微扰QCD在B介子跃迁形状因子研究中的应用
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摘要
自电弱统一的标准模型理论确立以后,标准模型的检测以及标准模型参数的确定成了物理学家的重要任务。B→轻介子遍举过程跃迁形状因子的研究对确定标准模型的基本参数和在发展QCD理论上起着重要的辅助作用。目前研究B→轻介子跃迁形状因子的方法主要有格点QCD、光锥QCD求和规则(QCD LCSR)和微扰QCD等。格点QCD结果只适用于软的区域,即q~2 > 15GeV~2。QCD LCSR方法适用于软和硬的区域,即q~2≤18GeV~2。而微扰QCD方法仅在大的反冲区域,即小q 2时才可靠。我们只有结合以上几种方法,才能获得对B→轻介子跃迁形状因子在整个能量区域行为的完整描述。
本文主要是在微扰QCD方法下,讨论B→π,K跃迁形状因子的性质,以及影响形状因子的主要因素,并通过与QCD LCSR的结果进行比较,确定计算所需参数的合理取值范围。为了克服多能标多自由度的麻烦,在微扰QCD方法中应用了kT因子化方法以分离长程和短程的贡献。在计算过程中,保留了介子波函数以及硬散射振幅中所涉及的横动量,同时由于Sudakov因子以及阈值求和效应在端点处能很好的压低端点奇异性,使得计算变得可靠。
在本文中,我们用微扰QCD方法系统地讨论了在大反冲区域, B→π,K跃迁形状因子和的性质。我们发现B→π,K跃迁形状因子和在大反冲区域,微扰QCD与QCD LCSR的结果是一致的,而且跃迁形状因子F+ B ,0→,Tπ( q2)和F+ B ,0→,T K( q2)随着B介子波函数的参数Λ的增大而减小,随着δ的增大而增大,其中Λ是B介子的有效质量,δ是决定B介子横向分布宽度的典型参数。随着K介子扭度-2波函数中第一个Gegenbauer动量a_1~K (1GeV) = 0.05±0.02的增大有微小的增大。在q~2 = 0处我们得到:的结果。我们还讨论了π、K介子和B介子波函数的各个不同组成部分对形状因子的贡献。结果发现π、K介子波函数中的Ψπ,K,B介子波函数中的ΨB对形状因子的贡献最大,而π、K介子波函数中的Ψσ,B介子波函数中的Δ对形状因子的影响很小,可以忽略。但π、K介子波函数中的Ψp和B介子波函数中的ΨB对形状因子的贡献比较大,为了获得更加合理的形状因子的结果,一般不能忽略π、K介子波函数中的Ψp和B介子波函数中的ΨB项的贡献。
B介子波函数是B介子衰变中不确定性的一个主要的来源。B→π和B→K跃迁形状因子为确定两个典型的唯象参数Λ和δ提供了一个很好的平台。本文通过kT因子化方法和QCD LCSR下B→π,K跃迁形状因子比较研究,对次领头阶Fock态扩展的B介子光锥波函数的性质作了深入的研究。在大反冲区域,用kT因子化方法对O (1 mb 2)阶的跃迁形状因子和作了详细的计算,并讨论了主要的理论上的不确定性。由于QCD LCSR适用于大的和中等的能量区域,我们采用了文献[1]中的QCD LCSR的结果进行的比较研究。结果我们发现在大反冲能量区域,当B介子中的两个唯象参数Λ∈[0.50,0.55]和δ∈[0.25,0.30]时,两种方法下和的结果是一致的。最后在kT因子化方法下,我们还讨论了B→K跃迁形状因子中的SU f(3)破缺效应,并得到较小的SU_f(3)破缺效应:。
It is an important task of physicists to test the Standard Model (SM) and to determine the parameters in the SM since the SM was established. A study of the B→light meson exclusive processes’transition form factors plays an importantly complementary role in determining the fundamental parameters in the SM and in developing the quantum chromodynamics (QCD) theory. There are various approaches to calculate the B→light meson transition form factors, such as the lattice QCD, the QCD light-cone sum rule (QCD LCSR) and the perturbative QCD (pQCD) approach and so on. The lattice QCD calculations are available only for the soft regions, i.e. q~2 > 15GeV~2. The QCD LCSR can treat both hard and soft contributions with q~2≤18GeV~2. The pQCD calculation is reliable only in the large recoil regions, i.e. in the small q~2 regions. The results from the pQCD approach, the lattice QCD approach, and the QCD LCSR are complementary to each other and by combining the results of those three approaches, one may obtain an understanding of the B→light meson transition form factors in the whole physical regions.
