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Pr Ps trt rsss - - PowerPoint PPT Presentation

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Pr Ps trt rsss t r rs tr sttt

slide-1
SLIDE 1

Pr♦❜✐♥❣ ●P❉s ✐♥ ♣❤♦t♦♣r♦❞✉❝t✐♦♥ ♣r♦❝❡ss❡s ❛t ❤❛❞r♦♥ ❝♦❧❧✐❞❡rs

❉♠✐tr② ■✈❛♥♦✈ ❙♦❜♦❧❡✈ ■♥st✐t✉t❡ ♦❢ ▼❛t❤❡♠❛t✐❝s P❍❖❚❖◆ ✷✵✶✺✱ ◆♦✈♦s✐❜✐rs❦

t✐♠❡❧✐❦❡✲❉❱❈❙ ✭r❡✈✐❡✇ ♦❢ ✇♦r❦✮✿ ❇✳ P✐r❡✱ ▲✳ ❙③②♠❛♥♦✇s❦✐✱ ❏✳ ❲❛❣♥❡r J/Ψ ♣❤♦t♦♣r♦❞✉❝t✐♦♥ ✭✐♥ ♣r♦❣r❡ss✮✿ ❉✳ ■✈❛♥♦✈✱ ▲✳❙③②♠❛♥♦✇s❦✐✱ ❏✳ ❲❛❣♥❡r

✶ ✴ ✸✵

slide-2
SLIDE 2

❉❱❈❙

❚❤❡ s✐♠♣❧❡st ❛♥❞ ❜❡st ❦♥♦✇♥ ♣r♦❝❡ss ✐s ❉❡❡♣❧② ❱✐rt✉❛❧ ❈♦♠♣t♦♥ ❙❝❛tt❡r✐♥❣✿ e p → e p γ

e e γ∗ p p γ

❋❛❝t♦r✐③❛t✐♦♥ ✐♥t♦ ●P❉s ❛♥❞ ♣❡rt✉r❜❛t✐✈❡ ❝♦❡✣❝✐❡♥t ❢✉♥❝t✐♦♥ ✲ ♦♥ t❤❡ ❧❡✈❡❧ ♦❢ ❛♠♣❧✐t✉❞❡✳ ❉■❙ : σ = P❉❋ ⊗ ♣❛rt♦♥✐❝ ❝r♦ss s❡❝t✐♦♥ ❉❱❈❙ : M = ●P❉ ⊗ ♣❛rt♦♥✐❝ ❛♠♣❧✐t✉❞❡

✷ ✴ ✸✵

slide-3
SLIDE 3
  • P❉s

◮ ●P❉s ❡♥t❡r ❢❛❝t♦r✐③❛t✐♦♥ t❤❡♦r❡♠s ❢♦r ❤❛r❞ ❡①❝❧✉s✐✈❡ r❡❛❝t✐♦♥s ✭❉❱❈❙✱

❞❡❡♣❧② ✈✐rt✉❛❧ ♠❡s♦♥ ♣r♦❞✉❝t✐♦♥✱ ❚❈❙ ❡t❝✳✮✱ ✐♥ ❛ s✐♠✐❧❛r ♠❛♥♥❡r ❛s P❉❋s ❡♥t❡r ❢❛❝t♦r✐③❛t✐♦♥ t❤❡♦r❡♠s ❢♦r ✐♥❝❧✉s✐✈❡ ✭❉■❙✱ ❡t❝✳✮

◮ ●P❉s ❛r❡ ❢✉♥❝t✐♦♥s ♦❢ x, t, ξ, µ2 F ◮ ❋✐rst ♠♦♠❡♥t ♦❢ ●P❉s ❡♥t❡rs t❤❡ ❏✐✬s s✉♠ r✉❧❡ ❢♦r t❤❡ ❛♥❣✉❧❛r ♠♦♠❡♥t✉♠

❝❛rr✐❡❞ ❜② ♣❛rt♦♥s ✐♥ t❤❡ ♥✉❝❧❡♦♥✱

◮ ✷✰✶ ✐♠❛❣✐♥❣ ♦❢ ♥✉❝❧❡♦♥✱ ◮ ❉❡❡♣❧② ❱✐rt✉❛❧ ❈♦♠♣t♦♥ ❙❝❛tt❡r✐♥❣ ✭❉❱❈❙✮ ✐s ❛ ❣♦❧❞❡♥ ❝❤❛♥♥❡❧ ❢♦r ●P❉s

❡①tr❛❝t✐♦♥✱

✸ ✴ ✸✵

slide-4
SLIDE 4

❉❱❈❙✱ ❉❱▼P

◮ ❉✐✣❝✉❧t✿ ❡①❝❧✉s✐✈✐t②✱ ✸ ✈❛r✐❛❜❧❡s✱ ●P❉ ❡♥t❡r t❤r♦✉❣❤ ❝♦♥✈♦❧✉t✐♦♥s✱ ♦♥❧②

  • P❉(ξ, ξ, t) ❛❝❝❡s✐❜❧❡ t❤r♦✉❣❤ ❉❱❈❙ ❛t ▲❖✦

◮ ✉♥✐✈❡rs❛❧✐t②✱ ◮ ✢❛✈♦✉r s❡♣❛r❛t✐♦♥✱

x′ = x − ξ , ξ ∼ Q2 W 2

✹ ✴ ✸✵

slide-5
SLIDE 5

❙♦✱ ✐♥ ❛❞❞✐t✐♦♥ t♦ s♣❛❝❡❧✐❦❡ ❉❱❈❙ ✳✳✳

N N’ q e e γ GPD ( a )

