基于统计的数据处理与理论之间的桥梁
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摘要
物理学归根结蒂是一门实验科学,是描述自然界最本质规律的科学。然而实验数据的堆砌不是我们对于自然规律的认识。从牛顿时代开始,物理学家通过运用了当时最先进的数学工具对实验现象归纳,整理和深化,提炼出具有普遍性的规律。今天我们仍在遵循这一过程,根据观测到的实验现象“猜到”物理定律。由于它的规律性和普遍性,它可以解释和预言其它物理现象。当然这不是全部过程。这些整理出来的规律还必须进一步得到实验的检验。当运用到解释自然现象时,如果理论预言和测量数据一致,说明理论的合理性,反之则说明得到的理论或者不对,或者有局限性需要推广和修正。这是一个不断重复的复杂过程,在这个过程中最关键的一个环节是建立实验数据与理论间的桥梁。例如,第谷—开普勒—牛顿关于万有引力的研究就是从纯粹观测数据到总结出规律,最后提炼出牛顿引力定律的漫长过程,其中任何一个环节都是必不可少的。然而在三个世纪之前,那时所涉及的物理不是很复杂,需要高度专业的知识也较少,这个中间环节也许还比较简单。然而随着科学的飞速发展,人类积累的知识越来越多,分工越来越细,学科也越来越复杂,一个人很难兼顾理论与实验,不论理论还是实验都需要越来越专越来越多的专业知识。理论越来越艰深,需要的数学工具越来越多。相应的,实验技术的发展也越来越迅速,微观物理随机的本性又使得粒子物理的实验都需要大统计量,数据分析技术也越来越专业,实验仪器越来越复杂,越来越昂贵,甚至到了单个国家难以承受的程度。物理学的复杂化使得理论和实验的分工越来越鲜明,已经很少有人能真正兼顾理论和实验。出现了理论物理学家不理解实验文章的关键和细节,不知道如何做做数据的统计分析,误差分析,背景检验和去除,这对判断理论与实验的符合程度是非常不利的。而且提出的模型往往没有考虑实验背景,也给实验家设计实验设置了困难。而实验的物理学家又看不懂理论物理学家提出的含有艰深数学知识的物理图像,不知道应该测量什么样的信号,不知道如何安排相应的实验来检验它。理论和实验之间似乎存在了一道鸿沟。这个时候就需要有这样一些人,他们既懂基本理论,又懂实验数据的处理方法,并致力于为理论物理学家和实验物理学家之间架设一个通道:对实验数据的分析的准确性和对理论模型的正确性、局限性做出判断,并且确定理论模型参数,提出疑难问题;另一个方向是从理论模型的出发,对测量指标的选定,包括背景的全面分析等等,让实验物理学家真正设计构造一个完整的实验。本论文的内容就是从这两个方向出发在理论和实验之间建立一座基于统计的桥梁。
在这个思想的指引下,我们在本论文中做了三个工作:1,系统地研究了在无粲稀有B衰变中湮灭图的贡献,这在以前的所有相应理论研究中都是认为很小而忽略不计的。通过研究B~+→K~+(?)~0和B~0→K~0(?)~0的分支比的实验数据我们发现,湮灭图的贡献不能是零。并且,我们还发现,非零的湮灭图在B~+→π~+K~0,K~+(?)~0的CP不对称比率中起了很关键的作用。在这个工作中我们还对新物理贡献提出了限制。2,第一次通过最小x~2数据处理方法对跃迁ψ(ns)→ψ(ms)+ππ和γ(ns)→γ(ms)+ππ的QCD多极展开的势模型方法的参数做了拟合,从实验数据中提取出了尽可能多的理论信息。通过研究,我们确定了关于b和c的hybrid态的势模型参数,这在以前是通过假定某个态是hybrid来确定的。从而保证了理论计算的可靠性。同时我们对η_b的质量做出预测。我们发现,夸克胶子混合态的基态在实验中并没有对应的观测态,这可能暗示我们夸克胶子混合态总是和正常的夸克反夸克对总是混合在一起。3,研究了在高能物理实验中Bell不等式的检验。我们首先第一次利用蒙特卡洛随机实验模拟方法模拟级联衰变J/ψ→γη_c→∧(?)→pπ~-(?)π~+的衰变产物两个π的动量方向的夹角,找出了要在传统量子力学和LHVT理论中做出明显区分所需要数据量的大小,然后仔细讨论了这种方法的优缺点;然后提出了在高能物理中满足爱因斯坦非定域条件的直接严格检验Bell不等式的一个新的建议,并仔细讨论了这种方法的优点以及它目前面临的困难。
Basically,physics is an experimental science.The stack of the experimental data,however,is not the laws which describe the essence of the nature.Since the era of Newton,physicists who synthesize,organize and deepen the experimental phenomenon by the use of the most tools of advanced mathematics,have obtained the universal law.Today we are still following this approach that we "guess" the physical law,which is able to interpret and predict the other physical phenomenon due to its regularity and universality,from the phenomenon of experiment.Of course,this is not the all work in physics,where the law induced from phenomenon must be proved by other new experiments.When the law is used to explain the natural phenomenon,one should say that the theory is reasonable if its predictions are consistent with the experimental data.Otherwise, one should treat the theory as a uncorrected one,or at least a limited one,which needs to be corrected and generalized.This is a repeated and complex process, where the key part is to establish a bridge between experimental data and theory. For instance,Tycho-Kepler-Newton's study on the law of gravitation is just a long process which starts from pure experimental data to Kepler laws,and finally to the law of gravitation.It is a process which took a long period in which every part is absolutely necessary.Three centuries ago,however,physics involved was not too complex to need high professional knowledge.The middle part in this period may be relatively simple.With the rapid development of science and technology, we have accumulated so much knowledge which needs highly specialized division. And then the discipline is more complex so that one person can hardly devote himself effectively for theory and experiment at the same time,since both theory and experiment all need more and more high professional knowledge.Theory is more and more difficult,while it needs more and more mathematical tools;Correspondingly, the development of experimental technology is so rapid,while the random essential of microphysics requires the enormous sample of the experiment of particle