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2022年考研考博-考博英语-复旦大学考试全真模拟易错、难点剖析B卷（带答案）一.综合题(共15题)1.翻译题人类是一个不断的自然进化过程的产物，其中包括无数次的遗传转化：这一不可阻挡的过程自45亿年前地球形成以来一直未曾间断过。
这一进化过程，受环境因素的影响，经过随机突变，形成了更具适应性的系统，从而保证了其连续性。
在动物世界，这导致了更高级物种的进化，并在人类身上达到了极致。
我认为人类掌握了自身的命运，因为人类已经获得创新思维的能力。
创新思维能力的获得大大加速了自然进化的过程。
它导致了人类文明诸多方面的巨大进步。
如在艺术、文学、医学、技术上，在属于人类智慧扩展前沿科学上尤其如此。
然而，正是科学的这些进步使得人类获得了自我毁灭的功能，导致了消灭人类自身的工具的发展。
Put the following passage into English【答案】Human being is a product of the constant evolutionary which involves numerous genetic transformations, and has gone uninterrupted since the Earth came into being 4.5 billion years ago. Subject to environmental factors and undergoing random mutation, this evolutionary process develops into a more adoptable system to ensure the continuity. In the animal world, this system leads to the evolution of more advanced species and reaches its peak. I think human beings master their own destinies, for they have obtained the creative thinking. Creative thinking greatly accelerates the speed of natural evolution. It leads to great achievements in human civilization, such as art, literature, medicine, technology, especially in science which stands for the forefront of the expansion of human intelligence. However, those advancements in science also enable humans to self-destruction, and result in the development of tools for destroying human beings.2.单选题The aim of making self-criticism for the mistake is to help us ______ so that we shall not repeat them later.问题1选项A.show offB.hold outC.measure upD.sober up【答案】D【解析】考查动词词组辨析。
中美犹他PhilExam3Which of the following are not major forms of air pollution? Ozone repletion。
How many of the world's people lack access to safe water? One billion.Each American produces about how many pounds of garbage per day? Seven pounds.Which type of resource depletion is marked by increasing rates of usage and sudden, complete depletion within a short period of time? Exponential depletion.Which of the following statements could not be made by a believer in ecological ethics?The world must be protected for the sake of human beings.Which of the following statements is true of the beliefs of deep ecology? Nonhuman parts of the environment deserve to be preserved for their own sake.What is one difficulty with Blackstone's theory of environmental rights? It fails to provide any nuanced guidance on difficult environmental choices.Which choice describes a problematic relationship of costs, one that actually encourages pollution? Private costs and social costs divergeWhich is not a problem when external costs are ignored? Society is forced to do without an important commodity.Internalizing the costs of pollution is problematic because: when several polluters are involved, it is impossible to discover who is being damaged by whom.Air pollution is not new -- it has been with us since the belching factory smokestacks of the industrial revolution. True。
二叠纪-三叠纪灭绝事件二叠纪-三叠纪灭绝事件（Permian–Triassic extinction event）是一个大规模物种灭绝事件，发生于古生代二叠纪与中生代三叠纪之间，距今大约2亿5140万年[1][2]。
若以消失的物种来计算，当时地球上70%的陆生脊椎动物，以及高达96%的海中生物消失[3]；这次灭绝事件也造成昆虫的唯一一次大量灭绝。
计有57%的科与83%的属消失[4][5]。
在灭绝事件之后，陆地与海洋的生态圈花了数百万年才完全恢复，比其他大型灭绝事件的恢复时间更长久[3]。
此次灭绝事件是地质年代的五次大型灭绝事件中，规模最庞大的一次，因此又非正式称为大灭绝（Great Dying）[6]，或是大规模灭绝之母（Mother of all mass extinctions）[7]。
二叠纪-三叠纪灭绝事件的过程与成因仍在争议中[8]。
根据不同的研究，这次灭绝事件可分为一[1]到三[9]个阶段。
第一个小型高峰可能因为环境的逐渐改变，原因可能是海平面改变、海洋缺氧、盘古大陆形成引起的干旱气候；而后来的高峰则是迅速、剧烈的，原因可能是撞击事件、火山爆发[10]、或是海平面骤变，引起甲烷水合物的大量释放[11]。
目录? 1 年代测定? 2 灭绝模式o 2.1 海中生物o 2.2 陆地无脊椎动物o 2.3 陆地植物? 2.3.1 植物生态系统? 2.3.2 煤层缺口o 2.4 陆地脊椎动物o 2.5 灭绝模式的可能解释? 3 生态系统的复原o 3.1 海洋生态系统的改变o 3.2 陆地脊椎动物? 4 灭绝原因o 4.1 撞击事件o 4.2 火山爆发o 4.3 甲烷水合物的气化o 4.4 海平面改变o 4.5 海洋缺氧o 4.6 硫化氢o 4.7 盘古大陆的形成o 4.8 多重原因? 5 注释? 6 延伸阅读? 7 外部链接年代测定在西元二十世纪之前，二叠纪与三叠纪交界的地层很少被发现，因此科学家们很难准确地估算灭绝事件的年代与经历时间，以及影响的地理范围[12]。
a rXiv:h ep-ph/954249v16Apr1995FERMILAB-CONF-95/067-T hep-ph/9504249LATTICE QCD AND THE STANDARD MODEL ∗ANDREAS S.KRONFELD Theoretical Physics Group,Fermi National Accelerator Laboratory,P.O.Box 500,Batavia,IL 60510,USA ABSTRACT Most of the poorly known parameters of the Standard Model cannot be determined without reliable calculations in nonperturbative ttice gauge theory provides a first-principles definition of the required functional integrals,and hence offers ways of performing these calculations.This paper reviews the progress in computing hadron spectra and electroweak matrix elements needed to determine αS ,the quark masses,and the Cabibbo-Kobayashi-Maskawa matrix.1IntroductionMany contemporary reviews of elementary particle physics start by celebrating (or lamenting!)the success of the Standard Model.Indeed,with some nineteen∗parameters the SU(3)×SU(1)×U(1)gauge theory explains an enormous array of experiments.Even a terse compendium1of the experiments is more than big enough tofill a phone book.A glance at Table1shows,however,that roughly half of the parameters are not so well determined.To test the Standard Model stringently, and thus to gain an inkling of what lies beyond,we must learn the values of these parameters more precisely.Except for the mass of the Higgs boson(or any other undiscovered remnant of electroweak symmetry breaking),the poorly known parameters all involve quarks. Other than top,2which decays too quickly for confinement to play a role,the masses of the quarks are a bit better than wild guesses.The information on the Cabibbo-Kobayashi-Maskawa(CKM)quark-mixing matrix is spotty,especially when one relaxes the assumption of three-generation unitarity,as shown in Table2.They are poorly determined simply because experiments measure properties not of quarks, but of the hadrons inside which they are confined.Of course,everyone knows what to do:calculate with QCD,the part of the Standard Model that describes the strong interactions.But then,the strong coupling is known only at the5%level;not bad, but nothing like thefine structure or Fermi constants.Moreover,the binding of quarks into hadrons is nonperturbative—the calculations cannot be done on the back of an envelope.The most systematic technique for understanding nonperturbative QCD is lat-tice gauge theory.The lattice provides quantumfield theory with a consistent and mathematically well-defined ultraviolet regulator.Atfixed lattice spacing,the quan-tities of interest are straightforward(combinations of)functional integrals.These integrals can be approximated by a variety of techniques borrowed from statistical mechanics.Especially promising is a numerical technique,the Monte Carlo method with importance sampling,which has become so pre-eminent that the young and uninitiated probably haven’t heard of any other.Results from lattice-QCD Monte Carlo calculations have begun to influence Ta-ble1.The world average for the SU(3)gauge couplingαS includes results from lattice calculations of the quarkonium spectrum,4,5,6and at the time of this con-ference an even more precise result had appeared.7The same calculations are also providing some of the best information on the charm8and bottom9masses.This is an auspicious beginning.Over the next several years the lattice QCD calculations will mature.They will help to determine the other unknowns—light quark masses and the CKM matrix.The third