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since the most reliable standard model ( sm ) evaluations of the anomalous magnetic moment of the muon differs three to four standard deviations from the measurements @xcite , it might be useful to examine predictions for this observable of the theories beyond the sm .
it is well known that the sm has three major obstacles : ( 1 ) massless neutrinos , ( 2 ) absence of a dark matter particle , and ( 3 ) absence of the lepton and baryon number violations .
we show in ref .
@xcite that the uv nonsingular theory , free of the @xmath0 global anomaly ( called the by theory in @xcite ) , is free of the sm deficiencies . besides three heavy majorana neutrinos as cold dark matter particle(s ) , the by theory contains three light majorana neutrinos with a relation on the three mixing angles , alowing the inclusion of the lepton cp violating phase .
the effects of the universal uv spacelike cut - off are studied in various strong and electroweak processes in refs .
the cosmological consequences of the nonsingular einstein - cartan theory of gravity can be envisaged in ref .
the minimal distance in the einstein - cartan cosmology is compatible with the uv cut - off of the by theory .    in this note
we want to inspect the impact of the uv cut - off on the radiative corrections of the anomalous magnetic moment of the muon .
next chapter deals with the explicit calculations , however the relevant detailed formulae the reader can find in the appendix .
the concluding section discusses the numerical results and their consequences .
the anomalous magnetic moment of the muon is one of the most precisely measured observable to the uncertainty of @xmath1 @xcite .
it is calculated within the perturbative quantum field theory to the very high order .
the perturbation theory works well and it is very accurate because of the very small fine structure constant .
the anomalous magnetic moment formula can be cast into transparent perturbation series where it is possible to compare and study any modification of the standard model ( sm ) @xcite .
we evaluate one loop corrections with virtual electroweak bosons within the uv finite by theory @xcite .
although this theory contains majorana light neutrinos , we can safely neglect their majorana character and their masses because of their smallness .
the heavy majorana neutrinos are coupled strongly to nambu - goldstone scalars at tree level , but not to electroweak gauge bosons .
they are , therefore , decoupled in the evaluation of the anomalous magnetic moment .
since the gauge invariant physical result can not depend on the choice of gauge , we can freely perform our calculations in the t hooft - feynman gauge with nambu - goldstone scalars instead in the unitary gauge where nambu - goldstone scalars are decoupled from lepton doublets @xcite .
however , the scalar doublet does not contain the higgs scalar @xcite since the noncontractible space is a symmetry breaking mechanism in the by theory and the uv cut - off is fixed at tree level by the weak boson mass @xmath2 , @xmath3 , @xmath4 @xcite .
the higgs scalar is decoupled from other particles in the brst transformations @xcite and does not play essential role in the proof of the renormalizability of the spontaneously broken gauge theories @xcite .
consequently , the uv finite by theory without the higgs scalar is also renormalizable .    it is necessary to comment the claim that the recently discovered @xmath5
scalar resonance is the sm higgs scalar @xcite .
cea @xcite proposed the most natural explanation of the @xmath5 resonance as a mixture of toponium and gluonium .
the possible new 750 gev heavy boson resonance at the lhc @xcite might be a perfect candidate for a heavier scalar twin of the @xmath5 boson @xcite .
let us go back to the description of the electroweak one loop contributions to the anomalous magnetic moment .
the sm one loop result takes the form @xcite ( @xmath6 denotes the mass of the muon and @xmath7 ) :    @xmath8    @xmath9    @xmath10    we have to rederive these results equiped with the sm feynman rules in the t hooft - feynman gauge .
one can straightforwardly extract the contributions with one virtual photon @xcite and one virtual w and z bosons @xcite in terms of the coefficient functions of the tensor and vector green functions that can be deduced from the scalar green functions - master integrals @xcite ( for definitions and explicit expressions see the appendix ) :    @xmath11    @xmath12    @xmath13 ( 2 c_{0}+ 3 c_{11 } + c_{21 } ) + s_{w}^{2}(1 - 2 s_{w}^{2 } ) \nonumber \\ & & \times ( c_{0 } + c_{11 } ) \ }    ( z\ boson ) = \frac{1}{48 m_{z}^{2}}[(3 - 4 c_{w}^{2})^{2 } - 5 ] , \end{aligned}\ ] ]    the deviation between the sm and the by theory could be found in the scalar master integrals .
the uv cut - off @xmath14 in the spacelike domain of the minkowski spacetime is introduced as a lorentz and gauge invariant quantity .
the analytical continuation to the timelike domain is performed on the riemann s sheets , when necessary . by the symmetrization of the external momenta of the master
integrals with the uv cut - off we insure their translational invariance .
consequently , all the master integrals of the by theory have a correct limit @xmath15 of the standard qft master integrals .
we left our presentation of the explicit results and comments to the next section .
the one loop results for the by theory follow from eqs .
