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Electroweak Phase Transition in the MSSM 4-Dimensional Lattice Simulations

a r X i v :h e p -p h /0001087v 2 6 J u n 2000

Electroweak Phase Transition in the MSSM:4-Dimensional Lattice Simulations

F.Csikor a ,Z.Fodor a ,P.Heged¨u s a ,A.Jakov′a c b ,S.D.Katz a ,A.Pir′o th a

a

Institute for Theoretical Physics,E¨o tv¨o s University,H-1117,P′a zm′a ny P.1A,Budapest,Hungary

b

Department of Theoretical Physics,Technical University,Budapest,H-1521,Budapest,Hungary

(February 1,2008)

Recent lattice results have shown that there is no Standard Model (SM)electroweak phase tran-sition (EWPT)for Higgs boson masses above ≈72GeV,which is below the present experimental limit.According to perturbation theory and 3-dimensional (3d)lattice simulations there could be an EWPT in the Minimal Supersymmetric Standard Model (MSSM)that is strong enough for baryoge-nesis up to m h ≈105GeV.In this letter we present the results of our large scale 4-dimensional (4d)lattice simulations for the MSSM EWPT.We carried out in?nite volume and continuum limits and found a transition whose strength agrees well with perturbation theory,allowing MSSM electroweak baryogenesis at least up to m h =103±4GeV.We determined the properties of the bubble wall that are important for a successful baryogenesis.PACS numbers:11.10.Wx,11.15.Ha,12.60.Jv,98.80.Cq

The visible Universe is made up of matter.This state-ment is mainly based on observations of the cosmic dif-fuse γ-ray background,which would be larger than the present limits if boundaries between “worlds”and “anti-worlds”existed [1].The observed baryon asymmetry of the universe was eventually determined at the EWPT [2].On the one hand this phase transition was the last instance when baryon asymmetry could have been gen-erated,around T ≈100?200GeV.On the other hand at these temperatures any B+L asymmetry could have been washed out.The possibility of baryogenesis at the EWPT is particularly attractive,since the underlying physics can be—and has already largely been—tested in collider experiments.

The ?rst detailed description of the EWPT in the SM was based on perturbative techniques [3],which resulted in O (100%)corrections between di?erent orders of the perturbative expansion for Higgs boson masses larger than about 60GeV.The dimensionally reduced 3d ef-fective model (e.g.[4])was also studied perturbatively and gave similar https://www.doczj.com/doc/e818624928.html,rge scale numerical sim-ulations both on 4d and 3d lattices were needed to ana-lyze the nature of the transition for realistic Higgs boson masses [5,6].These results are in complete agreement,and predict [7,8]an end point for the ?rst order EWPT at Higgs boson mass 72.0±1.4GeV [8],above which only a rapid cross-over can be seen.The present experimen-tal lower limit of the SM Higgs boson mass is by several standard deviations larger than the end point value,thus any EWPT in the SM is excluded.This also means that the SM baryogenesis in the early Universe is ruled out.In order to explain the observed baryon asymmetry,extended versions of the SM are necessary.Clearly,the most attractive possibility is the MSSM.According to perturbative predictions the EWPT could be much stronger in the MSSM than in the SM [9],in particu-lar if the stop mass is smaller than the top mass [10].

At two-loop level stop-gluon graphs give a considerable strengthening of the EWPT (e.g.third and fourth paper of [9]).A reduced 3d version of the MSSM has recently been studied on the lattice [11](including SU(3)×SU(2)gauge ?elds,the right-handed stop and the “light”combi-nation of the Higgses).The results show that the EWPT can be strong enough,i.e.v/T c >1,up to m h ≈105GeV and m ?t ≈165GeV (where m h is the mass of the lightest neutral scalar and m ?t is that of the stop squark).The possibility of spontaneous CP violation for a successful baryogenesis is also addresed [12].

In this letter we study the EWPT in the MSSM on 4d lattices and carry out in?nite volume and contin-uum limit extrapolations.Except for the U(1)sector and scalars with small Yukawa couplings,the whole bosonic sector of the MSSM is kept:SU(3)and SU(2)gauge bosons,two Higgs doublets,left-handed and right-handed stops and sbottoms.As it has been done in the SM case [8],fermions,owing to their heavy Matsubara modes,are included perturbatively in the ?nal result.This work extends the 3d study [11]in two ways:

a)We use 4d lattices instead of 3d.Note,that due to very soft modes—close to the end point in the SM—much more CPU time is needed in 4d than in 3d.However,this di?culty does not appear in the MSSM because the phase transition is strong and the dominant correlation lengths

are not that large in units of T ?1

c .Using unimprove

d lattic

e actions the leading corrections due to the ?nite lattice spacings are proportional to a in 3d and only to a 2in 4d.For O(a )improvement in the 3d case cf.[13].In 4d simulations we also have direct control over zero temperature renormalization e?ects.

b)We include both Higgs doublets,not only the light combination.According to standard baryogenesis sce-narios (see e.g.[14])the generated baryon number is di-rectly proportional to the change of βthrough the bubble wall:?β.(tan β=v 2/v 1,where v 1,2are the expectation

1

FIG.1.The phase diagram of the bosonic theory obtained by lattice simulations.

values of the two Higgses.)

