Looking at hadrons in the backward direction with hard ...Looking at hadrons in the backward direction with hard photons: the Transition Distribution Amplitudes & DVCS on virtual pions

Looking at hadrons in the backward direction with hard photons:the Transition Distribution Amplitudes

& DVCS on virtual pions

J.P. LansbergCPHT – Ecole polytechnique

Seminaire de physique des particules

LPT – Paris-Sud, Orsay

March 2, 2010

Collaborative work with S.J. Brodsky, M.Diehl, B. Pire and L. Szymanowski

J.P. Lansberg (CPHT – Ecole polytechnique) Transition Distribution Amplitudes March 2, 2010 1 / 31

Outline

Part 1: Reminders

1 Reminder on DIS and DVCS

Part 2: Backward regime

2 Definition of the Transition Distribution Amplitudes

3 Backward electroproduction of a pion

Part 3: Extensions

4 TDA studies at GSI/FAIR

5 TDA and Intrinsic Charm

Part 3: DVCS on virtual pions

6 A few words on DVCS on virtual-pion target

Part 4: Outlooks


Part I

Reminders


Reminder on DIS and DVCS

Looking into the proton . . .

ß Study of the proton content via (deeply) inelastic scattering (DIS):

γ⋆, µ

x

γ⋆, νq2

proton proton

x = x′

q2

x

usual parton distributions

Wµν = (−gµν +qµqνq2

)F1(x , q2)

+PµPνP.q

F2(x , q2)

P = Pµ − P.q

q2 qµ

ß Factorisation in the Bjorken limit: Q2 →∞, x fixed

ß Probability Distribution, since being an amplitude squared

x x

=

x2

Sum over spect.

> 0

ß Probability to find a parton with a momentum fraction x : q(x)F2(x , q2) = x

∑q

e2q q(x , q2)





γ⋆, µ

x

γ⋆, νq2

proton proton

x = x′

q2

x


Factorisation


)F1(x , q2)

+PµPνP.q

F2(x , q2)

P = Pµ − P.q

q2 qµ



x x

=

x2

Sum over spect.

> 0


∑q

e2q q(x , q2)





γ⋆, µ

x

γ⋆, νq2

proton proton

x = x′

q2

x


Factorisation


)F1(x , q2)

+PµPνP.q

F2(x , q2)

P = Pµ − P.q

q2 qµ



x x

=

x2

Sum over spect.

> 0


∑q

e2q q(x , q2)





γ⋆, µ

x

γ⋆, νq2

proton proton

x = x′

q2

x


Factorisation


)F1(x , q2)

+PµPνP.q

F2(x , q2)

P = Pµ − P.q

q2 qµ



x x

=

x2

Sum over spect.

> 0


∑q

e2q q(x , q2)



Interferences in the proton. . .

ß Study of interferences in the protonvia Deeply Virtual Compton Scattering (DVCS):

γ?

x x′

γQ2

hadron hadron

Pert.

t

Non-pert. object

x 6= x′

GPDGPD

W 2

For Q2 t, described in termsof 4 generalised parton distri-bution: GPDs

idem for meson electroproduction

ß Factorisation in the generalised Bjorken limit: Q2 →∞, t, x fixedß The GPDs are not probability distributions

x x′

=

x 6= x′

p p′

∗

p′p×

x′x

but are universal !ß Interpretration only at the amplitude level

Amplitude of probabilityfor a proton to emit a quark with x & to absorb another with x ′




ß Study of interferences in the protonvia Deeply Virtual Compton Scattering (DVCS):

γ⋆

x x′

γQ2

proton proton

Pert.

t

Non-pert. object

x 6= x′

GPDGPD

W 2Factorisation


idem for meson electroproductionß Factorisation in the generalised Bjorken limit: Q2 →∞, t, x fixedß The GPDs are not probability distributions

x x′

=

x 6= x′

p p′

∗

p′p×

x′x






ß Study of interferences in the proton

via Deeply Virtual Compton Scattering (DVCS):

γ⋆

x x′

Q2

proton protont

Non-pert. object

x 6= x′

GPD

ρ, π, . . .

Pert.

W 2factorisation




x x′

=

x 6= x′

p p′

∗

p′p×

x′x








γ⋆

x x′

Q2

proton protont

Non-pert. object

x 6= x′

GPD

ρ, π, . . .

