本文選題：重夸克偶素　切入點(diǎn)：非相對(duì)論量子色動(dòng)力學(xué)有效理論　出處：《西南大學(xué)》2017年碩士論文

【摘要】：論文基于非相對(duì)論量子色動(dòng)力學(xué)有效理論(NRQCD)研究了重夸克偶素產(chǎn)生過程γγ~*→η_c形狀因子的相對(duì)論修正。NRQCD是一個(gè)非常成功的量子色動(dòng)力學(xué)低能有效場論,它可以用來研究重夸克偶素的產(chǎn)生和湮滅過程。NRQCD因子化定理把一個(gè)過程因子化成一系列短程系數(shù)和長程矩陣元的乘積。其中短程系數(shù)包含了標(biāo)度大于m_Q部分的貢獻(xiàn),而小于此標(biāo)度的貢獻(xiàn)被歸入非微擾的長程矩陣元。短程系數(shù)可以進(jìn)行微擾計(jì)算,因此可以按耦合常數(shù)展開。而各個(gè)長程矩陣元是按重夸克偶素系統(tǒng)里面重夸克的特征速度展開的。這樣NRQCD因子化公式就把一個(gè)產(chǎn)生過程的振幅或者截面按耦合常數(shù)和特征速度做雙重展開。具體計(jì)算到哪一階需要根據(jù)精度要求以及展開級(jí)數(shù)的收斂性來決定。本論文計(jì)算了γγ~*→η_c形狀因子領(lǐng)頭階矩陣元對(duì)應(yīng)的短程系數(shù)(F)以及次領(lǐng)頭階矩陣元對(duì)應(yīng)的短程系數(shù)(G)。其中該過程的F目前在文獻(xiàn)已經(jīng)計(jì)算到了兩圈圖,并結(jié)合實(shí)驗(yàn)做了唯象討論。結(jié)果表明僅僅考慮相對(duì)論修正的領(lǐng)頭階貢獻(xiàn)尚不能跟實(shí)驗(yàn)取得一致。為了檢驗(yàn)NRQCD因子化公式的正確性以及預(yù)言能力,利用因子化理論領(lǐng)域常用的匹配方法,本論文研究了該過程的次領(lǐng)頭階矩陣元對(duì)應(yīng)的短程系數(shù)G,我們把G計(jì)算到微擾展開的次領(lǐng)頭階(也就是一圈圖階)。結(jié)合F和G并通過適當(dāng)?shù)倪x擇輸入?yún)?shù)做了詳盡的唯象分析和討論。此外論文也研究了γγ~*→η_b的形狀因子,未來實(shí)驗(yàn)可以檢驗(yàn)理論計(jì)算的正確性,從而檢驗(yàn)NRQCD理論。論文的計(jì)算過程中,利用高能軟件包FeynArts生成費(fèi)曼圖并生產(chǎn)費(fèi)曼振幅;利用FeynCalc進(jìn)行Dirac矩陣求積、Lorentz指標(biāo)縮并以及化簡表達(dá)式;利用Apart和FIRE軟件包對(duì)圈圖振幅進(jìn)行張量約化;最后一圈圖振幅只包含一些簡單的標(biāo)量圈積分,通過計(jì)算這些圈積分就最終得到了過程的振幅表達(dá)式。為了保證計(jì)算的正確性,我們對(duì)一些已有經(jīng)典過程重新進(jìn)行了計(jì)算,這其中包括:J/ψ→e~+e~-,η_c→γγ,e~+e~-→η_cγ的α_s及α_sν~2修正,計(jì)算結(jié)果與已有文獻(xiàn)一致。
[Abstract]:Based on the effective theory of non-relativistic quantum chromodynamics (NRQCD), the relativistic correction of the shape factor of 緯 ~ (緯) ~ (* *) _ (n _ (C)) in heavy quark production is studied. NRQCD is a very successful low-energy effective field theory of quantum chromodynamics.It can be used to study the production and annihilation process of heavy quarkopyne. NRQCD factorization theorem converts a process factor into the product of a series of short-range coefficients and long-range matrix elements.The short-range coefficient includes the contribution of the scale larger than the mQ part of the structure, while the contribution smaller than the scale is classified as the non-perturbation long-range matrix element.The short range coefficient can be calculated by perturbation, so it can be expanded according to the coupling constant.And each long range matrix element is expanded according to the characteristic velocity of heavy quark in heavy quark system.In this way, the NRQCD factorization formula expands the amplitude or cross section of a production process according to the coupling constant and the characteristic velocity.The order to be calculated depends on the accuracy requirement and the convergence of the expansion series.In this paper, we have calculated the short-range coefficients (F) corresponding to the leading matrix elements of the shape factor of 緯 ~ (緯) and 畏 _ c, and the short-range coefficients corresponding to the matrix elements of the sub-leading order.Among them, the F of the process has been calculated in the literature, and the phenomenological discussion has been done in combination with the experiment.The results show that the leading contribution of the relativistic correction is not consistent with the experimental results.In order to verify the correctness of the NRQCD factorization formula and its prediction ability, the matching methods commonly used in the field of factorization theory are used.In this paper, we study the short-range coefficient G corresponding to the sublead matrix element of the process. We calculate G to the sub-leader order of the perturbation expansion (that is, the order of a cycle graph).Combining F and G and selecting appropriate input parameters, the phenomenological analysis and discussion are made in detail.In addition, the shape factor of 緯 -T * * 畏 b is also studied in this paper. The correctness of the theoretical calculation and the NRQCD theory can be verified by future experiments.In the calculation process of the paper, we use the high-energy software package FeynArts to generate the Femannian diagram and produce the Feynman amplitude, use FeynCalc to make the Dirac matrix quadrature Lorentz index shrink and simplify expression, use Apart and FIRE software package to reduce the amplitude of the circle graph by Zhang Liang, and use the software package of Apart and FIRE to reduce the amplitude of cycle graph.The amplitude of the last cycle contains only some simple scalar cycle integrals, and the amplitude expression of the process is obtained by calculating these cycle integrals.In order to ensure the correctness of the calculation, we have recalculated some of the classical processes, including: J / 蠄 e ~ e ~ (-), 畏 _ c / 緯 ~ e ~ (-) ~ E ~ (-) ~ (-) _ _ _
【學(xué)位授予單位】：西南大學(xué)
【學(xué)位級(jí)別】：碩士
【學(xué)位授予年份】：2017
【分類號(hào)】：O572.2

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