physics,then the technology of data analysis is also more professional, at the same time the experimental apparatus is also more and more complex,more and more expensive,even that none of the countries in the world can afford it. The complication of physics makes the division more and more clear,so that we are hardly to find a person who masters theory and experiment at the same time. It appears that theory physicist can't understand the key point and the detail of a experimental paper,and that they don't known how to do statistical analysis of data,analysis of error and the test and elimination of the background.This is bad for judging the consistence of theory and experiment.And when they proposed a model which does not take consideration of the background,it also sets a barrier to the experimental physicist who wants to test it.The experimental physicist also can not understand the paper written by a theory physicist and described by advanced mathematical formulas,then they do not know which signal to measure, and how to set a experiment to check it.It seemed that there is a vast gap between theory and experiment.Such being the case,there is a requirement of people who not only know elementary theory but also know the procession of dealing with experimental data,and devote themselves to establishing a bridge between the theory physicist and experiment physicist:on the one hand,they should judge the veracity of the experimental data analysis,the validity and localization of theory model,and determinate the parameters of the theory model and raise difficult questions;on the other hand,they start from the theoretical model to the selection of the observation and the complete analysis of the background,and finally to the complete experiment set by experiment physicist.Our paper is devoted to establishing a bridge between theory and experiment from the two directions.
Under the guidance of this thought,we bring up three works in this paper: 1.we studied the contribution of the annihilation diagram in charmless B decay, which is thought to be negligible and thought it is small in all corresponding theoretical studies up to this time.Through the study on the data of branch ratio in B~+→K~+/(?)~0 and B~0→K~0/(?)~0 we found that,the contribution cannot be zero. And also we found that the nonzero contribution of annihilation diagram plays a important role in the CP asymmetry ratio ofB~+→π~+K~0,K~+(?)~0.In this work we also proposal a limit of the contribution of new physics.2.we first time study the fitting-data of parameters of potential model of QCD multipole-gluon-expansion method for the transition ofψ(ns)→ψ(ms)+ππandγ(ns)→γ(ms)+ππby using least x~2 method,extracting information of theory from the experimental data as much as possible.Through this study,we determined the parameters of potential model in the hybrids state,which was determined by assuming a state as hybrids before.Thus we ensured the reliability of the theoretical calculation.At the same time we made a prediction of the mass ofη_b.We found that the ground state of hybrids did not have a correspond state in experiment,where may be hints us the hybrids may be always together with the regular pair of quark and anti-quark.3.We studied the testing of Bell inequality in the experiment of high energy physics,we firstly at first time simulate the successive decay J/ψ→γη_c→∧(?)→pπ~-(?)π~+ by using Monte-Carlo random experiment method,recording the directions of momentum of the production pions in the decay,we found how large database we need to distinguish the different of traditional quantum mechanics and the LHVT,and then we discussed the advantage and disadvantage of this method;then we raised in high energy physics a new proposition which can test strictly the Bell inequality under Einstein's non-local condition,and we discussed the advantages and the difficulties of this method.
