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基底和膜层-基底系统的赝布儒斯特角计算(英文)刘华松;姜玉刚;王利栓;姜承慧;季一勤【期刊名称】《光子学报》【年(卷),期】2013(0)7【摘要】对基底和膜层-基底系统的赝布儒斯特角进行了数值计算.结果显示:当基底的消光系数小于0.01时,基底的赝布儒斯特角主要是由折射率决定;当基底的消光系数大于0.1时,基底的赝布儒斯特角不仅与折射率有关,而且还与消光系数有关,随着消光系数发生后周期性变化.研究表明:单层膜-基底系统的赝布儒斯特角主要由膜层的物理厚度、折射率、基底的光学常量所决定;在HfO2-硅和HfO2-融石英基底系统中,赝布儒斯特角随着入射光波长和膜层厚度的变化呈现准周期性规律变化,可能是由入射光在膜层的干涉效应引起的.【总页数】6页(P817-822)【关键词】光学常量;折射率;消光系数;膜层-基底系统;赝布儒斯特角【作者】刘华松;姜玉刚;王利栓;姜承慧;季一勤【作者单位】天津津航技术物理研究所天津市薄膜光学重点实验室,天津300192;同济大学物理系先进微结构材料教育部重点实验室,上海200092;哈尔滨工业大学光电子技术研究所可调谐激光技术国家级重点实验室,哈尔滨150080【正文语种】中文【中图分类】O484【相关文献】1.以介孔TiO2膜为过渡层在玻璃基底上制备Cu3(BTC)2连续膜 [J], 李力成;钱祺;王磊;仇龙云;王昊翊;张所瀛;杨祝红;李小保;赵学娟2.前列腺癌发生发展中基底细胞层和基底膜的改变 [J], 杨敏;刘爱军;韦立新;郭爱桃;宋欣;陈薇3.镍改性层增强铜基底沉积金刚石膜的形核（英文） [J], 刘学璋;魏秋平;翟豪;余志明;4.硅基底上生长金刚石层细晶粒的研究(英文) [J], 何敬晖;玄真武;刘尔凯5.在n型硅基底上二次注入硼离子金刚石膜的p-n结效应(英文) [J], 孙秀平;冯克成;李超;张红霞;费允杰因版权原因，仅展示原文概要，查看原文内容请购买。
中国实验诊断学 2020年1月 第24卷 第1期147文章编号:1007-4287(2020)01-0147-03Rho 蛋白调控血小板细胞骨架重排的分子机制研究进展杨颖，田文沁**基金项目：北京市自然科学基金(7194331),北大医学青年科技创新培育基金(BMU2018PYB012)*通讯作者(北京大学人民医院输血科，北京100044)血小板是血液循环中体积较小的无核细胞，由 骨髓中的巨核细胞产生，其在止血和血栓形成的过程中发挥了重要的作用当血管发生损伤时，血小板能够黏附于受损的血管内皮，并形成血栓，进而 发挥止血的作用⑵。
然而，血小板的过度活化可以 导致血栓性疾病的发生⑷。
血小板在活化的过程中会发生细胞骨架的重排，进而引起其形态变化、颗粒 分泌以及聚集等一系列改变。
骨架相关分子参与调 控血小板细胞骨架重排，这其中就包括Rho 蛋 白⑷。
本文拟对Rho 蛋白调控血小板细胞骨架重排的分子机制研究进展进行综述。
1 Rho 蛋白的概述Rh 。
蛋白是一组相对分子质量为20-25 kD 的三磷酸鸟昔(guanosine triphosphate, GTP)结合蛋 白，因其具有GTP 酶活性，又被称为Rho GTP 酶，Rho GTP 酶在调控细胞骨架重排方面发挥重要的 作用。
已知的Rh 。
蛋白家族有20余个成员，根据其结构和功能不同，可分为Rho 亚家族、Rac 亚家族、Cdc42亚家族、Rnd 亚家族、Rho BTB 亚家族 等"间。
其中，Cdc42、Racl 和RhoA 是目前研究最多的Rho 蛋白。
Rho 蛋白是一种开关蛋白，包括无 活性的GDP 结合的形式以及有活性的GTP 结合的形式，这二者之间在Rho 蛋白调控分子的调控下可 以相互转换活化的Rh 。
蛋白即GTP 结合的Rho 蛋白可以与下游的效应分子结合，发挥调控细 胞骨架重排、细胞迁移运动等作用⑷。
研究表明，Rho 蛋白家族的Cdc42、Racl 和RhoA 在血小板中 均有表达，它们在血小板收缩、伪足形成以及颗粒分泌等发面发挥了重要的调控作用O2 Rho 蛋白在血小板中的调控作用2.1 RhoA 调控血小板收缩并维持血栓稳定性当血小板激活剂如凝血酶、血栓烷类似物等与血小板表面膜受体结合后，可以使血小板活化。
以琼脂凝胶固定热聚IgG 制备类风湿关节炎免疫吸附剂的研究付春晓 陈长治 俞耀庭(南开大学分子生物所,生物活性材料开放实验室,天津 300071)摘 要: 以环氧氯丙烷对琼脂凝胶珠进行活化反应后键联热聚I gG,制成一种新型类风湿关节炎免疫吸附剂。
确定了最佳制备条件,使凝胶上环氧基的含量达110 mo l/g ,对热聚I gG 的固定量达6mg/g 。
在体外条件下吸附剂对三种类风湿因子Ig M RF,IgGRF 及IgAR F 的吸附量分别达3400、2250和2400I U/g,具有良好的应用前景。
关键词: 琼脂凝胶;热聚Ig G;免疫吸附剂;类风湿关节炎中图分类号: O63 文献标识码: A 文章编号: 1004-9843(1999)02-0145-04类风湿关节炎(Rheumatoid arthritis,RA)是一典型的自身免疫性疾病,在患者血浆中含有致病的自身抗体-类风湿因子(Rheumatoid factors,RF)及其免疫复合物。
利用血液灌流(Hemoperfusion,HP)选择性地清除这些致病性物质具有很好的治疗效果 1-3 ,而免疫吸附剂是这种疗法的核心和关键,它通常由水不溶性的高分子载体和对目标物质具有选择吸附能力的配基两部分组成。
一种理想的免疫吸附剂要求具有高的选择吸附活性、良好的血液相容性和适宜的机械强度。
琼脂糖凝胶具有良好的血液相容性和化学反应功能,是理想的载体材料 4 。
但是商品化的琼脂凝胶不仅价格昂贵,而且颗粒细小,血液通透性差。
本文合成了一种颗粒大(粒径为0.45~0.90mm)、价格低廉的琼脂凝胶珠,经环氧氯丙烷活化后作为吸附剂的载体。
热聚IgG 是在加热条件下由人Ig G 自身聚合而成的多聚体,能够特异性地结合RF 5,6 。
本文首次将其作为亲合配基固载到琼脂凝胶上,制成了一种新型RA 免疫吸附剂,并在体外条件下评价了该吸附剂对RF 的清除效果。
1 实验部分1.1 材料琼脂粉:生化试剂,北京益利精细化工有限公司;人Ig G:军事医学科学院微生物流行病研究所;类风湿因子-ELISA 试剂盒:南京军区总医院;重症RA 患者血清(其中IgMRF,IgGRF 和IgARF 的浓度分别为1000,800和750IU /mL):天津市第三中心医院提供;其他常规试剂均为分析纯。
空间计量 rho指标英文回答：The spatial metric rho is a measure of spatial autocorrelation, which quantifies the degree to which features in a spatial dataset are clustered or dispersed.It is commonly used in spatial analysis to identify areas of high or low clustering, and to explore the spatial relationships between different features.The rho statistic is calculated by comparing the observed spatial autocorrelation with the expected autocorrelation under the null hypothesis of complete spatial randomness. The null hypothesis assumes that the features in the dataset are randomly distributed, and that there is no spatial dependence between them. The observed spatial autocorrelation is calculated by measuring the average distance between features, and the expected autocorrelation is calculated by assuming that the features are randomly distributed.The rho statistic can range from -1 to 1. A value of -1 indicates perfect negative autocorrelation, meaning that the features are completely dispersed. A value of 0 indicates no spatial autocorrelation, meaning that the features are randomly distributed. A value of 1 indicates perfect positive autocorrelation, meaning that the features are completely clustered.The rho statistic can be used to identify areas of high or low clustering in a spatial dataset. Areas with high positive values of rho indicate areas where features are clustered together, while areas with high negative values of rho indicate areas where features are dispersed. The rho statistic can also be used to explore the spatial relationships between different features. For example, you could use the rho statistic to explore the relationship between the distribution of crimes and the distribution of poverty, or the relationship between the distribution of trees and the distribution of water bodies.The spatial metric rho is a powerful tool for spatialanalysis. It can be used to identify areas of high or low clustering, and to explore the spatial relationships between different features. The rho statistic is easy to calculate, and it can be applied to a wide range of spatial datasets.中文回答：空间计量 rho 指标是空间自相关的度量，它量化了空间数据集中要素聚集或分散的程度。
