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❚✇♦✲♣❤♦t♦♥ ❡①❝❤❛♥❣❡ ❝♦♥tr✐❜✉t✐♦♥ ✐♥ ❡❧❛st✐❝ ❡❧❡❝tr♦♥✲♣r♦t♦♥ s❝❛tt❡r✐♥❣✿ ♠❡❛s✉r❡♠❡♥ts ❛t ❱❊PP✲✸

■✳ ❆✳ ❘❛❝❤❡❦✱✶ ❏✳ ❆rr✐♥❣t♦♥✱✷ ▲✳ ▼✳ ❇❛r❦♦✈✱✶ ❱✳ ❋✳ ❉♠✐tr✐❡✈✱✶,✸ ❱✳ ❱✳ ●❛✉③s❤t❡✐♥✱✹ ❘✳ ❆✳ ●♦❧♦✈✐♥✱✶,✸ ❆✳ ❱✳ ●r❛♠♦❧✐♥✱✶ ❘✳ ❏✳ ❍♦❧t✱✷ ❱✳ ❱✳ ❑❛♠✐♥s❦②✱✶ ❇✳ ❆✳ ▲❛③❛r❡♥❦♦✱✶ ❙✳ ■✳ ▼✐s❤♥❡✈✱✶ ◆✳ ❨✉✳ ▼✉❝❤♥♦✐✱✶,✸ ❱✳ ❱✳ ◆❡✉❢❡❧❞✱✶ ❉✳ ▼✳ ◆✐❦♦❧❡♥❦♦✱✶ ❘✳ ❙❤✳ ❙❛❞②❦♦✈✱✶ ❨✉✳ ❱✳ ❙❤❡st❛❦♦✈✱✶,✸ ❱✳ ◆✳ ❙t✐❜✉♥♦✈✱✸ ❉✳ ❑✳ ❚♦♣♦r❦♦✈✱✶,✸ ❍✳ ❞❡ ❱r✐❡s✱✹ ❙✳ ❆✳ ❩❡✈❛❦♦✈✱✶ ❛♥❞ ❱✳ ◆✳ ❩❤✐❧✐❝❤✶

✶ ❇✉❞❦❡r ■♥st✐t✉t❡ ♦❢ ◆✉❝❧❡❛r P❤②s✐❝s ❙❇ ❘❆❙✱ ◆♦✈♦s✐❜✐rs❦✱ ❘✉ss✐❛ ✷❆r❣♦♥♥❡ ◆❛t✐♦♥❛❧ ▲❛❜♦r❛t♦r②✱ ❆r❣♦♥♥❡✱ ❯❙❆ ✸◆♦✈♦s✐❜✐rs❦ ❙t❛t❡ ❯♥✐✈❡rs✐t②✱ ◆♦✈♦s✐❜✐rs❦✱ ❘✉ss✐❛ ✹◆✉❝❧❡❛r P❤②s✐❝s ■♥st✐t✉t❡ ❛t ❚♦♠s❦ P♦❧②t❡❝❤♥✐❝❛❧ ❯♥✐✈❡rs✐t②✱ ❚♦♠s❦✱ ❘✉ss✐❛ ✺◆■❑❍❊❋✱ ❆♠st❡r❞❛♠✱ ❚❤❡ ◆❡t❤❡r❧❛♥❞s

❊▼■◆✲✷✵✶✷

■✳❆✳ ❘❛❝❤❡❦ ❊▼■◆✲✷✵✶✷ ❙❡♣t❡♠❜❡r ✷✶✱ ✷✵✶✷ ✶

Pr♦t♦♥ ❡❧❡❝tr♦♠❛❣♥❡t✐❝ ❢♦r♠ ❢❛❝t♦rs

❚❤❡ ❊▼ ❢♦r♠ ❢❛❝t♦rs ❛r❡ ❡ss❡♥t✐❛❧ ✐♥❣r❡❞✐❡♥ts ♦❢ ♦✉r ❦♥♦✇❧❡❣❞❡ ♦❢ t❤❡ ♥✉❝❧❡♦♥ str✉❝t✉r❡ ❛♥❞ t❤✐s ❥✉st✐✜❡s t❤❡ ❡✛♦rts ❞❡✈♦t❡❞ t♦ t❤❡✐r ❡①♣❡r✐♠❡♥t❛❧ ❞❡t❡r♠✐♥❛t✐♦♥

■♥ ♦♥❡✲♣❤♦t♦♥ ✭❇♦r♥✮ ❛♣♣r♦①✐♠❛t✐♦♥✿

◆✉❝❧❡♦♥ ❈✉rr❡♥t ❖♣❡r❛t♦r Γµ(q)

Γµ(q) = γµ❋✶(q✷) + ✐σµνqν

✷▼

❋✷(q✷)

❋✶(q✷) ✕ ♥♦♥ s♣✐♥ ✢✐♣ ❉✐r❛❝ ❋♦r♠ ❋❛❝t♦r ❋✷(q✷) ✕ s♣✐♥ ✢✐♣ P❛✉❧✐ ❋♦r♠ ❋❛❝t♦r ❙❛❝❤s ❋♦r♠ ❋❛❝t♦rs ❊❧❡❝tr✐❝ ❋♦r♠ ❋❛❝t♦r

• ❊(◗✷) = ❋✶(◗✷) − ◗✷

✹▼ ❋✷(◗✷)

▼❛❣♥❡t✐❝ ❋♦r♠ ❋❛❝t♦r

• ▼(◗✷) = ❋✶(◗✷) + ❋✷(◗✷)
• ❊ ≈ ●▼/µ♣ ≈ ●❉ ≡ (✶ + ◗✷/✵.✼✶)−✷

✐♥ ♥♦♥✲r❡❧❛t✐✈✐st✐❝ ❧✐♠✐t ●❊ ❛♥❞ ●▼ ❞❡s❝r✐❜❡ ❝❤❛r❣❡ ❛♥❞ ♠❛❣♥❡t✐③❛t✐♦♥ ❞✐str✐❜✉t✐♦♥ ✐♥ ♥✉❝❧❡♦♥

■✳❆✳ ❘❛❝❤❡❦ ❊▼■◆✲✷✵✶✷ ❙❡♣t❡♠❜❡r ✷✶✱ ✷✵✶✷ ✷

▼❡❛s✉r❡♠❡♥ts ♦❢ Pr♦t♦♥ ❢♦r♠ ❢❛❝t♦rs

❙t✉❞② ✇✐t❤ ❡❧❛st✐❝ ❡♣ s❝❛tt❡r✐♥❣ ❚❤❡ ❘♦s❡♥❜❧✉t❤ s❡♣❛r❛t✐♦♥ ♠❡t❤♦❞ ❛t ❝♦♥st❛♥t ◗✷

❘♦s❡♥❜❧✉t❤ ❋♦r♠✉❧❛

❘♦s❡♥❜❧✉t❤✱ ✶✾✺✵

❞σ ❞Ω = ❞σ ❞Ω

• ▼♦tt

· τ ǫ(✶ + τ) · ǫ τ ● ✷

❊ + ● ✷ ▼

• ✇❤❡r❡ τ = ◗✷/✹▼✷ ❛♥❞ ǫ =
• ✶ + ✷(✶ + τ) t❛♥✷(θ/✷)

−✶ P♦❧❛r✐③❡❞ ❜❡❛♠s ❛♥❞ t❛r❣❡ts ❛♥❞ r❡❝♦✐❧ ♣♦❧❛r✐♠❡t❡rs

❋♦r♠ ❢❛❝t♦r r❛t✐♦ ❢r♦♠ ♣♦❧❛r✐③❛t✐♦♥ tr❛♥s❢❡r

❆❦❤✐❡③❡r✱❘❡❦❛❧♦✱ ✶✾✻✽

• ❊
• ▼

= P❚ P▲ × ❑ ✇❤❡r❡ P❚ ❛♥❞ P▲ ✲ tr❛♥s✈❡rs❡ ❛♥❞ ❧♦♥❣✐t✉❞✐♥❛❧ ♣♦❧❛r✐③❛t✐♦♥ ❝♦♠♣♦♥❡♥ts ♦❢ ♣r♦t♦♥✱ ❑ = −

• τ(✶ + ǫ)/✷ǫ ✕ ❦✐♥❡♠❛t✐❝ ❢❛❝t♦r

■✳❆✳ ❘❛❝❤❡❦ ❊▼■◆✲✷✵✶✷ ❙❡♣t❡♠❜❡r ✷✶✱ ✷✵✶✷ ✸

■♥❝♦♥s✐st❡♥❝② ❄

2

, GeV

2

Q

1 2 3 4 5 6 7 8 9

M

G ⁄

E

G µ

0.2 0.4 0.6 0.8 1 1.2 1.4 1.6

Unpolarized data: Polarized data:

Walker (1994), global analysis Qattan (2005) Jones (2000), Punjabi (2005) Gayou (2002), Puckett (2011) Puckett (2010)

❈❧❡❛r ❞✐s❝r❡♣❛♥❝② ❜❡t✇❡❡♥ ✉♥♣♦❧❛r✐③❡❞ ❛♥❞ ♣♦❧❛r✐③❡❞ ❞❛t❛ ✐s ♦❜s❡r✈❡❞✳

❘❛❞✐❛t✐✈❡ ❝♦rr❡❝t✐♦♥s✱ ✐♥ ♣❛rt✐❝✉❧❛r✱ ❛ s❤♦rt✲r❛♥❣❡ ❚✇♦✲P❤♦t♦♥ ❊①❝❤❛♥❣❡ ✭❚P❊✮ ✐s ❛ ❧✐❦❡❧② ♦r✐❣✐♥ ♦❢ t❤❡ ❞✐s❝r❡♣❛♥❝②

■✳❆✳ ❘❛❝❤❡❦ ❊▼■◆✲✷✵✶✷ ❙❡♣t❡♠❜❡r ✷✶✱ ✷✵✶✷ ✹

■♥❝♦♥s✐st❡♥❝② ❄

2

, GeV

2

Q

1 2 3 4 5 6 7 8 9

M

G ⁄

E

G µ

0.2 0.4 0.6 0.8 1 1.2 1.4 1.6

Unpolarized data: Polarized data:

Walker (1994), global analysis Qattan (2005) Jones (2000), Punjabi (2005) Gayou (2002), Puckett (2011) Puckett (2010)

❈❧❡❛r ❞✐s❝r❡♣❛♥❝② ❜❡t✇❡❡♥ ✉♥♣♦❧❛r✐③❡❞ ❛♥❞ ♣♦❧❛r✐③❡❞ ❞❛t❛ ✐s ♦❜s❡r✈❡❞✳

❘❛❞✐❛t✐✈❡ ❝♦rr❡❝t✐♦♥s✱ ✐♥ ♣❛rt✐❝✉❧❛r✱ ❛ s❤♦rt✲r❛♥❣❡ ❚✇♦✲P❤♦t♦♥ ❊①❝❤❛♥❣❡ ✭❚P❊✮ ✐s ❛ ❧✐❦❡❧② ♦r✐❣✐♥ ♦❢ t❤❡ ❞✐s❝r❡♣❛♥❝②

■✳❆✳ ❘❛❝❤❡❦ ❊▼■◆✲✷✵✶✷ ❙❡♣t❡♠❜❡r ✷✶✱ ✷✵✶✷ ✹

❘❛❞✐❛t✐✈❡ ❈♦rr❡❝t✐♦♥s t♦ ❡❧❛st✐❝ ✭❡♣✮ s❝❛tt❡r✐♥❣

✏❊❧❛st✐❝✑ s❝❛tt❡r✐♥❣ ✭❡±♣ → ❡±♣✮✿ M❇♦r♥ M✷γ M✈❛❝ M❡

✈❡rt

M♣

✈❡rt

M❡

s❡❧❢

M♣

s❡❧❢

❇r❡♠sstr❛❤❧✉♥❣ ✭❡±♣ → ❡±♣ γ✮✿

∆ ∆

M❡

❜r❡♠

M♣

❜r❡♠

σ(❡±♣) = |M❇♦r♥|✷ ± ✷ R❡

• M†

❇♦r♥M✷γ

• +

+ ✷ R❡

• M†

❇♦r♥M✈❛❝

• + ✷ R❡
• M†

❇♦r♥M❡ ✈❡rt

• + ✷ R❡
• M†

❇♦r♥M♣ ✈❡rt

• + . . .

+ |M❡

❜r❡♠|✷ + |M♣ ❜r❡♠|✷ ± ✷ R❡

• M❡†

❜r❡♠M♣ ❜r❡♠

• + . . .

✭✶✮

• ❙t❛♥❞❛r❞ ✭s♦❢t ♣❤♦t♦♥s✮ ❘❈✿ ❞♦♠✐♥❛♥t ✭✐♥❢r❛✲r❡❞✮ ♣❛rt ❝❛♥ ❜❡ ❢❛❝t♦r✐③❡❞ ✐♥ t❤❡

♦❜s❡r✈❛❜❧❡s✳ ❍❛r❞ ♣❤♦t♦♥s ✐♥ ❜♦① ❛♥❞ ✲❜♦①✿ ✐♥t❡❣r❛❧ ♦✈❡r ♦✛✲s❤❡❧❧ ♣r♦t♦♥ ✐♥t❡r♠✐❞✐❛t❡ st❛t❡ ❝♦♥tr✐❜✉t✐♦♥s ♠✉st ❜❡ ♠❛❞❡✳

■✳❆✳ ❘❛❝❤❡❦ ❊▼■◆✲✷✵✶✷ ❙❡♣t❡♠❜❡r ✷✶✱ ✷✵✶✷ ✺

❘❛❞✐❛t✐✈❡ ❈♦rr❡❝t✐♦♥s t♦ ❡❧❛st✐❝ ✭❡♣✮ s❝❛tt❡r✐♥❣

✏❊❧❛st✐❝✑ s❝❛tt❡r✐♥❣ ✭❡±♣ → ❡±♣✮✿ M❇♦r♥ M✷γ M✈❛❝ M❡

✈❡rt

M♣

✈❡rt

M❡

s❡❧❢

M♣

s❡❧❢

❇r❡♠sstr❛❤❧✉♥❣ ✭❡±♣ → ❡±♣ γ✮✿

∆ ∆

M❡

❜r❡♠

M♣

❜r❡♠

σ(❡±♣) = |M❇♦r♥|✷ ± ✷ R❡

• M†

❇♦r♥M✷γ

• +

+ ✷ R❡

• M†

❇♦r♥M✈❛❝

• + ✷ R❡
• M†

❇♦r♥M❡ ✈❡rt

• + ✷ R❡
• M†

❇♦r♥M♣ ✈❡rt

• + . . .

+ |M❡

❜r❡♠|✷ + |M♣ ❜r❡♠|✷ ± ✷ R❡

• M❡†

❜r❡♠M♣ ❜r❡♠

• + . . .

✭✶✮

• ❙t❛♥❞❛r❞ ✭s♦❢t ♣❤♦t♦♥s✮ ❘❈✿ ❞♦♠✐♥❛♥t ✭✐♥❢r❛✲r❡❞✮ ♣❛rt ❝❛♥ ❜❡ ❢❛❝t♦r✐③❡❞ ✐♥ t❤❡

♦❜s❡r✈❛❜❧❡s✳

• ❍❛r❞ ♣❤♦t♦♥s ✐♥ ❜♦① ❛♥❞ ×✲❜♦①✿ ✐♥t❡❣r❛❧ ♦✈❡r ♦✛✲s❤❡❧❧ ♣r♦t♦♥ ✐♥t❡r♠✐❞✐❛t❡ st❛t❡

❝♦♥tr✐❜✉t✐♦♥s ♠✉st ❜❡ ♠❛❞❡✳

■✳❆✳ ❘❛❝❤❡❦ ❊▼■◆✲✷✵✶✷ ❙❡♣t❡♠❜❡r ✷✶✱ ✷✵✶✷ ✺

❉✐r❡❝t ♠❡❛s✉r❡♠❡♥t ♦❢ ❚P❊

▼❡t❤♦❞ ♦❢ ❞✐r❡❝t ♠❡❛s✉r❡♠❡♥t ♦❢ ❚P❊ ✿ ▼❡❛s✉r❡ t❤❡ r❛t✐♦ ♦❢ ♣♦s✐tr♦♥✲♣r♦t♦♥ t♦ ❡❧❡❝tr♦♥✲♣r♦t♦♥ ❡❧❛st✐❝ s❝❛tt❡r✐♥❣ ❝r♦ss✲s❡❝t✐♦♥ ⇒ ✐♥t❡r❢❡r❡♥❝❡ t❡r♠ ✐s ❡①tr❛❝t❡❞✿ ❘ = σ(❡+♣) σ(❡−♣) ≈ ✶ + ✹ R❡