The continuum lagrangian of the above theory in stan-dard notation reads

L =L g +L k +L V +L sm +L Y +L w +L s .

(1)

The gauge part,L g =1/4·F (w )

μνF (w )μν+1/4·F (s )

μνF (s )μνis the sum of weak and strong terms.The kinetic part is the sum of the covariant derivative terms of the two Higgs doublets (H 1,H 2),the left-handed stop-sbottom doublet (Q ),and the right-handed stop,sbottom singlets (U,D ):

L k =(D (w )μH 1)?(D (w )μH 1)+(D (w )

μH 2)?(D (w )μH 2)+(D (ws )μQ )?(D (ws )μQ )+(D (s )μU ?)?(D (s )μU ?)+(D (s )μD ?)?

(D (s )μD ?).The potential term for the Higgs

?elds reads L V =m 212[α1|H 1|2+α2|H 2|2

?(H ?1?H 2+

h.c.)]+g 2

w /8·(|H 1|4+|H 2|4?2|H 1|2|H 2|2+4|H ?1H 2|2),for which two dimensionless mass terms are de?ned,

α1=m 21/m 212and α2=m 22/m 2

12.One gets L sm =

m 2Q |Q |2+m 2U |U |2+m 2D |D |2

for the squark mass part,

and L Y =h 2t (|QU |2+|H 2|2|U |2+|Q ??H 2|2

)for the dominant Yukawa part.The quartic parts contain-ing the squark ?elds read L w =g 2

w /8·[2{Q }4?

|Q |4+4|H ?1Q |2

+4|H ?2Q |2?2|H 1|2|Q |2?2|H 2|2|Q |2]and L s =g 2s /8· 3{Q }4?|Q |4+2|U |4+2|D |4?6|QU |2?6|QD |2+6|U ?D |2+2|Q |2|U |2+2|Q |2|D |2?2|U |2|D |2 ,

where {Q }4=Q ?iαQ ?

jβQ iβQ jα.The scalar trilinear cou-plings have been omitted for simplicity.It is straightfor-ward to obtain the lattice action,for which we used the standard Wilson plaquette,hopping and site terms.

The parameter space of the above Lagrangian is many-dimensional.We analyze the e?ect of the strong sector on the EWPT by using three speci?c sets of parame-ters.In one case the strong coupling has its physical value,whereas in the two other cases it is somewhat larger and smaller.The experimental values are taken for the weak and Yukawa couplings,and tan β=6is

used.For the bare soft breaking masses our choice is m Q,D =250GeV,m U =https://www.doczj.com/doc/e818624928.html,ttice renormalization e?ects on these masses will be discussed later.

The simulation techniques are similar to those of the SU(2)-Higgs model [5](overrelaxation and heatbath al-gorithms are used for each scalar and gauge ?eld);some new methods will be published elsewhere [15].The anal-ysis is based on ?nite temperature simulations (in which the temporal extension of the lattice L t is much smaller than the spatial extensions L x,y,z ),and zero tempera-ture ones (with L t ≈L x,y,z ).For a given L t ,we ?x all parameters of the Lagrangian except α2.We tune α2to the transition point,α2c ,where we determine the jump of the Higgs ?eld,the shape of the bubble wall,and the change of βthrough the phase https://www.doczj.com/doc/e818624928.html,ing α2c and the parameter set of the ?nite temperature case,we perform T =0simulations and determine the masses (Higgses and W)and couplings (weak and strong)there.Extrapolations to the continuum limit and to in?nite vol-umes are based on simulations at temporal extensions L t =2,3,4,5and at various lattice volumes for each L t ,respectively.Approaching the continuum limit,we move on an approximate line of constant physics (LCP),on which the renormalized quantities (masses and couplings)are almost constant,but the lattice spacing approaches zero.Our theory is bosonic,therefore the leading cor-rections due to ?nite lattice spacings are expected to be proportional to a 2.This lattice spacing dependence is as-sumed for physical quantities in a ?→0extrapolations.We compare our simulation results with perturbation theory.We used one-loop perturbation theory without applying high temperature expansion (HTE).A speci?c feature was a careful treatment of ?nite renormalization e?ects,by taking into account all renormalization correc-tions and adjusting them to match the measured T =0spectrum [15].We studied also the e?ect of the domi-nant T =0two-loop diagram (“setting-sun”stop-gluon graphs,cf.?fth ref.of [9]),but only in the HTE.We ob-served less dramatic enhancement of the strength of the phase transition due to two-loop e?ects than in [9].Since the infrared behavior of the setting-sun graphs is not un-derstood,we use the one-loop technique with the T =0scheme de?ned above.This type of one-loop perturba-tion theory is also applied to correct the measured data to some ?xed LCP quantities,which are de?ned as the averages of results at di?erent lattice spacings,(i.e.our reference point,for which the most important quantity is the lightest Higgs mass,m h ≈45GeV).Fig.1.shows the phase diagram in the m 2U –T plane.One identi?es three phases.The phase on the left (large negative m 2U and small stop mass)is the “color-breaking”(CB)phase.The phase in the upper right part is the “symmetric”phase,whereas the “Higgs”phase can be found in the lower right part.The line separating the symmetric and Higgs phases is obtained from L t =3simulations,whereas the lines between these phases and

