Coupling From the Past- Nonconstructive

a r X i v :h e p -t h /9906141v 2 19 O c t 1999UPR-0849-T hep-th/9906141One-loop effective potential of N=1supersymmetrictheory and decoupling effectsI.L.Buchbinder ∗,M.Cvetiˇc +and A.Yu.Petrov ∗∗Department of Theoretical Physics,Tomsk State Pedagogical University634041Tomsk,Russia+Department of Physics and Astronomy,University of PennsylvaniaPhiladelphia,PA 19104–6396,USAAbstractWe study the decoupling effects in N =1(global)supersymmetric theories with chiral superfields at the one-loop level.Examples of gauge neutral chiral superfields with minimal (renormalizable)as well as non-minimal (non-renormalizable)couplings are considered,and decoupling in gauge theories with U (1)gauge superfields that cou-ple to heavy chiral matter is studied.We calculate the one-loop corrected effective Lagrangians that involve light fields and heavy fields with mass of order M .Elimina-tion of heavy fields by equations of motion leads to decoupling effects with terms that grow logarithmically with M .These corrections renormalize light fields and couplings in the theory (in accordance with the “decoupling theorem”).When the field theory is an effective theory of the underlying fundamental theory,like superstring theory,where the couplings are calculable,such decoupling effects modify the low energy predictions for the effective couplings of light fields.In particular,for the class of string vacua with an “anomalous”U (1),the vacuum restabilization triggers decoupling effects,which can significantly modify the low energy predictions for couplings of the surviving light fields.We also demonstrate that quantum corrections to the chiral potential depend-ing on massive background superfields and corresponding to supergraphs with internal massless lines and external massive lines can also arise at the two-loop level.Contents1Introduction22Effective action in the model of interacting light and heavy superfields42.1General structure of the effective action ......................52.2The effective equations of motion .........................82.3Calculation of the one-loop k¨a hlerian effective potential .............93One-loop effective action for minimal models133.1Calculation of the effective action (13)3.1.1The one-loop k¨a hlerian effective potential (13)3.1.2Corrections to the chiral potential (14)3.2The effective action for light superfields (18)3.2.1Contribution of the self-interaction of the light superfield (20)3.2.2Absence of the self-interaction of the light superfield (23)4One-loop effective action for non-minimal models244.1The model with heavy quantum superfields and external light superfields (25)4.1.1Calculation of the effective action (25)4.1.2Solving the effective equations of motion (27)4.2The model with light and heavy quantum superfields and light and heavyexternal superfields (29)4.2.1Calculation of the effective action (29)4.2.2Solution of the effective equations of motion (32)5Quantum corrections to the effective action in gauge theories335.1Gauge invariant model of massive chiral superfields (33)5.2One-loop k¨a hlerian potential in supersymmetric gauge theory (35)5.3Chiral potential corrections (40)5.4Strength depending contributions in the effective action (41)6Summary45 Appendix A47 Appendix B49 Appendix C52 1IntroductionThis paper is devoted to the calculation of the one-loop effective action for several models of the global N=1supersymmetric theory with chiral superfields and a subsequent study of some of their phenomenologically interesting aspects.In particular,we investigate in detail the decoupling effects due to the couplings of heavy and light chiral superfields in the theory and subsequent implications for the low energy effective action of light superfields.In principle the decoupling effects of heavyfields infield theory are well understood. According to the decoupling theorem[1,2](for additional references see,e.g.,[3])in thefield theory of interacting light(with masses m)and heavyfields(with masses M)the heavyfields decouple;the effective Lagrangian of the lightfields can be written in terms of the original classical Lagrangian of lightfields with loop effects of heavyfields absorbed into redefinitionsof new lightfields,masses and couplings,and the only new terms in this effective Lagrangianare non-renormalizable,proportional to inverse powers of M(both at tree-and loop-levels).In afield theory as an effective description of phenomena at certain energies,the rescaling of thefields and couplings due to heavyfields does not affect the structure of the couplings,since those are free parameters whose values are determined by experiments.On the other hand if thefield theory is describing an effective theory of an underlying fundamental theory,like superstring theory,where the couplings at the string scale are calculable,the decouplingeffects of the heavyfield can be important and can significantly affect the low energy pre-dictions for the couplings of lightfields at low energies.Therefore the quantitative study ofdecoupling effects at the loop-level in effective supersymmetric theories is important;it should improve our understanding of such effects for the effective Lagrangians from superstring the-ory and provide us with calculable corrections for the low energy predictions of the theory.We also note that as the decoupling theorem is based onfinite renormalization offields and