V_us From Hadronin Tau Decays

a r X i v :h e p -p h /0004257v 1 27 A p r 2000Theoretical Physics InstituteUniversity of MinnesotaTPI-MINN-00/17UMN-TH-1851-00April 2000Inclusive weak decay rates of heavy hadrons M.B.Voloshin Theoretical Physics Institute,University of Minnesota,Minneapolis,MN 55455and Institute of Theoretical and Experimental Physics,Moscow,117259Expanded version of a contribution to the final report book of the Fermilab Workshop on B Physics at Tevatron Abstract A compact review of the theory,including some recent developments,of inclusive weak decay rates of charmed and b hadrons with an emphasis on predictions that can be tested in the forthcoming experiments.1IntroductionThe dominant weak decays of hadrons containing a heavy quark,c or b,are caused by the decay of the heavy quark.In the limit of a very large mass m Q of a heavy quark Q the parton picture of the hadron decay should set in,where the inclusive decay rates of hadrons, containing Q,mesons(Q¯q)and baryons(Qqq),are all the same and equal to the inclusive decay rateΓparton(Q)of the heavy quark.Yet,the known inclusive decay rates[1]are conspicuously different for different hadrons,especially for charmed hadrons,whose lifetimes span a range of more than one order of magnitude from the shortestτ(Ωc)=0.064±0.020 ps to the longestτ(D+)=1.057±0.015ps,while the differences of lifetime among b hadrons are substantially smaller.The relation between the relative lifetime differences for charmed and b hadrons reflects the fact that the dependence of the inclusive decay rates on the light quark-gluon‘environment’in a particular hadron is a pre-asymptotic effect in the parameter m Q,which effect vanishes as an inverse power of m Q at large mass.A theoretical framework for systematic description of the leading at m Q→∞term in the inclusive decay rateΓparton(Q)∝m5Q as well as of the terms relatively suppressed by inverse powers of m Q is provided[2,3,4]by the operator product expansion(OPE)in m−1Q. Existing theoretical predictions for inclusive weak decay rates are in a reasonable agreement, within the expected range of uncertainty,with the data on lifetimes of charmed particles and with the so far available data on decays ofB mesons.The only outstanding piece of present experimental data is on the lifetime of theΛb baryon:τ(Λb)/τ(B d)≈0.8,for which ratio a theoretical prediction,given all the uncertainty involved,is unlikely to produce a number lower than0.9.The number of available predictions for inclusive decay rates of charmed and b hadrons is sufficiently large for future experimental studies tofirmly establish the validity status of the OPE based theory of heavy hadron decays,and,in particular,tofind out whether the present contradiction between the theory and the data onτ(Λb)/τ(B d)is a temporary difficulty,or an evidence of fundamentalflaws in theoretical understanding.It is a matter of common knowledge that application of OPE to decays of charmed and b hadrons has potentially two caveats.One is that the OPE is used in the Minkowsky kinematical domain,and therefore relies on the assumption of quark-hadron duality at the energies involved in the corresponding decays.In other words,it is assumed that sufficiently many exclusive hadronic channels contribute to the inclusive rate,so that the accidentals of the low-energy resonance structure do not affect the total rates of the inclusive processes. Theoretical attempts at understanding the onset of the quark-hadron duality are so farlimited to model estimates[5,6],not yet suitable for direct quantitative evaluation of possible deviation from duality in charm and b decays.This point presents the most fundamental uncertainty of the OPE based approach,and presently can only be clarified by confronting theoretical predictions with experimental data.The second possible caveat in applying the OPE technique to inclusive charm decays is that the mass of the charm quark,m c,may be insufficiently large for significant suppression of higher terms of the expansion in m−1c. The relative lightness of the charm quark,however,accounts for a qualitative,and even semi-quantitative,agreement of the OPE based predictions with the observed large spread of the lifetimes of charmed hadrons:the nonperturbative effects,formally suppressed by m−2c and m−3c are comparable with the‘leading’parton term and describe the hierarchy of the lifetimes.Another uncertainty of a technical nature arises from poor knowledge of matrix elements of certain quark operators over hadron,arising as terms in OPE.These can be estimated within theoretical models,with inevitable ensuing model dependence,or,where possible, extracted from the experimental data.With these reservations spelled out,we discuss here the OPE based description of inclusive weak decays of charm and b hadrons,with emphasis on specific experimentally testable predictions,and on the measurements,which would less rely on model dependence of the estimates of the matrix elements,thus allowing to probe the OPE predictions at a fundamental level.2OPE for inclusive weak decay ratesThe optical theorem of the scattering theory relates the total decay rateΓH of a hadron H Q containing a heavy quark Q to the imaginary part of the‘forward scattering amplitude’.For the case of weak decays the latter amplitude is described by the following effective operatorL eff=2Im i d4x e iqx T{L W(x),L W(0)} ,(1) in terms of which the total decay rate is given by1ΓH= H Q|L eff|H Q .(2) The correlator in equation(1)in general is a non-local operator.However at q2=m2Q the dominating space-time intervals in the integral are of order m−1Q and one can expand thecorrelator in x ,thus producing an expansion in inverse powers of m Q .The leading term in this expansion describes the parton decay rate of the quark.For instance,the term in the non-leptonic weak Lagrangian √q 1L γµQ L )(64π3ηnlq 3,due to the relation H Q |64π3 64π3 4π i c (3)i (Q Γ′i Q ),(4)where the superscripts denote the power of m −1Q in the relative suppression of the correspond-ing term in the expansion with respect to the leading one,G µνis the gluon field tensor,q i stand for light quarks,u,d,s ,and,finally,Γi ,Γ′i denote spin and color structures of the four-quark operators.The coefficients c (a )depend on the specific part of the weak interaction Lagrangian L W ,describing the relevant underlying quark process.One can notice the absence in the expansion (4)of a term suppressed by just one power of m −1Q ,due to non-existence of operators of suitable dimension.Thus the decay rates receiveno correction of relative order m −1Q in the limit of large m Q ,and the first pre-asymptoticcorrections appear only in the order m −2Q .The mechanisms giving rise to the three discussed terms in OPE are shown in Figure 1.The first,leading term corresponds to the parton decay,and does not depend on the light guark and gluon ‘environment’of the heavy quark in a hadron.The second term describes the effect on the decay rate of the gluon field that a heavy quark ‘sees’in a hadron.This term in fact is sensitive only to the chromomagnetic part of the gluon field,and contains the operator of the interaction of heavy quark chromomagnetic moment with the chromomagnetic field.Thus this term depends on the spin of the heavy quark,but does not depend on theflavors of the