2

FIG.2.The normalized and the critical temperature in the continuum limit.

the CB one are determined by keeping the lattice spac-ing?xed while increasing and decreasing the tempera-ture by changing L t to2and4,respectively.The shaded regions indicate the uncertainty in the critical tempera-tures.The phase transition to the CB phase is observed to be much stronger than that between the symmetric and Higgs phases.The qualitative features of this pic-ture are in complete agreement with perturbative and 3d lattice results[9–11];however,our choice of parame-ters does not correspond to a two-stage symmetric-Higgs phase transition.In this two-stage scenario there is a phase transition from the symmetric to the CB phase at some T1and another phase transition occurs at T2

The bare squark mass parameters m2Q,m2U,m2D re-ceive quadratic renormalization corrections.As it is well known,one-loop lattice perturbation theory is not su?-cient to reliably determine these corrections,thus we use the following method.We?rst determine the position of the non-perturbative CB phase transitions in the bare quantities(e.g.the triple point or the T=0transition for m2U in Fig.1).These quantities are compared with the prediction of the continuum perturbation theory,which gives the renormalized mass parameters on the lattice. Fig.2contains the continuum limit extrapolation for the normalized jump of the order parameter(v/T c:up-per data)and the critical temperature(T c/m W:lower data).The shaded regions are the perturbative predic-tions at our reference point(see above)in the contin-uum.Their widths re?ect the uncertainty of our refer-ence point,which is dominated by the error of m h.Note that v/T c is very sensitive to m h,which results in the large uncertainties.Results obtained on the lattice and in perturbation theory agree reasonably within the esti-

FIG.3.The cosmologically relevant v/T c>1region is below the lines.

mated uncertainties.(It might well be that the L t=2re-sults are not in the scaling region;leaving them out from the continuum extrapolation the agreement between the lattice and perturbative results is even better.)

Based on this agreement we use one-loop perturbation theory without HTE to determine cosmologically allowed regions in the m?t

R

vs.m h plane of the full MSSM(in-cluding fermions,m A=500GeV),see Fig. 3.The two lines for each m?t

L

(which intersect for lower val-ues of m?t

L

)correspond to upper bounds resulting from v n/T c=1(steeper curves,B1)and the T=0maximum MSSM Higgs mass(B2).v n is the non-perturbative Higgs expectation value,assumed to be larger than the pertur-bative one by14%,a correction factor obtained in the bosonic model(cf.Fig.2).For large m Q(e.g.600GeV, m?t

L

=630GeV)the region below B1is below B2.De-creasing m Q B2decreases and B1increases.At m Q=560 GeV(m?t

L

=590GeV)B1and B2intersect at the CB value of m?t

R

.Since B2is almost constant this yields the overall maximum Higgs mass for a successful baryogene-sis.For even smaller m Q(m?t

L

)both B1and B2are rel-evant.Note that the maximum Higgs mass corresponds to a?nite value of m Q≈560GeV,yielding m h=103±4 GeV(including also the uncertainties from Fig.2and the di?erence between the one and two-loop maximum Higgs mass calculations[17]).

In order to produce the observed baryon asymmetry,

a strong?rst order phase transition is not enough.Ac-

cording to standard MSSM baryogenesis scenarios[14] the generated baryon asymmetry is directly proportional to the variation ofβthrough the bubble wall separating the Higgs and symmetric phases.By using elongated lat-tice(2·L2·192),L=8,12,16at the transition point we study the properties of the wall.In our simulation pro-cedure we restrict the length of one of the Higgs?elds to a small interval between its values in the bulk phases.

As a consequence,the system?uctuates around a con-3

FIG.4.The pro?le of the wall for both of the Higgs ?elds for the lattice2·L2˙192.

?guration with two bulk phases and two walls between them.In order to have the smallest possible free en-ergy,the wall is perpendicular to the long direction.We eliminate the e?ect of the remaining zero mode by shift-ing the wall of each con?guration to some?xed position. Fig.4gives the bubble wall pro?les for both Higgs?elds. The measured width of the wall is[A+B·log(aLT c)]/T c A=10.8±.1and B=2.1±.1.This behavior indicates that the bubble wall is rough and without a pinning force of ?nite size its width diverges very slowly(logarithmically) [18].For the same bosonic theory the perturbative ap-proach predicts(11.2±1.5)/T c for the width. Transforming the data of Fig.4to|H2|2as a function of|H1|2,we obtain?β=0.0061±0.0003.The pertur-bative prediction at this point is0.0046±0.0010.Thus perturbative studies such as[19]are con?rmed by non-perturbative results.

To summarize,we presented4d lattice results on the EWPT in the MSSM.Our simulations were carried out in the bosonic sector of the MSSM.We found quite a good agreement between lattice results and our one-loop perturbative https://www.doczj.com/doc/e818624928.html,ing this agreement together with a careful analysis of its uncertainties,we determined the upper bound for the lightest Higgs mass for a success-ful baryogenesis in the full(bosonic+fermionic)MSSM, which turned out to be(103±4GeV)consistent with the3d analysis(≈105GeV).We analyzed the bubble wall pro?le separating the Higgs and symmetric phases. The width of the wall and the change inβis in fairly good agreement with perturbative predictions for typi-cal bubble sizes.Both the upper bound for m h and the smallness of?βindicate that experiments allow just a small window for MSSM baryogenesis.