Pert.

W 2factorisation



ß Factorisation in the generalised Bjorken limit: Q2 →∞, t, x fixed

ß The GPDs are not probability distributions

x x′

=

x 6= x′

p p′

∗

p′p×

x′x








γ⋆

x x′

Q2

proton protont

Non-pert. object

x 6= x′

GPD

ρ, π, . . .

Pert.

W 2factorisation




x x′

=

x 6= x′

p p′

∗

p′p×

x′x

but are universal !

ß Interpretration only at the amplitude levelAmplitude of probability

for a proton to emit a quark with x & to absorb another with x ′






γ⋆

x x′

Q2

proton protont

Non-pert. object

x 6= x′

GPD

ρ, π, . . .

Pert.

W 2factorisation




x x′

=

x 6= x′

p p′

∗

p′p×

x′x





Success of the factorised framework . . .

Angular dependence of measured asymmetries comingfrom Bethe-Heitler/ DVCS interferences

JLab data at Q2 = 2.3 GeV2, t = −0.28 and = −0.23 GeV2



Success of the factorised framework . . .

Angular dependence of measured asymmetries comingfrom Bethe-Heitler/ DVCS interferences

JLab data at Q2 = 2.3 GeV2, t = −0.28 and = −0.23 GeV2


Part II

Looking in the backward region


Definition of the Transition Distribution Amplitudes

Hard limit for backward exclusive processes

ß Let us analyse Hard Electroproduction of a meson

but backward !l

meson nearly atrest in thetarget rest frameproton

GPD

γ⋆

x x′

Q2

proton

Pert.

t

γ⋆

Q2

meson

Pert.

u

GPDproton

t → u

TDA

meson

x2 x3x1

proton

ß The kinematics imposes the exchange of 3 quarks in the u channel

ß Factorisation in the generalised Bjorken limit: Q2 →∞, u, x fixedB. Pire, L. Szymanowski, PLB 622:83,2005.

ß The object factorised from the hard part is a Transition DistributionAmplitude (TDA)

=p p′

∗

p×

p′

ß Interpretation at the amplitude level in the ERBL region (for xi > 0)

Amplitude of probability to find a meson within the proton !





but backward !l


GPD

γ⋆

x x′

Q2

proton

Pert.

t

γ⋆

Q2

meson

Pert.

u

GPDproton

t → u

TDA

meson

x2 x3x1

proton




=p p′

∗

p×

p′







but backward !l


GPD

γ⋆

x x′

Q2

proton

Pert.

t

γ⋆

Q2

meson

Pert.

u

GPDproton

t → u

TDA

meson

x2 x3x1

proton




=p p′

∗

p×

p′







but backward !l


GPD

γ⋆

x x′

Q2

proton

Pert.

t

γ⋆

Q2

meson

Pert.

u

GPDproton

t → u

TDA

meson

x2 x3x1

proton




=p p′

∗

p×

p′







but backward !l


GPD

γ⋆

x x′

Q2

proton

Pert.

t

γ⋆

Q2

meson

Pert.

u

GPDproton

t → u

TDA

meson

x2 x3x1

proton




=p p′

∗

p×

p′


Amplitude of probability to find a meson within the proton !J.P. Lansberg (CPHT – Ecole polytechnique) Transition Distribution Amplitudes March 2, 2010 8 / 31


p → π: parametrisation

ë p → π (at Leading twist)ß ∆T = 0: 3 TDAs (3× p(↑)→ uud(↑↑↓) + π)

TDA DA (Chernyak-Zhitnitsky)

4〈π0| εijkuiα(z1n)uj

β(z2n)dkγ(z3n) |p, sp〉 ∝h

Vπ0

1 (xi , ξ,∆2)(p/ C)αβ(N+

sp )γ+

Aπ0

1 (xi , ξ,∆2)(p/ γ5C)αβ(γ5N+

sp )γ+

Tπ0

1 (xi , ξ,∆2)(σρpC)αβ(γρN+

sp )γi

4〈0|εijkuiα(z1n)uj

β(z2n)dkγ(z3n)|p〉 ∝h

V (xi )(p/C)αβ(γ5N+sp )γ+

A(xi )(p/γ5C)αβ(N+sp )γ+

T (xi )(iσρp C)αβ(γργ5N+sp )γ

i

B. Pasquini et al., PRD 80:014017,2009.V π0

1 → D↑↑↓,↑ + D↑↓↑,↑Aπ

0

1 → D↑↑↓,↑ − D↑↓↑,↑T π0

1 → D↑↑↑,↓




ë p → π (at Leading twist)ß ∆T = 0: 3 TDAs (3× p(↑)→ uud(↑↑↓) + π)

