Dear friends,
If one stores the TLorentzVector components in the class as 'the invariant' and
a 3-vector in spherical coordinates, these sort of rounding problems
can be prevented (this is one of the cases I meant in one of my earlier
mails when we discussed about how to treat 4-vectors).
Another thing is (as was mentioned by somenone already, but I forgot the name
<must be the age!>) that by storing the invariant the particle identity (i.e. mass)
is always conserved in physics processes and doesn't have to be re-calculated
in case the energy/momentum changes.
Cheers,
Nick.
Matt Dobbs wrote:
>
> Hi,
>
> Looking at TLorentzVector class, I wish to find the cosine of the angle
> between the vector and the z axis. For this I would expect to use
> CosTheta() method which is defined in TLorentzVector.h as follows:
>
> inline Double_t TLorentzVector::CosTheta() const {
> Double_t ptot = Mag();
> return ptot == 0.0 ? 1.0 : fZ/ptot;
> }
>
> If I check the definition of Mag() I find that it is the invariant mass
> NOT the Magnitude of the three vector:
>
> inline Double_t TLorentzVector::Mag2() const {
> return T()*T() - Vect().Mag2();
> }
> inline Double_t TLorentzVector::Mag() const {
> Double_t mm = Mag2();
> return mm < 0.0 ? -TMath::Sqrt(-mm) : TMath::Sqrt(mm);
> }
>
> As example:
>
> root [49] v = new TLorentzVector(1,1,1,1.75)
> (class TLorentzVector*)0x8723668
> root [50] v.Vect().CosTheta()
> (Double_t)5.77350269189625731e-01
> root [51] v.Mag()
> (Double_t)2.50000000000000000e-01
> root [52] v.CosTheta()
> (Double_t)4.00000000000000000e+00
> (Root V2.22 Redhat linux 5.1)
> So v.Vect().CosTheta() gives the expected value but
> v.CosTheta() gives a non-physical cosine > 1.
>
> Have I misuderstood the meaning of CosTheta? It seems intuitive to me that
> TLorentzVector::Mag() would call TVector3::Mag() and likewise for
> TLorentzVector::CosTheta().
>
> ~Matt
>
> _________________________________________________________________________
> Matt D O B B S
> CERN EP Division, ATLAS Experiment Office Tel: 41.22.76.71272 (Swiss)
> Office: 40-1-C15, ATLAS Bldg. Home Tel: 0450 282544 (France)
> Email: Matthew.Adam.Dobbs@Cern.CH http://wwwhep.phys.uvic.ca/~mdobbs/
> Department of Physics and Astronomy, University of Victoria, Canada
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