Details of the present analysis will be discussed in a forthcoming publication[15].

This work was partially supported by Hungar-ian Science Foundation Grants OTKA-T22929-29803-M28413/FKFP-0128/1997.The simulations were carried out on the46G PC-farm at E¨o tv¨o s University.

The way常见用法

The way 的用法 Ⅰ常见用法: 1)the way+ that 2)the way + in which(最为正式的用法) 3)the way + 省略(最为自然的用法) 举例:I like the way in which he talks. I like the way that he talks. I like the way he talks. Ⅱ习惯用法: 在当代美国英语中,the way用作为副词的对格,“the way+ 从句”实际上相当于一个状语从句来修饰整个句子。 1)The way =as I am talking to you just the way I’d talk to my own child. He did not do it the way his friends did. Most fruits are naturally sweet and we can eat them just the way they are—all we have to do is to clean and peel them. 2)The way= according to the way/ judging from the way The way you answer the question, you are an excellent student. The way most people look at you, you’d think trash man is a monster. 3)The way =how/ how much No one can imagine the way he missed her. 4)The way =because

The way的用法及其含义(二)

The way的用法及其含义(二) 二、the way在句中的语法作用 the way在句中可以作主语、宾语或表语: 1.作主语 The way you are doing it is completely crazy.你这个干法简直发疯。 The way she puts on that accent really irritates me. 她故意操那种口音的样子实在令我恼火。The way she behaved towards him was utterly ruthless. 她对待他真是无情至极。 Words are important, but the way a person stands, folds his or her arms or moves his or her hands can also give us information about his or her feelings. 言语固然重要,但人的站姿,抱臂的方式和手势也回告诉我们他(她)的情感。 2.作宾语 I hate the way she stared at me.我讨厌她盯我看的样子。 We like the way that her hair hangs down.我们喜欢她的头发笔直地垂下来。 You could tell she was foreign by the way she was dressed. 从她的穿著就可以看出她是外国人。 She could not hide her amusement at the way he was dancing. 她见他跳舞的姿势,忍俊不禁。 3.作表语 This is the way the accident happened.这就是事故如何发生的。 Believe it or not, that's the way it is. 信不信由你, 反正事情就是这样。 That's the way I look at it, too. 我也是这么想。 That was the way minority nationalities were treated in old China. 那就是少数民族在旧中

(完整版)the的用法

定冠词the的用法: 定冠词the与指示代词this ,that同源,有“那(这)个”的意思,但较弱,可以和一个名词连用,来表示某个或某些特定的人或东西. (1)特指双方都明白的人或物 Take the medicine.把药吃了. (2)上文提到过的人或事 He bought a house.他买了幢房子. I've been to the house.我去过那幢房子. (3)指世界上独一无二的事物 the sun ,the sky ,the moon, the earth (4)单数名词连用表示一类事物 the dollar 美元 the fox 狐狸 或与形容词或分词连用,表示一类人 the rich 富人 the living 生者 (5)用在序数词和形容词最高级,及形容词等前面 Where do you live?你住在哪? I live on the second floor.我住在二楼. That's the very thing I've been looking for.那正是我要找的东西. (6)与复数名词连用,指整个群体 They are the teachers of this school.(指全体教师) They are teachers of this school.(指部分教师) (7)表示所有,相当于物主代词,用在表示身体部位的名词前 She caught me by the arm.她抓住了我的手臂. (8)用在某些有普通名词构成的国家名称,机关团体,阶级等专有名词前 the People's Republic of China 中华人民共和国 the United States 美国 (9)用在表示乐器的名词前 She plays the piano.她会弹钢琴. (10)用在姓氏的复数名词之前,表示一家人 the Greens 格林一家人(或格林夫妇) (11)用在惯用语中 in the day, in the morning... the day before yesterday, the next morning... in the sky... in the dark... in the end... on the whole, by the way...

“the way+从句”结构的意义及用法

“theway+从句”结构的意义及用法 首先让我们来看下面这个句子: Read the followingpassageand talkabout it wi th your classmates.Try totell whatyou think of Tom and ofthe way the childrentreated him. 在这个句子中,the way是先行词,后面是省略了关系副词that或in which的定语从句。 下面我们将叙述“the way+从句”结构的用法。 1.the way之后,引导定语从句的关系词是that而不是how,因此,<<现代英语惯用法词典>>中所给出的下面两个句子是错误的:This is thewayhowithappened. This is the way how he always treats me. 2.在正式语体中,that可被in which所代替;在非正式语体中,that则往往省略。由此我们得到theway后接定语从句时的三种模式:1) the way+that-从句2)the way +in which-从句3) the way +从句 例如:The way(in which ,that) thesecomrade slookatproblems is wrong.这些同志看问题的方法

不对。 Theway(that ,in which)you’re doingit is comple tely crazy.你这么个干法,简直发疯。 Weadmired him for theway inwhich he facesdifficulties. Wallace and Darwingreed on the way inwhi ch different forms of life had begun.华莱士和达尔文对不同类型的生物是如何起源的持相同的观点。 This is the way(that) hedid it. I likedthe way(that) sheorganized the meeting. 3.theway(that)有时可以与how(作“如何”解)通用。例如: That’s the way(that) shespoke. = That’s how shespoke.

