Yield Ratio

Figure 4.42 shows the invariant cross sections of all electron sources. In this analysis, not absolute normalizations of the cross sections but yield ratios are important. The yield ratios before and after the isolation cut are calculated as follows:

R⁰_i = Y_i⁰

!

j∈all sources

Y_j⁰, (4.54)

R^v_i = !^iso_i ·Y_i⁰

!

j∈all sources

!^iso_j ·Y_j⁰ = !^corr_i ·Y_i⁰

!

j∈all sources

!^corr_j ·Y_j⁰, (4.55) where

R⁰_i: the yield ratio ofi-th source before the isolation cut, R^v_i: the yield ratio of i-th source after the isolation cut,

As is mentioned in Sec. 4.1, the yield ratios of the charm and bottom electrons are not separated here, and are handled in being combined as the heavy-quark electrons.

The yield ratios of charm and bottom electrons are necessary to obtain!^corrof heavy-quark electrons. The mean of those of charm and bottom electrons is utilized as that of heavy quark electrons, and an error is assigned to cover the errors of both charm and bottom electrons. When the ratios are calculated, a weight which corresponds to the reconstruction efficiency is applied toY_i⁰. Although the absolute value of the efficiency does not evaluated in this analysis, its dependence on pT is evaluated with the sum ofY_i⁰and the measuredpT distribution of the inclusive electrons. The ratio of them represents not the absolute value but the dependence onpT of the reconstruction efficiency. Figure 4.41 shows the measured pT distribution of the inclusive electrons over the sum ofY_i⁰. ThepT distribution is normalized by the number of the inclusive electrons forpT > 1 GeV/c. The sum ofY_i⁰is not corrected by integrated luminosity.

The ratio increases at 1 < pT <2 GeV/c and is flat at pT >2 GeV/c. Figure 4.43

[GeV/c]

electron pT

1 2 3 4 5

measured (scaled) / expected

0 20 40 60 80 100

Figure 4.41: A relative reconstruction efficiency of electrons as a function of pT. The efficiency is the measured pT slope of the inclusive electrons over the sum ofY_i⁰. ThepT

distribution is normalized by the number of the inclusive electrons with pT > 1 GeV/c.

The sum ofY_i⁰ is not corrected by integrated luminosity.

and Fig. 4.44 show the yield ratios before and after the isolation cut. Before the isolation cut is applied, photonic electrons are the largest background, but decays from heavy quarkonia become the largest at pT > 2.5 GeV/c.

In order to check a consistency of the yield ratios and survival fraction, the hit distributions located close to associated hits to electron tracks are compared between the data and simulation. The hit distribution of the simulation is created by com-bining the distributions of all electron sources with respect to the yield ratios, shown

[GeV/c]

p

T

1 2 3 4 5 6

]

3

c

-2

[mb GeV

3

/dp σ

3

Ed

10

-11

10

-10

10

-9

10

-8

10

-7

10

-6

10

-5

10

-4

10

-3

10

-2

10

-1

Heavy quark γee

0→ π

conversion γ

γee

→ η

γee

’ → η

→ ee ρ

0ee π

→ ee and ω

→ ω

ηee

→ ee and φ

→ φ

contributions direct γ

Ke3

Heavy quarkonia

Figure 4.42: The invariant cross sections of electrons fromπ⁰ Dalitz decay (red),ηDalitz decay (cyan), η^# (yellow), ρ (blue), ω (dark green), φ (purple), direct virtual photon (ma-genta), kaon (silver), heavy quarkonia (brown), and heavy quark electrons (black), and conversion electrons (light green).

[GeV/c]

electron pT

1 2 3 4 5

fraction in total

0.0 0.2 0.4 0.6 0.8 1.0

Figure 4.43: Yield ratios before the isolation cut of electrons fromπ⁰ Dalitz decay (red), ηDalitz decay (cyan), heavy quarkonia (brown), heavy-quark electrons (black), conversion electrons (green), and the others (open black squares).

