王宏民， 孫獻(xiàn)靜

(1. 裝甲兵工程學(xué)院基礎(chǔ)部， 北京 100072； 2. 中國(guó)科學(xué)院高能物理研究所， 北京 100049)

高能質(zhì)子－質(zhì)子碰撞中的J/ψ和Υ產(chǎn)生

王宏民1， 孫獻(xiàn)靜2

(1. 裝甲兵工程學(xué)院基礎(chǔ)部， 北京 100072； 2. 中國(guó)科學(xué)院高能物理研究所， 北京 100049)

利用色玻璃凝聚理論(Color Glass Condensate, CGC)，在假定入射核和靶核分別處于稀-密極限狀態(tài)下分析了高能質(zhì)子-質(zhì)子碰撞中的璨(底)夸克對(duì)產(chǎn)生。在此基礎(chǔ)上，利用由適用于較小x區(qū)域的KLR-AdS/CFT(Kovchegov Lu Rezaeian Anti-de Sitter-space/Conformal Field Theory)色偶極模型獲得的偶極關(guān)聯(lián)因子，根據(jù)色蒸發(fā)模型(Color Evaporation Model, CEM)研究了高能質(zhì)子-質(zhì)子碰撞中產(chǎn)生的J/ψ和Υ介子微分截面隨快度和橫向動(dòng)量的變化規(guī)律。結(jié)果表明：理論值與歐洲大強(qiáng)子對(duì)撞機(jī)(Large Hadron Collider，LHC)實(shí)驗(yàn)結(jié)果基本一致，但在J/ψ產(chǎn)生截面的大橫向動(dòng)量區(qū)域還需要進(jìn)一步的理論研究。

色蒸發(fā)模型； 偶極關(guān)聯(lián)因子； 色玻璃凝聚

在實(shí)驗(yàn)方面，目前歐洲大強(qiáng)子對(duì)撞機(jī)(Large Hadron Cluider,LHC)ALICE合作組給出了質(zhì)子-質(zhì)子碰撞中J/ψ(Υ)介子產(chǎn)生截面的實(shí)驗(yàn)數(shù)據(jù)[4]。該實(shí)驗(yàn)中質(zhì)子-質(zhì)子碰撞的質(zhì)心能量很高(7 000 GeV)，需要涉及較小動(dòng)量分?jǐn)?shù)(x<10-6)區(qū)域的理論計(jì)算。由于傳統(tǒng)的GBW(Golec-Biernat Wüsthoff)模型[7]、IIM(Iancu Itakura Munier)模型[8]、MV(McLerran-Venugopalan)模型[9]以及Soyez模型[10]都建立在微擾量子色動(dòng)力學(xué)基礎(chǔ)上，在極小x區(qū)域它們的正確性值得懷疑。為了解釋LHC最新實(shí)驗(yàn)現(xiàn)象，筆者在計(jì)算靶核中的偶極關(guān)聯(lián)因子時(shí)采用了適用于較小動(dòng)量分?jǐn)?shù)的KLR-AdS/CFT(KovchegovLuRezaeianAnti-deSitter-space/ConformalFieldTheory)色偶極模型[11]。

1 理論模型

(1)

Sy(x2,kT)Sy(x2,pT+qT-kT),

(2)

(3)

(4)

(5)

(6)

式中：

(7)

aT=qT-kT，

(8)

p+=p0+p3，

(9)

q+=q0+q3，

(10)

1.2 計(jì)算J/ψ(Υ)介子產(chǎn)生截面的色蒸發(fā)模型

根據(jù)色蒸發(fā)模型，J/ψ介子產(chǎn)生的微分截面可表示為[6]

(11)

(12)

1.3KLR-AdS/CFT模型中的偶極關(guān)聯(lián)因子

KLR-AdS/CFT膠子量子態(tài)飽和模型建立在=4超楊米爾斯理論基礎(chǔ)上，它僅利用3個(gè)自由參數(shù)就很好地解釋了HERA加速器動(dòng)量分?jǐn)?shù)和四動(dòng)量都較小時(shí)的實(shí)驗(yàn)數(shù)據(jù)。在KLR-AdS/CFT模型中，偶極散射振幅可表示為[14-15]

(13)

相應(yīng)的飽和標(biāo)度為

(14)

式中：x為動(dòng)量分?jǐn)?shù)；rT為膠子的橫向位置；

(15)

其中，

(16)

通過擬合HERA實(shí)驗(yàn)數(shù)據(jù)可得到參數(shù)λ=20，M0=0.006 16[11]。

KLR-AdS/CFT模型中的偶極關(guān)聯(lián)因子可通過對(duì)式(13)進(jìn)行傅立葉變換得到[16-17]，即

(17)

2 結(jié)果與討論

由圖1、2可以看出：實(shí)驗(yàn)誤差在理論不確定區(qū)間內(nèi)，但當(dāng)橫向動(dòng)量較大時(shí)J/ψ介子實(shí)驗(yàn)值在理論不確定區(qū)間外。這是因?yàn)楫?dāng)PT較大時(shí)，動(dòng)量分?jǐn)?shù)x1和x2處在極限區(qū)域，這一區(qū)域的入射膠子分布函數(shù)及偶極關(guān)聯(lián)因子與擬合實(shí)驗(yàn)數(shù)據(jù)存在較大誤差[5，11]。

圖1 J/ψ(Υ)介子產(chǎn)生截面隨快度變化曲線

圖2 J/ψ(Υ)介子產(chǎn)生截面隨橫向動(dòng)量變化曲線

3 結(jié)論

筆者研究了LHC能量下質(zhì)子-質(zhì)子碰撞過程中的J/ψ(Υ)介子產(chǎn)生，可得出如下結(jié)論：1)色玻璃凝聚理論是解決膠子飽和實(shí)驗(yàn)現(xiàn)象的有效方法；2)KLR-AdS/CFT膠子飽和模型適用于碰撞能量較高時(shí)的理論計(jì)算。

然而，本文研究尚不能解釋大橫向動(dòng)量J/ψ介子產(chǎn)生現(xiàn)象，下一步將對(duì)此進(jìn)行重點(diǎn)研究。

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(責(zé)任編輯:尚菲菲)

J/ψ and Υ Generation in High Energy Proton-proton Collisions

WANG Hong-min1, SUN Xian-jing2

(1. Department of Fundamental Courses, Academy of Armored Force Engineering, Beijing 100072, China; 2. Institute of High Energy Physics, Chinese Academy of Science, Beijing 100049, China)

By assuming the projectile and target nuclei in the dilute-dense limit, the charm (bottom) quark pair productions in high energy proton-proton collisions are analyzed in the framework of the Color Glass Condensate (CGC). Then, with the Color Evaporation Model (CEM), the J/ψ and Υ mesons cross section as a function of transverse momentum and rapidity are studied. The dipole correlator is obtained from the KLR-AdS/CFT (Kovchegov Lu Rezaeian Anti-de Sitter-space/Conformal Field Theory) model, which is valid at very small momentum fraction x. It is shown that the theoretical results agree well with almost of all the experimental data form Large Hadron Collider(LHC). But the J/ψ mesons production at large transverse momentum should be further studied.

Color Evaporation Model (CEM); dipole correlator; Color Glass Condensate (CGC)

1672-1497(2017)02-0107-04

2017-01-12

國(guó)家自然科學(xué)基金資助項(xiàng)目(11305195/A050509)

王宏民(1975-)，男，副教授，博士。

O572.24+3

A

10.3969/j.issn.1672-1497.2017.02.022