❋✐❣✉r❡✿ ❉❡❡♣❧② ❱✐rt✉❛❧ ❈♦♠♣t♦♥ ❙❝❛tt❡r✐♥❣ ✭❉❱❈❙✮ ✿ lN → l′N′γ

✺ ✴ ✸✵

slide-6
SLIDE 6

✇❡ ❝❛♥ ❛❧s♦ st✉❞② t✐♠❡❧✐❦❡ ❉❱❈❙

❇❡r❣❡r✱ ❉✐❡❤❧✱ P✐r❡✱ ✷✵✵✷

N N’ q γ GPD e − e+ ( b )

❋✐❣✉r❡✿ ❚✐♠❡❧✐❦❡ ❈♦♠♣t♦♥ ❙❝❛tt❡r✐♥❣ ✭❚❈❙✮✿ γN → l+l−N′

❲❤② ❚❈❙✿

◮ ✉♥✐✈❡rs❛❧✐t② ♦❢ t❤❡ ●P❉s ◮ ❛♥♦t❤❡r s♦✉r❝❡ ❢♦r ●P❉s ◮ s♣❛❝❡❧✐❦❡✲t✐♠❡❧✐❦❡ ❝r♦ss✐♥❣ ◮ ❝♦✉❧❞ ❜❡ st✉❞✐❡❞ ❜♦t❤ ✐♥ ep ❛♥❞ pp

✻ ✴ ✸✵

slide-7
SLIDE 7
  • ❡♥❡r❛❧ ❈♦♠♣t♦♥ ❙❝❛tt❡r✐♥❣✿

γ∗(qin)N(p) → γ∗(qout)N ′(p′) ✈❛r✐❛❜❧❡s✱ ❞❡s❝r✐❜✐♥❣ t❤❡ ♣r♦❝❡ss❡s ♦❢ ✐♥t❡r❡st ✐♥ t❤✐s ❣❡♥❡r❛❧✐③❡❞ ❇❥♦r❦❡♥ ❧✐♠✐t✱ ❛r❡ t❤❡ s❝❛❧✐♥❣ ✈❛r✐❛❜❧❡ ξ ❛♥❞ s❦❡✇♥❡ss η > 0✿ ξ = −q2

  • ut + q2

in

q2

  • ut − q2

in

η , η = q2

  • ut − q2

in

(p + p′) · (qin + qout) .

◮ ❉❉❱❈❙✿

q2

in < 0 ,

q2

  • ut > 0 ,

η = ξ

◮ ❉❱❈❙✿

q2

in < 0 ,

q2

  • ut = 0 ,

x − x′ = η = ξ > 0

◮ ❚❈❙✿

q2

in = 0 ,

q2

  • ut > 0 ,

x′ − x = η = −ξ > 0

✼ ✴ ✸✵

slide-8
SLIDE 8

❈♦❡✣❝✐❡♥t ❢✉♥❝t✐♦♥s ❛♥❞ ❈♦♠♣t♦♥ ❋♦r♠ ❋❛❝t♦rs

❈❋❋s ❛r❡ t❤❡ ●P❉ ❞❡♣❡♥❞❡♥t q✉❛♥t✐t✐❡s ✇❤✐❝❤ ❡♥t❡r t❤❡ ❛♠♣❧✐t✉❞❡s✳ ❚❤❡② ❛r❡ ❞❡✜♥❡❞ t❤r♦✉❣❤ r❡❧❛t✐♦♥s✿ Aµν(ξ, η, t) = −e2 1 (P + P ′)+ ¯ u(P ′)

  • gµν

T

  • H(ξ, η, t) γ+ + E(ξ, η, t) iσ+ρ∆ρ

2M

  • + iǫµν

T

  • H(ξ, η, t) γ+γ5 +

E(ξ, η, t) ∆+γ5 2M u(P) , ❋❆❈❚❖❘■❩❆❚■❖◆✿ H(ξ, η, t) = + 1

−1

dx

  • q

T q(x, ξ, η)Hq(x, η, t) + T g(x, ξ, η)Hg(x, η, t)

  • H(ξ, η, t)

= − 1

−1

dx

  • q
  • T q(x, ξ, η)

Hq(x, η, t) + T g(x, ξ, η) Hg(x, η, t)

  • .