( 1 - 3 ) and the expansion formulas for scalar one , two and three point functions in the sm and the by theory presented in the appendix .
besides the difference between the sm and by in the cut - off ( @xmath16 or @xmath2 ) , one has to exclude the higgs boson contribution for the by theory ( @xmath17)@xcite :              @xmath22^{\gamma,1\ loop}=-6.09\times 10^{-11 } , \\ & & [ a_{\mu}^{by}-a_{\mu}^{sm}]^{w,1\ loop}=-4.307\times 10^{-10 } , \\ & & [ a_{\mu}^{by}-a_{\mu}^{sm}]^{z,1\ loop}=+1.595\times 10^{-10 } , \\ & & [ a_{\mu}^{by}-a_{\mu}^{sm}]^{\gamma+w+z,1\ loop}=-3.321\times 10^{-10 } , \end{aligned}\ ] ]          that the loop corrections of the by theory can not explain the deviation from the experimental value .
it seems that more reliable estimates of the hadronic contributions is necessary .
they should be studied by the nonperturbative methods supplemented by the experiments with hadrons @xcite .
the new experiments to measure the anomalous magnetic moment ot the muon are planned in the u.s.a . and japan with a good potential to further reduce the experimental error .
@xmath36 , \\ & & \lim_{m^{2}\rightarrow 0 } c_{21 } = -\frac{c_{24}(m^{2})}{d m^{2}}(m^{2}=0 ) -\frac{1}{2 } c_{11}(m^{2}=0 ) + \frac{m_{w}^{2}}{2}\frac{d c_{11}}{d m^{2}}(m^{2}=0 ) \\ & & \ \ \ \ \ \ \ + \frac{1}{2}\frac{d b_{1}(m^{2};0,m_{w}^{2})}{d m^{2}}(m^{2}=0 ) , \\ & & \frac{d c_{24}(m^{2})}{d m^{2}}(m^{2}=0)=\frac{1}{4}[c_{11}(m^{2}=0)-m_{w}^{2 } \frac{d c_{11}}{d m^{2}}(m^{2}=0 ) ] , \\ & & c_{11}(m^{2})=\frac{1}{2 m^{2}}[b_{0}(m^{2};0,m_{w}^{2})-b_{0}(0;m_{w}^{2},m_{w}^{2 } ) -(m^{2}-m_{w}^{2})c_{0 } ] , \\ & & b_{1}(m^{2};0,m_{w}^{2})=\frac{1}{2 m^{2}}[-a(m_{w}^{2})+a(0)+(m_{w}^{2}-m^{2 } ) b_{0}(m^{2};0,m_{w}^{2 } ) ] , \\ & & b_{0}^{\lambda}(0;0,m_{w}^{2})=\ln\frac{\lambda^{2}+m_{w}^{2}}{m_{w}^{2 } } , \end{aligned}\ ] ]      @xmath38 , \\ & & \frac{d^{2 } c_{0}^{\lambda}}{d ( m^{2})^{2}}(m^{2}=0)=\frac{1}{m_{w}^{6}}[-\frac{2}{3 } + \frac{4}{3}(-2(1+x)^{-5}+8(1+x)^{-4}-\frac{37}{3}(1+x)^{-3 } \\ & & \ \ \ + 9(1+x)^{-2}-3(1+x)^{-1}+\frac{1}{3})].\end{aligned}\ ] ]                                m. kado ( atlas collab . ) , `` results with the full 2015 data sample from the atlas experiment '' , presented at cern , december 15 , 2015 ; j. olsen ( cms collab . ) , `` cms 13 tev results '' , presented at cern , december 15 , 2015 .
the anomalous magnetic moment of the muon is an important observable that tests radiative corrections of all three observed local gauge forces : electromagnetic , weak and strong interactions . 
 high precision measurements reveal some discrepancy with the most accurate theoretical evaluations of the anomalous magnetic moment . 
 we show in this note that the uv finite theory can not resolve this discrepancy . 
 we believe that more reliable estimate of the nonperturbative hadronic contribution and the new measurements can resolve the problem .