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coleman and weinberg pointed out several years ago [ 1 ] that quantum loops and radiative corrections can play an important role in determining the structure of the vacuum of a quantum field or system of fields and particles . specifically they showed that while a scalar field with mass parameter @xmath0 and classical tree potential is unable to develop a vacuum expectation value ( vev ) and spontaneous symmetry breaking ( ssb ) , such vev and ssb become achievable when we take quantum loops into account . this is particularly so if the scalar field is coupled to a gauge field and dimensional transmutation can occur . the overall conclusion is that an alternative electroweak symmetry breaking ( ewsb ) mechanism exists along side the standard model ewsb mechanism that is based on the classical tree potential : @xmath1 with a non - zero negative mass parameter @xmath2 . the coleman - weinberg alternative model dispenses with the mass parameter @xmath3 in equation ( 1 ) but adds quantum loops or higher order potential terms . this alternative mechanism has become known as radiative electroweak symmetry breaking ( rewsb ) . + the fact is that these two mechanisms do not just differ in what terms appear or do not appear in the scalar field potential , but lead to very different physical perceptions of what causes electroweak symmetry breaking . the standard model based on equation ( 1 ) with its @xmath2 attributes electroweak symmetry breaking to a primordial fundamental scalar field that unlike any existing particle known so far has a negative mass parameter @xmath2 . in contrast , the coleman - weinberg rewsb mechanism would attribute ewsb to quantum dynamics and a quantum origin . such quantum dynamics if favored would widen the scope for our search and understanding of ewsb and the origin of mass . another way of looking at the matter is to say that in the standard model mechanism cewsb , the quantum system starts off with a pre - assigned mass scale @xmath4 compared to the coleman - weinberg model rewsb where the same quantum system is left to fix its own scale of dynamics . the question arises what role the pre - assigned scale parameter @xmath5 plays in the quantum dynamics , and whether we can find any observable features that distinguish the outcome of these two dynamics . + because of the widely differing physical interpretations of the two mechanisms , we consider it worthwhile to examine in some quantitative detail , what observational features and signatures distinguish rewsb on the one hand , from the conventional standard model electroweak symmetry breaking ( cewsb ) on the other hand . al . [ 2 - 6 ] have considered the problem from one perspective . + our approach to the problem is to first set out in section 2 , aspects of electroweak symmetry breaking that do not depend on any explicit choice of the scalar field potential @xmath6 . such aspects will therefore be common to both rewsb and cewsb and we may call these aspects the core of electroweak symmetry breaking . thereafter , we take up equation ( 1 ) in section 3 , with its @xmath7 , as one explicit choice of the scalar potential . then we work out what new relations besides the core ewsb equations , follow from this one choice of @xmath6 . these new relations or features we can call the specific signatures of the standard model cewsb . in section 4 , we make a different choice of the scalar potential , by setting @xmath3 which is the coleman - weinberg rewsb model , with quantum loops added . we work out the new features in relation to the core equations , and call these the signatures of rewsb . we proceed further in sections 5 and 6 , to re - examine the same rewsb using the more modern aspects of the coleman - weinberg model known as the renormalization group improved effective potential [ 7 - 10 ] . further improvement using 2-loop @xmath8 and @xmath9 functions is considered in section 7 . the two sets of signatures , cewsb and rewsb , are compared in section 8 . our final results and conclusions are stated in section 9 . in terms of a scalar field , the core features that break electroweak symmetry even when no explicit scalar potential is specified , are a complex scalar field that may or may not be a fundamental field . this complex scalar field must be a doublet under the electroweak @xmath10 gauge symmetry . the complex doublet scalar field must have a non zero vacuum expectation value we take to be v. given such a field one is able to immediately write or parameterize it in the form : + @xmath11 in which only one component field @xmath12 