✽ ✴ ✸✵

slide-9
SLIDE 9

▲❖ ❛♥❞ ◆▲❖ ❈♦❡✣❝✐❡♥t ❢✉♥❝t✐♦♥s

◮ ❉❱❈❙ ✈s ❚❈❙ ❛t ▲❖ ❛r❡ s✐♠♣❧② r❡❧❛t❡❞✿ DV CST q

= −e2

q 1 x+η−iε − (x → −x) =

(T CST q)∗

DV CS ˜

T q = −e2

q 1 x+η−iε + (x → −x) =

−(T CS ˜ T q)∗

DV CSRe(H) ∼ P

  • 1

x ± η Hq(x, η, t) ,

DV CSIm(H) ∼ iπHq(±η, η, t) ◮ ❉❉❱❈❙ ❛t ▲❖ DDV CST q = −e2 q

1 x + ξ − iε − (x → −x)

DDV CSRe(H) ∼ P

  • 1

x ± ξ Hq(x, η, t) ,

DV CSIm(H) ∼ iπHq(±ξ, η, t)

❇✉t t❤✐s ✐s ♦♥❧② tr✉❡ ❛t ▲❖✳ ❆t ◆▲❖ ❛❧❧ ●P❉s ❤✐❞❞❡♥ ✐♥ t❤❡ ❝♦♥✈♦❧✉t✐♦♥s✳

✾ ✴ ✸✵

slide-10
SLIDE 10

❚❈❙ ❛♥❞ ❇❡t❤❡✲❍❡✐t❧❡r ❝♦♥tr✐❜✉t✐♦♥ t♦ ❡①❝❧✉s✐✈❡ ❧❡♣t♦♥ ♣❛✐r ♣❤♦t♦♣r♦❞✉❝t✐♦♥✳

p p′ qin −∆ l− l+

❋✐❣✉r❡✿ ❚❤❡ ❋❡②♥♠❛♥ ❞✐❛❣r❛♠ ❢♦r t❤❡ ❇❡t❤❡✲❍❡✐t❧❡r ❛♠♣❧✐t✉❞❡✳

p p′ qin qout l− l+

❋✐❣✉r❡✿ ❚❤❡ ❋❡②♥♠❛♥ ❞✐❛❣r❛♠ ❢♦r t❤❡ ❈♦♠♣t♦♥ ❛♠♣❧✐t✉❞❡✳

✶✵ ✴ ✸✵

slide-11
SLIDE 11

❚❈❙

∆T

e(2) e(3) e(1)

boost

ϕ ϕ

e’ e’ e’ (2)

(1) (3)

p’

+ c.m. −

l l k’ k γ p c.m. k q q’ p p’ k’ θ ❋✐❣✉r❡✿ ❑✐♥❡♠❛t✐❝❛❧ ✈❛r✐❛❜❧❡s ❛♥❞ ❝♦♦r❞✐♥❛t❡ ❛①❡s ✐♥ t❤❡ γp ❛♥❞ ℓ+ℓ− ❝✳♠✳ ❢r❛♠❡s✳

❇✲❍ ❞♦♠✐♥❛♥t ❢♦r ♥♦t ✈❡r② ❤✐❣❤ ❡♥❡r❣✐❡s✳ ❚❤❡r❡❢♦r❡ ✇❡ ♥❡❡❞ t❤❡ ✐♥t❡r❢❡r❡♥❝❡ ♣❛rt ♦❢ t❤❡ ❝r♦ss✲s❡❝t✐♦♥✳ ❋♦r ✉♥♣♦❧❛r✐③❡❞ ♣r♦t♦♥s ❛♥❞ ♣❤♦t♦♥s✿ dσINT dQ′2 dt d cos θ dϕ ∼ cos ϕ · Re H(η, t)

✶✶ ✴ ✸✵

slide-12
SLIDE 12

❏▲❆❇ ✻ ●❡❱ ❞❛t❛

❘❛❢❛②❡❧ P❛r❡♠✉③②❛♥ P❤❉ t❤❡s✐s

❋✐❣✉r❡✿ e+e− ✐♥✈❛r✐❛♥t ♠❛ss ❞✐str✐❜✉t✐♦♥ ✈s q✉❛s✐✲r❡❛❧ ♣❤♦t♦♥ ❡♥❡r❣②✳ ❋♦r ❚❈❙ ❛♥❛❧②s✐s M(e+e−) > 1.1 GeV ❛♥❞ sγp > 4.6 GeV2 r❡❣✐♦♥s ❛r❡ ❝❤♦s❡♥✳ ▲❡❢t ❣r❛♣❤ r❡♣r❡s❡♥ts ❡✶✲✻ ❞❛t❛ s❡t✱ r✐❣❤t ♦♥❡ ✐s ❢r♦♠ ❡✶❢ ❞❛t❛ s❡t✳

✶✷ ✴ ✸✵

slide-13
SLIDE 13

❚❤❡♦r② ✈s ❡①♣❡r✐♠❡♥t

❘✳P❛r❡♠✉③②❛♥ ❛♥❞ ❱✳●✉③❡②✿ R =

  • dφ cos φ
  • dθ dσ
  • dφ
  • dθ dσ

2

  • t GeV

0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 R’