light quarks or antiquarks.Therefore this effect does not split the inclusive decay rates withinflavor SU(3)multiplets of heavy hadrons,but generally gives difference of the rates, say,between mesons and baryons.The dependence on the light quarkflavor arises from the third term in the expansion(4)which explicitly contains light quarkfields.Historically, this part is interpreted in terms of two mechanisms[2,8,9]:the weak scattering(WS)and the Pauli interference(PI).The WS corresponds to a cross-channel of the underlying decay, generically Q→q1q2q1,weak-scatters(annihilates)in the process q3.The Pauli interference effect arises when one of thefinal(anti)quarks in the decay of Q is identical to the spectator(anti)quark in the hadron,so that an interference of identical particles should be taken into account.The latter interference can be either constructive or destructive,depending on the relative spin-color arrangement of the(anti)quark produced in the decay and of the spectator one,thus the sign of the PI effect is found only as a result of specific dynamical calculation.In specific calculations,however,WS and PI arise from the same terms in OPE,depending on the hadron discussed,and technically there is no need to resort to the traditional terminology of WS and PI.q3q3--Q QQ QP P PPq qm5Q(Q( σ· B)Q m2Q(QΓ′Q)vvvFigure1:Graphs for threefirst terms in OPE for inclusive decay rates:the parton term, the chromomagnetic interaction,and the four-quark term.In what follows we discuss separately the effects of the three terms in the expansion(4) and their interpretation within the existing and future data.3The parton decay rateThe leading term in the OPE amounts to the perturbative expression for the decay rate of a heavy quark.In b hadrons the contribution of the subsequent terms in OPE is at the level of few percent,so that the perturbative part can be confronted with the data in its own right. In particular,for the B d meson the higher terms in OPE contribute only about1%of the total non-leptonic as well as of the semileptonic decay rate.Thus the data on these rates can be directly compared with the leading perturbative term in OPE.The principal theoretical topic,associated with this term is the calculation of QCD radiative corrections,i.e.of the factorηnl in eq.(3)and of a similar factor,ηnl,for semileptonic decays.It should be noted,that even at this,perturbative,level there is a known long-standing problem between the existing data and the theory in that the current world average for the semileptonic branching ratio for the B mesons,B sl(B)=10.45±0.21%,is somewhat lower than the value B sl(B)≥11.5preferred from the present knowledge of theoretical QCD radiative corrections to the ratio of non-leptonic to semileptonic decay rates(see e.g.[10]). However,this apparent discrepancy may in fact be due to insufficient‘depth’of perturbative QCD calculation of the ratioηnl/ηsl.In order to briefly elaborate on this point,we notice that the standard way of analyzing the perturbative radiative corrections in the nonleptonic decays is through the renormalization group(RG)summation of the leading log terms and the first next-to-leading terms[11,12]in the parameter L≡ln(m W/m b).For the semileptonic decays the logarithmic dependence on m W/m b is absent in all orders due to the weak current conservation at momenta larger than m b,thus the correction is calculated by the standard perturbative technique,and a complete expression in thefirst order inαs is available both for the total rate[13,14]and for the lepton spectrum[15].In reality however the parameter L≈2.8is not large,and non-logarithmic terms may well compete with the logarithmic ones. This behavior is already seen from the known expression for the logarithmic terms:when expanded up to the orderα2s the result of Ref.[16]for the rate of decays with singlefinal charmed quark takes the formΓ(b→c¯u d)+Γ(b→c¯u s)π+α2s6+2c(a)is known explicitly[16]and is quite weak:c(0)=19/2,c(1)=6,and c(m2c/m2b)≈9.0for the realistic mass ratio m c/m b≈0.3.One can see that the term with the single logarithm L contributes about two thirds of that with L2in the term quadratic inαs.Under such circumstances the RG summation of the terms with powers of L does not look satisfactory for numerical estimates of the QCD effects,at least at the so far considered level of thefirst next-to-leading order terms,and the next-to-next-to-leading terms can be equally important as the two known ones,which would eliminate the existing impasse between the theory and the data on B sl(B).One can present some arguments[17]that this is indeed the case for the b quark decay,although a complete calculation of these corrections is still unavailable.4Chromomagnetic and time dilation effects in decay ratesThe corrections suppressed by two powers of m−1Q to inclusive decay rates arise from two sources[7]:the O(m−2Q)corrections to the matrix element of the leading operator,(QQ|H Q =1−µ2π(H Q)−µ2g(H Q)Q(i D)2Q|H Q ,µ2g= H Q|2σµνGµνQ|H Q ,(7) with D being the QCD covariant derivative.The correction in equation(6)in fact corre-sponds to the time dilation factor m Q/E Q,for the heavy quark decaying inside a hadron, where it has energy E Q,which energy is contributed by the kinetic part(∝µ2π)and the chromomagnetic part(∝µ2g).The second term in OPE describes the effect of the chromo-magnetic interaction in the decay process,and is also expressed throughµ2g.The explicit formulas for the decay rates,including the effects up to the order m−2Q are found in[7]and for decays of the b hadrons read as follows.For the semileptonic decay rate Γsl(H b)=|V cb|2G2F m5b bb|H b 1+µ2g2dand for the non-leptonic decay rateΓnl(H b)=|V cb|2G2F m5b bb|H b 1+µ2g2d m2b I2(x) .(9) These formulas take into account only the dominant CKM mixing V cb and neglect the small one,V ub.The following notation is also used:x=m c/m b,I0(x,y,z)stands for the kinemat-ical suppression factor in a three-body weak decay due to masses of thefinal fermions.In particular,I0(x,0,0)=(1−x4)(1−8x2+x4)−24x4ln x,(10)I0(x,x,0)=(1−14x2−2x4−12x6)√1−4x21−4x2. Furthermore,I(x)=I0(x,0,0)+I0(x,x,0),andI2(x)=(1−x2)3+ 1+11−4x2−3x2(1−2x4)ln1+√1−√αs(m W) 4/b,(11)and b is the coefficient in the QCD beta function.The value of b relevant to b decays is b=23/3.Numerically,for x≈0.3,the expressions for the decay rates can be written asΓsl(H b)=Γpartonsl 1−µ2π(H b)−µ2g(H b)m2b ,Γnl(H b)=Γpartonnl 1−µ2π(H b)−µ2g(H b)m2b ,(12)whereΓparton is the perturbation theory value of the corresponding decay rate of b quark.The matrix elementsµ2πandµ2g are related to the spectroscopic formula for a heavy hadron mass M,M(H Q)=m Q+2m Q + (13)Being combined with the spin counting for pseudoscalar and vector mesons,this formula allows tofind the value ofµ2g in pseudoscalar mesons from the mass splitting:µ2g(B)=3Γnl(B)=1−µ2π(Λb)−µ2π(B)m2b.