acquires the non - zero vacuum expectation value written : @xmath13 this form of the scalar field is all that is required to derive many results and features of the ewsb . these several features include various charged and neutral currents as well as couplings of fermions and gauge bosons to the scalar field . the details of these core features can be seen in several places such as [ 11 ] . among these relations that we obtain without our specifying any explicit scalar potential , are the gauge boson masses : @xmath14 @xmath15    where @xmath16 is @xmath17 coupling constant , and @xmath18 is @xmath19 coupling constant . + it turns out also that a definitive numerical value of v = 246 gev can be obtained without recourse to any explicit choice of the scalar potential . one simply combines the v - a current structure of the gauge theory [ 11 ] , with such accessible processes as @xmath5 decays , and obtains expression for v in terms of the fermi constant : + @xmath20 given this value of v and the known masses of the gauge bosons stated in equations ( 4 ) and ( 5 ) , one deduces the values of the two gauge coupling constants at the ewsb scale v : @xmath21    similarly from yukawa couplings of equation ( 2 ) to fermions , we obtain fermion mass relations and couplings : @xmath22 where @xmath23 stands for yukawa coupling constant of a given fermion f , such as the top quark @xmath24 . again these relations do not require any explicit choice or specification of the scalar potential . in particular , the relations hold whether @xmath25 as in rewsb , or @xmath26 ( cewsb ) . + we now note one area where we are not able to obtain any information at all based on equation ( 2 ) alone , without specifying some explicit form of the scalar potential . this area is in the determination of physical higgs particle mass @xmath27 , and the self coupling parameter @xmath28 of the scalar field and its components . this becomes the area where we can focus our search for any distinguishing features between rewsb and cewsb . we will therefore proceed by devising ways to determine these two quantities @xmath27 and @xmath28 , first in a cewsb model and then in a rewsb model . both quantities turn out to be derivable from some explicit form of the scalar potential we now write as @xmath29 where @xmath30 stands for the scalar field ( component ) that has the non - zero vev . our main focus is in the structure and analysis of such two potentials @xmath31 and @xmath32 , and the higgs masses and couplings they predict . the conventional ewsb is based on equation ( 1 ) . this potential defines the ground state of the system @xmath33 and gives a value of the vev of @xmath30 in terms of the parameters of the chosen potential : @xmath34 with @xmath35 upon plugging equations ( 2 ) and ( 10 ) into equation ( 1 ) , we obtain a mass relation for the physical higgs particle h(x ) : it is : @xmath36 more formally the mass of the higgs particle is given in terms of a chosen potential by : @xmath37    equations ( 10 ) and ( 11 ) become new relations which used separately or in combination with the core equations ( 2 ) - ( 8) may lead to specific signatures of the cewsb . thus from equations ( 10 ) and ( 11 ) we get @xmath38 as a relation specific to cewsb model . we can go further to use the core value v = 246 gev and relate @xmath27 specifically to @xmath28 as : @xmath39 if we assume that the scalar field interaction was perturbative + in the dynamics leading to ewsb at scale v , and that @xmath40 , we obtain that : @xmath41 which becomes a signature of cewsb mechanism . on the other hand , if @xmath42 , then cewsb predicts @xmath43 gev . notably however , the cewsb does not give us any specific value for higgs mass nor a value for @xmath28 . we consider next the coleman weinberg rewsb potential and what signatures we can tag onto it . for a @xmath44 scalar field theory , coleman and weinberg obtained the general expression for its effective potential : @xmath45^n\ ] ] where @xmath46 is the classical field that has non - zero vacuum expectation value . @xmath47 are 1pi vertex greens functions to which n external legs @xmath48^n $ ] attach , each carrying zero momentum . when these 1pi functions are expanded perturbatively into feynman loops , the above series can be re - organized into a perturbative loop expansion for the same effective potential : @xmath49 where @xmath50 is the tree potential given by equation ( 1 ) ; @xmath51 is the one - loop potential ; @xmath52 is the 2-loop potential , etc . the above loop potentials require in general to be renormalized . the renormalized effective potential determines the state