  • 1
  • 0.8
  • 0.6
  • 0.4
  • 0.2

0.2 0.4 0.6 0.8 1

= 3.536 GeV

γ

E

2

= 1.3 GeV

2

Q

SC_D= 0.00 SC_D= 1.00 SC_D= 2.00 BH Dual Data

❋✐❣✉r❡✿ ❚❤♦❡r❡t✐❝❛❧ ♣r❡❞✐❝t✐♦♥ ♦❢ t❤❡ r❛t✐♦ R ❢♦r ✈❛r✐♦✉s ●P❉s ♠♦❞❡❧s✳ ❉❛t❛ ♣♦✐♥ts ❛❢t❡r ❝♦♠❜✐♥✐♥❣ ❜♦t❤ ❡✶✲✻ ❛♥❞ ❡✶❢ ❞❛t❛ s❡ts✳

✶✸ ✴ ✸✵

slide-14
SLIDE 14

❆♣♣r♦✈❡❞ ❡①♣❡r✐♠❡♥t ❛t ❍❛❧❧ ❇✱ ❛♥❞ ▲❖■ ❢♦r ❍❛❧❧ ❆✳

✶✹ ✴ ✸✵

slide-15
SLIDE 15

❯❧tr❛♣❡r✐♣❤❡r❛❧ ❝♦❧❧✐s✐♦♥s

σAB =

  • dkA dnA

dkA σγB(WA(kA)) +

  • dkB dnB

dkB σγA(WB(kB)) ✇❤❡r❡ kA,B = 1

2xA,B

√s✳

✶✺ ✴ ✸✵

slide-16
SLIDE 16

❇❍ ❛♥❞ ❚❈❙ ❝r♦ss s❡❝t✐♦♥s ❛t ❯P❈

100 1000 104 105 106 107 108 s GeV2 27.0 27.5 28.0 28.5 ΣBH pb

a

1000 104 105 106 107 5 10 15 20 25 30 35 s GeV2 ΣTCSpb

b

❋✐❣✉r❡✿ ✭❛✮ ❚❤❡ ❇❍ ❝r♦ss s❡❝t✐♦♥ ✐♥t❡❣r❛t❡❞ ♦✈❡r θ ∈ [π/4, 3π/4]✱ ϕ ∈ [0, 2π] ✱ Q′2 ∈ [4.5, 5.5] GeV2✱ |t| ∈ [0.05, 0.25] GeV2✱ ❛s ❛ ❢✉♥❝t✐♦♥ ♦❢ γp ❝✳♠✳ ❡♥❡r❣② sq✉❛r❡❞ s✳ ✭❜✮ σT CS ❛s ❛ ❢✉♥❝t✐♦♥ ♦❢ γp ❝✳♠✳ ❡♥❡r❣② sq✉❛r❡❞ s✱ ❢♦r ●❘❱●❏❘✷✵✵✽ ◆▲❖ ♣❛r❛♠❡tr✐③❛t✐♦♥s✱ ❢♦r ❞✐✛❡r❡♥t ❢❛❝t♦r✐③❛t✐♦♥ s❝❛❧❡s µ2

F = 4 ✭❞♦tt❡❞✮✱ 5 ✭❞❛s❤❡❞✮✱ 6

✭s♦❧✐❞✮ GeV2✳

❋♦r ✈❡r② ❤✐❣❤ ❡♥❡r❣✐❡s σT CS ❝❛❧❝✉❧❛t❡❞ ✇✐t❤ µ2

F = 6 GeV2 ✐s ♠✉❝❤ ❜✐❣❣❡r t❤❡♥

✇✐t❤ µ2

F = 4 GeV2✳ ❆❧s♦ ♣r❡❞✐❝t✐♦♥s ♦❜t❛✐♥❡❞ ✉s✐♥❣ ▲❖ ❛♥❞ ◆▲❖

  • ❘❱●❏❘✷✵✵✽ P❉❋s ❞✐✛❡r s✐❣♥✐✜❝❛♥t❧②✳

✶✻ ✴ ✸✵

slide-17
SLIDE 17

❚❤❡ ✐♥t❡r❢❡r❡♥❝❡ ❝r♦ss s❡❝t✐♦♥ ❛t ❯P❈

Π 2

Π

3 Π 2

2 Π 20 20 40 60 Φ dΣ dΦdtdQ’

2 pbGeV4

a

Π 2

Π

3 Π 2

2 Π 5 5 10 15 20 25 30 Φ dΣ dΦdtdQ’

2 pbGeV4

b

Π 2

Π

3 Π 2

2 Π 5 5 10 15 20 Φ dΣ dΦdtdQ’

2 pbGeV4

c

Total BH Int. Comp.