(15)The difference of the kinetic terms,µ2π(Λb)−µ2π(B),can be estimated from the mass formula:µ2π(Λb)−µ2π(B)=2m b m cM(B)−M is the spin-averaged mass of the mesons,e.g.with respect to those of the charmed hyperons in a reasonable agreement with the observed pattern of the lifetimes.It should be emphasized once again that the m−2Q effects do not depend on theflavors of the spectator quarks or antiquarks.Thus the explanation of the variety of the inclusive decay rates within theflavor SU(3)multiplets,observed for charmed hadrons and expected for the b ones,has to be sought among the m−3Q terms.5L(3)eff.Coefficients and operatorsAlthough the third term in the expansion(4)is formally suppressed by an extra power of m−1Q,its effects are comparable to,or even larger than the effects of the second term.This is due to the fact that the diagrams determining the third term(see Fig.1)contain a two-body phase space,while thefirst two terms involve a three-body phase space.This brings in a numerical enhancement factor,typically4π2.The enhanced numerical significance of the third term in OPE,generally,does not signal a poor convergence of the expansion in inverse heavy quark mass for decays of b,and even charmed,hadrons the numerical enhancement factor is a one time occurrence in the series,and there is no reason for similar‘anomalous’enhancement among the higher terms in the expansion.Here wefirst present the expressions for the relevant parts of L(3)eff for decays of b and c hadrons in the form of four-quark operators and then proceed to a discussion of hadronic matrix elements and the effects in specific inclusive decay rates.The consideration of the effects in decays of charmed hadrons is interesting in its own right,and leads to new predic-tions to be tested experimentally,and is also important for understanding the magnitude of the involved matrix elements using the existing data on charm decays.,induced We start with considering the term L(3)eff in b hadron non-leptonic decays,L(3,b)eff,nlby the underlying processes b→c c s,b→c c d.Unlike the case of three-body decay,the kinematical difference between the two-body states c u,involvedis of the order of m2c/m2b≈0.1and is rather small.At present level in calculation of L(3,b)eff,nlof accuracy in discussing this term in OPE,one can safely neglect the effect offinite charmedreads as[4]quark mass2.In this approximation the expression for L(3,b)eff,nl=|V bc|2G2F m2b bΓµb)(bΓµu)(L(3,b)eff,nl2The full expression for afinite charmed quark mass can be found in[21]˜C5(3q Γµq )+˜C 6(3q k Γµq i )+(17)1b Γµt a b )j a µ−(5˜C 2++˜C 2−−6˜C +˜C −)(3q Γq )=(s Γs )is used,the indices i,k are the color triplet ones,Γµ=γµ(1−γ5),and j a µ=dγµt a d +3(1−κ1/2)(˜C 2+−˜C 2−),˜C2=κ1/2(˜C 2+−˜C 2−),˜C 3=−13(1−κ1/2)(5˜C2++˜C 2−+6˜C +˜C −) ,˜C4=−14(˜C ++˜C −)2+14κ1/2(5˜C 2++˜C 2−−6˜C +˜C −).(18)The expression for the CKM dominant semileptonic decays of b hadrons,associated with the elementary process b →c ℓνdoes not look to be of an immediate interest.The reason is that this process is intrinsically symmetric under the flavor SU(3),and one expects no significant splitting of the semileptonic decay rates within SU(3)multiplets of the b hadrons.The only possible effect of this term,arising through a penguin-like mechanism can be in a small overall shift of semileptonic decay rates between B mesons and baryons.However,these effects are quite suppressed and are believed to be even smaller than the ones arisingform the discussed m −2b terms.For charm decays there is a larger,than for b hadrons,variety of effects associated with L (3)eff ,that can be studied experimentally,and we present here the relevant parts of the effective Lagrangian.For the CKM dominant non-leptonic decays of charm,originatingfrom the quark process c →s u4πC 1(d Γµd )+C 2(d Γµc )+C 3(3s Γµs )+C 4(3s k Γµs i )+(19)C 5(3u Γµu )+C 6(3u k Γµu i )+1c Γµt a c )j a µ−(5C 2++C 2−)(3s and c →d u4π{C 1(q Γµq )+C 2(q k Γµq i )+C 3(3q Γµq )+C 4(3q k Γµq i )+(20)2C 5(3u Γµu )+2C 6(3u k Γµu i )+2c Γµt a c )j a µ−(5C 2++C 2−)(3q Γq )=(s Γs )is used.The semileptonic decays of charm,the CKM dominant,associated with c →s ℓν,and the CKM suppressed,originating from c →s ℓν,contribute to the semileptonic decay rate,which certainly can be measured experimentally.The expression for the part of the effectiveLagrangian,describing the m −3Q terms in these decays is [17,24,25]L (3)eff,sl =G 2F m 2cc Γµc +2cγµγ5c )(c i Γµc k +2c i γµγ5c k )(3Even if the inclusive rate of these decays is not to be separated experimentally,they contribute about 10%of the total decay rate,and it is worthwhile to include their contribution in the balance of the total width.sin2θc L1(3dΓµd)+L2(3d kΓµd i) −2κ1/2(κ−2/9−1)(3B s oscillations. The data on decay rates of the cascade hyperonΞ0b are not yet available,while the currently measured lifetimes of B d and B s are within less than2%from one another.Theoretically, the difference of the lifetimes,associated with possible violation of the SU(3)symmetry and with breaking of the U symmetry of the effective Lagrangian(17),is expected to not exceed about1%.For the non-vanishing matrix elements of four-quark operators over pseudoscalar mesons one traditionally starts with the factorization formula and parametrizes possible deviation from factorization in terms of‘bag constants’.Within the normalization convention adopted here the relations used in this parametrization read asP Q QΓµq)(q =1P QQ ΓµQ )(q =1q stands for pseudoscalar meson made of Q and8π (˜C 2+−˜C 2−)B (m b )+1200MeV 2ps −1,(25)Γ(D ±)−Γ(D 0)=cos 4θc G 2F m 3c f 2D 3(C 2++C 2−)˜B (m c )∼−0.8 f DOn the contrary,inΩQ the two strange quarks form a J P=1+state,and a correlation between the spins of heavy and light quarks is present.The absence of spin correlation forthe heavy quark in the triplet of hyperons somewhat reduces the number of independentfour-quark operators,having nonvanishing diagonal matrix elements over these baryons. Indeed,the operators entering L(3)eff contain both vector and axial bilinear forms for the heavy quarks.However the axial part requires a correlation of the heavy quark spin withthat of a light quark,and is thus vanishing for the hyperons in the triplet.Therefore only the structures with vector currents are relevant for these hyperons.These structures are of thetype(qγµq)and(q kγµq i)with q being d,s or u.Theflavor SU(3)symmetrythen allows to express,for each of the two color combinations,the matrix elements of threedifferent operators,corresponding to threeflavors of q,over the baryons in the triplet interms of only two combinations:flavor octet andflavor singlet.Thus all effects of L(3)eff inthe triplet of the baryons can be expressed in terms of four independent combinations of matrix elements.These can be chosen in the following way:x= 1QγµQ)[(sγµs)] Ξ(d)Q−ΛQ= 1QγµQ) (dγµd) ΛQ−Ξ(u)Q,(27) y= 1Q iγµQ k)[(s kγµs i)] Ξ(d)Q−ΛQ= 1Q iγµQ k) (d kγµd i) ΛQ−Ξ(u)Q, with the notation for the differences of the matrix elements: O A−B= A|O|A − B|O|B ,for theflavor octet part and the matrix elements:x s=1QγµQ) (dγµd)+(3 H Q|(u kγµu i)+(s kγµs i)|H Q (28)for theflavor singlet part,where H Q stands for any heavy hyperon in the(anti)triplet.The initial,very approximate,theoretical estimates of the matrix elements[4]were es-sentially based on a non-relativistic constituent quark model,where these matrix elements are proportional to the density of a light quark at the location of the heavy one,i.e.in terms of the wave function,proportional to|ψ(0)|ing then the same picture for the matrix elements over pseudoscalar mesons,relating the quantity|ψ(0)|2to the annihilation constant f P,and assuming that|ψ(0)|2is approximately the same in baryons as in mesons, one arrived at the estimatey=−x=x s=−y s≈f2D M Dwhere the sign relation between x and y is inferred from the color antisymmetry of the constituent quark wave function for baryons.Since the constituent picture was believed to be valid at distances of the order of the hadron size,the estimate(29)was applied to the matrix elements in a low normalization point whereαs(µ)≈1.For the matrix elements of the operators,containing s quarks over theΩQ hyperon,this picture predicts an enhancement factor due to the spin correlation:ΩQ|(sΓµs)|ΩQ =− ΩQ|(s kΓµs i)|ΩQ =10[(C5−C3)x+(C6−C4)y],4πG2F m2cδnl,02≡Γnl∆S=∆C(Λc)−Γnl∆S=∆C(Ξ+c)=cos4θcdecays in the baryon triplet isδnl,1≡Γnl ∆S =0(Ξ0c )−Γnl ∆S =0(Λc )=cos 2θc sin 2θc G 2F m 2c12π[L 1x +L 2y ].