way 用法

表示“方式”、“方法”,注意以下用法: 1.表示用某种方法或按某种方式,通常用介词in(此介词有时可省略)。如: Do it (in) your own way. 按你自己的方法做吧。 Please do not talk (in) that way. 请不要那样说。 2.表示做某事的方式或方法,其后可接不定式或of doing sth。 如: It’s the best way of studying [to study] English. 这是学习英语的最好方法。 There are different ways to do [of doing] it. 做这事有不同的办法。 3.其后通常可直接跟一个定语从句(不用任何引导词),也可跟由that 或in which 引导的定语从句,但是其后的从句不能由how 来引导。如: 我不喜欢他说话的态度。 正:I don’t like the way he spoke. 正:I don’t like the way that he spoke. 正:I don’t like the way in which he spoke. 误:I don’t like the way how he spoke. 4.注意以下各句the way 的用法: That’s the way (=how) he spoke. 那就是他说话的方式。 Nobody else loves you the way(=as) I do. 没有人像我这样爱你。 The way (=According as) you are studying now, you won’tmake much progress. 根据你现在学习情况来看,你不会有多大的进步。 2007年陕西省高考英语中有这样一道单项填空题: ——I think he is taking an active part insocial work. ——I agree with you_____. A、in a way B、on the way C、by the way D、in the way 此题答案选A。要想弄清为什么选A,而不选其他几项,则要弄清选项中含way的四个短语的不同意义和用法,下面我们就对此作一归纳和小结。 一、in a way的用法 表示:在一定程度上,从某方面说。如: In a way he was right.在某种程度上他是对的。注:in a way也可说成in one way。 二、on the way的用法 1、表示:即将来(去),就要来(去)。如: Spring is on the way.春天快到了。 I'd better be on my way soon.我最好还是快点儿走。 Radio forecasts said a sixth-grade wind was on the way.无线电预报说将有六级大风。 2、表示:在路上,在行进中。如: He stopped for breakfast on the way.他中途停下吃早点。 We had some good laughs on the way.我们在路上好好笑了一阵子。 3、表示:(婴儿)尚未出生。如: She has two children with another one on the way.她有两个孩子,现在还怀着一个。 She's got five children,and another one is on the way.她已经有5个孩子了,另一个又快生了。 三、by the way的用法

The way的用法及其含义(一)

The way的用法及其含义(一) 有这样一个句子:In 1770 the room was completed the way she wanted. 1770年,这间琥珀屋按照她的要求完成了。 the way在句中的语法作用是什么?其意义如何?在阅读时,学生经常会碰到一些含有the way 的句子,如:No one knows the way he invented the machine. He did not do the experiment the way his teacher told him.等等。他们对the way 的用法和含义比较模糊。在这几个句子中,the way之后的部分都是定语从句。第一句的意思是,“没人知道他是怎样发明这台机器的。”the way的意思相当于how;第二句的意思是,“他没有按照老师说的那样做实验。”the way 的意思相当于as。在In 1770 the room was completed the way she wanted.这句话中,the way也是as的含义。随着现代英语的发展,the way的用法已越来越普遍了。下面,我们从the way的语法作用和意义等方面做一考查和分析: 一、the way作先行词,后接定语从句 以下3种表达都是正确的。例如:“我喜欢她笑的样子。” 1. the way+ in which +从句 I like the way in which she smiles. 2. the way+ that +从句 I like the way that she smiles. 3. the way + 从句(省略了in which或that) I like the way she smiles. 又如:“火灾如何发生的,有好几种说法。” 1. There were several theories about the way in which the fire started. 2. There were several theories about the way that the fire started.

way 的用法

way 的用法 【语境展示】 1. Now I’ll show you how to do the experiment in a different way. 下面我来演示如何用一种不同的方法做这个实验。 2. The teacher had a strange way to make his classes lively and interesting. 这位老师有种奇怪的办法让他的课生动有趣。 3. Can you tell me the best way of working out this problem? 你能告诉我算出这道题的最好方法吗? 4. I don’t know the way (that / in which) he helped her out. 我不知道他用什么方法帮助她摆脱困境的。 5. The way (that / which) he talked about to solve the problem was difficult to understand. 他所谈到的解决这个问题的方法难以理解。 6. I don’t like the way that / which is being widely used for saving water. 我不喜欢这种正在被广泛使用的节水方法。 7. They did not do it the way we do now. 他们以前的做法和我们现在不一样。 【归纳总结】 ●way作“方法,方式”讲时,如表示“以……方式”,前面常加介词in。如例1; ●way作“方法,方式”讲时,其后可接不定式to do sth.,也可接of doing sth. 作定语,表示做某事的方法。如例2,例3;

the-way-的用法讲解学习

t h e-w a y-的用法

The way 的用法 "the way+从句"结构在英语教科书中出现的频率较高, the way 是先行词, 其后是定语从句.它有三种表达形式:1) the way+that 2)the way+ in which 3)the way + 从句(省略了that或in which),在通常情况下, 用in which 引导的定语从句最为正式,用that的次之,而省略了关系代词that 或 in which 的, 反而显得更自然,最为常用.如下面三句话所示,其意义相同. I like the way in which he talks. I like the way that he talks. I like the way he talks. 一.在当代美国英语中,the way用作为副词的对格,"the way+从句"实际上相当于一个状语从句来修饰全句. the way=as 1)I'm talking to you just the way I'd talk to a boy of my own. 我和你说话就象和自己孩子说话一样. 2)He did not do it the way his friend did. 他没有象他朋友那样去做此事. 3)Most fruits are naturally sweet and we can eat them just the way they are ----all we have to do is clean or peel them . 大部分水果天然甜润,可以直接食用,我们只需要把他们清洗一下或去皮.