In this paper, we have dicussed the properties of B→π,K transition form factors within the pQCD and the main factors influencing the form factors. We get some resonable regions of parameters by comparing the results wihtin the pQCD and the QCD LCSR. To over come the trouble of multiple free-degree, we apply the kT factorization approach to separate the contributions of long-distance and short-distance. The transverse momentum dependence for the wavefunction, Sudakov effects and threshold effects are included to regulate the endpoint singularity and to derive a more reasonalbe result.
In this paper, we apply the pQCD approach to deal with the B→π,K transition form factors and in the large recoil regions. We find the results of and are consistent with the QCD LCSR results in the large recoil regions. We also find the form factors and will decrease with the increment ofΛ, and will increase with the increment ofδ, whereΛstands for the effective mass of B meson andδis a typical parameter that determines the broadness of the B meson transverse distribution. It can be found that the form factor shall be slightly increased with the increment of the first Gegenbauer moment a_1~K (1GeV) = 0.05±0.02 in twist-2 wave functionΨ_K. And we get . We also discuss the contributions of the form factors and from different parts of the pion, the kaon and the B meson wave functions. We find the most contributions of form factors come fromΨπ,K andΨB, but the contributions ofΨσfrom the pion and the kaon meson, the contribution ofΔfrom B meson are very small, and can be neglected in most of the calculations. The contributions ofΨp from the pion and the kaon meson, the contribution ofΨB from B meson are not very small, and can not be safely neglected for giving more resonable results of form factors.
The B meson wavefunction is a major source of uncertainty in the study of B meson decays. The B→πand B→K transition form factors provide a good platform to determine the possible regions for the two typical phenomenological parametersΛandδ. So the properties of the B meson light-cone wavefunction up to next-leading order Fock state expansion have been studied through a comparative study of the B→π,K transition form factors within the kT factorization approach and the QCD LCSR analysis in this paper. The transition form factors and are carefully re-calculated up to O (1 mb 2) within the kT factorization approach in the large recoil region, in which the main theoretical uncertainties are discussed. The QCD LCSR is applicable in the large and intermediate energy regions, and the QCD LCSR results in Ref. [1] are adopted for such a comparative study. It is found that when the two phenomenological parametersΛ∈[0.50,0.55] andδ∈[0.25,0.30], the results of and from these two approaches are consistent with each other in the large recoil energy region. Finally, to illustrate the SU f(3)-breaking effects in the B→K transition form factors within the kT factorization approach, we calculated the ratio: , which favors small SU_f(3)-breaking effects.
本文主要是在微扰QCD方法下,讨论B→π,K跃迁形状因子的性质,以及影响形状因子的主要因素,并通过与QCD LCSR的结果进行比较,确定计算所需参数的合理取值范围。为了克服多能标多自由度的麻烦,在微扰QCD方法中应用了kT因子化方法以分离长程和短程的贡献。在计算过程中,保留了介子波函数以及硬散射振幅中所涉及的横动量,同时由于Sudakov因子以及阈值求和效应在端点处能很好的压低端点奇异性,使得计算变得可靠。
在本文中,我们用微扰QCD方法系统地讨论了在大反冲区域, B→π,K跃迁形状因子和的性质。我们发现B→π,K跃迁形状因子和在大反冲区域,微扰QCD与QCD LCSR的结果是一致的,而且跃迁形状因子F+ B ,0→,Tπ( q2)和F+ B ,0→,T K( q2)随着B介子波函数的参数Λ的增大而减小,随着δ的增大而增大,其中Λ是B介子的有效质量,δ是决定B介子横向分布宽度的典型参数。随着K介子扭度-2波函数中第一个Gegenbauer动量a_1~K (1GeV) = 0.05±0.02的增大有微小的增大。在q~2 = 0处我们得到:的结果。我们还讨论了π、K介子和B介子波函数的各个不同组成部分对形状因子的贡献。结果发现π、K介子波函数中的Ψπ,K,B介子波函数中的ΨB对形状因子的贡献最大,而π、K介子波函数中的Ψσ,B介子波函数中的Δ对形状因子的影响很小,可以忽略。但π、K介子波函数中的Ψp和B介子波函数中的ΨB对形状因子的贡献比较大,为了获得更加合理的形状因子的结果,一般不能忽略π、K介子波函数中的Ψp和B介子波函数中的ΨB项的贡献。
B介子波函数是B介子衰变中不确定性的一个主要的来源。B→π和B→K跃迁形状因子为确定两个典型的唯象参数Λ和δ提供了一个很好的平台。本文通过kT因子化方法和QCD LCSR下B→π,K跃迁形状因子比较研究,对次领头阶Fock态扩展的B介子光锥波函数的性质作了深入的研究。在大反冲区域,用kT因子化方法对O (1 mb 2)阶的跃迁形状因子和作了详细的计算,并讨论了主要的理论上的不确定性。由于QCD LCSR适用于大的和中等的能量区域,我们采用了文献[1]中的QCD LCSR的结果进行的比较研究。结果我们发现在大反冲能量区域,当B介子中的两个唯象参数Λ∈[0.50,0.55]和δ∈[0.25,0.30]时,两种方法下和的结果是一致的。最后在kT因子化方法下,我们还讨论了B→K跃迁形状因子中的SU f(3)破缺效应,并得到较小的SU_f(3)破缺效应:。
