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basically , there are two competing explanations of the experimentally observed power - law behaviour of elastic hadronic form factors : hard scattering @xcite and the feynman mechanism @xcite . at sufficiently large momentum transfer , the feynman mechanism contribution is dominated by configurations in which one of the quarks carries almost all the momentum of the hadron . in qcd , this results in an extra @xmath5 suppression compared to the hard scattering term generated by the valence configurations with small transverse sizes and finite light - cone fractions of the total hadron momentum carried by each valence quark . the hard term , which eventually dominates , can be written in a factorized form @xcite,@xcite,@xcite , as a product of the perturbatively calculable hard scattering amplitude and two distribution amplitudes accumulating the necessary nonperturbative information . however , this mechanism involves exchange of virtual gluons , each exchange bringing in a suppression factor @xmath6 . hence , to describe existing data by the hard contribution alone , one should intentionally increase the magnitude of the hard scattering term by using distribution amplitudes with a peculiar `` humped '' profile @xcite . in this case , passive quarks carry a small fraction of the hadron momentum and , as pointed out in ref.@xcite , the `` hard '' scattering subprocess , even at rather large momentum transfers @xmath7 , is dominated , in fact , by very small gluon virtualities . this means that the hard scattering scenario heavily relies on the assumption that the asymptotic pqcd expressions are accurate even for momenta smaller than @xmath8 , @xmath9 in the region strongly affected by finite - size effects , nonperturbative qcd vacuum fluctuations @xmath10 including these effects shifts the hard contributions significantly below the data level even if one uses the humpy distribution amplitudes and other _ ad hoc _ modifications intended to increase the hard term ( see , @xmath11 @xcite ) . furthermore , as argued in ref.@xcite , the derivation of the humpy distribution amplitudes in @xcite implies a rather singular picture ( infinite correlation length ) of the qcd vacuum fluctuations . under realistic assumptions , it is impossible to get distribution amplitudes strongly differing from the smooth `` asymptotic '' forms . the latter are known to produce hard contributions which are too small to describe the data on elastic form factors . thus , there is an increasing evidence in favour of the alternative scenario , @xmath12 that for experimentally accessible momentum transfers the form factors are still dominated by the purely soft contribution corresponding to the feynman mechanism .    in the language of the light - cone formalism @xcite , the soft term is given by the overlap of the soft parts of the hadronic wave functions , @xmath9 is an essentially nonperturbative object . among the existing approaches to the nonperturbative effects in qcd , that which is closest to pqcd is the qcd sum rule method @xcite . qcd sum rules were originally used to calculate the soft contribution for the pion form factor in the region of moderately large @xcite,@xcite and then small momentum transfers @xcite . it should be emphasized that , in the whole region @xmath13[0ex]{$\sim$}}$}}3 \ , gev^2 $ ] , the results are very close to the experimental data : the feynman mechanism alone is sufficient to explain the observed behaviour of the pion form factor . for higher @xmath2 , the direct qcd sum rule method fails due to increasing contributions from higher condensates . however , a model summation of the higher terms into nonlocal condensates @xcite indicates that the soft term dominates up to @xmath14 @xcite . this conclusion is also supported by a recent calculation within the framework of the light - cone sum rules @xcite . an important observation made in ref.@xcite is that the results of the elaborate qcd sum rule analysis are rather accurately reproduced by a simple local quark - hadron duality prescription . the latter states that one can get an estimate for a hadronic form factor by considering transitions between the free - quark states produced by a local current having the proper quantum numbers , with subsequent averaging of the invariant mass of the quark states over the appropriate duality interval @xmath15 . the duality interval has a specific value for each hadron , @xmath11 @xmath16 for the pion and @xmath17 for the nucleon . the local duality ansatz , equivalent to fixing the form of a soft wave function , was used to estimate the soft contribution in the case of the proton magnetic form factor @xcite . the results agree with available data @xcite , @xcite over a wide region , @xmath18[0ex]{$\sim$}}$}}q^2 \ , { \raisebox{-.2ex}{$\stackrel{\textstyle < } { \raisebox{-.6ex}[0ex][0ex]{$\sim$}}$}}\ ,   20\ , gev^2 $ ] . furthermore , the calculation of ref.