TDA DA (Chernyak-Zhitnitsky)

4〈π0| εijkuiα(z1n)uj

β(z2n)dkγ(z3n) |p, sp〉 ∝h

Vπ0

1 (xi , ξ,∆2)(p/ C)αβ(N+

sp )γ+

Aπ0

1 (xi , ξ,∆2)(p/ γ5C)αβ(γ5N+

sp )γ+

Tπ0

1 (xi , ξ,∆2)(σρpC)αβ(γρN+

sp )γi

4〈0|εijkuiα(z1n)uj

β(z2n)dkγ(z3n)|p〉 ∝h

V (xi )(p/C)αβ(γ5N+sp )γ+

A(xi )(p/γ5C)αβ(N+sp )γ+

T (xi )(iσρp C)αβ(γργ5N+sp )γ

iB. Pasquini et al., PRD 80:014017,2009.V π0

1 → D↑↑↓,↑ + D↑↓↑,↑Aπ

0

1 → D↑↑↓,↑ − D↑↓↑,↑T π0

1 → D↑↑↑,↓




ß ∆T 6= 0: 8 TDAs ( 12 × 2× (2× 2× 2)× 1)

4〈π0(pπ)| εijkuiα(z1n)uj

β(z2n)dkγ(z3n) |p(p1, s)〉 =

ifN

fπ×h

Vπ0

1 (xi , ξ,∆2)(p/ C)αβ(N+)γ + Vπ0

2 (xi , ξ,∆2)(p/ C)αβ(∆/T N+)γ

+Aπ0

1 (xi , ξ,∆2)(p/ γ5C)αβ(γ5N+)γ + Aπ

0

2 (xi , ξ,∆2)(p/ γ5C)αβ(γ5∆/T N+)γ

+Tπ0

1 (xi , ξ,∆2)(σpµC)αβ(γµN+)γ + Tπ0

2 (xi , ξ,∆2)(σp∆T

C)αβ(N+)γ

+Tπ0

3 (xi , ξ,∆2)(σpµC)αβ(σµ∆T N+)γ + Tπ0

4 (xi , ξ,∆2)(σp∆T

C)αβ(∆/T N+)γi

B. Pasquini et al., PRD 80:014017,2009.

V π0

2 → D↑↓↑,↓ + D↑↑↓,↓ Aπ0

2 → D↑↓↑,↓ − D↑↑↓,↓T π0

2 → D↑↑↑,↑ + D↑↓↓,↑ T π0

3 → D↑↑↑,↑ − D↑↓↓,↑T π0

4 → D↑↓↓,↓




ß ∆T 6= 0: 8 TDAs ( 12 × 2× (2× 2× 2)× 1)

4〈π0(pπ)| εijkuiα(z1n)uj

β(z2n)dkγ(z3n) |p(p1, s)〉 =

ifN

fπ×h

Vπ0

1 (xi , ξ,∆2)(p/ C)αβ(N+)γ + Vπ0

2 (xi , ξ,∆2)(p/ C)αβ(∆/T N+)γ

+Aπ0

1 (xi , ξ,∆2)(p/ γ5C)αβ(γ5N+)γ + Aπ

0

2 (xi , ξ,∆2)(p/ γ5C)αβ(γ5∆/T N+)γ

+Tπ0

1 (xi , ξ,∆2)(σpµC)αβ(γµN+)γ + Tπ0

2 (xi , ξ,∆2)(σp∆T

C)αβ(N+)γ

+Tπ0

3 (xi , ξ,∆2)(σpµC)αβ(σµ∆T N+)γ + Tπ0

4 (xi , ξ,∆2)(σp∆T

C)αβ(∆/T N+)γi

B. Pasquini et al., PRD 80:014017,2009.

V π0

2 → D↑↓↑,↓ + D↑↑↓,↓ Aπ0

2 → D↑↓↑,↓ − D↑↑↓,↓T π0

2 → D↑↑↑,↑ + D↑↓↓,↑ T π0

3 → D↑↑↑,↑ − D↑↓↓,↑T π0

4 → D↑↓↓,↓J.P. Lansberg (CPHT – Ecole polytechnique) Transition Distribution Amplitudes March 2, 2010 10 / 31