• M†

❇♦r♥M✷γ

• |M❇♦r♥|✷

,

ε

st❛t✉s ❝✐r❝❛ ✷✵✵✼✿ ❊①♣❡r✐♠❡♥t❛❧ ❞❛t❛ ✕ ❢r♦♠ ✶✾✻✵✲t❤ ▼❛♥② t❤❡♦r❡t✐❝❛❧✴♣❤❡♥♦♠❡♥♦❧♦❣✐❝❛❧ ❛♣♣r♦❛❝❤❡s✱ ♣r♦❞✉❝✐♥❣ ❝❧❡❛r❧② ❞✐✛❡r❡♥t r❡s✉❧ts ♥❡✇ ♣r❡❝✐s❡ ❞❛t❛✱ ❡s♣❡❝✐❛❧❧② ❢♦r ε ≤ ✵.✺ ❛r❡ r❡q✉✐r❡❞ t♦ ✈❡r✐❢② t❤❡ ♠♦❞❡❧s

■✳❆✳ ❘❛❝❤❡❦ ❊▼■◆✲✷✵✶✷ ❙❡♣t❡♠❜❡r ✷✶✱ ✷✵✶✷ ✻

▼✐❧❡st♦♥❡s ♦❢ t❤❡ ◆♦✈♦s✐❜✐rs❦ ❡①♣❡r✐♠❡♥t

• ❚❤❡ ♣r♦♣♦s❛❧ ✇❛s ♣✉❜❧✐s❤❡❞ ✭❆✉❣ ✷✵✵✹✮✿ ♥✉❝❧✲❡①✴✵✹✵✽✵✷✵
• ❉❛t❛ t❛❦✐♥❣✿

❘✉♥ ❉✉r❛t✐♦♥ ❊❜❡❛♠✱ ◆✉♠❜❡r ♦❢

• ❧✉♠✐♥♦s✐t②✱
• ❡❱

❡++❡− ❝②❝❧❡s ♣❜−✶ ❊♥❣✐♥❡❡r✐♥❣ r✉♥ ▼❛②✕❏✉❧ ✷✵✵✼ ✶✳✻ ✾✵ ✶✷ ❘✉♥ ■ ❙❡♣✕❉❡❝ ✷✵✵✾ ✶✳✻ ✶✶✵✵ ✸✷✹ ❘✉♥ ■■ ❙❡♣ ✷✵✶✶ ✕ ▼❛r ✷✵✶✷ ✶✳✵ ✷✸✺✵ ✻✵✵ ❘✉♥ ■■■ ❆♣r ✷✵✶✷ ✵✳✻ ✷✷✵ ✶✽

• ❙♦♠❡ ♣r❡❧✐♠✐♥❛r② r❡s✉❧ts ✇❡r❡ ♣✉❜❧✐s❤❡❞ ✭❉❡❝ ✷✵✶✶✮✿ ❛r❳✐✈✿✶✶✶✷✳✺✸✻✾
• ❋✐♥❛❧ r❡s✉❧ts ♦❢ t❤❡ ❞❛t❛ ❛♥❛❧②s✐s ❛r❡ ❡①♣❡❝t❡❞ ✐♥ ✷✵✶✸

■✳❆✳ ❘❛❝❤❡❦ ❊▼■◆✲✷✵✶✷ ❙❡♣t❡♠❜❡r ✷✶✱ ✷✵✶✷ ✼

◆♦✈♦s✐❜✐rs❦ ❡①♣❡r✐♠❡♥t ❛t t❤❡ ❱❊PP✕✸ st♦r❛❣❡ r✐♥❣

❆ ♣r❡❝✐s✐♦♥ ♠❡❛s✉r❡♠❡♥t ♦❢ t❤❡ r❛t✐♦ ❘ = σ(❡+♣)/σ(❡−♣) ❛t t❤❡ ❱❊PP✕✸ st♦r❛❣❡ r✐♥❣ ❛t t❤❡ ❡♥❡r❣② ♦❢ ❡❧❡❝tr♦♥✴♣♦s✐tr♦♥ ❜❡❛♠s ♦❢ ✶✳✻ ●❡❱ ✭r✉♥ ■✮✱ ✶✳✵ ●❡❱ ✭r✉♥ ■■✮ ❛♥❞ ✵✳✻ ●❡❱ ✭r✉♥ ■■■✮✳ ❑✐♥❡♠❛t✐❝ ♣❛r❛♠❡t❡rs ♦❢ t❤r❡❡ r✉♥s

P❛r❛♠❡t❡r ❘✉♥ ■ ❘✉♥ ■■ ❘✉♥ ■■■ ▲❆ ▼❆ ❙❆ ▲❆ ▼❆ ▲❆ ▼❆ ❊❜❡❛♠✱ ●❡❱ ✶✳✻ ✶✳✵ ✵✳✻

• ■❜❡❛♠❞t✱ ❦❈

✺✹ ✶✵✵ ✸

θ❡±

✺✺◦÷✼✺◦ ✶✺◦÷✷✺◦ ✽◦÷✶✺◦ ✻✺◦÷✶✵✺◦ ✶✺◦÷✷✺◦ ✼✺◦÷✶✶✵◦ ✷✺◦÷✸✺◦ ◗✷, ●❡❱✷ ✶.✷✻÷ ✵.✶✻÷ ✵.✵✺÷ ✵.✼✶÷ ✵.✵✼÷ ✵.✸✻÷ ✵.✵✻÷ ÷✶.✻✽ ÷✵.✹✶ ÷✵.✶✻ ÷✶.✵✽ ÷✵.✶✼ ÷✵.✺✷ ÷✵.✶✷

ε

✵.✸✼÷ ✵.✾✵÷ ✵.✾✼÷ ✵.✶✽÷ ✵.✾✶÷ ✵.✶✽÷ ✵.✽✸÷ ÷✵.✺✽ ÷✵.✾✼ ÷✵.✾✾ ÷✵.✺✶ ÷✵.✾✼ ÷✵.✹✹ ÷✵.✾✶ ∆❘/❘✱ st❛t✳ ✶✳✶✪ ✵✳✶✪ ✖ ✵✳✸✪ ✖ ✵✳✽✪ ✖

❚❤❡ s♠❛❧❧❡st ❛♥❣❧❡ r❡❣✐♦♥s ✇❡r❡ ✉s❡❞ ❢♦r ❧✉♠✐♥♦s✐t② ♠♦♥✐t♦r✐♥❣ ♦♥❧②✳

■✳❆✳ ❘❛❝❤❡❦ ❊▼■◆✲✷✵✶✷ ❙❡♣t❡♠❜❡r ✷✶✱ ✷✵✶✷ ✽

❱❊PP✕✸ ❡❧❡❝tr♦♥✲♣♦s✐tr♦♥ st♦r❛❣❡ r✐♥❣

❱❊PP✕✸ ✐s ❛ ❜♦♦st❡r ❢♦r t❤❡ ❱❊PP✕✹▼ ❡❧❡❝tr♦♥✲♣♦s✐tr♦♥ ❝♦❧❧✐❞❡r✳

❱❊PP✕✸ ♣❛r❛♠❡t❡rs ❢♦r ❡− ❜❡❛♠✿ ❊❧❡❝tr♦♥ ❡♥❡r❣② ❊✵ ✷ ●❡❱ ▼❡❛♥ ❜❡❛♠ ❝✉rr❡♥t ■✵ ✶✺✵ ♠❆ ❊♥❡r❣② s♣r❡❛❞ ∆❊/❊ ✵✳✵✺✪ ❘❋ ❍❱ ♠❛❣♥✐t✉❞❡ ❯✼✷ ✵✳✽ ▼❱ r❡✈♦❧✉t✐♦♥ ♣❡r✐♦❞ ❚ ✷✹✽✳✶✹ ♥s ❜✉♥❝❤ ❧❡♥❣t❤ σ▲ ✶✺ ❝♠ ✈❡rt✐❝❛❧ ❜❡❛♠ s✐③❡∗ σ③ ✵✳✺ ♠♠ ❤♦r✐③♦♥t❛❧ ❜❡❛♠ s✐③❡∗ σ① ✷✳✵ ♠♠ ✈❡rt✳ β✲❢✉♥❝t✐♦♥∗ β③ ✷ ♠ ❤♦r✐③✳ β✲❢✉♥❝t✐♦♥∗ β① ✻ ♠ ■♥❥❡❝t✐♦♥ ❜❡❛♠ ❡♥❡r❣②❊✐♥❥ ✸✺✵ ▼❡❱ ■♥❥❡❝t✐♦♥ r❛t❡ ˙ ■✐♥❥ ✶✳✺·✶✵✾ s−✶

