Accessing the real part of the forward Compton & elastic J/psi - PowerPoint PPT Presentation

Accessing the real part of the forward Compton & elastic J/psi scattering amplitudes off the proton Oleksii Gryniuk, Marc Vanderhaeghen JGU, Mainz, Germany Summer School 2016 September 22, 2016

Outline • Accessing the real part of the forward Compton scattering amplitude off the proton • Accessing the real part of the forward elastic J/psi - p scattering amplitude • Summary

Forward Compton scattering off the proton ɣ ɣ p p

Forward Compton scattering off the proton T γ p ( ν ) ɣ ɣ spin-averaged amplitude: ≡ ν = W 2 − M 2 p p pq p kinematic variable: M p 2 M p

Forward Compton scattering off the proton T γ p ( ν ) ɣ ɣ spin-averaged amplitude: ≡ ν = W 2 − M 2 p p pq p kinematic variable: M p 2 M p Im T γ p ( ν ) = ν 4 π σ tot γ p ( ν ) unitarity

Forward Compton scattering off the proton T γ p ( ν ) ɣ ɣ spin-averaged amplitude: ≡ ν = W 2 − M 2 p p pq p kinematic variable: M p 2 M p Im T γ p ( ν ) = ν 4 π σ tot γ p ( ν ) unitarity causality + crossing + low energy theorem subtracted dispersion relation: Z 1 σ tot γ p ( ν 0 ) + ν 2 Re T γ p ( ν ) = − α ν 0 2 − ν 2 d ν 0 2 π 2 M p 0

Forward Compton scattering off the proton — motivation resonance region higher energies… 600 200 fit I Block - Halzen [PRD70, 091901(R) (2004)] saturated fit II Donnachie - Landshof [PLB595, 393 (2004)] Froissart bound Armstrong et al . Armstrong et al . 500 180 MacCormick et al . Caldwell et al . (~ log 2 𝜉 ) LEGS Collaboration H1 Collaboration Bartalini et al . ZEUS Collaboration 400 160 σ tot σ abs [ µ b ] σ [ µ b] 300 140 Regge with 200 120 hard pomeron (~ 𝜉 0.45 ) 100 100 10 1 10 2 0.25 0.30 0.35 0.40 0.45 0.50 0.55 0.60 0.65 ν [ GeV ] W [GeV]

Forward Compton scattering off the proton — motivation resonance region higher energies… 600 200 fit I Block - Halzen [PRD70, 091901(R) (2004)] saturated fit II Donnachie - Landshof [PLB595, 393 (2004)] Froissart bound Armstrong et al . Armstrong et al . 500 180 MacCormick et al . Caldwell et al . (~ log 2 𝜉 ) LEGS Collaboration H1 Collaboration Bartalini et al . ZEUS Collaboration 400 160 σ tot σ abs [ µ b ] σ [ µ b] 300 140 Regge with 200 120 hard pomeron (~ 𝜉 0.45 ) 100 100 10 1 10 2 0.25 0.30 0.35 0.40 0.45 0.50 0.55 0.60 0.65 DR ν [ GeV ] W [GeV] 10 5 Damashek-Gilman Block - Halzen Armstrong et al . Donnachie - Landshof 5 A2 Collaboration Alvensleben et al . fit I 0 fit II 0 Alvensleben et al . -3.03 Re f [ µ b · GeV ] Re f [ µ b · GeV ] ReT -5 -5 -10 -10 -12.3 -15 -15 -20 0.0 0.5 1.0 1.5 2.0 2.5 2 4 6 8 10 12 ν [ GeV ] W [GeV] OG, F. Hagelstein, V. Pascalutsa, a single existing direct experimental datapoint (1972) PRD 92 , 074031 (2015)