@xcite correctly reproduces ( without any adjustable parameter ) , the observed magnitude of the helicity - nonconservation effects @xmath19 with @xmath20 @xcite . it is difficult to understand the origin of such a large scale within the hard scattering scenario , since possible sources of helicity nonconservation in pqcd include only small scales like quark masses , intrinsic transverse momenta @xmath10 , and one would rather expect that @xmath21 . thus , the study of spin - related properties provides a promising way for an unambiguous discrimination between soft and hard scenarios .    of a particular interest there is the @xmath0 transition . a special attention to this process was raised by the results @xcite of the analysis of inclusive slac data which indicated that the relevant form factor drops faster than predicted by the quark counting rules . the relevant hard scattering contribution was originally considered in ref.@xcite , where it was observed that the hard scattering amplitude in this case has an extra suppression due to cancellation between symmetric and antisymmetric parts of the nucleon distribution amplitude , and it was conjectured that the faster fall - off found in @xcite can be explained by the dominance of some non - asymptotic contribution . later , it was claimed @xcite that , by appropriately choosing the distribution amplitudes , one can get a leading - twist hard term comparable in magnitude with the data . furthermore , the results of a recent reanalysis @xcite of the inclusive slac data are rather consistent with the @xmath22 behaviour , and this revived the hope that the @xmath0 form factor can be still described by pqcd .    however , the important result of the pqcd calculation @xcite is that the lowest - twist hard contribution has the property @xmath23 . experimentally , the ratio @xmath1 is rather small @xcite , which indicates that the leading - twist pqcd term is irrelevant in the region @xmath24[0ex]{$\sim$}}$}}\ , 3 \ , gev^2 $ ] . in the present paper , we use the local quark - hadron duality to estimate the soft contribution for the @xmath25 and @xmath26 form factors of the @xmath0 transition to study whether the soft contribution is large enough to describe the data and whether the relative smallness of the electric form factor persists in the region of moderately large momentum transfers @xmath27[0ex]{$\sim$}}$}}q^2 { \raisebox{-.2ex}{$\stackrel{\textstyle < } { \raisebox{-.6ex}[0ex][0ex]{$\sim$}}$}}\ , 15 \ , gev^2 $ ] . the starting object for a qcd sum rule analysis of the @xmath0 transition is the 3-point correlator : @xmath28 of the electromagnetic current @xmath29 and two ioffe currents @xcite @xmath30    we use the following parameterization for the projections of @xmath31 and @xmath32 onto the nucleon and @xmath33-isobar states , respectively : @xmath34 here , @xmath35 is the dirac spinor of the nucleon while @xmath36 is the spin-3/2 rarita - schwinger wave function for the @xmath33-isobar , @xmath9 @xmath37 , @xmath38 , @xmath39 , @xmath40 ; with @xmath41 being the nucleon mass and @xmath42 that of @xmath33 . we use the notation @xmath43 .    on the hadronic level , the @xmath0 transition makes the following contribution to the correlator ( [ 1 ] ) : @xmath44 where @xmath45 is the @xmath0 vertex function @xmath46 ( @xmath47 ) and @xmath48 the projector onto the isobar state @xmath49    the form factors @xmath50 are related to a more convenient set @xmath51 by @xmath52 @xmath53 @xmath54 ( see , @xmath11 @xcite ) . one should not confuse the magnetic form factor @xmath26 given by eq.([8 ] ) with the effective form factor mentioned in refs.@xcite,@xcite . in particular , the form factor @xmath55 defined by eq.(6.2 ) of ref.@xcite can be written in terms of @xmath26 and @xmath25 ( defined by eqs.(8),(9 ) above ) as @xmath56 where @xmath57 is the energy of the virtual photon in the proton rest frame . note that , for large @xmath2 , our @xmath26 and @xmath55 of eq.(6.2 ) of ref.@xcite have the same power behaviour . multiplying all the factors in eq.([5 ] ) explicitly , one ends up with a rather long sum of different structures @xmath58 accompanied by the relevant invariant amplitudes @xmath59 , each of which is a combination of the three independent transition form factors listed above . to incorporate the local quark - hadron duality , we write down the dispersion relation for each of the invariant amplitudes : @xmath60 where @xmath61 , @xmath62 . the perturbative contributions to the amplitudes @xmath63 can also be written in the form of eq.