∗ ♣❛r❛♠❡t❡rs ✐♥ t❤❡ ❝❡♥t❡r ♦❢ ✷♥❞ str❛✐❣❤t s❡❝t✐♦♥ ✭✐♥ ■♥t❡r♥❛❧ ❚❛r❣❡t ❆r❡❛✮

▲❛r❣❡st ❡+ ❝✉rr❡♥t✿ ✻✵ ♠❆

Internal Target Area

VEPP-3

■✳❆✳ ❘❛❝❤❡❦ ❊▼■◆✲✷✵✶✷ ❙❡♣t❡♠❜❡r ✷✶✱ ✷✵✶✷ ✾

❱❊PP✕✸ ■♥t❡r♥❛❧ ❚❛r❣❡t s❡❝t✐♦♥

t❛r❣❡t t❤✐❝❦♥❡ss = ✶ − ✷ × ✶✵✶✺❛t/❝♠✷

■✳❆✳ ❘❛❝❤❡❦ ❊▼■◆✲✷✵✶✷ ❙❡♣t❡♠❜❡r ✷✶✱ ✷✵✶✷ ✶✵

❉❡t❡❝t♦r ♣❛❝❦❛❣❡ ❢♦r t❤❡ r✉♥ ■

e /e

+ – beam

= 1.6 GeV E

p e

Drift chambers

* * * * * * *

Plastic scintillators Storage cell ( target) H2 Sandwiches at small angle Aperture counters

CsI CsI CsI CsI CsI CsI CsI CsI CsI CsI CsI CsI CsI CsI CsI CsI NaI NaI NaI NaI NaI NaI NaI NaI

8.3 X0 8.3 X0 10.6 X0 10.6 X0

Proportional chambers 0.5 m

■✳❆✳ ❘❛❝❤❡❦ ❊▼■◆✲✷✵✶✷ ❙❡♣t❡♠❜❡r ✷✶✱ ✷✵✶✷ ✶✶

❉❡t❡❝t♦r ♣❛❝❦❛❣❡ ❢♦r t❤❡ r✉♥s ■■✱ ■■■

Storage cell (hydrogen target) 0.5 m Drift chambers Proportional chambers

NaI NaI NaI CsI CsI CsI

* * * *

e /e beam

+ -

Scintillators (polystyrene)

*

= 1 GeV E

e p

■✳❆✳ ❘❛❝❤❡❦ ❊▼■◆✲✷✵✶✷ ❙❡♣t❡♠❜❡r ✷✶✱ ✷✵✶✷ ✶✷

❉❡t❡❝t♦r ❛♥❞ t❛r❣❡t ❛t ❱❊PP✕✸

■✳❆✳ ❘❛❝❤❡❦ ❊▼■◆✲✷✵✶✷ ❙❡♣t❡♠❜❡r ✷✶✱ ✷✵✶✷ ✶✸

❙❡❧❡❝t✐♦♥ ♦❢ t❤❡ ❡❧❛st✐❝ s❝❛tt❡r✐♥❣ ❡✈❡♥ts

❝♦rr❡❧❛t✐♦♥s ❝❤❛r❛❝t❡r✐st✐❝ ❢♦r t✇♦✲❜♦❞② ✜♥❛❧ st❛t❡✿

❈♦rr❡❧❛t✐♦♥ ❜❡t✇❡❡♥ ♣♦❧❛r ❛♥❣❧❡s ✭θ❡± ✈s✳ θ♣✮ ❈♦rr❡❧❛t✐♦♥ ❜❡t✇❡❡♥ ❛③✐♠✉t❤❛❧ ❛♥❣❧❡s ✭φ❡± ✈s✳ φ♣✮ ❈♦rr❡❧❛t✐♦♥ ❜❡t✇❡❡♥ ❧❡♣t♦♥ s❝❛tt❡r✐♥❣ ❛♥❣❧❡ ❛♥❞ ♣r♦t♦♥ ❡♥❡r❣② ✭θ❡± ✈s✳ ❊♣✮ ❈♦rr❡❧❛t✐♦♥ ❜❡t✇❡❡♥ ❧❡♣t♦♥ s❝❛tt❡r✐♥❣ ❛♥❣❧❡ ❛♥❞ ❡❧❡❝tr♦♥ ❡♥❡r❣② ✭θ❡± ✈s✳ ❊❡±✮

♣❛rt✐❝❧❡ ■❉✿

❚✐♠❡✲❖❢✲❋❧✐❣❤t ❛♥❛❧②s✐s ❢♦r ❧♦✇✲❡♥❡r❣② ♣r♦t♦♥s ∆❊✕❊ ❛♥❛❧②s✐s ❢♦r ♠✐❞❞❧❡✲❡♥❡r❣② ♣r♦t♦♥s ❊♥❡r❣② ❞❡♣♦s✐t✐♦♥ ✐♥ ❊▼✲❝❛❧♦r✐♠❡t❡r ❢♦r ❡❧❡❝tr♦♥s✴♣♦s✐tr♦♥s

■✳❆✳ ❘❛❝❤❡❦ ❊▼■◆✲✷✵✶✷ ❙❡♣t❡♠❜❡r ✷✶✱ ✷✵✶✷ ✶✹

▼❈ s✐♠✉❧❛t✐♦♥ ♦❢ t❤❡ st❛♥❞❛r❞ r❛❞✐❛t✐✈❡ ❝♦rr❡❝t✐♦♥s

❙t❛♥❞❛r❞ ♣r❡s❝r✐♣t✐♦♥ ✇✐t❤ s♦❢t✲♣❤♦t♦♥ ♣❡❛❦✐♥❣ ❛♣♣r♦①✐♠❛t✐♦♥ ✐s ♥♦t ❛♣♣❧✐❝❛❜❧❡✳ ❉❡t❛✐❧❡❞ ▼❈✲s✐♠✉❧❛t✐♦♥ ✇✐t❤ ❛ ❞❡❞✐❝❛t❡❞ ❡✈❡♥t ❣❡♥❡r❛t♦r ✐s ♠❛♥❞❛t♦r②✳ ❚❤❡ ✜rst✲♦r❞❡r ❜r❡♠sstr❛❤❧✉♥❣✿ ❝❛❧❝✉❧❛t✐♦♥ ❜② ❋❛❞✐♥ ✫ ❋❡❧❞♠❛♥ ✐♥st❡❛❞ ♦❢ t❤❡ s✐♠♣❧✐✜❡❞ s♦❢t✲♣❤♦t♦♥ ♦♥❡✳ ❈❛❧❝✉❧❛t✐♦♥ ❜② ❋❛❞✐♥ ✫ ●❡r❛s✐♠♦✈ t♦ ❛❝❝♦✉♥t ❢♦r ❜r❡♠sstr❛❤❧✉♥❣ ✇✐t❤ ∆✲✐s♦❜❛r ❡①❝✐t❛t✐♦♥✳ ◆❡✇ ❡✈❡♥t ❣❡♥❡r❛t♦r ❊❙❊PP ✭❞❡✈❡❧♦♣❡❞ ❜② ❆✳●r❛♠♦❧✐♥✮ ✐s ❛♣♣❧✐❡❞ t♦ t❤❡ ▼♦♥t❡✲❈❛r❧♦ ❞❡t❡❝t♦r s✐♠✉❧❛t✐♦♥ ✉s✐♥❣ t❤❡ ●❡❛♥t✹ s♦❢t✇❛r❡ ♣❛❝❦❛❣❡✳

), degree φ ∆ = θ ∆ Cut on angular correlation ( 2 4 6 8 10

MC

Ratio R 1 1.01 1.02 1.03 1.04 1.05 1.06 1.07

Soft photon approximation (SPA) Calculation by Fadin & Feldman (FF) Calculation by Fadin & Gerasimov (FG)

