Working on ZDC energy distribution #38

notebooks/modules/physics/analysis/ITSvsTPC_events.py

@@ -18,7 +18,7 @@ def ShowComparisonSame(title, arrs, xlabel, labels, colors, nBins=100, ranges=(0
 
     for i in range(l):
         ax.hist(arrs[i], bins=nBins, range=ranges,
-                color=colors[i], histtype='step', linewidth=2, label=labels[i]+f' | {(arrs[i] < 0.15).sum()}')
+                color=colors[i], histtype='step', linewidth=2, label=labels[i]) #+f' | {(arrs[i] < 0.15).sum()}')
         ax.legend(prop={'size': 14})
         ax.tick_params(axis='both', which='major', labelsize=10)
         ax.set_xlabel(xlabel, fontdict={'size': 14})

notebooks/modules/physics/vector.py

@@ -0,0 +1,66 @@
+import numpy as np
+import pandas as pd
+
+def RotateToVector(dir_mom_tracks : pd.DataFrame, trans_tracks : pd.DataFrame):
+    """
+    Function defines components for rotation matrix that describes transition to the new
+    coordinate system which OZ axis direct along momentum of input dir_mom_tracks and rotate provided dir_mom_tracks.
+    """
+    alpha_denom = np.sqrt(dir_mom_tracks.T_Py**2+dir_mom_tracks.T_Pz**2)
+
+    dir_mom_tracks['sa'] = dir_mom_tracks.T_Py / alpha_denom
+    dir_mom_tracks['ca'] = dir_mom_tracks.T_Pz / alpha_denom
+
+    beta_denom = np.sqrt(dir_mom_tracks.T_Px**2 + (dir_mom_tracks.T_Py * dir_mom_tracks['sa'] + dir_mom_tracks.T_Pz*dir_mom_tracks['ca'])**2)
+
+    dir_mom_tracks['sb'] = dir_mom_tracks.T_Px / beta_denom
+    dir_mom_tracks['cb'] = (dir_mom_tracks.T_Py * dir_mom_tracks['sa'] + dir_mom_tracks.T_Pz*dir_mom_tracks['ca']) / beta_denom
+
+
+    dir_mom_tracks['prx'] = dir_mom_tracks.T_Px * dir_mom_tracks['cb'] - dir_mom_tracks.T_Py * dir_mom_tracks['sa'] * dir_mom_tracks['sb'] - dir_mom_tracks.T_Pz * dir_mom_tracks['ca'] * dir_mom_tracks['sb']
+
+    dir_mom_tracks['pry'] = dir_mom_tracks.T_Py * dir_mom_tracks['ca'] - dir_mom_tracks.T_Pz * dir_mom_tracks['sa']
+
+    dir_mom_tracks['prz'] = dir_mom_tracks.T_Px * dir_mom_tracks['sb'] + dir_mom_tracks.T_Py * dir_mom_tracks['sa'] * dir_mom_tracks['cb'] + dir_mom_tracks.T_Pz * dir_mom_tracks['ca']* dir_mom_tracks['cb']
+
+    dir_mom_tracks['l'] = np.sqrt(dir_mom_tracks.T_Px**2+dir_mom_tracks.T_Py**2+dir_mom_tracks.T_Pz**2)
+    dir_mom_tracks['lr'] = np.sqrt(dir_mom_tracks.prx**2+dir_mom_tracks.pry**2+dir_mom_tracks.prz**2)
+    dir_mom_tracks['E'] = np.sqrt(dir_mom_tracks.T_Px**2 + dir_mom_tracks.T_Py**2 +
+                    dir_mom_tracks.T_Pz**2 + (0.001*Rho0.mass)**2)
+    dir_mom_tracks['rE'] = np.sqrt(dir_mom_tracks.prx**2 + dir_mom_tracks.pry**2 +
+                    dir_mom_tracks.prz**2 + (0.001*Rho0.mass)**2)
+
+    trans_tracks['prx'] = trans_tracks.T_Px * dir_mom_tracks['cb'] - trans_tracks.T_Py * dir_mom_tracks['sa'] * dir_mom_tracks['sb'] - trans_tracks.T_Pz * dir_mom_tracks['ca'] * dir_mom_tracks['sb']
+
+    trans_tracks['pry'] = trans_tracks.T_Py * dir_mom_tracks['ca'] - trans_tracks.T_Pz * dir_mom_tracks['sa']
+
+    trans_tracks['prz'] = trans_tracks.T_Px * dir_mom_tracks['sb'] + trans_tracks.T_Py * dir_mom_tracks['sa'] * dir_mom_tracks['cb'] + trans_tracks.T_Pz * dir_mom_tracks['ca']* dir_mom_tracks['cb']
+
+def BoostToSystem(y : pd.Series, G : pd.Series, tracks):
+    """
+    Lorentz boost to new system which move related original along OZ with
+    y, G parameters.
+    """
+
+    tracks['y'] = y
+    tracks['G'] = G
+
+    tracks['oE'] = np.sqrt(tracks.T_Px**2 + tracks.T_Py**2 +
+                    tracks.T_Pz**2 + (0.001*PiPlus.mass)**2)
+
+    tracks['rE'] = np.sqrt(tracks.prx**2 + tracks.pry**2 +
+                    tracks.prz**2 + (0.001*PiPlus.mass)**2)
+
+    tracks['lpr'] = np.sqrt(tracks.prx**2 + tracks.pry**2 +
+                    tracks.prz**2 )   
+
+    tracks['brpz'] = tracks.y * tracks.prz - tracks.G * tracks.rE
+
+def CosTheta(tracks1 : pd.DataFrame, tracks2 : pd.DataFrame) -> pd.Series:
+    """
+    Cosine of theta where a theta is an angle between vectors from tracks1 and tracks2.
+    """
+    l1 = np.sqrt(tracks1.iloc[:,0]**2 + tracks1.iloc[:,1]**2 + tracks1.iloc[:,2]**2)
+    l2 = np.sqrt(tracks2.iloc[:,0]**2 + tracks2.iloc[:,1]**2 + tracks2.iloc[:,2]**2)
+    t1t2 = tracks1.iloc[:,0]*tracks2.iloc[:,0] + tracks1.iloc[:,1]*tracks2.iloc[:,1] + tracks1.iloc[:,2]*tracks2.iloc[:,2]
+    return t1t2 / (l1*l2)