Studying Trilinear Gauge Couplings at Linear Collider Energies

重庆2024年07版小学英语第四单元测验卷考试时间：100分钟（总分:140）A卷考试人：_________题号一二三四五总分得分一、综合题(共计100题)1、听力题：A _______ is a reaction that releases light and heat.2、听力题：A __________ is a visual representation of a chemical reaction.3、听力题：The playground is _______ (fun) for kids.4、What do you call the first letter of the alphabet?A. AB. BC. CD. D答案：A5、听力题：A __________ is a measure of how tightly packed particles are in a substance.6、听力题：The __________ is a region known for its handicrafts.7、What is 7 + 6?A. 12B. 13C. 14D. 15答案: B8、听力题：The chemical formula for amyl acetate is ______.My grandma loves to share her __________ (传统故事).10、How many eyes does a typical person have?A. OneB. TwoC. ThreeD. Four11、填空题：A ________ (大象) is the largest land animal and has a long trunk.12、听力题：The __________ is the movement of the earth's plates.13、听力题：The girl loves to ________.14、听力题：A solution that has a higher concentration of solute than solvent is called a ______ solution.15、community service project) addresses local challenges. 填空题：The ____16、What do we call a piece of furniture you sleep on?A. ChairB. SofaC. BedD. Table17、听力题：The Earth’s atmosphere protects us from harmful ______ (radiation).18、How many legs does a spider have?A. 6B. 8C. 10D. 1219、填空题：The __________ (历史的多样性视角) enrich discussions.20、填空题：I call my grandfather . (我称呼我的祖父为)They play _____ (football/piano) after school.22、What do you call the process by which plants lose water?A. PhotosynthesisB. TranspirationC. RespirationD. Germination答案:B23、What is the name of the famous bridge in San Francisco?A. Golden Gate BridgeB. Brooklyn BridgeC. Tower BridgeD. Sydney Harbour Bridge答案：A24、选择题：What do we drink in the morning?A. MilkB. WaterC. JuiceD. All of the above25、听力题：The balloon is ___ (floating/deflating).26、听力题：The process of breaking down food is a type of _____ reaction.27、听力题：The train is ______ (fast) and convenient.28、What is the name of the first artificial satellite launched into orbit?A. Sputnik 1B. Explorer 1C. Vanguard 1D. Luna 129、听力题：The boy has a new ________.30、What is the name of the first living creature in space?A. LaikaB. BelkaD. Yuri31、Which of these is a mode of transportation?A. AppleB. TrainC. ChairD. House32、What do you call a group of wolves?A. PackB. FlockC. SchoolD. Pride答案:A33、听力题：Astrobiology studies the possibility of ______ in the universe.34、填空题：My family has a ______ at home.35、听力题：A _______ is a process that involves cooling.36、听力题：She is _____ (drawing) with chalk.37、听力题：The chemical formula for carbon dioxide is __________.38、听力题：A sound's pitch is determined by its frequency, while its loudness is determined by its ______.39、填空题：My brother is my adventurous _______ who loves to explore nature.40、填空题：My best friend is __________. (忠诚)41、填空题：My mom cooks ______ (美味的) food.42、What is the capital of Mongolia?A. UlaanbaatarC. DarkhanD. Choibalsan43、听力题：A _______ is a process that uses heat to change a substance.44、听力题：A __________ is a mixture that has uniform composition throughout.45、听力题：My cousin is very ____ (funny) and makes me laugh.46、What do you call the act of making food ready for eating?A. CookingB. PreparingC. BakingD. Grilling答案: B47、填空题：The ______ (种植园) produces coffee beans.48、填空题：I enjoy spending time with my __________. (家人)49、听力题：The chemical formula for potassium perchlorate is _____.50、填空题：The kitten likes to _______ (睡觉) on my lap.51、What type of music is characterized by strong rhythms and often includes drums?A. ClassicalB. JazzC. RockD. Pop答案：C52、听力题：The ________ (teamwork) improves results.53、What is the capital of Bhutan?A. ThimphuB. ParoD. Phuentsholing答案:A54、What is the main ingredient used to make beer?A. CornB. WheatC. BarleyD. Rice答案:C55、What is the name of the fictional character who wears a red coat and has a pet fox?A. Peter PanB. Paddington BearC. Winnie the PoohD. The Gruffalo答案: B56、填空题：My ___ (小狗) loves to dig in the sand.57、What is the opposite of ‘strong’?A. WeakB. PowerfulC. ToughD. Sturdy58、填空题：The __________ (历史的丰富内涵) inspire creativity.59、选择题：What do we call the time when the sun rises?A. DawnB. NoonC. DuskD. Midnight60、How many players are on a soccer team?A. ElevenB. TenC. NineD. Twelve61、What do you call the liquid that comes from trees?A. GumC. SapD. Juice答案:C62、填空题：My neighbor, ______ (我的邻居), has two cats.63、填空题：The teacher helps _____ (学生) reach their goals.64、听力填空题：I think that every skill learned is a step towards our __________.65、What do you call a young goat?A. KidB. CalfC. FoalD. Lamb66、What do plants need to grow?A. Sunlight, water, and soilB. Darkness, salt, and airC. Sugar, heat, and rocksD. None of the above答案：A67、听力题：The capital of Vietnam is __________.68、What is the shape of a basketball?A. SquareB. TriangleC. RectangleD. Circle答案:D69、填空题：I enjoy doing ______ (运动) because it keeps me fit and active. My favorite is ______ (游泳).70、填空题：My cousin has a __________仓鼠. (可爱的)The _____ (ocean) is blue.72、听力题：A rainbow is formed by the ______ (refraction) of light.73、填空题：I have a _____ (跳棋) set that I play with my family.我有一个跳棋游戏，和家人一起玩。