way的用法总结大全

way的用法总结大全 way的用法你知道多少,今天给大家带来way的用法,希望能够帮助到大家,下面就和大家分享,来欣赏一下吧。 way的用法总结大全 way的意思 n. 道路,方法,方向,某方面 adv. 远远地,大大地 way用法 way可以用作名词 way的基本意思是“路,道,街,径”,一般用来指具体的“路,道路”,也可指通向某地的“方向”“路线”或做某事所采用的手段,即“方式,方法”。way还可指“习俗,作风”“距离”“附近,周围”“某方面”等。 way作“方法,方式,手段”解时,前面常加介词in。如果way前有this, that等限定词,介词可省略,但如果放在句首,介词则不可省略。

way作“方式,方法”解时,其后可接of v -ing或to- v 作定语,也可接定语从句,引导从句的关系代词或关系副词常可省略。 way用作名词的用法例句 I am on my way to the grocery store.我正在去杂货店的路上。 We lost the way in the dark.我们在黑夜中迷路了。 He asked me the way to London.他问我去伦敦的路。 way可以用作副词 way用作副词时意思是“远远地,大大地”,通常指在程度或距离上有一定的差距。 way back表示“很久以前”。 way用作副词的用法例句 It seems like Im always way too busy with work.我工作总是太忙了。 His ideas were way ahead of his time.他的思想远远超越了他那个时代。 She finished the race way ahead of the other runners.她第一个跑到终点,远远领先于其他选手。 way用法例句

the_way的用法大全教案资料

t h e_w a y的用法大全

The way 在the way+从句中, the way 是先行词, 其后是定语从句.它有三种表达形式:1) the way+that 2)the way+ in which 3)the way + 从句(省略了that或in which),在通常情况下, 用in which 引导的定语从句最为正式,用that的次之,而省略了关系代词that 或 in which 的, 反而显得更自然,最为常用.如下面三句话所示,其意义相同. I like the way in which he talks. I like the way that he talks. I like the way he talks. 如果怕弄混淆,下面的可以不看了 另外,在当代美国英语中,the way用作为副词的对格,"the way+从句"实际上相当于一个状语从句来修饰全句. the way=as 1)I'm talking to you just the way I'd talk to a boy of my own. 我和你说话就象和自己孩子说话一样. 2)He did not do it the way his friend did. 他没有象他朋友那样去做此事. 3)Most fruits are naturally sweet and we can eat them just the way they are ----all we have to do is clean or peel them . 大部分水果天然甜润,可以直接食用,我们只需要把他们清洗一下或去皮. the way=according to the way/judging from the way 4)The way you answer the qquestions, you must be an excellent student. 从你回答就知道,你是一个优秀的学生. 5)The way most people look at you, you'd think a trashman was a monster. 从大多数人看你的目光中,你就知道垃圾工在他们眼里是怪物. the way=how/how much 6)I know where you are from by the way you pronounce my name. 从你叫我名字的音调中,我知道你哪里人. 7)No one can imaine the way he misses her. 人们很想想象他是多么想念她. the way=because 8) No wonder that girls looks down upon me, the way you encourage her. 难怪那姑娘看不起我, 原来是你怂恿的

the way 的用法

The way 的用法 "the way+从句"结构在英语教科书中出现的频率较高, the way 是先行词, 其后是定语从句.它有三种表达形式:1) the way+that 2)the way+ in which 3)the way + 从句(省略了that或in which),在通常情况下, 用in which 引导的定语从句最为正式,用that的次之,而省略了关系代词that 或in which 的, 反而显得更自然,最为常用.如下面三句话所示,其意义相同. I like the way in which he talks. I like the way that he talks. I like the way he talks. 一.在当代美国英语中,the way用作为副词的对格,"the way+从句"实际上相当于一个状语从句来修饰全句. the way=as 1)I'm talking to you just the way I'd talk to a boy of my own. 我和你说话就象和自己孩子说话一样. 2)He did not do it the way his friend did. 他没有象他朋友那样去做此事. 3)Most fruits are naturally sweet and we can eat them just the way they are ----all we have to do is clean or peel them . 大部分水果天然甜润,可以直接食用,我们只需要把他们清洗一下或去皮.

the way=according to the way/judging from the way 4)The way you answer the qquestions, you must be an excellent student. 从你回答就知道,你是一个优秀的学生. 5)The way most people look at you, you'd think a trashman was a monster. 从大多数人看你的目光中,你就知道垃圾工在他们眼里是怪物. the way=how/how much 6)I know where you are from by the way you pronounce my name. 从你叫我名字的音调中,我知道你哪里人. 7)No one can imaine the way he misses her. 人们很想想象他是多么想念她. the way=because 8) No wonder that girls looks down upon me, the way you encourage her. 难怪那姑娘看不起我, 原来是你怂恿的 the way =while/when(表示对比) 9)From that day on, they walked into the classroom carrying defeat on their shoulders the way other students carried textbooks under their arms. 从那天起,其他同学是夹着书本来上课,而他们却带着"失败"的思想负担来上课.

