最低质量负宇称核子态中的混合角对夸克超精细相互作用的检验_英文_

最低质量负宇称核子态中的混合角对夸克超精细相互作用的检验_英文_ ()第 31 卷 第 3 期2006 年 6 月 西 南 师 范 大 学 学 报 自然科学版 Vol . 3 1 No . 3 ( J un . 2006 )J o urnalof So ut hwest China Nr moal U nive rsit y Nat ural Science () 文章编号 : 1000 5471 200603 0044 04 A Test of Quark Hyperf ine Interact ion : Mixing ? Angles in the Lo west Ma ss Nega t ive Par ity Nucleons C H EN Ho ng H U A N G Sh u2yi , S c hool of Physic s a nd Te c hnolo gy , S out hw e s t Unive rsit y , Chong qing 400715 , China Abstract : The mixing angles in t he lo west ma ss negative pa rit y nucleo ns a re calculated by using t he interquar k hy2 perfine interactio ns w hich are induced by o ne gl uo n excha nge and o ne pio n excha nge re spectively. It i s fo und t hat t he diff erence i s lar ge bet ween t wo ki nds of exchanges , a nd t he exp erimental data o n such mixing angle s f avo r o ne gl uo n excha nge clea rly. Key words : nucleo n ; negative p arit y state ; mixing a ngle s ; o ne2gl uo n2excha nge ; o ne2pio n2excha nge + Document code : A CLC number : O5721 24 6 ; O5721 34 ( ) The ba r yo n s ha ve hi sto ricall y p la ye d a ce nt ral role i n qua nt um ch ro mo dyna mic s Q CDa nd it s app lica2 tio n s. U ntil we lea r n ho w to u se Q CD to co mp ut e ha dro n p rop e rtie s ri go ro u sl y , p a r ticula rl y i n lo w2e ner gy regi me , we mu st cop e wit h t he“Q CD2i n spi red”mo del s. A t p re se nt , mo st of t he t heo retical wo r k o n ba r y2 o n e xcit atio n sp ect r um ha s bee n ba sed o n p he no me nolo gical mo del s. A mo ng t he se mo del s , t he mo st sys2 t e matic a nd succe ssf ul o ne i s co n stit ue nt qua r k mo del , i n w hich t he gl uo nic degree s of f ree do m a re rep laced ( ) by eff ective po t e ntial s. Fo r co n stit ue nt qua r k s i n ba r yo n s , t he o ne2gl uo n e xc ha nge O GEwa s fi r st app lied [ 1 3 ] to ba r yo n s by Isgur a nd Ka rl wit h so me succe sse s. The succe sse s of Isgur2 Ka rl mo del a re due to t he O GE2i nduced hyp e rfi ne i nt eractio n s of colo r ma gnetic dipole2dipole co up li ng , w hile spi n2o r bit co up li ng i n t hat mo del wa s di sca r de d i n view of dat a w hic h de ma nd t hat suc h fo rce s be small . In f act , t he re e xi st s ca n2 cellatio n bet wee n t he O GE2i nduce d spi n2o r bit co up li ng a nd t he i nevit a ble Tho ma s2p rece ssio n2i nduce d spi n2 [ 4 ] o r bit co up li ng of t he co nfi ni ng po t e ntial . Rece nt ly , it ha s bee n a r gued by Glozma n a nd Ri skat hat t he e n2 ( ) ti re spi n2dep e nde nt co up li ng bet wee n co n stit ue nt qua r k s i s due to o ne2pio n e xcha nge O P E. In Glozma n2 Ri ska mo del , t he O P E p ro duce s t he hyp e rfi ne i nt eractio n s wit ho ut spi n2o r bit co up li ng. Thi s mo del at lea st ha s a f u nda me nt al f law t hat t he zero t h2o r der co nfi ni ng po t e ntial will p ro duce ver y st ro ng spi n2o r bit fo rce s t hro ugh Tho ma s p rece ssio