Convolution of a BW lineshape

Roofit and RooStats
1

I had a question related to RooFit. Can I analytically convolve a Briet-Wigner with a sum of a Gaussian and asymmetric Gaussian functions? I can do it well for a sum of two Gaussian functions, what we usually call a double Gaussian function. However, I am breaking my head for the former case. I can do it numerically, but the solution though works is not a cute one.

Please let me know how to proceed.

Many thanks,
Gagan

2

Hi,

The convolution of the Gaussian with a Breit_Wigner is the Voigt function which is provided in RooFit in the RooVoigtian function. I don’t know how do you express your asymmetric gaussian functions, maybe you can compute the convolution analytically. I don’t think RopFit provides a pdf for this distribution, but if you can make the convolution analytically, you should be able to write your own pdf implementing it.

Best Regards

Lorenzo

3

Hi Lorenzo;

I know about RooVoigtian function but what I am looking forward is the convolution of the Briet-Wigner with an asymmetric Gaussian (sigma_L is different from sigma_R unlike a standard Gaussian function).

Thanks,
Gagan

4

Hi,

I don’t know if you can compute analytically the convolution integral. As I said, if it is possible then you should create your own class implementing it. Otherwise use the numerical (FFT based is recommended) convolution

Lorenzo