drawdal.C

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// ****************************************************************
// drawdal.C(double m0, double m1, double m2, double m3, TString opt="Lsame", int n=200)
// ****************************************************************
// 
// Simple macro to draw Dalitz Plot border (m0+m2)^2:(m1+m2)^2 above a histogram
// USAGE: .x drawdal.C(M, m0, m1, m2, <opt>, <n>)
//   M         : Mass of mother system
//   m0,m1,m2  : masses of three daughters
//   <opt>     : draw option for the TGraph; default: "Lsame"
//   <n>       : number of points in TGraph: default: 200
//
// ****************************************************************
//  K.Goetzen, GSI, 10/2015
// ****************************************************************

Double_t simin(Int_t i, Double_t m0, Double_t m1, Double_t m2, Double_t m3)
{
        Double_t result = 0.;
        
        switch (i)
        {
        case 1:  result = (m2+m3)*(m2+m3);
                break;
        case 2:  result = (m1+m3)*(m1+m3);
                break;
        case 3:  result = (m1+m2)*(m1+m2);
                break;
        }
        return result;
}

Double_t simax(Int_t i, Double_t m0, Double_t m1, Double_t m2, Double_t m3)
{
        Double_t result = 0.;
        
        switch (i)
        {
        case 1:  result = (m0-m1)*(m0-m1);
                break;
        case 2:  result = (m0-m2)*(m0-m2);
                break;
        case 3:  result = (m0-m3)*(m0-m3);
                break;
        }
        return result;
}

Double_t lambda(Double_t x, Double_t y, Double_t z)
{
  return x*x + y*y + z*z - 2.*x*y - 2.*y*z - 2.*z*x; 
}

Double_t s2min(Double_t s1, Double_t m0, Double_t m1, Double_t m2, Double_t m3)
{
        Double_t s      = m0*m0;
        Double_t lamterm = sqrt( lambda(s1,s,m1*m1) ) * sqrt( lambda(s1, m2*m2, m3*m3) );
         
        Double_t result  = m1*m1 + m3*m3 + ( (s-s1-m1*m1)*(s1-m2*m2+m3*m3) - lamterm )/(2.*s1);
        
        return result;
}

Double_t s2max(Double_t s1, Double_t m0, Double_t m1, Double_t m2, Double_t m3)
{
        Double_t s      = m0*m0;
        Double_t lamterm = sqrt( lambda(s1,s,m1*m1) ) * sqrt( lambda(s1, m2*m2, m3*m3) );
         
        Double_t result  = m1*m1 + m3*m3 + ( (s-s1-m1*m1)*(s1-m2*m2+m3*m3) + lamterm )/(2.*s1);
        
        return result;
}


void CreateGraph(TGraph* g, Int_t n, Double_t m, Double_t m1, Double_t m2, Double_t m3)
{
        Double_t s1minl = simin(1, m, m1, m2, m3);
        Double_t s1maxl = simax(1, m, m1, m2, m3);
        
        Double_t binw = (s1maxl-s1minl)/(Double_t)(n);
        
        Int_t i=0;
        
        Double_t ymin,ymax,x;
        
        for (i=0; i<n; i++)
        {
                x = i*binw + s1minl;
                if (x<=s1minl) x=s1minl+binw/20;
                if (x>=s1maxl) x=s1maxl-binw/20;
                
                ymin = s2min(x, m, m1, m2, m3);
                ymax = s2max(x, m, m1, m2, m3);
                
                g->SetPoint(i,x,ymin);
                g->SetPoint(n*2-i,x,ymax);
        }

        g->SetPoint(n,s1maxl,s2min(s1maxl-binw/20,m,m1,m2,m3));
        g->GetPoint(0,x,ymin);
        g->SetPoint(n*2,x,ymin);
        
}

drawdal(double m0, double m1, double m2, double m3, TString opt="Lsame", int n=200)
{
        TGraph *g=new TGraph(n);
        g->SetLineColor(2);
        g->SetLineStyle(2);
        g->SetLineWidth(2);
        CreateGraph(g,n,m0,m1,m2,m3);
        g->Draw(opt);
}