Evidence for jet structure in hadron product by e＋e－

G. Hanson et al.

Phys. Rev. Lett. 35 (1975) 1609

Contents:

1. Introduction

2. Experiment at SLAC

3. Analysis

4. Results

5. Summary

Suzuki Kento

Shibata lab.

Physics Colloquium July 7th, 2008

Evidence for Jet Structure in Hadron Production

1. Introduction

jet

jet

q

q

e

e

−

+

+

→

γ

*

→

+

→

+

At large value of E

_c.m

the

hadron jets in e

＋

_e

－

annihilation can be observed.

e＋

e－

q

q

This paper reports the first

evidence for the existence of

the hadron jet in e

＋

_e

－

annihilation.

Jet : collimated sprays of

hadrons

γ* jet e＋ e－ q q virtual photon jet jet jet

2. Experiment at SLAC

The experiment was carried out at the SPEAR storage ring of SLAC, USA.

Data were collected at E_c.m. of 3.0, 3.8, 4.8, 6.2 and 7.4 GeV. beam Electron-positron collider (The diameter of the coil of the magnet) 3m jet 50°~130°

3. Analysis

∑

∑

⊥

=

i i i i

p

p

S

₂min 2

2

)

(

3

r

(

1) Sphericity（球形指数）

The sphericity

S

determines how jet-like an event is.

Choose the axis which minimizes

the value of

2

i i

p

⊥

∑

p_⊥ : the transverse momentum with respect to the chosen axis.

where the summation is over all detected particles

Chosen axis

S →1 S →0

( p_i is the momentum of each particle.)

(2) Two models : jet model and phase-space model

ϕ

θ

α

θ

α

σ

2

cos

sin

cos

1

2

P

2 2

d

d

+

+

∝

Ω

　

　

Simulation based on the two models

・

_Isotropic

phase-space model

・

_{Jet model}

(3) The angular distribution of the jet axis

The angular distribution of the jet axis is expected to be

Monte Carlo simulation is an important method for comparison with data.

P

4. Results

(1) Mean Sphericity vs. Center of Mass Energy

・

The mean

S

_{of the data}

decreases with E

_c.m.

.

・

The mean

S

_{of the jet model}

also decreases with E

_c.m.

. But the

phase-space model increases

with E

_c.m.

.

Phase-space model Jet model Mean Sphericity E_c.m. ( GeV )

The mean S of the data and the two models

The jet model agrees with the data.

But the phase-space model does not.

77

(2) Sphericity distribution of events

Sphericity S

The figures in this page and

previous page indicate that the jet model agrees with the data.

〔Ec.m=3.0 GeV〕 〔Ec.m=6.2 GeV〕 〔Ec.m=7.4 GeV〕 0 0.2 0.4 0.6 0.8 Number of Events (a) (b) (C)

This is an evidence for jet

・ The data

The peak of S distribution shifts to lower value at higher energies.

・ The two models

Jet model : the peak of S distribution shifts to lower value at higher

energies.

Phase-space model : the peak of S

distribution stays around 0.4.

At E_c.m. = 6.2 and 7.4 GeV

The jet model agrees with the data. But the phase-space model does not.

(3) Another evidence for jet

05

.

0

47

.

0

2

=

±

P

At 7.4 GeV the beam is transversely polarized due to synchrotron radiation.

The angular distribution of the jet axis is expected to be

ϕ

θ

α

θ

α

σ

2

cos

sin

cos

1

2

P

2 2

d

d

_∝

₊

₊

Ω

　

　

Azimuthal Angle of Jet Axis φ (degrees)

Number

of

Events

Experimental data ： The angular

distribution of the jet axis indeed has dependence on azimuthal angle φ.

Another evidence for jet

φ : the azimuthal angle of the jet axis with respect to the plane of the storage ring.

φ

The plane of the storage ring

θ

e＋ e－

Jet axis

99

5.

Summary

• This paper reports the first evidence for the existence of the hadron jet.

• The hadron jet is produced in e＋_e－_{annihilation.}

• The experiment was carried out at SLAC-SPEAR.

• Data were collected at E_c.m. of 3.0, 3.8, 4.8, 6.2 and 7.4 GeV.

• Sphericity is an important quantity for the analysis. →The mean S of the data decreases with E_c.m..

→The peak of S distribution shifts to lower value.

• Two models ( jet model and phase-space model ) are compared with data. →The jet model agrees with the data.

→The phase-space model disagrees with the data.

• The distribution of the jet axis has dependence on azimuthal angle φ.

Jet became later an important subject of QCD (quark-gluon physics ).

These are evidence for jet.

・ ビームの偏極について

B e＋ e－ z シンクロトロン加速器にて加速され た電子・陽電子ビームはシンクロト ン放射をして徐々に偏極される （sokolov-terenov効果）。このと き陽電子は磁場と同じ向きに、電 子は磁場とは反対向きに偏極され る。今回のSLACの実験ではビーム の偏極度をPとして

05

.

0

47

.

0

2

=

±

P

という値となっている。また対消滅により生成される仮想光子のスピンのｚ成 分は０。つまりスピンの方向は貯蔵リング面内にあることがわかる。

ϕ

θ

α

θ

α

σ

2

cos

sin

cos

1

2

P

2 2

d

d

+

+

∝

Ω

　

　

T L L T

σ

σ

σ

σ

α

+

−

=

σ_Ｔ : Transverse production cross section σ_Ｌ ： Longitudinal production cross section

12

.

0

78

.

0

±

=

α

ジェット軸の角度分布 ：

σ

∝

₁

+

₍

₀

_.

₇₈

±

₀

_.

₁₂

₎

_cos

2

θ

Ω

d

d

・ ジェット軸の角度分布

・ 仮想光子について

重心系 ) 0 , 0 , , ( p₁ c E ) 0 , 0 , , ( p₁ c E − 運動量保存則により光子 の4元運動量は

)

0

,

0

,

0

,

2

(

c

E

q

μ

=

つまり光子の不変質量が e＋ _e－

0

2

2

≠

=

c

E

M

となりゼロではなくなるので、この光子は仮想光子であると考えられる。

・ 球形指数について

∑

⎟

⎟

⎟

⎠

⎞

⎜

⎜

⎜

⎝

⎛

−

−

−

−

−

−

−

−

−

=

i i i i i i i i i i i i i i i i i i i

p

p

p

p

p

p

p

p

p

p

p

p

p

p

p

p

p

p

T

2 3 2 2 3 1 3 3 2 2 2 2 1 2 3 1 2 1 2 1 2

r

r

r

この行列の固有値を得るために対角化させる k k k

u

u

T

r

=

λ

r

(k=1,2,3)

∑

∑

⊥

=

+

+

=

i i i i

p

p

S

₂min 2 3 2 1 3

2

)

(

3

3

r

λ

λ

λ

λ

λ₃は最小の固有値。かつ固有ベクトルにたいして垂直 方向の運動量成分の２乗和を表す。このλ₃の固有ベク トルがジェット軸と定義される。