(33)Finally,the Cabibbo suppressed semileptonic decay rates are equal for Λc and Ξ0c ,due to the ∆V =0property of the corresponding interaction.Thus the only difference for these isδsl,1≡Γsl ∆S =0(Λc )−Γsl ∆S =0(Ξ+c )=−sin 2θc G 2F m 2c4πcos 2θ x cos 2θ(C 5−C 3)+sin 2θ(2C 5−C 1−C 3)−23L 2,(35)and∆2=δnl,02−2δsl,0+2δsl,1=G 2F m 2c 3(cos 2θ−sin 2θ)L 1+y cos 4θ(C 4−C 2)+2m c2,(37)while the dependence of the thus extracted matrix element y on the normalization point µis shown in Fig.24.23456-0.04-0.020.02yxκFigure 2:The values of the extracted matrix elements x and y in GeV 3vs.the normalization point parameter κ=αs (µ)/αs (m c ).The thick lines correspond to the central value of the data on lifetimes of charmed baryons,and the thin lines show the error corridors.Theextracted values of x and y scale as m −2c with the assumed mass of the charmed quark,andthe plots are shown for m c =1.4GeV .Notably,the extracted values of x and y are in a drastic variance with the simplistic constituent model:the color antisymmetry relation,x =−y ,does not hold at any reasonable µ,and the absolute value of x is substantially enhanced 5Once the non-singlet matrix elements are determined,they can be used for predicting differences of other inclusive decay rates within the triplet of charmed hyperons as well as for the b baryons.Due to correlation of errors in x and y it makes more sense to express the predictions directly in terms of the total decay rates of the charmed hyperons.The thus arising relations between the rates do not depend on the normalization parameter µ.In this way one finds [28]for the difference of the Cabibbo dominant semileptonic decay rates between either of the Ξc hyperons and Λc :Γsl (Ξc )−Γsl (Λc )≈δsl,0=0.13∆1−0.065∆2≈0.59±0.32ps −1.(38)When compared with the data on the total semileptonic decay rate of Λc ,Γsl (Λc )=0.22±0.08ps −1,this prediction implies that the semileptonic decay rate of the charmed cascade hyperons can be 2–3times larger than that of Λc .The predictions found in a similar way for the inclusive Cabibbo suppressed decay ratesare[28]:for non-leptonic decaysδnl,1=0.082∆1+0.054∆2≈0.55±0.22ps−1(39) and for the semileptonic onesδsl,1=tan2θcδsl,0≈0.030±0.016ps−1.(40) For the only difference of the inclusive rates in the triplet of b baryons,Γ(Λb)−Γ(Ξ−b), onefinds an expression in terms of x and y,or alternatively,in terms of the differences∆1 and∆2between the charmed hyperons,Γ(Λb)−Γ(Ξ−b)=cos2θc|V bc|2G2F m2bm2c(0.85∆1+0.91∆2)≈0.015∆1+0.016∆2≈0.11±0.03ps−1.(41) When compared with the data on the total decay rate ofΛb this result predicts about14% longer lifetime ofΞ−b than that ofΛb.The singlet matrix elements x s and y s(cf.eq.(28))are related to the shift of the average decay rate of the hyperons in the triplet:3 Γ(ΛQ)+Γ(Ξ1Q)+Γ(Ξ2Q) .(42) For the charmed baryons the shift of the dominant non-leptonic decay rate is given by[29]δ(3,0)nl8π(C 2++C2−)κ5/18(x s−3y s),(43)while for the b baryons the corresponding expression reads asδ(3)8π(˜C+−˜C−)2˜κ5/18(x s−3y s).(44) The combination x s−3y s of the SU(3)singlet matrix elements cancels in the ratio of the shifts for b hyperons and the charmed ones:δ(3)cos4m2bC2++C2− αs(m c)Γc≈0.0025δ(3,0)nl˜C)2/(C2++C2−),which parametrically is of the second order inαs,and numerically is only −about0.12.An estimate ofδ(3)Γc for charmed baryons.The latter shift can be conservatively bounded from aboveΓc=6.0±0.7ps−1,which then by the average total decay rate of those baryons:δ(3,0)nlyields,using eq.(45),an upper boundδ(3)Γc the contribution of the‘parton’term,which can be estimated from the decay rate of D0with account of the O(m−2c)effects,as amounting to about3ps−1.(One should also take into account the semileptonic contribution to the total decay rates,which however is quite small at this level of accuracy).Thus a realistic evaluation ofδ(3)Γb due to the non-singlet operators is one third of the splitting(41),i.e.about5%.Adding to this the1%shift of the average width and another1%difference from the meson decays due to the suppression of the latter by the m−2b chromomagnetic effects,one concludes that at the present level of theoretical understanding it looks impossible to explain a more than10%enhancement of the total decay rate ofΛb relative to B d,where an ample3%margin is added for the uncertainties of higher order terms in OPE as well as for higher order QCD radiative effects in the discussed corrections. In other words,the expected pattern of the lifetimes of the b hyperons in the triplet,relative to B d,isτ(Ξ0b)≈τ(Λb)<τ(B d)<τ(Ξ−b),(46) with the“best”theoretical estimate of the differences to be about7%for each step of the inequality.For the double strange hyperonsΩc andΩb there is presently no better approach to evaluating the four-quark matrix elements,than the use of simplistic relations,like(30) based on constituent quark model.Such relations imply that the effects of the strange quark,WS and PI,in theΩQ baryons are significantly enhanced over the same effects in the cascade hyperons.In charmed baryons a presence of strange spectator quark enhances the decay through positive interference with the quark emerging from the c→s transition in the decay.ForΩc this implies a significant enhancement of the total decay rate[4],which is in perfect agreement with the data on theΩc lifetime.Also a similar enhancement is expected for the semileptonic decay rate ofΩc.In b baryons,on the contrary,the interference effect。

中英文对照学习版Harry Potter and the Prisoner of Azkaban《哈利波特与阿兹卡班囚徒》Chapter SixteenProfessor Trelawney’s Prediction第16章特里劳尼教授的预言Harry’s euphoria at finally winning the Quidditch Cup lasted at l east a week. Even the weather seemed to be celebrating; as June approached, the days became cl oudl ess and sultry, and all anybody felt like doing was strolling into the grounds and fl opping d own on the grass with several pints of iced pumpkin juice, perhaps playing a casual game of Gobstones or watching the giant squid propel itself dreamily across the surface of the lake.终于夺得了魁地奇杯，哈利的兴奋劲至少维持了一个星期。

连天气都像是在庆祝。

临近六月，白天变得晴朗无云，热烘烘的，让人只想带上几品脱冰镇南瓜汁溜达到场地上去，一屁股坐下来，也许可以随意玩上几局高布石，或者看着巨乌贼在湖面上梦幻般地游动。

But they coul dn't. The exams were nearly upon them, and instead of lazing around outsid e, the stud ents were forced to remain insid e the castle, trying to bully their brains into concentrating whil e enticing wafts of summer air drifted in through the wind ows. Even Fred and George Weasl ey had been spotted working; they were about to take their O.W.Ls (Ordinary Wizarding Levels). Percy was getting ready to sit his N.E.W.Ts (Nastily Exhausting Wizarding Tests), the highest qualification Hogwarts offered. As Percy hoped to enter the Ministry of Magic, he need ed top grad es. He was becoming increasingly edgy, and gave very severe punishments to anybody who disturbed the quiet of the common room in the evenings. In fact, the only person who seemed more anxious than Percy was Hermione.可是不行。

