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the radiative return method @xcite ( look @xcite for a short introduction ) is a powerful tool in the measurement of @xmath6 , crucial for predictions of the hadronic contributions to @xmath7 , the anomalous magnetic moment of the muon , and to the running of the electromagnetic coupling from its value at low energy up to @xmath8 ( for recent reviews look @xcite ) . due to a complicated experimental setup , the use of monte carlo ( mc ) event generators @xcite , which includes various radiative corrections
@xcite is indispensable .
some more extensive analysis of that subject can be found also in @xcite .
the most important hadronic mode , i.e. @xmath9 , is currently measured by kloe @xcite , and babar @xcite by means of radiative return method .
this measurement can suffer from a background from the process @xmath0 , as suggested in @xcite , for at least two reasons : 1 . at present kloe measures only pions ( + missing momenta ) in the final state and for that particular measurement
there is no difference between photon(s ) and pair production .
2 . the @xmath1 pair can escape detection , being lost outside a detector , e.g. in the beam pipe , or having energy below a detection threshold . again
a monte carlo study is unavoidable , if one likes to know the actual value of the pair production contribution in a given experimental setup , as the analytical , completely inclusive , calculations might lead to misleading results .
+ 0.5 cm + 0.3 cm + 0.5 cm    in fig.[f00 ] different types of diagrams contributing to process @xmath10 are shown schematically . in the present version of the monte carlo program
we include only two gauge invariant sets of diagrams from fig.[f00]a and [ f00]b .
the former represents initial state radiation ( isr ) , and the latter final state radiation ( fsr ) , of an @xmath11 pair from @xmath12 production diagram .
we use scalar qed ( sqed ) to model fsr @xmath11 pair emission and @xmath13 dominance model for @xmath14 coupling ( see @xcite for details ) . the diagrams from fig.[f00]c , representing pion pair emission from t  channel bhabha process , together with s - channel bhabha pion pair emission ( not shown in fig.[f00 ] ) , will be included in the new version @xcite of the presented generator , completing the discussion of this paper .
the contribution from @xmath15 pion pair production process ( fig.[f00]d ) is negligible for da@xmath4ne energy @xcite , and as its interference with other diagrams does not contribute to the cross section integrated over charge symmetric cuts , these contributions are not relevant , at least for @xmath4factories .    for parametrisation of the phase space
we use the following variables : @xmath16invariant mass of @xmath9 system , @xmath17invariant mass of @xmath1 system , polar and azimuthal angles of @xmath18 momentum , defined in the centre - of - mass ( cm ) frame of initial @xmath1 pair , polar and azimuthal angles of @xmath19 momentum , defined in @xmath20- rest frame and polar and azimuthal angles of @xmath21 momentum , defined in @xmath22- rest frame .
all four vectors are boosted into the initial @xmath1 cm frame after being generated and all necessary cuts can be applied at this stage of the generation .
channel variance reduction method was used to improve efficiency of the generator and all details will be given in a separate publication @xcite .
we have performed a number of standard tests to ensure that the written fortran code is correct .
gauge invariance of the sum of the amplitudes was checked analytically separately for set of diagrams from fig.[f00]a and [ f00]b .
we use helicity amplitudes in ekhara to calculate square of the matrix element describing the @xmath10 process , but as a cross check , we have used also the standard trace technique to calculate the square of the matrix element , summed over polarisations of initial and final leptons . both results were compared numerically scanning the physical phase space , and the biggest relative difference between the two results found was at the level of @xmath23 . it was necessary to use quadrupole precision of the real numbers for the trace technique result , as one can observe severe cancellations between various terms . the phase space volume calculated by monte carlo program was cross checked with the gauss integration and the relative difference at the level of @xmath24 was well within the errors of the mc result , which were of the same order .