a rXiv:n ucl-t h /441v28Ma y2The decay ρ0→π++π−+γand the coupling constant g ρσγA.Gokalp ∗and O.Yilmaz †Physics Department,Middle East Technical University,06531Ankara,Turkey(February 8,2008)Abstract The experimental branching ratio for the radiative decay ρ0→π++π−+γis used to estimate the coupling constant g ρσγfor a set of values of σ-meson parameters M σand Γσ.Our results are quite different than the values of this constant used in the literature.PACS numbers:12.20.Ds,13.40.HqTypeset using REVT E XThe radiative decay processρ0→π++π−+γhas been studied employing different approaches[1,5].There are two mechanisms that can contribute to this radiative decay: thefirst one is the internal bremsstrahlung where one of the charged pions from the decay ρ0→π++π−emits a photon,and the second one is the structural radiation which is caused by the internal transformation of theρ-meson quark structure.Since the bremsstrahlung is well described by quantum electrodynamics,different methods have been used to estimate the contribution of the structural radiation.Singer[1]calculated the amplitude for this decay by considering only the bremsstrahlung mechanism since the decayρ0→π++π−is the main decay mode ofρ0-meson.He also used the universality of the coupling of theρ-meson to pions and nucleons to determine the coupling constant gρππfrom the knowledge of the coupling constant gρter,Renard [3]studied this decay among other vector meson decays into2π+γfinal states in a gauge invariant way with current algebra,hard-pion and Ward-identities techniques.He,moreover, established the correspondence between these current algebra results and the structure of the amplitude calculated in the single particle approximation for the intermediate states.In corresponding Feynman diagrams the structural radiation proceeds through the intermediate states asρ0→S+γwhere the meson S subsequently decays into aπ+π−pair.He concluded that the leading term is the pion bremsstrahlung and that the largest contribution to the structural radiation amplitude results from the scalarσ-meson intermediate state.He used the rough estimate gρσγ≃1for the coupling constant gρσγwhich was obtained with the spin independence assumption in the quark model.The coupling constant gρππwas determined using the then available experimental decay rate ofρ-meson and also current algebra results as3.2≤gρππ≤4.9.On the other hand,the coupling constant gσππwas deduced from the assumed decay rateΓ≃100MeV for theσ-meson as gσππ=3.4with Mσ=400MeV. Furthermore,he observed that theσ-contribution modifies the shape of the photon spectrum for high momenta differently depending on the mass of theσ-meson.We like to note, however,that the nature of theσ-meson as a¯q q state in the naive quark model and therefore the estimation of the coupling constant gρσγin the quark model have been a subject ofcontroversy.Indeed,Jaffe[6,7]lately argued within the framework of lattice QCD calculation of pseudoscalar meson scattering amplitudes that the light scalar mesons are¯q2q2states rather than¯q q states.Recently,on the other hand,the coupling constant gρσγhas become an important input for the studies ofρ0-meson photoproduction on nucleons.The presently available data[8] on the photoproduction ofρ0-meson on proton targets near threshold can be described at low momentum transfers by a simple one-meson exchange model[9].Friman and Soyeur [9]showed that in this picture theρ0-meson photoproduction cross section on protons is given mainly byσ-exchange.They calculated theγσρ-vertex assuming Vector Dominance of the electromagnetic current,and their result when derived using an effective Lagrangian for theγσρ-vertex gives the value gρσγ≃2.71for this coupling ter,Titov et al.[10]in their study of the structure of theφ-meson photoproduction amplitude based on one-meson exchange and Pomeron-exchange mechanisms used the coupling constant gφσγwhich they calculated from the above value of gρσγinvoking unitary symmetry arguments as gφσγ≃0.047.They concluded that the data at low energies near threshold can accommodate either the second Pomeron or the scalar mesons exchange,and the differences between these competing mechanisms have profound effects on the cross sections and the polarization observables.It,therefore,appears of much interest to study the coupling constant gρσγthat plays an important role in scalar meson exchange mechanism from a different perspective other than Vector Meson Dominance as well.For this purpose we calculate the branching ratio for the radiative decayρ0→π++π−+γ,and using the experimental value0.0099±0.0016for this branching ratio[11],we estimate the coupling constant gρσγ.Our calculation is based on the Feynman diagrams shown in Fig.1.Thefirst two terms in thisfigure are not gauge invariant and they are supplemented by the direct term shown in Fig.1(c)to establish gauge invariance.Guided by Renard’s[3]current algebra results,we assume that the structural radiation amplitude is dominated byσ-meson intermediate state which is depicted in Fig. 1(d).We describe theρσγ-vertex by the effective LagrangianL int.