For reader's convenience and understand,we arrange this thesis as follows:
Chapter One,introduction.We briefly introduced the relation between theory and experiment,the motivation of this thesis.
Chapter Two,data analysis under statistics.We introduce the common knowledge of data analysis,such as chisquare method,error transfer and error analysis,confidence level and confidence interval,test of hypothesis,preliminary of Monte-Carlo method.
Chapter Three,raise theoretical question through experimental data.We study model of the rare B decay from experimental data.This chapter divided into two part.Firstly we introduced the common flavor SU(3) model and quark diagram model of the rare B decay.Secondly we introduced how to get the limitation of the theoretical model through analytical method from experimental data.And then we introduced how to get a limitation from experimental data through chisquare fit method.In the last section of this chapter,we introduced the information which may be contained in the measurement of branch ration in B~+→K~+(?)~0 and B~0→K~0(?)~0.The experimental data show that the annihilation amplitude is not zero in these decays.Whereas the nonzero annihilation amplitude plays a important role in the CP violation in B~+→π~+K~0,K+(?)~0.With these measurement of branch ratio,we proved that there is a absolutely 5%bound of CP asymmetry in B~+→π+K~0 through the relation of these decay amplitude. However,this CP asymmetry can be large as 90%in B~+→K~+(?)~0.Future experimental data will test these predictions.
Chapter Four,use least x~2 fit method analysis hybrids.One of the important task of high energy physics is searching exotic state,such as glueball,hybrids and multi-quark state.The transitionψ(ns)→ψ(ms)+ππandγ(ns)→γ(ms)+ππraised great interest,since they may reveal the character of hybrids.In this work,we use the theoretical frame established by Yan and Kuang to analyze the transition mode.Interestingly,when we noted that the intermediate state is the hybrids,we can determine the mass spectrum of hybrids by fitting data.The theory predict that the ground state of hybrids is 4.23 GeV(for charmium) and 10.79 GeV(对于bottonium),which is not corresponding to any state measured by experiments,thus this may hint that the hybrids together with quarkium consist the physical state.The potential of these hybrids has compared with the result obtained by lattice with corresponding parameters.
Chapter Five,raise suggestion about experiments through theoretical model. We introduced the theory of Bell inequality and the status of experimental study, gave the simulated result from different experiment apparatus.And we raised some suggestion.Besides using laser,it is very tempting to test directly the Bell inequality in high energy physics,where the spin correlation is what the original Bell inequality studied.In this work,we follow the literate which proposed to test the Bell inequality in the successive decay J/ψ→γη_c→∧(?)→pπ~-(?)π~+.Our aim is twofold,namely,we use the Monte-Carlo method which based on quantum field theory to simulate this process.Because the under principle is quantum field theory,which means we admit the validity of quantum picture.If this is true,namely,if the quantum field theory is true,we need to find out how big the database must be to distinguish clearly the deviation from the local hidden variable theory.We found that this may be realized in the updated BESⅢ.There is some critics on our suggestion,we will continue to discuss these problems in Chapter Six.
Chapter Six,the expansion and depth discuss about Bell inequality.Usually the testing of Bell inequality always receives various questions,so is our method which we followed in Chapter Five.We studied how can testing strictly the Bell inequality under the Einstein non-local condition.And then we gave our improved scheme.It can help us to remove the confusion from the critics.In this chapter we detailed the discussion about this scheme,its advantages and its difficulties. This reform may be realized in the updated factory,such as BESⅢ.
Chapter Seven,discussion and outlook.We reviewed our work in this thesis, presented the sense of the bridge established between experiment and theory.