我心目中的科学家英语作文范文In my view, scientists are akin to modern-day alchemists, weaving intricate narratives of discovery within the fabric of the universe. They are the navigators of the unknown, wielding curiosity as their compass and reason as their sail. Let me take you on a journey through the corridors of my mind, where the portrait of a scientist unfolds in vibrant hues of intellect and ingenuity.Imagine a world where equations dance across chalkboards like cosmic ballets, where the language of atoms whispers secrets only the keenest ears can decipher. This is the realm of the scientist, where every question is a breadcrumb leading to the banquet of knowledge. They are the architects of understanding, building bridges between the tangible and the intangible.At the heart of scientific inquiry lies a relentlesspursuit of truth. It is a quest fueled not by ego, but by an insatiable hunger to unravel the mysteries of existence. From the microscopic dance of particles to the grandorchestration of galaxies, scientists peer through the veil of ignorance, seeking to illuminate the darkness with the torch of reason.Yet, amidst the chaos of experimentation and the labyrinth of data, there exists a quiet humility. For every answer uncovered reveals a dozen new questions, each more tantalizing than the last. The scientist is a humble pilgrim, journeying ever deeper into the unknown, guided by the twin beacons of curiosity and skepticism.But make no mistake, theirs is not a solitary endeavor. Science is a tapestry woven from the threads of collaboration and cooperation. Across continents and disciplines, scientists join hands in a symphony of discovery, harmonizing their efforts to conquer the frontiers of knowledge. In this global chorus, no voice is too small, no contribution too insignificant. For it is in diversity that the true power of science resides, drawing strength from the myriad perspectives that illuminate the path forward.And yet, for all their brilliance, scientists are not immune to the foibles of humanity. Egos clash like tectonic plates, and dogma can obscure the light of reason. But in the crucible of debate and discourse, truth emerges triumphant, tempered by the fire of scrutiny.So, what then defines the essence of a scientist? Is it the accolades adorning their walls or the equations etched in their minds? Perhaps it is neither, but rather the spark of curiosity that ignites their soul. For in the end, it isnot the destination that defines us, but the journey we undertake in pursuit of understanding.In my eyes, the scientist is more than a mere mortal; they are the custodians of curiosity, the stewards of skepticism, and the architects of enlightenment. They are the poets of the cosmos, crafting verses of truth in the language of the universe. And as long as there are questions left unanswered, their quest shall endure, a testament to the indomitable spirit of human intellect.。

The Flow of HistoryGrowing up, I was always fascinated by the stories of the past. The tales of ancient civilizations, the rise and fall of empires, and the lives of great leaders captivated my imagination. It was as if history was a grand tapestry, woven with threads of time, and I was eager to explore every inch of it.My journey into the depths of history began with a simple book from the school library. It was a biography of Cleopatra, the last Pharaoh of Ancient Egypt. The book painted a vivid picture of her life, from her struggles for power to her tragic end. I was mesmerized by her intelligence, her charisma, and her indomitable spirit. She was a woman who defied the odds and stood against the might of Rome, and her story inspired me to learn more about the world that she lived in.As I delved deeper into history, I discovered the rich tapestry of human experience. I learned about the great civilizations that shaped the world, from the Egyptians and the Greeks to the Romans and the Chinese. I marveled at their achievements in art, science, and philosophy, and I was humbled by their struggles and failures.One of the most intriguing periods in history for me is the Renaissance. It was a time of great change and innovation, when artists, scientists, and thinkers challenged the status quo and pushed the boundaries of human knowledge. The works of Leonardo da Vinci, Michelangelo, and Galileo Galilei were not just artistic masterpieces, but also testaments to the human spirits boundless curiosity and creativity.History is also a record of human folly and conflict. The two World Wars, for instance, were devastating events that claimed millions of lives and reshaped the world in profound ways. The Holocaust, a dark chapter in human history, is a stark reminder of the horrors that can arise from hatred and prejudice. These events, though painful, serve as important lessons for future generations, urging us to strive for peace and understanding.In my exploration of history, I have come to appreciate the interconnectedness of our world. The Silk Road, for example, was a network of trade routes that connected the East and the West, facilitating the exchange of goods, ideas, and cultures. The impact of this ancient trade route can still be felt today, as it laid the foundation for globalization and cultural diversity.Moreover, history has shown me the power of resilience and perseverance. The story of Nelson Mandela, who fought against apartheid and became the first black president of South Africa, is a testament to the human spirits ability to overcome adversity andinjustice. His life serves as an inspiration for people around the world to stand up for what is right, no matter the odds.In conclusion, history is a rich and complex narrative that offers valuable insights into the human experience. It is a mirror that reflects our past, present, and future, and it is a guide that helps us navigate the complexities of our world. As I continue to explore the flow of history, I am reminded of the words of the philosopher George Santayana: Those who cannot remember the past are condemned to repeat it. Let us learn from history, so that we may build a better future for all.。

经典英语诗歌：《奥兹曼迪亚斯》下面店铺为大家带来经典英语诗歌：《奥兹曼迪亚斯》，欢迎大家阅读!I met a traveler from an antique land,我遇见一位来自古国的旅人Who said----"Two vast and trunkless legs of stone他说：有两条巨大的石腿Stand in the desert...Near them, on the sand,半掩于沙漠之间Half sunk, a shattered visage lies, whose frown,近旁的沙土中，有一张破碎的石脸And wrinkled lip, and sneer of cold command,抿着嘴，蹙着眉，面孔依旧威严Tell that its sculptor well those passions read想那雕刻者，必定深谙其人情感Which yet survive, stamped on these lifeless things,那神态还留在石头上The hand that mocked them, and the heart, that fed;而私人已逝，化作尘烟And on the pedestal, these words appear:看那石座上刻着字句："My name is Ozymandias, King of Kings,“我是万王之王,奥兹曼斯迪亚斯Look on my works, ye Mighty, and despair!"功业盖物,强者折服”Nothing besides remains. Round the decay此外，荡然无物Of that colossal Wreck, boundless and bare废墟四周，唯余黄沙莽莽The lone and level sands stretch faraway.”寂寞荒凉，伸展四方。