❆♥❣✉❧❛r ❝♦rr❡❧❛t✐♦♥s

(e), deg

p

θ

• p

θ

• 4
• 2

2 4 500 1000 1500 2000 2500 Entries 64809

GEANT4 DATA

• = 0.8

σ

• angles correlation

Θ

, deg

p

ϕ

• e

ϕ

176 178 180 182 184 500 1000 1500 2000 2500 3000 3500 4000 Entries 77505

GEANT4 DATA

• = 0.7

σ

• angles correlation

φ

■✳❆✳ ❘❛❝❤❡❦ ❊▼■◆✲✷✵✶✷ ❙❡♣t❡♠❜❡r ✷✶✱ ✷✵✶✷ ✶✺

▼❈ s✐♠✉❧❛t✐♦♥ ♦❢ ❜❛❝❦❣r♦✉♥❞ ♣r♦❝❡ss❡s

• ❊❆◆❚✹ ❞❡t❡❝t♦r ♠♦❞❡❧

▼❆■❉✷✵✵✼ ❛♥❞ ✷✲P■❖◆✲▼❆■❉ ❜❛s❡❞ ❡✈❡♥t ❣❡♥❡r❛t♦r ❢♦r s✐♥❣❧❡✲ ❛♥❞ ❞♦✉❜❧❡✲♣✐♦♥ ❡❧❡❝tr♦✲♣r♦❞✉❝t✐♦♥ ❊❙❊PP ❡✈❡♥t ❣❡♥❡r❛t♦r ❢♦r ❡❧❛st✐❝ ✭❡♣✮ s❝❛tt❡r✐♥❣ ✇✐t❤ ❜r❡♠sstr❛❤❧✉♥❣

❙♣❡❝tr✉♠ ♦❢ ❜❡❛♠ ❡♥❡r❣②✱ r❡❝♦♥str✉❝t❡❞ ❢r♦♠ ❡♥❡r❣② ❛♥❞ ❞✐r❡❝t✐♦♥ ♦❢ ♣❛rt✐❝❧❡ ❞❡t❡❝t❡❞ ✐♥ ▲❆ ❛r♠✱ ❛ss✉♠✐♥❣ t❤✐s ✐s ❡❧❛st✐❝ s❝❛tt❡r❡❞ ❡− ✭❢♦r ❊❡± = ✶ ●❡❱✮✱ ❛❢t❡r ❝✉ts ♦♥ (∆φ, ∆θ) ❛♣♣❧✐❡❞✿

reconstructed beam energy, MeV 200 400 600 800 1000 1200 5000 10000 15000 20000 25000 ) γ e' p ( → e p

+

π e' n → e p π e' p → e p

+

π n → * p γ

+

π

• π

p → * p γ MC Total DATA

• < 6.0

θ ∆ , φ ∆

DATA and ESEPP+MAID2007+GEANT4

✇❤❡♥ ❛❧❧ ❝✉ts ❛♣♣❧✐❡❞✿ ◆❜❛❝❦❣r♦✉♥❞ ◆❡❧❛st✐❝ ✶

■✳❆✳ ❘❛❝❤❡❦ ❊▼■◆✲✷✵✶✷ ❙❡♣t❡♠❜❡r ✷✶✱ ✷✵✶✷ ✶✻

▼❈ s✐♠✉❧❛t✐♦♥ ♦❢ ❜❛❝❦❣r♦✉♥❞ ♣r♦❝❡ss❡s

• ❊❆◆❚✹ ❞❡t❡❝t♦r ♠♦❞❡❧

▼❆■❉✷✵✵✼ ❛♥❞ ✷✲P■❖◆✲▼❆■❉ ❜❛s❡❞ ❡✈❡♥t ❣❡♥❡r❛t♦r ❢♦r s✐♥❣❧❡✲ ❛♥❞ ❞♦✉❜❧❡✲♣✐♦♥ ❡❧❡❝tr♦✲♣r♦❞✉❝t✐♦♥ ❊❙❊PP ❡✈❡♥t ❣❡♥❡r❛t♦r ❢♦r ❡❧❛st✐❝ ✭❡♣✮ s❝❛tt❡r✐♥❣ ✇✐t❤ ❜r❡♠sstr❛❤❧✉♥❣

❙♣❡❝tr✉♠ ♦❢ ❜❡❛♠ ❡♥❡r❣②✱ r❡❝♦♥str✉❝t❡❞ ❢r♦♠ ❡♥❡r❣② ❛♥❞ ❞✐r❡❝t✐♦♥ ♦❢ ♣❛rt✐❝❧❡ ❞❡t❡❝t❡❞ ✐♥ ▲❆ ❛r♠✱ ❛ss✉♠✐♥❣ t❤✐s ✐s ❡❧❛st✐❝ s❝❛tt❡r❡❞ ❡− ✭❢♦r ❊❡± = ✶ ●❡❱✮✱ ❛❢t❡r ❝✉ts ♦♥ (∆φ, ∆θ) ❛♣♣❧✐❡❞✿

reconstructed beam energy, MeV 200 400 600 800 1000 1200 5000 10000 15000 20000 25000 ) γ e' p ( → e p

+

π e' n → e p π e' p → e p

+

π n → * p γ

+

π

• π

p → * p γ MC Total DATA

• < 3.0

θ ∆ , φ ∆

DATA and ESEPP+MAID2007+GEANT4

✇❤❡♥ ❛❧❧ ❝✉ts ❛♣♣❧✐❡❞✿ ◆❜❛❝❦❣r♦✉♥❞/◆❡❧❛st✐❝ < ✶%

■✳❆✳ ❘❛❝❤❡❦ ❊▼■◆✲✷✵✶✷ ❙❡♣t❡♠❜❡r ✷✶✱ ✷✵✶✷ ✶✻

❙✉♣♣r❡ss✐♦♥ ♦❢ t❤❡ s②st❡♠❛t✐❝s✿ ❛❧t❡r♥❛t✐♦♥ ♦❢ ❡− ❛♥❞ ❡+

❉❛t❛ ❝♦❧❧❡❝t✐♦♥ ✇✐t❤ ❡− ❛♥❞ ❡+ ❜❡❛♠s ✇❛s ❛❧t❡r♥❛t❡❞ r❡❣✉❧❛r❧②✳ ❚❤✐s ❛❧❧♦✇s ✉s t♦ s✉♣♣r❡ss ❡✛❡❝ts ♦❢ s❧♦✇ ❞r✐❢t ✐♥ t✐♠❡ ♦❢ t❤❡ t❛r❣❡t t❤✐❝❦♥❡ss✱ ❞❡t❡❝t✐♦♥ ❡✣❝✐❡♥❝② ❛♥❞ s♦♠❡ ♦t❤❡r ♣❛r❛♠❡t❡rs✳ ❖♥❡ ❝②❝❧❡ ✭❡+ ❛♥❞ ❡− ❜❡❛♠s✮ ♣❡r ✶ ❤♦✉r ❛♣♣r♦①✐♠❛t❡❧②✳ ❙t❛rt✐♥❣ ❛♥❞ ❡♥❞✐♥❣ ✈❛❧✉❡s ♦❢ ❜❡❛♠ ❝✉rr❡♥ts ❛♥❞ ❜❡❛♠ ❧✐❢❡t✐♠❡ ❢♦r ❡− ❛♥❞ ❡+ ❜❡❛♠s ✐♥ ❡❛❝❤ ❝②❝❧❡ ✇❡r❡ ❦❡♣t ❛s ❝❧♦s❡ ❛s ♣♦ss✐❜❧❡✳ ❈♦♥tr✐❜✉t✐♦♥ t♦ t❤❡ s②st❡♠❛t✐❝ ❡rr♦r✿ < ✵.✷%

■✳❆✳ ❘❛❝❤❡❦ ❊▼■◆✲✷✵✶✷ ❙❡♣t❡♠❜❡r ✷✶✱ ✷✵✶✷ ✶✼

❙✉♣♣r❡ss✐♦♥ ♦❢ t❤❡ s②st❡♠❛t✐❝s✿ ❜❡❛♠ ♣♦s✐t✐♦♥

❯s✐♥❣ t❤❡ ❱❊PP✕✸ ❜❡❛♠ ♦r❜✐t st❛❜✐❧✐③❛t✐♦♥ s②st❡♠✳ ❈♦♥t✐♥✉♦✉s ♠❡❛s✉r❡♠❡♥t ♦❢ t❤❡ ❜❡❛♠ ♣♦s✐t✐♦♥ ❛t t❤❡ ❡♥tr❛♥❝❡ ❛♥❞ ❡①✐t ♦❢ t❤❡ ❡①♣❡r✐♠❡♥t❛❧ s❡❝t✐♦♥ ❜② ♣✐❝❦✲✉♣ ❡❧❡❝tr♦❞❡s✳ P❡r✐♦❞✐❝❛❧ ✏❛❜s♦❧✉t❡✑ ❜❡❛♠ ♣♦s✐t✐♦♥ ♠❡❛s✉r❡♠❡♥ts ✉s✐♥❣ ♠♦✈❛❜❧❡ s❤✉tt❡rs✳ ❉❡t❡r♠✐♥❛t✐♦♥ ♦❢ ❜❡❛♠ ♣♦s✐t✐♦♥ ✐♥ t❤❡ t❛r❣❡t ❢r♦♠ ❞❛t❛ ❛♥❛❧②s✐s✳ ▼❡❛s✉r❡♠❡♥t ♦❢ ❜❡❛♠ ♣♦s✐t✐♦♥ ❜② t❤❡ ✷P✸ ♣✐❝❦✲✉♣ ❡❧❡❝tr♦❞❡✿

