直线对撞机上四体末态过程的QCD修正研究
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摘要
当前标准模型虽然已经取得了巨大的成功,但是其理论上还存在诸如等级差问题等许多问题,从而我们相信标准模型只是一个更基本理论在较低能量下的近似。不幸的是标准模型中给予规范玻色子和费米子质量的Higgs玻色子迄今为止也还没有在实验上观测到。而这些问题的解决都需要依靠更高能量下对撞机上的实验。未来的国际直线对撞机(ILC)被设计为一个在TeV能标下能运行正-负电子、光子-光子和电子-光子等对撞模式的对撞机。与即将运行的大型强子对撞机(LHC)相比,它能提供更加干净的信号。所以在ILC上能够精确的验证标准模型理论和寻找新物理现象。
由于Higgs玻色子还没有被发现,所以Higgs粒子的直接观测是ILC上最重要目标之一。而top夸克由于其具有巨大的质量,一些与top夸克有关的物理现象对新物理十分敏感,所以ILC上top物理的研究是另一个重要的工作。在本论文中,我们研究了ILC上t(?)b(?)和W+W-b(?)产生过程。t(?)b(?)产生事例中包含了探测Yukawa耦合的重要过程t(?)H产生过程的信号和本底,而W+W-b(?)产生过程中包含了HZ信号,t(?)对信号以及其它本底。这两个过程对于Higgs物理和top物理的研究都具有重要意义。我们计算了这两个过程的领头阶和QCD次领头阶的贡献。
本论文研究中的主要的创新之处如下:
●在高对撞能量下,未来对撞机上许多物理过程都会有大的s道压低效应,这些过程的主要贡献就会来自于t道或u道。据我们所知,一般的计算四体相空间积分的Monte Carlo程序都是采用反复使用因子化公式将四体相空间因子化为多个两体相空间的乘积的方法来进行积分,这种方法可以很好的处理s道占优的情况,但是对于t道或u道占优的过程来说就不是很有效。对于后一种情况,我们建立了一种新的四体末态相空间Monte Carlo积分的方法来计算t道或u道占优的过程。
●在我们完整的四体末态过程的单圈修正计算中会遇到六点标量和张量积分函数的计算。在此之前只有德国的A.Denner等人给出过包含三阶以下六点函数的计算。我们将其结果扩展到了六点四阶函数,同时还独立的推导出了另一个六点标量和一阶到四阶张量函数的计算公式,并将两种方法相互做了检验,其结果是一致的。最终我们针对相空间中不同区域,结合两种方法开发了完整的六点标量和张量(一阶到四阶)函数计算程序。
●在多体末态(n＞2)过程计算中,人们经常会遇到不稳定粒子的共振问题。对于不稳定粒子的共振的处理传统上有许多方法比如有效拉氏量方法和窄宽度近似等等。但是在包含次领头阶贡献的计算中如果直接采用这些处理方法就不能够保汪规范不变性。所以我们在计算中采用了能在单圈阶上保证规范不变性的复质量方案(CMS)来处理不稳定粒子的共振问题。并且我们根据CMS方案的需要将单圈积分函数表达式解析延拓到了复质量平面,并开发了计算包含复质量的单圈积分函数的程序。
Although the Standard Model(SM)has got a great success,it still has many theoretical problems,such as the hierarchy problem.We believe that the SM is only a lower energy approximation of a more basic theory.Unfortunately,the Higgs boson,which gives masses to gauge bosons and fermions in the SM,has not been directly observed in experiment until now.The solution of these problems requires the future experiments operated in the machines with more higher colliding energy.The future International Linear Collider (ILC)is designed as a TeV scale collider machine operating with electron-positron, photon-photon,electron-photon colliding modes.Compared with the Large Hardron Collider (LHC),it can provide much more clean signals.Therefore,it is possible to probe the SM theory in high precision and search for new physics by using the ILC.
