistic Hami tonianins sthereduced mass ast .( ,where〆i l i inear potent ial i ialhas been replaced by the more rea in ing potent cl st and the conf . The f hyper inespl i ing of s…statesi t t s now given to be. 38 -・溌 - テ えα g羊 揚. 5‐ 2 ) (. 吻. lavors ionfor3f lat (五ng to t ing constant αsi : he asy〕mptoticf The coupl reedom re sset accor. )ニ (q2 αs. ー 侮2 αs ). 5‐3 ( ). ・十 番 α緬 引o g影. imat ing く αs (q2 ) t Here wetaketwo prescriptionsfores 2 q =. 3 ) s to subst 61 i tute one’ i. 3Sり]2 γ[肌(. 5- 4a ( ). )subs i i r i t tut ng t e reduced masssquared sone* and 官l eotheri 5-4b) ( l l i l r f i it i h t fh 16 Gev2 ing 入 = 0 th constants γ and ぴ. Choos wi . ,t e nmmer ca resu so yPe nesp t ngs lavors arel i ionsof quark f e5‐ Y for various combinat stedinthe Tabl l d t f bl l i From Tabl e5 , we see thatthe extended quark mode g ves reasona y goo resu s or ical pr { 五ct ionsexcept l ike quark a l l int に ner e i so gives good nuu ther case A or β, whi ‐ e 仕l e po e i r l luesofα& Fort l icald i賃erencebetweenthetwo mode eformer t si sintheva ヤー ガ◇ A-cri , i i do Un *) Th i v sf orm wassuggestedby Dr ‐ .C.Habeof Hokka. 0) (2.

(10) . 21. HADRON MASS SPL工TT工NGIN AN E×TENDED QUARK POTENTIAL MODEL l Tab e5. “ ” l dinesp Hy l i ingsforS‐wave mesonsarei t t { 4a )and“B“f e n Mev rom Eq rom Eq ) 1 . A aref - ‐. 5 4b ( ) ‐ . PRED1CT1ON 脳[ ] ev. αs EXTENDED. POINT. EXTENDED. DATA. POINT. A. B. A. B. A. B. D*-D. 0 377 .. 0 378 ‐. 0 642 ‐. 0 890 .. 205. 206. 98. 136. 142. D斉一Ds. 0 368 ‐. 0 337 ‐. 0 624 ‐. 0 706 ‐. 168. 154. 87. 98. 140. マーガ c. 0 310 ‐. 0 310 ‐. 0 520 .. 482 0 .. 116 input ( ). 116 i ( ) nput. 49. 45. 116. *-に Rr. 0 636 .. 0 404 ‐. 1 215 ‐. 1 182 ‐. 451. 286. 408. 398. 390. β一死. 0 727 ‐. 0 445 .. 1 469 .. 1 469 .. 658. 403. 620. 620. 620. i t ( ) npu. i t ( ) npu. T冊ガ b. 212 0 .. 211 0 .. 0 338 -. 0 327 ‐. 13. 13. 10. 10. β*-β. 254 0 ‐. 0 336 ‐. 0 410 .. 0 806 .. 40. 53. 23. 45. 46. β審‐BS. 252 0 ‐. 0 300 .. 0 407 .. 0 631 .. 36. 43. 22. 34. 47. ,A. B. l ICo i imatei l iable the values of αsremainsma i n ner ]mPared▽晒せ1山国ty calest sre ,andthenu ,but i l i 5-4b)mayseem morefavorable ti ter el at snotfor 廿i ng Eq - lnthePresent mode -( ,Case B us h l ive treatment o ider i ts f αs and our nonpertu fthespin n nericalresul ng nu] 二 rbat Cons ,t e va ues o dependentforces ‐. ミ6 Di scuss lon lnpoint l f f ikeConst i i tuentquarks - rom U嘘tybyabout40%,and ane×pansion ersf , 伽れ/粥sd tot hef i 3)breakinginc torderinSU( rs . 刀 r sa ~15% e ]lor ‐ lnthepresentextendedConstituent. 68 andgs /& = 0 96 andthe mag Pmtudeofせi esy lnmet quark, 粥“/粥8= 0 ly breakingin quark ‐ ‐ l ight ly smal l l int ike quark and Wi l th the po th g i tesmal massi ss er(~30%)than Wi ti ‐ s qui. (~5%) ‐ As a result of Eqs 2-5a 2-6 ( 五nary ) and( ) e nom「elativistic approximation for せl e or ‐( , せl iderablyimproved: sCons quark i. 〈静 め = ★ <〆 鰯〉= ★ Q2~2 6 ) ‐. 6‐1 ( ). Wi故 our value ofgk,this quantityisreduced tolessthan l/2 of meoriginalvalue‐ An other success of the po int 1 ike constituent quark model in dea1 ing wi th the stat i - c ies o fhadronsi i ion for the proton mag口etic mo立Ient l h d d sthe pred ct t t propert n x n e e e e ‐ 1 4 ) i tuent quark ばIodel Const , we have ~ ? “り /g 『 ~ 伽 g『 ”. 財/ ノ ヒ メ⑦) 〆. (6‐2). ins 1-リー Hereg『 ==1 十 ”星mi teadofEq l i i stheusuale ect romag皿et cgyroma鱒口et cfactorof .( the 泌 quark‐ l f we assu工nethe gy丁○.nagnetiC factor to bes imi 1arto the Color gyromagnet i c. 1) (2.