a r X i v :h e p -p h /9705306v 1 13 M a y 199718May 1997hep-ph/9705306Distinguishing gauge-mediated from unified-supergravity spectraAlessandro StrumiaDipartimento di Fisica,Universit`a di Pisa and INFN,sezione di Pisa,I-56126Pisa,ItaliaAbstractWe show that gauge-mediation and unified-supergravity give sufficiently firm and different predictions for the spectrum of supersymmetric particles to make it possible to discriminate the two scenarios even if the messenger mass is close to the unification scale.1According to our present theoretical understand-ing,the presence of supersymmetric partners of the three generation of fermions has a very different im-pact on flavour physics,depending on the relative order of few fundamental high-energy scales.If the hard-ness scale of the supersymmetry-breaking soft terms (‘mediation scale ’,M M )is higher than the hardness scale of the standard Yukawa couplings (‘flavour scale ’,M F )or of the unification scale M U ≈2·1016GeV,we expect that the sfermion mass matrices contain new sources of flavour and CP violation,most likely de-tectable due to the heavyness of the top quark [1].In this case it is quite possible that the consequent ef-fects,due to virtual sparticles exchanges,will be dis-covered even before than the sparticles themselves.If instead the supersymmetry-breaking soft terms are me-diated at a lower scale where the flavour and unifica-tion physics have decoupled,we expect that the only flavour violation present at low energies is described by the supersymmetrized extension of the standard CKM matrix.In this case supersymmetric loops could give non negligible contributions only to ‘standard’flavour and/or CP violating effects,mainly to the b →sγand b →sℓ+ℓ−decays [2].If this view is correct,the forthcoming experimentsabout flavour physics should either discover some signal(or combination of signals),thus giving a strong hint infavour of the first scenario,or exclude new flavour andCP violations up to a certain level,making the first sce-nario less interesting.In any event,it is clearly useful to have an alternative way of discriminating between the two scenarios.If the mediation scale is sufficientlylow (M M <∼108GeV)the decay within the detector of the lightest supersymmetric particle (LSP)into a grav-itino would give such an incontrovertible signal.No such a clean signal is present in the remaining range of M M .In this paper we want to show that,within reason-ably minimal models,the spectrum of the supersym-metric particles typical of the two scenarios is suffi-ciently different that is possible to recognize which of the two scenarios is actually realized,even if the medi-ation scale gets close to the unification scale.2Both the two scenarios outlined above can be re-alized in a clean and predictive way.The first case,M M >∼min(M F ,M U ),arises naturally if supergravity interactions mediate the soft terms [3].In this case the hardness scale of the soft terms,M M ,is the re-duced Planck mass.Low energy physics suggests that the field theory at this high scale has a unified gauge group,G ⊇SU(5)⊃SU(3)c ⊗SU(2)L ⊗U(1)Y ,so that the sparticle masses are subject to unification re-lations.Neglecting,for the moment,SU(5)-breakingeffects,unified supergravity predictsM 5=M i (M U )(1a)11.41.210.80.60.40.2m a s s r a t i o M 2/m L1.210.80.60.4mass ratio M 3/m d RFigure 1:Correlations (M 3/m ˜d R ,M 2/m ˜L)as predicted by unified supergravity (continuous line)and gauge-mediation (dashed lines)for different values of the messenger scale and of the parameter η,defined in (2).We have employed α3(M Z )=0.118.The supergravity and gauge-mediation predictions with M M =1015GeV are also shown for α3(M Z )=0.125(lower lines).In the shaded area it is possible to observe the clean signature of LSP decay.The dotted line refers to a non minimal unification model,as discussed in the text.m ¯5=m ˜L (M U )=m ˜d R (M U )(1b)m 10=m ˜e R (M U )=m ˜Q(M U )=m ˜u L (M U )(1c)where M i (M U )are the three gaugino mass parameters (i =1,2,3runs over the three factors of the SM gauge group)and m ˜f (M U )are the soft mass terms for thesfermions ˜f,all renormalized at the unification scale M U .Unacceptably large flavour violations are avoided if the sparticles of the first generation are degenerate with the corresponding ones of the second generationat a level that,for our present purposes,can be consid-ered perfect.For the purposes of this paper,the third generation sparticles are less interesting because theirunification relations are easily broken [4]and corrected by not sufficiently controlled RGE effects [5].Also the second scenario,M M <min(M U ,M F ),arises naturally if the soft terms are communicated by the standard gauge interactions at some ‘media-tion scale’M M ,lower than the unification scale 1,where some charged ‘messenger’superfields feel directly the4πM 0,(2a)m 2R (M M )=η·c i R M 2i (M M ),(2b)where m R are the soft mass terms for the fields R =˜Q,˜u R ,˜d R ,˜e R ,˜L,h u ,h d ,and the various quadratic Casimir coefficients c i R are listed in table 1.Here M 0is an overall mass scaleand ηparametrizes the different minimal models.Forexample η=(n 5+3n 10)−1/2in models where a gauge singlet couples supersymmetry breaking to n 5copies ofmessenger fields in the 5⊕¯5representation of SU(5)and to n 10copies in the 10⊕1.41.210.80.60.40.2m a s s r a t i o M 1/m e R1.210.80.60.4mass ratio M 3/m u RFigure 2:As in fig.1,except that we plot the correlations (M 3/m ˜u R ,M 2/m ˜e R )involving masses of sparticles unified in a 10of SU(5).not employ the additional prediction that the A -terms vanish at the messenger scale.Gauge-mediation models have the generic problem that gauge interactions alone cannot mediate the ‘µ-term’,as well as the corresponding ‘B ·µ-term’,since these terms break a Peccei-Quinn symmetry.Since the unknown physics required to solve this problem may easily give rise to unknown non minimal contributions to the soft terms in the Higgs sector [9],we will con-centrate on the safer predictions for sfermion masses.3The two scenarios do not differ in their predictions for gaugino masses.We now show that these scenarios give instead sufficiently different predictions for some scalar masses 2.The main feature at the basis of this fact is that,even for a messenger scale close to the unifi-cation scale,only the MSSM gauge bosons are relevant for mediating supersymmetry breaking.As a conse-quence,the Casimir coefficients are different for par-ticles coming from the same unified representation,so that the gauge-mediated spectrum is not unified even when the messenger mass is close to the unification scale.we show the mass ratios(M3/m˜uR ,M1/m˜eR)involv-ing sfermions unified in a10of SU(5).The gaugino mass parameters M i are of course again related among themselves and we have varied the ratio between gaug-ino and scalar masses in a reasonable range3,as indi-cated in the plots.As anticipated,the difference be-tween the