Since the Higgs boson has not yet been discovered by now,one of the most important physics goal at the ILC is to directly discover the Higgs boson.The study of top physics is another important task at the ILC,since the phenomena involving top quark is sensitive to the new physics due to its huge mass.In this thesis,I present the study the processes of t(?)b(?)and W+W-b(?)production at ILC.The t(?)b(?)production events contains the signals and background of the t(?)H production process,which is important for probing Yukawa coupling.The W+W-b(?)production process includes the HZ,t(?)-pair production events and their backgrounds.Both the HZ,t(?)-pair production processes are all important for the research of the Higgs physics and the top physics.Our calculations of these two processes are implemented up to QCD next-to-leading order.
The main innovations in this thesis are listed below:
●In the very high collision energy,many physical processes at the future colliders have large s-channel suppression effect.Their main contributions are always from t- or u-channel.As we know,the general Monte Carlo program for four-body phase space integral,which is implemented by repeatedly factorizing four-body phase space as several two-body phase spaces,works well for process dominated by schannel, but is not efficient for the process donainated by t- or u-channel.For the later case,we create a new four-body space Monte Carlo integral method to calculate process dominated by t- or u-channel.
●Scalar and tensor 6-point integral functions are present during our calculations of complete NLO corrections for the processes with tour final particles.Before our works,only A.Denner et al.had provided the calculations involving only the tensor 6-point integral functions up to three-rank.We extend their expressions to four-rank tensor integral functions and use another method to derive the scalar and tensor 6-point functions up to four-rank independently.We have done cross check by using both two expressions,and got a good agreement.Finally,we combine both methods to create program codes for calculating the complete scalar and tensor(up to fourrank) 6-point integral functions in different phase space regions.
●In calculating of the processes with final multi-particles(n＞2),people always suffer from the trouble due to unstable particle(resonance).There are some traditional methods to deal with the resonance problem,such as effective theory,narrow-width approximation and etc.Since these methods cannot guarantee to preserve the gauge invariance,they cannot be adopted directly to the calculation for the processes up to NLO,especially when the concerned process has several resonance channels.So we use the complex mass scheme(CMS)method which can preserve the gauge invariance in the calculations up to one-loop order to deal with the resonance problem. In this work we extend the expressions for calculating one-loop integral functions to the complex mass plane according to the requirement of the CMS method and develop the program codes for calculating one-loop integrals with complex masses.
由于Higgs玻色子还没有被发现,所以Higgs粒子的直接观测是ILC上最重要目标之一。而top夸克由于其具有巨大的质量,一些与top夸克有关的物理现象对新物理十分敏感,所以ILC上top物理的研究是另一个重要的工作。在本论文中,我们研究了ILC上t(?)b(?)和W+W-b(?)产生过程。t(?)b(?)产生事例中包含了探测Yukawa耦合的重要过程t(?)H产生过程的信号和本底,而W+W-b(?)产生过程中包含了HZ信号,t(?)对信号以及其它本底。这两个过程对于Higgs物理和top物理的研究都具有重要意义。我们计算了这两个过程的领头阶和QCD次领头阶的贡献。
本论文研究中的主要的创新之处如下:
●在高对撞能量下,未来对撞机上许多物理过程都会有大的s道压低效应,这些过程的主要贡献就会来自于t道或u道。据我们所知,一般的计算四体相空间积分的Monte Carlo程序都是采用反复使用因子化公式将四体相空间因子化为多个两体相空间的乘积的方法来进行积分,这种方法可以很好的处理s道占优的情况,但是对于t道或u道占优的过程来说就不是很有效。对于后一种情况,我们建立了一种新的四体末态相空间Monte Carlo积分的方法来计算t道或u道占优的过程。
●在我们完整的四体末态过程的单圈修正计算中会遇到六点标量和张量积分函数的计算。在此之前只有德国的A.Denner等人给出过包含三阶以下六点函数的计算。我们将其结果扩展到了六点四阶函数,同时还独立的推导出了另一个六点标量和一阶到四阶张量函数的计算公式,并将两种方法相互做了检验,其结果是一致的。最终我们针对相空间中不同区域,结合两种方法开发了完整的六点标量和张量(一阶到四阶)函数计算程序。
●在多体末态(n＞2)过程计算中,人们经常会遇到不稳定粒子的共振问题。对于不稳定粒子的共振的处理传统上有许多方法比如有效拉氏量方法和窄宽度近似等等。但是在包含次领头阶贡献的计算中如果直接采用这些处理方法就不能够保汪规范不变性。所以我们在计算中采用了能在单圈阶上保证规范不变性的复质量方案(CMS)来处理不稳定粒子的共振问题。并且我们根据CMS方案的需要将单圈积分函数表达式解析延拓到了复质量平面,并开发了计算包含复质量的单圈积分函数的程序。