column of Tables1and2lists relevant quantities or processes,and the rest of this talk explains how the programfits together.Table1:Parameters of the standard model and lattice calculations that will help de-termine them.Numerical values taken from the1994Review of Particle Properties,1 except m t(Ref.2),sinδ,andθQCD.The strong couplingαS refers to the gauge couplingsαem1/137.036105G F 1.166GeV−2αS0.116±0.005∆m1P–1S;scalingelectroweak massesm Z91.19GeVm H>58GeVlepton massesm e0.51100MeVmµ105.66MeVmτ1777MeVquark massesm u2–8MeV m2π,m2Km d5–15MeV m2π,m2Km s100–300MeV m2Km c 1.0–1.6GeV m J/ψm b 4.1–4.5GeV mΥm t174±10+13−12GeVCKM matrixs120.218–0.224K→πeνs230.032–0.048B→D∗lνs130.002–0.005B→πlνsinδ=0B K,B B,B BsQCD vacuum angleθQCD<10−9d nSect.2gives the non-expert some perspective on the conceptual and numerical strengths and weaknesses of lattice QCD.Sect.3reviews1)the status of the light hadron spectrum and the propects for extracting m u,m d,and m s;and2)results for the quarkonium spectrum,which yieldαS,m b,and m c.Sect.4outlines lattice QCD calculations of electroweak,hadronic matrix elements that are needed to pin down the unitarity triangle of the CKM matrix.There are,of course,many other inter-esting applications to electroweak phenomenology;for more comprehensive reviews2Table2:Ranges for CKM matrix elements|V qr|assuming unitarity but not three generations.Numerical values taken from the1994Review of Particle Properties. In three generations|V ud|=s12,|V cb|=s23,and|V ub|=s13,to excellent approxi-mation.parameter value or range related lattice calculationsall degrees of freedom in a block of size a4.The limit“a→0”can be obtained not only literally,but also by improving the action of the blockedfields.These observations apply to any cutoffscheme for quantumfield theory.A nice introduction to the renormalization-group aspects is a summer-school lecture by Lepage.11In lattice gauge theory a is nothing but the spacing between lattice sites. If there are N on a side,L=Na.For given N one can compute the integrals numerically.With the107–1010-dimensional integrals that arise,the only viable technique is a statistical one:Monte Carlo with importance sampling.To compute masses the observable O=Φ(t)Φ†(0),whereΦ(t)is an operator at time t with theflavor and angular-momentum quantum numbers of the state of interest.One can construct such operators using symmetry alone.The radial quantum number would require a solution of the theory,but that’s what we’re after.The“two-point function”Φ(t)Φ†(0) = n| 0|Φ|n |2e−m n t,(2)where the sum is over the radial quantum number.The exponentials are a happy consequence of the weight e−S in eq.(1).It is advantageous because at long times t only the lowest-lying state survives.In a numerical calculation masses are obtained byfitting two-point functions,once single-exponential behavior is verified.Since Φis largely arbitrary,some artistry enters:if single-exponential behavior sets in sooner,the statistical quality of the mass estimate is better.To compute a matrix element of part of the electroweak Hamiltonian,H,the observable O=Φπ(tπ)H(t h)Φ†B(0)for the transition from hadron“B”to hadron “π.”At long times t h and tπ−t h the“three-point function”Φπ(tπ)H(t h)Φ†B(0) ≈ 0|Φπ|π e−mπ(tπ−t h) π|H|B e−m B t h B|Φ†B|0 ,(3) plus excited-state contributions.If,as in decays of hadrons to leptons,the hadronic final-state is the vacuum,a two-point function will do:H(t)Φ†B(0) = n 0|H|B n e−m n t B n|Φ†B|0 .(4)The desired matrix elements π|H|B and 0|H|B can be obtained from eq.(3) and(4),because the masses andΦ-matrix elements are obtained from eq.(2).To obtain good results from eqs.(2)–(4),it is crucial to devise nearly optimal op-erators in the two-point analysis.Consumers of numerical results from lattice QCD should be wary of results,still too prevalent in the literature,that are contaminated by unwanted states.In the numerical work that mostly concerns us here,the integrals are computed at a sequence offixed a’s and L’s.One adopts a standard mass,say mρ,and defines(amρ)lQCDa=to obtain the latice spacing in physical units,and other quantities are predicted viam B=(am B)lQCDmρ=limL→∞lima→0am B(a,L)But theβfunction of quenched and genuine QCD differ,as one sees in perturbation theory,so one cannot expect agreement at all scales.As with any model,only inspecial cases can one argue that these effects are correctable or negligible;thesecases will be highlighted in the rest of the talk.3From Hadron Spectra to the QCD Parameters3.1Light hadrons and light-quark massesOver the past few years a group at IBM has carried out a systematic calculationof the light-hadron spectrum using the dedicated supercomputer GF11.13They havenumerical data for5different combinations of(a,L).At L≈2.3fm there arethree lattice spacings varying by a factor of∼2.5.At the coarsest lattice spacing(a−1≈1.4GeV)there are three volumes,up to almost2.5fm.A variety of quark masses are used,and the physical strange quark is reached by interpolation,whereasthe light(up and down)through extrapolation.The mass dependence is assumedlinear,as expected from weakly broken chiral symmetry,and the data substantiate the assumption.The units(ttice spacing)has beenfixed with mρand the quark masseswith mπand m K.Thefinal results,after extrapolation to the continuum limit andinfinite volume,are shown in Fig.1for two vector mesons and six baryons.(Thequark-mass interpolation could reach only the combination mΞ+mΣ−m N.)Despite the quenched approximation the agreement with experiment is spectacular.Fig.1also includes results from the same investigation for decay constants.The agreement of fπ/mρand f K/mρis not as good as for the masses.Because ofthe quenched approximation,this is not entirely unexpected.Recall the argumentconcerning distance scales and effective theories in sect.2.1.The binding mechanismresponsible for the masses encompasses distances out to the typical hadronic radius. The decay constant,on the other hand,is proportional to the wavefunction at the origin and thus is more sensitive to shorter distance scales.One sees better agreement when forming the ratio f K/fπ,which—recall eq.(5)and subsequent discussion—is like retuning to the shorter distance.One would like to use the hadron masses to extract the quark masses.Becauseof confinement,the quark mass more like a renormalized coupling than the classicalconcept of mass.Calculations like the one described above yield immediately thebare mass of the lattice theory.More useful to others would be the(m d+m u),2∆m2du=m2d−m2u,and m s.Ratios of the light-quark masses are currently best estimated using chiral perturbation theory.18To set the overall scale requires a dynamical calculation in QCD.In lattice QCD,ˆm and m s can be extracted from6K* φ N Ξ+Σ-N ∆ Σ* Ξ* Ω 10f π 10f K f K /f πm X/mρFigure 1:The spectrum and decay constants of the light hadrons.Error bars are from lattice calculations in the quenched approximation,13,14and •denotes experiment.the variation in the square of the pseudoscalar mass between m 2πand m 2K .Themost difficult quark-mass combination is∆m 2du ,which causes the isospin-violatingend of the splittings in hadron multiplets.Since chiral perturbation theory provides a formula for ∆m 2du /m 2s with only second-order corrections,it is likely that the best determination of ∆m 2du will come from combining the formula with a lattice QCD result for m s .Using the compliation of quenched and unquenched results of Ukawa,19Mack-enzie 20has estimated ˆm MS (1GeV)∼65MeV.Thesymbol ∼stresses the lack of error bar.This is outside the ranges of 3.5–11.5MeV and 100–300MeV indicated in Table 1.A more recent analysis of the strange quark finds m3.2Quarkonia,αS,and heavy-quark massesQuarkonia are bound states of a heavy quark and heavy anti-quark.Threefamilies of states exist,charmonium(ηc,J/ψ,etc),bottomonium(ηb,Υ,etc),andthe as yet unobserved B c(b¯c and¯bc bound states).Compared to light hadrons,these systems are simple.The quarks are nonrelativistic,and potential models givean excellent empirical description.But a fundamental treatment of these systemsrequires nonperturbative QCD,ttice QCD.