HEP’97#535DELPHI97-114CONF96 Submitted to Pa7,820July,1997 Pl15Measurement of the using-decaysat LEP-2PreliminaryDELPHI CollaborationM.Battaglia,B.Erˇz en,B.Golob,D.Liko,T.Podobnik,S.Staniˇc,A.TomaradzeAbstractDecays of-bosons,produced at LEP-2,can be exploited to measure the element of the Cabibbo-Kobayashi-Maskawa matrix.The value can be extracted either from the measured hadronic branching ratio of-decays or by tagging theflavour of hadronic jets, produced in-decays.Applying the two methods on the data,collected during thefirst year of the LEP high-energy run,DELPHI obtains.Paper submitted to the HEP’97ConferenceJerusalem,August19-261IntroductionIn the Standard Model with as the gauge group of the electroweak interaction,the quark mass eigenstates are not the same as the weak eigenstates.For the six quarks,the twobases are related by the unitary Cabibbo-Kobayashi-Maskawa(CKM)matrix[1,2,3].Apart from the matrix elements describing the decays of the heavy-quark,the value of theelement relating the quarks of the second generation is known with the poorest precision.Theabsolute error on the,determined in semileptonic decays of mesons[3],is18%and is dominated by the poorly known hadronic form-factors.Hadronic decays of charged weak bosons,produced in the interactions at theupgraded LEP-2collider,offer an alternative ly,in the decaysis proportional to the appropriate CKM matrixelement.Therefore,from the measured rate of theThroughout the paper references to a specific charge state are meant to imply the charge conjugate state as well,unless explicitly stated otherwise.impact parameter with respect to the interaction point is determined with an accuracy of around 70m.The barrel and the forward electromagnetic calorimeters are used to measure the deposited electromagnetic energy of particles with43137and1036.5,143.5170,respectively.The hadron calorimeter measures the energy of hadrons with the polar angle larger than10.Electron candidates are identified by the characteristic energy deposition in the electromag-netic calorimeters.Efficiency for the detection of high-momentum electrons,determined by the simulation and by the measurement of Bhabha events,is(772)%.Muons are recognized by the associated hits in the muon chambers,surrounding the hadron calorimeter,and by the energy deposition in the hadronic calorimeter,compatible with the deposition of a minimum ionizing particle.Efficiency for the identification,obtained by the simulation and from the measured decays,is estimated to be(921)%.Identification of charged hadrons,on the other hand,relies on the specific ionization energy loss per unit length()in the TPC,and on the information from the system of Ring Imaging Cherenkov(RICH)counters.The latter consists of two independent detectors,the Barrel and the Forward RICH,covering together over90%of the full solid angle.Each of the RICH detectors contains two radiators of different refractive indices,allowing in this way for particle identification in the momentum range between0.7and25GeV/c.In the present analysis the HADSIGN tagging routine is used[5].The algorithm provides charged kaon identification with efficiencies between80%and45%,and corresponding purities between60%and85%, depending on the particle momentum and quality of the track reconstruction.Simulated-events,used in the analysis,were generated with the PYTHIA5.7gen-erator[6].The fragmentation model,incorporated in the simulation,is tuned to the DELPHI data measured at LEP-1[7].3Determination of the from the hadronic branching ra-tio of theThe-dependence of the cross-section can be parametrized as[8]channel.An additional correction factor(see Fig.1.a)comes from the-dependent total widths in the-propagators. Consequently,the value of the reflects in rates also for the decays others than0.80.911.11.21.30.80.91 1.1 1.2a)k f (k )0501001500.51 1.5kN u m b e r o f e v e n t s Total 4-jet2-jet l ν2 l νb)Figure 1:a)Correction factor to the cross section,coming from the -dependent widths in the -propagators.The full line shows the correction for the 172GeV centre-of-mass energy and the dashed line the correction for 161GeV .b)Number of fully hadronic,mixed and fully leptonic decays of -pairs with respect to the ratio .The numbers correspond to an integrated luminosity of approximately 10pb at 172GeV centre-of-mass energy and were evaluated in the leading-order approximation.When extracting theone can therefore neglect the value of the total cross-section and use only the measured hadronic branching ratio of the .The analysed data were collected with the DELPHI spectrometer at the centre-of-mass (CMS)energies of 161GeV and 172GeV and correspond to the integrated luminosities of 9.93pb and 9.98pb ,bining the results from the two samples,DELPHI obtains [9]:Assuming all other parameters of the Standard Model to be fixed at the presently measured values [3],the measured branching ratio can be converted intoThe systematic error on the includes also a contribution due to uncertainties on the other parameters of the Standard Model (e.g.uncertainties on and ;see Table 1).4Tagging the flavour of hadronic jetsAn additional information about the value can be obtained by tagging the flavour of hadronic jets,arising from fragmentation of the primary quarks from the -decays.Be-fore the flavour tagging,-enhanced samples were selected as described in the following paragraphs.In an event,charged particles were selected within a polar angle between and and with a momentum between 0.4GeV/c and the beam momentum.In addition,the length of the reconstructed tracks had to be larger than 15cm,their impact parameters,both longitudinal andtransverse with respect to the beam axis,should not exceed4cm,while the maximum allowed uncertainty on the momentum measurement was100%.Neutral particles,on the other hand, were accepted if they deposited more than0.5GeV energy in the electromagnetic or hadronic calorimeters.For each event all selected particles were clustered into jets using the LUCLUS algorithm[6].To accept a particle in a jet,a maximal distance[6]between the particle and the jet was allowed.Events were then arranged in three classes:fully hadronic decays where both and decayed into quarks,mixed decays where one of the two gauge bosons decayed into an electron or a muon and an appropriate neutrino,and mixed decays with a tau lepton and a tau neutrino.For the candidates,the number of reconstructed hadronic jets was required to be at least three.All particles were then forced into a four jet configuration and,in order to improve the momentum and energy resolution,a kinematically constrainedfit was performed[12],imposing the momentum conservation and the nominal-mass to di-jet combinations.In an event,the jet pairing which minimized the of thefit was chosen.For thecandidates,an isolated track of a highly energetic particle,i.e.a lepton candidate,was required.In particular,in an event the particle with the smallest value for the ratio was chosen,where is the momentum of the candidate while the sum runs over momenta of all particles in a20cone around the candidate’s direction.The remaining tracks were then forced into a two-jet topology.In the case of candidates for the tau lepton mixed decays,on the other hand,the events were forced into configurations with three hadronic jets.In addition,at least one tau-jet candidate was required,identified as a low energy lepton or a low multiplicity narrow jet,isolated from the rest of the event.Requirements,concerning the