Although the Standard Model(SM)has got a great success,it still has many theoretical problems,such as the hierarchy problem.We believe that the SM is only a lower energy approximation of a more basic theory.Unfortunately,the Higgs boson,which gives masses to gauge bosons and fermions in the SM,has not been directly observed in experiment until now.The solution of these problems requires the future experiments operated in the machines with more higher colliding energy.The future International Linear Collider (ILC)is designed as a TeV scale collider machine operating with electron-positron, photon-photon,electron-photon colliding modes.Compared with the Large Hardron Collider (LHC),it can provide much more clean signals.Therefore,it is possible to probe the SM theory in high precision and search for new physics by using the ILC.
Since the Higgs boson has not yet been discovered by now,one of the most important physics goal at the ILC is to directly discover the Higgs boson.The study of top physics is another important task at the ILC,since the phenomena involving top quark is sensitive to the new physics due to its huge mass.In this thesis,I present the study the processes of t(?)b(?)and W+W-b(?)production at ILC.The t(?)b(?)production events contains the signals and background of the t(?)H production process,which is important for probing Yukawa coupling.The W+W-b(?)production process includes the HZ,t(?)-pair production events and their backgrounds.Both the HZ,t(?)-pair production processes are all important for the research of the Higgs physics and the top physics.Our calculations of these two processes are implemented up to QCD next-to-leading order.
The main innovations in this thesis are listed below:
●In the very high collision energy,many physical processes at the future colliders have large s-channel suppression effect.Their main contributions are always from t- or u-channel.As we know,the general Monte Carlo program for four-body phase space integral,which is implemented by repeatedly factorizing four-body phase space as several two-body phase spaces,works well for process dominated by schannel, but is not efficient for the process donainated by t- or u-channel.For the later case,we create a new four-body space Monte Carlo integral method to calculate process dominated by t- or u-channel.
●Scalar and tensor 6-point integral functions are present during our calculations of complete NLO corrections for the processes with tour final particles.Before our works,only A.Denner et al.had provided the calculations involving only the tensor 6-point integral functions up to three-rank.We extend their expressions to four-rank tensor integral functions and use another method to derive the scalar and tensor 6-point functions up to four-rank independently.We have done cross check by using both two expressions,and got a good agreement.Finally,we combine both methods to create program codes for calculating the complete scalar and tensor(up to fourrank) 6-point integral functions in different phase space regions.
●In calculating of the processes with final multi-particles(n＞2),people always suffer from the trouble due to unstable particle(resonance).There are some traditional methods to deal with the resonance problem,such as effective theory,narrow-width approximation and etc.Since these methods cannot guarantee to preserve the gauge invariance,they cannot be adopted directly to the calculation for the processes up to NLO,especially when the concerned process has several resonance channels.So we use the complex mass scheme(CMS)method which can preserve the gauge invariance in the calculations up to one-loop order to deal with the resonance problem. In this work we extend the expressions for calculating one-loop integral functions to the complex mass plane according to the requirement of the CMS method and develop the program codes for calculating one-loop integrals with complex masses.
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