†Potential models can be exploited,however,to estimate lattice artifacts,and in the quenched approximation they canbe used to make corrections.Many states have been observed in the lab,providingcross-checks of the methodology of uncertainty estimation.Once the checks are satisfactory,one can use the spectra to determineαS,m c,and m b.One can also have some confidence in further applications,such as the phenomenology of D and B mesons discussed in sect.4.For charm,and especially for bottom,the quark mass is close to the ultravioletcutoff,1/a orπ/a,of present-day numerical calculations.Originally lattice gaugetheory was formulated assuming m q a≪1,so quarks m q a∼1require some reassess-ment.There are four ways to react.The patient,stolid way is to wait ten years,until computers are powerful enough to reach a cutoffof20GeV—not very inspir-ing.The naive way is to extrapolate from smaller masses,assuming the m q a≪1interpretation of the lattice theory is adequate;history shows that naive extrapola-tions can lead to naive and,thus,unacceptable error estimates.The insightful wayis to formulate an effective theory for heavy quarks with a lattice cutoff;22,23thisis the computationally most efficient approach,and when the effectiveness of the heavy-quark expansion is a priori clear,it is the method of choice.The compulsiveway to examine a wide class of lattice theories without assuming either m q a≪1orm q≫(ΛQCD,a−1);by imposing physical normalization conditions on masses and matrix elements,it is possible to interpret the correlation functions at any valueof m q a.24The underlying reason is that the lattice theory is completely compatiblewith the heavy-quark limit,so the mass-dependent interpretation connects smoothlyonto both the insightful method for m q a≫1and the standard method for m q a≪1.Fig.2shows the charmonium spectrum,on a scale appropriate to the spin-averaged spectrum.Light quark loops are quenched in these calculations.25,26Theagreement with experimental measurements is impressive,but Fig.2barely displaysthe attainable precision.Fig.3shows thefine and hyperfine structure of the P states, now for bottomonium.25(The1P1state h b has not been observed in the lab;the h c has been seen.)The authors of Ref.25also have results with the virtual quark loops from two light quarks,i.e.up and down are no longer quenched,but strange still is.The agreement is comparable.27To obtain these results only two parameters have been adjusted.The standardFigure2:A comparison of the charmonium spectrum as calculated in lattice QCD, using two different methods.Ref.25:◦,Ref.26:2.From Ref.6.mass in eq.(5)is∆m1P–1S,the spin-averaged splitting of the1P and1S states,which is insensitive to the quark mass.By the renormalization group,this is equivalent to eliminating the bare gauge coupling,or to determiningΛQCD.The bare quark mass is adjusted to obtain the spin average of the1S states that is measured in the lab. Otherwisefigs.2and3represent predictions of quenched QCD.The success of these calculations permits one to extract the basic parameters,αS and m q.There are four steps:pute the charm-and bottomonium spectra with n f,MC=0,2or3flavorsof virtual quark loops.(n f,MC=0corresponds to the quenched approxima-tion;n f,MC=2quenches just the strange quark;n f,MC=3would be the real world.)2.With perturbation theory,convert the bare lattice couplingα(n f,MC)0to thequark-potential(V)orMS scheme.The natural scale for this conversion is near(but not quite29)π/a.3.Unless n f,MC=3,correct for the quenched approximation.9−40−2020MeVχb 1r MS (π/a )and am460MeV ,(8)where the numerator is the 1P–1S splitting in lattice units.Steps1and 4are explained above.Step 2requires one-loop perturbation theory,suitably optimized.29Step 3is crucial,because without it the results have no busi-ness in Table 1.Consider first αS ,and recall the idea of treating the quenched approximation as an effective theory.One sees that the couplings are implicitly matched at some scale q Q characteristic of quarkonia.So the matching hypothesis,supported by figs.2and 3,asserts α(n f,MC )S (q Q )=α(3)S (q Q ).(9)Potential models tell us that 200<q c <800MeV and 200<q b <1400MeV.Step 3yields α(n f,MC )S (π/a ),so one can use the two-loop perturbative renormalization group to run from π/a to q Q .The perturbative running is an overestimate if q Q is10taken at the lower end of these ranges.‡This argument was used for the original lattice determinations of the strong coupling,4,5and its reliability was confirmed in n f,MC=2calculations.28Currently the most accurate result is from Ref.7,α(3)V(8.2GeV)=0.196±0.003,(10)based on n f,MC=0and n f,MC=2results,with an extrapolation in n f.The V scheme is preferred for the matching argument,not only for physical reasons,but also because of its empirical scaling behavior.29The scaling behavior implies that one can run with the two-loop renormalization group to high scales and convert to other schemes.For comparison to other determinations,eq.(10)corresponds toαMS.To determine the quark mass the one applies the same renormalization-group argument.But,quark masses don’t run below threshold!9Hence,for heavy quarks§m(n f,MC) Q (m Q)=m(n f,MC)Q(q Q)=m(3)Q(q Q)=m(3)Q(m Q).The only corrections areperturbative,from lattice conventions toMS convention may be more appropriate.Eq.(12b)corresponds to mb,‡For light hadrons,qlight∼ΛQCD,so there would be no perturbative control whatsoever.§For light quarks the threshold is deep in brown muck,and all bets are off.11North American,Japanese,and European taxpayers provide us with lots of money for the relevant experiments,because they want to know the CKM factors.But unless we calculate the inherently nonperturbative QCD factor,they will be sorely disappointed.It is convenient to start with the assumption of three-generation unitarity.ThenV ud V∗ub+V cd V∗cb+V td V∗tb=0,(14) an equation that prescribes a triangle in the complex plane.Dividing by V cd V∗cb and writing V ud V∗ub/V cd V∗cb=¯ρ+i¯η,one sees that unitarity predictsV td V∗tb= G2F q2dq2Figure4:The Isgur-Wise functionξ(ω)(essentially the form factor A1of the text) from lattice QCD and CLEO.The kinematic variableω=v a·v b=1−(q2max−q2)/2m B m D∗.From Ref.36.corrections31(estimated to be small)and known radiative corrections.Other form factors,which are phase-space suppressed near q2max,are also related by heavy-quark symmetry to A1(q2).Hence,eq.