of ewsb and the higgs mass through the standard equations : @xmath53 @xmath54 @xmath55    for a purely scalar field theory , the above loops involve only virtual scalar particles . when however other fields are present in the system that can couple radiatively to the scalar field , the loop contributions of these other fields to @xmath56 have to be taken into account . in the specific case of ewsb where fermions and gauge bosons are present besides the scalar field , the coleman weinberg potential generalizes to include quarks , leptons and gauge boson loops . these extended loop calculations have been carried out in a number of places [ 7 , 11 ] . we write down some of the results up to 1-loop potential for rewsb . in one form cheng and li write [ 11 ] : @xmath57 where @xmath58 is the renormalization scale ; and c is given by : @xmath59\ ] ] here @xmath60 are vector boson masses ( @xmath61 ; @xmath62 is scalar ( physical higgs ) boson mass , and @xmath63 are the fermion masses , quarks and leptons . + using core equations ( 4)-(8 ) without using any equations from cewsb section 3 , we can rewrite equation ( 21 ) in terms of coupling constants as follows : @xmath64\ ] ]    if we neglect contributions from all leptons and quarks except the top quark , we can write the rewsb potential equation ( 20 ) up to 1-loop potential finally as [ 2 ] : @xmath65 ( log\frac{\phi^2}{m^2 } - \frac{25}{6})\ ] ] here @xmath24 is the top quark loop yukawa coupling . the neglect of other fermion couplings follows from equation ( 8) , where a fermion yukawa coupling is proportional to its mass , and the top quark with its dominant mass clearly overshadows all other fermions . regarding the parameter m in the above equation , we note that in the absence of a pre - set mass scale @xmath3 in the rewsb system , the quantum dynamics sets its own scale which we take to be the renormalization scale m , as well as the scale of any ssb in the system . therefore we can re - define our renormalization conditions on the effective potential as ; @xmath66    @xmath67    @xmath68    in place of equation ( 23 ) , we can also write the 1-loop effective potential in the form due to ford et.al . [ 8 ] , and to casas et . al.[9 - 10 ] . @xmath69    we will work with the form ( 23 ) . we plug equation ( 23 ) into equations ( 24 ) - ( 26 ) and obtain relations that embody rewsb signatures : @xmath70 putting c value from equation ( 22 ) we obtain a quadratic equation for @xmath28 : @xmath71 using the core coupling values from equation ( 7 ) , the quadratic equation becomes : @xmath72 this gives two possible values of @xmath28 in terms of top quark yukawa coupling constant @xmath24 , both at the renormalization scale m = @xmath73 : @xmath74 and @xmath75 if we require that both coupling constants are positive : @xmath76 then solution ( 31 ) implies that @xmath77 with @xmath78 at @xmath79 . on the other hand , based on equation ( 32 ) , we find at @xmath80 while for @xmath81 decreases to zero , @xmath82 . this solution would indicate that the scalar dynamics in the ewsb has a coupling constant @xmath28 that lies between zero and a value 0.004456 while the yukawa top quark coupling has a value that lies between zero and 0.502758496 . we may take the mean of each parameter as its value at the ewsb scale in this case of solution ( 32 ) . then analogous to equation ( 7 ) we can write the @xmath81 and @xmath24 values at the ewsb scale for solution ( 32 ) as : @xmath83 in this way , we may claim that solution ( 32 ) represents a situation where @xmath84 at ewsb , while solution ( 31 ) represents a situation where @xmath85 at ewsb scale . these two situations we can also try to distinguish in our signature analysis of rewsb . + in the case of solution ( 31 ) , we can use the known top quark mass of 175 gev along side equation ( 8) to estimate @xmath24 at ewsb scale . we get that @xmath86 giving a corresponding value of @xmath28 from equation ( 31 ) : @xmath87    as seen from equations ( 33 ) and ( 34 ) both solutions ( 31 ) and ( 32 ) are perturbative , if we define perturbativity condition as : @xmath88 the two solutions differ however in a profound way . this is that if the dynamics of ewsb is very weakly perturbative ( both @xmath28 and @xmath89 very small ) as per equations ( 32 ) and ( 33 ) , rewsb predicts that the top quark coupling is relatively much stronger than the scalar self interaction @xmath28 at the ewsb scale . on the other hand , if the ewsb dynamics is more strongly coupled , ( both @xmath28 and @xmath24 large ) , though still perturbative as per equations ( 31 ) and ( 34 ) , the scalar self coupling