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the investigation of the nucleon structure in the framework of qcd is a major task in today s particle physics . generalized parton distributions ( gpds ) have opened new ways of studying the complex interplay of longitudinal momentum and transverse coordinate space as well as spin and orbital angular momentum degrees of freedom in the nucleon . the twist-2 gpds @xmath0 , @xmath1 , @xmath2 and @xmath3 of quarks in the nucleon are defined by the following parameterization of off - forward nucleon matrix elements @xmath4 for the helicity independent vector case , and @xmath5 for the helicity dependent axial vector case @xcite . wilson lines ensuring gauge invariance of the bilocal operators are denoted by @xmath6 . here and in the following we do not show explicitly the dependence of the gpds on the resolution scale @xmath7 . fig.([fig : gpds ] ) shows the definition of the particle momenta and helicities . the momentum transfer ( squared ) is given by @xmath8 ( @xmath9 ) . using the light cone vector @xmath10 we define the longitudinal momentum transfer by @xmath11 . the proper definition of the twist-2 tensor or quark helicity flip gpds @xmath12 , @xmath13 , @xmath14 and @xmath15 can be found in @xcite . gpds provide a solid framework in qcd to relate many different aspects of hadron pyhsics :    * the forward limit @xmath16 of certain gpds reproduces the well known parton distributions , that is @xmath17 , @xmath18 and @xmath19 . * the integral over the longitudinal momentum fraction @xmath20 of the gpds gives the dirac , pauli , axial , pseudo - scalar , tensor etc . form factors , @xmath21 , @xmath22 , @xmath23 , @xmath24 , @xmath25 etc . * the fourier transforms @xmath26 of the gpds @xmath0 , @xmath2 and @xmath12 at @xmath27 are coordinate space probability densities in the impact parameter @xmath28 @xcite . * the forward limit of the @xmath29-moment of the gpd @xmath1 , @xmath30 , allows for the determination of the quark orbital angular momentum contribution to the nucleon spin , @xmath31 , where @xmath32 is the quark momentum fraction . the fact that the impact parameter dependent quark distributions like @xmath33 have the interpretation of probability densities in the transverse plane marks a major step forward in the understanding of the nucleon structure . a very interesting observation in this respect is that at large longitudinal momentum fraction , @xmath34 , i.e. when the active parton carries the whole nucleon momentum and the spectators give only a negligible contribution , the active parton becomes the center of momentum of the nucleon at @xmath35 . accordingly , the impact parameter profile of the nucleon will be strongly peaked at @xmath36 . keeping in mind that the parton distributions eventually vanish in the limit @xmath34 , we expect that @xmath37 . transferred to momentum space , we have the striking prediction that the normalized gpd @xmath38 will be constant in the limit @xmath34@xcite . interesting recent results on gpds using available experimental data on form factors and pdfs can be found in @xcite .    on the lattice side , we can not deal directly with matrix elements of bilocal light - cone operators . therefore we first transform the lhs in eqs.([vectorop],[axialvectorop ] ) to mellin space by integrating over @xmath29 , i.e. @xmath39 . this results in matrix elements of towers of local operators which are in turn parameterized in terms of so - called generalized form factors ( gffs ) @xmath40 , @xmath41 where the subtraction of traces is implicit . the explicit parameterization for the tower of vector operators , @xmath42 , is given in @xcite in terms of the gffs @xmath43 and @xmath44 . in the axial vector case , the corresponding expression in terms of the gffs @xmath45 and @xmath46 is shown in @xcite . parameterizations for the tensor gpds have been derived recently in @xcite . having computed the gffs in e.g. lattice qcd , it is fairly simple to get the moments of the corresponding gpds by using the following polynomial relations @xcite @xmath47 in the limit @xmath48 , the complete nucleon structure related to @xmath0 and @xmath2 is according to eq.([invv ] ) represented by the sets of gffs @xmath49 and @xmath50 , @xmath51 . the lattice calculation and extraction of the gffs from nucleon two- and three - point - functions follows the standard procedure as outlined in e.g. @xcite . our dynamical computations are currently based on a set of coupling- and quark mass - combinations with up to @xmath52 configurations and with pion masses ranging from @xmath53 down to @xmath54 gev . the lattice spacing lies in between @xmath55 and @xmath56 fm . since we are using non - perturbatively @xmath57 improved wilson fermions , we do not expect strong discretization effects @xcite . a list of the parameters is given in fig.([fig : para ] ) . we do not take into account the disconnected contributions which are numerically much harder to evaluate . this is irrelevant as long as we concentrate on the iso - vector channel @xmath58 ( as we do here ) , for which the disconnected pieces would cancel due to iso - spin symmetry .    to give an overview of our results we show in fig.([fig : first13550 ] ) the lowest three moments of the gpds @xmath59 , @xmath60 and @xmath61 as well as the lowest two moments of @xmath62 . up to now , only the lowest moments @xmath63 which we show here are non - perturbatively renormalized , and operator mixing has to be taken into account for a proper renormalization of the @xmath64-moments for @xmath65 @xcite . we do not expect the renormalization to affect the following general discussion and the extraction of the dipole masses below . please note that for reasons of clarity @xmath66 has been shifted upwards by @xmath67 , as indicated by the superscript arrow in fig.