parameters as all parameters in the effective theory(fields,masses,couplings)are determinedfrom the corresponding string theory and hence cannot be renormalized.Therefore we willuse consistence with the decoupling theorem only to check the results.Effective theories of N=1supersymmetric four-dimensional perturbative string vacuacan be obtained by employing techniques of two-dimensional conformalfield theory[4].In particular the k¨a hlerian and the chiral(super-)potential can be calculated explicitly at thetree level.While the chiral potential terms calculated at the string tree-level are protectedfrom higher genus corrections(for a representative work on the subject see,e.g.,[5,6],and references therein),the k¨a hlerian potential is not.Such higher genus corrections to thek¨a hlerian potential could be significant;however,their structure has not been studied verymuch.In this paper we shall not address these issues and assume that the string theory calculation provides us with a(reliable,calculable)form of the effective theory at M string,which would in turn serve as a starting point of our study.One of the compelling motivations for a detailed study of decoupling effects is the phe-nomenon of vacuum restabilization[7]for a class of four-dimensional(quasi-realistic)heteroticsuperstring vacua with an“anomalous”U(1).(On the open Type I string side these effects are closely related to the blowing-up procedure of Type I orientifolds and were recently stud-ied in[8].)For such string vacua of perturbative heterotic string theory,the Fayet-Iliopoulos (FI)D-term is generated at genus-one[9],thus triggering certainfields to acquire vacuumexpectation values(VEV’s)of order M String∼g gauge M P lanck∼5×1017GeV along D-and F-flat directions of the effective N=1supersymmetric theory.(Here g gauge is the gauge coupling and M P lanck the Planck scale.)Due to these large string-scale VEV’s a numberof additionalfields obtain large string-scale masses.Some of them in turn couple through(renormalizable)interactions to the remaining lightfields,and thus through decoupling ef-fects affect the effective theory of lightfields at low energies.(For the study of the effective Lagrangians and their phenomenological implications for a class of such four-dimensional string vacua see,e.g.,[10]–[12]and references therein.)The tree level decoupling effects within N=1supersymmetric theories,were studiedwithin an effective string theory in[13].In a related work[14]it was shown that the lead-ing order corrections of order1important next order effects in the effective chiral potential[15].In addition,in[15]the nonrenormalizable modifications of the k¨a hlerian potential(as was also pointed out in[16]) were systematically studied.These tree level decoupling effects(as triggered by,e.g.,vac-uum restabilization for a class of string vacua)lead to new nonrenormalizable interactions which are competitive with the nonrenormalizable terms that are calculated directly in the superstring theory.In this paper we consider one-loop decoupling effects in N=1supersymmetric theory. We study both the effects on chiral(gauge neutral)superfields and on the effects of gauge superfields.(In another context see[17].)It turns out that an essential modification of low energy predictions takes place not only for chiral superfields[18]but also for gauge superfields. As stated earlier such effective Lagrangians arise naturally due to the vacuum restabilization for a class of supersymmetric string vacua and trigger couplings between heavyfields with mass scale M∼1017GeV and the light(massless)fields[19].(Note however,that we do not include supergravity effects which could also be significant.)As a result wefind that the one-loop effective action after a redefinition offields,masses and couplings coincides with the one-loop effective action of the corresponding theory where heavy superfields are completely absent,in accordance with the decoupling theorem.How-ever,since the masses and the couplings of thefields are calculable in string theory(at the mass scale M string),the decoupling effects add additional corrections to the effective action of the light superfields.These corrections grow logarithmically with M(mass of the heavy superfields)and modify the effective couplings in an essential way,which for a class of string vacua under consideration can be significant.Another interesting result presented in this paper pertains to the chiral effective potential. When the chiral potential depends on massive superfields,quantum corrections due to these fields appear earlier than in the case when one considers lightfields only.This paper is organized as follows.In Section2the general structure of the effective action studied is given and the general approach to addressing the decoupling effects is presented. Section3is devoted to the study of the effective action for the“minimal”model with one heavy and one light(gauge neutral)chiral superfield.In Section4the leading order decou-pling corrections to the effective action for non-minimal models(with more general couplings) are considered.Section5is devoted to the investigation of the one-loop decoupling effects in N=1supersymmetric theory with U(1)gauge vector superfields and chiral superfields charged under U(1).A summary and discussion of the obtained results are given in Section 6.In Appendix A details of the calculation of the one-loop k¨a hlerian effective potential for the minimal model are presented,in Appendix B the calculation of the one-loop k¨a hlerian effective action via diagram technique for the minimal model is described,and in Appendix C details of the calculation for the effective action of non-minimal models are given.2Effective action in the model of interacting light and heavy superfields2.1General structure of the effective actionN=1supersymmetric actions with chiral supermultiplets arise as a subsector of an effective theory of N=1supersymmetric string vacua.Such calculations are carried out for per-turbative string vacua primarily by employing conformalfield theory techniques.