constant @xmath28 is relatively much larger than the top quark yukawa coupling constant @xmath24 . these signatures of the rewsb can be ascertained experimentally . + we can go further to analyze equations ( 25 ) and ( 23 ) for higgs mass . we obtain : @xmath90 using @xmath91 from equation ( 28 ) , this becomes : @xmath92\ ] ]    using core values from equation ( 7 ) we can rewrite equation ( 37 ) as : @xmath93\ ] ] next we use equation ( 31 ) or ( 32 ) to eliminate @xmath28 . we obtain : @xmath94\ ] ] finally using core equations ( 7 ) and ( 8) we obtain a higgs boson mass for the rewsb model : @xmath95\ ] ] taking a top quark mass @xmath96 this evaluates to @xmath97 ( the positive value ) . this appears high . the coleman - weinberg 1-loop effective potential equation ( 23 ) used in the above analysis of rewsb , has the feature that it was defined at one and only one arbitrarily chosen mass scale point m which is the renormalization scale of the otherwise divergent effective potential . this one scale point m had also to be chosen as the ewsb point @xmath98 , with @xmath99 this restricted choice of @xmath100 was necessitated by the need for the log terms in equations ( 23 ) - ( 27 ) to vanish or remain small and perturbative . this feature of the coleman - weinberg potential equation ( 23 ) remains even if we make another arbitrary choice of the renormalization point m. we remain bound to study our effective potential and its signature values , only for field values @xmath30 in the vicinity of an arbitrarily chosen renormalization scale m. in effect , @xmath101 can not be studied generally as a function of higgs field @xmath100 to ascertain how the potential behaves in these other regions of larger or smaller @xmath30 , and to what extent any new features such as new minima or maxima of @xmath102 found in those regions , affect or modify the ewsb features or signatures of @xmath103 found from earlier limited observation at one arbitrary renormalization point m. a way out of the problem is to free @xmath103 of its dependence on the renormalization scale m. that is we make @xmath103 a physical observable , whose field @xmath30 and coupling constant parameters @xmath104 can now vary widely over any desired domains , unaffected by any one arbitrarily chosen renormalization point m. of course this freedom of the parameters of @xmath103 to vary widely still calls for some restraint such that the perturbative character of the overall loop expansion equations ( 15 ) and ( 16 ) can still be guaranteed . both objectives and the automatic summing up of leading logarithms , are achieved by making the entire effective potential equation ( 15 ) or ( 16 ) , satisfy a renormalization group equation(rge ) given by : @xmath105 v_{eff}(m , \lambda , g_i , \phi .. ) = 0\ ] ] here @xmath106 , and @xmath107 are the rg functions ( the beta functions and the anomalous dimension @xmath108 of the higgs field ) . this rge has a standard solution we write in the form : @xmath109 and call the rg improved effective potential . all its parameters @xmath110 vary or run widely , each in a coordinated manner prescribed by its beta or gamma function . the variable @xmath111 parameterizes the arbitrary renormalization scale , while the parameters of @xmath112 run according to the equations : @xmath113 @xmath114 with : @xmath115 also : @xmath116 @xmath117    in the above equations , @xmath118 is some fixed initial renormalization point or reference scale , which we shall choose as @xmath119 , the @xmath120 gauge boson mass . similarly the value of the higgs field @xmath121 at @xmath122 we shall choose as the field with vev @xmath123 where @xmath124 gev . the beta and gamma functions have to be calculated separately to some loop order , and plugged into the above running equations . explicit expressions of these @xmath125 and @xmath126 functions computed to 1-loop and 2-loop orders for the ewsb system , have been tabulated by ford et al . [ 8 ] . we shall rely on their values to compute numerically the parameters @xmath127 defined in equations ( 43)-(47 ) . + in order to solve these integral and differential equations , we require to specify the boundary conditions of the equations . these boundary conditions are the values of the parameters at some chosen scale we specify as @xmath122 which means scale @xmath128gev . our explicit values of these parameters at @xmath122 we take from equations ( 7 ) , ( 33 ) and ( 34 ) . + once we have computed the explicit details of how the parameters vary with @xmath111 over a wide range of values in equations ( 43 ) - ( 47 ) , our aim will be to use the new rg improved effective potential equation ( 42 ) to re - examine the issue of signatures of rewsb . to proceed with the analysis , we need first to expand equation ( 42 ) into perturbative loop series and truncate the series at a convenient loop order chosen here as 1-loop order . thus by analogy with equations ( 16 ) and ( 20 ) , we write our rg improved effective potential equation ( 42 ) as : @xmath129 to 1-loop order we write the rg improved rewsb potential as : @xmath130 ( log\frac{\phi^2(t)}{m^2(t ) } - \frac{25}{6})\ ] ] which replaces equation ( 23 ) . similarly , corresponding to equation ( 27 ) we would now write the rg improved 1-loop potential of ford et . 