基態(tài)張量介子及其軌道激發(fā)態(tài)研究

魏科偉, 于鳳軍, 張楨君,2

(1.安陽師范學(xué)院 物理與電氣工程學(xué)院 河南 安陽 455000；2.中國科學(xué)院 云南天文臺 云南 昆明 650011)

?

基態(tài)張量介子及其軌道激發(fā)態(tài)研究

魏科偉1, 于鳳軍1, 張楨君1,2

(1.安陽師范學(xué)院 物理與電氣工程學(xué)院 河南 安陽 455000；2.中國科學(xué)院 云南天文臺 云南 昆明 650011)

張量介子; 質(zhì)量譜; Regge唯象學(xué)

0 引言

表1 軌道激發(fā)態(tài)13F4和13H6九重態(tài)Tab.1 The orbital excited 13F4 and 13H6 nonets

目前格點QCD在處理激發(fā)態(tài)時仍然存在較大誤差和很多困難[3], 唯象模型通常被用來解決涉及非微擾效應(yīng)的問題.Regge唯象學(xué)起源于在復(fù)角動量空間分析散射振幅的性質(zhì)[4], 在研究強子質(zhì)量譜方面簡潔有效, 一直得到廣泛的重視和應(yīng)用[5-19].

1 Regge唯象

Regge唯象學(xué)的一個重要特點就是通過Regge軌跡，把粒子的總角動量J和粒子質(zhì)量的平方M2聯(lián)系起來,Regge軌跡由一系列內(nèi)部量子數(shù)和介子的J的奇偶 (對于重子, 為總角動量J-1/2的奇偶)來決定[20]. 對于介子,Regge軌跡通常參數(shù)化為

(1)

Regge截距相加性關(guān)系式:

(2)

Regge斜率倒數(shù)相加性關(guān)系式:

(3)

此外有一個從t-道極點的留數(shù)乘積得到的Regge斜率相乘的關(guān)系式[23-24],

(4)

在先前的工作中,已經(jīng)證實了斜率相乘性關(guān)系式(4)不能準(zhǔn)確地描述當(dāng)前的介子譜, 同時斜率倒數(shù)相加性關(guān)系式(3)可以很好地描述介子譜[18], 本文計算中將舍去(4)式.

當(dāng)組分夸克的質(zhì)量mi

(5)

當(dāng)mi

(6)

可以得到同一N2S+1LJ多重態(tài)中6個介子質(zhì)量之間的關(guān)系,

(7)

2 計算結(jié)果

(7)式中, 當(dāng)i=n,j=s,k=b時, (這里和下文中,n代表u或者d味夸克), 可得

(8)

表2 13P2多重態(tài)中介子的質(zhì)量Tab.t. MeV

2.2 張量13P2多重態(tài)各成員的Regge斜率和Regge截距

(9)

(10)

表3 13P2多重態(tài)中各成員Regge軌跡斜率和截距Tab.3 The Regge slopes and intercepts (0) of the 13P2 multiplet

2.3 軌道激發(fā)態(tài)13F4，13H6，13K8介子九重態(tài)的質(zhì)量

(11)

表4 軌道激發(fā)態(tài)13F4,13H6,13K8九重態(tài)的質(zhì)量Tab.4 Masses of the orbital excited 13F4, 13H6 and 13K8 nonets MeV

3 討論

3) 在表3中, 列出了求得的基態(tài)13P2多重態(tài)中不同夸克組成的介子的Regge軌跡斜率和截距. Regge截距和斜率參數(shù)是強子動力學(xué)重要的基本參數(shù), 對譜學(xué)和非譜學(xué)的研究都有重要的意義[19,21,34], 本文用這些參數(shù)計算了13P2的軌道激發(fā)態(tài)13F4,13H6,13K8九重態(tài)的質(zhì)量.

4 小結(jié)

[1] Godfery S, Napolitano J . Light meson spectroscopy[J]. Rev Mod Phys，1999,71: 1411-1462.

[2] Beringer J, Arguin J F, Barnett R M，et al. Review of particle physics (RPP) [J]. Phys Rev, 2012(D86) :010001.

[3] Li Baiqing, Chao Kuangta. Higher charmonia and X,Y,Z states with screened potential [J]. Phys Rev, 2009(D79): 094004.

[4] Regge T. Introduction to complex orbital momenta [J]. Nuovo Cim, 1959, 14: 951-976.

[5] 魏科偉，祁敬娟，張靜．矢量介子第一徑向激發(fā)態(tài)質(zhì)量譜的研究[J]． 鄭州大學(xué)學(xué)報: 理學(xué)版，2013, 45(4): 72-76.

[6] 董新平．基于QCD 求和規(guī)則的4+K介子質(zhì)量[J]．鄭州大學(xué)學(xué)報: 理學(xué)版，2010, 42(4): 69-71.