(16)provides an essentially model-independent32 way to determine|V cb|.The difficulty with the model-independent analysis is that the decay rate vanishes at q2max.To aid experimentalists’extrapolation to that point,several groups33,34,35 have used quenched lattice QCD to compute the slope of A1.A typical analysis is tofit the slope to lattice-QCD numerical data,and thenfit the normalization to CLEO’s experimental data,as shown in Fig.4.For example,Simone of the UKQCD Collaborationfinds36|V cb|=0.034+3+2−2−2 1.49ps.(17) Thefirst error is experimental;the second is from the lattice-QCD slope.Unfor-tunately,it is not clear how to correct for the quenched approximation,and the13associated uncertainty has not been estimated.Moreover,consistency checks of varying lattice spacing,volume,etc,are still in progress.Nevertheless,the overall consistency with experiment,shown in Fig.4,is encouraging.|V ub|can be obtained from the semi-leptonic decays B→ρlνand B→πlν. Expanding in q2near q2max=(m B−mπ)2,the differential decay rate for B→πlνreadsdΓ24π3 mπ2G2F m2Wm2K f2KˆB K|V ud V us|2|V cb|2×3¯η |V cb|2(1−¯ρ)y tη2f2(y t)+y c(η3f3(y t)−η1) ,(19) where y q=m2q/m2W.This formula assumes three-generation unitarity and neglects the deviation of|V cs|and|V tb|from unity.Theηi and f i multiplying the CKM factors arise from box diagrams and their QCD corrections.37The nonperturbative QCD factor is8m s.The23%uncertainty is an estimate of O(m s−m d)bining the errors and converting to the renormalization-group invariant that appears in eq.(19),one finds38ˆBK=(αThis result places a high standard on calculations ofˆB K,whether by lattice QCD or any other method.Would-be competitors must not only reach10%uncertainties, they must do so with an error analysis as thorough and forthright as Ref.38.Mixing in the B0–¯B0system is also sensitive to V td.In the Standard Model the mass splitting is given byx d=∆m Bd16π2m BdηB f2(y t) 83m2Bqf2BqˆBB q,whichis the B q–¯B q transition matrix element of a∆B=2operator.The calculation of the decay constant f B has received a great deal of attention over the last several years,42but the matrix element needed here,8MS =1.3±0.2,mt,¶Nonperturbative QCD is needed to extract these results!15-1-0.500.51¯ρ¯00.51¯η¯Figure 5:Constraints on (¯ρ,¯η)from |εK |(solid hyperbolae),|V ub /V cb |(dashed circles with origin (0,0)),and x d /x s (dash-dotted circles with origin (1,0)),and contempo-rary uncertainties.What if lattice QCD calculation and the experiments improve?Consider for the masses m c,MS=175±5,(27)for the hadronic matrix elementsˆBK =0.825±0.027,|f B d /f B s |=0.90±0.02,|B B d /B B s |=1.0±0.1,(28)in particular eliminating almost all the statistical error in ˆBK ;for “experimental”CKM results |V cb |=0.035±0.002,|V ub /V cb |=0.080±0.004“low,”=0.091±0.004“high,”(29)and for neutral B mixing measurementsx d =0.72±0.04,x s =18±2.(30)Fig.6shows how this 5–10%level of precision improves the limits on (¯ρ,¯η).The16-1-0.500.51¯ρ¯00.51¯η¯Figure 6:Constraints on (¯ρ,¯η)from |εK |(solid hyperbolae),low |V ub /V cb |(dashed circles with origin (0,0))or high |V ub /V cb |(dotted circles with origin (0,0)),and x d /x s (dash-dotted circles with origin (1,0)),and improved (5–10%)uncertainties.wildest guess remains x s ,so ignore the dashed-dotted curves momentarily.The region allowed by the hyperbolic band from εK and the circular band from |V ub /V cb |shrinks if |V ub |is too small.The tension between these two constraints is partly a consequence of the low value of |V cb |suggested by eq.(17).Increasing |V cb |brings the hyperbolic band down more rapidly than it shrinks the circular band.If the real-world values of |V cb |and |V ub /V cb |allow a sizable region,as for the dot-ted circles in Fig.6,neutral B mixing becomes crucial.The constraint becomes more restrictive as x s increases.Unfortunately,the experimental measurement becomes more difficut as x s increases.If it proves impossible to obtain useful information on x s ,one can return to eq (22),and focus on x d alone.The lattice-QCD calculations of 8seem fairly estimated.The quenched approximation is another matter.In quarko-nia,one can correct for it with potential models,yielding determinations ofαS andthe charm and bottom masses.The quenched error in B K is also thought to beunder control,and—taking the error bars at face value—B K is no longer the limit-ing factor in the|εK|constraint on the unitarity triangle.A second class consists of f B,the semi-leptonic form factors of K and D mesons(not discussed in thistalk,but see Ref.42),and the Isgur-Wise function.These quantities are essentialfor direct determinations of thefirst two rows of the CKM matrix.The quenched-approximation calculations are in good shape,but the the corrections to it cannotbe simply estimated.A third class consists of the semi-leptonic decay B→πlνandneutral B mixing,for which only exploratory work has appeared.Nevertheless,all QCD quantities discussed here will follow a conceptually clear path to ever-more-precise results.The next ten years or so will almost certainly wit-ness computing and other technical improvements that will allow for wide-ranging calculations without the quenched approximation.By then the most efficient tech-niques for extracted the most relevant information will have been perfected.AcknowledgementsThe Adriatic glistened in the moonlight as it lapped against the quay.In the bar of the Hotel Neptun a winsome lounge singer cooed“...strangers in the night, exchanging glances,....”I looked up at the waiter and said,“Molim pivo,”when a man strolled into the bar,clapped me on the back,and cried,“Ay,you kook,what’s new?”In a different place and a different time he had rescued my sanity,if not my life.I peered into his eyes and replied,“It’s the same old story,always the same. 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研究掺杂浓度对n-GaN和p-GaN载流子浓度和迁移率的影响摘要在载流子的热运动过程中，载流子与晶格、杂质和缺陷不断碰撞，散射方向发生不规则的变化。
无机晶体不是理想的晶体，但有机半导体本质上是无定形的。
因此，晶格散射和电离杂质散射存在。
因此，载流子迁移率只有一定的数值。
迁移率是衡量半导体导电性的一个重要参数。
它决定半导体材料的导电性，影响器件的工作速度。
对n型GaN和p型GaN的迁移率是反映半导体的导电性的重要参数。
相同的掺杂浓度，当载流子的迁移率越大时，半导体材料的导电率越高。
迁移率的大小不仅与电导率的强弱有关，而且直接决定着载体运动的速度。
它直接影响半导体器件的工作速度。
本文研究掺杂浓度对n-GaN和p-GaN载流子浓度和迁移率的影响。
关键词：掺杂浓度； n-GaN； p-GaN；载流子浓度；迁移率；影响目录引言 (3)一 GaN族载流子浓度 (3)1.1 GaN族载流子浓度的提高和降低 (3)1.2 辐照产生的氮空位破坏耗尽区两侧电荷平衡 (3)二 n-GaN和p-GaN载流子浓度测量 (4)2.1 高温电子辐照检测 (4)2.2 蓝带的低密度饱和机理分析 (5)2.3 p-GaN和n-GaN (7)3 掺杂浓度对n-GaN和p-GaN载流子浓度和迁移率的影响模拟计算结果与讨论 (8)3.1 长波和短波处探测器的量子效率 (8)3.2 差值影响规律 (9)3.3 掺杂浓度临界点的反向偏压和误差影响 (11)四 p-GaN层载流子浓度和耗尽区宽度的关系 (13)五结论 (14)引言GaN是一种重要的Ⅲ-Ⅴ族半导体材料，是制备蓝光和紫外波段半导体发光器件的理想材料。
目前广泛使用的掺杂技术是用镁选择p型氮化镓材料。
因为GaN的生长过程中，Mg结合在高温生长气氛氨分解产生的氢形成Mg-H复合体。
因此，有必要在高温下直接退火以激活镁，从而获得较高的p电导率[ 2 ]。
迄今为止，优良的p型导电GaN的获得仍是一个有待进一步研究和解决的难题。