-0.2 cm -0.2
cm    inclusive analytical formulae from @xcite provide additional , nontrivial tests of the implementation of the contributions from fig.[f00]a .
formula ( 23 ) from @xcite provides @xmath25 differential cross section ( other variables are integrated over the whole allowed range ) valid for large @xmath25 . in fig.[f0]a
, we compare the values of the integrals , over 10 equally spaced intervals of @xmath25 , obtained by means of mc program and one - dimensional gauss integration of the above mentioned analytical formula .
the gauss routine , which we use , guarantees precision of 12 significant digits .
one observes a relatively good agreement for values of @xmath26 and worse for @xmath25 nearby @xmath9 production threshold , as expected from the applicability of the analytical formula .
ekhara results agree much better ( see fig.[f0]b ) with known analytically doubly differential cross section @xmath27 @xcite , integrated over the whole allowed range of @xmath28 and 10 equally spaced intervals of @xmath25 .
the exact analytical result was integrated numerically , using recursively one - dimensional 8-point gauss procedure and dividing the region of integration into pieces small enough to guarantee the overall accuracy of 10 significant digits . from fig.[f0]b
it is clear that a technical precision of ekhara of the order of 0.1% was achieved .
-0.2 cm -0.2 cm    for isr of @xmath1 pair ( fig.[f00]a ) , a factorisation similar to photon emission holds @xcite and adding isr pair production to isr photon production results just in a change of the radiator function , thus radiative return method still can be used @xcite . on the other hand , fsr of @xmath1 pair ( fig.[f00]b )
is model dependent , the same way as it is the emission of a real photon , and the question of its relative , to isr , contribution to the cross section is as important as for the photon emission .
one can observe , that @xmath1 pair emission resembles a lot photon emission , with big contributions of fsr for inclusive configurations ( fig.[f1]a ) of a @xmath4factory , which can be easily reduced , by suitable cuts , to a negligible level ( fig.[f1]b ) .
moreover , the cuts which reduce photon fsr reduces as well the @xmath1 pair fsr . in addition , analogously to photon fsr , @xmath1 pair fsr is completely negligible at @xmath5factories .
-0.2 cm -0.2 cm    the most relevant information , how big is the contribution of the process @xmath10 in comparison to the main process used in the radiative return method , mainly @xmath29 , is presented in fig.[f2 ] for da@xmath4ne energy , both without any cuts ( fig.[f2]a ) , and with cuts resembling kloe event selection @xcite ( fig.[f2]b ) . the results of @xmath29 cross section were obtained using phokhara 3.0 mc generator @xcite and in the following , whenever we refer to @xmath29 cross section we mean cross section obtained using phokhara 3.0 . as one can see from fig.[f2 ] , the contribution of the @xmath1 pair production is below 0.5% , independently on the cuts .
it is @xmath25 dependant , being big for low @xmath25 values .
even if it is small , this 0.5% contribution can become important , when aiming at the precision below , or of the order of 1% , for the @xmath30 cross section measurement . at @xmath5factories , the relative contribution of the pair production might be as big as 0.9% ( fig.[f4]a ) and it is again @xmath25 and cut dependent ( fig.[f4]b ) .
-0.2 cm -0.2 cm    -0.4 cm    -0.2 cm -0.2 cm
-0.4 cm    as stated already , isr of electron pairs can be treated in a similar way as isr of photons resulting in the change of radiator function in the radiative return method .
however , one can alternatively try to treat it as a background to the process with photon(s ) emission . in this case , the most natural way of reducing that background is to veto the electron ( positron ) in the final state . in fig.[f3
] we show an example of such a procedure performed for @xmath4factory energy .
we assume here that an electron or positron can be seen , and the event rejected , if its angle with respect to the beam axis is bigger then 20@xmath31 .
fig.[f3]a shows that up to 50% of the events pass the rejection procedure , when no other cuts are applied .
however , in the case of kloe event selection , which requires that the @xmath1 pair is emitted along the beam axis , one rejects only a small fraction of these events ( fig.[f3]b ) .
-0.2 cm -0.2 cm    the situation is completely different at @xmath5factories , where one can almost completely reduce the background coming from @xmath1 pairs ( fig.[f5 ] ) , by rejecting the events with at least one charged lepton , electron or positron , in the detector .
we have constructed the monte carlo generator ekhara , which simulates the reaction @xmath0 based on initial and final state emission of a @xmath1 pair from @xmath2 production diagram .
a detailed study of this process , as a potential background for @xmath3 measurement via radiative return method , shows that it can become important , when the experimental precision will reach 1% , or better .
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a monte carlo generator ( ekhara ) has been constructed to simulate the reaction @xmath0 based on initial and final state emission of a @xmath1 pair from @xmath2 production diagram . 
 a detailed study of the process , as a potential background for @xmath3 measurement via radiative return method , is presented for @xmath4- and @xmath5- factory energies .