Convolution of a function to a resol function with E depend


I am trying to make a convolution using RooFFTConv between a some MC true energy distribution and some Gaussian resolution function. But I need the Gaussian width to depend on the energy.

Essentially just doing the integral below.

C(x) = integral { expo(-ax’) gaus[x’-x,sigma(x’)] dx’ }

I found an example using RooFormulaVar but testing this with just some narrow Gaussians, the width of the resulting convolved function does not seem to increase with energy.

Attached is a plot generated by the snippet of codes below. As you see the width of convolved function does not increase when the initial function is center around 10 or 90…

RooRealVar S1True("S1True","S1True",0,100); 
RooRealVar S1Reco("S1Reco","S1Reco",0,100);
RooPlot* frame1 = w->var("S1True")->frame(Title("S1 Spectra"));

RooFormulaVar S1Sigma("S1Sigma", "sqrt(@0)", RooArgList(S1True));
RooGaussian ResFuncS1("ResFuncS1", "ResFuncS1",S1Reco,S1True,S1Sigma);
RooRealVar MeanNarrowGaus("MeanNarrowGaus","MeanNarrowGaus",10,0,100);
RooRealVar SigmaNarrowGaus("SigmaNarrowGaus","SigmaNarrowGaus",0.1,0,100);
RooGaussian NarrowGaus("NarrowGaus", "NarrowGaus",S1True,MeanNarrowGaus,SigmaNarrowGaus);
RooFFTConvPdf NarrowGausConvRes("NarrowGausConvRes","NarrowGausConvRes",S1Reco,NarrowGaus,ResFuncS1);
NarrowGausConvRes.plotOn(frame1,LineColor(kGreen), Name("S1True"), FillColor(0));

RooGaussian NarrowGaus2("NarrowGaus2", "NarrowGaus2",S1True,MeanNarrowGaus,SigmaNarrowGaus);
RooFFTConvPdf NarrowGausConvRes2("NarrowGausConvRes2","NarrowGausConvRes2",S1Reco,NarrowGaus2,ResFuncS1);
NarrowGausConvRes2.plotOn(frame1,LineColor(kGreen), Name("S1True"), FillColor(0));

Thanks for any help or suggestions,

I found a solution here, (but it’s a bit slow)

But the method uses RooProdPDF.createProjection method. It looks like this is done using numeric integration. This causes the codes to take ~ 3 minutes to run instead of the RooFFTConv < 10 seconds. Does anyone have experience with speeding up this creatProjection method?