a r X i v :h e p -p h /9606354v 2 1 J u l 1996UH-515-848-96OHSTPY-HEP-E-96-006February 1,2008Nonleptonic Decays and Lifetimes ofb-quark and c-quark HadronsThomas E.BrowderUniversity of Hawaii at Manoa,Honolulu,Hawaii 96822,U.S.A.,Klaus HonscheidOhio State University,Columbus,Ohio 43210,U.S.A.,Daniele Pedrini Istituto Nazionale di Fisica Nucleare -sezione di Milano,I-20133Milan,Italy KEY WORDS :bottom decays,charm decays,heavy flavor,hadronic decays Abstract We review recent experimental results on lifetimes and hadronic decays of hadrons that contain c and b quarks.The theoretical implications of these results are also considered.An understanding of hadronic decays of heavy quarks is required to interpret the CP violating asymmetries in B decays that will be observed in experiments planned for the near future.To appear in Annual Review of Nuclear and Particle Science,Vol.46.A copy of this review can be obtained via anonymous ftp or from our WWW site.Anonymous ftp Node Directory:pub/hepex/khWWW URL /∼phys111/b-physics/bphysics.htmlContentsI Introduction4 II Experimental Study of Charm and Bottom Decay6A High Energy Collider Experiments (7)B Averaging Experimental Results (7)III Lifetime Measurements8A Theoretical Expectations for Lifetimes of Hadrons with Heavy Quarks..9B Techniques for Charm Lifetime Measurements (10)C Techniques for Beauty Lifetime Measurements (11)1Averaging B hadron Lifetime Measurements (12)D Results on Lifetimes of Hadrons That Contain c Quarks (13)E Results on Lifetimes of Hadrons That Contain b Quarks (13)1B−and¯B0Lifetime Measurements (14)2B s Lifetime Measurements (15)3b Baryon Lifetime Measurements (15)4Measurements of Lifetime Ratios (16)F Lifetime Summary (16)IV Nonleptonic Decays of c-quark Hadrons17A Introduction (17)B Double Cabibbo Suppressed Decays (17)C Amplitude Analyses of Hadronic Charm Decays (18)D Hadronic Decays of Charmed Baryons (19)V Inclusive B Decay19A Motivation (19)B Inclusive B Decay to Mesons (20)C Inclusive B Decay to Baryons (21)D Charm Production in B Decay (23)VI Exclusive Hadronic B Decay25A Measurements of D(nπ)−Final States (25)B Measurements of D∗(nπ)−Final States (25)C Polarization in B→D∗+ρ−Decays (25)D Measurements of D∗∗Final States (26)E Exclusive Decays to D and D s Mesons (27)F Exclusive B Decay to Baryons (27)G Color Suppressed B decay (27)1Exclusive B Decays to Charmonium (28)2Polarization in B→ψK∗ (29)3Exclusive Decays to a D0(∗)and a Neutral Meson (29)VII Hadronic Decays:Theoretical Interpretation30A The Effective Hamiltonian (30)B Factorization (30)C Final State Interactions (31)D Heavy Quark Effective Theory (32)E FSI in Charm Decay (33)F Tests of the Factorization Hypothesis (35)1Tests of Factorization with Branching Fractions (35)2Factorization and Angular Correlations (37)3Applications of Factorization (38)4Factorization in Color Suppressed Decay (39)G Determination of the Color Suppressed Amplitude (40)1Color Suppression in B and D Decay (40)2Determination of|a1|,|a2|and the Relative Sign of(a2/a1) (41)H The Sign of a2/a1and the Anomalous Semileptonic Branching Ratio (43)VIII Conclusions45 REFERENCES48I.INTRODUCTIONHeavy-flavor physics began in1974with the discovery of the J/ψmeson[1],a narrow resonance at a mass of3.1GeV.The J/ψwas quickly identified as a bound state of a charm and anti-charm quarks,a previously unobserved quarkflavor with a mass around1.5GeV.Charm was not only thefirst heavyflavor quark,it was also thefirst quark whose existence was predicted before its discovery.In1970,Glashow,Illiopoulos,and Maiani introduced the GIM mechanism and postulated a new type of quark in order to explain the absence of flavor-changing neutral currents in kaon decay[2].In1977,the second heavyflavor,the bottom(or b)quark with a mass of m b∼5GeV/c2 and a charge of-1/3,was observed at Fermilab in the bound states of theΥfamily[3].The recent observation of the top quark by the CDF and D0collaborations[4]completes the three quark families of the Standard Model:u d c s t bThe six quarks are divided naturally into heavy and lightflavors.The c,b,and t quarks are called heavy because their masses are larger than the QCD scale,Λ,while the masses of the remaining quarks are lighter.Weak decays of heavy quarks test the Standard Model and can be used to determine its parameters,including the weak mixing angles of the Cabibbo-Kobayashi-Maskawa(CKM) matrix[5].In addition,the study of heavy quark decay provides important insight into the least well understood sector of the strong interaction:the non-perturbative regime which describes the formation of hadrons from quarks.In the Standard Model the charm(bottom)quark decays through the weak charged current into a light quark with a charge of−1/3(+2/3),i.e.,an s(c)or d(u)quark.The coupling is proportional to the element V Qq of the CKM mixing matrix,where Q denotes a heavy quark,either c or b.In charm decays the CKM matrix can be approximated by a2×2 rotation matrix with one real angle,the Cabibbo angleθc∼140.In this approximation, the c→W s transition,proportional to cosθc,is favoured with respect to the c→W d transition proportional to sinθc.These two types of transitions are called Cabibbo-favoured and Cabibbo-suppressed,respectively.The lowest order decay diagrams for charm(bottom)mesons are shown in Fig.1.The spectator diagram(Figs.1(a)and(b)),in which the light antiquark does not take part in the weak interaction,is thought to be dominant.As in muon decay,the decay rate for this diagram is proportional to m5Q.In the external spectator diagram(Fig.1(a)) color is automatically conserved,while the internal spectator amplitude(Fig.1(b))is color suppressed since the color of the quarks from the virtual W must match the color of the quarks from the parent meson.In the na¨ıve quark model the color matching factorξhas a value of 1/N c=1/3,so that the decay rate should be reduced by a factor1/18(=(1/3)2×(1/√In addition,there are small contributions from the penguin diagram and the box dia-grams,which are responsible for B0−K0π0or rescatter via the intermediate state K−π+,since K−π+→II.EXPERIMENTAL STUDY OF CHARM AND BOTTOM DECAY For many years after the discovery of the charm quark infixed-target and e+e−collisions, e+e−colliders provided most of the results in the study of charmed hadrons.In the mid-eighties,however,the introduction of silicon vertex detectors madefixed-target experiments competitive once again[9].Now Fermilabfixed-target experiments dominate several areas of charm physics including lifetime measurements and rare decay searches.Table I gives the sizes of charm data samples from e+e−colliding beam experiments[6]. The major advantage offered by e+e−annihilation is that the fraction of hadronic events containing heavy quarks is relatively large and hence backgrounds are small.Infixed target experiments the production cross section is larger but the fraction of hadronic events that contain charm particles is much smaller.The charm hadroproduction cross section is on the order of20µb(for an incident proton momentum of∼400GeV/c),but charm events represent only about10−3of the total cross section[6].Photoproduction has a smaller charm cross section but a larger fraction of charm produced.Table II gives the number of reconstructed charm decays for severalfixed-target experiments.The current data samples contain O(105)reconstructed charm decays.Samples with O(106)reconstructed events are expected during the next few years from Fermilab experiments E781(SELEX)and E831 (FOCUS),as