(Though less powerful techniques,e.g.,sigma-model approach,in which the integration over massivestring modes is carried out in the the background of the ten-dimensional manifold with thestructure M4×K where M4is a four-dimensional Minkowski space and K is a suitable six-dimensional compact(Calabi-Yau)manifold,can also be employed.)The resulting effectivetheories contain as an ingredient N=1chiral superfieldsΦi with actionS[Φ,¯Φ]= d8zK(¯Φi,Φi)+( d6zW(Φi)+h.c.)(2.1) HereΦi=Φi(z),z A≡(x a,θα,¯θ˙α);a=0,1,2,3;α=1,2,˙α=˙1,˙2,d8z=d4xd2θd2¯θ. Real function K(¯Φi,Φi)is called the k¨a hlerian potential,the holomorphic function W(Φi)is called the chiral potential[20].Expression(2.1)represents the most general action of gauge neutral chiral superfields which does not contain higher derivatives at a component level[20]. We refer to this action as the chiral superfield model of a general form.In a special case K(¯Φi,Φi)=Φ¯Φ,W(Φi)∼Φ3we obtain the well-known Wess-Zumino model.For W(Φi)=0 the present theory represents itself as a N=1supersymmetric four-dimensional sigma-model (see,e.g.,[6]).The action(2.1),which originates from superstring theory,can be treated as a classical effective action of the fundamental theory,suitable for description of phenomena at energies much less than the Planck scale.Such models of chiral superfields are widely used for the study of possible phenomenological implications of superstring theories(see,e.g.,recent papers[8,10,11,12,18]and references therein).One of the most important aspects of the study of these models pertains to the investigation of the decoupling effects,which is the main subject of the present paper.The starting point in the study of the decoupling effects is the model with the classicalaction(2.1)and,for the sake of simplicity,two chiral superfields:a light one,φ,and a heavyone,Φ,i.e.Φi={Φ,φ}.The aim is to to calculate the low-energy effective action in the one-loop approximation and to compute the one-loop corrected effective action of light superfield, only.We refer to the model in which the k¨a hlerian potential is of the canonical(minimal)form:K(Φ,¯Φ,φ,¯φ)=Φ¯Φ+φ¯φ(2.2) as the minimal model,and the model in whichK(Φ,¯Φ,φ,¯φ)=Φ¯Φ+φ¯φ+˜K(Φ,¯Φ,φ,¯φ)(2.3) with˜K=0–as the non-minimal one(in analogy with[10]).We assume that the function ˜K(Φ,¯Φ,φ,¯φ)can be expanded into power series in superfieldsΦ,¯Φ,φ,¯φwhere the leading order term is at least of the third order in the chiral superfields(and thus proportional to at least one inverse power of M)˜K(Φ,¯Φ,φ,¯φ)=φ¯Φ2M...(2.4)The chiral potential M is taken to be of the form:W=MM+...(2.6) with M as a massive parameter.Hence the possible vertices of interaction of superfields havethe formφΦ2,Φφ2,Φ¯φ2M...The effective actionΓ[Φ,¯Φ,φ,¯φ]is defined as the Legendre transform from the generating functional of connected Green functions[21]W[J,¯J]:exp(i¯h(S[Ψ,¯Ψ,ϕ,¯ϕ]++( d6z(JΨ+jϕ)+h.c.)))(2.7)Γ[Φ,¯Φ,φ,¯φ]=W[J,¯J]−( d6z(JΦ+jφ)+h.c.)Γ[Φ,¯Φ,φ,¯φ]can be calculated using the loop-expansion method.This method employs the splitting of all the chiral superfields into a sum of the background superfieldsΦ,φand the quantum onesΦq,φq,using the ruleΦ→Φ+√¯hφqAs a result the action(2.1)after such changes can be written asS q= d8zK(Φ+√¯h¯Φq,φ+√¯h¯φq)++[ d6zW(Φ+√¯hφq)+h.c.](2.9) and the effective action takes the form:exp(i¯hS[Φ+√¯h¯Φq,φ+√¯h¯φq]−−√δΦ(z)Φq(z)+δΓ(for details see[20,21]).The effective action(2.10)can be cast in the formΓ[Φ,¯Φ,φ,¯φ]= S[Φ,¯Φ,φ,¯φ]+˜Γ[Φ,¯Φ,φ,¯φ].Here˜Γ[Φ,¯Φ,φ,¯φ]is a quantum correction in effective action which can be expanded into power series in¯h as˜Γ[Φ,¯Φ,φ,¯φ]=∞ n=1¯h nΓ(n)[Φ,¯Φ,φ,¯φ](2.11) The one-loop quantum correctionΓ(1)to the effective action is defined through the fol-lowing expression[21]:e iΓ(1)= DΦq D¯Φq Dφq D¯φq exp(iS(2)q)(2.12) Here S(2)q corresponds to the part of S q(2.9)which is quadratic in quantum superfields.It is of the formS(2)q= d8z(KΦ¯ΦΦq¯Φq+Kφ¯Φφq¯Φq+KΦ¯φΦq¯φq+Kφ¯φφq¯φq)++[ d6zWΦΦΦ2q+WφΦΦqφq+Wφφφ2q+h.c.](2.13) As a result we arrive at the one-loop effective action of the formΓ[Φ,¯Φ,φ,¯φ]=S+¯hΓ(1)= d8zK(Φ,¯Φ,φ,¯φ)+[ d6zW(Φ,φ)+h.c.]++¯h( d8zK(1)(Φ,¯Φ,φ,¯φ)+( d6zW(1)(Φ,φ)+h.c.))(2.14)Here we suppose that the one-loop correction in the effective actionΓ(1)can be represented in the formΓ(1)= d8zK(1)(Φ,¯Φ,φ,¯φ)+( d6zW(1)(Φ,φ)+h.c.)+...(2.15) Dots denote terms that depend on the supercovariant derivatives of the chiral superfields.The loop corrected effective action has the following structureΓ[Φ,¯Φ,φ,¯φ]= d8zL eff(Φ,D AΦ,D A D BΦ,¯Φ,D A¯Φ,D A D B¯Φ,φ,D Aφ,D A D Bφ,¯φ,D A¯φ,D A D B¯φ)+( d6zL(c)eff(Φ,φ)+h.c.)+...(2.16)Here D A are supercovariant derivatives,D A=(∂a,Dα,¯D˙α).L eff is the effective super-Lagrangian that we write in the formL eff=K eff(Φ,¯Φ,φ,¯φ)+...K=K(Φ,¯Φ,φ,¯φ)+∞n=1¯h n K(n)(2.17)and L(c)is the effective chiral LagrangianL(c)=W eff(Φ,φ)+...