The way的用法及其含义(三)

The way的用法及其含义(三) 三、the way的语义 1. the way=as(像) Please do it the way I’ve told you.请按照我告诉你的那样做。 I'm talking to you just the way I'd talk to a boy of my own.我和你说话就像和自己孩子说话一样。 Plant need water the way they need sun light. 植物需要水就像它们需要阳光一样。 2. the way=how(怎样,多么) No one can imagine the way he misses her.没人能够想象出他是多么想念她! I want to find out the way a volcano has formed.我想弄清楚火山是怎样形成的。 He was filled with anger at the way he had been treated.他因遭受如此待遇而怒火满腔。That’s the way she speaks.她就是那样讲话的。 3. the way=according as (根据) The way you answer the questions, you must be an excellent student.从你回答问题来看,你一定是名优秀的学生。 The way most people look at you, you'd think a trash man was a monster.从大多数人看你的目光中,你就知道垃圾工在他们眼里是怪物。 The way I look at it, it’s not what you do that matters so much.依我看,重要的并不是你做什么。 I might have been his son the way he talked.根据他说话的样子,好像我是他的儿子一样。One would think these men owned the earth the way they behave.他们这样行动,人家竟会以为他们是地球的主人。

way的用法

一.Way:“方式”、“方法” 1.表示用某种方法或按某种方式 Do it (in) your own way. Please do not talk (in) that way. 2.表示做某事的方式或方法 It’s the best way of studying [to study] English.。 There are different ways to do [of doing] it. 3.其后通常可直接跟一个定语从句(不用任何引导词),也可跟由that 或in which 引导的定语从句 正:I don’t like the way he spoke. I don’t like the way that he spoke. I don’t like the way in which he spoke.误:I don’t like the way how he spoke. 4. the way 的从句 That’s the way (=how) he spoke. I know where you are from by the way you pronounce my name. That was the way minority nationalities were treated in old China. Nobody else loves you the way(=as) I do. He did not do it the way his friend did. 二.固定搭配 1. In a/one way:In a way he was right. 2. In the way /get in one’s way I'm afraid your car is in the way, If you are not going to help,at least don't get in the way. You'll have to move-you're in my way. 3. in no way Theory can in no way be separated from practice. 4. On the way (to……) Let’s wait a few moments. He is on the way Spring is on the way. Radio forecasts said a sixth-grade wind was on the way. She has two children with another one on the way. 5. By the way By the way,do you know where Mary lives? 6. By way of Learn English by way of watching US TV series. 8. under way 1. Elbow one’s way He elbowed his way to the front of the queue. 2. shoulder one’s way 3. feel one‘s way 摸索着向前走;We couldn’t see anything in the cave, so we had to feel our way out 4. fight/force one’s way 突破。。。而前进The surrounded soldiers fought their way out. 5.. push/thrust one‘s way(在人群中)挤出一条路He pushed his way through the crowd. 6. wind one’s way 蜿蜒前进 7. lead the way 带路,领路;示范 8. lose one‘s way 迷失方向 9. clear the way 排除障碍,开路迷路 10. make one’s way 前进,行进The team slowly made their way through the jungle.

the way的用法大全

在the way+从句中, the way 是先行词, 其后是定语从句.它有三种表达形式:1) the way+that 2)the way+ in which 3)the way + 从句(省略了that或in which),在通常情况下, 用in which 引导的定语从句最为正式,用that的次之,而省略了关系代词that 或in which 的, 反而显得更自然,最为常用.如下面三句话所示,其意义相同. I like the way in which he talks. I like the way that he talks. I like the way he talks. 如果怕弄混淆,下面的可以不看了 另外,在当代美国英语中,the way用作为副词的对格,"the way+从句"实际上相当于一个状语从句来修饰全句. the way=as 1)I'm talking to you just the way I'd talk to a boy of my own. 我和你说话就象和自己孩子说话一样. 2)He did not do it the way his friend did. 他没有象他朋友那样去做此事. 3)Most fruits are naturally sweet and we can eat them just the way they are ----all we have to do is clean or peel them . 大部分水果天然甜润,可以直接食用,我们只需要把他们清洗一下或去皮. the way=according to the way/judging from the way 4)The way you answer the qquestions, you must be an excellent student. 从你回答就知道,你是一个优秀的学生. 5)The way most people look at you, you'd think a trashman was a monster. 从大多数人看你的目光中,你就知道垃圾工在他们眼里是怪物. the way=how/how much 6)I know where you are from by the way you pronounce my name. 从你叫我名字的音调中,我知道你哪里人. 7)No one can imaine the way he misses her. 人们很想想象他是多么想念她. the way=because 8) No wonder that girls looks down upon me, the way you encourage her. 难怪那姑娘看不起我, 原来是你怂恿的 the way =while/when(表示对比) 9)From that day on, they walked into the classroom carrying defeat on their shoulders the way other students carried textbooks under their arms.