well as in e+e−annihilation from CLEO III at CESR.Most of the current knowledge of the decays of B mesons is based on analyses of data collected by experiments at CESR and DORIS.These experiments record data at theΥ(4S) resonance,which is the lowest lying b¯b resonance above the threshold for B¯B pair production. The observed events originate from the decay of either a B or a¯B meson as there is not sufficient energy to produce additional particles.The B mesons are also produced nearly at rest.The average momentum is about330MeV so the average decay length is approximately 30µm.In recent years,advances in detector technology,in particular the introduction of high resolution silicon vertex detectors have allowed experiments at high energy colliders(i.e. LEP,SLC and the TEVATRON)to observe decay vertices of b quarks.This has led to precise lifetime measurements,as well as to the direct observation of time dependent B−¯B mixing and to the discovery of new b-flavored hadrons.Thefirst fully reconstructed B mesons were reported in1983by the CLEO I collaboration. Since then the CLEO1.5experiment has collected a sample with an integrated luminosity of212pb−1,the ARGUS experiment has collected246pb−1,and to date the CLEO II experiment has collected about4fb−1,of which up to3fb−1have been used to obtain the results described in this review.For quantitative studies of B decays the initial composition of the data sample must be known.The ratio of the production of neutral and charged B mesons from theΥ(4S)is, therefore,an important parameter for these experiments.The ratio is denoted f+/f0and is measured by CLEO[10]to be,f+B(Υ(4S)→B0¯B0)=1.13±0.14±0.13±0.06.The third error is due to the uncertainty in the ratio of B0and B+lifetimes.This result is consistent with equal production of B+B−and B0¯B0pairs and unless explicitly statedotherwise we will assume that f+/f0=1.The assumption of equal production of charged and neutral B mesons is further supported by the near equality of the observed B−and ¯B0masses.Older experimental results which assumed other values of fand f0have been+rescaled.Two variables are used to isolate exclusive hadronic B decay modes at CLEO and AR-GUS.To determine the signal yield and display the data the beam constrained mass is formedM2B=E2beam− i p i 2,(1)where p i is the reconstructed momentum of the i-th daughter of the B candidate.An example is shown in Fig.3.The resolution in this variable is determined by the beam energy spread, and is about2.7MeV for CLEO II,and about4.0MeV for ARGUS.These resolutions are a factor of ten better than the resolution in invariant mass obtained without the beam energy constraint.The measured sum of charged and neutral energies,E meas,of correctly reconstructed B mesons produced at theΥ(4S),must also equal the beam energy,E beam,to within the experimental resolution.Depending on the B decay mode,σ∆E,the resolution on the energy difference∆E=E beam−E meas varies between14and46MeV.Note that this resolution is usually sufficient to distinguish the correct B decay mode from a mode with one additional or one fewer pion.A.High Energy Collider ExperimentsThe four LEP experiments and SLD operate on the Z0resonance.At this energy,the cross section for b¯b production is about6.6nb and the signal-to-noise ratio for hadronic events is1:5,comparable to theΥ(4S)pared with e+e−annihilation,the b¯b production cross section at hadron colliders is enormous,about50µb at1.8TeV.However, a signal-to-background ratio of about1:1000makes it difficult to extract b quark signals and to fully reconstruct B mesons.The kinematic constraints available on theΥ(4S)cannot be used on the Z0.However, due to the large boost the b quarks travel≈2.5mm before they decay and the decay products of the two b-hadrons are clearly separated in the detector.The large boost makes precise lifetime measurements possible.B.Averaging Experimental ResultsTo extract B meson branching fractions,the detection efficiencies are determined from a Monte Carlo simulation and the yields are corrected for the charmed meson branching fractions.In order to determine world average branching fractions for B and D meson decays the results from individual experiments must be normalized with respect to a common set of absolute branching fractions of charm mesons and baryons.The branching fractions for the D0and D+modes used to calculate the B branching fractions are given in Table XIII.For the D0→K−π+branching fraction we have chosen an average of values recently reportedby the CLEO II,ARGUS and ALEPH experiments[11].The value B(D+→K−π+π+)= 8.9±0.7%is used in this review to normalize branching fractions for D+modes.Our value for B(D0→K−π+π0)is calculated using a recent result from CLEO II[12],B(D0→K−π+π0)/B(D0→K−π+)=(3.67±0.08±0.23),averaged with an older measurement from ARGUS[13].The branching ratios of other D0decay modes relative to D0→K−π+ are taken from the PDG compilation[14].The D+branching ratios are also taken from the PDG compilation[14].The CLEO II results for D+→K−π+π+,however,has been re-scaled to account for the new D0→K−π+branching fraction.For older measurements of B decays involving D∗mesons,the branching fractions have been rescaled to account for improved measurements of the D∗branching fractions.Branching ratios for all D s decay modes are normalized relative to B(D+s→φπ+).Two model-independent measurements of the absolute branching fraction for D+s→φπ+have been published by BES[15]and CLEO[16].These have been averaged to determine the value used here(Table XIV).Branching ratios involving D∗s modes are also re-scaled to account for the isospin violating decay D∗s→D sπ0recently observed by CLEO[17].The determination of branching fractions for B decays to charmed baryons requires knowledge of B(Λ+c→pK−π+).The uncertainty in this quantity is still large as it can only be determined by indirect and somewhat model dependent methods.In this review we use B(Λ+c→pK−π+)=4.4±0.6%as determined by the particle data group[14].However, recent studies of baryon production in B decay indicate that the production model that is assumed in many of the determinations of B(Λc→pK−π+)isflawed(see Section VC for a detailed discussion).An alternate method used by CLEO[18]is based on a measure-ment of the relative semileptonic rate,Γ(Λc→pK−π+)/Γ(Λc→Λℓ+νℓ).With additional assumptions this leads to B(Λ+c→pK−π+)=5.9±0.3±0.14%Statistical errors are recalculated in the same way as the branching ratios.For results from individual experiments on B decays tofinal states with D mesons two systematic errors are quoted.The second systematic error contains the contribution due to the uncertainties in the D0→K−π+,D+→K−π+π+or D+s→φπ+branching fractions.This will allow easier rescaling at a time when these branching fractions are measured more precisely.Thefirst systematic error includes the experimental uncertainties and when relevant the uncertainties in the ratios of charm branching ratios,e.g.