([11 ] ) . evidently , the physical perturbative spectral densities @xmath64 differ from their perturbative analogues , the difference being most pronounced in the resonance region , @xmath9 for small @xmath65 and @xmath66 values . in particular , @xmath64 contains the double @xmath67-function term corresponding to the @xmath0 transition : @xmath68 while the perturbative spectral densities @xmath69 are smooth functions of @xmath65 and @xmath66 . the local quark - hadron duality assumes , however , that the two spectral densities are in fact dual to each other : @xmath70 @xmath9 they give the same result when integrated over the appropriate duality intervals @xmath71 . the latter characterize the effective thresholds for higher states with the nucleon or , respectively , @xmath33-isobar quantum numbers . as noted in ref.@xcite , the local duality prescription can be treated as a model for the soft wave functions : @xmath72 @xmath9 @xmath15 and @xmath73 also set the scale for the width of the transverse momentum distribution . using this model , we can obtain a good estimate for the overlap of the soft wave functions only in the intermediate @xmath2-region where the soft contribution is sensitive mainly to the @xmath74-widths of the quark distributions rather than to their detailed forms . from experience with the proton form factor calculations , we expect that local duality will work in the region between @xmath75 and @xmath76 . the low-@xmath2 region @xmath24[0ex]{$\sim$}}$}}1 \ , gev^2 $ ] , in which there appear large nonperturbative contributions due to the long - distance propagation in the @xmath2-channel , can be analyzed within a full - framed qcd sum rule approach supplemented by the formalism of induced condensates @xcite or bilocal operators @xcite .    applying the local quark - hadron duality to the two - point correlators of @xmath31- or , respectively , @xmath77-currents , we obtain simple relations between the duality intervals @xmath15 , @xmath73 and the residues @xmath78 , @xmath79 of the ioffe currents : @xmath80 after the duality intervals are fixed ( @xmath11 from the qcd sum rule analysis of the relevant two - point function @xcite ) , the local duality estimates for the form factors do not have any free parameters . now , choosing a particular lorentz structure @xmath58 , one can get the local duality estimate for the relevant combination of the form factors . one should remember , however , that not all the invariant amplitudes are equally reliable . to compare the contributions related to different structures , one should specify a reference frame . in our case , the most relevant is the infinite momentum frame where @xmath81 while @xmath82 is fixed . so , @xmath83 , the structures with the maximal number of the `` large '' factors @xmath84 are more reliable than those in which @xmath84 is substituted by the `` small '' parameter @xmath85 or by @xmath86 . however , dealing with the @xmath77-current in the @xmath33-channel , one should realize that @xmath32 has also a nonzero projection onto the spin-1/2 isospin-@xmath87 states @xmath88 : @xmath89 where @xmath90 is a constant , @xmath91 is the mass of the spin-1/2 state @xmath88 and @xmath92 the relevant dirac spinor satisfying @xmath93 .    from eq.([15 ] ) , it follows that any amplitude containing the @xmath84-factor , is `` contaminated '' by the transitions into the spin-1/2 states . these states lie higher than the @xmath33-isobar and , in principle , one can treat them as a part of the continuum . then , however , there will be strong reasons to expect that the duality interval @xmath73 for the `` contaminated '' invariant amplitudes deviates from that for the amplitudes containing only the spin-3/2 contributions in the @xmath77-channel . another possibility is to project out the amplitudes which have contributions due to the transitions into spin-@xmath94 isospin-@xmath87 states . to achieve this , it is convenient to use the basis in which @xmath95 is always placed at the leftmost position . then , according to eqs.([5]-[7 ] ) , the invariant amplitudes corresponding to the structures with @xmath96 and @xmath97 are free from the contributions due to the spin-1/2 isospin-3/2 states . in this basis , keeping only the terms with @xmath96 and @xmath97 in eq.([5 ] ) , we get @xmath98 \frac{3(m+m)}{8 m } ( g_m^*(q^2)+g_e^*(q^2))\right .   \nonumber \\ \left . + \frac{q_\mu}{2 } \left ( m [ \gamma_\nu , \hat{p } ] + m [ \gamma_\nu , ( \hat{p } - \hat{q } ) ] \right ) g_1(q^2 ) \right .   \nonumber \\ \left . - p_\nu [ \hat{p},\hat{q } ] g_2(q^2 ) - q_\nu [ \hat{p},\hat{q } ] \left(g_3(q^2 ) - \frac12 g_2(q^2 ) \right ) + ... \right )   \ . \label{16}\end{aligned}\ ] ]    hence , from the invariant amplitudes related to the structures proportional to @xmath96 , we can get the local duality estimates for the form factors @xmath99 . similarly , extracting the structure @xmath100 $ ] , we get an expression for @xmath101 . counting the powers of @xmath102 , we expect that results for @xmath103 are less reliable than those for @xmath104 and @xmath105 , while results for @xmath106 are less reliable than those for @xmath103 .    