predictions is not unobservably small,even for M M=1015GeV.In our plots we have included2-loop RGE effects[13] and threshold corrections at the electroweak scale,com-puted in logarithmic approximation[14].These effects give a shift of the predictions that,in the plots,is at most20%of the‘distance’between the two more sim-ilar cases of supergravity and gauge-mediation with M M=1015GeV.Furthermore,the shift is almost equal for the two analogous spectra.We have preferred to plot the gaugino and scalar mass parameters commonly used to parametrize the sparticle spectrum rather than the physical masses of the same particles.With this choice,each plot covers practically the fully general dependence on all the su-persymmetric parameters,i.e.the predictions are prac-tically independent on the other supersymmetric pa-rameters that do not appear in the plots(theµterm, the overall scale of supersymmetric particles,tanβ, etc.).More precisely,these variables affect our plots only through two loop RGE effects and threshold cor-rections.Since it is conceivable that also these param-eters will be measured,we have not included the rel-atively small uncertainties associated with their varia-tions.Rather we have assignedfixed reasonable values to these parameters,as we now discuss in some detail:•As said,we have not plotted sparticle pole masses.For example m˜uR is the soft term m˜uR(m˜uR).Tocompute the physical masses one has to add the well known SU(2)L⊗U(1)Y-breaking effects,that depend on tanβ,and the known full one-loop ef-fects,that give up to10%corrections[15].With this choice our plots are valid for any moderate value of tanβ(we have used tanβ=2)4.•The overall scale of sparticle masses has been fixed by choosing M3=500GeV.Any other rea-sonable value of this measurable parameter gives a shift comparable to the uncertainty associated with the experimental error onα3,as discussed below.c Q i c u R i cd R i c L i ce R i115210632338300Table1:Values of the Casimir coefficients for the MSSMfields.The coefficients c h u i and c h d i are equal to c L i.•In the supergravity case,the mass ratios infig.s1,2depend on the ratio m¯5/m10only via numeri-cally irrelevant two loop and threshold effects atthe electroweak scale.In any case we have chosenm¯5≈1.3m10in order to obtain a slepton massratio similar to the one predicted by the high-M Mgauge-mediated scenario.Moreover,we have assumed that the(again irrel-evant)masses of third generation sfermions are,at the unification scale,50%smaller than the cor-responding ones of the other generation,as sug-gested by RGE effects above the unification scale.We have set all the A-terms at zero at the unifi-cation scale.In principle,only the stop A term,A t,could be relevant for our purposes.In prac-tice,the induced effects(via two loop RGE andvia threshold effects)are again negligible5.•In the gauge-mediation case,we have neglected(computable)‘threshold’corrections at the mes-senger scale.We expect that these corrections beimportant only in the case of light messengers,i.e.when the difference with the unified super-gravity scenario is large anyhow.•The experimental error on the strong couplingconstant,that induce large RGE effects,is suffi-ciently small for our purposes.The predictionshave been plotted forα3(M Z)=0.118.To ap-preciate the impact of this uncertainty,we havealso plotted the predictions of supergravity andof gauge-mediation with a very high messengerscale,M M=1015GeV,for a somewhat highervalue ofα3,α3(M Z)=0.125,favoured by unifi-cation.•In both the minimal models considered,the Higgsmasses are expected to give a non zero contribu-tion toX Y≡Tr Y R m2R=(m2h u−m2h d)+···that,via one-loop RGE effects,induces a∼5%correction to the sfermion masses,proportionalto their hypercharges Y.We postpone a discus-sion of this more dangerous correction to the nextsection,where we will consider non minimal ef-fects that could affect the predictions(1)and(2). Finally,as pointed out in ref.[7],we also notice that the mass ratios under consideration have a moderate sensivity to the‘minimal gauge-mediation’parameters, M M,η,and can thus be employed for determining their values.4We now discuss how non minimal contributions to the soft terms could affect the picture described above. As anticipated,we expect that in both scenarios the scalar masses receive a∼5%correction induced,via RGE effects,by different boundary conditions for the Higgs masses,m h u=m h d.In the case of gauge-mediation models,such a correction could be much larger.In fact the U(1)Y gauge interactions can me-diate,at one-loop,a very large contribution to the squared scalar masses m2R,proportional to the hyper-charge Y R[6]:α1(M M)δm2R=ηη′Y Rfields with other representations,in such a way that the lightfields do not originate from the same unified multiplet.A large mixing is however theoretically dis-favoured,since the additionalflavour structures neces-sary to realize it,easily produce unacceptableflavour and/or CP violating effects at low energy(appropriate symmetries could avoid this conclusion).Barring these mixing effects,the soft masses of the sfermions of1st and2nd generation with negligible Yukawa couplings are subject to threshold corrections,which are again controllable via the corresponding effects in the gauge couplings.In particular the corrections to unification of sfermion masses(1b,c)are small in models that pre-serve the successful GUT prediction of gauge coupling unification.As a significant example of these facts,we can con-sider an interesting model with large‘threshold’cor-rections with respect to‘minimal’unification,that still gives rise to a successful unification prediction for the gauge couplings.In unified models derived from per-turbative string theory[19],the adjoint of SU(5)that breaks SU(5)to the standard-model gauge group has aflat potential,so that its fragments not eaten by the vector bosons do not get a mass at the unification scale. If,for some reason,these chiral supermultiplets with the same gauge charges of the SM gauge bosons get mass at an intermediate scale around1013GeV,the gauge couplings unify close to the Planck scale[20]. We see that the predictions of this model for the scalar masses(dotted lines infig.s1and2)do not significantly differ from the minimal unification scenario(continu-ous lines).5In conclusion we have shown that the predictions for the sparticle spectrum of gauge mediated and unified-supergravity scenarios,as obtained under rather gen-eral conditions,are sufficiently different to allow the discrimination between the two scenarios,provided that the sparticle masses,or rather the appropriate ratios of sparticle masses,are measured with sufficient pre-cision.If supersymmetric particles are discovered,it is conceivable that such measurements will be done at the next generation of accelerators,supplementing the data obtainable at the hadron collider LHC[10,21], with those obtainable at an e−e+linear collider[10].References[1]R.Barbieri and L.Hall,Phys.Lett.B338(1994)212;S.Dimopoulos and L.Hall,Phys.Lett.B344(1995)185;R.Barbieri,L.Hall and A.Strumia,Nucl.Phys.B445(219) 1995and Nucl.Phys.B449(1995)437.