(11) . 22. Masanobu HI RANoand Yasuo MATSUDA. factor we can Pred i imi lar Values ofthe Proton magnetic moment cts ‐ ,. l lreProduced in the l are We l These adVantages ofthe Po int ike constituent quark ばl ode ‐ i ions in the extended cons t tuent l i tuent quark l ther the cal culat 1 l ode extended const ‐ Fはr l iable as t he SU ( 3 )sym met ry andthe nol甘elativistic aPProximation are picture are more re l bettersa i i t edandthe quark‐gluon coupling constantremainssmal sf .. i ion Thefun heraPP1 ; cat. 5 ) last i tto future resolution1 to experi sl ef lnents ofde c phenomenai ePine ‐. referenCes. 1975 ) iand s la 1 ashow Phys )A.De Ru ju . .Rev .D12 ( ‐L.G1 ,147 , H.Georg D25( 2 9 4 4 R 1 9 8 1 P ) H d N ・ h 2 e )C v n S r s a ea E 国 y ~ m . ‐ - . ・ , , 1973 ) 3 tal )M.Hi ranoe . -Theor .Phys .49( . ,2047 ,Prog 1978 ) suda rano and Y.Mat 4 suda ranoand Y‐Mat )M.Hi ; M.Hi . ‐ Theor ‐Phys . 60 ( , Prog . Theor ,1490 ,Prog 1979 Phys ) . .62( ,501 dp. t 紅l 1975 ) r l比 landF nqa 5 )J ;E.Laer ‐Schmi ‐Langhamme .Rev ‐D12( ,1 ,2821 .B.KO樽滋andL.Susskind,Phys 1986 M.Ze t t ) rwas . .173B ( .Le ,437 ,Phys T h Phys 1989 P ) 6 )M‐Hi r o e o r r ranoa .d Y.Mat suda g ‐81 ( . . . ,172 , 1979 l t t ) A B d f f i l i i ti d 7 r a ey )Forexampl c n … w a v e m e s o n s a m x n e e r a e g p . ‐898( .Le ,116 . ,Phys , , K‐Mor ia M.Compos in i 55 1 9 8 5 1 2 4 t 5 P h R L t t t ( ) andC l 8 r e )P s e v y ; y .Rebbi , ‐ , . . .D‐Stack , .de Forcrand andj , in i i tyandC. 1987 t ) ike t t ar r Phys 1986 t t ) ; M.Compos ;Y.Ko ‐59( .Rev .Le ,K.Mor ,962 ‐Le ‐57( .Rev ,Phys ,44 1987 Rebbi ) . .Rev .D36 ( ,3450 ,Phys 1962 ) 1962 ) 9 l l )M.Ge -Mann ;S ‐ .27( .Phys .Theor .okubo ,949 ‐125 ( . Rev ,Prog ,1067 ,Phys 65B( 1 9 7 2 9 6 3 i P h L ) t t 10 t )H.J e zer s y . ‐ ‐Schn . , , 1986 l l ion ) t t 11 )R704Co aborat . .171B( ‐Le ,135 ,Phys 1992 l ) 12 )Pa貧i c edata gr oup .Rev .D45( ‐ ,Phys 1979 ) 1977 fol ) i ; 13 )A.Fenl s ;J andez ‐Pachecoand1 .Rev .D20( .S.Kang .Rev .D16( ,2978 .A.Gr ,Phys ,1510 ,Phys 1980 ) N.Bank ands . .Rev .D21( .N.Jena ,2647 ,Phys 1976 ) 14 )Y.Mat suda . ‐Phys .55( .Theor ,777 ,Prog i47 ( 1992 bata ) 15 )T‐Si sur . ,455 ,But. 2) (2.

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