It is an important task of physicists to test the Standard Model (SM) and to determine the parameters in the SM since the SM was established. A study of the B→light meson exclusive processes’transition form factors plays an importantly complementary role in determining the fundamental parameters in the SM and in developing the quantum chromodynamics (QCD) theory. There are various approaches to calculate the B→light meson transition form factors, such as the lattice QCD, the QCD light-cone sum rule (QCD LCSR) and the perturbative QCD (pQCD) approach and so on. The lattice QCD calculations are available only for the soft regions, i.e. q~2 > 15GeV~2. The QCD LCSR can treat both hard and soft contributions with q~2≤18GeV~2. The pQCD calculation is reliable only in the large recoil regions, i.e. in the small q~2 regions. The results from the pQCD approach, the lattice QCD approach, and the QCD LCSR are complementary to each other and by combining the results of those three approaches, one may obtain an understanding of the B→light meson transition form factors in the whole physical regions.
In this paper, we have dicussed the properties of B→π,K transition form factors within the pQCD and the main factors influencing the form factors. We get some resonable regions of parameters by comparing the results wihtin the pQCD and the QCD LCSR. To over come the trouble of multiple free-degree, we apply the kT factorization approach to separate the contributions of long-distance and short-distance. The transverse momentum dependence for the wavefunction, Sudakov effects and threshold effects are included to regulate the endpoint singularity and to derive a more reasonalbe result.
In this paper, we apply the pQCD approach to deal with the B→π,K transition form factors and in the large recoil regions. We find the results of and are consistent with the QCD LCSR results in the large recoil regions. We also find the form factors and will decrease with the increment ofΛ, and will increase with the increment ofδ, whereΛstands for the effective mass of B meson andδis a typical parameter that determines the broadness of the B meson transverse distribution. It can be found that the form factor shall be slightly increased with the increment of the first Gegenbauer moment a_1~K (1GeV) = 0.05±0.02 in twist-2 wave functionΨ_K. And we get . We also discuss the contributions of the form factors and from different parts of the pion, the kaon and the B meson wave functions. We find the most contributions of form factors come fromΨπ,K andΨB, but the contributions ofΨσfrom the pion and the kaon meson, the contribution ofΔfrom B meson are very small, and can be neglected in most of the calculations. The contributions ofΨp from the pion and the kaon meson, the contribution ofΨB from B meson are not very small, and can not be safely neglected for giving more resonable results of form factors.
The B meson wavefunction is a major source of uncertainty in the study of B meson decays. The B→πand B→K transition form factors provide a good platform to determine the possible regions for the two typical phenomenological parametersΛandδ. So the properties of the B meson light-cone wavefunction up to next-leading order Fock state expansion have been studied through a comparative study of the B→π,K transition form factors within the kT factorization approach and the QCD LCSR analysis in this paper. The transition form factors and are carefully re-calculated up to O (1 mb 2) within the kT factorization approach in the large recoil region, in which the main theoretical uncertainties are discussed. The QCD LCSR is applicable in the large and intermediate energy regions, and the QCD LCSR results in Ref. [1] are adopted for such a comparative study. It is found that when the two phenomenological parametersΛ∈[0.50,0.55] andδ∈[0.25,0.30], the results of and from these two approaches are consistent with each other in the large recoil energy region. Finally, to illustrate the SU f(3)-breaking effects in the B→K transition form factors within the kT factorization approach, we calculated the ratio: , which favors small SU_f(3)-breaking effects.
引文
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