“the-way+从句”结构的意义及用法知识讲解

“the way+从句”结构的意义及用法 首先让我们来看下面这个句子: Read the following passage and talk about it with your classmates. Try to tell what you think of Tom and of the way the children treated him. 在这个句子中,the way是先行词,后面是省略了关系副词that 或in which的定语从句。 下面我们将叙述“the way+从句”结构的用法。 1.the way之后,引导定语从句的关系词是that而不是how,因此,<<现代英语惯用法词典>>中所给出的下面两个句子是错误的:This is the way how it happened. This is the way how he always treats me. 2. 在正式语体中,that可被in which所代替;在非正式语体中,that则往往省略。由此我们得到the way后接定语从句时的三种模式:1) the way +that-从句2) the way +in which-从句3) the way +从句 例如:The way(in which ,that) these comrades look at problems is wrong.这些同志看问题的方法不对。

The way(that ,in which)you’re doing it is completely crazy.你这么个干法,简直发疯。 We admired him for the way in which he faces difficulties. Wallace and Darwin greed on the way in which different forms of life had begun.华莱士和达尔文对不同类型的生物是如何起源的持相同的观点。 This is the way (that) he did it. I liked the way (that) she organized the meeting. 3.the way(that)有时可以与how(作“如何”解)通用。例如: That’s the way (that) she spoke. = That’s how she spoke. I should like to know the way/how you learned to master the fundamental technique within so short a time. 4.the way的其它用法:以上我们讲的都是用作先行词的the way,下面我们将叙述它的一些用法。

定冠词the的12种用法

定冠词the的12种用法 定冠词the 的12 种用法,全知道?快来一起学习吧。下面就和大家分享,来欣赏一下吧。 定冠词the 的12 种用法,全知道? 定冠词the用在各种名词前面,目的是对这个名词做个记号,表示它的特指属性。所以在词汇表中,定冠词the 的词义是“这个,那个,这些,那些”,可见,the 即可以放在可数名词前,也可以修饰不可数名词,the 后面的名词可以是单数,也可以是复数。 定冠词的基本用法: (1) 表示对某人、某物进行特指,所谓的特指就是“不是别的,就是那个!”如: The girl with a red cap is Susan. 戴了个红帽子的女孩是苏珊。 (2) 一旦用到the,表示谈话的俩人都知道说的谁、说的啥。如:

The dog is sick. 狗狗病了。(双方都知道是哪一只狗) (3) 前面提到过的,后文又提到。如: There is a cat in the tree.Thecat is black. 树上有一只猫,猫是黑色的。 (4) 表示世界上唯一的事物。如: The Great Wall is a wonder.万里长城是个奇迹。(5) 方位名词前。如: thenorth of the Yangtze River 长江以北地区 (6) 在序数词和形容词最高级的前面。如: Who is the first?谁第一个? Sam is the tallest.山姆最高。 但是不能认为,最高级前必须加the,如: My best friend. 我最好的朋友。 (7) 在乐器前。如: play the flute 吹笛子

Way的用法

Way用法 A:I think you should phone Jenny and say sorry to her. B:_______. It was her fault. A. No way B. Not possible C. No chance D. Not at all 说明:正确答案是A. No way,意思是“别想!没门!决不!” 我认为你应该打电话给珍妮并向她道歉。 没门!这是她的错。 再看两个关于no way的例句: (1)Give up our tea break? NO way! 让我们放弃喝茶的休息时间?没门儿! (2)No way will I go on working for that boss. 我决不再给那个老板干了。 way一词含义丰富,由它构成的短语用法也很灵活。为了便于同学们掌握和用好它,现结合实例将其用法归纳如下: 一、way的含义 1. 路线

He asked me the way to London. 他问我去伦敦的路。 We had to pick our way along the muddy track. 我们不得不在泥泞的小道上择路而行。 2. (沿某)方向 Look this way, please. 请往这边看。 Kindly step this way, ladies and gentlemen. 女士们、先生们,请这边走。 Look both ways before crossing the road. 过马路前向两边看一看。 Make sure that the sign is right way up. 一定要把符号的上下弄对。 3. 道、路、街,常用以构成复合词 a highway(公路),a waterway(水路),a railway(铁路),wayside(路边)

way与time的特殊用法

way/time的特殊用法 1、当先行词是way意思为”方式.方法”的时候,引导定语从句的关系词有下列3种形式: Way在从句中做宾语 The way that / which he explained to us is quite simple. Way在从句中做状语 The way t hat /in which he explained the sentence to us is quite simple. 2、当先行词是time时,若time表示次数时,应用关系代词that引导定语从句,that可以省略; 若time表示”一段时间”讲时,应用关系副词when或介词at/during + which引导定语从句 1.Is this factory _______ we visited last year? 2.Is this the factory-------we visited last year? A. where B in which C the one D which 3. This is the last time _________ I shall give you a lesson. A. when B that C which D in which 4.I don’t like the way ________ you laugh at her. A . that B on which C which D as 5.He didn’t understand the wa y ________ I worked out the problem. A which B in which C where D what 6.I could hardly remember how many times----I’ve failed. A that B which C in which D when 7.This is the second time--------the president has visited the country. A which B where C that D in which 8.This was at a time------there were no televisions, no computers or radios. A what B when C which D that

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