ρσγ=e4πMρMρ)2 3/2.(3)The experimental value of the widthΓ=151MeV[11]then yields the value g2ρππ2gσππMσ π· πσ.(4) The decay width of theσ-meson that follows from this effective Lagrangian is given asΓσ≡Γ(σ→ππ)=g2σππ8 1−(2Mπ2iΓσ,whereΓσisgiven by Eq.(5).Since the experimental candidate forσ-meson f0(400-1200)has a width (600-1000)MeV[11],we obtain a set of values for the coupling constant gρσγby considering the ranges Mσ=400-1200MeV,Γσ=600-1000MeV for the parameters of theσ-meson.In terms of the invariant amplitude M(Eγ,E1),the differential decay probability for an unpolarizedρ0-meson at rest is given bydΓ(2π)31Γ= Eγ,max.Eγ,min.dEγ E1,max.E1,min.dE1dΓ[−2E2γMρ+3EγM2ρ−M3ρ2(2EγMρ−M2ρ)±Eγfunction ofβin Fig.5.This ratio is defined byΓβRβ=,Γtot.= Eγ,max.50dEγdΓdEγ≃constant.(10)ΓσM3σFurthermore,the values of the coupling constant gρσγresulting from our estimation are in general quite different than the values of this constant usually adopted for the one-meson exchange mechanism calculations existing in the literature.For example,Titov et al.[10] uses the value gρσγ=2.71which they obtain from Friman and Soyeur’s[9]analysis ofρ-meson photoproduction using Vector Meson Dominance.It is interesting to note that in their study of pion dynamics in Quantum Hadrodynamics II,which is a renormalizable model constructed using local gauge invariance based on SU(2)group,that has the sameLagrangian densities for the vertices we use,Serot and Walecka[14]come to the conclusion that in order to be consistent with the experimental result that s-waveπN-scattering length is anomalously small,in their tree-level calculation they have to choose gσππ=12.Since they use Mσ=520MeV this impliesΓσ≃1700MeV.If we use these values in our analysis,we then obtain gρσγ=11.91.Soyeur[12],on the other hand,uses quite arbitrarly the values Mσ=500 MeV,Γσ=250MeV,which in our calculation results in the coupling constant gρσγ=6.08.We like to note,however,that these values forσ-meson parameters are not consistent with the experimental data onσ-meson[11].Our analysis and estimation of the coupling constant gρσγusing the experimental value of the branching ratio of the radiative decayρ0→π++π−+γgive quite different values for this coupling constant than used in the literature.Furthermore,since we obtain this coupling constant as a function ofσ-meson parameters,it will be of interest to study the dependence of the observables of the reactions,such as for example the photoproduction of vector mesons on nucleonsγ+N→N+V where V is the neutral vector meson, analyzed using one-meson exchange mechanism on these parameters.AcknowledgmentsWe thank Prof.Dr.M.P.Rekalo for suggesting this problem to us and for his guidance during the course of our work.We also wish to thank Prof.Dr.T.M.Aliev for helpful discussions.REFERENCES[1]P.Singer,Phys.Rev.130(1963)2441;161(1967)1694.[2]V.N.Baier and V.A.Khoze,Sov.Phys.JETP21(1965)1145.[3]S.M.Renard,Nuovo Cim.62A(1969)475.[4]K.Huber and H.Neufeld,Phys.Lett.B357(1995)221.[5]E.Marko,S.Hirenzaki,E.Oset and H.Toki,Phys.Lett.B470(1999)20.[6]R.L.Jaffe,hep-ph/0001123.[7]M.Alford and R.L.Jaffe,hep-lat/0001023.[8]Aachen-Berlin-Bonn-Hamburg-Heidelberg-Munchen Collaboration,Phys.Rev.175(1968)1669.[9]B.Friman and M.Soyeur,Nucl.Phys.A600(1996)477.[10]A.I.Titov,T.-S.H.Lee,H.Toki and O.Streltrova,Phys.Rev.C60(1999)035205.[11]Review of Particle Physics,Eur.Phys.J.C3(1998)1.[12]M.Soyeur,nucl-th/0003047.[13]S.I.Dolinsky,et al,Phys.Rep.202(1991)99.[14]B.D.Serot and J.D.Walecka,in Advances in Nuclear Physics,edited by J.W.Negeleand E.Vogt,Vol.16(1986).TABLESTABLE I.The calculated coupling constant gρσγfor differentσ-meson parametersΓσ(MeV)gρσγ500 6.97-6.00±1.58 8008.45±1.77600 6.16-6.68±1.85 80010.49±2.07800 5.18-9.11±2.64 90015.29±2.84900 4.85-10.65±3.14 90017.78±3.23Figure Captions:Figure1:Diagrams for the decayρ0→π++π−+γFigure2:The photon spectra for the decay width ofρ0→π++π−+γ.The contributions of different terms are indicated.Figure3:The pion energy spectra for the decay width ofρ0→π++π−+γ.The contri-butions of different terms are indicated.Figure4:The decay width ofρ0→π++π−+γas a function of minimum detected photon energy.Figure5:The ratio Rβ=Γβ。