(2.18)K eff is the k¨a hlerian effective potential that depends only on the chiral superfieldsΦ,¯Φ,φ,¯φbut not on their(covariant)derivatives.W eff is the chiral effective potential that depends on on(holomorphic)chiral superfields{Φ,φ},only.Dots denote the terms that depend on the the space-time derivatives of chiral superfields only.Furthermore,one can prove that the one-loop correction to the chiral potential is zero(for the N=1supersymmetric theory which does not include gauge superfields).However,higher corrections can exist(cf.[22]–[24]),i.e.W eff(Φ,φ)=W(Φ,¯φ)+∞n=2¯h n W(n)(Φ,φ)(2.19)Here K(n)and W(n)are loop corrections to the k¨a hlerian and chiral potential,respectively.Since in this paper we concentrate on the one-loop corrected effective action only,we are mainly interested in the correction to the k¨a hlerian potential which is the leading term in the one-loop corrected low-energy effective action.(At low energies(E≪M)higher derivative terms are suppressed.)Our ultimate goal is to obtain the effective action for light superfields,only.For that purpose one must eliminate heavy superfields from the one-loop effective actionΓ[Φ,¯Φ,φ,¯φ] (2.14)by means of the effective equations of motion.These equations can be solved by an iterative method up to a certain order in the inverse mass M of heavy superfield.Substituting a solution of these equations into the effective action(2.14)we then obtain the one-loop corrected effective action of light superfields only.In the following subsection we shall describe the procedure in detail.2.2The effective equations of motionThe effective equations of motion for heavy superfields in the model with the effective action (2.14,2.15)are of the formδΓ4¯D2(∂K∂Φ)+∂Wδ¯Φ=0:−1∂¯Φ+∂K(1)∂¯Φ=0(2.20)The effective equations of motion for light superfields have an analogous form.We consider the case when the interactions with the gauge superfields are absent(see however Section5) and W(1)=0(which is absent at one-loop level(cf.,discussion above)).The equations(2.20)can be solved via an iterative method,described below.We can represent the heavy superfieldΦin the formΦ=Φ0+Φ1+...+Φn+...(2.21) whereΦ0is zeroth-order approximation,Φ1isfirst-order one,etc..We assume that|D2Φ|≪M¯Φsince the superfieldΦis heavy,and thus the assumption is valid.The zeroth-order approximationΦ0can be found from the condition∂WAfter a substitution of the expansion(2.21)into equations(2.20)we arrive at the following equation for the(n+1)-th-order solution for¯Φn+1(∂¯W∂¯Φ)|Φ=Φ0+...+Φn=(2.22)=¯D2∂Φ|Φ=Φ0+...+Φn−∂K∂Φ|Φ=Φ0+...+Φn−∂K(1)2Φ2+˜W(see eqs.(2.5-2.6),eq.(2.23))can be rewritten in the formM¯Φn+1+(∂¯˜W∂¯Φ)|Φ=Φ0+...+Φn=(2.23)=¯D2∂Φ|Φ=Φ0+...+Φn−∂K∂Φ|Φ=Φ0+...+Φn−∂K(1)which represents itself as a column q =uv.The action for q reads asS 0q =−14¯D 2q −ψand ¯χ[q ]=14D 2q −¯ψ)δ(14¯D2−1214D 2q −¯ψ)δ(12T r log ∆(2.32)Here T r is a functional supertrace,andS [q ]=116(K ψ¯ψ−1){D 2,¯D2}−14¯W′′D 2(2.34)The terms proportional to the supercovariant derivatives of K ψ¯ψ,W ′′and ¯W′′are omitted since the one-loop k¨a hlerian effective potential by definition does not depend on the deriva-tives of superfields.In order to determine T r log ∆we use the Schwinger representationT r log ∆=trds∂sΩ=Ω˜∆(2.35)Here ˜∆is a matrix operator of the form ˜∆=−14W ′′¯D2−116A (s )D 2¯D2+18B α(s )D α¯D2+14C (s )D 2+1i˙A=F +AF 2−CW ′′(2.38)1i˙C=−¯W ′′−A ¯W ′′2+CF 2and an analogous system of equations for ˜A,˜B,˜C ,which can be obtained from this one by changing W ′′into ¯W ′′and vice versa.Here F =1−K ψ¯ψ.Since the initial condition for ΩisΩ|s =0=1the initial conditions for A,˜A,B,˜B,C,˜C )are A |s =0=˜A |s =0=C |s =0=˜C |s =0=0.The solution for B α,˜B ˙αevidently has the form B α=˜B ˙α=0.The manifest form of thematrices A,˜AC,˜C ,necessary for exact calculations,is of the form A =A 11A 12A 21A 22;C =C 11C 12C 21C 22(2.39)Here index 1denotes the sector of heavy superfield Φand 2the sector of light superfield φ.Now let us solve the system for matrices A,C .The solution for ˜A,˜C can be easily obtained in an analogous way since the system with B α=˜B ˙α=0is invariant under the change A →˜A,C →˜C.Let us study the solution for A,C which should be chosen in the formA =A i +A 0(2.40)C =C i +C 0Here A i ,C i is a partial solution of the inhomogeneous system,and A 0,C 0is a general solution of the homogeneous system.It is straightforward to see that A i =−12−1,C i =0.And A 0,C 0should satisfy the system of equations1i˙C0=A 0¯G 2+C 0F 2A 0,C 0should be chosen to be of the form A 0=a 0exp(iωs ),C 0=c 0exp(iωs )where a 0,c 0,ωare some functions of the background superfields and the d’Alembertian operator,but are independent of s .As a result we arrive at the equations for a 0,c 0:a 0(ω1−F 2)+c 0W ′′=0(2.42)c 0(ω1−F 2)+a 0¯W′′2=0This system of equations has a non-trivial solution atdetω12−F 2W′′¯W ′′2ω12−F 2=0(2.43)In principle,parameters ωcan be found from this equation.Their exact form is determined by the structure of the matrix W ′′and F .It turns out that for the specific cases studied in detail the subsequent sections (minimal (Section 3)and non-minimal (Section 4)cases)these parameters are different.As a result the final solution can be cast in the form:A =ka 0k exp(iωk s )−12∞dsi∂16π2(is )2.A ,and ˜Aare functions of 2.Hence in order to calculate the one-loop k¨a hlerian effective potential it is necessary to find A and ˜Aand to expand them into a power series in 2.In this section we addressed in detail the techniques needed to calculate the one-loop corrected effective action,to eliminate the heavyfields and to obtain the effective action of lightfields only.In the subsequent sections these techniques will be applied to obtain the explicit form of the one-loop corrected actions for specific models.In Section5we shall also include interactions with the U(1)vector superfields and modify the procedure accordingly. 