8 ] and casas et . 9 - 10 ] : @xmath131 we will work with equation ( 49 ) , and comment on equation ( 50 ) later . our analysis of equation ( 49 ) now proceeds in stages as follows . + first we note that by construction the full ( untruncated ) rg improved effective potential equation ( 42 ) or ( 48 ) becomes independent of scale , satisfying : @xmath132 this scale invariance applies also to all order derivatives of @xmath112 with respect to any of its parameters such as @xmath30 . thus we also have the conditions : @xmath133 and : @xmath134 the implication of these equations is that equations ( 24)-(26 ) from which we determine the state of occurrence of ssb and the resulting higgs mass as well as signatures of rewsb ( all arising from inherent dynamics of the system ) , have become independent of any one choice of renormalization scale t or m(t ) at which we evaluate the system . in a way , @xmath112 is now defined simultaneously over a whole range of the renormalization scale from @xmath135 to @xmath136 at any one point of which we can freely compute the dynamical quantities in equations ( 24 ) - ( 26 ) and determine at what points we have ssb and its corresponding mass spectra , unaffected by the value of the renormalization scale t at that point , except that the results obtained at any one t scale or point , differ from the results at another t scale or point by mere change or transformation of scale , but not intrinsic difference of dynamics of the system . + we note however that the above discussion regarding scale invariance of the rg improved effective potential holds strictly only where the potential is not truncated as in equations ( 49 ) and ( 50 ) . where @xmath112 is truncated and its arguments are evaluated with beta and gamma functions that are also computed only to a finite order ( 1-loop , 2-loop , ... beta and gamma functions ) , equations ( 51)-(53 ) cease to hold exact . we correct for this by looking for a restricted stretch of the t scale , call it @xmath137 with @xmath138 , where the truncated functions in equations ( 49 ) - ( 53 ) may still be considered reasonably flat or minimally dependent on t. we work with such flat regions for potentials ( 49)- ( 53 ) , in place of the region @xmath139 of the exact scale invariant quantities . now we analyze equations ( 49 ) , ( 24)-(26 ) . + our first step is to compute the various running parameters of @xmath140 specified in equations ( 43 ) - ( 47 ) . we illustrate our computational procedures by first considering the simpler case of 1-loop beta and gamma functions . later we treat the case of 2-loop beta and gamma functions . to 1-loop beta and gamma functions [ 8 ] , the running parameter equations to compute are : + @xmath141 @xmath142 @xmath143 with @xmath144 from equation ( 7 ) and @xmath145 + also we get values of @xmath146 by numerically integrating the following equations : @xmath147}\ ] ] @xmath148 where @xmath149 ; and @xmath150 here we use as boundary values , the pair of values ( @xmath151 ) from equation ( 34 ) . later we shall consider the other pair of values ( @xmath152 ) of equation ( 33 ) . finally we have for the @xmath153 and @xmath154 : @xmath155dt'\right)\ ] ] with this integral separated into two parts for purposes of numerical computation : @xmath156dt ' = \frac{1}{16 \pi^2}\int_{g_{t0}}^{g_t(t)}[3 g_t^2]dg_t(t ' ) - \frac{1}{16 \pi^2}\int_0^t [ \frac{9}{4 } g_2 ^ 2 + \frac{3}{4 } g_1 ^ 2]dt'\ ] ] we proceeded by assigning only positive values to scale t , and insisting in our numerical computations of equations ( 54 ) - ( 60 ) that we obtain only matching positive values of the coupling constants @xmath157 , and @xmath158 . the results we obtained are shown in * figure 1*. the potential @xmath112 equation ( 49 ) is next plotted against t , to search for a scale region @xmath137 where @xmath112 is reasonably flat , independent of t. from the plot shown in * fig . 