Thermo-Calc®User’s GuideVersion PThermo-Calc Software ABStockholm Technology ParkBjörnnäsvägen 21SE-113 47 Stockholm, SwedenCopyright © 1995-2003 Foundation of Computational ThermodynamicsStockholm, Sweden目录第1部分一般介绍 (12)1.1 计算热力学 (12)1.2 Thermo-Calc软件/数据库/界面包 (12)1.3 致谢 (13)1.4 版本历史 (13)1.5 Thermo-Calc软件包的通用结构 (13)1.6 各类硬件上Thermo-Calc软件包的有效性 (14)1.7 使用Thermo-Calc软件包的好处 (14)第2部分如何成为Thermo-Calc专家 (14)2.1 如何容易地使用本用户指南 (14)2.2 如何安装和维护Thermo-Calc软件包 (16)2.2.1 许可要求 (16)2.2.2 安装程序 (16)2.2.3 维护当前和以前版本 (16)2.2.4 使TCC执行更方便 (16)2.3 如何成为Thermo-Calc专家 (16)2.3.1 从TCSAB与其世界各地的代理获得迅速技术支持 (17)2.3.2 日常使用各种Thermo-Calc功能 (17)2.3.3 以专业的和高质量的标准提交结果 (17)2.3.4 通过各种渠道相互交换经验 (17)第3部分Thermo-Calc软件系统 (17)3.1 Thermo-Calc软件系统的目标 (17)3.2 一些热力学术语的介绍 (18)3.2.1 热力学 (18)3.2.2 体系、组元、相、组成、物种（System, component, phases, constituents and species） (18)3.2.3 结构、亚点阵和位置 (19)3.2.4 成分、构成、位置分数、摩尔分数和浓度(composition, constitution, site fractions, molefractions and concentration) (19)3.2.5 平衡态和状态变量 (19)3.2.6 导出变量 (22)3.2.7 Gibbs相规则 (25)3.2.8 状态的热力学函数 (25)3.2.9 具有多相的体系 (25)3.2.10 不可逆热力学 (26)3.2.11 热力学模型 (26)3.2.12 与各种状态变量有关的Gibbs能 (27)3.2.13 参考态与标准态 (27)3.2.14 溶解度范围 (28)3.2.15 驱动力 (28)3.2.16 化学反应 (28)3.2.17 与平衡常数方法相对的Gibbs能最小化技术 (28)3.2.18 平衡计算 (29)3.3 热力学数据 (30)3.3.1 数据结构 (30)3.3.3 数据估价 (32)3.3.6 数据加密 (33)3.4 用户界面 (34)3.4.1 普通结构 (34)3.4.2 缩写 (34)3.4.3 过程机制（history mechanism） (35)3.4.4 工作目录和目标目录(Working directory and target directory) (35)3.4.5 参数转换为命令 (36)3.4.6 缺省值 (36)3.4.7 不理解的问题 (36)3.4.8 帮助与信息 (36)3.4.9 出错消息 (36)3.4.10 控制符 (36)3.4.11 私人文件 (36)3.4.12 宏工具 (37)3.4.13 模块性 (37)3.5 Thermo-Calc中的模块 (37)3.5.1 基本模块 (37)3.7 Thermo-Calc编程界面 (39)3.7.1 Thermo-Calc作为引肇 (39)3.7.2 Thermo-Calc应用编程界面：TQ和TCAPI (40)3.7.3 在其它软件包中开发Thermo-Calc工具箱 (43)3.7.4 材料性质计算核材料工艺模拟的应用 (43)3.8 Thermo-Calc的功能 (44)3.9 Thermo-Calc应用 (44)第4部分Thermo-Calc数据库描述 (45)4.1 引言 (45)4.2 Thermo-Calc数据库描述形式 (45)第5部分数据库模块（TDB）——用户指南 (55)5.1 引言 (55)5.2 TDB模块中用户界面 (56)5.3 开始 (56)5.3.1 SWITCH-DATABASE (56)5.3.2 LIST-DATABASE ELEMENT (56)5.3.3 DEFINE_ELEMENTS (56)5.3.4 LIST_SYSTEM CONSTITUENT (56)5.3.5 REJECT PHASE (56)5.3.6 RESTORE PHASE (56)5.3.7 GET_DATA (56)5.4 所有TDB监视命令的描述 (56)5.4.1 AMEND_SELACTION (56)5.4.6 DEFINE_SPECIES (58)5.4.7 DEFINE_SYSTEM (58)5.4.8 EXCLUDE_UNUSED_SPECIES (58)5.4.9 EXIT (58)5.4.10 GET_DATA (58)5.4.11 GOTO_MODULE (59)5.4.12 HELP (59)5.4.13 INFORMA TION (59)5.4.14 LIST_DATABASE (60)5.4.15 LIST_SYSTEM (60)5.4.16 MERGE_WITH_DA TABASES (61)5.4.17 NEW_DIRECTORY_FILE (61)5.4.18 REJECT (61)5.4.19 RESTORE (62)5.4.20 SET_AUTO_APPEND_DA TABASE (62)5.4.21 SWITCH_DA TABASE (63)5.5 扩展命令 (64)第6部分数据库模块（TDB）——管理指南 (64)6.1 引言 (64)6.2 TDB模块的初始化 (65)6.3 数据库定义文件语法 (66)6.3.1 ELEMENT (67)6.3.2 SPECIES (67)6.3.3 PHASE (67)6.3.4 CONSTITUENT (67)6.3.5 ADD_CONSTITUENT (68)6.3.6 COMPOUND_PHASE (68)6.3.7 ALLOTROPIC_PHASE (68)6.3.8 TEMPERA TURE_LIMITS (68)6.3.9 DEFINE_SYSTEM_DEFAULT (69)6.3.10 DEFAULT_COMMAND (69)6.3.11 DATABASE_INFORMATION (69)6.3.12 TYPE_DEFINITION (69)6.3.13 FTP_FILE (70)6.3.14 FUNCTION (70)6.3.15 PARAMETER (72)6.3.16 OPTIONS (73)6.3.17 TABLE (73)6.3.18 ASSESSED_SYSTEMS (73)6.3.19 REFERENCE_FILE (74)6.3.20 LIST_OF_REFERENCE (75)6.3.21 CASE与ENDCASE (76)6.3.22 VERSION_DA TA (76)6.5 数据库定义文件实例 (77)6.5.1 例1：一个小的钢数据库 (77)6.5.2 例2：Sb-Sn系个人数据库 (78)第7部分制表模块（TAB） (81)7.1 引言 (81)7.2 一般命令 (81)7.2.1 HELP (81)7.2.2 GOTO_MODULE (81)7.2.3 BACK (82)7.2.4 EXIT (82)7.2.5 PATCH (82)7.3 重要命令 (82)7.3.1 TABULATE_SUBSTANCE (82)7.3.2 TABULATE_REACTION (85)7.3.3 ENTER_REACTION (86)7.3.4 SWITCH_DA TABASE (87)7.3.5 ENTER_FUNCTION (88)7.3.6 TABULATE_DERIV A TIVES (89)7.3.7 LIST_SUBSTANCE (91)7.4 其它命令 (92)7.4.1 SET_ENERGY_UNIT (92)7.4.2 SET_PLOT_FORMAT (92)7.4.3 MACRO_FILE_OPEN (92)7.4.4 SET_INTERACTIVE (93)7.5 绘制表 (93)第8部分平衡计算模块（POL Y） (94)8.1 引言 (94)8.2 开始 (95)8.3 基本热力学 (95)8.3.1 体系与相 (95)8.3.2 组元（Species） (95)8.3.3 状态变量 (96)8.3.4 组分 (97)8.3.5 条件 (98)8.4 不同类型的计算 (98)8.4.1 计算单一平衡 (98)8.4.2 性质图的Steping计算 (99)8.4.3 凝固路径模拟 (99)8.4.4 仲平衡与T0温度模拟 (99)8.4.5 相图的Mapping计算 (101)8.4.6 势图计算 (101)8.4.7 Pourbaix图计算 (101)8.4.8 绘制图 (101)8.5.4 更高阶相图 (104)8.5.5 性质图 (104)8.6 普通命令 (104)8.6.1 HELP (104)8.6.2 INFORMA TION (104)8.6.3 GOTO_MODULE (105)8.6.4 BACK (105)8.6.5 SET_INTERACTIVE (105)8.6.6 EXIT (106)8.7 基本命令 (106)8.7.1 SET_CONDITION (106)8.7.2 RESET_CONDITION (107)8.7.3 LIST_CONDITIONS (107)8.7.4 COMPUTE_EQUILIBRIUM (107)8.7.6 DEFINE_MATERIAL (108)8.7.6 DEFINE_DIAGRAM (111)8.8 保存和读取POL Y数据结构的命令 (112)8.8.1 SA VE_WORKSPACES (112)8.8.2 READ_WORKSPACES (113)8.9 计算与绘图命令 (114)8.9.1 SET_AXIS_V ARIABLE (114)8.9.2 LIST_AXIS_V ARIABLE (114)8.9.3 MAP (114)8.9.4 STEP_WITH_OPTIONS (115)8.9.5 ADD_INITIAL_EQUILIBRIUM (117)8.9.6 POST (118)8.10 其它有帮助的命令 (118)8.10.1 CHANGE_STA TUS (118)8.10.2 LIST_STA TUS (119)8.10.3 COMPUTE_TRANSITION (120)8.10.4 SET_ALL_START_V ALUES (121)8.10.5 SHOW_V ALUE (122)8.10.6 SET_INPUT_AMOUNTS (122)8.10.7 SET_REFERENCE_STA TE (122)8.10.8 ENTER_SYMBOL (123)8.10.9 LIST_SYMBOLS (124)8.10.10 EV ALUATE_FUNCTIONS (124)8.10.11 TABULATE (124)8.11 高级命令 (125)8.11.1 AMEND_STORED_EQUILIBRIA (125)8.11.3 DELETE_INITIAL_EQUILIBRIUM (126)8.11.4 LIST_INITIAL_EQUILIBRIA (126)8.11.5 LOAD_INITIAL_EQUILIBRIUM (126)8.11.10 SELECT_EQUILIBRIUM (128)8.11.11 SET_NUMERICAL_LIMITS (128)8.11.12 SET_START_CONSTITUTION (129)8.11.13 SET_START_V ALUE (129)8.11.14 PATCH (129)8.11.15 RECOVER_START_V ALUE (129)8.11.16 SPECIAL_OPTIONS (129)8.12 水溶液 (132)8.13 排除故障 (133)8.13.1 第一步 (133)8.13.2 第二步 (133)8.13.3 第三步 (133)8.14 频繁提问的问题 (134)8.14.1 程序中为什么只得到半行？ (134)8.14.2 在已经保存之后为什么不能绘图？ (134)8.14.3 为什么G.T不总是与-S相同？ (134)8.14.4 如何获得组元偏焓 (135)8.14.5 为什么H(LIQUID) 是零而HM(LIQUID)不是零 (135)8.14.6 即使石墨是稳定的为什么碳活度小于1？ (135)8.14.7 如何获得过剩Gibbs能？ (135)8.14.8 当得到交叉结线而不是混溶裂隙时什么是错的？ (135)8.14.9 怎么能直接计算最大混溶裂隙？ (136)第9部分后处理模块（POST） (136)9.1 引言 (136)9.2 一般命令 (137)9.2.1 HELP (137)9.2.2 BACK (137)9.2.3 EXIT (137)9.3 重要命令 (137)9.3.1 SET_DIAGRAM_AXIS (137)9.3.2 SET_DIAGRAM_TYPE (138)9.3.3 SET_LABEL_CORVE_OPTION (139)9.3.5 MODIFY_LABEL_TEXT (139)9.3.6 SET_PLOT_FORMAT (140)9.3.7 PLOT_DIAGRAM (141)9.3.8 PRINT_DIAGRAM (142)9.3.9 DUMP_DIAGRAM (143)9.3.10 SET_SCALING_STA TUS (144)9.3.11 SET_TITLE (144)9.3.12 LIST_PLOT_SETTINGS (144)9.4 实验数据文件绘图命令 (144)9.4.1 APPEND_EXPERIMENTAL_DA TA (144)9.4.2 MAKE_EXPERIMENTAL_DA TAFILE (145)9.5.3 SET_AXIS_LENGTH (147)9.5.4 SET_AXIS_TEXT_STATUS (147)9.5.5 SET_AXIS_TYPE (147)9.5.6 SET_COLOR (147)9.5.7 SET_CORNER_TEXT (148)9.5.8 SET_FONT (148)9.5.9 SET_INTERACTIVE_MODE (149)9.5.10 SET_PLOT_OPTION (149)9.5.11 SET_PREFIX_SCALING (149)9.5.12 SET_REFERENCE_STA TE (149)9.5.13 SET_TIELINE_STA TE (150)9.5.14 SET_TRUE_MANUAL_SCALING (150)9.5.15 TABULATE (150)9.6 奇特的命令 (150)9.6.1 PATCH_WORKSPACE (150)9.6.2 RESTORE_PHASE_IN_PLOT (150)9.6.3 REINIATE_PLOT_SETTINGS (151)9.6.4 SET_AXIS_PLOT_STATUS (151)9.6.5 SET_PLOT_SIZE (151)9.6.6 SET_RASTER_STATUS (151)9.6.8 SUSPEND_PHASE_IN_PLOT (151)9.7 3D图标是：命令与演示 (151)9.7.1 CREATE_3D_PLOTFILE (153)9.7.2 在Cortona VRML Client阅读器中查看3D图 (154)第10部分一些特殊模块 (155)10.1 引言 (155)10.2 特殊模块生成或使用的文件 (156)10.2.1 POL Y3文件 (156)10.2.2 RCT文件 (156)10.2.3 GES5文件 (156)10.2.4 宏文件 (157)10.3 与特殊模块的交互 (157)10.4 BIN模块 (157)10.4.1 BIN模块的描述 (157)10.4.2 特定BIN模块数据库的结构 (161)10.4.3特定BIN计算的演示实例 (162)10.5 TERN 模块 (162)10.5.1 TERN 模块的描述 (162)10.5.2 特殊TERN模块数据库的结构 (166)10.5.3 TERN模块计算的演示实例 (167)10.6 POT模块 (167)10.7 POURBAIX 模块 (167)10.8 SCHAIL 模块 (167)11.2 热化学 (168)11.2.1 一些术语的定义 (168)11.2.2 元素与物种（Elements and species） (168)11.2.3 大小写模式 (169)11.2.4 相 (169)11.2.5 温度与压力的函数 (169)11.2.6 符号 (170)11.2.7 混溶裂隙 (170)11.3 热力学模型 (170)11.3.1 标准Gibbs能 (171)11.3.2 理想置换模型 (171)11.3.3 规则溶体模型 (171)11.3.4 使用组元而不是元素 (172)11.3.5 亚点阵模型—化合物能量公式 (172)11.3.6 离子液体模型，对具有有序化趋势的液体 (172)11.3.7 缔合模型 (173)11.3.8 准化学模型 (173)11.3.9 对Gibbs能的非化学贡献（如铁磁） (173)11.3.10 既有有序-无序转变的相 (173)11.3.11 CVM方法：关于有序/无序现象 (173)11.3.12 Birch-Murnaghan模型：关于高压贡献 (173)11.3.13 理想气体模型相对非理想气体/气体混合物模型 (173)11.3.14 DHLL和SIT模型：关于稀水溶液 (173)11.3.15 HKF和PITZ模型：对浓水溶液 (173)11.3.16 Flory-Huggins模型：对聚合物 (173)11.4 热力学参数 (173)11.5 数据结构 (175)11.5.1 构造 (175)11.5.2 Gibbs能参考表面 (175)11.5.3 过剩Gibbs能 (175)11.5.4 存储私有文件 (175)11.5.5 加密与不加密数据库 (176)11.6 GES系统的应用程序 (176)11.7 用户界面 (176)11.7.1 模块性和交互性 (177)11.7.2 控制符的使用 (177)11.8 帮助与信息的命令 (177)11.8.1 HELP (177)11.8.2 INFORMATION (177)11.9 改变模块与终止程序命令 (178)11.9.1 GOTO_MODULE (178)11.9.2 BACK (178)11.9.3 EXIT (178)11.10 输入数据命令 (178)11.10.4 ENTER_SYMBOL (180)11.10.5 ENTER_PARAMETER (181)11.11 列出数据的命令 (183)11.11.1 LIST_DATA (183)11.11.2 LIST_PHASE_DA TA (183)11.11.3 LIST_PARAMETER (184)11.11.4 LIST_SYMBOL (185)11.11.5 LIST_CONSTITUENT (185)11.11.6 LIST_STATUS (185)11.12 修改数据命令 (185)11.12.1 AMEND_ELEMENT_DA TA (185)11.12.2 AMEND_PHASE_DESCRIPTION (186)11.12.3 AMEND_SYMBOL (188)11.12.4 AMEND_PARAMETER (189)11.12.5 CHANGE_STATUS (191)11.12.6 PATCH_WORKSPACES (191)11.12.7 SET_R_AND_P_NORM (191)11.13 删除数据的命令 (192)11.13.1 REINITIATE (192)11.13.2 DELETE (192)11.14 存储或读取数据的命令 (192)11.14.1 SA VE_GES_WORKSPACE (192)11.14.2 READ_GES_WORKSPACE (193)11.15 其它命令 (193)11.15.1 SET_INTERACTIVE (193)第12部分优化模块（PARROT） (193)12.1 引言 (193)12.1.1 热力学数据库 (194)12.1.2 优化方法 (194)1 2.1.4 其它优化软件 (195)12.2 开始 (195)12.2.1 试验数据文件：POP文件 (195)12.2.2 图形试验文件：EXP文件 (197)12.2.3 系统定义文件：SETUP文件 (197)12.2.4 工作文件或存储文件：PAR文件 (198)12.2.5 各种文件名与其关系 (198)12.2.6 交互运行PARROT模块 (199)12.2.6.3 绘制中间结果 (199)12.2.6.4 实验数据的选择 (199)12.2.6.6 优化与连续优化 (200)12.2.7 参数修整 (200)12.2.8 交互完成的变化要求编译 (201)12.3 交替模式 (201)12.4 诀窍与处理 (201)12.4.4 参数量 (201)12.5 命令结构 (201)12.5.1 一些项的定义 (201)12.5.2 与其它模块连接的命令 (201)12.5.3 用户界面 (201)12.6 一般命令 (201)12.7 最频繁使用的命令 (202)12.8 其它命令 (203)第13部分编辑-实验模块（ED-EXP） (203)第14部分系统实用模块（SYS） (203)14.1 引言 (203)14.2 一般命令 (203)14.2.1 HELP (203)14.2.2 INFORMA TION (204)14.2.4 BACK (205)14.2.5 EXIT (205)14.2.6 SET_LOG_FILE (205)14.2.7 MACRO+FILE_OPEN (205)14.2.8 SET_PLOT_ENVIRONMENT (206)14.3 Odd命令 (207)14.3.1 SET_INTERACTIVE_MODE (207)14.3.2 SET_COMMAND_UNITS (207)14.3.4 LIST_FREE_WORKSPACE (207)14.3.5 PATCH (207)14.3.6 TRACE (207)14.3.7 STOP_ON_ERROR (208)14.3.8 OPEN_FILE (208)14.3.9 CLOSE_FILE (208)14.3.10 SET_TERMINAL (208)14.3.11 NEWS (208)14.3.12 HP_CALCULATOR (208)14.4 一般信息的显示 (209)第15部分数据绘图语言（DATAPLOT） (215)第1部分一般介绍1.1 计算热力学在近十年内与材料科学与工程相联系的计算机计算与模拟的研究与发展已经为定量设计各种材料产生了革命性的方法，热力学与动力学模型的广泛结合使预测材料成分、各种加工后的结构和性能。
第一章绪论一简答题1. 21世纪是生命科学的世纪。
20世纪后叶分子生物学的突破性成就，使生命科学在自然科学中的位置起了革命性的变化。