在这个思想的指引下,我们在本论文中做了三个工作:1,系统地研究了在无粲稀有B衰变中湮灭图的贡献,这在以前的所有相应理论研究中都是认为很小而忽略不计的。通过研究B~+→K~+(?)~0和B~0→K~0(?)~0的分支比的实验数据我们发现,湮灭图的贡献不能是零。并且,我们还发现,非零的湮灭图在B~+→π~+K~0,K~+(?)~0的CP不对称比率中起了很关键的作用。在这个工作中我们还对新物理贡献提出了限制。2,第一次通过最小x~2数据处理方法对跃迁ψ(ns)→ψ(ms)+ππ和γ(ns)→γ(ms)+ππ的QCD多极展开的势模型方法的参数做了拟合,从实验数据中提取出了尽可能多的理论信息。通过研究,我们确定了关于b和c的hybrid态的势模型参数,这在以前是通过假定某个态是hybrid来确定的。从而保证了理论计算的可靠性。同时我们对η_b的质量做出预测。我们发现,夸克胶子混合态的基态在实验中并没有对应的观测态,这可能暗示我们夸克胶子混合态总是和正常的夸克反夸克对总是混合在一起。3,研究了在高能物理实验中Bell不等式的检验。我们首先第一次利用蒙特卡洛随机实验模拟方法模拟级联衰变J/ψ→γη_c→∧(?)→pπ~-(?)π~+的衰变产物两个π的动量方向的夹角,找出了要在传统量子力学和LHVT理论中做出明显区分所需要数据量的大小,然后仔细讨论了这种方法的优缺点;然后提出了在高能物理中满足爱因斯坦非定域条件的直接严格检验Bell不等式的一个新的建议,并仔细讨论了这种方法的优点以及它目前面临的困难。
Basically,physics is an experimental science.The stack of the experimental data,however,is not the laws which describe the essence of the nature.Since the era of Newton,physicists who synthesize,organize and deepen the experimental phenomenon by the use of the most tools of advanced mathematics,have obtained the universal law.Today we are still following this approach that we "guess" the physical law,which is able to interpret and predict the other physical phenomenon due to its regularity and universality,from the phenomenon of experiment.Of course,this is not the all work in physics,where the law induced from phenomenon must be proved by other new experiments.When the law is used to explain the natural phenomenon,one should say that the theory is reasonable if its predictions are consistent with the experimental data.Otherwise, one should treat the theory as a uncorrected one,or at least a limited one,which needs to be corrected and generalized.This is a repeated and complex process, where the key part is to establish a bridge between experimental data and theory. For instance,Tycho-Kepler-Newton's study on the law of gravitation is just a long process which starts from pure experimental data to Kepler laws,and finally to the law of gravitation.It is a process which took a long period in which every part is absolutely necessary.Three centuries ago,however,physics involved was not too complex to need high professional knowledge.The middle part in this period may be relatively simple.With the rapid development of science and technology, we have accumulated so much knowledge which needs highly specialized division. And then the discipline is more complex so that one person can hardly devote himself effectively for theory and experiment at the same time,since both theory and experiment all need more and more high professional knowledge.Theory is more and more difficult,while it needs more and more mathematical tools;Correspondingly, the development of experimental technology is so rapid,while the random essential of microphysics requires the enormous sample of the experiment of particle physics,then the technology of data analysis is also more professional, at the same time the experimental apparatus is also more and more complex,more and more expensive,even that none of the countries in the world can afford it. The complication of physics makes the division more and more clear,so that we are hardly to find a person who masters theory and experiment at the same time. It appears that theory physicist can't understand the key point and the detail of a experimental paper,and that they don't known how to do statistical analysis of data,analysis of error and the test and elimination of the background.This is bad for judging the consistence of theory and experiment.And when they proposed a model which does not take consideration of the background,it also sets a barrier to the experimental physicist who wants to test it.The experimental physicist also can not understand the paper written by a theory physicist and described by advanced mathematical formulas,then they do not know which signal to measure, and how to set a experiment to check it.It seemed that there is a vast gap between theory and experiment.Such being the case,there is a requirement of people who not only know elementary theory but also know the procession of dealing with experimental data,and devote themselves to establishing a bridge between the theory physicist and experiment physicist:on the one hand,they should judge the veracity of the experimental data analysis,the validity and localization of theory model,and determinate the parameters of the theory model and raise difficult questions;on the other hand,they start from the theoretical model to the selection of the observation and the complete analysis of the background,and finally to the complete experiment set by experiment physicist.Our paper is devoted to establishing a bridge between theory and experiment from the two directions.