Backward electroproduction of a pion

More quantitatively: the pionic content of the proton

JPL, B. Pire, L. Szymanowski,PRD 75:074004,2007

ß Let us analyse the soft pion limit

〈πa(k)|O|p(p, s)〉 =− i

fπ〈0|[Qa

5 ,O]|p(p, s)〉

+igA

4fπp · kXs′

〈0|O|p(p, s ′)〉u(p, s ′)k/γ5τau(p, s)

ß Direct relation between the TDAs, 〈πa(k)|O|p(p, s)〉, andthe proton wavefunction (DAs), 〈0|O|p(p, s)〉

proton

x3

x2

x1

V π0

1 (x1, x2, x3, ξ,∆2)

Eπ→mπ→ 1

4ξV` x1

2ξ,x2

2ξ,x3

2ξ

Áπ

0

1 (x1, x2, x3, ξ,∆2)

Eπ→mπ→ 1

4ξA` x1

2ξ,x2

2ξ,x3

2ξ

´Tπ0

1 (x1, x2, x3, ξ,∆2)

Eπ→mπ→ 3

4ξT` x1

2ξ,x2

2ξ,x3

2ξ

´ß Similar relations obtained for the proton-pion DAs 〈0|O|π(k)p(p, s)〉

V.M Braun et al. PRD75:014021,2007

ß Note that Eπ = mπ in the proton r.f. ⇔ ξ = M−mπM+mπ

' 0.74 6= 1






〈πa(k)|O|p(p, s)〉 =− i

fπ〈0|[Qa

5 ,O]|p(p, s)〉

+igA

4fπp · kXs′

〈0|O|p(p, s ′)〉u(p, s ′)k/γ5τau(p, s)


proton

x3

x2

x1

V π0

1 (x1, x2, x3, ξ,∆2)

Eπ→mπ→ 1

4ξV` x1

2ξ,x2

2ξ,x3

2ξ

Áπ

0

1 (x1, x2, x3, ξ,∆2)

Eπ→mπ→ 1

4ξA` x1

2ξ,x2

2ξ,x3

2ξ

´Tπ0

1 (x1, x2, x3, ξ,∆2)

Eπ→mπ→ 3

4ξT` x1

2ξ,x2

2ξ,x3

2ξ




' 0.74 6= 1






〈πa(k)|O|p(p, s)〉 =− i

fπ〈0|[Qa

5 ,O]|p(p, s)〉

+igA

4fπp · kXs′

〈0|O|p(p, s ′)〉u(p, s ′)k/γ5τau(p, s)


proton

x3

x2

x1

V π0

1 (x1, x2, x3, ξ,∆2)

Eπ→mπ→ 1

4ξV` x1

2ξ,x2

2ξ,x3

2ξ

Áπ

0

1 (x1, x2, x3, ξ,∆2)

Eπ→mπ→ 1

4ξA` x1

2ξ,x2

2ξ,x3

2ξ

´Tπ0

1 (x1, x2, x3, ξ,∆2)

Eπ→mπ→ 3

4ξT` x1

2ξ,x2

2ξ,x3

2ξ




' 0.74 6= 1



Beyond the soft limit

ß The factorised framework goes beyond the soft limit

ß One needs input from models, such asthe pion cloud model, ... B. Pasquini, et al.PRD 80:014017,2009.

0

0.4

0.8

1.21.6

00.4

0.81.2

1.6

0.1

0.3

0.5

0

0.4

0.8

1.21.6

0.1

0.3

V1pΠ

x1 x20

0.4

0.81.2

1.6

0.40.8

1.2

1.6

0

-0.01

0.01

0

0.4

0.81.2

1.6

0

-

A1pΠ

x1 x2

0

0.4

0.8

1.21.6

00.4

0.81.2

1.6

0.5

1

1.5

2

0

0.4

0.8

1.21.6

0.5

1

V2pΠ

x1 x20

0.4

0.8

1.21.6

0.40.8

1.2

1.6

0.4

0.8

1.2

0

0.4

0.8

1.21.6

0.4

T3pΠ

x1 x2




ß The factorised framework goes beyond the soft limitß One needs input from models, such asthe pion cloud model, ... B. Pasquini, et al.PRD 80:014017,2009.

