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the search for new physics beyond the standard model in the future will follow two main paths : higher energy and high 
intensity  @xcite .
neutrino facilities will play an important role in this program : neutrino masses take us beyond the standard model , and a full determination of the pattern of @xmath1 masses and mixing will require dedicated high  intensity neutrino beams  @xcite .
however , a high  intensity @xmath1 beam can be used not only to study neutrino properties , but also as a sensitive probe of the electroweak interaction .
indeed , it has been shown that a wide spectrum of otherwise very difficult or impossible measurements of strong and electroweak processes would become possible at a high  energy neutrino factory  @xcite .
here we start addressing the issue whether equally interesting measurements might also be possible with a _ low energy _ but sufficiently intense @xmath1 beam .
indeed , the main role so far of low  energy tests of the standard model  @xcite has been in the study of rare processes . here
we will investigate whether with sufficiently high  intensity they may lead to competitive measurements of standard model parameters , specifically the electroweak mixing angle .
the development of future neutrino facilities is driven by the study of neutrino masses and mixings , and will happen in three stages . in
the first phase various facilities will produce conventional @xmath1 beams from the decay of a secondary meson beam ( producing typically @xmath2 @xmath1/year ) .
examples of such facilities ( now under construction or just commissioned ) are minos and no@xmath1a , the cern / gran sasso beam , and t2k . in the second stage ,
planned for the beginning of the next decade , `` superbeams '' , i.e. conventional beams but with intensities about hundred times higher , should be constructed , exploiting very high  intensity , and relatively low energy primary proton beams .
examples of such facilities are the second phase of t2k , exploiting a 50 gev and 7 mw proton synchrotron at jparc , and a possible high  energy superbeam at cern exploiting a 3.5  gev , 45  mw superconducting proton linac ( spl ) . in the third phase , starting perhaps towards the end of the next decade , neutrinos from decays of a _ primary _ beam are planned .
two possible kinds of primary beams are envisaged : either a neutrino factory , i.e. relatively high  energy ( tens of gev ) muon beam , or a @xmath0beam , i.e. relatively low  energy ( few gev ) radioactive nuclei .
the advantage of using a primary beam are higher intensity and a better control on the neutrino energy spectrum .
the @xmath0 beam has the further advantage of giving a pure beam of electronic @xmath1 or @xmath3 , with essentially no contamination from @xmath4 or wrong  sign neutrinos .
the neutrino factory gives a beam which is exactly 50% @xmath5 and @xmath6 .
because neutrinos only couple to weak interactions , they are an ideal probe of electroweak parameters , specifically of the electroweak mixing angle ( weinberg angle ) which controls the relative strength of neutral ( nc ) and charged current ( cc ) couplings .
electron elastic scattering offers an ideally clean setting for this measurement , which is competitive at a high energy neutrino factory  @xcite , but ( because the cross section grows linearly with the energy ) at a low  energy facility very high intensities are required  @xcite
. a measurement of the weinberg angle can be obtained from the cc / nc deep - inelastic scattering ratio : this measurement at present is almost competitive , but marred by the uncertainty related to parton distributions  @xcite .
it would certainly be competitive at a neutrino factory  @xcite .
as the energy is lowered , the relative ( quasi)elastic contribution to the total cross section grows , and at an energy @xmath7 the elastic and inelastic contribution are of comparable size ( see fig .
[ xsect ] ) . at this energy ,
at which perturbative treatment of inelastic contribution breaks down anyway , the relative elastic contribution is sizable , while total cross section is still reasonably large .
this energy is relevant for future facilities , such as jparc , a low 
energy @xmath0 beam or the spl superbeam , and it is natural to ask whether elastic or quasielastic scattering can be used for competitive measurements of weinberg angle .    nucleon cross sections vs. energy . ]
[ xsect ]    the answer is not obvious , because ( quasi)elastic cross sections depend on eight independent form factors  @xcite : two pairs of electric and magnetic form factors for proton and neutron targets , a pair of strange electric and magnetic form factors ( the same for protons and neutrons ) and a pair of axial isotriplet and strange form factors ( the same for protons and neutrons , up to signs ) .
the question is then whether the uncertainty in the form factors knowledge spoils the extraction of @xmath8 from these cross sections .
the simplest answer to the above question is obtained by a counting of the relevant physical observables . with proton and neutron ( from deuterium or other nuclei ) targets and @xmath1 and @xmath9 beams
, one can measure four independent nc and two independent cc cross sections .