试阐述分子生物学研究领域的三大基本原则，三大支撑学科和研究的三大主要领域？答案：（1）研究领域的三大基本原则：构成生物大分子的单体是相同的；生物遗传信息表达的中心法则相同；生物大分子单体的排列（核苷酸，氨基酸）导致了生物的特异性。
（2）三大支撑学科：细胞学，遗传学和生物化学。
（3）研究的三大主要领域：主要研究生物大分子结构与功能的相互关系，其中包括DNA和蛋白质之间的相互作用；激素和受体之间的相互作用；酶和底物之间的相互作用。
2. 分子生物学的概念是什么？答案：有人把它定义得很广：从分子的形式来研究生物现象的学科。
但是这个定义使分子生物学难以和生物化学区分开来。
另一个定义要严格一些，因此更加有用：从分子水平来研究基因结构和功能。
从分子角度来解释基因的结构和活性是本书的主要内容。
3 二十一世纪生物学的新热点及领域是什么？答案：结构生物学是当前分子生物学中的一个重要前沿学科，它是在分子层次上从结构角度特别是从三维结构的角度来研究和阐明当前生物学中各个前沿领域的重要学科问题，是一个包括生物学、物理学、化学和计算数学等多学科交叉的，以结构（特别是三维结构）测定为手段，以结构与功能关系研究为内容，以阐明生物学功能机制为目的的前沿学科。
这门学科的核心内容是蛋白质及其复合物、组装体和由此形成的细胞各类组分的三维结构、运动和相互作用，以及它们与正常生物学功能和异常病理现象的关系。
分子发育生物学也是当前分子生物学中的一个重要前沿学科。
人类基因组计划，被称为“21世纪生命科学的敲门砖”。
“人类基因组计划”以及“后基因组计划”的全面展开将进入从分子水平阐明生命活动本质的辉煌时代。
目前正迅速发展的生物信息学，被称为“21世纪生命科学迅速发展的推动力”。
尤应指出，建立在生物信息基础上的生物工程制药产业，在21世纪将逐步成为最为重要的新兴产业；从单基因病和多基因病研究现状可以看出，这两种疾病的诊断和治疗在21世纪将取得不同程度的重大进展；遗传信息的进化将成为分子生物学的中心内容”的观点认为，随着人类基因组和许多模式生物基因组序列的测定，通过比较研究，人类将在基因组上读到生物进化的历史，使人类对生物进化的认识从表面深入到本质；研究发育生物学的时机已经成熟。
a r X i v :h e p -p h /0403258v 1 24 M a r 2004ρ-meson form factors and QCD sum rules.V.V.Braguta a and A.I.Onishchenko ba)Institute for High Energy Physics,Protvino,Russia b)Department of Physics and Astronomy Wayne State University,Detroit,MI 48201,USAAbstractWe present predictions for ρ-meson form factors obtained from the analysis of QCD sum rules in next-to-leading order of perturbation theory.The radiative corrections turn out to be sizeable and should be taken into account in rigorous theoretical analysis.1IntroductionThe method of QCD sum rules [1]is designed to estimate low-energy characteristics of hadrons,such as masses,decay constants and form factors.Within this framework we analyze the correlation func-tion of currents in deep euclidean region with the help of operator product expansion,which allows us to take into account both perturbative and nonperturbative contributions.The presence of latter could be traced to the non-vanishing values of vacuum QCD condensates.Physical quantities,we are interested in,are determined by matching this correlator to its phenomenological representation.In this work we performed an analysis of three-point sum rules for ρ-meson form factors at intermediate momentum transfer.Basically,it is an extension of already available LO analysis [2]to include radiative corrections.To compute radiative corrections we used the technic already developed and tested in the analysis of pion electromagnetic form factor within NLO QCD sum rule setup both with pseudoscalar and axial-vector pion interpolating currents [3,4].The paper is organized as follows.In section 2we describe our framework and give explicit expressions for next-to-leading order corrections to double spectral density.Section 3contains our numerical analysis and expressions for the contributions of gluon and quark condensates.Finally,in section 4we draw our conclusions.2The methodTo determine ρ-meson electromagnetic form factors we will use the method of three-point QCD sum rules.Within this framework ρ-meson is described as a result of an action of vector interpolating current on vacuum state.We define the vacuum to ρ-meson transition matrix element of vector current as0|j µ|ρ+,ǫ =m 2ρexpression forρ-meson electromagnetic vertex could be written in terms of three form factors: ρ+(p′,ǫ′)|j elµ|ρ+(p,ǫ) =−ǫ∗βǫα [(p′+p)µgαβ−p′αgβµ−pβgαµ]F1(Q2)+[gµαqβ−gµβqα]F2(Q2)+12(µ−1)−m2ρ(2π)2 ρpertµαβ(s1,s2,Q2)The integration region in(7)is determined by condition1−1≤s 2−s 1−q 24πρ(1)µαβ(s 1,s 2,Q 2)+...(10)Figure 2:NLO diagramsAt leading order in coupling constant we have only one diagram depicted in Fig.1,contributing to three-point correlation function.At next to leading order we have 6diagrams shown in Fig.2.The calculation of corresponding double spectral density was performed with the standard use of Cutkosky rules.In the kinematic region q 2<0,we are interested in,there is no problem in applying Cutkosky rules for determination of ρµαβ(s 1,s 2,Q 2)and integration limits in s 1and s 2.The non-Landau type singularities,not accounted for by Cutkosky prescription,do not show up here.The calculation could be considerably simplified with the use of Lorentz decomposition of double spectral density based on a fact,that our spectral density is subject to three transversality conditions:ρµαβq µ=ρµαβp α=ρµαβp ′β=0ρµαβ=A 1[(Q 2+x )p α1−(x +y )p α2][(y −x )p β1+(Q 2+x )p β2][(Q 2+y )p µ1+(Q 2−y )p µ2]−12A 3[(Q 2+x )p α1−(x +y )p α2][2(p β2−p β1)p µ2+(Q 2+y )g µβ]−11In our case this inequality is satisfied identically.where x=s1+s2,y=s1−s2and p1=p,p2=p′.The four independent structures A i(we suppressed the dependence on kinematical invariants)are given by a solution of system of linear equations:I1=ρµαβpµ1pα2pβ1=k24(x+Q2) kA1−3A2−A3−A4 (13) I3=ρµαβpα2gµβ=k4(y−Q2) kA1−A2−A3−3A4 ,(15)where k=λ(s1,s2,−Q2).Solving this system it is easy tofind explicit expressions for A i in terms of I i(functional dependence on kinematical invariants is assumed):A1=20(Q2+x)k2I2−2(Q2−y)k2I4,(16)A2=4(Q2+x)kI2,(17)A3=4(Q2+y)kI3,(18)A4=4(Q2−y)k I4.