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

Accessing the real part

• f the forward Compton & elastic J/psi

scattering amplitudes off the proton

Oleksii Gryniuk, Marc Vanderhaeghen

September 22, 2016

JGU, Mainz, Germany

Summer School 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

ɣ ɣ p p

Forward Compton scattering off the proton

Forward Compton scattering off the proton

pq Mp ≡ ν = W 2 − M 2

p

2Mp

spin-averaged amplitude:

Tγp(ν)

kinematic variable:

ɣ ɣ p p

Forward Compton scattering off the proton

pq Mp ≡ ν = W 2 − M 2

p

2Mp

spin-averaged amplitude: unitarity

Tγp(ν)

kinematic variable:

Im Tγp(ν) = ν 4π σtot

γp (ν)

ɣ ɣ p p

Forward Compton scattering off the proton

pq Mp ≡ ν = W 2 − M 2

p

2Mp

causality + crossing + low energy theorem spin-averaged amplitude: unitarity

Tγp(ν)

kinematic variable:

Im Tγp(ν) = ν 4π σtot

γp (ν)

Re Tγp(ν) = − α Mp + ν2 2π2 Z 1 σtot

γp (ν0)

ν02 − ν2 dν0

subtracted dispersion relation:

ɣ ɣ p p

0.25 0.30 0.35 0.40 0.45 0.50 0.55 0.60 0.65 ν [GeV] 100 200 300 400 500 600 σabs [µb]

fit I fit II Armstrong et al. MacCormick et al. LEGS Collaboration Bartalini et al.

101 102 W [GeV] 100 120 140 160 180 200 σ [µb]

Block - Halzen [PRD70, 091901(R) (2004)] Donnachie - Landshof [PLB595, 393 (2004)] Armstrong et al. Caldwell et al. H1 Collaboration ZEUS Collaboration

Regge with hard pomeron (~ 𝜉 0.45) saturated Froissart bound (~ log2𝜉)

Forward Compton scattering off the proton — motivation

resonance region higher energies…

σtot

OG, F. Hagelstein, V. Pascalutsa, PRD92, 074031 (2015)

0.25 0.30 0.35 0.40 0.45 0.50 0.55 0.60 0.65 ν [GeV] 100 200 300 400 500 600 σabs [µb]

fit I fit II Armstrong et al. MacCormick et al. LEGS Collaboration Bartalini et al.

2 4 6 8 10 12 W [GeV]

• 20
• 15
• 10
• 5

5 10 Re f [µb·GeV]

Block - Halzen Donnachie - Landshof Alvensleben et al.

101 102 W [GeV] 100 120 140 160 180 200 σ [µb]

Block - Halzen [PRD70, 091901(R) (2004)] Donnachie - Landshof [PLB595, 393 (2004)] Armstrong et al. Caldwell et al. H1 Collaboration ZEUS Collaboration

0.0 0.5 1.0 1.5 2.0 2.5 ν [GeV]

• 15
• 12.3
• 10
• 5
• 3.03

5 Re f [µb·GeV]

Damashek-Gilman Armstrong et al. A2 Collaboration fit I fit II Alvensleben et al.

Regge with hard pomeron (~ 𝜉 0.45) saturated Froissart bound (~ log2𝜉)

DR

a single existing direct experimental datapoint (1972)

Forward Compton scattering off the proton — motivation

resonance region higher energies…

ReT

σtot

OG, F. Hagelstein, V. Pascalutsa, PRD92, 074031 (2015)

0.25 0.30 0.35 0.40 0.45 0.50 0.55 0.60 0.65 ν [GeV] 100 200 300 400 500 600 σabs [µb]

fit I fit II Armstrong et al. MacCormick et al. LEGS Collaboration Bartalini et al.

2 4 6 8 10 12 W [GeV]

• 20
• 15
• 10
• 5

5 10 Re f [µb·GeV]

Block - Halzen Donnachie - Landshof Alvensleben et al.

101 102 W [GeV] 100 120 140 160 180 200 σ [µb]

Block - Halzen [PRD70, 091901(R) (2004)] Donnachie - Landshof [PLB595, 393 (2004)] Armstrong et al. Caldwell et al. H1 Collaboration ZEUS Collaboration

0.0 0.5 1.0 1.5 2.0 2.5 ν [GeV]

• 15
• 12.3
• 10
• 5
• 3.03

5 Re f [µb·GeV]

Damashek-Gilman Armstrong et al. A2 Collaboration fit I fit II Alvensleben et al.