3One-loop effective action for minimal modelsIn this section we study decoupling effects for the model with minimal k¨a hlerian potential (2.2)K=Φ¯Φ+φ¯φ.Thefirst part consists of calculating the one-loop correction to the k¨a hlerian effective potential.In the second part we solve the effective equations of motion for the heavy superfields.As a result we arrive at the effective action of the light superfields.3.1Calculation of the effective action3.1.1The one-loop k¨a hlerian effective potentialHere we are going to calculate the one-loop contribution to k¨a hlerian effective potential by means of the effective equations of motion.We study the minimal model with the chiral potential in the formW=13!gφ3(3.1)with the corresponding functions in W′′(see eq.(2.25))Wφφ=λΦ+gφWφΦ=λφWΦΦ=M(3.2) The total classical action with the chiral potential(3.1)is of the formS= d8z(φ¯φ+Φ¯Φ)+[ d6z(13!gφ3)+h.c.](3.3)Note that the chiral potential used is of the“minimal”form:it involves the renormalizable terms only and the renormalizable coupling between the light and heavy superfields is linear in the heavyfields,which yields a dominant contribution in the study of the decoupling effects.These types of couplings are typical for a class of effective string models after the vacuum restabilization was taken into account,and thus this minimal model provides a prototype example for the study of decoupling effects in N=1supersymmetric theories. (The results for this model and the physics consequences were presented in[18].For the sake of completeness we present here the intermediate steps in the derivation.)In order tofind the one-loop k¨a hlerian effective potential we should determine the operator Ω(s)that satisfies the equation(2.35).For the case of this minimal model this equation leads to the following system of equations for matrices A,C:1i˙C=−¯W′′−A¯W′′2with the analogous equations for˜A,˜C.Initial conditions are A|s=0=˜A|s=0=C|s=0=˜C|s=0=0.Calculations described in Appendix A show that the one-loop contribution to k¨a hlerian effective potential is of the form:K(1)=−1(|λΦ+gφ|2−M2)2+4|λ2Φ¯φ+λMφ+λg|φ|2)|2)××log(|λΦ+gφ|2+2λ2φ¯φ+M2+ µ2+ +(|λΦ+gφ|2+2λ2φ¯φ+M2− (|λΦ+gφ|2−M2)2+4|λ2Φ¯φ+λMφ+λg|φ|2|2)2MΦ2+Φφ2)+h.c.)−1(|λΦ+gφ|2−M2)2+4|λ2Φ¯φ+λMφ+λg|φ|2)|2)××log(|λΦ+gφ|2+2λ2φ¯φ+M2+ µ2+ +(|λΦ+gφ|2+2λ2φ¯φ+M2− (|λΦ+gφ|2−M2)2+4|λ2Φ¯φ+λMφ+λg|φ|2|2)corrections to the chiral effective potential one must set¯Φ=¯φ=0.Possible vertices contributing to one-loop effective potential should be quadratic in quantum superfields[21]. They have the formK¯φ¯φ¯φ2,Kφφφ2,(Kφ¯φ−1)φ¯φ,12WΦφΦφ,K¯Φ¯Φ¯Φ2,KΦΦΦ2,(KΦ¯Φ−1)Φ¯Φ,142)g(Φ)(3.6)Namely,after a transformation to an integral over the chiral superspace by the ruled8zF(Φ,¯Φ)= d6z(−¯D24(2−m2))g(Φ)(3.8) A transformation to the form of an integral over the chiral superspace leads tod6zf(Φ)(2(2π)4f(Φ)(p2decreases a number of D,¯D-factors by4and the corresponding scaling dimension by2.Each propagator of a massless superfield gives no contribution(scaling dimension0)since it has the form(cf.[20])G(z1,z2)=−D21¯D2216δ12=0.Hence a contribution of such a diagram is equal to zero,and a one-loop contribution to the chiral effective potential is absent:W(1)(Φ)=0.We note that this situation is analogous to the general model of one chiral superfield studied in[27].However,higher order(loop)corrections to the chiral effective potential can arise not only for diagrams with external massless lines but also for those with heavy external lines, in spite of the fact that it was commonly believed that quantum corrections to the chiral effective potential for massive superfields are absent.For example,consider the supergraph|¯D 2||¯D 2¯D2D 2D 2D 2D 2−−−−Here a double line denotes the external superfield Φ,and a single line corresponds to thepropagator <φ¯φ>of the massless superfield φ.A contribution of such a supergraph is of the form I =d 4p 1d 4p 2(2π)8d 4θ1d 4θ2d 4θ3d 4θ4d 4θ5(gk 2l 2(k+p 1)2(l +p 2)2(l +k )2(l +k +p 1+p 2)2××δ13¯D 2316δ14δ42D 21¯D 253!)2λ3d 4p 1d 4p 2(2π)8d 2θΦ(−p 1,θ)Φ(−p 2,θ)Φ(p 1+p 2,θ)××k 2p 21+l 2p 22+2(kl )(p 1p 2)3!)2λ3d 2θd 4p 1d 4p 2(2π)8k 2p 21+l 2p 22+2(kl )(p 1p 2)3!)2λ3d 2θd 4x 1d 4x 2d 4x 3d 4p 1d 4p 2。

