Such a measurement is crucial to extract the direct photon signal, but the measurement of neutral meson provides also direct information about the QGP and hadron gas properties :
1. The freeze-out conditions (low pT neutral pion spectra)
2. The restoration of the SU(1) symmetry (pT eta meson spectrum, X. Huang PRD53(96)5034)
3. The jet-plasma interaction physics via the high pT spectra of neutral mesons.
The invariant mass spectrum is built by full combination of the photons pairs in a given event:
M_inv = sqrt (2 E1 E2 (1 - cos(theta_12)))
where Ei are the energies of the photons and theta_12 the relative angle. Since the combinatorial background strongly depends on pT values, the invariant mass spectrum is constructed as a 2D histogram transverse momentum versus invariant mass.
I have developed a aliroot compiled macro AnaPhotons_v1.C (see also in the PHOS directory in ALICE_ROOT). This macro can (must) be compilated in the aliroot framework:
.includepath ${ALICE_ROOT}/PHOS
.L AnaPhotons_v1.C++
The version v1 of this macro contains two functions :
void AnaMinv(char * filename)
This funcion analyses the RecParticles in PHOS (electromagntic showers) and builds the invariant mass versus transverse momentum spectra for two pT range: 0-10 GeV/c and 0 - 100 GeV/c. In addition, it calculates the combinatorial background (extension _back). The phase space histograms are also built, and the distributions of photon pair asymmetry and photon pair DeltaR are calculated. The combinatorial background is calculated by ramdomizing the bi-dimensional spectra of pseudo-rapidity versus phi and randomizing the 1D spectrum of pT. The bidimensional spectrum GetRandom2() is necesary to keep the correlation between pseudo-rapidity and phi (mainly due to dead modules). We assume, as one would expect, that the pT distribution is independent on the pseudo-rapidiy & phi values (see the code of AnaMin function in AnaPhotons_v1.C for more details).
The output file name is given by sprintf(outputname,"%s.Minv",filename);
void AnaPtSpectrum(char * filename, Int_t NumberPerPtBin, Option_t * particle, Option_t * opt)
This function calculates de pT spectrum from file created by AnaMinv (extension ".Minv"). Background spectrum is normalized in the invariant mass range 200 to 400 MeV/c. The number of neutral mesons is then calculated, and errors are evaluated. NumberPerPtBin means number of bins in the pT spectrum per pT bin in the original 2D spectrum. NumberPerPtBin=1 means a bin of 250 MeV/c, and NumberPerPtBin=4 means a 1 GeV/c bin. Two particles can be considered "pion" or "eta". For pions, the invariant mass spectrum is integrated from 112 MeV/c2 to 152 MeV/c2 and for eta mesons, from 468 MeV/c2 to 628 MeV/c2 Finally, the option opt allow for two different pT range 0 - 10 GeV/c or 0 - 100 GeV/c. The output file name is sprintf(filenameout,"%s.PtSpectrum_%d_%s_%s",filename, NumberPerPtBin, particle, opt); and contains a TGraphErrors class with the number of neutral mesons per pT bin.
Large multiplicity of a flat neutral pion pT distribution
Enclosed, you will find the invariant mass analysis (done with the AnaPhotons_v1.C macro) for the pT range 1-2 GeV/c. In this simulation, 100 neutrla pions per envent over the PHOS acceptance region where generated and a flat pT distribution from 0.5 to 5 GeV/c was considered. We observe that the calculated background fits well th invariant mass spectrum around the pi0 peak.
Enclose the difference between signal and background after an integral normalisation in the mass range 200 - 400 MeV/c^2
Number of pion as a function of pT. Error bars contains the contribution from statistics, background and normalization:
AnaPtSpectrum("galice_111.root.Minv",2,"pion","low")
Now, the results if we ask for the eta meson yield. As one could expect, the yields are compatible with zero, since we have only simulated neutral pions! :
AnaPtSpectrum("galice_111.root.Minv",2,"eta","low")
HIJING events
We have redo the precedent analysis for 200 HIJING event with the maximal expected multiplicity in the PHOS acceptance region. The pi0 peak is not observed due to the high statistical errors:
Enclosed, the difference between signal and background after an integral normalisation in the mass range 200 - 400 MeV/c^2. The pi0 peak is not observed, however a correlation is clearly observed for invariant masses below 50 MeV/c^2. This correlation could be originated, as we will see later, by the presence of baryons and anti baryons in the HIJING events.
The pT spectrum for pi0 and eta mesons are then evaluated:
Flat pT distribution of Anti neutrons
The invariant mass analysis of antineutrons shows up a correlation at low invaraint mass, as it is observed for the HIJING events