0

0.4

0.8

1.21.6

00.4

0.81.2

1.6

0.1

0.3

0.5

0

0.4

0.8

1.21.6

0.1

0.3

V1pΠ

x1 x20

0.4

0.81.2

1.6

0.40.8

1.2

1.6

0

-0.01

0.01

0

0.4

0.81.2

1.6

0

-

A1pΠ

x1 x2

0

0.4

0.8

1.21.6

00.4

0.81.2

1.6

0.5

1

1.5

2

0

0.4

0.8

1.21.6

0.5

1

V2pΠ

x1 x20

0.4

0.8

1.21.6

0.40.8

1.2

1.6

0.4

0.8

1.2

0

0.4

0.8

1.21.6

0.4

T3pΠ

x1 x2




ß The factorised framework goes beyond the soft limitß One needs input from models, such asthe pion cloud model, ... B. Pasquini, et al.PRD 80:014017,2009.

0

0.4

0.8

1.21.6

00.4

0.81.2

1.6

0.1

0.3

0.5

0

0.4

0.8

1.21.6

0.1

0.3

V1pΠ

x1 x20

0.4

0.81.2

1.6

0.40.8

1.2

1.6

0

-0.01

0.01

0

0.4

0.81.2

1.6

0

-

A1pΠ

x1 x2

0

0.4

0.8

1.21.6

00.4

0.81.2

1.6

0.5

1

1.5

2

0

0.4

0.8

1.21.6

0.5

1

V2pΠ

x1 x20

0.4

0.8

1.21.6

0.40.8

1.2

1.6

0.4

0.8

1.2

0

0.4

0.8

1.21.6

0.4

T3pΠ

x1 x2



Backward Electroproduction of a pion: II

ß First evaluation: backward electroproduction of a pion for Eπ → mπ

using the soft limit for the TDAs

TDA

DAℓ1

ℓ3

k1 k3

Mh

P (p1)

P ′(p2)γ⋆(q)

π(pπ)

ß The amplitude at the Leading-twist accuracy:

Mλs1s2

= −i(4παs)2

√4παemf 2

N

54fπQ4u(p2, s2)ε/(λ)γ5u(p1, s1)

×1+ξ∫−1+ξ

d3x

1∫0

d3y

(2

7∑α=1

Tα +14∑α=8

Tα

)






TDA

DAℓ1

ℓ3

k1 k3

Mh

P (p1)

P ′(p2)γ⋆(q)

π(pπ)


Mλs1s2

= −i(4παs)2

√4παemf 2

N

54fπQ4u(p2, s2)ε/(λ)γ5u(p1, s1)

×1+ξ∫−1+ξ

d3x

1∫0

d3y

(2

7∑α=1

Tα +14∑α=8

Tα

)






TDA

DAℓ1

ℓ3

k1 k3

Mh

P (p1)

P ′(p2)γ⋆(q)

π(pπ)


Mλs1s2

= −i(4παs)2

√4παemf 2

N

54fπQ4u(p2, s2)ε/(λ)γ5u(p1, s1)

×1+ξ∫−1+ξ

d3x

1∫0

d3y

(2

7∑α=1

Tα +14∑α=8

Tα

)



Hard part: Mh for γ?p → pπ0 at ∆T = 0

JPL, B. Pire, L. Szymanowski,PRD 75:074004,2007.



Backward Electroproduction of a pion: III


At ξ = 0.8 and using CZ Distribution Amplitudes, one gets:

TDA

DAℓ1

ℓ3

k1 k3

Mh

P (p1)

P ′(p2)γ⋆(q)

π(pπ)

0.1

1

10

100

0 2 4 6 8 10

dσ /d

Ω∗ π|

θ∗ π=π

(nb/

sr)

Q2 (GeV2)

NOTE: the result with asymptotic DAs is not zero !



Backward Electroproduction of a pion: III


At ξ = 0.8 and using CZ Distribution Amplitudes, one gets:

TDA

DAℓ1

ℓ3

k1 k3

Mh

P (p1)

P ′(p2)γ⋆(q)

π(pπ)

0.1

1

10

100

0 2 4 6 8 10

dσ /d

Ω∗ π|

θ∗ π=π

(nb/

sr)

Q2 (GeV2)

NOTE: the result with asymptotic DAs is not zero !