Research ObjectivesThe MILC Collaboration is engaged in a broad research program in Quantum Chromodynamics (QCD).This research addresses fundamental questions in high energy and nuclear physics,and is directly related to major experimental programs in thesefields.It includes studies of the mass spectrum of strongly interacting particles,the weak interactions of these particles,and the behavior of strongly interacting matter under extreme conditions.The Standard Model of High Energy Physics encompasses our current knowledge of the funda-mental interactions of subatomic physics.It consists of two quantumfield theories:the Weinberg-Salaam theory of electromagnetic and weak interactions,and QCD,the theory of the strong interac-tions.The Standard Model has been enormously successful in explaining a wealth of data produced in accelerator and cosmic ray experiments over the past thirty years;however,our knowledge of it is incomplete because it has been difficult to extract many of the most interesting predictions of QCD,those that depend on the strong coupling regime of the theory,and therefore require non-perturbative calculations.At present,the only means of carrying out non-perturbative QCD calculations fromfirst principles and with controlled errors,is through large scale numerical sim-ulations within the framework of lattice gauge theory.These simulations are needed to obtain a quantitative understanding of the physical phenomena controlled by the strong interactions,to de-termine a number of the fundamental parameters of the Standard Model,and to make precise tests of the Standard Model’s range of validity.Despite the many successes of the Standard Model,it is believed by high energy physicists that to understand physics at the shortest distances,a more general theory,which unifies all four of the fundamental forces of nature,will be required.The Standard Model is expected to be a limiting case of this more general theory,just as classical mechanics is a limiting case of the more general quantum mechanics.A central objective of the experimental program in high energy physics,and of lattice QCD simulations,is to determine the range of validity of the Standard Model,and to search for new physics beyond it.Thus,QCD simulations play an important role in efforts to obtain a deeper understanding of the fundamental laws of physics.QCD is formulated in the four-dimensional space-time continuum;however,in order to carry out numerical calculations one must reformulate it on a lattice or grid.It should be emphasized that the lattice formulation of QCD is not merely a numerical approximation to the continuum formu-lation.The lattice regularization of QCD is every bit as valid as continuum regularizations.The lattice spacing a establishes a momentum cutoffπ/a that removes ultraviolet divergences.Stan-dard renormalization methods apply,and in the perturbative regime they allow a straightforward conversion of lattice results to any of the standard continuum regularization schemes.Lattice QCD calculations proceed in two steps.In thefirst,one uses importance sampling tech-niques to generate gauge configurations,which are representative samples from the Feynman path integrals that define QCD.These configurations are saved,and in the second step they are used to calculate a wide variety of physical quantities.It is necessary to generate configurations with a range of lattice spacings,and then perform extrapolations to the zero lattice spacing limit.Fur-thermore,the computational cost of calculations rises as the masses of the quarks,the fundamental constituents of strongly interacting matter,decrease.Until recently,it has been too expensive to carry out calculations with the masses of the two lightest quarks,the up and the down,set to their physical values.Instead,one has performed calculations for a range of up and down quark masses, and extrapolated to their physical values guided by chiral perturbation theory,an effectivefield theory that determines how physical quantities depend on the masses of the lightest quarks.The extrapolations in lattice spacing(continuum extrapolation)and quark mass(chiral extrapolation) are the major sources of systematic errors in QCD calculations,and both must be under control in order to obtain trustworthy results.In our current simulations,we are,for thefirst time,working at or near the physical masses of the up and down quarks.The gauge configurations produced in these simulations greatly reduce,and will eventually eliminate,the systematic errors associatedwith the chiral extrapolation.A number of different formulations of QCD on the lattice are currently in use by lattice gauge theorists,all of which are expected to give the same results in the continuum limit.In recent years, major progress has been made in thefield through the development of improved formulations(im-proved actions)which reducefinite lattice spacing artifacts.Approximately twelve years ago,we developed one such improved action called asqtad[1],which significantly increased the accuracy of our simulations for a given amount of computing resources.We have used the asqtad action to generate an extensive library of gauge configurations with small enough lattice spacings and light enough quark masses to perform controlled calculations of a number of physical quantities. Computational resources provided by the DOE and NSF have enabled us to complete our program of generating asqtad gauge configurations.These configurations are publicly available,and have been used by us and by other groups to study a wide range of physical phenomena of importance in high energy and nuclear physics.Ours was thefirst set of full QCD ensembles that enabled control over both the continuum and chiral extrapolations.We have published a review paper describing the asqtad ensembles and the many calculations that were performed with them up to2009[2]. Over the last decade,a major component of our work has been to use our asqtad gauge config-urations to calculate quantities of importance to experimental programs in high energy physics. Particular emphasis was placed on the study of the weak