Forward Compton scattering off the proton — motivation resonance region higher energies… 600 200 fit I Block - Halzen [PRD70, 091901(R) (2004)] saturated fit II Donnachie - Landshof [PLB595, 393 (2004)] Froissart bound Armstrong et al . Armstrong et al . 500 180 MacCormick et al . Caldwell et al . (~ log 2 𝜉 ) LEGS Collaboration H1 Collaboration Bartalini et al . ZEUS Collaboration 400 160 σ tot σ abs [ µ b ] σ [ µ b] 300 140 Regge with 200 120 hard pomeron (~ 𝜉 0.45 ) 100 100 10 1 10 2 0.25 0.30 0.35 0.40 0.45 0.50 0.55 0.60 0.65 DR ν [ GeV ] W [GeV] 10 5 Damashek-Gilman Block - Halzen Armstrong et al . Donnachie - Landshof 5 A2 Collaboration Alvensleben et al . fit I 0 fit II 0 Alvensleben et al . -3.03 Re f [ µ b · GeV ] Re f [ µ b · GeV ] ReT -5 -5 -10 -10 -12.3 -15 -15 -20 0.0 0.5 1.0 1.5 2.0 2.5 2 4 6 8 10 12 ν [ GeV ] W [GeV] OG, F. Hagelstein, V. Pascalutsa, a single existing direct experimental datapoint (1972) PRD 92 , 074031 (2015) Let’s redo the experiment at JLab!

Lepton pair photoproduction dominant l − l + q q l − q q' l + l + l − T µ ν q' q' p p p' p' p p' Bethe-Heitler Compton

Lepton pair photoproduction q 0 2 6 = 0 quasi-real dominant l − l + q q l − q q' l + l + l − T µ ν q' q' p p p' p' p p' t 6 = 0 quasi-forward Bethe-Heitler q 0 2 → 0 quasi-forward-real Compton contribution: t → 0 ✓ � g µ ν + q 0 µ q ν ◆ T µ ν T 1 ' unpoll qq 0 ✓ ◆ ✓ ◆ P µ − qP P ν − qP 1 qq 0 q 0 µ qq 0 q ν T 2 + M 2 P = 1 ν = qP ν , t, q 0 2 ) ' T FRCS T 1 ( e ( e ν ) 2( p + p 0 ) e 1 M ν , t, q 0 2 ) ' � qq 0 qq 0 = q 0 2 − t ν 2 T FRCS T 2 ( e ( e ν ) 1 e 2

Lepton pair photoproduction q 0 2 6 = 0 quasi-real dominant l − l + q q l − q q' l + l + l − T µ ν q' q' p p p' p' p p' t 6 = 0 quasi-forward Bethe-Heitler 10 2 2 d Ω e-e+ cm ( µ b/GeV 4 sr) E γ = 2.2 GeV q 0 2 → 0 quasi-forward-real Compton contribution: -t = 0.027 GeV 2 2 = 0.0006 GeV 2 M ll t → 0 ✓ � g µ ν + q 0 µ q ν ◆ T µ ν T 1 ' unpoll qq 0 ✓ ◆ ✓ ◆ P µ − qP P ν − qP 1 d σ /dt dM ll 10 qq 0 q 0 µ Full qq 0 q ν T 2 + M 2 P = 1 ν = qP ν , t, q 0 2 ) ' T FRCS T 1 ( e ( e ν ) 2( p + p 0 ) e 1 M ν , t, q 0 2 ) ' � qq 0 Bethe-Heitler qq 0 = q 0 2 − t ν 2 T FRCS T 2 ( e ( e ν ) 1 e 2 1 -150 -100 -50 0 50 100 150 θ e-e+ cm (deg)

Interference term l + ↔ l − Bethe-Heitler Compton l − l + ↔ l − : l + ↔ l − : q l − q q' odd l + even l + T µ ν q' p p p' p'

Interference term l + ↔ l − Bethe-Heitler Compton l − l + ↔ l − : l + ↔ l − : q l − q q' odd l + even l + T µ ν q' p p p' p' Observable: | T CS + T BH | 2 = | T CS | 2 + 2 Re T CS T BH + | T BH | 2 even even odd

Forward-backward asymmetry interference d Ω ( θ cm ) − d σ d σ d Ω ( θ cm − π ) 2 Re T CS T BH d Ω ( θ cm − π ) = A FB ≡ | T CS | 2 + | T BH | 2 d Ω ( θ cm ) + d σ d σ θ cm — scattering angle in a lepton pair CM frame A FB A FB 0.05 0.05 Data: DESY (1972) E γ = 2.2 GeV -t = 0.027 GeV 2 0.025 0 Born M ll = 0.025 GeV -0 -0.05 -0.025 -0.1 Full -0.05 -0.15 Born -0.075 -0.2 E γ = 2.2 GeV -0.1 -0.25 Full -t = 0.027 GeV 2 -0.125 -0.3 50 o < θ e-e+ cm < 150 o -0.15 -0.35 0 20 40 60 80 100 120 140 160 180 0 0.01 0.02 0.03 0.04 0.05 θ e-e+ cm (deg) M ll (GeV)