positrons electrons positrons electrons

horizontal vertical

1 mm

❈♦♥tr✐❜✉t✐♦♥ t♦ t❤❡ s②st❡♠❛t✐❝ ❡rr♦r✿ < ✵.✷%

■✳❆✳ ❘❛❝❤❡❦ ❊▼■◆✲✷✵✶✷ ❙❡♣t❡♠❜❡r ✷✶✱ ✷✵✶✷ ✶✽

❙✉♣♣r❡ss✐♦♥ ♦❢ t❤❡ s②st❡♠❛t✐❝s✿ ❜❡❛♠ ❡♥❡r❣②

❘❡❝♦♥str✉❝t✐♦♥ ♦❢ ❜❡❛♠ ❡♥❡r❣② ❢r♦♠ t❤❡ ❡♥❡r❣② s♣❡❝tr✉♠ ♦❢ ❧❛s❡r ♣❤♦t♦♥s ❜❛❝❦s❝❛tt❡r❡❞ ♦♥ ❜❡❛♠ ♣❛rt✐❝❧❡s✳ ✭●✉r❛♠ ❑❡③❡r❛s❤✈✐❧✐ ✐s ❛ ❢♦✉♥❞❡r ❛♥❞ ❞❡✈❡❧♦♣❡r ♦❢ t❤✐s ♠❡t❤♦❞✐q✉❡ ❛t ❇✉❞❦❡r ■♥st✐t✉t❡✮

❊❜❡❛♠ = ✵.✺ · ω♠❛① ·

• ✶ +
• ✶ + ♠✷

❡/ω✵ω♠❛①

• ❚❤✐s ❛❧❧♦✇s ✉s t♦ t✉♥❡ t❤❡ ❱❊PP✕✸ ♦♣❡r❛t✐♦♥ r❡❣✐♠❡s ❛♥❞ t♦

♠♦♥✐t♦r t❤❡ ❜❡❛♠s ❡♥❡r❣② ❞✉r✐♥❣ t❤❡ ❡①♣❡r✐♠❡♥t✳

❱❊PP✕✸ ❡♥❡r❣② ♠❡❛s✉r❡♠❡♥t

• electrons
• positrons

1 MeV

❈♦♥tr✐❜✉t✐♦♥ t♦ t❤❡ s②st❡♠❛t✐❝ ❡rr♦r✿ < ✵.✶% ♣❤♦t♦♥ s♣❡❝tr✉♠

■✳❆✳ ❘❛❝❤❡❦ ❊▼■◆✲✷✵✶✷ ❙❡♣t❡♠❜❡r ✷✶✱ ✷✵✶✷ ✶✾

❙✉♣♣r❡ss✐♦♥ ♦❢ t❤❡ s②st❡♠❛t✐❝s✿ ❜❡❛♠ ❡♥❡r❣②

❘❡❝♦♥str✉❝t✐♦♥ ♦❢ ❜❡❛♠ ❡♥❡r❣② ❢r♦♠ t❤❡ ❡♥❡r❣② s♣❡❝tr✉♠ ♦❢ ❧❛s❡r ♣❤♦t♦♥s ❜❛❝❦s❝❛tt❡r❡❞ ♦♥ ❜❡❛♠ ♣❛rt✐❝❧❡s✳ ✭●✉r❛♠ ❑❡③❡r❛s❤✈✐❧✐ ✐s ❛ ❢♦✉♥❞❡r ❛♥❞ ❞❡✈❡❧♦♣❡r ♦❢ t❤✐s ♠❡t❤♦❞✐q✉❡ ❛t ❇✉❞❦❡r ■♥st✐t✉t❡✮

❊❜❡❛♠ = ✵.✺ · ω♠❛① ·

• ✶ +
• ✶ + ♠✷

❡/ω✵ω♠❛①

• ❚❤✐s ❛❧❧♦✇s ✉s t♦ t✉♥❡ t❤❡ ❱❊PP✕✸ ♦♣❡r❛t✐♦♥ r❡❣✐♠❡s ❛♥❞ t♦

♠♦♥✐t♦r t❤❡ ❜❡❛♠s ❡♥❡r❣② ❞✉r✐♥❣ t❤❡ ❡①♣❡r✐♠❡♥t✳

❱❊PP✕✸ ❡♥❡r❣② ♠❡❛s✉r❡♠❡♥t

• electrons
• positrons

1 MeV

❈♦♥tr✐❜✉t✐♦♥ t♦ t❤❡ s②st❡♠❛t✐❝ ❡rr♦r✿ < ✵.✶% ♣❤♦t♦♥ s♣❡❝tr✉♠

❚♦t❛❧ s②st❡♠❛t✐❝ ❡rr♦r ✐s ❁ ✵✳✸✪

■✳❆✳ ❘❛❝❤❡❦ ❊▼■◆✲✷✵✶✷ ❙❡♣t❡♠❜❡r ✷✶✱ ✷✵✶✷ ✶✾

❚❤r❡❡ ❡①♣❡r✐♠❡♥ts ❛✐♠❡❞ ❛t ♠❡❛s✉r✐♥❣ t❤❡ r❛t✐♦ ❘

◆♦✈♦s✐❜✐rs❦ ❡①♣❡r✐♠❡♥t ✭❊❜❡❛♠ = ✶.✻✱ ✶✳✵ ❛♥❞ ✵✳✻ ●❡❱✮ ❈▲❆❙ ❅ ❏▲❛❜ ❡①♣❡r✐♠❡♥t ✭❊❜❡❛♠ = ✵.✺ ÷ ✹ ●❡❱✮ ❖▲❨▼P❯❙ ❅ ❉❊❙❨ ❡①♣❡r✐♠❡♥t ✭❊❜❡❛♠ = ✷ ●❡❱✮