the number of independent amplitudes can be diminished by taking some explicit projection of the original amplitude @xmath107 . in particular , if one multiplies @xmath108 by @xmath109 , the invariant amplitude corresponding to the structure @xmath110 $ ] is proportional to the quadrupole form factor @xmath111 : @xmath112 g_c^*(q^2 ) + \ldots \right \ } \ . \label{17}\end{aligned}\ ] ]    another possibility is to take the trace of @xmath113 . the result is proportional to the magnetic form factor @xmath26 : @xmath114 however , one should remember that the trace of @xmath108 is not free from contributions due to spin-1/2 isospin-3/2 states . though the invariant amplitude related to the trace of @xmath108 is contaminated by the transitions into spin-1/2 isospin-3/2 states , it makes sense to consider this amplitude because it has the simplest perturbative spectral density : @xmath115 where @xmath116 imposing the local duality prescription , we get @xmath117 where @xmath118 is a universal function @xmath119 and @xmath120 . as we will see , the results for other invariant amplitudes can be conveniently expressed through @xmath118 . the function @xmath118 depends on the duality intervals @xmath15 and @xmath73 . we fix the nucleon duality interval @xmath15 at the standard value @xmath121 extracted from the analysis of the two - point function and used earlier in the nucleon form factor calculations . the results of the existing two - point function analysis for the @xmath33-isobar @xcite are compatible with the @xmath33 duality interval @xmath73 in the range @xmath122 to @xmath123 . to fine - tune the @xmath73 value , we consider two independent sum rules for the @xmath104 form factor @xmath124 and @xmath125 extracted from the invariant amplitudes corresponding to the structures @xmath126 $ ] and @xmath127 $ ] , respectively ( recall that @xmath128 is the proton s momentum and @xmath129 is that of @xmath33 ) .    taking the ratio of these two relations , one can investigate their mutual consistency and test the overall reliability of the quark - hadron duality estimates .    indeed , on the `` hadronic '' side , we have the ratio @xmath130 of the isobar and nucleon masses , while on the `` quark '' side we have the ratio of two explicit and non - trivially related functions . the consistency requires , first , that the ratio of these functions must be close to a constant and , second , that this constant must be close to the experimental value for the ratio of the isobar and nucleon masses : @xmath131 . on fig.1 , we plot the @xmath2-dependence for the ratio of the right hand sides of eqs.([23 ] ) and ( [ 24 ] ) for the standard value @xmath121 of the nucleon duality interval and three different values of @xmath73 . one can see that one should not rely on local duality estimates below @xmath132 . however , above @xmath132 , the ratio is pretty constant for all three values of @xmath73 , and rather close to 1.3 . the best agreement is reached for @xmath133 , and we will use this value as the basic isobar duality interval in further calculations . in particular , the @xmath134 parameter will be fixed by @xmath135 ( cf . eq.([14 ] ) ) .    from eqs.([8 ] ) and ( [ 9 ] ) , it follows that @xmath104 is proportional to the difference of the magnetic @xmath136 and electric @xmath137 transition form factors : @xmath138    according to eq.([16 ] ) , the sum @xmath139 of these form factors can be obtained from the invariant amplitude corresponding to the structure @xmath140 $ ] . applying the local duality prescription , we obtain @xmath141 \ . \label{26}\end{aligned}\ ] ]    now , having expressions both for @xmath142 and @xmath143 , we can calculate @xmath26 and @xmath25 . the results for the combinations @xmath144 and @xmath145 are shown on figs.2 and 3 , respectively . it should be noted that , though @xmath118 has the @xmath146 asymptotics for large @xmath2 ( see eq.([22 ] ) , the local duality results are fairly consistent with the @xmath22-behaviour in the wide range @xmath147[0ex]{$\sim$}}$}}q^2 { \raisebox{-.2ex}{$\stackrel{\textstyle < } { \raisebox{-.6ex}[0ex][0ex]{$\sim$}}$}}20 \ , gev^2 $ ] . an important observation is that @xmath25 is predicted to be much smaller than @xmath26 ( see fig.3 ) . it should be noted that if the @xmath0 transition form factors are calculated in a purely pqcd approach ( in which only the @xmath148 double - gluon - exchange diagrams are taken into account ) , the sum of electric and magnetic form factors @xmath149 is suppressed for asymptotically large @xmath2 by a power of @xmath5 @xcite . this is because the matrix element @xmath150 violates the helicity conservation requirement for the hard subprocess amplitude . in other words , the pqcd prediction is that should behave