Regge with hard pomeron (~ 𝜉 0.45) saturated Froissart bound (~ log2𝜉)

DR

a single existing direct experimental datapoint (1972)

Forward Compton scattering off the proton — motivation

resonance region higher energies…

ReT

Let’s redo the experiment at JLab!

σtot

Lepton pair photoproduction

p q l+ p' q' l− T µν p q l+ p' q' l−

+

p' q' l− l q p

Bethe-Heitler Compton dominant

Lepton pair photoproduction

p q l+ p' q' l− T µν p q l+ p' q' l−

+

p' q' l− l q p

Bethe-Heitler q02 6= 0 t 6= 0 dominant quasi-real quasi-forward

q02 → 0 t → 0

quasi-forward-real Compton contribution:

+ 1 M 2 ✓ P µ − qP qq0 q0µ ◆ ✓ P ν − qP qq0 qν ◆ T2 T µν

unpoll

' ✓ gµν + q0µqν qq0 ◆ T1

T2(e ν, t, q02) ' qq0 e ν2 T FRCS

1

(e ν) T1(e ν, t, q02) ' T FRCS

1

(e ν)

qq0 = q02 − t 2 P = 1 2(p + p0)

e ν = qP M

Lepton pair photoproduction

p q l+ p' q' l− T µν p q l+ p' q' l−

+

p' q' l− l q p

Bethe-Heitler q02 6= 0 t 6= 0 dominant

Eγ = 2.2 GeV

• t = 0.027 GeV2

Mll

2 = 0.0006 GeV2

θe-e+ cm (deg) dσ/dt dMll

2 d Ωe-e+ cm (µb/GeV4 sr)

1 10 10 2

• 150
• 100
• 50

50 100 150

Bethe-Heitler Full

quasi-real quasi-forward

q02 → 0 t → 0

quasi-forward-real Compton contribution:

+ 1 M 2 ✓ P µ − qP qq0 q0µ ◆ ✓ P ν − qP qq0 qν ◆ T2 T µν

unpoll

' ✓ gµν + q0µqν qq0 ◆ T1

T2(e ν, t, q02) ' qq0 e ν2 T FRCS

1

(e ν) T1(e ν, t, q02) ' T FRCS

1

(e ν)

qq0 = q02 − t 2 P = 1 2(p + p0)

e ν = qP M

Interference term

p q l+ p' q' l− p q l+ p' q' l− T µν

• dd

l+ ↔ l− : even l+ ↔ l− : Bethe-Heitler Compton

l+ ↔ l−

Interference term

p q l+ p' q' l− p q l+ p' q' l− T µν

• dd

l+ ↔ l− : even l+ ↔ l− : Bethe-Heitler Compton

Observable:

even even

l+ ↔ l−

• dd

|TCS + TBH|2 = |TCS|2 + 2 Re TCS TBH + |TBH|2

Forward-backward asymmetry

Eγ = 2.2 GeV

• t = 0.027 GeV2

Mll = 0.025 GeV

θe-e+ cm (deg) AFB

• 0.15
• 0.125
• 0.1
• 0.075
• 0.05
• 0.025

0.025 0.05 20 40 60 80 100 120 140 160 180

Eγ = 2.2 GeV

• t = 0.027 GeV2

50o < θe-e+ cm < 150o

Mll (GeV) AFB

• 0.35
• 0.3
• 0.25
• 0.2
• 0.15
• 0.1
• 0.05

0.05 0.01 0.02 0.03 0.04 0.05

Born Full Born Full Data: DESY (1972)

AFB ≡

dσ dΩ(θcm) − dσ dΩ(θcm − π) dσ dΩ(θcm) + dσ dΩ(θcm − π) =

2 Re TCS TBH |TCS|2 + |TBH|2

— scattering angle in a lepton pair CM frame

θcm interference

Future experiments at JLab

HPS (Heavy Photon Search)

some preliminary results:

Z e

−

A' Z e

−

Mll : 0.01 — 0.1 GeV

background — of our interest: initial process of interest: E12 - 11 - 006

ep → ep(e−e+)

beam energies: 1.1, 2.2, 4.4, 6.6 GeV

p p J/psi J/psi

Forward J/psi - p scattering

Forward J/psi - p scattering — motivation

Tψp(ν = νel) = 8π(M + Mψ) aψp

J/psi - p s-wave scattering length Bψ ' 8π(M + Mψ)aψp 4MMψ ρnm J/psi binding energy in a nuclear matter (linear density approximation):

• is there a J/psi - nucleus bound state?