[2]See,e.g.,S.Bertolini,F.Borzumati,A.Masiero and G.Ri-dolfi,Nucl.Phys.B353(1991)591;J.Hewett,J.D.Wells, Phys.Rev.D55(1997)5549;N.G.Deshpande, B.Dutta and S.Oh,hep-ph/9611443.[3]R.Barbieri,S.Ferrara and C.A.Savoy,Phys.Lett.119B(1982)343;P.Nath,R.Arnowitt and A.Chamseddine, Phys.Rev.Lett.49(1982)970.[4]L.Hall,J.Lykken and S.Weinberg,Phys.Rev.D27(1983)2359;Y.Kawamura,H.Murayama and M.Yamaguchi, Phys.Rev.D51(1995)1337;A.Pomarol and S.Dimopou-los,Nucl.Phys.B453(1995)83.[5]L.Ib´a˜n ez, C.Lopez and C.Mu˜n oz,Nucl.Phys.B256(1985)218;A.Boquet,J.Kaplan and C.A.Savoy,Nucl.Phys.B262(1985)299.[6]L.Alvarez-Gaume,M.Claudson and M.B.Wise,Nucl.Phys.B207(1982)96;M.Dine and W.Fishler,Nucl.Phys.B204(1982)346.[7]S.Dimopoulos,S.Thomas and J.D.Wells,Phys.Lett.B357(1995)573;[8]J.A.Bagger,K.Matchev,D.M.Pierce and R.Zhang,Phys.Rev.D55(1997)3188.[9]G.Dvali,G.F.Giudice and A.Pomarol,Nucl.Phys.B478(1996)31.[10]See, e.g.,M.E.Peskin,Prog.Theor.Phys.Suppl.123(1996)507and references therein.[11]S.Martin and P.Ramond,Phys.Rev.D48(1993)5365;H.-C.Cheng and L.J.Hall,Phys.Rev.D51(1995)5289.[12]S.Dimopoulos and G.F.Giudice,Phys.Lett.B357(1995)573;G.Dvali and A.Pomarol,Phys.Rev.Lett.77(1996) 3728.[13]S.P.Martin and M.T.Vaghn,Phys.Rev.D50(1994)2282;Y.Yamada,Phys.Rev.D50(1994)3537;I.Jack and D.R.T.Jones,Phys.Lett.B333(1994)373.[14] hanas and K.Tamvakis,Phys.Lett.B348(1995)451;A.Dedes,hanas and K.Tamvakis,Phys.Rev.D53(1996)3793.[15]See,for example,D.M.Pierce,J.A.Bagger,K.Matchev,R.Zhang,hep-ph/9606211and references therein. 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a r X i v :h e p -e x /0105063v 1 22 M a y 2001QUARTIC GAUGE BOSON COUPLINGS RESULTS AT LEPM.MUSY CERNThe study of charged and neutral boson vertices has been performed in different production channels at the LEP experiments.Decay rates and kinematic properties of these events are exploited to set constraints on the corresponding gauge couplings.1IntroductionThe study of quartic gauge boson couplings (QGCs)has become possible due to the recent theoretical developments on this topic.The presence of QGCs affects the data collected for different final states at LEP.The continous increase of the centre-of-mass energy in e +e −collisions allowed for the precise measurement of the W-pair cross section and couplings.Now,also the study of radiative W-pair events,e +e −→W +W −γ,has become possible.The Standard Model (SM)predicts the existence of quartic gauge boson couplings leading to W +W −γproduction via s -channel exchange of a γor a Z boson as shown in Fig.1a.The contribution of these two quartic Feynman diagrams with respect to the other competing diagrams,mainly initial state radiation,is negligible at the LEP centre of mass energies.Nonetheless,the process leading to the W +W −γfinal state can be sensitive to anomalous contributions to the SM quartic vertices W +W −γγand W +W −Z γ.The theoretical framework of Ref.[1]is used for the parametrisation of such anomalous couplings.The existence of Anomalous QGCs would also affect the e +e −→νe ¯νe γγprocess via the W +W −fusion Feynman diagram containing the W +W −γγvertex 2(see Figure 1b).In the SM the reaction e +e −→ν¯νγγproceeds predominantly through s -channel Z exchange and t -channel W exchange,with the two photons coming from initial state radiation,whereas the SM contribution from the W +W −fusion is again negligible at LEP.AQGCs would enhance the ν¯νγγproduction rate,especially for the hard tail of the photon energy distribution and for photons produced at large angles with respect to the beam direction.eeeeγγFigure 1:Feynman diagrams containing a four boson vertex leading to the (a)W +W −γ,(b)ν¯νγγ,and (c)Z γγfinal states.Finally,the Z γγproduction (see Fig.1c)can also be exploited to derive limits on AQGCs,as it will be discussed in the next paragraph.2QGCs Analyses at LEPTable 1shows the different data sets used for the AQGCs analyses at LEP.L3W +W −γ189-202GeV189-202GeV189GeVZ γγ130-202GeV Opal E γ>10GeV|cos θγ|<0.94cos θfγ<0.9–√s (GeV)σW W γ (p b )00.10.20.30.40.5Figure 2:Measured cross section for the process e +e −→W +W −γ.The resulting cross sections for the L3experiment are:σW W γ(188.6GeV)=0.29±0.08±0.02pb σW W γ(194.4GeV)=0.23±0.10±0.02pb σW W γ(200.2GeV)=0.39±0.12±0.02pbwhile for Opal,the measurement at 189GeV gives σW W γ=0.136±0.037±0.008pb,where the first error is statistic and the second systematic.All the obtained results are compatible with the SM expectations.Figure 2shows the L3measured cross section as a fuction of√The information from theν¯νγγtotal cross section,together with the information derived from the shape and normalisation of the photon spectra in W+W−γevents,produces the fol-lowing ADL combined limits on charged AQGCs using the data set of Table1(first two lines):−0.022GeV−2<a0/Λ2<0.021GeV−2−0.043GeV−2<a c/Λ2<0.058GeV−2−0.022GeV−2<a n/Λ2<0.020GeV−2,in good agreement with the SM expectation of zero for each coupling.The Feynman diagram of Fig.1c involves only neutral bosons,and it is not present in the SM.Besides,as it has been recently indicated3,under more general assumptions the quartic couplings in the neutral sector,still named a0/Λ2,and a c/Λ2in Ref.[1],can be regarded as independent from those in the charged sector.For this reason,on the experiimental side,the convention was used to keep apart the measurements in these channels not performing any combinations,in the wait for a unified theoretical approach.To obtain limits on AQGCs in the neutral sector,the hadronic Zγγ→qqγγevents are used. The signal consists in an enhancement in the rate of high energy photons,while the background mainly comes from doubly radiative returns to the Z.Figure3shows the Zγγcross section as predicted by the EEZGG2program a.The same program is used to model AQGCs and tofit these couplings to the observed data distributions of P Tγ1(for L3),Eγand max|cosθγi|(for Opal). The following LEP combined bounds are derived4:−0.0048GeV−2<a0/Λ2<0.0056GeV−2−0.0052GeV−2<a c/Λ2<0.0099GeV−2All experimental observations are compatible with the SM predictions.3ConclusionsThe measurements of rare processes as Zγγ,W+W−γandν¯νγγconstitute an important test of the SM.Preliminary results on AQGCs were presented here,including new results in the W+W−γchannel up to the centre-of-mass energy of202GeV with a significant increase in the final precision.References1.J.W.Stirling and A.Werthenbach,Phys.Lett.B446,369.2.J.W.Stirling and A.Werthenbach,Eur.Phys.J.C14(2000)103.3.G.Belanger and F.Boudjema,Nucl.Phys.B288(1992)201.4.The Opal Collaboration,ICHEP abs572(2000),Opal PN452;The L3Collaboration,ICHEP abs.505(2000),CERN-EP/2000-006.Recoil Mass (GeV)E v e n t s /5 G e V246810121400.511.5√s/GeVOPAL Preliminaryσ(e +e -→q q γγ) /p bFigure 3:Cross section for the process e +e −→Z γγas a function of√。