2 * we see that equation ( 49 ) is reasonably scale invariant in the region : @xmath159 . this allows us to compute the quantities : @xmath160 and @xmath161 at any point within this flat @xmath137 region , and to run the quantities down to our reference scale @xmath122 . it is in this way that we obtain below , a higgs ( running ) mass at the electroweak scale @xmath122 . the relevant quantities to compute and run in region @xmath162 are : @xmath163 implying a ssb condition any where in region @xmath137 given by : @xmath164 where : @xmath165\ ] ] also : @xmath166 which combined with equation ( 62 ) gives within region @xmath137 , a running higgs mass of : @xmath167 a plot of this @xmath168 is shown in * figure 2 * and yields a higgs ( running ) mass value of @xmath169 gev at the electroweak scale t = @xmath137 = 0 . the corresponding physical higgs mass differs from this by only a small vacuum polarization correction discussed by casas et . al . [ 9,10 ] we will not go into this . + based on * figure 2 * , we can interpret the region @xmath170 not only as a region beyond which the 1-loop truncated rg improved effective potential is not reliable , but also as a cut off point @xmath171 beyond which the standard model ewsb theory is probably not valid . this will lead us to say that radiative electroweak symmetry breaking ( rewsb ) with rg improved effective potential ( at 1-loop beta function ) predicts a higgs mass around 245.6 gev , as well as a cut off energy scale @xmath172 gev or less . we examine next the features of rewsb in the case @xmath174 at electroweak scale , presented by equation ( 33 ) , in place of equation ( 34 ) . we recall that equations ( 33 ) and ( 34 ) provided us a means to discriminate between two scenarios where at ewsb scale , the scalar field coupling @xmath28 is stronger ( equation ( 34 ) ) or weaker ( equation ( 33 ) ) than the top quark yukawa coupling . our calculations in sections 4 and 5 , dealt with the case @xmath175 . here we re - compute the same rg improved effective potential equation ( 49 ) under this alternative solution equation ( 33 ) . specifically we take as our new boundary values , the values given in equation ( 33 ) : @xmath176 and @xmath177 . we then re - compute our running parameters and the effective potential ( 49 ) , together with the running higgs mass . the results and features we find with equation ( 33 ) and the 1-loop beta and gamma function equations ( 43 ) - ( 47 ) are shown in * figure 3 * . they lead us to a running higgs mass of only 6.65gev shown in * figure 4*. since experiments already rule out such low mass higgs boson , we can draw one conclusion that the rewsb model clearly selects only the solution ( 34 ) : @xmath178 at ewsb scale . + working now with only solution ( 34 ) , we consider finally the case of 2-loop beta and gamma function rg improvement of the effective potential equation ( 49 ) . according to kastening [ 12],bando et . al [ 13 ] , one gets optimal improvement of a 1-loop effective potential if we evaluate it using 2-loop beta and gamma functions . we test this out by re - computing our rewsb features and comparing with our 1-loop results of sections 4 and 5 . accordingly , we replace equations ( 54 ) to ( 60 ) by the following 2-loop beta function running parameters : @xmath179 } \ ] ] @xmath180 } \ ] ] @xmath181 } \ ] ] with @xmath144 and @xmath182 as before . + for 2-loop @xmath183 and @xmath158,we compute positive values of the upper integration limits @xmath184 and @xmath158 that match an assigned t value in the equations : @xmath185 and : @xmath186 where : @xmath187 the boundary values we use are from equation ( 34 ) : @xmath188 and @xmath189 also because of the greatly intertwined nature of the 2-loop @xmath190 functions and the running parameters , certain approximations had to be made in which quantities like @xmath191 , in the above integrands , were treated as constants having values corresponding to a chosen t value , or else to their known 1-loop values . + finally for @xmath153 and @xmath154 we have the 2-loop gamma function equation : @xmath192dt'\right)\ ] ] where : @xmath193 the results of computing these 2-loop running parameters , and plugging into equations ( 49 ) , ( 24 ) - ( 26 ) , are shown in * figures 5 and 6 . * some individual running parameters appear greatly modified at the 2-loop level . this is particularly so for @xmath158 and @xmath194 seen from figures 1 and 6 . correspondingly , the 2-loop rg improved effective potential does not exhibit much of a flat @xmath137 region seen in figure 6 compared to 1-loop figure 2 . the value of running higgs mass at ewsb scale : @xmath122 predicted in both cases is however about the same : @xmath195 gev . we can compare these features of our rg improved rewsb with features found in conventional electroweak symmetry breaking calculations . we already showed in section 3 that cewsb ( at tree level ) , does not predict any explicit value of the higgs mass @xmath27 nor the scalar coupling constant @xmath28 . but the conventional electroweak symmetry breaking potential ( with @xmath196 can also have higher order potential terms added to it as in equation ( 16 ) , and treated to a rg group improvement as for our rewsb model considered in sections 5 and 6 . this has been done by a number of authors [ 7 - 17 ] , particularly ford et . al . [ 8 ] and casas et we can look at these rg improved cewsb results and compare them to our rewsb results to see any particular signature features . these authors [ 8 - 10 ] worked with 1-loop effective potential of the form shown in equations ( 27 ) and ( 50 ) to which non - zero scalar field mass term @xmath197 is added from equation ( 1 ) . this rg improved cewsb equation ( 50 ) is then analyzed by the usual equations ( 24 ) - ( 26 ) , combined with the additional requirement of vacuum stability or @xmath198 . al [ 9,10 ] obtained a higgs mass estimate of @xmath199gev , to be compared with our explicit rewsb result of running higgs mass @xmath169 gev . admittedly , many of these cewsb rg improved effective potential analysis , were done at a time the top quark mass was still considered unknown free parameter , in contrast to our treatment . al . [ 8 ] for example stated their result in terms of the top quark mass : @xmath200gev . overall , there appears a need to re - analyze the rg improved cewsb effective potential case for better comparison with rewsb , and to ascertain the role the scalar field mass parameter @xmath26 actually plays . + another comparison we can make is with the recent work of elias et . al.[2 - 6 ] who analyzed the same radiative electroweak symmetry breaking ( rewsb ) , and raised the same issue of the possible experimentally accessible signature differences of rewsb and cewsb . they worked not with the standard coleman - weinberg feynman loop calculated effective potential equations ( 15 ) , ( 23 ) , ( 27 ) , ( 49 ) , ( 50 ) , but took advantage of the fact that the loop calculated effective potentials invariably involved leading logarithms as in equation ( 20 ) , multiplied by a factor c that involves products of ew coupling constants and the scalar field @xmath30 . al . showed that this usual coleman - weinberg rg improved effective potential in the particular case of rewsb can be realized as a direct summation to infinity of leading logarithm terms . putting such leading logarithm parameterized effective potential through the usual equations ( 24 ) - ( 26 ) , elias et . al . obtained a rewsb higgs mass ranging in value from @xmath201 gev . they obtained ssociated scalar field coupling @xmath202 . these results are comparable to our values @xmath203 gev , and @xmath204 . their values for other ew coupling constants are also very comparable , thus while for the top quark , elias et . al . obtained the value @xmath205 at ewsb scale , we obtained in equation ( 34 ) the value @xmath206 . +   + we find close agreement between our results based on the standard coleman - weinberg loop calculated , and renormalization group improved , effective potential , and the elias et . al . results based on direct summation of leading logarithm terms . basing on both calculations of the same radiative electroweak symmetry breaking ( rewsb ) , we can re - affirm that rewsb model not only remains a viable mechanism of electroweak symmetry breaking , but is able to give an explicit value of the ( running ) higgs mass . the ( running ) higgs mass predicted by the rewsb mechanism , lies in the range 215 - 250 gev , at electroweak scale . in contrast the cewsb models of ford et . al [ 8 ] , casas et al . [ 9.10 ] and others [ 7,14 - 16 ] , are only able to put a lower bound typically @xmath207gev on the higgs mass . because of this limited information from cewsb , we can not use the higgs mass value as a conclusive signature to distinguish between rewsb from cewsb . + we are left to consider the coupling constants @xmath28 and @xmath24 of the system . our calculations established two points regarding @xmath28 and @xmath24 . we found that of the two possibilities : @xmath208 or @xmath173 at ewsb scale , the @xmath209 is the correct one , while the case @xmath173 that implies a higgs mass @xmath210 is already ruled out by experiment . explicitly , we obtained in our equation ( 34 ) that the ratio @xmath211 . elias et . al . found a