γ

J/Ψ P e− e+ P’ c c

• 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)
• M. E. Luke, A. V. Manohar and M. J. Savage, Phys. Lett. B 288, 355 (1992)
• S. J. Brodsky and G. A. Miller, Phys. Lett. B 412, 125 (1997)
• S. H. Lee and C. M. Ko, Phys. Rev. C 67, 038202 (2003)
• K. Tsushima, D. H. Lu, G. Krein and A. W. Thomas, Phys. Rev. C 83, 065208 (2011)

…

Forward J/psi - p scattering

spin-averaged amplitude:

kinematic variable:

p p J/psi J/psi

Tψp(ν)

ν ≡ p q = s − u 4

Forward J/psi - p scattering

spin-averaged amplitude:

kinematic variable:

p p J/psi J/psi

Tψp(ν)

ν ≡ p q = s − u 4

unitarity

Im Tψp(ν) = 2√s qψp σtot

ψp(ν)

causality + crossing

subtracted dispersion relation:

Re Tψp(ν) = Tψp(0) + 2 π ν2 Z 1

νel

dν0 1 ν0 Im Tψp(ν0) ν0 2 − ν2

directly sensitive to aψp

Forward J/psi - p scattering

spin-averaged amplitude:

kinematic variable:

p p J/psi J/psi

Tψp(ν)

ν ≡ p q = s − u 4

unitarity

Im Tψp(ν) = 2√s qψp σtot

ψp(ν)

causality + crossing

subtracted dispersion relation:

Re Tψp(ν) = Tψp(0) + 2 π ν2 Z 1

νel

dν0 1 ν0 Im Tψp(ν0) ν0 2 − ν2

σtot

ψp = σel ψp + σinel ψp

σel

ψp ∝ Cel

⇣ 1 − νel ν ⌘bel ✓ ν νel ◆ael σinel

ψp

∝ Cin ⇣ 1 − νin ν ⌘bin ✓ ν νin ◆ain

parameterising cross section: directly sensitive to aψp

Forward J/psi - p scattering

Vector meson dominance (VMD) assumption:

σel

ψp =

✓Mψ efψ ◆2 ✓ qγp qψp ◆2 σ(γp → ψp) σinel

ψp

= ✓Mψ efψ ◆2 ✓ qγp qψp ◆2 σ(γp → c¯ cX) dσ dt

• t=0

(γp → ψp) = ✓efψ Mψ ◆2 ✓qψp qγp ◆2 dσ dt

• t=0

(ψp → ψp)

forward differential cross section:

• K. Redlich, H. Satz and G. M. Zinovjev, Eur. Phys. J. C 17, 461 (2000)
• V. D. Barger and R. J. N. Phillips, Phys. Lett. B 58, 433 (1975)

Forward J/psi - p scattering

HERA/ZEUS (1995) EMC (1982) Fermilab (1980) CERN/WA58 (1987) SLAC (1984) σ (γp ccX) (μb) 0.01 0.1 1 10 W (GeV) 10 100 HERA (2002) Fermilab (1981) EMC (1980) SLAC (1975) Tψp(0) = 45 Tψp(0) = 22.45 Tψp(0) = 0 dσ/dt (t=0) (nb/GeV2) 1 10 100 W (GeV) 10 100 HERA (2002) Fermilab/E401 (1981) Fermilab/E516 (1983) Fermilab/E687 (1993) SLAC (1975) Cornell (1975) σ (γp J/ψ p) (nb) 0,1 1 10 100 W (GeV) 10 100

Vector meson dominance (VMD) assumption:

σel

ψp =

✓Mψ efψ ◆2 ✓ qγp qψp ◆2 σ(γp → ψp) σinel

ψp

= ✓Mψ efψ ◆2 ✓ qγp qψp ◆2 σ(γp → c¯ cX) dσ dt

• t=0

(γp → ψp) = ✓efψ Mψ ◆2 ✓qψp qγp ◆2 dσ dt

• t=0

(ψp → ψp)

forward differential cross section:

• K. Redlich, H. Satz and G. M. Zinovjev, Eur. Phys. J. C 17, 461 (2000)
• V. D. Barger and R. J. N. Phillips, Phys. Lett. B 58, 433 (1975)