a rX iv:c ond-ma t/971187v1[c ond-m at.m es -hall]11No v1997A Chern-Simons Effective Field Theory for the Pfaffian Quantum Hall State E.Fradkin 1,Chetan Nayak 2,A.Tsvelik 3,Frank Wilczek 41Dept.of Physics,University of Illinois at Urbana-Champaign,Urbana,IL,618012Institute for Theoretical Physics,University of California,Santa Barbara,CA,93106-40303Department of Theoretical Physics,University of Oxford,1Keble Road,OX13NP,U.K.4School of Natural Sciences,Institute for Advanced Study,Olden Lane,Princeton,N.J.08540We present a low-energy effective field theory describing the universality class of the Pfaffian quantum Hall state.To arrive at this theory,we observe that the edge theory of the Pfaffian state of bosons at ν=1is an SU (2)2Kac-Moody algebra.It follows that the corresponding bulk effective field theory is an SU (2)Chern-Simons theory with coupling constant k =2.The effective field theories for other Pfaffian states,such as the fermionic one at ν=1/2are obtained by a flux-attachment procedure.We discuss the non-Abelian statistics of quasiparticles in the context of this effective field theory.I.INTRODUCTION Recently there has been considerable interest in a new class of quantum Hall states,combinining aspects of BCS pairing with Laughlin-type ordering [1–6].The states appear to be incompressible,and to exhibit non-Abelian statistics.Their properties have mainly been inferred by extrapolation in quantum statistics (of electrons)from ordinary superconductors [2],from numerical studies [2,6],and from the existence of attractive trial wave functions [1–5].To assure ourselves of the robustness of these properties,and for calculational purposes,it is important to have a low-energy,long-wavelength effective field theory.In this paper,we shall supply such a theory.Analyses of the ground states of the lowest Landau level Hamiltonian with three-body interactions of the form H = i>j>k δ′(z i −z j )δ′(z i −z k )(1)have unearthed a number of fascinating properties of these states [1–5].In particular,at Landau level filling fraction ν=1/2,the ground state is the so-called Pfaffian state,ΨPf =Pf 14ℓ20 |z i |2(2)(where Pf 1z 1−z 21z i −z j i>j(z i −z j )q e −1z i −z j i>j (z i−z j )2e −1z j −z k →Pf (z j−η1)(z j −η2)(z k −η3)(z k −η4)+(j ↔k )However,this is not the only four-quasihole state with quasiholes atη1,η2,η3,η4.Pf(13)(24)and Pf(14)(23)seem to be equally good.In fact,only two of these three are linearly independent,as a consequence of the identity[3]:Pf(12)(34)−Pf(14)(23)=η14η238+1√z i−z j→Pf θa(z i−z j)z k+1−z k+214ℓ20 |z i|2(10)The arbitrary distinct positive integers p1,...,p k correspond to the creation of neutral fermionic excitations;this is the c=1/2sector of the edge theory.S(z1,...,z N)is a symmetric polynomial;this modification of the ground state corresponds to the creation of chiral bosonic excitations in the c=1charged sector of the edge theory.Atν=1/2, the compactification radius of the boson is R=1/√2+1.The specific form of the trial wavefunctions considered above played a crucial role in the determination of the properties of the Pfaffian state,such as the non-Abelian braiding statistics.Of course,we would like to believe that the Pfaffian state is a representative of an entire universality class of states which have the same‘topological properties’,such as braiding statistics and ground state degeneracy on the torus.To investigate the existence and stability of this universality class,we need a low-energy,long-wavelength effectivefield theory for the Pfaffian state. An effectivefield theory for the Laughlin states atν=1/(2k+1)was obtained by a Landau-Ginzburg construction L eff=ψ∗(i∂0−(a0+A0))ψ+¯h22k+11The fundamental objects in the Landau-Ginzburg theory are auxiliary bosons,ψ,which are electrons withfictitious flux attached via a.The fractionally charged,anyonic quasiparticles are vortices.In a dual theory,which results from integrating out the auxiliary bosons,the quasiparticles are fundamental:L dual=2k+12+1.We will use this edge theory to deduce the effectivefield theory of the bulk(which is dual tothe Landau-Ginzburg theory).Ourfirst step will be to show how this is done in the simplest case(for reasons which will become clear)of a Pfaffian state of bosons atν=1.We will then check that this effectivefield theory reproduces the bulk properties exhibited by the wavefunctions.Finally,we will comment on the stability of the state.II.EFFECTIVE FIELD THEORY OF THE BOSONIC PF AFFIAN STATE ATν=1The edge theory of the bosonic Pfaffian state atν=1has c=1z2+f abc J c(0)16π d2x tr g−1∂µg g−1∂µg +2k+2=3/2;which is the central charge ofa triplet of Majorana fermions which indicates the equivalency between these two models.Hence,we may take the chiral sector of the SU(2)2WZW model as the edge theory of the bosonic Pfaffian state atν=1.Now,we are most of the way home because the bulk theory corresponding to the chiral SU(2)2WZW model is simply the SU(2)Chern-Simons theory with Chern-Simons coefficient k=2[7],S=23f abc a aµa bνa cλ (17)where a aµis an SU(2)gaugefield.An alternative approach begins with the coset construction of the c=1/2theory [9,10],but it is less transparent,so we do not pursue it further.III.TOPOLOGICAL PROPERTIES IN THE EFFECTIVE FIELD THEORYWe can now check that the effectivefield theory(17)predicts the same topological properties as the analysis of trial wavefunctions.Let usfirst consider the ground state degeneracy on a torus,which we know to be three for bosons at ν=1.The Hilbert space of the Chern-Simons theory(17)(since the Chern-Simons Hamiltonian vanishes,all statesare ground states)on a torus can be obtained in the following way[7,8].Consider the path integral of(17)over the three-dimensional region M enclosed by a torus,∂M=T2,Ψ[a]= α|T2=a Dαe2 M d3xǫµνλ(αaµ∂ναaλ+24π M d3xǫµνλ(αaµ∂ναaλ+24π d3xǫµνλ(αaµ∂ναaλ+2Since(21)tells us how amplitudes are modified by braiding operations,it gives us a direct handle on the eigenvalues of the braiding matrix.Consider an arbitrary state|ψ in the two-dimensional space of states with four quasiholes. According to the skein relation,q−1|ψ −q B2|ψ = q1/2−q−1/2 B|ψ (22)where B is the braiding operator for two of the quasiparticles.(22)implies a quadratic equation for the eigenvalues of B which yields the eigenvalues e−3πi/8and eπi/8,again in agreement with(8).We can also obtain the quasiparticle statistics from the braiding matrices of the spin-1/2vertex operators in the SU(2)2WZW model.According to[9],these follow from the fusion rules and anomalous dimensions in that conformal field theory.IV.EFFECTIVE FIELD THEORY OF THEν=1/2PF AFFIAN STATEWe would now like to deform the theory(17)so that it describes the fermionic Pfaffian state atν=1/2.(Of course,by the same procedure,we could also obtain the effectivefield theory for fermionic Pfaffian states at any even denominator or for bosonic Pfaffian states at any odd denominator.)The idea is to use theflux-attachment procedure [11–14]to change the bosons into fermions and simultaneously change thefilling fraction fromν=1toν=1/2.To do this,we introduce a U(1)gaugefield,cµ,which couples to the charge current,ǫµαβF3αβ.Thefield cµwill attach a flux tube to each electron through the Chern-Simons equation:ǫµαβ∂αcβ=−jµ=ǫµαβF3αβ(23) This equation follows from the actionS=23f abc a aµa bνa cλ +14πcµǫµαβ∂αcβ(24)which is our proposed effectivefield theory for the fermionic Pfaffian state atν=1/2.Equation(24)needs some explanation because the term which couples a aµand cµbreaks the SU(2)gauge invariance down to the smaller U(1)subgroup generated by T3(as does the coupling to the electromagneticfield,which has the same form).The action(17)and the equations of motion which follow from it are invariant under the transformationa aµT a→g a aµT a g−1−∂µg g−1(25) where g is an SU(2)-valued function which must become identity at the boundary.As a result of(25),the time-evolution of a aµ(in the bulk)is not well-defined because a given set of initial conditions can lead to infinitely many possible solutions,each related to the others by the gauge transformation(25).To put it differently,the action does not specify a dynamics for the longitudinal part of the gaugefield,which decouples from the transverse part.On the other hand,gauge-invariant quantities,such as F aαβF aµνhave perfectly well-defined time-evolution since they are independent of the longitudinal part of a aµ.For calculational purposes,we can choose a particular gauge,thereby specifying a dynamics for the longitudinal part of a aµ.Of course,gauge-invariant quantities will not depend on this choice.In(24),however,the cµǫµαβF3αβterm breaks gauge-invariance by coupling the transverse part of the gaugefield to the longitudinal part.As a result of its coupling to the longitudinal part of a aµ,the transverse part no longer has a well-defined time-evolution either.We can only make sense of the action(24)if we understand the SU(2)part of the action to be gauge-fixed.One possible choice is Coulomb gauge,a a0=0,or the weaker condition a10=a20=0which preserves the U(1)gauge symmetry generated by T3.In this gauge,there is a constraint,F a12=0(26) which generates time-independent gauge transformations.We can impose another condition to eliminate this residual gauge symmetry,but we do not have to.Once we have imposed Coulomb gauge,a given set of initial conditions leads to a unique solution.The time-independent gauge transformations connect different gauge-equivalent initial conditions, but do not render the time evolution ill-defined.In other words,we have a hugely redundant,but completely well-defined dynamics.Hence,we can take(24)as our effectivefield theory,provided we understand the SU(2)gaugefield to be gauge-fixed in the Coulomb gauge or another suitable gauge.Alternatively,and more profoundly,we can view the cµǫµαβF3αβterm as a gauge-fixed form of the gauge invariant operator L spinL spin≡1∆+0(−i∂µ+cµ)∆aǫµαβF aαβ+c.c.