I'm having trouble to do the following numerical integrations:
iEAs[Q_?NumericQ, m1_?NumericQ, m2_?NumericQ, mh_?NumericQ, V_?NumericQ, Vc_?NumericQ, A_?NumericQ, Ac_?NumericQ] := m1 Q NIntegrate[ x (A Ac (m2 + m1 (-1 + x)) + V Vc (m1 + m2 - m1 x))/(8 \[Pi]^2 (-mh^2 (-1 + x) + (m2^2 + m1^2 (-1 + x)) x)), {x, 0, 1}, MaxRecursion -> 100, WorkingPrecision -> 13];
iEAf[Q_?NumericQ, m1_?NumericQ, m2_?NumericQ, mh_?NumericQ, V_?NumericQ, Vc_?NumericQ, A_?NumericQ, Ac_?NumericQ] := m1 Q NIntegrate[-( (A Ac (12 m2 (1 + x) + m1 (1 - 9 x - 12 x^2)) + V Vc (12 m2 (1 + x) + m1 (-1 + 9 x + 12 x^2))))/(96 \[Pi]^2 (-m2^2 (-1 +x) + (mh^2 + m1^2 (-1 + x)) x)), {x, 0, 1}, MaxRecursion -> 100, WorkingPrecision -> 13];
iVAv[G_?NumericQ, m1_?NumericQ, m2_?NumericQ, M_?NumericQ, V_?NumericQ, Vc_?NumericQ, A_?NumericQ, Ac_?NumericQ] := G m1 NIntegrate[- (A Ac (-3 m2 (1 + x) + m1 (-3 + x + 2 x^2)) + V Vc (3 m2 (1 + x) + m1 (-3 + x + 2 x^2)))/(8 \[Pi]^2 (M^2 (-1 + x) - (m2^2 + m1^2 (-1 + x)) x)), {x, 0, 1}, MaxRecursion -> 100, WorkingPrecision -> 13];
iVAf[Q_?NumericQ, m1_?NumericQ, m2_?NumericQ, M_?NumericQ, V_?NumericQ, Vc_?NumericQ, A_?NumericQ, Ac_?NumericQ] := m1 Q NIntegrate[ -( (V Vc (m1 - 2 m2 + m1 x) + A Ac (m1 + 2 m2 +
m1 x))/(4 \[Pi]^2 (M^2 + (m1^2 + m2^2) (-1 + x)))), {x, 0, 1}, MaxRecursion -> 100, WorkingPrecision -> 13];
Then when I try to calculate my other function, that is just a sum of several of those integrals taken with diferent arguments, I get the following errror:
During evaluation of In[1]:= NIntegrate::zeroregion: Integration region {{1.000000000000,0.999999999999999999999999999972752437499605743914855469900697130}} cannot be further subdivided at the specified working precision. NIntegrate assumes zero integral there and on any further indivisible regions. >>
During evaluation of In[1]:= NIntegrate::inumri: The integrand -((3.94734084367020280294200477311377373096717807463275517933069283*10^-10 (1.2679004580000000000 (1+x)+0.10565837150000000000 (1-9 x-12 x^2)))/(-0.0111636914680320122499999999999999999999999999999999999999121163 (-1+x)+0.011163691468032012250 (-1+x) x)) has evaluated to Overflow, Indeterminate, or Infinity for all sampling points in the region with boundaries {{0.999999999999999999999999999972752437499605743914855469900697130,0.999999999999999999999990130457402984116116415865423076016809530}}.
>
During evaluation of In[1]:= NIntegrate::zeroregion: Integration region {{1.000000000000,0.999999999999999999999999999972752437499605743914855469900697130}} cannot be further subdivided at the specified working precision. NIntegrate assumes zero integral there and on any further indivisible regions. >>
During evaluation of In[1]:= NIntegrate::inumri: The integrand -((3.94734084367020280294200477311377373096717807463275517933069283*10^-10 (1.2679004580000000000 (1+x)+0.10565837150000000000 (1-9 x-12 x^2)))/(-0.0111636914680320122499999999999999999999999999999999999999121163 (-1+x)+0.011163691468032012250 (-1+x) x)) has evaluated to Overflow, Indeterminate, or Infinity for all sampling points in the region with boundaries {{0.999999999999999999999999999972752437499605743914855469900697130,0.999999999999999999999990130457402984116116415865423076016809530}}.