[7] 胥愛軍, 馬冰, 馮學(xué)超, 等. 介子九重態(tài)質(zhì)量關(guān)系研究[J]. 鄭州大學(xué)學(xué)報:理學(xué)版, 2004, 36(1): 33-36.

[8] Wei Kewei, Guo Xinheng . Mass spectra of doubly heavy mesons in Regge phenomenology [J]. Phys Rev, 2010(D81): 076005.

[9] Guo Xinheng, Wei Kewei, Wu Xinghua. Some mass relations for mesons and baryons in Regge phenomenology [J]. Phys Rev, 2008(D78): 056005.

[11]Feng Xuechao, Wei Kewei, Wu Jie, et al. Mass spectrum of 11P1meson state and mixing angle of strange axial-vector mesons [J]. Adv High Energy Phys, 2013,2013:704529.

[12]Ebert D, Faustov R N, Galkin V O. Spectroscopy and Regge trajectories of heavy quarkonia andBcmesons [J]. Eur Phys J, 2011(C71): 1825.

[14]Zhang Ailin. Charmonium spectrum and new observed states [J]. Phys Lett, 2007(B647): 140-144.

[15]Li Demin, Wei Kewei, Yu Hong. A possible assignment for the ground scalar meson nonet [J]. Eur Phys J, 2005(A25): 263-266.

[17]馮學(xué)超,常同欽. 對23P2介子九重態(tài)中同位旋標(biāo)量成員的質(zhì)量分析[J]. 物理學(xué)報, 2012, 61(23): 231401.

[18]魏科偉, 陳兵, 王振洋，等. 矢量介子及其激發(fā)態(tài)的討論 [J]. 物理學(xué)報， 2013, 62(18): 181101.

[19]Li Demin, Ma Bing, Li Yuxiao. Meson spectrum in Regge phenomenology [J]. Eur Phys J, 2004(C37): 323-333.

[20]Chew G F, Frautschi S C. Regge trajectories and the principle of maximum strength for strong interactions [J]. Phys Rev Lett,1962(8): 41-44.

[21]Basdevant J L, Boukraa S. Successes and difficulties of unified quark-anti-quark potential models [J]. Z Phys,1985(C28): 413-426.

[22]Kaidalov A B. Hadronic mass relations from topological expansion and string model [J]. Z Phys,1982(C12): 63-66.

[23]Pasupathy J. Interrelations between meson spectra[J]. Phys Rev Lett,1976(37): 1336-1338.

[24]Igi K. Factorization of regge slopes for ordinary and new hadrons [J]. Phys Lett,1977(B66): 276-278.

[25]Brisudova M M, Burakovskyand L, Goldmann T. Effective functional form of Regge trajectories [J]. Phys Rev,2000(D61):054013.

[26]Abd El-Hady A, Spence J R, Vary J P. Radiative decays ofBcmesons in a Bethe-Salpeter model [J]. Phys Rev,2005(D71): 34006.

[27]Davies C T H, Hornbostel K, Lepage G P, et al.Bcspectroscopy from lattice QCD [J]. Phys Lett,1996(B382): 131-137.

[28]Roncaglia R, Dzierba A, Lichtenberg D B,et al. Predicting the masses of heavy hadrons without an explicit hamiltonian [J]. Phys Rev,1995(D51):1248-1257.

[29]Gupta S N, Johnson J M.Bcspectroscopy in a quantum chromodynamic potential model [J]. Phys Rev,1996(D53): 312-314.

[30]Ebert D, Faustov R N, Galkin V O. Properties of heavy quarkonia andBcmesons in the relativistic quark model [J]. Phys Rev,2003(D67): 014027.

[31]Zeng J, Van Orden J W, Roberts W. Heavy mesons in a relativistic model [J]. Phys Rev, 1995(D52): 5229-5241.

[32]Godfrey S. Spectroscopy ofBcmesons in the relativized quark model [J]. Phys Rev, 2004(D70): 054017.

[34]Burakovsky L, Goldman T. On the Regge slopes intramultiplet relation [J]. Phys Lett,1998(B434): 251-256.

Study of Tensor Mesons and Its Orbital Excited States

WEI Ke-wei1, YU Feng-jun1, ZHANG Zhen-jun1,2

(1.CollegeofPhysicsandElectricalEngineering,AnyangNormalUniversity,Anyang455000,China;2.YunnanObservatoryofChineseAcademyofSciences,Kunming650011,China)

tensor meson; mass spectrum; Regge phenomenology

2014-10-13

國家自然科學(xué)基金資助項目，編號U1204115；河南省教育廳科學(xué)技術(shù)研究重點項目，編號12B140001.

魏科偉(1980-)，男，河南駐馬店人，副教授，博士，主要從事高能物理理論研究，E-mail:weikw@hotmail.com.

TP183

A

1671-6841(2015)01-0087-06

10.3969/j.issn.1671-6841.2015.01.019