(30)4πNow we need no extra constraints.It is noteworthy that while the ordinary Chern-Simons terms are completely general covariant,potential term(29)is invariant only under volume preserving diffeomorphisms.This should not be disturbing,however,because there is a preferred density–though not a preferred shape–associated with incom-pressible quantum Hall liquid.The non-asymptotic form,withλ1,2finite,allows in principle for the description of localized vortex configurations.Because theflux-attachment only affects the‘trivial’U(1)part of the topological properties of the Pfaffian state, the quasiparticle statistics,degeneracy on the torus,etc.can be inferred from those atν=1.It is straightforward to generalize this construction to include more generalfilling factors.Essentially,all that is required is to attach an even number offlux quanta in addition to the procedure we used to map bosons to fermions. This is the standard procedure that is followed to generate the Jain fractions in the fermionic version of the abelian Chern-Simons theory of the FQHE[14].There is,however,a significant subtlety concerning the global consistency of the implementation offlux attachment commonly used in the condensed matter literature,when it is applied to closed surfaces of non-trivial topology.Indeed,the action for the Abelian gaugefield is ordinarily written with a Chern-Simons term with a coefficientθ=1/(2πm),where m is an even integer.This is inconsistent with the requirement of quantization of the Chern-Simons coupling constant needed for a Chern-Simons gauge theory on a closed manifold [15].We should instead take this coefficient to be1and put the coefficient1/θ=(2πm)in front of the term(27) which couples the two gaugefields.In the Appendix we give a more careful discussion of this point,and derive the proper procedure fromfirst principles.V.DISCUSSION1.A main motivation for our effectivefield theory is to establish the existence of a universality class of quantum Hall states of which the Pfaffian state(3)is a representative.The most salient property of this universality classis a 2n −1-fold degenerate set of 2n -quasihole states which transform as the spinor representation of SO (2n )as the quasiholes wind about each other.This is a bit worrisome since arbitrary perturbations might be expected to break this degeneracy.In particular,impurities or small variations in the inter-electroninteractions could,potentially,do this,thereby spoiling the non-Abelian statistics.With theeffective field theories (17)or (24)in hand,however,it is clear that this degeneracy is,indeed,stable in the long-wavelength limit.The leading perturbations are Maxwell terms of the form F a µνF µνa which are irrelevant by one power of q or ωcompared to the Chern-Simons terms.Perturbations which couple to the charge density,such as a random potential or Coulomb interactions,couple to the field strength of the U (1)gauge field in (24).Hence,(24)is just as stable as an Abelian quantum Hall state,at least as far as such perturbations are concerned.2.A Landau-Ginzburg theory of the Pfaffian state should take a paired order parameter as its starting point.Indeed,this is strongly suggested by the appearance of the fields ∆0,∆a in the gauge-invariant form of the effective field theory (30).This leads one to the Landau-Ginzburg theory of a superconductor,but with an Abelian Chern-Simons field to cancel the magnetic field or,in other words,to a theory almost identical to the theory of a Laughlin state (11).The crucial difference is that the paired order parameter must have a structure which allows the existence of neutral fermionic modes at vortex cores,where the gap to an unpaired fermion vanishes.The reader may recall that Bogoliubov-de Gennes quasiparticles in a superconductor become neutral fermions on the Fermi surface and are therefore natural candidates for the zero modes we are looking for.We could then,as in [4–6],interpret the 2n −1-fold degeneracy in terms of the occupation of fermionic zero modes associated with the vortices.This raises the interesting prospect that the duality transformation between the Landau-Ginzburg theory –in which the electrons are the fundamental objects –and the dual theory of equation (17)or (24)–in which the quasiparticles are fundamental –is a highly non-trivial transformation relating two theories which,at first glance,appear to be radically different.3.The observed plateaus at ν=5/2(in other words,ν=1/2in the second Landau level)in a single-layer system and ν=1/2in a double-layer system are promising hunting grounds for excitations with non-Abelian statistics.One way to experimentally determine whether either one is described by the Pfaffian state (2)is to measure the quasihole statistics.To do this,we would like to observe how the quantum state of the system transforms when quasiholes are braided.An elegant way to do this utilizes the two point-contact interferometer proposed by Chamon,et.al.[16].AFIG.2.In the two point-contact interferometer of Chamon,et.al.,quasiholes can tunnel from the lower edge to the upper edge by one of two interfering paths.The interference is controlled by varying the flux,Φ,and number of quasiholes,N q ,in the central region.In this device (see figure 2),quasiholes injected at point A along the bottom edge of the quantum Hall bar can tunnel to the other edge at either of two point-contacts.A quasihole which tunnels at the second point-contact will follow a path which encircles a central region containing flux Φas well as N q quasiholes.As a result of the flux Φ,it will aquire an Aharonov-Bohm phase which depends on its fractional charge.Its state will also be tranformed because its trajectory braids the N q quasiholes in the central region.Consequently,the interference between the two tunneling paths will depend on the charge and statistics of the quasiholes.As discussed by Chamon,et.al.[16],if we hold the electron number (and therefore the quasihole number)in the central region fixed,then the conductance will oscillate as a function of Φwith period e2|t 1|2+|t 2|2 +Re t ∗1t 2e iα ψ|B N q |ψ (31)where t 1and t 2are the tunneling amplitudes at the two point-contacts.Now,the matrix element ψ|B N q |ψ is given precisely by the expectation value in the effective field theory (17)of the Wilson lines of figure 3or,simply,by theJones polynomial V N(eπi/4)of these loops.qFIG.3.The matrix element ψ|B N|ψ is the expectation value of these Wilson lines.The loop on the left represents aqquasihole which tunnels at the second point contact,thereby encircling the N q quasiholes on the right.In other words,if the Pfaffian state exists in nature,a two point-contact interferometer will measure the Jones polynomial!By studying the dependence on N q–the conductance will exhibit the periodicities of the two eigenvalues –we will be able to extract the non-Abelian statistics.of B NqVI.ACKNOWLEDGEMENTSThis work was supported in part by the NSF,grant numbers NSF DMR94-24511at UIUC,and NSF PHY94-07194 at ITP-UCSB.EF was a participant at the ITP Program on Quantum Field Theory in Low Dimensions,and thanks the Director of ITP for his kind hospitality. C.N.would like to thank ICTP,Trieste for hospitality during the workshop on Open Problems in Strongly Correlated Systems,where part of this work was done.A.M.T.is grateful to I.I.Kogan for interesting discussions.APPENDIX A:We will show how to defineflux attachment in a manner compatible with the requirement of quantization of the abelian Chern-Simons coupling constant or,what is the same,of invariance under large gauge tranformations.This issue does not arise for the non-abelian sector since its coupling constant is already correctly quantized.Consider a theory of particles(infirst quantization)which interact with each other as they evolve in time.We will assume in what follows that the particles are fermions(in two spacial dimensions)and that their worldlines never cross.The actual choice of statistics is not important in what follows but the requirement of no crossing is important and,for bosons,it implies the assumption that there is a hard-core interaction while for fermions the Pauli principle takes care of this issue automatically.For simplicity,we will assume that the time evolution is periodic,with a very long period.The worldlines of the particles can be represented by a conserved current jµ.For a given history of the system,the worldlines form a braid with a well defined linking numberνL[jµ],given byνL[jµ]= d3x jµ(x)Bµ(x)(A1) where jµand Bµare related through Amp`e re’s Lawǫµνλ∂νBλ(x)=jµ(x)(A2) Under the assumption of the absence of crossing of the worldlines of the particles,the linkingνL[jµ]is a topological invariant.Thus,if S[jµ]is the action for a given history,the quantum mechanical amplitudes of all physical observables remain unchanged if the action is modified byS[jµ]→S[jµ]+2πnνL[jµ](A3) where n is an arbitrary integer.The quantum mechanical amplitudes are sums over histories of the particles,and take the formAmplitude∝ [jµ]e iS[jµ]+2πinνL[jµ]e iφ[jµ](A4)whereφ[jµ]is a phase factor which accounts for the statistics of the particles.However,the amplitudes remain unchanged if the integrand of Eq.A4is mulitiplied by1written as the expression 1≡ D bµ xδ(ǫµνλ∂νbλ−jµ)=N D bµD aµexp i2π[ǫµνλ∂νbλ−jµ](A6)We can then compute this amplitude as a path integral of a theory in which the particles whose worldlines are represnted by the currents jµ,interact with the gaugefields aµand bµ.These interactions are encoded in the effective actionS eff[a,b,j]=14πǫµνλbµ∂νbλ(A7)where we have solved the constraint j=∂∧b to write the term of the winding number in the form of a Chern-Simons action for the gaugefield bµ[17,18].Hence,the amplitudes can be written in terms of a path integral over an abelian Chern-Simons gaugefield with a correctly quantized coupling constant equal to2n21[1]G.Moore and N.Read,Nucl.Phys.B360(1991),362.[2]M.Greiter,X.G.Wen,and F.Wilczek,Nucl.Phys.B374(1992),567.[3]C.Nayak and F.Wilczek,Nucl.Phys.B479(1996),529.[4]ovanovic and N.Read,Phys.Rev.B53(1996),13559.[5]E.H.Rezayi and N.Read,Phys.Rev.B56(1996),16864.[6]F.D.M.Haldane,private communication.[7]E.Witten,Commun.Math.Phys.121(1989),351.[8]E.Verlinde,Nucl.Phys.B300(1988),351.[9]G.Moore and N.Seiberg,Comm.Math.Phys.123(1989),77.[10]I.I.Kogan,Phys.Lett.390B(1997),189.[11]D.Arovas,J.R.Schrieffer,F.Wilczek,and A.Zee,Nucl.Phys.B251(1984)917.[12]S.C.Zhang,T.Hansson and S.Kivelson,Phys.Rev.Lett.62(1989)82.[13]A.L.Fetter,C.Hanna and ughlin,Phys.Rev.B39(1989),9679.[14]A.Lopez and E.Fradkin,Phys.Rev.B44(1991),5246.[15]Y.Hosotani,Phys.Rev.Lett.62(1989),2785.[16]C.de C.Chamon,D.S.Freed,S.A.Kivelson,S.L.Sondhi and X-G.Wen,Phys.Rev.B55(1997),2331.[17]F.Wilczek and A.Zee,Phys.Rev.Lett.51(1983),2250.[18]Y.S.Wu and A.Zee,Phys.Lett.147B(1984),325.[19]See,for instance,X-G.Wen,Adv.Phys.44(1995),405.。