Future experiments at JLab HPS (Heavy Photon Search) ep → ep ( e − e + ) E12 - 11 - 006 initial process of interest: beam energies: 1.1, 2.2, 4.4, 6.6 GeV − e M ll : 0.01 — 0.1 GeV A' Z some preliminary results: background — of our interest: − e Z

Forward J/psi - p scattering J/psi J/psi p p

Forward J/psi - p scattering — motivation e − c γ J/ Ψ c e + P’ P probe of the colour deconfinement at high energies through the • propagation of a J/Psi in a quark-gluon plasma D. Kharzeev and H. Satz, Phys. Lett. B 334 , 155 (1994) D. Kharzeev, H. Satz, A. Syamtomov and G. Zinovjev, Eur. Phys. J. C 9 , 459 (1999) is there a J/psi - nucleus bound state? • T ψ p ( ν = ν el ) = 8 π ( M + M ψ ) a ψ p J/psi - p s-wave scattering length J/psi binding energy in a nuclear matter (linear density approximation): B ψ ' 8 π ( M + M ψ ) a ψ p ρ nm 4 MM ψ M. E. Luke, A. V. Manohar and M. J. Savage, Phys. Lett. B 288 , 355 (1992) S. H. Lee and C. M. Ko, Phys. Rev. C 67 , 038202 (2003) … S. J. Brodsky and G. A. Miller, Phys. Lett. B 412 , 125 (1997) K. Tsushima, D. H. Lu, G. Krein and A. W. Thomas, Phys. Rev. C 83 , 065208 (2011)

Forward J/psi - p scattering T ψ p ( ν ) J/psi J/psi spin-averaged amplitude: p p ν ≡ p q = s − u kinematic variable: 4

Forward J/psi - p scattering T ψ p ( ν ) J/psi J/psi spin-averaged amplitude: p p ν ≡ p q = s − u kinematic variable: 4 Im T ψ p ( ν ) = 2 √ s q ψ p σ tot ψ p ( ν ) unitarity causality + crossing subtracted dispersion relation: Z 1 Re T ψ p ( ν ) = T ψ p (0) + 2 d ν 0 1 Im T ψ p ( ν 0 ) π ν 2 ν 0 2 − ν 2 ν 0 ν el directly sensitive to a ψ p

Forward J/psi - p scattering T ψ p ( ν ) J/psi J/psi spin-averaged amplitude: p p ν ≡ p q = s − u kinematic variable: 4 Im T ψ p ( ν ) = 2 √ s q ψ p σ tot ψ p ( ν ) unitarity parameterising cross section: causality + crossing σ tot ψ p = σ el ψ p + σ inel ψ p ⌘ b el ✓ ν ◆ a el subtracted dispersion relation: ⇣ 1 − ν el σ el ψ p ∝ C el ν ν el Z 1 Re T ψ p ( ν ) = T ψ p (0) + 2 d ν 0 1 Im T ψ p ( ν 0 ) ⌘ b in ✓ ν π ν 2 ◆ a in ⇣ 1 − ν in σ inel ν 0 2 − ν 2 ∝ C in ν 0 ψ p ν el ν ν in directly sensitive to a ψ p

Forward J/psi - p scattering K. Redlich, H. Satz and G. M. Zinovjev, Eur. Phys. J. C 17 , 461 (2000) Vector meson dominance (VMD) assumption: V. D. Barger and R. J. N. Phillips, Phys. Lett. B 58 , 433 (1975) ◆ 2 ✓ q γ p ◆ 2 ✓ M ψ forward differential cross section: σ el ψ p = σ ( γ p → ψ p ) ef ψ q ψ p ◆ 2 d σ ◆ 2 ✓ q ψ p � � ✓ ef ψ d σ � � ( γ p → ψ p ) = ( ψ p → ψ p ) ◆ 2 ✓ q γ p � � ◆ 2 ✓ M ψ dt M ψ q γ p dt � � t =0 t =0 σ inel = σ ( γ p → c ¯ cX ) ψ p ef ψ q ψ p