reconstructed energy and the particle multiplicity of the events,were very mild so that they did not reject any-pair decays but they did diminish some of the background,e.g.a great deal of events.At this stage a single event could also enter more than one of the three classes.After the preselection,several kinematical properties of the events were combined in order to separate the-pair signal from the remaining background.For the fully hadronic channel, the number of originally reconstructed jets,the energy of these jets,the probability for the kinematically constrainedfit,the angle between the fastest jets from each of the two chosen di-jets,and the effective CMS energy were used.The latter was estimated from the photon radiated off the initial state.For this purpose either the energy of an isolated highly energetic photon was used if such a photon was reconstructed in the detector,or the photon direction was assumed to be parallel to the beam axis and the photon momentum was calculated under the assumption of a two-jet topology of the event[10,11].The discriminating power of these variables steams from the fact that the most severe background,coming from theevents are also expected to be distributed less uniformly than jets from the-pair decays.A similar set of variables was used to describe the shape of mixed-decays:the probability for the kinematically constrainedfit,the effective CMS energy,the total multiplicity,the aplanarity of the event,the transverse missing momentum,and the number of reconstructed jets and their angular distribution.In addition,for mixed decays with electrons or muons the momentum spectrum of the lepton candidates was also also exploited as well as the distribution of the events with respect to the angle between the lepton and the direction of the missing momentum,the muon and electron identification criteria in the DELPHI detector,and the isolation of the lepton candidates from the rest of the event. The latter was defined by the energy,deposited inside a10cone around the lepton direction. The isolation of tau-jet candidates was,on the other hand,defined in terms of the energy ofcharged particles inside a30cone around the-candidate.Tau jet candidates were also tried to be distinguished from the rest of hadronic jets and missassociated tracks by the number of the tracks in the jet and,as in the case of electrons and muons,by the angle that they formed with the missing momentum direction.Relying on the corresponding simulated distributions,one can calculate a probability that a measured event with a given value of a particular variable originates from a-pair decay.By multiplying probabilities from all listed quantities for each of the three classes single discrimi-nating variables,and were obtained.To avoid multiple counting,every event was put in the class with the largest value of the discriminating variable.Due to the small num-ber of events the two classes of mixed decay candidates were then merged into one common class.Figure2shows the measured distributions for fully hadronic and mixed decay events according to the separating variables,as well as the expected distributions from corresponding simulated-decays and from the background.For further analysis only events on the right of the arrows were taken into account in order to maximize the product of the selection efficiency and the purity of the selected samples.After the selection,theflavour-tagging of the jets was applied.The tagging relies on the information from the DELPHI vertex and tracking detectors and on the charged particle identi-fication with the RICH counters.In order to separate jets,originating from primary quarks with differentflavours,the following discriminating properties were used:-and-jets can be tagged by the high momentum charged kaons,detected in the system of DELPHI RICH counters.These kaons are very likely to contain a primary-quark or an-quark from a decay.Figure3.a shows the expected spectra for the leading particles identified as charged kaons in jets with-,-,-and-flavour,respectively.Using the same arguments,if a fast particle in a hadronic jet is an identified pion it is an indication for a-or-jet(see Fig.3.b for illustration).In each jet,the momentum dependent probability for a particular jetflavour was calculated by considering only the fastest identified particle in the jet.In addition,such a particle was required to be among the leading three particles in the jet.To distinguish between quarks and antiquarks of the sameflavour the charge of identified particles is also used.As a minor contribution to theflavour separation,the momentum distribution of identified muons,neutral kaons and-baryons was also used.Muons are a signature for semilep-tonic decay of charm hadrons,while reconstructed’s and’s serve as an indication for a primary-quark.-jets can also be separated from the-,-and-jets by the lifetime tag that is based upon the impact parameter distribution of particles,ascribed to a particular jet[5,13].From this distribution one can build a probability that all particles in a jet originate from the primary vertex.This probability is,due to thefinite lifetime and the larger mass of the -quark,smaller for charm than for light-quark jets(see Fig.4).In the same way as in the event selection procedure,the describedflavour signatures were combined into probabilities for each jet to originate from a-,-,-or-quark.The impact of the combinatorial background was reduced by exploiting the correlation between the direction of a jet and theflavour of its primary ly,’s produced in collisions are partly polarized along their momenta and’s in the opposite direction[14]. Therefore,because of the structure of the-decays,down-like quarks and anti-quarks, i.e.,,,willfly mainly along the momentum of the parent(Fig.5.a).The twofoldDELPHI4q d N /d P 4q2ql νd N /d P 2q l ν4q d N /d P 4q2ql νd N /d P 2q l ν101101011010101101011010Figure 2:Distributions of events in selected classes with respect to the discriminating variables for the two classes:fully hadronic candidates (a)and c))and candidates for mixed decays (b)and d)).The upper row shows distributions for 172GeV energy and the lower row for 161GeV .Measured spectra are displayed as dots with error bars,expected signals as open histograms and background as hatched histograms.The background is a sum of contributions fromDELPHI0255075102030p [GeV/c ] d N /d p s:c:d:u:a)050100150102030p [GeV/c ]d N /d p s:d:b)Figure 3:a)Momentum spectra of identified charged kaons in simulated -,-,-and -jets when the kaon is the leading particle in the jet.b)Momentum spectra of leading particles,iden-tified as pions in -and -jets,respectively.The number of entries in Figs.3and 4corresponds to approximately 15000generated events.DELPHI P Md N /d P M c :s,u,d:025050000.51Figure 4:Simulated distributions of the probabilities that all charged particles in a jet come from the main vertex,for -jets (full histogram)and for -,-or -jets (dotted histogram).