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various condensates are related to non - perturbative properties of qcd .
the importance of the condensates such as @xmath1 and @xmath2 are well - known .    though the dimension two operators such as mass terms are not brst invariant in yang - mills ( ym ) theory , it was pointed out recently that these operators contain a gauge invariant physical part and that a special combination of them can be ( on - shell ) brst invariant @xcite @xcite @xcite .
it was argued that the minimum of @xmath3 along the gauge orbit can have a definite physical meaning , and how to define the physical part non - perturbatively @xcite .
there is a brst - invariant composite operator of mass dimension 2 @xcite as a linear combination of @xmath4 and quadratic ghost , averaged in spacetime : @xmath5.\ ] ] in the lorentz gauge , it reduces to the same form as the known curci - ferrari mass term .
but we do not include it in the lagrangian .
therefore our theory is usual ym .
it is easily seen that this operator is on - shell brst invariant : @xmath6 .
the @xmath4 part should be divided into the physical ( transverse ) part and other unphysical ( longitudinal and scalar ) part .
when we take the vacuum expectation value , the @xmath7 part precisely cancels this unphysical part .
thus the operator has a gauge invariant expectation value , though the remaining physical part is nonlocal . especially in the landau gauge @xmath8 , @xmath9 .
since these operators are not brst invariant as local polynomials , they do not appear in ope of usual gauge invariant quantities .
but they may appear in ope of brst non - invariant quantities such as .
in fact , this operator in the landau gauge has been estimated in various methods .
boucaud et al.@xcite have simulated the lattice propagator and used ope fit to obtain @xmath10 .
verschelde et al .
@xcite discussed the effective potential of @xmath4 .
here we take the schwinger - dyson ( sd ) equation approach .
recent investigations @xcite@xcite of euclidean pure su@xmath11 yang - mills theory in the lorentz gauge show @xmath12 the transverse gluon propagator vanishes , while the fp ghost propagator is enhanced in the infrared limit @xmath13 .
that is , the ghost propagator behaves more singularly than the free propagator in low energy region .
these results mean the ir ghost dominance .
this is consistent with the well - known gribov prediction and the confinement criterion due to kugo and ojima .
but these results are strongly dependent on approximations in the calculation .
simple bare vertex approximation fails to reproduce 1-loop perturbative result .
this situation is very different from the case of fermion sd equation .
in addition to the approximation ambiguity , we pay attention to the in the uv propagators which may come from ope ( @xmath14 condensate ) or renormalon or some other non - perturbative effects .
we consider the sd equation for the gluon propagator @xmath15 and ghost propagator @xmath16 in pure ym theory in the landau gauge .
for the gluon propagator @xmath15 , we adopt the brown - penington projection @xmath17 to remove a tadpole graph .
next , we neglect all 2-loop diagrams and adopt higashijima - miransky approximation to the internal propagators .    thus the relevant sd equations become @xmath18{ghost_sdeq.eps } \end{array}\ ] ] @xmath18{gluon_sdeq1loop.eps } \end{array}\ ] ]
at this stage , in addition to propagators @xmath15 and @xmath19 , the vertices @xmath20 and @xmath21 are unknown . in the landau gauge , the ghost - gluon vertex @xmath20 does not have divergence .
so our main attention directs to approximate @xmath21 .    in the investigations @xcite
@xcite @xcite @xcite , various ansatz are adopted to @xmath21 . in @xcite @xcite , the bare or the slavnov - taylor ( st ) improved vertex is adopted .
this procedure is similar to the case of fermion sd . in @xcite @xcite ,
improved vertices are used to reproduce the uv 1-loop perturbative result correctly where free parameters @xmath22 and @xmath23 are introduced in @xcite . it does not change uv leading exponent .
bloch @xcite used a similar ansatz derived from his own argument based on multiplicative renormalizability .
but in their cases , infrared solutions become very delicate in the sense that whether ghost dominance property is realized or not depends on the choice of parameters or the effect of 2-loop diagrams .
the simple bare vertex approximation can not reproduce even the 1-loop perturbative result , while the ir solutions are very sensitive to the choice of vertex correction . in order
to get rid of this difficulty , we consider the higher logarithmic terms in the uv asymptotic solution .
we are interested in the  non - perturbative " power correction terms too .    to obtain the solutions
, we define the gluon form factor @xmath24 and the ghost one @xmath19 by multiplying @xmath25 to the propagators .    for the uv asymptotic solutions , we adopt the new ansatz which has logarithmic ( perturbative ) powers and power ( non - perturbative ) corrections as @xcite @xmath26    we use the two parameter ansatz @xcite for the renormalized triple gluon vertex @xmath27 simply introducing parameters makes a result more ambiguous . in our approach , new parameters will be automatically determined by considering subleading solutions and ope consistency .
we put these into sd equations , and get infinite series of algebraic equations with respect to coefficients @xmath28 @xmath29 @xmath30 @xmath31 @xmath32 and parameters @xmath33 .
we first find that without power corrections ( @xmath34 , @xmath35 ) the ansatz can not satisfy the coupled sd equation for large @xmath25 , even if we include the logarithmic corrections @xmath36 .
a self - consistent solution is obtained when @xmath37 for arbitrary value of @xmath22 and @xmath23 .
these reproduce leading exponents and beta function in agreement with 1-loop perturbation .
the remaining coefficients are determined successively except for one degrees of freedom @xmath38 .
@xmath39 coefficients @xmath40 and @xmath41 ( overall normalization ) will be determined if we fix the renormalization condition . @xmath42 and @xmath43 ( coefficients of power correction ) are not determined . except for @xmath44 ( or ) , all the other coefficients and exponents are calculated by simple algebraic equations up to any finite orders .
the logarithmic expansions seem to converge in uv region .
the additional logarithmic exponent of the power correction calculated from ope is @xmath45 .
corresponding exponent from the sd solutions in bare vertex approximation is @xmath46 @xcite .    in the improved vertex case ( [ results ] ) , only one unknown parameter @xmath38 governs this exponent .
we use the relation ( [ results ] ) to determine the parameter .
when we set @xmath47 ( or @xmath48 ) , the exponent @xmath49 becomes @xmath50 which reproduces the leading ope .
moreover , this value for @xmath51 leads to the ghost dominance solution in the ir region .
we have found the asymptotic sd solutions of the gluon and ghost propagators in su(@xmath52 ) yang - mills in landau gauge for the ansatz using power and logarithmic expansion .
contrary to the fermion sd case , the bare vertex approximation can not reproduce the uv solution consistent with the uv perturbation and the uv ope .
we have found the consistent solution by considering the uv higher order corrections .    using the same vertex ansatz ( 4 ) determined as above , we have obtained also the ir solutions which have the same form as the power - law solutions [ 6 ] : @xmath53 .
therefore the existence of non - perturbative power correction does not influence the ir solution .
ir ghost dominance is realized , and the color confinement criterion of kugo and ojima is satisfied .
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we have found ultraviolet asymptotic slutions of the schwinger - dyson equation for the gluon and ghost propagators which have simultaneously the perturbative logarithmic correction and the non - perturbative @xmath0 power correction . by including the perturbative corrections 
 , the power correction reproduces exactly the leading ope result suggesting the existence of dimension two condensate .