Forward J/psi - p scattering

HERA/ZEUS (1995) EMC (1982) Fermilab (1980) CERN/WA58 (1987) SLAC (1984) σ (γp ccX) (μb) 0.01 0.1 1 10 W (GeV) 10 100 HERA (2002) Fermilab (1981) EMC (1980) SLAC (1975) Tψp(0) = 45 Tψp(0) = 22.45 Tψp(0) = 0 dσ/dt (t=0) (nb/GeV2) 1 10 100 W (GeV) 10 100 HERA (2002) Fermilab/E401 (1981) Fermilab/E516 (1983) Fermilab/E687 (1993) SLAC (1975) Cornell (1975) σ (γp J/ψ p) (nb) 0,1 1 10 100 W (GeV) 10 100

simultaneously fitting

Vector meson dominance (VMD) assumption:

σel

ψp =

✓Mψ efψ ◆2 ✓ qγp qψp ◆2 σ(γp → ψp) σinel

ψp

= ✓Mψ efψ ◆2 ✓ qγp qψp ◆2 σ(γp → c¯ cX) dσ dt

• t=0

(γp → ψp) = ✓efψ Mψ ◆2 ✓qψp qγp ◆2 dσ dt

• t=0

(ψp → ψp)

forward differential cross section:

Bψ ∼ 3 MeV

aψp ∼ 0.05 fm

• K. Redlich, H. Satz and G. M. Zinovjev, Eur. Phys. J. C 17, 461 (2000)
• V. D. Barger and R. J. N. Phillips, Phys. Lett. B 58, 433 (1975)

Lepton pair photoproduction

VMD

p J/psi p J/psi p ɣ p J/psi

Lepton pair photoproduction

γ p → J/ψ p → e−e+ p VMD

p J/psi p J/psi p ɣ p J/psi

Lepton pair photoproduction

γ J/ψ e− e+ p p

p p e− e+ γ

dilepton photoproduction through J/psi:

Bethe-Heitler:

+

γ p → J/ψ p → e−e+ p

Mψ ' ie3 q0 2 f 2

ψ

2M 1 q0 2 M 2

ψ + iMψΓψ

Tψp ✓ ν = 1 2(s M 2

ψ M 2)

◆

× εµ(q, λ) · ¯ u(l−, s−)γνv(l+, s+)

× ¯ N(p0, s0

p)

⇢✓ gµν − q0µqν q · q0 ◆ + q · q0 (q · P)2 ✓ P µ − q · P q · q0 q0 µ ◆ ✓ P ν − q · P q · q0 qν ◆ N(p, sp)

t → 0

VMD

p J/psi p J/psi p ɣ p J/psi

Forward-backward asymmetry

AFB =

dσ dΩ(θCM) − dσ dΩ(θCM − π) dσ dΩ(θCM) + dσ dΩ(θCM − π)

Eγ = 10 GeV

• t = 0.6 GeV2

θe-e+ cm = 0 θe-e+ cm = 40° θe-e+ cm = 145° AFB −0.3 −0.2 −0.1 0.1 0.2 Mll (GeV) 2.95 3.00 3.05 3.10 Eγ = 10 GeV

• t = 0.6 GeV2

θe-e+ cm = 40° Tψp(0) = 0 Tψp(0) = 22.45 Tψp(0) = 45 AFB −0.3 −0.2 −0.1 0.1 0.2 Mll (GeV) 2.95 3.00 3.05 3.10 OG, M. Vanderhaeghen, PRD 94, 074001 (2016)

Upcoming experiment at JLab (Hall C) [PR12-16-007]

kinematic acceptance:

Summary

• probing the real part of the forward Compton and elastic

J/psi scattering amplitudes at various kinematics directly appears to be a missing tool for a thorough study of the processes

• a dilepton photoproduction experiment is proposed to

access the forward amplitudes directly

• some of the existing facilities are capable of carrying out

the proposed experiment in the near future

Interference term

2 T ∗

BH · TqCS ' e6 GE T1

L D M 2

ll t ·

n I II + III IV

• ,

D = 1 t 4M 2 I = 1 2Mν2 ⇥ a2 (2ME)2⇤ ⇥ t M 2

ll

⇤ n ⇥ t M 2

ll

⇤ a + (2ME) b

• II

= 2 ν ⇥ a2 (2ME)2⇤ t b III = 4M n ⇥ t M 2

ll

⇤2 a (2ME) ⇥ t + M 2

ll

⇤ b

• IV

= 16 M m2 ⇥ t M 2

ll

⇤ (Da + b) + (2ME) Db