Backward Electroproduction of a pion: IV


á Model-independent predictions

ß Scaling law for the amplitude:

M(Q2) ∝ α2s (Q2)

Q4

ß Approximate Q2-independence of the ratios

M(γ?p → pπ)

M(γ?p → pγ),M(γ?p → pγ)

M(γ?p → p)and

dσ(pp→`+`−π0)dQ2

dσ(pp→`+`−)dQ2

(see later)

ß Dominance of γ?Tp → pπ, . . .

ß Spinorial structures at ∆T 6= 0:u(p2, s2)ε/(λ)γ5u(p1, s1) and εµ∆T ,ν u(p2, s2)(σµν + gµν)γ5u(p1, s1)

At ∆T 6= 0, σTT 6= 0 and cos 2ϕ dependence





á Model-independent predictionsß Scaling law for the amplitude:

M(Q2) ∝ α2s (Q2)

Q4


M(γ?p → pπ)


M(γ?p → p)and


dσ(pp→`+`−)dQ2

(see later)









M(Q2) ∝ α2s (Q2)

Q4


M(γ?p → pπ)


M(γ?p → p)and


dσ(pp→`+`−)dQ2

(see later)









M(Q2) ∝ α2s (Q2)

Q4


M(γ?p → pπ)


M(γ?p → p)and


dσ(pp→`+`−)dQ2

(see later)









M(Q2) ∝ α2s (Q2)

Q4


M(γ?p → pπ)


M(γ?p → p)and


dσ(pp→`+`−)dQ2

(see later)






Backward Electroproduction of a meson: data

ß Data from JLab exist for the π Analysis approved, out soon (K. Park)

ß “Visible signal in the yield of ω at 180” (G. Huber, Sept. 09)

ß Data for the electroduction of η (V. Kubarovsky, P. Stoler)

To be modelled

ß We are working on the theory(∆T 6= 0, DGLAP-region contribution, other models, ...)



Lattice calculations

Gavela, King, Sachrajda, Martinelli,...a lattice computation of proton decay amplitudes

Nucl.Phys.B312:269,1989

á Calculation of the matrix elements for the GUT decays

p → π0e+ p → π+ν p → K 0 + lepton

á Evaluation of the two moments matrix elements

εijk〈π0|(uiCd j)ukγ |P〉 = A1Nγ εijk〈π0|(uiCγ5d

j)(γ5uk)γ |P〉 = A2Nγ

á Update of this study would be very usefulß would fix the normalisation of the TDAs via Sum Rulesß would give information on their t-dependence


Part III

Extensions


TDA studies at GSI/FAIR

TDAs in exclusive processes at GSI/FAIR

JPL, B. Pire, L. Szymanowski PRD76 :111502(R),2007

ß pp → γ?π0 can be studied by PANDAß Involves the same TDAs as for backward electroproduction

In the GPD case, after crossing, we have to deal with GDAs

k1 k3

p(pp) π(pπ)

Mh

ℓ1DA

p(pp)

ℓ3

TDA

γ⋆(q) ℓ−

ℓ+





ß GSI-FAIR: Ep ≤ 15 GeV ⇒W 2 ≤ 30 GeV2

0.01

0.1

1

10

100

6 12 18 24 30

dσ /d

t| ∆T=

0 (n

b/G

eV2 )

W2 (GeV2) (a)

|pzπ|=0

|pzπ|=155 MeV

0.01

0.1

1

10

100

5 10 15 20

dσ /d

t dQ

2 | ∆T=

0 (p

b/G

eV4 )

Q2 (GeV2) (b)

W2=5 GeV2

W2=10 GeV2

W2=20 GeV2

ß σ`+`−π0

(7 < Q2 < 8GeV2,W 2 = 10GeV2,∆T < 0.5GeV) ∼ 100fb.ß Expected

∫dtL of about 2 fb−1 for a 100-day experiment

ß Other channels are also of much interest, such aspp → `+`−η or pp → `+`−ρ0






0.01

0.1

1

10

100

6 12 18 24 30

dσ /d

t| ∆T=

0 (n

b/G

eV2 )