n . The rece nt e xt e n sio n s of t he Glozma n2Ri ska mo del to i ncl ude vecto r me so n ρe xcha nge have at t e mp t e d to o ve rco me t hi s f law . It i s fo u nd t hat 2me so n e xc ha nge ca n p ro duce a ver y [ 5 ] st ro ng spi n2o r bit i nt e ractio n w hic h mi ght ca ncel wit h Tho ma s p rece ssio n i n co nfi ni ng po t e ntial . B ut such a n a r ra nge me nt off e r s no i mp ro ve me nt o ve r t he o ri gi nal sit uatio n . Here , we will avoi d t he t heo retical fo undatio n s a nd p ractical detail s of two model s. In order to test t he two quarks co uplings in baryo n , we will in2 stead accep t two original model s and calculate mixing angles of t he lowest mass negative parit y nucleo ns. ? 收稿日期 : 2005 10 20 ( ) 作者简介 : 黄淑一 1981 , 女 , 四川南部人 , 硕士研究生 , 主要从事强子物理理论研究. 通讯作者 : 陈 洪 , 教授 , 博士生导师. 1 Quark Hyperf ine Interact ion The eff ective hyp e rfi ne i nt eractio n bet wee n t wo qua r k s ha s t he fo r m of colo r ma gnetic dipole2dipole [ 1 3 ]co up li ng ? ? π8 1 () δ(ρ)ρ ρ S1 ?S2 + { 3 S1 ? S2 ? - S1 ?S2 ( ) 1 V o ge = C3 ρ3 2 ραWhe re S, Sa re t he spi n s of t he t wo qua r k s , 2= r- ri s a vecto r bet wee n t he m , C = / 3 2 mi s a n o 1 2 1 2 s αverall co n st a nt ,i s qua r k2gl uo n co up li ng co n st a nt a nd m i s qua r k ma ss. The fi r st t er m i s called t he co n2 s t act t er m a nd t he seco nd i s t he t e n so r t e r m . No t e t hat t he se t wo t e r m s a re p a r t s of t he sa me p hysical i nt er2 actio n . A ssumi ng t hat t he t wo qua r k s i nt eract by e xc ha ngi ng a ma ssle ss pio n , t he O P E2i nduced i nt e ractio n [ 4 ]bet wee n t wo qua r k s t a ke s fo r m ? ? π 4 1 ρ ρ ) δ(ρ)S?S+ 3 S? S ? - S?S( τ τ( - 1 2 1 1 V = D 22 1? 2 2 ) ope 3 ρ3 2 ατ( ) Whe re D = χ/ 2 2 mi s a no t he r co n st a nt , a nd a re t hree 2 ×2 SU 2f la vo r mat rice s of t wo qua r k s. 1 , 2 () () ττThe mai n diff ere nce bet wee n Eq1 1a nd 2i s t he e xt ra f acto r ?i n V a nd co efficie nt of t he co nt act 1 2 op e t er ( π) m relative to t he t e n so r t e r m . It i s i nt e re sti ng to no t e t hat t he coefficie nt of - 4/ 3i n O P E ca se i s t he sa me a s fo r t he i nt eractio n of t wo elect ric dipole s. 2 Negat ive Parity States The lo w ma ss negative p a rit y st at e s of li ght ba r yo n s , co n si sti ng of ua nd dqua r k s , a re a ssi gned to a 702 () () p let of SU 6i n qua r k spi n2f la vo r sp ace a nd a 82p let of SU 3i n qua r k f la vo r sp ace . Thi s mea n s t hat t he o r bit wave f unctio n s a nd f lavo r wave f unctio n s have mi xe d p er mut atio nal symmet r y. The wa vef unctio n s i n χψλρspi n , o r bit , a nd f la vo r sp ace s a re rep re se nt ed u si ng , , a nd < , re sp ectivel y. The upp er la bel a nd i n t he se wa vef unctio n s de no t e symmet r y a nd a nti symmet r y unde r p er mut atio n of qua r k s nu mber 1 a nd 2 , a nd s de no t e s to t al symmet r y u nder p e r mut atio