(19)At Born level and expressions for I i are easy tofind and they are given by(s3=Q2)[2]:I(0)1=−3s1s2s3k1/2,(21)I(0)3=−3s2s3k1/2,(23) The calculation of NLO radiative corrections to double spectral density is in principle straightfor-ward.One just needs to consider all possible double cuts of diagrams,shown in Fig. 2.However, the presence of collinear and soft infrared divergences calls for appropriate regularization of arising divergences at intermediate steps of calculation and makes the whole analytical calculation quite involved.We will present the details of NLO calculation in one of our future publications.Here we give onlyfinal results:k1/2I(1)1=−s31+s2s21+s22s1−s32+(s1+s2)s23−s21s3−s22s3+s1s2s3−16log2(v1)−16log(v3)log(v1)−16log(v4)log(v1)+2log(v1)−4log2(v3)−4log2(v4)−2log(v2)−2log(v3)−8log(v3)log(v4)−8Li2 x2y2 −8Li2 z1s2 +8Li2 z1−32log 2(v 1)−32log(v 3)log(v 1)−32log(v 4)log(v 1)+4log(v 1)−8log 2(v 3)−8log 2(v 4)−4log(v 2)−4log(v 3)−16log(v 3)(v 4)−16Li 2 x 2y 2 −16Li 2 z 1s 2+16Li 2z 1x 1−16Li 2y 1s 1−16Li 2z 1z 2,(26)k 1/2I (1)4=2s 21−2s 22+2s 23−8s 1s 2+s 1s 3−32log 2(v 1)−32log(v 3)log(v 1)−32log(v 4)log(v 1)+4log(v 1)−8log 2(v 3)−8log 2(v 4)−4log(v 2)−4log(v 3)−16log(v 3)log(v 4)−16Li 2x 2y 2 −16Li 2 z 1s 2+16Li 2 z 12(s 1−s 2−Q 2)−1k,(28)x 2=12√2(s 1+Q 2−s 2)−1k,(30)y 2=12√2(s 1+s 2+Q 2)−1k,(32)z 2=12√2s 1(s 1−s 2−Q 2)+1k,(34)v 2=12s 2√2s 1(s 1+s 2+Q 2)+1k,(36)v 4=s 1Q 2,(38)v 6=1−z 1correlators with spectral representation,derived from a double dispersion relation at q 2≤0:Πµαβ(p 21,p 22,q 2)=1(s 1−p 21)(s 2−p 22)ds 1ds 2+subtractions .(40)Assuming that the dispersion relation(40)iswellconvergent,the physical spectral functions aregenerally saturated by the lowest lying hadronic states plus a continuum starting at some thresholdss th 1and s th2:ρphys µαβ(s 1,s 2,Q 2)=ρres µαβ(s 1,s 2,Q 2)+θ(s 1−s th 1)·θ(s 2−s th 2)·ρcont µαβ(s 1,s 2,Q 2),(41)whereρres µαβ(s 1,s 2,Q 2)=m 4ρ2m 2ρP µ(p 2αp 2β+p 1αp 1β) F 1(Q 2)−F 2(Q 2)+21+Q 2m 2ρ 1+Q 22m 2ρF 3(Q 2)−12m 2ρq µ(p 1αp 1β−p 2αp 2β) F 1(Q 2)+F 2(Q 2) −g αβP µF 1(Q 2)+(g αµp 1β+g βµp 2α) F 1(Q 2)+F 2(Q 2)−(g αµp 2β+g βµp 1α)1+Q 2n !−d m !−d (2π)2∞ds 1∞ds 2exp−s 1M 22ρ(pert |phys )µαβ(s 1,s 2,q 2),(44)In what follows we put M 21=M 22=M 2.If M 2is chosen to be of order 1GeV 2,then the right hand side of (44)in the case of physical spectral density will be dominated by the lowest hadronic state contribution,while the higher state contribution will be suppressed.F 1(Q 2)123400.050.10.150.20.25Figure 3:Q 2dependence of F 1electric form factorQ2Now let us recall that our sum rules also receive power corrections proportional to QCD vacuum condensates.The evaluation of power corrections is simplified if performed directly for the Borel transformed expression of three-point correlation function and this is the reason why we delayed their discussion up to his moment.The quark condensate contribution is known already for a long time and is given by [2]:Φ ¯q q2µαβ(M 2,M 2,q 2)=4παs M 4P µ(p 1αp 1β+p 2αp 2β)13−18M 2Q 4+2Q 2Q 2−36M 4M 2+16P µp 1βp 2α+q µ(p 1αp 1β−p 2αp 2β)5−18M 2Q 4+2Q 2M 2−2Q 4M 2.(45)The correction due to gluon condensate was only partially computed in [2],where subset of diagrams as well as part of Lorentz structures were considered.Taking everything into account we get 2:Φ G 2µαβ(M 2,M 2,q 2)=αs2See Appendix A for the details of calculationP µp 1βp 2α4M 2+(p 1µp 2βp 2α+p 2µp 1βp 1α)−4M 2−2g µβp 2α−2p 1βg µα−Q 2M 2p 1αg µβ+5p 2βg µα+5p 1αg µβ.(46)F 2(Q 2)123400.10.20.30.4Figure 4:Q 2dependence of F 2magnetic form factorQ 2Equating Borel transformed theoretical and physical parts of QCD sum rules we get F 1(Q 2)=g 2ρm 2ρ2exp2m 2ρM 2dx ′x ′dy ′s ′3(x ′+s ′3)A (0)2exp[−x ′]+αsM 2dx′x ′dy ′s ′3(x ′+s ′3)A (1)2exp[−x ′]+640π38π2M2M 2s 04πs 081M 6αs 0|¯q q |0 2(4−s ′3)−π2πG 2ρσ|0,(48)F 3(Q 2)=g 2ρm 2ρexp 2m 2ρM 2dx ′ x ′dy ′ 2s ′1A (0)3+2s ′2A (0)4−2s ′3A (0)2−8s ′1s ′2s ′3A (0)1 exp[−x ′]+αs M 20dx′x ′dy ′2s ′1A (1)3+2s ′2A (1)4−2s ′3A (1)2−8s ′1s ′2s ′3A (1)1 exp[−x ′]−512π33M 4s ′30|αsM 2,y ′=yM 2,s ′2=s 2M 2was introduced.F 3(Q 2)123400.020.040.060.08Figure 5:Q 2dependence of F 3quadrupole form factorQ2F 2(1GeV 2)1234560.320.330.340.350.36Figure 6:Borel mass M 2dependence of ρ-meson magnetic form factor at Q 2=1GeV 2M2Here,for continuum subtraction we used so called ”triangle”model.To verify the stability of our results with respect to the choice of continuum model we checked,that the usual ”square”model gives similar predictions for pion electromagnetic form factor provided s 0∼1.5s 1is chosen 3.Inwhat follows we set s 0=2.2.This value coincides with one used in the previous analysis[2]andisinagreementwiththevalueofcontinuumthreshold employed in the analysis of corresponding two-point QCD sum rules.For the rest of parameters entering