lower ratio of 2.15 . the two results are however consistent to the extent @xmath212 +   + if we accept the rewsb value of higgs mass of 215 - 250 gev as physical higgs mass holding whether the mechanism of ewsb is by rewsb or by cewsb , we can deduce the corresponding @xmath213 value from equations ( 13 ) and ( 14 ) . we find @xmath214 to be compared with @xmath215 at the same higgs mass of 245.6 gev . we conclude as did elias et . al . [ 2,3 ] , that the rewsb mechanism is associated with a greatly enhanced scalar field coupling @xmath216 . + this can become an important signature difference between rewsb and cewsb that can be verified experimentally . the fact is that based on equations ( 1 ) and ( 2 ) , the individual scalar field components @xmath217 all couple with the same strength , @xmath213 or @xmath218 depending on the model . when this fact is combined with the equivalence theorem [ 18 ] between ewsb nambu - goldstone bosons and linearly polarized gauge bosons , one comes to the conclusion that interactions of @xmath219 can provide experimentally observable coupling constant based signature differentiation between rewsb and cewsb , a fact pointed out by elias et . al . [ 2,3 ] , but needing further study . + the observed enhanced coupling @xmath220 by itself calls for explanation . it suggests as part of our main finding that the scalar field couples less strongly to achieve the same end result of ewsb in a quantum system that has a pre - set mass scale @xmath221 , compared to the same quantum system with no pre - set scale @xmath3 . the same scalar field couples more strongly in the latter case . whether this is a general principle of quantum dynamics is something for further study . +   + * references :* + 1 . s. coleman and e. weinberg , phys . d7 ( 1973 ) 1888 . v. elias , r.b . mann , d.g.c.mckeon , and t.g . steele , phys . 91 , 251601 . f. a. chishtie , v. elias , and t. g. steele , intern . a20 ( 2005 ) 6241 . v. elias , r.b . mann , d.g.c . mckeon and t.g . steele , nucl . b678 ( 2004 ) 147 . + 5 . v. elias , r. b. mann , d.g.c . mckeon and t.g . steele , arxiv.hep-ph/0508107 ( 2005 ) . f. a. chistie , v. elias , r.b . mann , d.g.c.mckeon , and t.g . steele , nucl . b 743 ( 2006 ) 1034 . + 7 . m. sher , phy . report 179 ( 1989 ) 273 . c.ford , d.r.t.jones , p.w stephenson and m b einhorn , nucl . phys.b395 ( 1993 ) 17 . casas , j.r . espinosa , m. quiros and a. riotto , nucl . b436 ( 1995 ) 3 ; ( e ) b439 ( 1995 ) 466 . casas , j.r . espinosa , m. quiros , phys . b342 ( 1995 ) 171 . t. p. cheng and l. f. li , gauge theory of elementary particle physics , oxford university press ( 1984 ) . b. kastening : phys . b283 ( 1992 ) 287 . m. bando , t. kugo , m. maekawa and h. nakano , phys . b301 ( 1993 ) 83 ; prog . ( 1993 ) 405 . g. altarelli and g. isidori phys . b 337 ( 1994 ) 141 + 15.m . lindner , m. sher and h.w . zaglauer , phys . lett . b228 ( 1989 ) 139 . vincenzo branchina and hugo faivre , phys . d72 ( 2005 ) 065017 . p. kielanowski , s.r . juarez w , and h.g . solis - rodriguez , phys . d72 ( 2005 ) 096003 ) . + 18 . p. n. maher , l. durand and k. riesseimann , phys . d 48 ( 1993 ) 1061 . + * figure captions : *    figure 1 : running parameters of rg improved effective potential at 1-loop @xmath222 and @xmath126 functions and for equation ( 34 ) , @xmath223 . + figure 2 : flatness @xmath137 test and running higgs mass plot yielding a running higgs mass intercept of @xmath169 gev at ew scale t = 0 . + figure 3 : running parameters of rg improved effective potential at 1-loop @xmath222 and @xmath126 functions , with @xmath224 , equation ( 33 ) case . + figure 4 : flatness @xmath137 and running higgs mass plots at 1-loop @xmath222 and @xmath126 functions , and for @xmath224 equation ( 33 ) case . + figure 5 : running parameters of rg improved effective potential at 2-loop @xmath222 and @xmath126 functions and for equation ( 34 ) , @xmath223 . + figure 6 : 2-loop @xmath222 and @xmath126 functions flatness @xmath137 and running higgs mass plots , yielding a running higgs mass intercept of @xmath169 gev at ew scale t = 0 .
we present a comparative study of radiative electroweak + symmetry breaking and conventional standard model breaking , and pose the question whether experiments can distinguish one breaking mode from the other . 
 the importance of the problem lies in the fact that the two breaking modes have very different physical interpretations concerning the mechanism of spontaneous electroweak symmetry breaking and the origin of mass .    _ 
 keywords : radiative electroweak symmetry breaking _ + * pacs : 12.38.-t , *   + e - mail : fndili@uh.edu