❋✐❣✉r❡✿ ❚❤❡ ❞✐✛❡r❡♥t✐❛❧ ❝r♦ss s❡❝t✐♦♥s ✭s♦❧✐❞ ❧✐♥❡s✮ ❢♦r t = −0.2 GeV2✱ Q′2 = 5 GeV2 ❛♥❞ ✐♥t❡❣r❛t❡❞ ♦✈❡r θ = [π/4, 3π/4]✱ ❛s ❛ ❢✉♥❝t✐♦♥ ♦❢ ϕ✱ ❢♦r s = 107 GeV2 ✭❛✮✱ s = 105 GeV2✭❜✮✱ s = 103 GeV2 ✭❝✮ ✇✐t❤ µ2

F = 5 GeV2✳ ❲❡ ❛❧s♦ ❞✐s♣❧❛② t❤❡

❈♦♠♣t♦♥ ✭❞♦tt❡❞✮✱ ❇❡t❤❡✲❍❡✐t❧❡r ✭❞❛s❤✲❞♦tt❡❞✮ ❛♥❞ ■♥t❡r❢❡r❡♥❝❡ ✭❞❛s❤❡❞✮ ❝♦♥tr✐❜✉t✐♦♥s✳

✶✼ ✴ ✸✵

slide-18
SLIDE 18

❯P❈ ❘❛t❡ ❡st✐♠❛t❡s

❚❤❡ ♣✉r❡ ❇❡t❤❡ ✲ ❍❡✐t❧❡r ❝♦♥tr✐❜✉t✐♦♥ t♦ σpp✱ ✐♥t❡❣r❛t❡❞ ♦✈❡r θ = [π/4, 3π/4]✱ φ = [0, 2π]✱ t = [−0.05 GeV2, −0.25 GeV2]✱ Q′2 = [4.5 GeV2, 5.5 GeV2]✱ ❛♥❞ ♣❤♦t♦♥ ❡♥❡r❣✐❡s k = [20, 900] GeV ❣✐✈❡s✿ σBH

pp

= 2.9♣❜ . ❚❤❡ ❈♦♠♣t♦♥ ❝♦♥tr✐❜✉t✐♦♥ ✭❝❛❧❝✉❧❛t❡❞ ✇✐t❤ ◆▲❖ ●❘❱●❏❘✷✵✵✽ P❉❋s✱ ❛♥❞ µ2

F = 5 GeV2✮ ❣✐✈❡s✿

σT CS

pp

= 1.9♣❜ . ▲❍❈✿ r❛t❡ ∼ 105 ❡✈❡♥ts✴②❡❛r ✇✐t❤ ♥♦♠✐♥❛❧ ❧✉♠✐♥♦s✐t② ✭1034 ❝♠−2s−1✮

✶✽ ✴ ✸✵

slide-19
SLIDE 19

❈♦✉❧❞ ♦♥❡ ❛❝❝❡ss ●P❉s ✐♥ t❤❡ ❯P❈ ♣r♦❞✉❝t✐♦♥ ♦❢ ❤❡❛✈② ♠❡s♦♥s❄

❲❡ ❤❛✈❡ ❣♦♦❞ ❞❛t❛✦ ❙❡❡ ❍✶ ✷✵✶✸ ♣❛♣❡r✿

[GeV]

p γ

W 10

2

10

3

10 p) [nb] ψ J/ → p γ ( σ 10

2

10

3

10 photoproduction ψ Elastic J/

H1 data HE H1 data LE H1(2005) Fit HE, LE, H1(2005) Zeus(2002) E401, E516 LHCb(2013)

photoproduction ψ Elastic J/

✶✾ ✴ ✸✵

slide-20
SLIDE 20

❈♦♠❜✐♥❡❞ ❈♦❧❧✐♥❡❛r ◗❈❉ ❛♥❞ ◆❘◗❈❉ ❢❛❝t♦r✐③❛t✐♦♥s✿

t✇✐st ∼ 1/Mn ❛♥❞ ✈❡❧♦❝✐t② ∼ v

c

m ❡①♣❛♥s✐♦♥s✿ M ∼ O1V m3 1/2

1

  • −1

dx

  • Tg(x, ξ) F g(x, ξ, t) + Tq(x, ξ)F q,S(x, ξ, t)
  • ,

F q,S(x, ξ, t) =

  • q=u,d,s

F q(x, ξ, t) . F g(q)(x, ξ, t; µ2

F ) ✕ t❤❡ ❣❧✉♦♥ ✭q✉❛r❦✮ ●P❉s✱ m ✐s ❛ ♣♦❧❡ ♠❛ss ♦❢ ❤❡❛✈② q✉❛r❦✱

ξ = M 2/(2W 2 − M 2) ✐s t❤❡ s❦❡✇❡❞♥❡ss ♣❛r❛♠❡r❡r✳ ◆❘◗❈❉ ✕ ❛❧❧ ✐♥❢♦r♠❛t✐♦♥ ❛❜♦✉t t❤❡ q✉❛r❦♦♥✐✉♠ str✉❝t✉r❡ ✐s ❡♥❝♦❞❡❞ ✐♥ t❤❡ ◆❘◗❈❉ ♠❛tr✐① ❡❧❡♠❡♥t O1V ✇❤✐❝❤ ❡♥t❡rs t❤❡ ❧❡♣t♦♥✐❝ ❞❡❝❛② r❛t❡ Γ[V → l+l−] = 2e2

qπα2

3 O1V m2

  • 1 − 8αS

3π 2 .