they depend on eight form factors and the weinberg angle .
hence , at least three form factors have to be input to the analysis .
it is convenient to input the electric form factors , whose forward value is fixed by charge .    assuming a flux @xmath10 with energy @xmath11  gev one gets @xmath12 elastic cc events and @xmath13 nc events with either beam or target after one year of running with each beam .
this flux and energy are typical e.g. of a low 
energy @xmath0beam , with a detector located at a distance of @xmath14  km .
assuming that the five independent form factors and the weinberg angle are determined in each angular bin this leads to a statistical error @xmath15  @xcite .
the further theoretical error due to the electric form factor is negligible .
it is important to observe that these form factors must be input if one wishes to extract all the other form factors and @xmath16 .
however , the cross section can actually be measured in a large number of angular ( or @xmath17 ) bins ( e.g. several dozens ) .
one may thus choose to parametrize the form factors and fit these parameters as well as @xmath16 . clearly , with , say , 20 bins and several cross sections even with a very general parametrization all form factors can be determined together with the weinberg angle .
this suggests that a more detailed analysis is worthwhile .
the main experimental constraint is the possibility to detect cc and nc events with a neutrino beam energy between one and a few gev .
this rules out water cherenkov detectors , because the cherenkov threshold @xmath18 for the recoiling proton implies that only protons with recoil momentum @xmath19  gev can be detected , which removes most of the cross section .
a more promising alternative is a liquid ar tpc  @xcite . in this case
, the only constraint is that the recoiling proton leaves a sufficiently long track so that it is not confused with nucleon motion due to nuclear effects .
this gives a constraint on the proton energy @xmath20  mev i.e. @xmath21  mev . with a beam energy of the order of 1 gev ,
about 75% of the scattering events survives this kinematic cut .
however , recoiling neutrons can not be detected .
this implies that neutron neutral current ( nc ) events are essentially lost and one is left with only four independent cross sections .    in order to maximize the flux
, one may envisage the option of having a near detector , located at a few hundreds of meters from the source , thereby obtaining fluxes by many orders of magnitude larger than those at the far detector used for oscillations studies .
however , in a realistic analysis one should keep into account that an argon tpc might have difficulties in handling interaction rates much larger than a few events per spill .
this would put a bound on the maximum flux .      in order to get a more quantitative estimate of the accuracy
one can reach in the weinberg angle determination , we have generated scattering events assuming an incoming flux @xmath22 , @xmath23 , with fixed energy @xmath24  gev .
these parameters are typical e.g. of t2k ( first phase ) with a near detector at about 300  m from the source . in the present analysis we have considered the case of a liquid argon detector with a mass of 10  ktons .
an increase in the detector mass would correspond to a reduction in the fit uncertainty that can be easily obtained by standard statistical analysis .
we have assumed @xmath25 and all the nucleon form factors as given in ref .
@xcite and in ref .
@xcite for the axial and strange form factors ; in particular for the strange magnetic form factor we used @xmath26 , with @xmath27 the neutrino momentum transfer , @xmath28 , @xmath29 nucleon mass , @xmath30 and @xmath31 .    we have then performed a fit to the events thus generated , leaving as free parameters @xmath16 and the forward value of the strange magnetic form factor @xmath32 .
we have then repeated this fit by varying the value of the forward strange axial form factor @xmath33 , considering one @xmath34 variation around its central value ( @xmath35 ) .
these are the only forward form factors which are affected by a significant uncertainty .
other form factor parameters have a more moderate impact .
we get @xmath36 , where the systematic error is due to the variation of the strange axial form factor within the range indicated .
clearly , a more detailed analysis  @xcite would require either fitting of all form factors , or varying some of their parameters within errors .
in such an analysis we will also introduce a study of the systematical uncertainty related to the choice of the form factor parametrization .
however , on the basis of this first estimates , we conclude that a determination of @xmath16 with an uncertainty of a few percent is not unreasonable .
one of us , v.a . , is deeply grateful to the now 2006 organizers for providing a stimulating human and scientific atmosphere .
he also would like to thank in particular a. guglielmi , m. mezzetto and e. torrente - lujan for useful discussions .
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we discuss the possibility of using future high  intensity low  
 energy neutrino beams for precision tests of the standard model . 
 in particular we consider the determination of the electroweak mixing angle from elastic and quasi  
 elastic neutrino  nucleon scattering at a superbeam or @xmath0beam .