n s of t hree qua r k s. Igno ri ng t he colo r wavef unctio n w hic h i s a n2 Ψ ti symmet ric , t he to t al wavef unctio n i s to t all y symmet ric under all p er mut atio n s a nd ha s t he follo wi ng [ 6 ] fo r ms. λλ 1 3 12 ρ ρ λ λ ρ ρ λ ρ (χψ (χψ = χψ) χψ) N P- < - 11+ < J = , J 11 11 11 2 2 2 ( )3 1 1 3 5 s λ4 λ ρ ρ χ(ψ ψ)N P=< + < J = , , J 11 11 2 2 2 2 w here t he sp atial wa vef unctio n s a re a ssumed to be ha r mo nic o scillato r fo r m | nρlρnλlλ , L M 〉wit h ra dial qua nt um numbe r nλρ a nd a ngula r mo me nt um lλρ fo r i nt er nal coo r di nat e s of t hree qua r k s.,, 1 1 λ )ρ ( ( rr) =2 r3 =1+ r21r- - 2 6 2 The e xp licit fo r m of t he se sp ace wavef u nctio n i s λρ ψ ψ= | 0001 , 1 M〉= | 0100 , 1 M〉11 11 3 Mixing of Negat ive Parity States The st at e s wit h t he sa me i so spi n a nd hyp ercha r ge a re i n ge neral e xp ect ed to mi xt ure bo t h at t he SU ( ) () 3a nd SU 6level . Fo r lo w ma ss ne gative p a rit y st at e s of li ght ba r yo n , we defi ne mi xi ng mat ri x a s fol2 [ 7 ]lo w s 2 θθ N PN co s - si nJ J ( )4 = 4 θθsi n co s N PJ N J θ) ( w here t he mi xi ng a ngleca n be o bt ai ned by dia go nalizi ng t he hyp e rfi ne i nt e ractio n V o ge o r V ope i n st at e 2 4 sp ace co n si sti ng of N Pa nd N P. The J st at e s a re ei ge n st at e s of t he mat ri xJ J 2 2 2 4 〈P| | P〉〈P| H | P〉 H J J J J ( )5 2 4 4 4 H | P〉〈P| H | P〉 〈P|J J J J w here H i s to t al hyp erfi ne i nt e ractio n , w hich sum s o ve r all t hree qua r k p ai r s i n nucleo n . Si nce t he wa ve2 f unctio n s a re symmet ric under all t h ree qua r k p air s , we ca n o bt ai n H by multip l yi ng eit her V o r V by o ge ope t hree . The calculatio n s of t he se mat ri x ele me nt s a re si mp le a nd t e dio u s. - 3 απ) (In t he J = 1/ 2 secto r , t he mat ri x ha s t he follo wi ng fo r m i n t he unit of C fo r O GE , - 1 1 ( )6 1 0 B y dia go nalizi ng t he a bo ve mat ri x , we ca n o bt ai n t he ei ge nval ue s a nd t he co r re spo ndi ng eige n st at e s. The ( ) lo we st e ner gy st at e E = - 11 618of t he mat ri x a bo ve i s- P - 2 4 )( = 01 851 | 01 526 | J = 1/ 2 〉N P〉- N P〉 7 | O GE1/ 2 1/ 2 θθ2 Fo r O P E , we ha ve to dia goThe n t he mi xi ng si n= 01 526 , co r re spo ndi ng to mi xi ng a ngle of = 311 717?. s s 3 π) α(nalize t he mat ri x i n t he unit of D/ 5 - 3 - 2 ( )8 5 - 3 2 ( ) Wit h t hi s mat ri x , t he lo we st e ner gy st at e E = - 31 905i s - - 2 4 P ( )| = 1/ 2 〉= 01 906 | N P〉+ 01 424 | N P〉 J 9 O PE 1/ 2 1/ 2 θθThe n t he mi xi ng si n= - 01 424 , co r re spo ndi ng to mi xi ng a ngle of = - 251 097?. s s - Si mila r fo r t he ca se of J = 3/ 2 , we ha ve to dia go nalize t he follo wi ng mat rice s 1 5 3 - 1 - - 2 10 10 ( )10 1 9 3 29 - - 5 10 10 10 3 3 απαπ i n t he unit s of C/ fo r O GE a nd D/ fo r O P E , re sp ectivel y. The lo we st e ne r gy st at e s a nd mi xi ng a ngle s a re 2 4 P - = 01 994 | θ N P〉+ 01 111 | N