W2 (GeV2) (a)

|pzπ|=0

|pzπ|=155 MeV

0.01

0.1

1

10

100

5 10 15 20

dσ /d

t dQ

2 | ∆T=

0 (p

b/G

eV4 )

Q2 (GeV2) (b)

W2=5 GeV2

W2=10 GeV2

W2=20 GeV2

ß σ`+`−π0









0.01

0.1

1

10

100

6 12 18 24 30

dσ /d

t| ∆T=

0 (n

b/G

eV2 )

W2 (GeV2) (a)

|pzπ|=0

|pzπ|=155 MeV

0.01

0.1

1

10

100

5 10 15 20

dσ /d

t dQ

2 | ∆T=

0 (p

b/G

eV4 )

Q2 (GeV2) (b)

W2=5 GeV2

W2=10 GeV2

W2=20 GeV2

ß σ`+`−π0






Future application to charmonium production

ë J/ψ decay in proton antiprotonwell accounted by the perturbative mechanism

c

c

J/ψ

p

p

ë pp → J/ψπ0 at small tcan be described likewise

J/ψ

p

c

c

π0p

ß this process is used to search for new charmonium states (hc ,. . . )ß will be extensively studied at GSIß For now, comparisons are possible with previous calculations

Soft pion limit M.K. Gaillard, et al., PLB 110:489,1982.

T.Barnes, X.Li, PRD 75:054018,2007





c

c

J/ψ

p

p


J/ψ

p

c

c

π0p



T.Barnes, X.Li, PRD 75:054018,2007





c

c

J/ψ

p

p


J/ψ

p

c

c

π0p



T.Barnes, X.Li, PRD 75:054018,2007


TDA and Intrinsic Charm

Heavy quarks in the proton . . .

ß Protons can contain nonperturbative fluctuations of heavy quarks QQfor instance the so called Intrinsic Charm

S.J. Brodsky et al. PLB93:451-455,1980

proton

uu

d

Q

Q

ß Key point: large-x heavy-quark content at low Q2

does not come from gluon splitting from DGLAP evolution

ß Recent global PDF analyis: one can accomodate more IC than expected〈xcc〉 ' 3% is possible

µ = 1.3→ 100 GeV J.Pumplin et al. PRD75:054029,2007.

ß bb et tt also possible but suppressed as M−2Q

ß Could be uncovered in diffractive Higgs productione.g. S.J Brodsky et al. , PRD73:113005,2006






proton

uu

d

Q

Q












proton

uu

d

Q

Q












proton

uu

d

Q

Q










ß The real impact of IC is controversial: difficult to find an undisputable probe

ß Dedicated test: γ?p → p J/Ψ in the TDA regionS.J. Brodsky, JPL, work in progress

TDA

DAℓ1

ℓ3

k1 k3

Mh

P (p1)

P ′(p2)γ⋆(q)

J/ψ(pψ)

Proton J/ψ

u du

〈J/ψ|ǫabcua(x1)ub(x2)d

c(x3)|Proton〉

ß one needs sufficient W 2 to be away from the thresholdÞ at threshold (M + mψ), the proton and the J/ψ have no relative momentum

ß For W M + mψ,Þ t → 0: usual diffractive production: target stays nearly at rest, J/ψ fastÞ u → 0: “backward” region: J/ψ nearly at rest, proton fast

ß JLab 12(11) GeV →Wmax =√

(0.942 + 2 · 11 · 0.94) ' 4.64 GeV:not quite enough

ß Only COMPASS could do itÞ 1 < Q2 < 7 GeV2

Þ 0.03 < xB < 0.2: for large Q2, W ∈ [5 : 15] GeV




ß The real impact of IC is controversial: difficult to find an undisputable probeß Dedicated test: γ?p → p J/Ψ in the TDA region

S.J. Brodsky, JPL, work in progress

TDA

DAℓ1

ℓ3

k1 k3

Mh

P (p1)

P ′(p2)γ⋆(q)

J/ψ(pψ)

Proton J/ψ

u du


c(x3)|Proton〉












TDA

DAℓ1

ℓ3

k1 k3

Mh

P (p1)

P ′(p2)γ⋆(q)

J/ψ(pψ)

Proton J/ψ

u du


c(x3)|Proton〉












TDA

DAℓ1

ℓ3

k1 k3

Mh

P (p1)

