How to make a good scatter plot

Question

I have the following cross section:

c = 0.117
At= 1.37375
sigma[Y_,m_] = ((c^2)/(256*Pi))*( (1/2) ( Y/m )  *Abs [At] )^2 *10^8

When I make ListPlot for sigma versus Y at m=173, I use the following:

list1 = Table[{Y, sigma[Y, 173]}, {Y, 0.8, 1.2, 0.01}]
ListPlot[list1, Frame -> True]

I get the following plot:

Actually I don't want the shape of the plot to be like that, I'd like to have a scatter plot like for instance:

The figures from [arXiv:1312.1935 [hep-ph]]. kaba which is plotted in (a) and (b) is just a cross section multiplied by a branching ratio, (I think Mathematicians familiar with these expressions), so kaba is not so far from the cross section sigma[Y,m] I mentioned ..

Come to my simple (didnt't work) trail to make plot like these. I read in some examples of ListPlot in MMA that RandomReal can be used to generate more points to have no just a straight line, but when I write

list1 := Table[{Y, sigma[Y, 173]+RandomReal[]}, {Y, 0.8, 1.2, 0.01}]
ListPlot[list1, Frame -> True]

I get

very different points than my first plot and even when the steps decreased for say 0.001 I couldn't get a good scatter plot like (b) or (a) in the referred figure ,

so any help to write a better code to enhance my plot ?

Answer 1

Here is a generic answer. Let say you have a function f[x] and you want to make a noisy plot out of it.

f[x_] := Sin[x];
list1 = Table[{Y, f[Y]}, {Y, 0., 12, 0.01}];
ramp = 0.2  (*noise amplitude*)
list2 = Table[{Y, f[Y] + RandomReal[{-ramp, ramp}]}, {Y, 0., 12, 0.01}];
Show[ListPlot[list2, Frame -> True], 
ListLinePlot[list1, Frame -> True, PlotStyle -> Red]]

Considering your example

ramp = 0.005
Show[ListLinePlot[Table[{Y, sigma[Y, m]}, {m, 100, 500, 100},{Y, 0.8, 1.2, 0.01}], 
Frame -> True, PlotLegends -> Range[100, 500, 100]],
ListPlot[Table[{Y, sigma[Y, m] + RandomReal[{-ramp, ramp}]}, {m, 100, 500, 100},
{Y, 0.8, 1.2, 0.001}], Frame -> True]]

Answer 2

Unfortunately, I can't comment due to lack of reputation, so I hope I might be excused for writing as an answer what should be a comment. I'd like to have a link to your posted scatter plots. They look to me like either experimental results from particle physics experiments or numerical simulation data from theoretical particle physics, Standard Model for the Higg's boson I'd suppose. In the case of experimental data, it should be obvious where the clutter comes from. In the case of the numerical results, we're probably dealing with highly elaborated numerical calculations which do have a certain error margin ("asymptotic convergence" in Quantum Field Theories when doing Feynman diagram expansion, Quantum Field theory on finite meshes etc.) which produces the clutter. In your case, you have an analytical, smooth function you are evaluating. Where should any clutter come from if you plot something like that? If you do want clutter in your plot and you have a reason coming from the physics of the problem, I would suggest varying your constants with some uncertainty variation (a white noise or a Gaussian within the uncertainty limits) so that for each point of the plots, your physical constants vary slightly which will result in some kind of clutter. I however question whether you can expect any clutter in the first place.