decays and mixings of strongly interact-ing particles in order to determine some of the least well known parameters of the standard model and to provide precise tests of the standard model.The asqtad ensembles have enabled the calcu-lation of a number of physical quantities to a precision of1%–5%,and will enable many more quantities to be determined to this precision in the coming years.These results are already having an impact on experiments in high energy physics;however,in some important calculations,partic-ularly those related to tests of the standard model,higher precision is needed than can be provided by the existing asqtad ensembles.In order to obtain the required precision,we are now working with the Highly Improved Staggered Quark(HISQ)action developed by the HPQCD Collabora-tion[3].We have performed tests of scaling in the lattice spacing using HISQ valence quarks with gauge configurations generated with HISQ sea quarks[4].We found that lattice artifacts for the HISQ action are reduced by approximately a factor of2.5from those of the asqtad action for the same lattice spacing,and taste splittings in the pion masses are reduced by approximately a factor of three,which is sufficient to enable us to undertake simulations with the mass of the Goldstone pion at or near the physical pion mass.(“Taste”refers to the different ways one can construct the same physical particle in the staggered quark formalism.Although particles with different tastes become identical in the continuum limit,their masses can differ atfinite lattice spacing).More-over,the improvement in the quark dispersion relation enables us to include charm sea quarks in the simulations.The properties of the HISQ ensembles are described in detail in Ref.[5],and the first physics calculations using the physical quark mass ensembles in Refs.[6,7,8].The current status of the HISQ ensemble generation project is described at the link HISQ Lattice Generation and some initial calculations with them at Recent Results.The HISQ action also has major advan-tages for the study of QCD at high temperatures,so we have started to use it in our studies of this subject.Projects using the HISQ action will be a major component of our research for the next several years.Our research is currently focused on three major areas:1)the properties of light pseudoscalar mesons,2)the decays and mixings of heavy-light mesons,3)the properties of strongly interacting matter at high temperatures.We briefly discuss our research in each of these areas at the link Recent Results.References[1]The MILC Collaboration:C.Bernard et al.,Nucl.Phys.(Proc.Suppl.),60A,297(1998);Phys.Rev.D58,014503(1998);G.P.Lepage,Nucl.Phys.(Proc.Suppl.),60A,267(1998);Phys.Rev.D59,074501(1999);Kostas Orginos and Doug Toussaint(MILC),Nucl.Phys.(Proc.Suppl.),73,909(1999);Phys.Rev.D59,014501(1999);Kostas Orginos,Doug Tou-ssaint and R.L.Sugar(MILC),Phys.Rev.D60,054503(1999);The MILC Collaboration:C.Bernard et al.,Phys.Rev.D61,111502(2000).[2]The MILC Collaboration: A.Bazavov et al.,Rev.Mod.Phys.82,1349-1417(2010)[arXiv:0903.3598[hep-lat]].[3]The HPQCD/UKQCD Collaboration: E.Follana et al.,Phys.Rev.D73,054502(2007)[arXiv:hep-lat/0610092].[4]The MILC Collaboration: A.Bazavov al.,Phys.Rev.D82,074501(2010)[arXiv:1004.0342].[5]The MILC Collaboration: A.Bazavov al.,Phys.Rev.D87,054505(2013)[arXiv:1212.4768].[6]The MILC Collaboration: A.Bazavov et al.,Phys.Rev.Lett.110,172003(2013)[arXiv:1301.5855].[7]The Fermilab Lattice and MILC Collaborations:A.Bazavov,et al.,Phys.Rev.Lett.112,112001(2014)[arXiv:1312.1228].[8]The MILC Collaboration:A.Bazavov et al.,Proceedings of Science(Lattice2013)405(2013)[arXiv:1312.0149].。

建筑工程专业英语词汇1建筑工程专业英语词汇 1英语小札 2009-12-03 10:22:00 阅读49 评论0 字号：大中小订阅建设,建筑,修建 to build, to construct建筑学 architecture修筑,建筑物 building房子 house摩天大楼 skyscraper公寓楼 block of flats (美作:apartment block)纪念碑 monument宫殿 palace庙宇 temple皇宫,教堂 basilica大教堂 cathedral教堂 church塔,塔楼 tower十层办公大楼 ten-storey office block柱 column柱列 colonnade拱 arch市政 town planning (美作:city planning)营建许可证,建筑开工许可证 building permission绿地 greenbelt建筑物的三面图 elevation设计图 plan比例尺 scale预制 to prefabricate挖土,掘土 excavation基 foundations, base, subgrade打地基 to lay the foundations砌好的砖列 course of bricks脚手架 scaffold, scaffolding质量合格证书 certification of fitness原材料 raw material底板 bottom plate垫层 cushion侧壁 sidewall中心线 center line条形基础 strip footing附件 accessories型钢 profile steel钢板 steel plate熔渣 slag飞溅 welding spatter定位焊 tacking引弧 generating of arc熄弧 quenching of arc焊道 welding bead坡口 beveled edges外观检查 visual inspection重皮 double-skin水平方向弧度 radian in horizontal direction 成型 molding直线度 straightness accuracy焊缝角变形 welding line angular distortion 水平度 levelness铅垂度 verticality翘曲变形 buckling deformation角尺 angle square对接焊缝 butt weld母材 parent metal法兰密封面 flange sealing surface夹层 interlayer表面锈蚀浓度 surface corrosion concentration挠曲变 bending deformation超声波探伤 ultrasonic testing/ ultrasonic examination 压力容器 pressure vessel预制下料 prefabrication baiting排版直径 set-type diameter焊缝 welding line中幅板 center plate测量方法 measuring method基准点 datum mark跳焊 skip welding允许偏差 allowable variation补强板 stiffening plate开孔 tapping对接接头 banjo fixing butt jointing角钢 angle iron安装基准圆 installation fundamental circle吊装立柱 hoisting upright column焊接钢管 welded steel pipe向心斜拉筋 centripetal canting pull rope带板 band plate槽钢胀圈 channel steel expansion ring环口 collar extension局部变形 local distortion环缝 circumferential weld顶板 top plate拱顶 vault顶板加强肋 stiffening rib对接 