[GeV/c]

electron pT

1 2 3 4 5

fraction in total

0.0 0.2 0.4 0.6 0.8 1.0

Figure 4.44: Yield ratios after the isolation cut of electrons from π⁰ Dalitz decay (red), ηDalitz decay (cyan), heavy quarkonia (brown), heavy-quark electrons (black), conversion electrons (green), and the others (open black squares).

in Fig. 4.43. Figure 4.45 shows the hit distributions. The red represents the inclu-sive electrons of the data. The blue and magenta represent the electrons from π⁰, conversion electrons in the simulation, respectively. The green and black represent the uncorrelated hits and the sum of electrons from all the sources, respectively. The distribution of the uncorrelated hits is the hit distribution of hadrons. The hit dis-tributions are successfully reproduced by the simulation at any pT range. The main contribution for the hit distribution of B0 is the electrons from π⁰, and that of B1 is conversion electrons. Therefore, yields of the conversion electrons and the electrons from π⁰ decays are successfully evaluated by the simulation. The contribution of conversion electrons is small in B0 though that of B1 is large. This is because hits created by a conversion pair are reconstructed into a hit cluster, not into two, since the conversion point is too close to B0. The negative side of cdphi distributions are mainly reproduced by the distributions of the uncorrelated hits for any pT ranges though main contributors are different at each range, i.e. the main contributors at 1 < pT < 2 GeV/c are the conversion electrons and the electrons from π⁰ decays, and that at 3 < pT < 4 GeV/c is the heavy quark electrons. It suggests that the uncorrelated term, !^r, does not depend on sources of electrons and can be well approximated by the survival fraction of hadrons.

Another consistency check is performed by comparing the yields of the inclusive electrons of the data and the simulation after the isolation cut. This comparison also provide a good test of the yield and survival fraction of each electron source. The yield of the inclusive electrons of the simulation is calculated as follows:

Y_s^v = !

i∈all sources

!^iso_i ·Y_i⁰ (4.56)

= !

i∈all sources

!^corr_i !^r·R_i⁰ Y_d⁰, (4.57) where

Y_s^v: the yield of the inclusive electrons in the simulation after the isolation cut, Y_i⁰: the yield of i-th source before the isolation cut,

Y_d⁰: the yield of the inclusive electrons in the data before the isolation cut, R⁰_i: the yield ratio ofi-th source before the isolation cut, shown in Fig. 4.43.

The survival fraction of hadrons is utilized as !^r. Figure 4.46 shows the yields of the inclusive electrons of the data and the simulation. The crosses and the open circles represent the yield of the data and the simulation, respectively. The black, the red, the green, and the brown circles represent the yields of heavy-quark electrons, conversion electrons, the electrons fromπ⁰ decays, and form heavy quarkonia, respectively. The

cdphi [rad]

-0.05 0.00 0.05

10 102

103

104 B0

: 1-2GeV/c pT

cdphi [rad]

-0.05 0.00 0.05

1 10 102

103 B0

: 2-3GeV/c pT

cdphi [rad]

-0.05 0.00 0.05

10-1

1 10

102 B0

: 3-4GeV/c pT

cdphi [rad]

-0.05 0.00 0.05

10 102

103

104 B1

: 1-2GeV/c pT

cdphi [rad]

-0.05 0.00 0.05

1 10 102

103 B1

: 2-3GeV/c pT

cdphi [rad]

-0.05 0.00 0.05

10-1

1 10

102 B1

: 3-4GeV/c pT

cdphi [rad]

-0.05 0.00 0.05

10 102

103

104 B2

: 1-2GeV/c pT

cdphi [rad]

-0.05 0.00 0.05

1 10 102

103 B2

: 2-3GeV/c pT

cdphi [rad]

-0.05 0.00 0.05

10-1

1 10

102 B2

: 3-4GeV/c pT

cdphi [rad]

-0.05 0.00 0.05

10 102

103

104 B3

: 1-2GeV/c pT

cdphi [rad]

-0.05 0.00 0.05

1 10 102

103 B3

: 2-3GeV/c pT

cdphi [rad]

-0.05 0.00 0.05

10-1

1 10

102 B3

: 3-4GeV/c pT

Figure 4.45: Hit distributions located close to associated hits to electron tracks. The red represents the distributions of the inclusive electrons of the data. The blue, the magenta, the green, and the black represent the distributions of the simulation of the electrons from π⁰, conversion electrons, the uncorrelated hits, and the sum of electrons from all the sources.

[GeV/c]

p

T

1 2 3 4 5

T

dN/dp

10

2

10

3

10

4

10

5

[GeV/c]

p

T

1 2 3 4 5

simulation / data

0.8 1.0 1.2

Figure 4.46: Yields of the inclusive electrons of the data and the simulation after the isolation cut. The crosses and the open circles represent the yield of the data and the simulation, respectively. The black, the red, the green, and the brown circles represent the yields of heavy-quark electrons, conversion electrons, the electrons fromπ⁰ decays, and form heavy quarkonia, respectively.

ドキュメント内 重心エネルギー200GeVの陽子衝突における、セミレプトニック崩壊モードを用いたチャームとボトムの測定 (ページ 131-138)