TF1

In ROOT you can fit histograms (or TEfficiency objects) using formulas that you provide, and that have free parameters. For an efficiency curve a TMath::Erf() is usually a good fit function. But you can't really use it as is. Let's see what it looks like:

// This lambda defines the values of the function. For now we don't use p:
auto myErf0Lambda = [](double* x, double* p) { return TMath::Erf(x[0]); };
// When drawing, show between -10..10
TF1* myErf0 = new TF1("myErf0", myErf0Lambda, -10, 10);
myErf0->Draw();

This is the same one but moved around to match the concept of efficiencies:

auto myErf1Lambda = [](double* x, double* p) 
      { return (TMath::Erf((x[0]-5)/3) + 1)/2 * 0.8; };
TF1* myErf1 = new TF1("myErf1", myErf1Lambda, -10, 10);
myErf1->Draw();

We can re-write this using parameter notation:

auto myErf2Lambda = [](double* x, double* p) { 
        return (TMath::Erf((x[0]-p[0])/p[1]) + 1)/2 * p[2]; };
TF1* myErf2 = new TF1("myErf2", myErf2Lambda, 
           -10, 10, 3 /*number of parameters*/);
myErf2->SetParameter(0, 5.);
myErf2->SetParameter(1, 3.);
myErf2->SetParameter(2, 0.8);
myErf2->Draw();

Try out what happens when you change the values for 5, 3 and 0.8 (simply by calling myErf2->SetParameter(...);)!

Fitting a TF1

Now that we have a nice TF1 we can fit it to the TEfficiency object by calling eff->Fit(). Here is the complete code you need to add to the end of effX():

...
void effX() {
...
   auto effErf = [](double* x, double* p) {
      return (TMath::Erf((x[0] - p[0]) / p[1]) + 1) / 2. * p[2];
   };

   TF1* myErf = new TF1("myErf", effErf, 0., 10., 3);
   myErf->SetParameter(0, 5.);
   myErf->SetParameter(1, 5.);
   myErf->SetParameter(2, 1.);

   eff->Fit(myErf);
}

Parameter Initialization and Fitting

You must initialize the parameters to sensible values - this is especially important for higher dimensional fits, e.g. with a TF2. Fitting is magic, but only within limits. Try with completely bogus parameters and you'll see how the fit fails!