✷✵ ✴ ✸✵

slide-21
SLIDE 21

❍❛r❞ s❝❛tt❡r✐♥❣ ❦❡r♥❡❧s✿

Tg(x, ξ) = ξ (x − ξ + iε)(x + ξ − iε) Ag x − ξ + iε 2ξ

  • ,

Tq(x, ξ) = Aq x − ξ + iε 2ξ

  • .

◮ ▲❖

A(0)

g

(y) = αS A(0)

q

(y) = 0 .

◮ ◆▲❖

❉✳ ❨✉✳ ■✈❛♥♦✈ ✱ ❆✳ ❙❝❤❛❢❡r ✱ ▲✳ ❙③②♠❛♥♦✇s❦✐ ❛♥❞ ●✳ ❑r❛s♥✐❦♦✈ ✲ ❊✉r✳P❤②s✳❏✳ ❈✸✹ ✭✷✵✵✹✮ ✷✾✼✲✸✶✻ Tq(x, ξ) = α2

S(µR)CF

2π fq x − ξ + iε 2ξ

  • ,

fq(y) = ln 4m2 µ2

F

  • (1 + 2y)

ln(−y) 1 + y − ln(1 + y) y

  • − π2 13(1 + 2y)

48y(1 + y) + 2 ln 2 1 + 2y + ln(−y) + ln(1 + y) 1 + 2y + (1 + 2y)

  • ln2(−y)

1 + y − ln2(1 + y) y

  • + 3 − 4y + 16y(1 + y)

4y(1 + y) Li2(1 + 2y) − 7 + 4y + 16y(1 + y) 4y(1 + y) Li2(−1 − 2y)

✷✶ ✴ ✸✵

slide-22
SLIDE 22

P❤♦t♦♣r♦❞✉❝t✐♦♥ ❛♠♣❧✐t✉❞❡ ❛♥❞ ❝r♦ss s❡❝t✐♦♥ ✲ ▲❖

10 20 50 100 200 500 1000 W 0.1 10 1000 105

Im M

200 400 600 800 1000 W 1000 2000 3000 4000

Σnb

❋✐❣✉r❡✿ ✭❧❡❢t✮ ■♠❛❣✐♥❛r② ♣❛rt ♦❢ t❤❡ ❛♠♣❧✐t✉❞❡ M ❛♥❞ ✭r✐❣❤t✮ ♣❤♦t♦♣r♦❞✉❝t✐♦♥ ❝r♦ss s❡❝t✐♦♥ ❛s ❛ ❢✉♥❝t✐♦♥ ♦❢ W = √sγp ❢♦r µ2

F = M2 J/ψ × {0.5, 1, 2}✳

✷✷ ✴ ✸✵

slide-23
SLIDE 23

P❤♦t♦♣r♦❞✉❝t✐♦♥ ❝r♦ss s❡❝t✐♦♥ ✲ ▲❖ ❛♥❞ ◆▲❖

◆▲❖✴▲❖ ❢♦r ❧❛r❣❡ W✿ ∼ αS(µR)Nc π ln 1 ξ

  • ln
  • 1

4M 2 V

µ2

F

  • 10

20 50 100 200 500 1000 W 0.1 1 10 100 1000

Σnb

❋✐❣✉r❡✿ P❤♦t♦♣r♦❞✉❝t✐♦♥ ❝r♦ss s❡❝t✐♦♥ ❛s ❛ ❢✉♥❝t✐♦♥ ♦❢ W = √sγp ❢♦r µ2

F = M2 J/ψ × {0.5, 1, 2}✲ ▲❖ ❛♥❞ ◆▲❖✳ ❚❤✐❝❦ ❧✐♥❡s ❢♦r ▲❖ ❛♥❞ ◆▲❖ ❢♦r

µ2

F = 1/4M2 J/ψ✳

✷✸ ✴ ✸✵

slide-24
SLIDE 24

❍✐❣❤✲❡♥❡r❣② r❡s✉♠♠❛t✐♦♥

◮ ❲❤② ◆▲❖ ❝♦rr❡❝t✐♦♥s ❛r❡ ❧❛r❣❡ ❛t s♠❛❧❧ xB❄

❧❛r❣❡ ❝♦♥tr✐❜✉t✐♦♥ ❝♦♠❡s ❢r♦♠ ξ ≪ x ≪ 1 ✭Q = M✮ ImAg ∼ Hg(ξ, ξ) + 3αs π

  • log Q2

µ2

F

− log 4

  • 1
  • ξ

dx x Hg(x, ξ) Hg(x, ξ) ∼ xg(x) ∼ const✱ t❤❡r❡❢♦r❡

  • dx/xHg(x, ξ) ∼ log(1/ξ)Hg(ξ, ξ)

x ∼ sγ∗g

Q2 ✱ ❇♦r♥ ❝♦♥tr✐❜✉t✐♦♥ ❢♦r ❇❋❑▲✿

γ∗ γ∗

✷✹ ✴ ✸✵

slide-25
SLIDE 25

❆t ❤✐❣❤❡r ♦r❞❡rs ♣♦✇❡rs ♦❢ ❡♥❡r❣② ❧♦❣ ❛r❡ ❣❡♥❡r❛t❡❞ ImAg ∼ Hg(ξ, ξ) +

1

  • ξ

dx x Hg(x, ξ)