烟台2024年小学4年级下册英语第六单元综合卷[有答案]考试时间：80分钟（总分:120）A卷考试人：_________题号一二三四五总分得分一、综合题(共计100题)1、听力题：The car is _____ fast. (going)2、听力题：The chemical symbol for nitrogen is _______.3、填空题：The _______ (马) pulls a cart.4、Which planet is known for its great red spot?A. EarthB. JupiterC. MarsD. Saturn答案:B5、What is the name of the famous ancient city located in Peru?A. Machu PicchuB. TikalC. PetraD. Angkor Wat答案: A6、听力题：The chemical formula for sodium sulfite is ______.7、听力题：A __________ is created when two or more substances react.8、听力题：The atmosphere contains layers, including the troposphere and ______.9、听力题：Space is a vacuum, meaning it has no ______.10、What is the capital city of Tunisia?A. TunisB. SfaxC. KairouanD. Bizerte11、填空题：The ________ (气候适应) is necessary for survival.12、听力题：Earth has one moon, while Mars has ______.13、听力题：The tree is ___ (full) of leaves.14、听力题：In a chemical reaction, substances change into new __________.15、听力题：The superhero is very ___ (brave).16、填空题：The bear searches for _________ in the forest. (食物)17、填空题：I want to learn how to ______.18、听力题：I want to _____ (travel/go) to the beach.19、填空题：He is a _____ (医生) who helps sick people.20、What is the capital of the United Kingdom?a. Londonb. Edinburghc. Dublind. Cardiff答案:a21、What is the capital of Tajikistan?a. Dushanbeb. Khujandd. Qurghonteppa答案:a22、What is the primary color of the sun?A. YellowB. BlueC. RedD. Green23、选择题：What do we call the area of land that is covered in rocks?A. MountainB. HillC. PlateauD. Desert24、听力题：The _______ can attract butterflies.25、What is the hardest natural substance?A. GoldB. IronC. DiamondD. Silver答案: C26、填空题：The doctor, ______ (医生), gives advice on staying healthy.27、听力题：My grandma loves to bake ____ (bread).28、听力题：The Earth's rotation creates patterns in ocean ______.29、听力题：The snow is ______ on the ground. (falling)30、听力题：The main method of separating mixtures in a laboratory is _____.31、What do you call a place where animals are kept for public display?A. ParkB. ZooC. Farm答案: B32、What do bees make?A. MilkB. HoneyC. ButterD. Sugar答案:B33、填空题：The __________ (历史的交织) illustrates interconnectedness.34、填空题：I like to ______ (完成) my chores on time.35、听力题：We will _______ (go) to the theater tonight.36、What is the capital of Egypt?A. CairoB. GizaC. AlexandriaD. Luxor答案: A. Cairo37、What do you call the person who teaches you in school?A. DoctorB. TeacherC. ChefD. Engineer答案：B38、填空题：The _____ (露水) on the grass is refreshing in the morning.39、填空题：We have a ______ (丰富的) library collection.40、填空题：She is a _____ (记者) who reports on local news.41、听力题：The periodic table organizes elements by their ______.42、听力题：The capital of South Korea is __________.43、听力题：Many _______ are known for their vibrant colors.44、What do you call the place where you buy books?A. LibraryB. BookstoreC. SupermarketD. School45、听力题：My favorite season is ______ (winter).46、听力题：A light-year is a measure of ______.47、填空题：There are many ______ (花) in the garden. They are very ______ (美丽).48、填空题：During lunch, I like to eat _______ (食物) with my friends. We talk about our _______ (事情).49、填空题：My dad is my hero _______ because he protects me.50、听力题：The chemical symbol for yttrium is _______.51、What is the capital of Monaco?A. Monte CarloB. Monaco CityC. La CondamineD. Moneghetti答案:B. Monaco City52、填空题：A ferret is a playful ________________ (小动物).53、填空题：Certain plants can regenerate after ______ (火灾).54、听一听，选一选。