ε

0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 2

, GeV

2

Q

0.5 1 1.5 2 2.5

Kinematic coverage

V E P P

• 3

, I I VEPP-3, I O L Y M P U S

• 2

1 2 CLAS-2011 area VEPP-3, III

Kinematic coverage

■✳❆✳ ❘❛❝❤❡❦ ❊▼■◆✲✷✵✶✷ ❙❡♣t❡♠❜❡r ✷✶✱ ✷✵✶✷ ✷✵

❚P❊ ❡①♣❡r✐♠❡♥t ❛t ❈▲❆❙ ✭❏▲❛❜ ❍❛❧❧ ❇✮

❞❛t❛ t❛❦✐♥❣ ❝♦♠♣❧❡t❡❞ ✐♥ ❋❡❜✲✷✵✶✶ s♦ ❢❛r ♥♦ ♣r❡❧✐♠✐♥❛r② r❡s✉❧ts r❡♣♦rt❡❞

■✳❆✳ ❘❛❝❤❡❦ ❊▼■◆✲✷✵✶✷ ❙❡♣t❡♠❜❡r ✷✶✱ ✷✵✶✷ ✷✶

❖▲❨▼P❯❙ ❡①♣❡r✐♠❡♥t ❛t ❉❊❙❨

✜rst ♠♦♥t❤✲❧♦♥❣ r✉♥ ✐♥ ❋❡❜r✉❛r②✲✷✵✶✷ ❛♥♦t❤❡r ✷ ♠♦♥t❤s ♦❢ r✉♥♥✐♥❣ ✐♥ ❖❝t✲❉❡❝

■✳❆✳ ❘❛❝❤❡❦ ❊▼■◆✲✷✵✶✷ ❙❡♣t❡♠❜❡r ✷✶✱ ✷✵✶✷ ✷✷

❈♦♠♣❛r✐s♦♥ ♦❢ ❚❤r❡❡ ❚P❊ ❊①♣❡r✐♠❡♥ts

❱❊PP✲✸ ❖▲❨▼P❯❙ ❊●✺ ❈▲❆❙ ◆♦✈♦s✐❜✐rs❦ ❉❊❙❨ ❏▲❛❜ ❇❡❛♠ ❡♥❡r❣② ✸ ✜①❡❞ ✶✭✰✶❄✮ ✜①❡❞ ✇✐❞❡ s♣❡❝tr✉♠ ❡q✉❛❧✐t② ♦❢ ❡± ❜❡❛♠ ❡♥❡r❣② ♠❡❛s✉r❡❞ ❛ss✉♠❡❞ r❡❝♦♥str✉❝t❡❞ ♣r❡❝✐s❡❧② ✭♠❡❛s✉r❡❞❄✮ ❡+/❡− s✇❛♣♣✐♥❣ ❢r❡q✉❡♥❝② ❤❛❧❢✲❤♦✉r ✽ ❤♦✉rs s✐♠✉❧t❛♥❡♦✉s❧② ❡+/❡− ❧✉♠✐ ♠♦♥✐t♦r ❡❧❛st✐❝ ❧♦✇✲◗✷ ❡❧❛st✐❝ ❧♦✇✲◗✷✱ ❢r♦♠ s✐♠✉❧❛t✐♦♥ ▼ö❧❧❡r✴❇❤❛❜❤❛ ❡♥❡r❣② ♦❢ s❝❛tt❡r❡❞ ❡± ❊▼✲❝❛❧♦r✐♠❡t❡r ♠❛❣✳ ❛♥❛❧②s✐s ♠❛❣✳ ❛♥❛❧②s✐s ♣r♦t♦♥ P■❉ ∆❊/❊✱ ❚❖❋ ♠❛❣✳ ❛♥❛❧②s✐s✱ ❚❖❋ ♠❛❣✳ ❛♥❛❧②s✐s✱ ❚❖❋ ❡+/❡− ❞❡t❡❝t♦r ❛❝❝❡♣t❛♥❝❡ ✐❞❡♥t✐❝❛❧ ❜✐❣ ❞✐✛❡r❡♥❝❡ ❜✐❣ ❞✐✛❡r❡♥❝❡ ❧✉♠✐♥♦s✐t② ✶.✵ × ✶✵✸✷ ✷.✵ × ✶✵✸✸ ✷.✺ × ✶✵✸✷ s②st❡♠❛t✐❝ ❡rr♦r < ✵.✸% ✶✪ ✶✪ ◆♦✈♦s✐❜✐rs❦ ❡①♣❡r✐♠❡♥t ✐s ✐♥❢❡r✐♦r t♦ t❤❡ ♦t❤❡r t✇♦ ✐♥ ❡①♣❡r✐♠❡♥t❛❧ ❧✉♠✐♥♦s✐t② ❛♥❞ ✐♥ q✉❛❧✐t② ♦❢ ♣❛rt✐❝❧❡ ■❉❀ ❤♦✇❡✈❡r✱ t❤❡ ❞❡t❡❝t♦r ♣❡r❢♦r♠❛♥❝❡ ✐s s✉✣❝✐❡♥t ❢♦r r❡❧✐❛❜❧❡ ✐❞❡♥t✐✜❝❛t✐♦♥ ♦❢ ❡❧❛st✐❝ s❝❛tt❡r✐♥❣ ❡✈❡♥ts❀ ♥♦♥✲♠❛❣♥❡t✐❝ ❞❡t❡❝t♦r✱ ♠❡❛s✉r❡♠❡♥t ♦❢ ❜❡❛♠s ❡♥❡r❣②✱ ❢r❡q✉❡♥t s✇❛♣♣✐♥❣ ♦❢ ❡+/❡− ❜❡❛♠s ❛❧❧♦✇ ❧♦✇❡st s②st❡♠❛t✐❝ ❡rr♦r❀ ◆♦✈♦s✐❜✐rs❦ ✐s t❤❡ ✜rst t♦ ♣r♦✈✐❞❡ r❡s✉❧ts ♦♥ ♣r❡❝✐s❡ ♠❡❛s✉r❡♠❡♥t ♦❢ ❘(❡±♣) r❛t✐♦✳

■✳❆✳ ❘❛❝❤❡❦ ❊▼■◆✲✷✵✶✷ ❙❡♣t❡♠❜❡r ✷✶✱ ✷✵✶✷ ✷✸

Pr❡❧✐♠✐♥❛r② r❡s✉❧ts ♦❢ t❤❡ ◆♦✈♦s✐❜✐rs❦ ❚P❊ ❡①♣❡r✐♠❡♥t

❘✉♥ ■ ✭✷✵✵✾✮✿ ❘✉♥ ■■ ✭✷✵✶✶✕✷✵✶✷✮✿ ❊❜❡❛♠ = ✶.✻ ●❡❱ ❊❜❡❛♠ = ✶ ●❡❱

ε

0.2 0.4 0.6 0.8 1

Ratio R (radiatively corrected)

0.9 0.95 1 1.05 1.1

PRELIMINARY

Anderson (1966), E = 1.2 GeV Bartel (1967), E = 2.34 GeV Anderson (1968), E = 1.2 GeV This experiment, E = 1.6 GeV Theory (Blunden et al.), E = 1.6 GeV Coulomb corrections, E = 1.6 GeV

2

, GeV

2

Q 0.5 1 1.5 2

ε

0.2 0.4 0.6 0.8 1

Ratio R (radiatively corrected)

0.9 0.95 1 1.05 1.1

PRELIMINARY

Browman (1965), E = 0.85 GeV Anderson (1966), E = 1.2 GeV Anderson (1968), E = 1.2 GeV Bouquet (1968), E = 0.981 GeV This experiment, E = 1 GeV Theory (Blunden et al.), E = 1 GeV Coulomb corrections, E = 1 GeV

2

, GeV

2

Q 0.2 0.4 0.6 0.8 1 1.2

❚❤❡♦r②✿ ❏✳ ❆rr✐♥❣t♦♥ ❛♥❞ ■✳ ❙✐❝❦✱ P❤②s✳ ❘❡✈✳ ❈✼✵ ✭✷✵✵✹✮ ✵✷✽✷✵✸ P✳ ●✳ ❇❧✉♥❞❡♥✱ ❡t ❛❧✳✱ P❤②s✳ ❘❡✈✳ ❈✼✷ ✭✷✵✵✺✮ ✵✸✹✻✶✷

❖♥❧② st❛t✐st✐❝❛❧ ❡rr♦rs ❛r❡ s❤♦✇♥✳ t❤❡ st❛♥❞❛r❞ r❛❞✐❛t✐✈❡ ❝♦rr❡❝t✐♦♥s ❛r❡ t❛❦❡♥ ✐♥t♦ ❛❝❝♦✉♥t✳ s♦♠❡ ♠✐♥♦r ❝♦rr❡❝t✐♦♥s ❤❛✈❡ ♥♦t ②❡t ❜❡❡♥ ♠❛❞❡