Under the guidance of this thought,we bring up three works in this paper: 1.we studied the contribution of the annihilation diagram in charmless B decay, which is thought to be negligible and thought it is small in all corresponding theoretical studies up to this time.Through the study on the data of branch ratio in B~+→K~+/(?)~0 and B~0→K~0/(?)~0 we found that,the contribution cannot be zero. And also we found that the nonzero contribution of annihilation diagram plays a important role in the CP asymmetry ratio ofB~+→π~+K~0,K~+(?)~0.In this work we also proposal a limit of the contribution of new physics.2.we first time study the fitting-data of parameters of potential model of QCD multipole-gluon-expansion method for the transition ofψ(ns)→ψ(ms)+ππandγ(ns)→γ(ms)+ππby using least x~2 method,extracting information of theory from the experimental data as much as possible.Through this study,we determined the parameters of potential model in the hybrids state,which was determined by assuming a state as hybrids before.Thus we ensured the reliability of the theoretical calculation.At the same time we made a prediction of the mass ofη_b.We found that the ground state of hybrids did not have a correspond state in experiment,where may be hints us the hybrids may be always together with the regular pair of quark and anti-quark.3.We studied the testing of Bell inequality in the experiment of high energy physics,we firstly at first time simulate the successive decay J/ψ→γη_c→∧(?)→pπ~-(?)π~+ by using Monte-Carlo random experiment method,recording the directions of momentum of the production pions in the decay,we found how large database we need to distinguish the different of traditional quantum mechanics and the LHVT,and then we discussed the advantage and disadvantage of this method;then we raised in high energy physics a new proposition which can test strictly the Bell inequality under Einstein's non-local condition,and we discussed the advantages and the difficulties of this method.
For reader's convenience and understand,we arrange this thesis as follows:
Chapter One,introduction.We briefly introduced the relation between theory and experiment,the motivation of this thesis.
Chapter Two,data analysis under statistics.We introduce the common knowledge of data analysis,such as chisquare method,error transfer and error analysis,confidence level and confidence interval,test of hypothesis,preliminary of Monte-Carlo method.
Chapter Three,raise theoretical question through experimental data.We study model of the rare B decay from experimental data.This chapter divided into two part.Firstly we introduced the common flavor SU(3) model and quark diagram model of the rare B decay.Secondly we introduced how to get the limitation of the theoretical model through analytical method from experimental data.And then we introduced how to get a limitation from experimental data through chisquare fit method.In the last section of this chapter,we introduced the information which may be contained in the measurement of branch ration in B~+→K~+(?)~0 and B~0→K~0(?)~0.The experimental data show that the annihilation amplitude is not zero in these decays.Whereas the nonzero annihilation amplitude plays a important role in the CP violation in B~+→π~+K~0,K+(?)~0.With these measurement of branch ratio,we proved that there is a absolutely 5%bound of CP asymmetry in B~+→π+K~0 through the relation of these decay amplitude. However,this CP asymmetry can be large as 90%in B~+→K~+(?)~0.Future experimental data will test these predictions.
Chapter Four,use least x~2 fit method analysis hybrids.One of the important task of high energy physics is searching exotic state,such as glueball,hybrids and multi-quark state.The transitionψ(ns)→ψ(ms)+ππandγ(ns)→γ(ms)+ππraised great interest,since they may reveal the character of hybrids.In this work,we use the theoretical frame established by Yan and Kuang to analyze the transition mode.Interestingly,when we noted that the intermediate state is the hybrids,we can determine the mass spectrum of hybrids by fitting data.The theory predict that the ground state of hybrids is 4.23 GeV(for charmium) and 10.79 GeV(对于bottonium),which is not corresponding to any state measured by experiments,thus this may hint that the hybrids together with quarkium consist the physical state.The potential of these hybrids has compared with the result obtained by lattice with corresponding parameters.
Chapter Five,raise suggestion about experiments through theoretical model. We introduced the theory of Bell inequality and the status of experimental study, gave the simulated result from different experiment apparatus.And we raised some suggestion.Besides using laser,it is very tempting to test directly the Bell inequality in high energy physics,where the spin correlation is what the original Bell inequality studied.In this work,we follow the literate which proposed to test the Bell inequality in the successive decay J/ψ→γη_c→∧(?)→pπ~-(?)π~+.Our aim is twofold,namely,we use the Monte-Carlo method which based on quantum field theory to simulate this process.Because the under principle is quantum field theory,which means we admit the validity of quantum picture.If this is true,namely,if the quantum field theory is true,we need to find out how big the database must be to distinguish clearly the deviation from the local hidden variable theory.We found that this may be realized in the updated BESⅢ.There is some critics on our suggestion,we will continue to discuss these problems in Chapter Six.
Chapter Six,the expansion and depth discuss about Bell inequality.Usually the testing of Bell inequality always receives various questions,so is our method which we followed in Chapter Five.We studied how can testing strictly the Bell inequality under the Einstein non-local condition.And then we gave our improved scheme.It can help us to remove the confusion from the critics.In this chapter we detailed the discussion about this scheme,its advantages and its difficulties. This reform may be realized in the updated factory,such as BESⅢ.
Chapter Seven,discussion and outlook.We reviewed our work in this thesis, presented the sense of the bridge established between experiment and theory.
引文
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