([fig : first13550 ] ) , lower left panel . all gffs have been fitted using a standard dipole ansatz , @xmath68 except for the pseudo - scalar ff @xmath69 , where we used a dipole ansatz including the pion - pole , @xmath70 the fits given by the gray bands in figs.([fig : first13550 ] ) show an overall satisfactory description of the lattice numbers . while the statistical errors for the lowest two moments are rather small , they tend to be somewhat larger for the @xmath64-moment . the statistics are particularly poor for @xmath71 , @xmath72 and the @xmath73 gffs , which are not shown in this work . it turns out that the moments of @xmath0 and @xmath2 in the iso - vector channel are a factor of @xmath74 smaller than the corresponding moments of @xmath1 and @xmath3 , while @xmath75 which contributes to both @xmath0 and @xmath1 is compatible with zero . our results indicate furthermore strong cancellations of @xmath76 and @xmath77 flavor contributions in the iso - singlet channel for the helicity independent gpd @xmath78 . let us now take a look at the @xmath79-dependence of the gpds and the impact parameter dependent quark distribution @xmath80 . the observation from section ( [ intro ] ) that @xmath81 translates directly to the statement that the gffs @xmath49 become constant for very large @xmath10 since increasingly more weight lies on values of @xmath29 close to one for @xmath82 . to be precise , we expect that @xmath83 , independent of @xmath79 . since the values for the momentum transfer squared in our computation are unevenly distributed in the interval @xmath84 gev , and since there is in particular a gap between @xmath85 and the smallest non - zero @xmath79 which can be realized on the given lattices , @xmath86 , it is not useful to perform a discrete fourier transformation ( ft ) of our results to impact parameter space . instead , we directly use the continuous ft of the dipole ansatz eq.([dipole ] ) . the normalized impact parameter dependent moments @xmath87 with @xmath88 are shown in fig.([fig : impact ] ) . for reasons of comparison we show in fig.([fig : impact ] ) also the corresponding gffs , normalized to @xmath89 . the gray bands in the impact parameter plot reflect the errors associated with the dipole masses , @xmath90 . the results in fig.([fig : impact ] ) show very nicely the anticipated flattening of the gffs and the narrowing of the corresponding distributions in impact parameter space , going from @xmath63 to @xmath91 . this flattening of the gpds has first been observed in @xcite . since we have results for a large number of pion masses at hand , it is mandatory to concentrate in the following on the important issue of the @xmath92 dependence and the chiral extrapolation of our calculation . due to the use of wilson fermions , the dominant part of our computation is for pion masses above @xmath93 mev where chiral perturbation theory in its current form is most probably not applicable . in particular for the dipole masses @xmath94 , we therefore resort to a purely phenomenologically motivated pion mass dependence of the form @xmath95 . we have checked that a linear dependence on @xmath92 is clearly unfavored by our results .    for the following analysis we have normalized our results to @xmath96 first . one option is then to perform dipole fits for all individual @xmath97 , @xmath98 combinations for a given moment @xmath10 and fit the pion mass dependence of the dipole masses with the given ansatz . however to optimally utilize the information on the dipole masses from our collection of results , it is better to use a combined dipole - mass / pion - mass fit of the simple form @xmath99 depending on the two parameters @xmath100 and @xmath101 . having done the fit , we may shift the raw numbers to a common curve given by eq.([chiraldipole ] ) at the physical pion mass , @xmath102 mev . the results of this procedure are shown in fig.([fig : alldata1 ] ) for the gffs @xmath103 and @xmath104 , @xmath105 . the fit parameters are found to be @xmath106 although the corresponding rather large error does not allow for a definite conclusion , it is interesting to note that the slope @xmath101 changes sign going from @xmath107 to @xmath108 . we observe an overall nice clustering of the lattice points in fig.([fig : alldata1 ] ) much in favor of our ansatz eq.([chiraldipole ] ) . the actual fits are given by the gray bands and show a very good @xmath109 lying below @xmath110 for the helicity independent and below @xmath111 for the helicity dependent case . in particular for @xmath104 , a small fraction of the lattice points seem to be significantly below the main line . future investigations have to show if this is due to an unaccounted dependence on the lattice spacing , the ( finite ) lattice volume or just insufficient statistics . an attempt to compare our results for the axial and tensor coupling , @xmath112 and @xmath113 , with chiral perturbation theory is described in @xcite . we plan to extract the quark orbital angular momentum contribution to the nucleon spin as soon as the missing renormalization constants become available . we have computed the lowest moments of gpds for a number of different pion masses in the range above @xmath114 mev . the results are very well described by a combined dipole - 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we present recent results on generalized parton distributions from dynamical lattice qcd calculations . 
 our set of twelve different combinations of couplings and quark masses allows for a preliminary study of the pion mass dependence of the transverse nucleon structure .