asymptotically like @xmath146 , while each of @xmath136 and @xmath137 behaves like @xmath22 . as a result , asymptotically @xmath151 . however , we consider here only the soft contribution generated by the feynman mechanism for which the helicity conservation arguments are not applicable . thus , for the soft term , there are no _ a priori _ grounds to expect that @xmath151 . the smallness of @xmath152 dictated by local duality , strongly contrasts with the pqcd - based expectation that @xmath153 , and this allows for an experimental discrimination between the two competing mechanisms . one should realize , however , that @xmath25 is obtained in our calculation as a small difference between two large combinations @xmath154 and @xmath155 , both dominated by @xmath26 . hence , even a relatively small uncertainty in either of these combinations ( which is always there , since the local duality gives only approximate estimates ) can produce a rather large relative uncertainty in the values of @xmath137 . in this situation , we restrict ourselves to a conservative statement that the electric form factor @xmath25 is small compared to @xmath26 in the whole experimentally accessible region without insisting on a specific curve for @xmath25 . experimental points for @xmath136 shown in fig.2 were taken from the results for the @xmath55 form factor obtained from analysis of inclusive data @xcite , @xcite . since our results give a very small value for the ratio @xmath156 , the @xmath137 term in eq.([gt ] ) can be neglected . one can see that , in the @xmath157[0ex]{$\sim$}}$}}3 \ , gev^2 $ ] region , the local duality predictions @xmath26 are close to the results of the recent analysis @xcite .    the magnetic form factor @xmath26 can also be obtained from eq.([21 ] ) . if one takes the basic duality interval @xmath133 , the resulting values of @xmath26 ( fig.2 ) are somewhat smaller than those obtained by combining the results for @xmath154 and @xmath155 . as emphasized earlier , the spin-1/2 states also contribute to the trace of @xmath108 , and the duality interval in this case can be different from the basic value . in fact , taking @xmath158 in eq.([21 ] ) , we get a curve for @xmath159 ( fig.2 ) essentially coinciding with those obtained from the sum of @xmath154 and @xmath155 . the quadrupole ( coulomb ) form factor @xmath111 can be calculated from the expression ( [ 17 ] ) for the contracted amplitude @xmath160 : @xmath161 \ . \label{30}\end{aligned}\ ] ] again , @xmath111 is essentially smaller than @xmath26 ( see fig.4 ) . furthermore , eq.([30 ] ) predicts that , for large @xmath2 , the quadrupole form factor @xmath111 has an extra @xmath5 suppression compared to @xmath26 . in fact , if the duality intervals are equal , @xmath162 , the suppression is even stronger , namely , by two powers of @xmath5 . we applied the local quark - hadron duality prescription to estimate the soft contribution to the @xmath163 transition form factors . we observed a reasonable agreement between the results obtained from different invariant amplitudes . we found that the transition is dominated by the magnetic form factor @xmath26 while electric @xmath25 and quadrupole @xmath111 form factors are small compared to @xmath26 for all experimentally accessible momentum transfers . numerically , our estimates for @xmath55 are close to those obtained from a recent analysis of inclusive data @xcite . hence , there is no need for a sizable hard - scattering contribution to describe the data . furthermore , if future exclusive measurements at cebaf would show that the ratio @xmath1 is small above @xmath132 , this would give an unambiguous experimental proof of the dominance of the soft contribution . we are very grateful to p.stoler , n.isgur , v.burkert and c.e.carlson for discussions which strongly motivated this investigation . we thank c. keppel for providing us with the results of her analysis and f.gross , r.schiavilla , m.j.musolf , w.j . van orden , j.l . goity and i.v.musatov for interest in this work and critical comments . s.j . brodsky and g.r . farrar , phys . 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we use local quark - hadron duality to estimate the purely nonperturbative soft contribution to the @xmath0 form factors . 
 our results are in agreement with existing experimental data . 
 we predict that the ratio @xmath1 is small for all accessible @xmath2 , in contrast to the pqcd expectations that @xmath3 . 
 -48pt -0.5 cm -0.5 cm    cebaf - th-95 - 11    * quark - hadron duality and @xmath0 form factors *    v.m . belyaev@xmath4    _ continuous electron beam accelerator facility + newport news , va 23606 , usa _    a.v . radyushkin + _ physics department , old dominion university , _ + _ norfolk , va 23529 , usa _ + _ and _ + _ continuous electron beam accelerator facility , _ + _ newport news , va 23606 , usa _