θj d N /d θj d-like:u-like:a)θWd N /d θW W +:W -:b)00.20.40.6012300.20.40.60123Figure 5:a)Simulated distribution of the angle between the momenta of the ’s and the of corresponding jets from down-like (solid line)or up-like (dotted line)quarks from the ’s decays at a centre-of-mass energy of 172GeV .b)Angular distributions of ’s (solid line)and of ’s (dotted line)with respect to the direction of the positron beam.ambiguity whether the down-like quark is really a quark (or )or an antiquark ()can further be resolved by determining the charge of the parent .In four-jet events one can de-termine the sign of the -charge by making use of the strong correlation between the direction of the ’s and their charge [14,15].Namely,momenta of positively charged gauge bosons point mainly into the hemisphere,determined by the direction of the positron beam (Fig.5.b).In decays,the charge of the ’s was determined by the charge of lepton candidates from leptonic -decays.The correlations between the jet direction and the flavour of the primary quark were then incorporated into the probabilities .Note,however,that the polarizationof the’s (Fig. 5.a),and thus also the background rejection power,substantially increase with the increasing CMS energy,attainable in the coming years of LEP-2.When combining the flavours of the two jets from hadronic -decays,for different com-binations were considered:Decays intoand and:and forDELPHI00.050.100.20.40.60.81P cs d N /d P c s cs:ud:Figure 6:distributions for simulated -jets (dashed histogram).5Determination of the by tagging the flavour of the jetsThe value of thewas extracted from the data by fitting the expected distributions to the spectra of the selected di-jet combinations by using the maximum-likelihood method.The likelihood functionwas constructed as a multinomial probability [16]to observe out of measured di-jets in the first bin of the distribution,in the second bin,etc.The probability that a di-jet,randomly picked up from the selected sample of WW-candidates,would fall into the -th bin,depends on the value of the and was determined by the simulated signal and background samples.Thedistributions,extracted from the selected and quarks:DELPHId N /d P c sP cs036912151802468Figure 7:Measured spectra (points with error bars)together with the best fit simulated predictions (histograms)for decays (a)and c))and for05101520253035P csd N /d P c s Figure 8:The sum of the and the(lightest shading),,Table1:The list of contributions to the systematic uncertainties on the measurement of the for the two methods and for the combined result.Note that for thefirst method the error due to thefinite Monte Carlo(MC)sample is included in the error coming from the efficiency calculation.Source of uncertainty From BR(Efficiency calculation-Background normalization“CC03”-correction factorsLifetime tag-,spectra-MC statistics-Combinedwhile tagging theflavour of jets from-decays givesThe precision of the two values combined,already surpasses the precision of the combination of all previous measurements[19,20,21, 22].Moreover,unlike the accuracy of the previous measurements,limited by the uncertainties from the theoretical input,the uncertainty on this result is dominated by the statistical error. Until the end of LEP-2it can be therefore expected that the precision will be substantially improved.AcknowledgementIt is a pleasure to thank our technical collaborators and the funding agencies for their support in building and operating the DELPHI detector.At the same time,we are also greatly indebted to the members of the CERN-SL Division for the excellent performance of the LEP collider.References[1]N.Cabibbo,Phys.Rev.Lett.10(1963)531.[2]M.Kobayashi,T.Maskawa,Progr.Theor.Phys.49(1973)652.[3]Particle Data Group,Review of Particle Physics,Phys.Rev.D54(1996)1.[4]DELPHI Collaboration,P.Aarnio et al,Nucl.Instr.Meth.A303(1991)233.[5]DELPHI Collaboration,P.Abreu et al.,Nucl.Instr.Meth.A378,(1996)57.[6]T.Sj¨o strand,PYTHIA5.7/JETSET7.4,CERN-TH.7112/93(1993).[7]DELPHI Collaboration,P.Abreu et al.,Z.Phys.C73(1996)11.[8]A.Ballestrero et al.,Determination of the Mass of the W Boson,Physics at LEP2,eds.G.Altarelli,T.Sj¨o strand and F.Zwirner,CERN96-01(1996)V ol.1,p.141.[9]DELPHI Collaboration,P.Buschmann et al.,Measurement of the-pair cross-section andof the mass in interactions at172GeV,DELPHI note97-108CONF90;Paper #347submitted to the HEP’97Conference,Jerusalem,August19-26.[10]DELPHI Collaboration,P.Abreu et al.,Measurement and interpretation of the-paircross-section in interactions,CERN-PPE97-09,submitted to Phys.Lett.B. 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时间暂停的英语作文Title: The Frozen Moment: An Exploration of Time Paused。

Time, an ever-flowing river, suddenly comes to a standstill. The world around us freezes in its tracks, leaving us suspended in a singular moment. What would we do if time paused, if the universe granted us a fleeting glimpse into eternity? This scenario sparks curiosity and contemplation, inviting us to explore the depths of such an extraordinary phenomenon.In this frozen moment, every detail becomes magnified, every sensation heightened. The stillness of the air, the silence that envelops us—it's as if the universe itself is holding its breath. In this suspended state, we find ourselves confronted with the essence of existence,stripped of the distractions of the passing seconds.With time on pause, we are granted the opportunity to reflect on our lives, to ponder the paths we've taken andthe ones we've yet to tread. It's a moment of introspection, a chance to delve into the depths of our souls and discover what truly matters to us. In the quietude of this frozen world, we find clarity amidst the chaos of everyday life.But amidst the serenity, there is also a sense of urgency. For as beautiful as this moment may be, we knowthat it is but a temporary respite from the relentless march of time. We are reminded of our mortality, of thefinite nature of our existence. And so, even as we revel in the stillness, there is a part of us that yearns for the world to resume its motion, to continue on its journey through the vast expanse of eternity.In this frozen moment, we are also confronted with the fragility of our relationships, the fleeting nature of human connections. Loved ones are frozen in time, their smiles and laughter preserved for eternity. And yet, thereis a bittersweetness to it all, a reminder that even the most precious moments are ephemeral.But perhaps, amidst the melancholy, there is also hope.For in this frozen world, we are given the chance to mend broken relationships, to cherish the ones we hold dear, to make amends for past wrongs. It's a reminder that time is a precious gift, one that should not be squandered or taken for granted.As the world remains suspended in time, we are left to ponder the mysteries of the universe. What caused this pause in the cosmic dance? Is it a glimpse into a higher reality, a fleeting moment of transcendence? Or is it simply a quirk of fate, a random occurrence in the tapestry of existence?Whatever the explanation may be, one thing is certain: this frozen moment is a testament to the beauty and wonder of the world we inhabit. It's a reminder that even in the darkest of times, there is still magic to be found, still moments of awe and wonder waiting to be discovered.And so, as we stand on the precipice of eternity, let us embrace this frozen moment with open arms. Let us savor the stillness, the silence, the beauty of the world aroundus. For even as time resumes its inexorable march, we will carry with us the memory of this fleeting glimpse into eternity, a reminder of the infinite possibilities that lie ahead.。