Γ(D0→K−π+π+π−)/Γ(D0→K−π+)and the error in the D∗branching fractions.For modes involving D+s mesons,thefirst systematic error also includes the uncertainties due to the D0and D+branching ratios.For all other modes only one systematic error is given.For the world averages,the statistical and the first systematic error are combined in quadrature while the errors due to the D0,D+and D s branching ratio scales are still listed separately.With the improvement in the precision of the D0and D∗branching fractions these are no longer the dominant source of systematic error in the study of hadronic B meson decay. The errors on the D+s andΛ+c branching ratio scales remain large.III.LIFETIME MEASUREMENTSA.Theoretical Expectations for Lifetimes of Hadrons with Heavy QuarksIn the naive spectator model the external spectator amplitude is the only weak decay mechanism and thus the lifetimes of all mesons and baryons containing heavy quarks should be equal.Differences in hadronic decay channels and interference between contributing am-plitudes modify this simple picture and give rise to a hierarchy of lifetimes.Experimentally, wefind the measured lifetimes to be significantly different.For example,the D+lifetime is ∼2.5times longer than the D0lifetime.The decay width of charmed hadrons(Γtot=Γl+Γsl+Γhad)is dominated by the hadronic component.For example,for the D+meson onefinds that the semileptonic component,Γsl=(16.3±1.8)×1010s−1,is a small fraction of the total widthΓ=(94.6±1.4)×1010s−1. The contribution from purely leptonic decays can be neglected.Measurements of the lifetime ratioτ(D+)/τ(D0)=2.547±0.044[14]and of the inclusive semileptonic branching ratios,D+→eX=(17.2±1.9)%[14]and D0→eX=(6.64±0.18±0.29)%(using a recent result from CLEO[20]),show that the D0and D+semileptonic decay widths are nearly equal.τ(D+)Γ(D0→eX)B(D+→eX)×3.W-exchange contributions(Fig.2(d))which can be large if the baryon contains a d-quark(as in theΛc andΞ0c baryons).Neglecting mass differences and Cabibbo-suppressed decays,the nonleptonic decay rates forcharm baryons are qualitatively given by:Γ(Λc)=Γspec+Γdes.int.+Γexch.(4)Γ(Ξ+c)=Γspec+Γdes.int.+Γcon.int.Γ(Ξ0c)=Γspec+Γcon.int.+Γexch.Γ(Ωc)=Γspec+Γcon.int.where spec denotes the spectator component,exch denotes the W-exchange component, con.int denotes the componet from constructive interference and des.int denotes the destruc-tive interference component.Models with different relative weights for these non-spectatoreffects lead to different predictions.There are two models,one by Guberina,R¨u ckl,and Trampetic[21]and the other by Voloshin and Shifman[22]that predict a baryon lifetimehierarchyτ(Ωc)∼τ(Ξ0c)<τ(Λc)<τ(Ξ+c)Guberina,R¨u ckl,and Trampetic(5)τ(Ωc)<τ(Ξ0c)<τ(Λc)∼τ(Ξ+c)Voloshin and Shifman Since the ground state hadrons containing b quarks decay weakly,their lifetimes should be typical of the weak interaction scale,in the range of0.1–2ps.Ten years ago,before the MAC[23]and MARK II[24]collaborations presented thefirst measurements of the b lifetime,the only phenomenological guide to the strength of the coupling between the quark generationswas the Cabibbo angle.If the coupling between the third and second generations(|V cb|)had the same strength as the coupling between the second andfirst(|V cs|),the b lifetime would be about0.1ps.The measurements of lifetimes from the PEP experiments that indicated avalue longer than1ps were not anticipated and it was then deduced that the CKM matrix element|V cb|was very small.As in the charm sector we expect a lifetime hierarchy for b-flavored hadrons.However,since the lifetime differences are expected to scale as1/m2Q,where m Q is the mass of the heavy quark,the variation in the b system should be significantly smaller,on the order of 10%or less[25].For the b system we expectτ(B−)≥τ(¯B0)≈τ(B s)>τ(Λ0b)(6) Measurements of lifetimes for the various b-flavored hadrons thus provide a means to deter-mine the importance of non-spectator mechanisms in the b sector.B.Techniques for Charm Lifetime MeasurementsThe measurements of the charm hadron lifetimes are dominated byfixed target experi-ments using silicon vertex detectors.The measurement of the lifetime is,in principle,very simple.One measures the decay length L=βγct to extract the proper time t.The typicalproper time for a c-hadron decay is in the range10−12−10−13s,so that high precision vertex detectors are necessary.The lifetimes are determined using a binned maximum likelihood fit to the distribution of reduced proper time,which is defined as t′=t−Nσ/βγc,where σis the error on the longitudinal displacement(L)between the primary and the secondary vertex(typically about400µm).The value of N varies depending on the analysis(typi-cally N=3).The reduced proper time avoids the use of large corrections at short t and is equivalent to starting the clock at a later time.Corrections for acceptance and hadronic absorption at long times and resolution at short times are included in thefitting function. Events from the mass sidebands are used to model the background lifetime distribution.This technique must be modified slightly for measurements of the short lived charmed hyperons,for example,theΩc lifetime is comparable to the E687lifetime resolution,i.e., around0.05ps[26].In E687,thefit is performed for all observed times greater than−0.05 ps in order to retain sufficient statistics.The effect of resolution is significant;it is included in the analysis by convoluting the exponential decay and the resolution function[27].C.Techniques for Beauty Lifetime MeasurementsThe lifetime of a particle is related to its decay length,L b,byL bτb=in such semileptonic decays the neutrino is not detected so the b hadron is not completely reconstructed.One then has to rely on Monte Carlo simulations to estimate the b momentum and to extract the proper time distribution from the decay length measurements.For inclusive lifetime measurements,the presence of a high p⊥lepton or aψmeson is usually sufficient to demonstrate the presence of a b quark,while for exclusive measurements of individual b hadron lifetimes an additional decay particle has to be reconstructed in order to establish a signature characteristic for the decaying b hadron(Fig4(b)).TheΛb lifetime, for example,is measured using a sample of events containingΛ+cℓ−orΛℓ−combinations.In early experiments the vertexing precision was not adequate to measure the decay length,l=γβcτ,directly.The impact parameter method shown schematically in Fig.4(a) was developed as alternative.Because of thefinite lifetime of the b hadron,a lepton from the semileptonic decay of the heavy quark will miss the primary vertex where the b hadron was produced.The miss distance or impact parameter,δ,is given byδ=γβcτb sinαsinθ.