Rolling contact fatigue is the phenomenon by which the durability of the contact surfaces is reduced due to repeated contact in rolling.滚动接触疲劳是在滚动过程中由于反复接触造成接触表面强度降低的现象。

滚动接触疲劳是齿轮轴承和凸轮的主要失效形式，这一发现被广泛用于机床汽车和航空工业中。

通过对生产技术的改进，新材料、更好的热处理工艺和优越的表面处理技术的持续研究来提高滚动接触疲劳强度正在发展用以减少失效同时减小组建的尺寸。

每一次提高材料性能的尝试都要求在滚动接触疲劳试验装置中进行大量的实验评估。

Various Rolling contact fatigue test rigs use two-roller, three-roller (nut cracker), 各种滚动接触疲劳试验机使用两辊、三辊（脆性）、滚子和平面的和多辊的配置，这些配置取决于研究目的。

.从圆柱滚子球形滚子到球面圆锥楔形滚子的几何样本被用于模仿最终应用的工作情况。

通过有无自重的杠杆，弹簧、气动、液压系统对滚子加载。

由于滚动接触疲劳强度的评估基于统计方法，测试大量的样本要将消耗相当长的时间。

这个试验台必须具有足够的强度和通用性来适应广泛的应用。

并且应该用小样本和提高测试速度来减少评估中的过度花费。

In rolling contact fatigue, the failure point is not well defined as the components can run even after a single pit formation with slight deterioration in the performance.对于滚动接触疲劳，故障点不是很明确，因为即使随着性能略有下降形成点蚀组件仍然可以运行。