  • n=1

Cn(L) ¯ αn

s

(n − 1)! logn−1 x ξ Cn(L) ✲ ♣♦❧②♥♦♠✐❛❧s ♦❢ L = log Q2

µ2

F ✱ ♠❛①✐♠✉♠ ♣♦✇❡r ✐s Ln

◮ ❖♥❡ ❝❛♥ ❝❛❧❝✉❧❛t❡ Cn(L) ✉s✐♥❣ ❇❋❑▲ ❡q✉❛t✐♦♥ ✐♥ D = 4 + 2ǫ ❞✐♠❡♥s✐♦♥s✳ ◮ ❈♦♥s✐st❡♥t❧② ✇✐t❤ ❝♦❧❧✐♥❡❛r ❢❛❝t♦r✐③❛t✐♦♥✱ ✐♥ t❡r♠s ♦❢ ❝♦rr❡❝t✐♦♥s t♦ ❝♦❡✛✳

❢✉♥❝t✐♦♥s ❛♥❞ ❛♥♦♠❛❧♦✉s ❞✐♠❡♥s✐♦♥s❀ s❛②✱ ✐♥ MS s❝❤❡♠❡

◮ ❢♦r ❉■❙ ❛ t❡❝❤♥✐q✉❡ s✉❣❣❡st❡❞ ❜② ❈❛t❛♥✐✱ ❈✐❛❢❛❧♦♥✐ ❛♥❞ ❍❛✉t♠❛♥♥❀

❬❈❛t❛♥✐✱ ❍❛✉t♠❛♥♥ ✬✾✹❪

◮ ❚❤❡ ♠❡t❤♦❞ ✉s❡❞ ✐♥ ❉■❙ ❝❛♥ ❜❡ ❣❡♥❡r❛❧✐③❡❞ t♦ ❡①❝❧✉s✐✈❡✱ ♥♦♥❢♦r✇❛r❞

♣r♦❝❡ss❡s✳

✷✺ ✴ ✸✵

slide-26
SLIDE 26

❈♦❡✛✳ ❢✉♥❝t✐♦♥s ❛t s♠❛❧❧ ① ✴ t❤❡✐r ▼❡❧❧✐♥ ♠♦♠❡♥ts ❛t N → 0

L = log

  • Q2

µ2

F

  • ,

x = ¯

αs N

♦✉r r❡s✉❧t ❢♦r J/Ψ, Υ 1 + x(L − log 4) + x2 6

  • π2 + 3 log2 4 + 3L(L − log 16)
  • + · · · + O(x10)

FL ✕ ❬❈❛t❛♥✐✱ ❍❛✉t♠❛♥♥ ✬✾✹❪ µ2

F = Q2

FL✿ 1 − 1

3 x + 2.13 x2 + 2.27 x3 + 0.434 x4 + . . .

J/Ψ, Υ✿ 1 − 1.39 x + 2.61 x2 + 0.481 x3 − 4.96 x4 + . . . µ2

F = Q2/4

FL✿ 1 + 1.05 x + 2.63 x2 + 5.35x3 + 8.97 x4 + . . . J/Ψ, Υ✿ 1 + 0. x + 1.64 x2 + 3.21 x3 + 1.08 x4 + . . .

✷✻ ✴ ✸✵

slide-27
SLIDE 27

❙♦♠❡ ✐♠♣❧❡♠❡♥t❛t✐♦♥ ❢♦r Υ ♣❤♦t♦♣r♦❞✉❝t✐♦♥

ImAg ∼ Hg(ξ, ξ) +

1

  • ξ

dx x Hg(x, ξ)

  • n=1

Cn(L) ¯ αn

s

(n − 1)! logn−1 x ξ ✇✐t❤♦✉t ❧♦ss ♦❢ ❛❝❝✉r❛❝② Hg(x, ξ) → xg(x)✱ ❜✉t ▲❖ ✕ Hg(ξ, ξ) s❤♦✉❧❞ ❜❡ ❦❡♣t✳ Cn(L) ✲ Ln ♣♦❧②♥♦♠✐❛❧s ✇❡ ❤❛✈❡ ❝❛❧❝✉❧❛t❡❞✱ L = log Q2

µ2

F

✐♥ t❤❡ ♥✉♠❡r✐❝s ❜❡❧♦✇ ✇❡ ✉s❡❞✿

◮ ✕ ❈❚❊◗✻▼ P❉❋s ◮ ❢♦r ▲❖ t❡r♠✿ x g(x) → Hg(ξ, ξ) ✕ ❘❛❞②✉s❤❦✐♥ ❉❉ ♠♦❞❡❧ ◮ s✉❜st✐t✉t❡ t❤❡ ✜rst t❡r♠ ✭n = 1✮ ✐♥ t❤❡ s✉♠✱ ❜② t❤❡ ❡①❛❝t ◆▲❖ ❝♦❡✣❝✐❡♥t ◮ ❜✉t