(8) whereαis the angle between the lepton and the b directions andθis the polar angle. The b direction is usually approximated by the axis of the hadronic jet.A negative sign is assigned to the impact parameter if the lepton track crosses the jet axis behind the beam spot indicating a mismeasured lepton or a background event.The main advantage of the impact parameter method is that it is rather insensitive to the unknown boost of the parent; asγβincreases with the b momentum,sinαdecreases approximately as1/γβforβ≈1.In experiments with sufficient statistics and vertex resolution,the decay length for the b hadron vertex is reconstructed by using the lepton track and the direction of the recon-structed charm meson as shown in Fig4(b).The momentum of the b hadron is estimated by using the observed decay products,the missing momentum and a correction factor de-termined from a Monte Carlo simulation.The proper time distribution is then given by an exponential convoluted with a Gaussian resolution function and the momentum correction factor.A maximum likelihoodfit is used to extract the lifetime[39].1.Averaging B hadron Lifetime MeasurementsTo obtain the most precise value for inclusive and exclusive b lifetimes the results of life-time measurements from different experiments have been ing the conventional approach of weighting the measurements according to their error does not take into account the underlying exponential decay-time distribution.If a measurementfluctuates low then its weight in the average will increase,leading to a bias towards low values.This is particularly relevant for low statistics measurements such as the B s lifetime.According to a study by Forty[28],this bias can be avoided if the weight is calculated using the relative errorσi/τi.1 Wefind a1-3%difference in the average lifetimes computed,with the second method giving the larger value.A slight bias of the latter method towards higher lifetime values could beavoided by taking into account asymmetric errors.This effect has been found empirically to be rather small and we omit this additional complication in the calculation of our lifetime averages.D.Results on Lifetimes of Hadrons That Contain c QuarksThe experimental results are summarized in Fig.5where updated world averages for the c-hadron lifetimes are given[14][27][29].From these results,the full lifetime hierarchy can be studied.The measurements of the charm hadron lifetimes are now extremely precise.Systematic effects will soon become the largest component of the error for some measurements e.g.the D0and D+lifetimes.These systematic effects are due to the uncertainty in the D momentum distribution,to the nuclear absorption of the D meson or its decay products in the target, and to the lifetime of the background.In the baryon sector the measurements are still statistics limited.There are now results for theΩc lifetime from E687[27]and WA89[29]which complete the baryon hierarchy.It is quite remarkable that the lifetime of this rare and short lived baryon is now being measured.The world averages for lifetime measurements are now dominated by results from E687, which is the only single experiment which has measured all the charmed hadron lifetimes[30] [27].The results are internally consistent and the ratios of lifetimes,which characterize the hierarchy,are to a large extent unbiased by systematic effects[31].For the charm mesons lifetimes a clear pattern emerges,in agreement with the theoretical predictionsτ(D0)<τ(D s)<τ(D+)(9) The meson lifetimes are now measured at the level of few percent,probably beyond the ability to compute them.The near equality ofτ(D s)andτ(D0)is direct evidence for the reduced weight of the non-spectator(W-exchange and W-annihilation)in charm meson decays[32].The agreement between the measurements of charm baryon lifetimes and theoretical expectations is remarkable,since in addition to the exchange diagram,there are constructive as well as destructive contributions to the decay rate.The experimental results lead to the following baryon lifetime hierarchyτ(Ωc)≤τ(Ξ0c)<τ(Λc)<τ(Ξ+c)(10) Although statistically limited the present values tend to favor the model of Guberina,R¨u ckl, and Trampetic[21].E.Results on Lifetimes of Hadrons That Contain b QuarksInclusive measurements of the b lifetime were important historically to establish the long b lifetime.In addition,they provided thefirst evidence that the coupling between the second and third quark generation is quite small.They are still needed for some electroweak studies such as the determination of the forward-backward asymmetry in Z→b¯b where the different hadrons containing b quarks are not distinguished.For B physics,i.e.the study of B mesondecays,exclusive measurements of individual b hadron lifetimes are preferable.For example, to extract the value of the CKM matrix element|V cb|from measurements of semileptonic B decays the average of the B+and¯B0lifetimes should be used rather than the inclusive b lifetime which contains additional contributions from B s mesons and b baryons.The current world average for the inclusive b lifetime which includes many measurements is[34],<τb>=1.563±0.019ps.The world average for this quantity in1992was(1.29±0.05)ps.The substantial change in the value has been attributed to several improvements:the use of neutral energy when calculating the b jet direction,and better knowledge of the resolution function as a result of the use of silicon vertex detectors[28],[33].Precise measurements of exclusive lifetimes for b-flavored hadrons have been carried out by CDF[35],[37],by some of the LEP experiments[38]–[48]and by SLD[49].The most recent results and the techniques used are given in Table III.1.B−and¯B0Lifetime MeasurementsThe best statistical precision in the determination of exclusive lifetimes is obtained from measurements using lepton-particle correlations.For example,a sample of B0candidates can be obtained from events with lepton-D∗+correlations of the correct sign;these events originate from the decay¯B0→D∗+ℓ−ν,D∗+→D0π+and D0→K−π+(see Fig.4(b)for the method and Fig.6for the CDF results).The pion from the strong decay and the lepton form a detached vertex.This information combined with the direction of the reconstructed D0meson determines the location of the B decay vertex so that the decay length can be measured.To obtain the lifetime from the decay length,requires knowledge ofγβwhich is estimated from the momenta of the observed decay products.Since the neutrino is not observed,a correction is made to determine the boost factor.The uncertainty in the size of this correction is included in the systematic error and is typically on the order of3%. Another systematic problem is the contamination from decays B−→D∗∗l−ν,followed by D∗∗→D∗+π−where theπ−from the strong decay of the D∗∗(p-wave)meson is not detected.These backgrounds will lead to a B−meson contamination in the¯B0lifetime sample(and vice-versa).Since the branching fractions for such decays are poorly measured, this is another important systematic limitation and gives a contribution of order5%to the systematic error.Significant contributions to the systematic error also result from the uncertainty in the level of background and its lifetime spectrum.More detailed discussions of exclusive lifetime measurements can be found in recent reviews by Sharma and Weber[33] and Kroll[34].The systematic problems associated with the boost correction and the contamination from poorly measured backgrounds can be avoided by using fully reconstructed decays such as¯B0→D+π−or B−→ψK−.However,since exclusive B branching ratios are small,this method has much poorer statistical precision.In hadron collider experiments,this approach has been successfully used to determine the¯B0,B−,and B s lifetimes from exclusive modes withψmesons e.g.¯B0→ψK∗0,B−→ψK−[36]and B s→ψφ[37].。