our expressions for form factors we used the following values 4:m ρ=0.77GeV ,0|αs2m ρ(F 1(Q 2)+F 2(Q 2)),(51)F LL (Q 2)= p ′,ǫL |j el0|p,ǫL /2E =F 1(Q 2)−Q2m 2ρ1+Q 2m 2ρ+14For numerical values of QCD condensates we took central values of estimates made in [5]4ConclusionWe presented the results forρ-meson electromagnetic form factors in the framework of three-point NLO QCD sum rules.The radiative corrections are sizeable(∼30%in the case of F1form factor and somewhat smaller for two other form factors)and should be taken into account when precision data onρ-meson form factors become available.The work of V.B.was supported in part by Russian Foundation of Basic Research under grant 01-02-16585,Russian Education Ministry grant E02-31-96,CRDF grant MO-011-0and Dynasty foundation.The work of A.O.was supported by the National Science Foundation under grant PHY-0244853and by the US Department of Energy under grant DE-FG02-96ER41005. References[1]M.A.Shifman,A.I.Vainshtein and V.I.Zakharov,Nucl.Phys.B147,385(1979).M.A.Shif-man,A.I.Vainshtein and V.I.Zakharov,Nucl.Phys.B147,448(1979).[2]B.L.Ioffe and A.V.Smilga,Nucl.Phys.B216,373(1983).[3]V.V.Braguta and A.I.Onishchenko,arXiv:hep-ph/0311146.[4]V.V.Braguta and A.I.Onishchenko,arXiv:hep-ph/0403240.[5]B.L.Ioffe,Phys.Atom.Nucl.66,30(2003)[Yad.Fiz.66,32(2003)][arXiv:hep-ph/0207191].[6]A.Samsonov,JHEP0312,061(2003)[arXiv:hep-ph/0308065].[7]T.M.Aliev,I.Kanik and M.Savci,Phys.Rev.D68,056002(2003)[arXiv:hep-ph/0303068].[8]F.T.Hawes and M.A.Pichowsky,Phys.Rev.C59,1743(1999)[arXiv:nucl-th/9806025].[9]M.B.Hecht and B.H.J.McKellar,Phys.Rev.C57,2638(1998)[arXiv:hep-ph/9704326].[10]J.P.B.de Melo and T.Frederico,Phys.Rev.C55,2043(1997)[arXiv:nucl-th/9706032].[11]V.Fock,Phys.Z.Sowjetunion12,404(1937).[12]J.S.Schwinger,Phys.Rev.82,664(1951).[13]V.M.Belyaev and A.V.Radyushkin,Phys.Rev.D53,6509(1996)[arXiv:hep-ph/9509267].[14]V.M.Belyaev and I.I.Kogan,Int.J.Mod.Phys.A8,153(1993).A Gluon condensate correctionHere we present details on the evaluation of power corrections proportional to gluon condensate. This calculation could be relatively easy performed directly for the Borel transformed expression of three-point correlation function.Unfortunately,one of the methods(calculation in coordinate space), we will discuss below,does not allow us to subtract continuum contribution for gluon condensate correction.However,the form of the obtained expression leads us to the conclusion,that this contribution is simply absent in ourfinal result.This conclusion is based on a fact,that typical11continuum contribution may show up only as incomplete Γ-functions.The latter are in fact present in contributions of each separate diagram,but they are canceling in the sum.The gluon condensate contribution to the three-point sum rules is given by diagrams with two external gluon vacuum fields,depicted in Fig.7.For calculations wehaveusedthe Fock-Schwinger fixed point gauge [11,12]:x µA a µ(x )=0,(53)where A a µ,a ={1,2,...,8}is the gluon field.The use of this gauge allows us express gauge potentialA µ(x )in terms of field strength and its covariant derivatives at origin:A a µ(x )=−13x νx α(D αG µν)a (0)+......(54)or in momentum representation:A a µ(k )=−1∂k νδ4(k )−1∂k α∂k νδ4(k )+...(55)So,basically,the calculation of gluon condensate correction is the ordinary calculation in back-ground of vacuum gluon fields in the form of (54)or (55).Finally,vacuum averaging is performedaccording to rule:0|G µνG b ρσ|0 =12π2r /8π2r α4π2r /192π2r/2λa G a αβ,˜Gαβ=1241k 2P 21P 2212p 1p 2k a )k 1kp 1p 2k 1k 2p 1−k 2p 2k 1k 2p 1p 2k f )p 2k d )k 1p 1p 2k 2k 1Figure 7:The gluon condensate contribution to three-point QCD sum rules.The directions of p 1,k 1,k 2momenta are incoming,and that of p 2is outgoing.13+1P21P22Tr[γµ P2γα kγβ P1+2γµγβ kγαP1·P2] +1k2P41P42=1∂p1ρ∂p2σ d4k kµ4∂2λ3/2s2(s1−s2−Q2)p1µ+s1(s2−s1−Q2)p2µ576 0|G2µν|0∂4∂p1ρ∂p1ρ∂2(P2−m2)n=1(M2)ne−m2/M2(62)we come to thefinal expression for gluon condensate contribution presented in the main body of the paper.Now,let us make a few comments about calculation of gluon condensate contribution within coordinate space representation5.The coordinate space amplitude corresponding to this contribution easily follows from an expression of quark propagator in the background gluonfield(57).However, its Borel transformation is not that trivial.To do it,wefirst convert our result into momentum space with the help of the following formula[14]:1(x−y)2l y2m x2n =(−1)l+m+n+1(τ1τ2+τ2τ3+τ3τ1)l+m+n−2(63)The factors in numerator could be incorporated via:xµ→−i∂∂p1µ.(64) The Borel transformation of the resulting expression is performed with the help of the following formula:B P2(M2)e−τP2=δ(1−τM2)(65) Thefinal expression for gluon condensate contribution obtained within this approach coincides with the result obtained in momentum representation and serves as a check of our result.。