✇❡ ✉s❡ ✜①❡❞ ♦r❞❡r ◆▲❖ ❛♣♣r♦❛❝❤ t♦ µF ❡✈♦❧✉t✐♦♥ ♦❢ ❣❧✉♦♥ ●P❉

✷✼ ✴ ✸✵

slide-28
SLIDE 28

❈♦♠♣❛r✐s♦♥ ✇✐t❤ ❩❊❯❙ ✭✾✻✲✵✼✮ ✹✻✽ ♣❜−1 ❞❛t❛✿

σγp→Υ(1S)p = 160 ± 51+48

−21 pb

❢♦r < W >= 100 ●❡❱ σγp→Υ(1S)p = 321 ± 88+45

−114 pb

❢♦r < W >= 180 ●❡❱ ■♥♣✉t ❢♦r ♦✉r ❝❛❧❝✉❧❛t✐♦♥✿ mb = 4.9 ●❡❱ , bΥ = 4.5 ●❡❱−2 ❖✉r r❡s✉❧ts✿ Q2/4 < µ2

F < Q2

σLO(100) = 214 ÷ 185 pb , σres(100) = 159 ÷ 144 pb σLO(180) = 492 ÷ 358 pb , σres(180) = 427 ÷ 332 pb Q2/2 < µ2

F < Q2

σLO(100) = 214 ÷ 202 pb , σres(100) = 159 ÷ 156 pb σLO(180) = 492 ÷ 430 pb , σres(180) = 345 ÷ 332 pb

✷✽ ✴ ✸✵

slide-29
SLIDE 29

LO ✈s ❘❡s✉♠♠❡❞ ❝r♦ss s❡❝t✐♦♥

100 200 300 400 500 600 700 800W, GeV 500 1000 1500 2000 2500 3000 sigma, pb

100 ●❡❱2 < µ2

F < 50 ●❡❱2 100 200 300 400 500 600 700W, GeV 500 1000 1500 2000 2500 3000 sigma, pb

100 ●❡❱2 < µ2

F < 25 ●❡❱2

✷✾ ✴ ✸✵

slide-30
SLIDE 30

❙✉♠♠❛r②

◮ ●❉Ps ❡♥t❡r ❢❛❝t♦r✐③❛t✐♦♥ t❤❡♦r❡♠s ❢♦r ❤❛r❞ ❡①❝❧✉s✐✈❡ r❡❛❝t✐♦♥s ✐♥ ❛ s✐♠✐❧❛r

♠❛♥♥❡r ❛s P❉❋s ❡♥t❡r ❢❛❝t♦r✐③❛t✐♦♥ t❤❡♦r❡♠ ❢♦r ❉■❙

◮ ❉❱❈❙ ✐s ❛ ❣♦❧❞❡♥ ❝❤❛♥♥❡❧✱ ❛ ❧♦t ♦❢ ♥❡✇ ❉❱❈❙ ❡①♣❡r✐♠❡♥ts ♣❧❛♥♥❡❞ ✲

❏▲❆❇ ✶✷✱ ❈❖▼P❆❙❙✱ ❊■❈✭❄✮

◮ ●P❉s ✐♥ ♦t❤❡r ❡①❝❧✉s✈❡ ♣r♦❝❡ss❡s ✲ ❚❈❙✱ ❉❱▼P✱ ♣❤♦t♦♣r♦❞✉❝t✐♦♥ ♦❢

❤❡❛✈② ♠❡s♦♥s✳✳✳

◮ ❚❈❙ ❛❧r❡❛❞② ♠❡❛s✉r❡❞ ❛t ❏▲❆❇ ✻ ●❡❱✱ ❜✉t ♠✉❝❤ r✐❝❤❡r ❛♥❞ ♠♦r❡

✐♥t❡r❡st✐♥❣ ❦✐♥❡♠❛t✐❝❛❧ r❡❣✐♦♥ ❛✈❛✐❧❛❜❧❡ ❛❢t❡r ✉♣❣r❛❞❡ t♦ ✶✷ ●❡❱✱ ♠❛②❜❡ ♣♦ss✐❜❧❡ ❛t ❈❖▼P❆❙❙✳

◮ ❯❧tr❛♣❡r✐♣❤❡r❛❧ ❝♦❧❧✐s✐♦♥s ❛t ❤❛❞r♦♥ ❝♦❧❧✐❞❡rs ♦♣❡♥s ❛ ♥❡✇ ✇❛② t♦ ♠❡❛s✉r❡

  • P❉s✱

◮ ◆▲❖ ❝♦rr❡❝t✐♦♥s ❛r❡ ✈❡r② ✐♠♣♦rt❛♥t✿ ❧❛r❣❡ ❢♦r ❚❈❙❀ ❞r❛♠❛t✐❝ ❢♦r ❱▼

♣❤♦t♦♣r♦❞✉❝t✐♦♥✳

◮ ❍✐❣❤ ❡♥❡r❣② r❡s✉♠♠❛t✐♦♥ ♥❡❡❞❡❞ ❢♦r ❱▼ ♣❤♦t♦♣r♦❞✉❝t✐♦♥ ✭✐♥ ♣r♦❣r❡ss✮✳

✸✵ ✴ ✸✵