       Num. integration problem in Mathematica

• To: mathgroup at smc.vnet.net
• Subject: [mg53782] Num. integration problem in Mathematica
• From: "Antonio Cardoso" <acardoso at scientist.com>
• Date: Thu, 27 Jan 2005 05:41:20 -0500 (EST)
• Sender: owner-wri-mathgroup at wolfram.com

```Hello, I'm trying to solve this numerical integration in Mathematica:

Ma = 10^10;
m1 = 0.06*10^(-9);
mPl = 1.221*10^19;

v = 174;
lambda = 0.4;
yt = 0.6;
gy = ((1/81)*4*Pi)^0.5;
g2 = ((1/38)*4*Pi)^0.5;
g3 = ((1/26)*4*Pi)^0.5;

mH = ((3/16)*g2^2 + (1/16)*gy^2 + (1/4)*yt^2 + (1/2)*lambda)^0.5*Ma;
mL = ((3/32)*g2^2 + (1/32)*gy^2)^0.5*Ma;
mQ = ((1/6)*g3^2 + (3/32)*g2^2 + (1/288)*gy^2 + (1/16)*yt^2)^0.5*Ma;
mU = ((1/6)*g3^2 + (1/18)*gy^2 + (1/8)*yt^2)^0.5*Ma;

aH = mH^2/Ma^2;
aL = mL^2/Ma^2;
aQ = mQ^2/Ma^2;

x = s/Ma^2;

smin = Max[(mQ + mU)^2, (mL + Ma)^2];
s = smin/y;

NIntegrate[s^0.5*BesselK[1,s^0.5/Ma]*(3/(4*Pi))*(Ma*m1/v^2)*yt^2*((x-1-aL)*(x-2*aQ)/(x*(x-aH)^2))*(((1+aL-x)^2-4*aL)*(1-4*aQ/x))^0.5*(1/y^2),{y,0,1},MinRecursion->10,MaxRecursion->35,WorkingPrecision->35]

but it can't give me the right answer. I't gives the error:

NIntegrate::slwcon:
Numerical integration converging too slowly; suspect one of the following: singularity, value of the integration being 0, oscillatory integrand, or insufficient WorkingPrecision. If your integrand is oscillatory try using the option Method->Oscillatory in NIntegrate.

I have already tried to change the options, like WorkingPrecision, PrecisionGoal, SingularityDepth, etc., but it didn't work.

Can someone help me to solve this problem?

Thank you,

Antonio Cardoso
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