>
During evaluation of In[1]:= NIntegrate::slwcon: Numerical integration converging too slowly; suspect one of the following: singularity, value of the integration is 0, highly oscillatory integrand, or WorkingPrecision too small. >>
During evaluation of In[1]:= NIntegrate::eincr: The global error of the strategy GlobalAdaptive has increased more than 400 times. The global error is expected to decrease monotonically after a number of integrand evaluations. Suspect one of the following: the working precision is insufficient for the specified precision goal; the integrand is highly oscillatory or it is not a (piecewise) smooth function; or the true value of the integral is 0. Increasing the value of the GlobalAdaptive option MaxErrorIncreases might lead to a convergent numerical integration. NIntegrate obtained -1.102332818474*10^-28 and 1.773650837526`13.*^-29 for the integral and error estimates. >>
During evaluation of In[1]:= NIntegrate::slwcon: Numerical integration converging too slowly; suspect one of the following: singularity, value of the integration is 0, highly oscillatory integrand, or WorkingPrecision too small. >>
During evaluation of In[1]:= NIntegrate::eincr: The global error of the strategy GlobalAdaptive has increased more than 400 times. The global error is expected to decrease monotonically after a number of integrand evaluations. Suspect one of the following: the working precision is insufficient for the specified precision goal; the integrand is highly oscillatory or it is not a (piecewise) smooth function; or the true value of the integral is 0. Increasing the value of the GlobalAdaptive option MaxErrorIncreases might lead to a convergent numerical integration. NIntegrate obtained 1.68427508260603075850603189688997779553482730498560866417565317
63.*^-25 and 6.25652496229563136928773273149849536309587019886986176252873178
63.*^-26 for the integral and error estimates. >>During evaluation of In[1]:= NIntegrate::slwcon: Numerical integration converging too slowly; suspect one of the following: singularity, value of the integration is 0, highly oscillatory integrand, or WorkingPrecision too small. >>
During evaluation of In[1]:= General::stop: Further output of NIntegrate::slwcon will be suppressed during this calculation. >>
During evaluation of In[1]:= NIntegrate::eincr: The global error of the strategy GlobalAdaptive has increased more than 400 times. The global error is expected to decrease monotonically after a number of integrand evaluations. Suspect one of the following: the working precision is insufficient for the specified precision goal; the integrand is highly oscillatory or it is not a (piecewise) smooth function; or the true value of the integral is 0. Increasing the value of the GlobalAdaptive option MaxErrorIncreases might lead to a convergent numerical integration. NIntegrate obtained -1.343930509261*10^-26 and 7.504336838898`13.*^-27 for the integral and error estimates. >>
During evaluation of In[1]:= General::stop: Further output of NIntegrate::eincr will be suppressed during this calculation. >>
During evaluation of In[1]:= NIntegrate::zeroregion: Integration region {{1.000000000000,0.999999999999999999999999999972752437499605743914855469900697130}} cannot be further subdivided at the specified working precision. NIntegrate assumes zero integral there and on any further indivisible regions. >>
During evaluation of In[1]:= General::stop: Further output of NIntegrate::zeroregion will be suppressed during this calculation. >>
During evaluation of In[1]:= NIntegrate::inumri: The integrand -((3.94734084367020280294200477311377373096717807463275517933069283*10^-10 (1.2679004580000000000 (1+x)+0.10565837150000000000 (1-9 x-12 x^2)))/(-0.0111636914680320122499999999999999999999999999999999999999121163 (-1+x)+0.011163691468032012250 (-1+x) x)) has evaluated to Overflow, Indeterminate, or Infinity for all sampling points in the region with boundaries {{0.999999999999999999999999999972752437499605743914855469900697130,0.999999999999999999999990130457402984116116415865423076016809530}}.
>
During evaluation of In[1]:= General::stop: Further output of NIntegrate::inumri will be suppressed during this calculation. >>
Out[56]= -0.1054127670153 - 0.10565837150000000000 NIntegrate[-(0.0006115582135884999042 \ 0.0006115582135884999042 (12 0.10565837150000000000 (1 + x) + 0.10565837150000000000 (1 - 9 x - 12 x^2)) + 0 0 (12 0.10565837150000000000 (1 + x) + 0.10565837150000000000 (-1 + 9 x + 12 x^2)))/(96 [Pi]^2 (-0.10565837150000000000^2 (-1 + x) + (0^2 + 0.10565837150000000000^2 (-1 + x)) x)), {x, 0, 1}, MaxRecursion -> 100, WorkingPrecision -> 13]
I have tried many methods of integration. For most of them I get the kind of error above, for local adaptive methods I don't get any error, but I left Mathematica running for a whole afternoon and it didn't finish the calculation (it just kept running).
I need the WorkingPrecision->13 because I'm going to compare this result with the electron anomalous magnetic moment (which has got 12 significant digits for it's experimental value). My final goal is to use thse integrals for several values of it's parameters, and then make RegionPlots comparing my calculations with the experimental value.
EDIT: If I get divergences it is fine for me to discard the parameter values (m2, mh and M) where they happen.
So, if anyone can find a way to solve my problem, I would be very grateful.
\[Pi]^2
, as it now appears in the code block. $\endgroup$