butt joint胎具 clamping fixture卷板机 plate bending rolls中心支架 center bearing bracket椭圆度 ovality等分线 bisectrix搭接宽度 lap width点焊 spot welding搭接焊 overlap welding对称 symmetrically螺旋爬梯 cockle stairs放料阀 baiting valve液位计 content gauge芬兰维萨拉 Vailsla OY美国美科 "Met-coil, USA"集中式空调系统 centralized air conditioning system 裙房 annex热源 heat source平面位置的空间 space of planimetric position密封性能 sealing performance机房 machine room节点 timing专业 "profession or discipline 都可以,要根据上下文"连体法兰 coupling flange垂直井笼 vertical well cage变风量 variable air rate施工面展开 construction unfolds违约行为 noncompliance合同交底- contract presentation管理承包商 Management Contractor party工程量 work amount实施的形象进度 progress of implementation完工资料 as-built documentation文整 clear-up审核 review汽车式起重机 Autocrane深化图纸 deepen drawing设备配置计划 equipment furnishment plan结构预埋配合阶段 Structure pre-embedment assistance stage精装修阶段 Fine fitment stage工程施工阶段 Construction stage工程竣工阶段 Completion stage台钻 Bench drill冲击钻 Churn drill手电钻 Electric portable drill砂轮切割机 Abrasive cutting off machine角钢卷圆机 Angle iron rolling machine管道切断器 Pipe cutting machine铜管调直机 Copper pipe straightening machine管道压槽机 Book joint setting machine for pipes管道压槽机 Book joint setting machine for pipes角向磨光机 Angle polishing machine电动套丝机 Electric threading machine电动卷扬机 Electric winch电动试压泵 Motor-driven pressure test pump手动试压泵 Manual pressure test pump阀门试压机 Valve pressure test device阀门试压机 Valve pressure test deviceTDC(F)风管加工流水线 TDC(F)air ductwork fabrication stream line等离子切割机 Plasma cutting machineTDC(F)法兰条成型机 TDC(F) flange strip shaping mill勾码成型机 Forming machine for flange clampTDC(F)风管加工成型机 TDC(F) duct fabrication shaping mill 多普勒超声波流量检测仪 Doppler ultrasonic flow detector 温、湿度传感器 "Temperature, humidity senor"精密声级计 Precision sound level meter风管漏风量测试仪、风室式漏风测试装置 "Duct air leakage tester, airchamber air leakage testing device"风罩式风量测试仪 Air hood air rate tester微压计、毕托管、热球（电）风速仪 "Micromanometer , pitot tube, hot bulb(electrical) anemoscope"潜水泵 Submerged pump电动弯管机 Electric pipe bender铜管弯管机 Copper pipe bender液压弯管机 Hydraulic pipe bender电动剪刀 Electric clipper液压铆钉钳 Hydraulic riveting clamp线槽电锯 Trunking electric saw开孔器 Tapper电动空压机 Electric air compressor液压千斤顶 Hydraulic jack液压手推车 Hydraulic trolley焊条烘干箱 Welding rod drying box手拉葫芦 Chain block道（垫）木 Sleeper转速表 Tachometer电流钳型表 Clip-style ammeter压力表 Pressure gauge接地电阻测试仪 Earthing resistance testing device 氧气表 Oxygen gauge乙炔表 Acetylene gauge对讲机 Walkie talkie文件和资料 documents and information?建设单位 Construction unit安装单位 Installation unit二、道路工程英语词汇桥梁 bridge公路干道 highway工程工程学 engineering公路工程 highway engineering路基 roadbase路面 pavement构造物建造构成制造 construct施工（名） construction试验室 laboratory现场检测 field test（名）试验检验（不）进行试验 experiment试验检测测量 test质量上流社会的 quality合格，取得资格 qualify材料 material沥青柏油以沥青铺（一般指沥青路）asphalt沥青（指原材料） bitumen沥青的 bituminous沥青混合料 bituminous mixture混凝土 concrete钢筋混凝土 RC (reinforced concrete)信誉信用贷款 credit进度快慢 tempo计划 plan评定 evaluation检查（名）检验 inspection标准水准规格标准的合格的 standard技术性的工业的 technical技术技巧技术的工艺的专门的 technic水泥 cement碎石路碎石路 macadam砂砾碎石砂砾层 gravel钢筋 reinforcing steel bar或reinfored steel 石石头石场石的石制的 stone检查员 inspector测量（名） measuring测量（及）检测（及）勘测测绘（名）survey 设备仪器装置 device申请 application铺路工人 paver经理 manager加强 reinforce（被加强的 reinforced ）sign 签字署名通知list 表名册目录列举tabulation 制表列表表格mapping 绘图制图camera 照相机photo 照片给。

suzuki偶联实验报告Suzuki Coupling Experiment ReportIntroductionThe Suzuki coupling reaction, also known as the Suzuki-Miyaura reaction, is a widely used method in organic synthesis for the formation of carbon-carbon bonds. This reaction involves the coupling of an aryl halide with an organoborane in the presence of a palladium catalyst and a base. The Suzuki coupling reaction has found numerous applications in the synthesis of pharmaceuticals, agrochemicals, and materials science.Experimental ProcedureIn this experiment, we aimed to perform a Suzuki coupling reaction between bromobenzene and phenylboronic acid to form biphenyl. The reaction was carried out in a three-necked round-bottom flask equipped with a reflux condenser. The reaction mixture consisted of bromobenzene, phenylboronic acid, palladium catalyst, and a base in a suitable solvent. The reaction was heated under reflux for a specified period of time, and the progress of the reaction was monitored by TLC (thin-layer chromatography).Results and DiscussionThe Suzuki coupling reaction proceeded smoothly, and the desired product, biphenyl, was obtained in good yield. The reaction was monitored by TLC, which showed the disappearance of the starting materials and the appearance of the product. The reaction conditions, including the choice of solvent, base, andcatalyst, were found to have a significant impact on the reaction efficiency. The use of an appropriate base and solvent is crucial for the success of the Suzuki coupling reaction.ConclusionIn conclusion, the Suzuki coupling reaction is a powerful method for the formation of carbon-carbon bonds. This experiment demonstrated the successful synthesis of biphenyl through the Suzuki coupling reaction, highlighting the importance of reaction conditions and catalyst choice. The versatility and efficiency of this reaction make it a valuable tool in the field of organic synthesis.References1. Miyaura, N.; Suzuki, A. "Palladium-Catalyzed Cross-Coupling Reactions of Organoboron Compounds." Chemical Reviews, 1995, 95 (7), 2457-2483.2. Suzuki, A. "Cross-Coupling Reactions of Organoboranes: An Easy Way to Construct C-C Bonds." Pure and Applied Chemistry, 1991, 63 (3), 419-422.。