P〉 = - 61 364? | J = 3/ 2 〉 3/ 2 3/ 2 O GEd( )11 2 4 P - θ = 01 630 | N P〉- 01 777 | N P〉 J 3/ 2 〉d= 501 952? | = 3/ 2 3/ 2 O PE ( )12 () () It i s ea sil y see n f ro m 11a nd 12t hat t he lo we st e ner gy st at e i s p re do mi na nt l y spi n do ublet fo r O GE , w hile t he lo we st e ner gy st at e i s p redo mi na nt l y spi n qua rt et fo r O P E. Ta ble 1 The Compar ison of the Obta ined Mixing Angles in the Lo west Ma ss Negat ive Parity Nucleons f or O GE and OPE with Experimental Data ( EXP1 ) 4 ?State s Co upling Mixing a ngle/ P/ % J O GE 32 28 P -O P E - 25 18 J = 1/ 2 EXP1 [ 7 ] + 32 28 O GE - 6 1 P -O P E J = 3/ 2 51 60 EXP1 [ 7 ] - 10 3 4 Discussion The o bt ai ne d mi xi ng a ngle s i n t he lo we st ma ss negative p a rit y nucleo n s fo r O GE a nd O P E a re summa2 rized i n Ta ble 1 . It sho ul d be e mp ha sized t hat t he mi xi ng a ngle s a re p a ra met er2f ree det er mi ned , i ndep e nd2 ( e nt of sp ect ral fit s to t he ma sse s of t he st at e s. The st re ngt h of t he co up li ng eit her C fo r O GE o r D fo r ) O P Ef acto rize s f ro m t he mi xi ng mat rice s a nd t he sa me mi xi ng i s o bt ai ned re ga r dle ss of t hi s co up li ng st re ngt h . The wavef unctio n s a re a ssumed to be ha r mo nic o scillato r , w hic h i s app rop riat e fo r t he se st at e s si nce t hey a re t he gro und st at e s i n t he negative p a rit y secto r . The pio n ma ss i s a ssumed to be ze ro i n t he co up li ng fo r O P E , si nce t he pio n ma ss i s ver y small . The no n2zero pio n ma sse s do no t cha nge si gnifica nt l y t he n umber s give n i n Ta ble 1 . It ca n be see n f ro m Ta ble 1 t hat t he diff ere nce bet wee n O GE a nd O P E i s la r ge , a nd t he p ref ere nce fo r O GE i s no w una mbi guo u s. Ref erences : [ 1 ] Isgur N , Karl G. Hyperfine Interactio ns in Negative Pa rit y Ba r yo ns [J ] . Phys L et t B , 1977 , 73 : 109 113 . [ 2 ] Isgur N , Karl G. P2Wave Ba r yo ns in t he Q ua r k Mo del [J ] . Phys Rev D , 1978 , 18 : 4187 4205 . [ 3 ] Isgur N , Ka rl G. Po sitive2Pa rit y Excited Ba r yo ns in a Q ua r k Mo del wit h Hyp erfine Interactio ns [J ] . Phys Rev D , 1979 , 19 : 2653 2677 . [ 4 ] Golzman L Y , Ri ska D O . The Spect r um of t he N ucleo ns a nd t he St ra nge Hypero ns a nd Chiral Dyna mic s [J ] . Phys Rep , 1996 , 268 : 263 303 . [ 5 ] Isgur N. Critique of a Pion Exchange Model for Interquark Forces [J ] . Phys Rev D , 2000 , 62 : 0504026 1 0504026 10. () [ 6 ] Chen H , Yang J J . L ight Ba r yo n Spect ra in a Chiral Q ua r k Mo del [J ] . Int Mo d Phys E , 1999 , 8 2: 159 166 . () [ 7 ] Hey A J G , Litchfield , Cashmo re R J . 546. SU 6and Decay of Baryo n Resonances [J ] . Nucl Phys B , 1975 , 95 : 516W 最低质量负宇称核子态中的混合角对夸克超精细相互作用的检验 黄淑一 ,陈洪 西南大学 物理科学与技术学院 , 重庆 400715 π摘要 : 分别用单胶子交换和单介子交换产生的夸克超精细相互作用 , 计算了最低质量负宇称核子态中的混合角 . 结果表 明 , 两种交换之间的差别较大 , 混合角的实验数据更倾向于支持单胶子交换 . π 关键词 : 核子 ; 负宇称态 ; 混合角 ; 单胶子交换 ; 单介子交换 责任编辑 潘春燕