Photon Conversion

Photon Source

[GeV/c]

pion pT

0 5 10 15 20

]3c-2 [mb GeV3 /dpσ3 E d

10-9

10-7

10-5

10-3

10-1

10

[GeV/c]

pion pT

0 5 10 15 20

(cross section) / (fitting curve) -1

-0.3 -0.2 -0.1 0.0 0.1 0.2 0.3

Figure 4.35: Left : The invariant cross section of π⁰ and a fitting curve of modified Hagedorn function.

Right : Deviations of the invariant cross section from the fitting curve.

is evaluated based on the electrons from hadron Dalitz decays. Figure 4.36 shows the ratio of conversion electrons and electrons from π⁰ Dalitz decay as a function of electron pT which is evaluated by a π⁰ single-track simulation with the PISA simulation. The red line shows a result of fitting by a constant. The ratio is flat and a dependence on the pT is small.

A contribution from the direct radiation has two process. One is real photons produced in initial hard scattering processes, i.e. direct real photons convert to elec-tron pairs in material in the experimental setup. The other is direct virtual photons.

Every source of real photons also accompanies virtual photons. In the case of theπ⁰, these two sources correspond to the γγ decay and Dalitz decay, which is also called an internal conversion. Similarly, direct real photon production is accompanied by direct virtual photon production, i.e. the emission of e⁺e pairs. The spectrum of the real direct photon has been measured by PHENIX experiment [74], and the spectrum is parametrized. The corresponding conversion electron spectrum is added to the conversion electrons. The ratio of virtual direct photons to real direct photons de-pends onpT because the phase space for dielectron emission increases with increasing pT. The same effect is seen in the Dalitz decays of light neutral mesons, i.e. the branching ratio of Dalitz decay relative to two photon decay increases as the mass of the hadron increases. Consequently, the ratio of virtual and real direct photon emission increases with pT or, to be more precise, with a logarithmic dependence.

Such dependence is implemented based on the theory. The systematic error of the direct photon measurement is directly propagated to the electron spectrum.

Evaluation of Material

The contribution of the conversion electrons largely depends on the material of the experimental setup. Photon conversions mainly occur at the beam pipe and B0 of the

/ ndf

χ

82.68 / 74 p0 1.017 ± 0.016

[GeV/c]

electron p

0 2 4 6 8

conversion / Dalitz decay

0 1 2

/ ndf

χ

82.68 / 74 p0 1.017 ± 0.016

Figure 4.36: The ratio of conversion electrons and electrons from π⁰ Dalitz decay as a function of electron pT evaluated by a π⁰ single-track simulation. The red line shows a result of fitting by a constant.

VTX for the electrons which passed the analysis cuts. Since the conversion occurred inside the silicon sensor of the VTX, the contribution depends on not only the amount of the material but also the depth of the sensor where the electrons converted inside the sensor can be detected.

The ratio of pairs of conversion electrons (conversion pairs) and those of electrons from hadron decays (decay pairs) is evaluated by using two distributions related to

is calculated as follows:

.u= −→pe++−→pe−

|−→pe++−→pe−|, (4.39) .v= −→pe+× −→pe−

|−→pe+× −→pe−|, (4.40) .

w=.u×.v, (4.41)

−

→ez = (0,0,1), (4.42)

.a= −→u × −→ez

|−→u × −→ez|, (4.43)

φV =cos⁻¹(.w·.a). (4.44)

The distributions of the conversion pairs and the decay pairs have different fea-tures. [75] The pair-mass distribution of the conversion pairs has a peak at∼20 MeV though the actual pair-mass is ∼0 MeV. The pair mass of off-vertex tracks is recon-structed to slightly different value from the actual value due to the algorithm of pT

reconstruction of CNTs. In the algorithm, a track is assumed to come from the col-lision vertex, and thus, pT of an off-vertex track is reconstructed to a different value, which depends on the created point of the pair. This is the reason why the pair-mass distribution of the conversion pairs has the peak at2= 0 though the actual pair mass is almost 0. The peak corresponds to the conversion at the beam pipe, which locates atr = 2.0 cm, and B0, which locates at r= 2.5 cm. The φV distribution of the con-version pairs has a peak atφV = 0 due to small opening angles of the pairs. On the other hand, the pair-mass distribution of the decay pairs has a peak around 10 MeV, and the φV distribution is flat.

The evaluation is performed with a π⁰ single-track simulation. Almost 80% of photons and the decay pairs are from π⁰ decays. and the pair-mass distribution where the mass is less than 0.1 GeV, and the φV distribution are well reproduced by scaling those ofπ⁰ decays. The second largest source is decays fromηmeson, and the contribution is ∼15%. Since the ratio of branching ratios between η → e⁺e⁻γ and η → 2γ, 1.780, is slightly different from that of π⁰, 1.188, the result evaluated with the π⁰ simulation is corrected with the difference. The remaining 5% was included in a systematic error. The distributions of the pair mass and φV are made for the conversion and decay pairs by the simulation. The normalization of the distributions are performed with respect to the branching ratios of π⁰ → 2γ and π⁰ → e⁺e⁻γ.

Then, two distributions of the data are fitted with two parameters, a and r, at the same time as follows:

φV(data) =a·(φV(C) +r·φV(D)), (4.45) Mee(data) =a·(Mee(C) +r·Mee(D)), (4.46) where φV(data) and Mee(data) are the distributions of φV and pair mass in data, respectively, φV(C) and Mee(C) are those of the pairs from photon conversions and

φV(D) and Mee(D) are from the Dalitz decays. The fitting is performed where the pair mass is less than 0.1 GeV. If all of the pairs are fromπ⁰decays and the conversion pairs are simulated exactly, r should be 1. The fitting result is shown in Fig. 4.37.

The black histogram represents the distributions of the data. The blue, magenta, and red histograms represent the conversion pairs, decay pairs, and sum of them in the simulation. The ratio, r, evaluated by the fitting was 1.091±0.067 and χ²/NDF was 3.40. The ratio of the number of decay pairs and the conversion pairs fromπ⁰ decays is 1.188 and that fromπ⁰ andη decays is (1.188×0.8 + 1.780×0.15)/0.95 = 1.281.

Therefore, rshould be multiplied by 1.188/1.281, and corrected from 1.091±0.067 to 1.012±0.062. Finally, the yield of the conversion electrons in simulations are corrected by 1/1.012 and the error of√

0.062²+ 0.05² is assigned as a systematic error for the correction factor.

pair mass [GeV]

0.000 0.02 0.04 0.06 0.08 0.10 100

200 300

φV

0 1 2 3

200 400

Figure 4.37: The pair-mass (left) andφV (right) distributions ofe⁺-e⁻ pairs. The black histogram represents the distributions of the data. The blue, magenta, and red histograms represent the distributions of conversion pairs, the decay pairs, and sum of them in the simulation. The histograms of the conversion pairs and the decay pairs are scaled with fitting results.