■✳❆✳ ❘❛❝❤❡❦ ❊▼■◆✲✷✵✶✷ ❙❡♣t❡♠❜❡r ✷✶✱ ✷✵✶✷ ✷✹

❈❛❧❝✉❧❛t✐♦♥ ❜② ❇❧✉♥❞❡♥ ❡t ❛❧✳✿ r❡s✉❧ts ❢♦r µ●❊/●▼

❖r✐❣✐♥❛❧ ♣❧♦t✿

⇒ ⇒

r❡s✉❧ts ❢♦r ❘♦s❡♥❜❧✉t❤ s❡♣❛r❛t✐♦♥ ❞❛t❛ r❡s✉❧ts ❢♦r P♦❧❛r✐③❛t✐♦♥ ❚r❛♥s❢❡r ❞❛t❛

1 2 3 4 5 6 0.2 0.4 0.6 0.8 1 1.2 M

Q2

2

(GeV ) G / G

E

µp

PT LT PT + TPE

P✳ ●✳ ❇❧✉♥❞❡♥✱ ❲✳ ▼❡❧♥✐t❝❤♦✉❦ ❛♥❞ ❏✳ ❆✳ ❚❥♦♥✱ P❤②s✳ ❘❡✈✳ ❈ ✼✷ ✭✷✵✵✺✮ ✵✸✹✻✶✷

■✳❆✳ ❘❛❝❤❡❦ ❊▼■◆✲✷✵✶✷ ❙❡♣t❡♠❜❡r ✷✶✱ ✷✵✶✷ ✷✺

❈♦♥❝❧✉s✐♦♥

❚❤❡ ✜rst ♣r❡❝✐s✐♦♥ ♠❡❛s✉r❡♠❡♥t ♦❢ t❤❡ r❛t✐♦ ❘ = σ(❡+♣)/σ(❡−♣) ❤❛s ❜❡❡♥ ♣❡r❢♦r♠❡❞✳ ❉❛t❛ t❛❦✐♥❣ ❤❛s ❜❡❡♥ ❝♦♠♣❧❡t❡❞✱ ❛♥❛❧②s✐s ✐s ✐♥ ♣r♦❣r❡ss✳ ❙②st❡♠❛t✐❝ ❡rr♦rs ✐♥ ❱❊PP✲✸ ❡①♣❡r✐♠❡♥t ✐s ❡①♣❡❝t❡❞ t♦ ❜❡ ❧♦✇❡r t❤❛♥ t❤♦s❡ ❛t ❖▲❨▼P❯❙ ❛♥❞ ❈▲❆❙ ❚P❊ ❡①♣❡r✐♠❡♥ts✳ ■t ✐s ✈❡r② ✐♠♣♦rt❛♥t t♦ ❝❛r❡❢✉❧❧② ❝♦♥s✐❞❡r t❤❡ st❛♥❞❛r❞ r❛❞✐❛t✐✈❡ ❝♦rr❡❝t✐♦♥s✳ Pr♦❝❡❞✉r❡ ♦❢ ❛❝❝♦✉♥t ❢♦r ❘❈ ❤❛s ❜❡❡♥ ❞❡✈❡❧♦♣❡❞ ✭❊❙❊PP ❡✈❡♥t ❣❡♥❡r❛t♦r + ●❡❛♥t✹ ❞❡t❡❝t♦r s✐♠✉❧❛t✐♦♥✮✳ Pr❡❧✐♠✐♥❛r② r❡s✉❧ts ❛r❡ ♣r❡s❡♥t❡❞✳ ❚❤❡② ❛r❡ ❝♦♥s✐st❡♥t ✇✐t❤ t❤❡ t❤❡♦r❡t✐❝❛❧ ♣r❡❞✐❝t✐♦♥s ❜② ❇❧✉♥❞❡♥ ❡t ❛❧✳ ❋✐♥❛❧ r❡s✉❧ts ♦❢ t❤❡ ❡①♣❡r✐♠❡♥t ❛r❡ ❡①♣❡❝t❡❞ ✐♥ ✷✵✶✸✳ ❙✉♣♣♦rt

❚❤✐s ✇♦r❦ ✇❛s s✉♣♣♦rt❡❞ ❜② ▼✐♥✐str② ♦❢ ❊❞✉❝❛t✐♦♥ ❛♥❞ ❙❝✐❡♥❝❡ ♦❢ t❤❡ ❘✉ss✐❛♥ ❋❡❞❡r❛t✐♦♥❀ ❘❋❇❘ ❣r❛♥ts✿ ✵✽✲✵✷✲✵✵✻✷✹✲❛✱ ✵✽✲✵✷✲✵✶✶✺✺✲❛❀ ❘✉ss✐❛♥ ❋❡❞❡r❛❧ ❆❣❡♥❝② ❢♦r ❊❞✉❝❛t✐♦♥✱ ❙t❛t❡ ❈♦♥tr❛❝t P✺✷✷❀ ❘✉ss✐❛♥ ❋❡❞❡r❛❧ ❆❣❡♥❝② ❢♦r ❙❝✐❡♥❝❡ ❛♥❞ ■♥♥♦✈❛t✐♦♥✱ ❈♦♥tr❛❝t ✵✷✳✼✹✵✳✶✶✳✵✷✹✺✳✶❀ ❯❙ ❉❖❊ ❣r❛♥t✿ ❉❊✲❆❈✵✷✲✵✻❈❍✶✶✸✺✼❀ ❯❙ ◆❙❋ ❣r❛♥t✿ P❍❨✲✵✸✲✺✹✽✼✶

■✳❆✳ ❘❛❝❤❡❦ ❊▼■◆✲✷✵✶✷ ❙❡♣t❡♠❜❡r ✷✶✱ ✷✵✶✷ ✷✻

❆♣♣❡♥❞✐①

❇❛❝❦✉♣ s❧✐❞❡s

■✳❆✳ ❘❛❝❤❡❦ ❊▼■◆✲✷✵✶✷ ❙❡♣t❡♠❜❡r ✷✶✱ ✷✵✶✷ ✷✼

❙✉♣❡r✲❘♦s❡♥❜❧✉t❤ ❡①♣❡r✐♠❡♥t

■✳ ❆✳ ◗❛tt❛♥ ❡t ❛❧✳✱ P❤②s✳ ❘❡✈✳ ▲❡tt✳ ✾✹ ✭✷✵✵✺✮ ✶✹✷✸✵✶ ❯s❡s ♠♦❞✐✜❡❞ ❘♦s❡♥❜❧✉t❤ s❡♣❛r❛t✐♦♥ t❡❝❤♥✐q✉❡✱ ❞❡t❡❝t✐♥❣ ♣r♦t♦♥✿ ❜❧❛❝❦ ♣♦✐♥ts

■✳❆✳ ❘❛❝❤❡❦ ❊▼■◆✲✷✵✶✷ ❙❡♣t❡♠❜❡r ✷✶✱ ✷✵✶✷ ✷✽

❇❡❛♠ ✐♥t❡❣r❛❧ ❝♦❧❧❡❝t✐♦♥ ❞✉r✐♥❣ r✉♥ ■ ❛♥❞ r✉♥ ■■

Day of year-2009

24/09 01/10 08/10 15/10 22/10 29/10 05/11 12/11 19/11 26/11 03/12 10/12 17/12 24/12 31/12

Beam integral per shift, C

100 200 300 400 500 600 700

Beam integral collection, run I day night

Total beam integral, kC

20 40 60

54.27 kC

Day of year-2011/2012

24/09 08/10 22/10 05/11 19/11 03/12 17/12 31/12 14/01 28/01 11/02 25/02 10/03

Beam integral per shift, C

100 200 300 400 500 600 700

Beam integral collection, run II

day night

Total beam integral, kC

50 100

99.90 kC

■✳❆✳ ❘❛❝❤❡❦ ❊▼■◆✲✷✵✶✷ ❙❡♣t❡♠❜❡r ✷✶✱ ✷✵✶✷ ✷✾

❘❛t✐♦ ❘ ❛s ❛ ❢✉♥❝t✐♦♥ ♦❢ ❦✐♥❡♠❛t✐❝ ❝✉ts

❘❯◆ ■■

❘❛✇ ❞❛t❛ ❢♦r t❤❡ r❛t✐♦ ❘✿ ❘❛❞✐❛t✐✈❡❧② ❝♦rr❡❝t❡❞ r❛t✐♦ ❘✿ ε

0.2 0.4 0.6 0.8 1

Ratio R

0.99 1 1.01 1.02 1.03 1.04 1.05 1.06 1.07 1.08

• 3

±

• 6

±

ε

0.2 0.4 0.6 0.8 1

Ratio R

0.99 1 1.01 1.02 1.03 1.04 1.05 1.06 1.07 1.08

• 3

±

• 6

±

❚❤❡ ❡①♣❡r✐♠❡♥t❛❧❧② ♠❡❛s✉r❡❞ r❛t✐♦ ❘ ❜❡❢♦r❡ ✭❧❡❢t ✜❣✉r❡✮ ❛♥❞ ❛❢t❡r ✭r✐❣❤t ✜❣✉r❡✮ t❛❦✐♥❣ ✐♥t♦ ❛❝❝♦✉♥t t❤❡ r❛❞✐❛t✐✈❡ ❝♦rr❡❝t✐♦♥s ✭❋❋ ♠♦❞❡❧✮✳ ❘❡❞ ♠❛r❦❡rs ❝♦rr❡s♣♦♥❞ t♦ t❤❡ ❝✉t ∆θ = ∆φ = ✸◦ ♦♥ t❤❡ ❛♥❣✉❧❛r ❝♦rr❡❧❛t✐♦♥s✱ ❜❧✉❡ ♠❛r❦❡rs ❝♦rr❡s♣♦♥❞ t♦ t❤❡ ❝✉t ∆θ = ∆φ = ✻◦ ✭❞❛t❛ ❢♦r ▲❆ r❛♥❣❡ ♦❢ t❤❡ ❘✉♥ ■■✮✳

■✳❆✳ ❘❛❝❤❡❦ ❊▼■◆✲✷✵✶✷ ❙❡♣t❡♠❜❡r ✷✶✱ ✷✵✶✷ ✸✵