P ′(p2)γ⋆(q)

J/ψ(pψ)

Proton J/ψ

u du


c(x3)|Proton〉


ß For W M + mψ,Þ t → 0: usual diffractive production: target stays nearly at rest, J/ψ fast

Þ u → 0: “backward” region: J/ψ nearly at rest, proton fastß JLab 12(11) GeV →Wmax =

√(0.942 + 2 · 11 · 0.94) ' 4.64 GeV:

not quite enoughß Only COMPASS could do it

Þ 1 < Q2 < 7 GeV2







TDA

DAℓ1

ℓ3

k1 k3

Mh

P (p1)

P ′(p2)γ⋆(q)

J/ψ(pψ)

Proton J/ψ

u du


c(x3)|Proton〉












TDA

DAℓ1

ℓ3

k1 k3

Mh

P (p1)

P ′(p2)γ⋆(q)

J/ψ(pψ)

Proton J/ψ

u du


c(x3)|Proton〉












TDA

DAℓ1

ℓ3

k1 k3

Mh

P (p1)

P ′(p2)γ⋆(q)

J/ψ(pψ)

Proton J/ψ

u du


c(x3)|Proton〉









Heavy quarks in the proton . . .S.J. Brodsky, JPL, work in progress

ß Modelling the proton to charmonium TDA (pseudoscalar case)

Þ “SU(4)” spin-flavour symmetry:

V p→Q = T p→Q Ap→Q = 0

Þ Non-relativistic approx for QQ: Charmonium DA ∝ fQδ(xc − xc)(xc + xc = xQ)

Þ Light cone inspired form for the 5 particle IC Fock State

ψ(x1, x2, x3, xc ,xc ,Q2) = δ(1−

∑i

xi )

Γ

(m2p − m2

c( 1xc

+ 1xc

)− m2q( 1

x1+ 1

x2+ 1

x3))

(1)

(Effective masses (from the kT integration) m2c ' 1.8 GeV, m2

q ' 0.45 GeV)

Þ Only in ERBL region (xi > 0)

Þ Stay tuned !









ψ(x1, x2, x3, xc ,xc ,Q2) = δ(1−

∑i

xi )

Γ

(m2p − m2

c( 1xc

+ 1xc

)− m2q( 1

x1+ 1

x2+ 1

x3))

(1)


q ' 0.45 GeV)


Þ Stay tuned !









ψ(x1, x2, x3, xc ,xc ,Q2) = δ(1−

∑i

xi )

Γ

(m2p − m2

c( 1xc

+ 1xc

)− m2q( 1

x1+ 1

x2+ 1

x3))

(1)


q ' 0.45 GeV)


Þ Stay tuned !









ψ(x1, x2, x3, xc ,xc ,Q2) = δ(1−

∑i

xi )

Γ

(m2p − m2

c( 1xc

+ 1xc

)− m2q( 1

x1+ 1

x2+ 1

x3))

(1)


q ' 0.45 GeV)


Þ Stay tuned !









ψ(x1, x2, x3, xc ,xc ,Q2) = δ(1−

∑i

xi )

Γ

(m2p − m2

c( 1xc

+ 1xc

)− m2q( 1

x1+ 1

x2+ 1

x3))

(1)


q ' 0.45 GeV)


Þ Stay tuned !J.P. Lansberg (CPHT – Ecole polytechnique) Transition Distribution Amplitudes March 2, 2010 25 / 31

Part IV

DVCS on virtual pions


A few words on DVCS on virtual-pion target


π+

neutron

e e′

proton

γ?

TDA + GPD

γ

π+

Þ e(`) + p(p)→ e(`′) + γ(q′) + π+(p′π) + n(p′) q = `− `′

pπ = p − p′ xB = Q2

2p·q y = p·qp·` t = (p − p′)2 xπ = pπ·`

p·`(xπ =fraction of energy of the virtual pion from the proton in the ep c.m)

Þ For the πγ subprocess,we further define:

tπ = (pπ − p′π)2 sπ = (pπ + q)2 xπB = Q2

2pπ·q

Þ GPD regime: |tπ| Q2

Þ One pion-exchange approximation: t small.

This imposes xπ not too large (−t ≥ x2πm2

N

1−xπ)

Þ On the other hand, xπmin ≈ 1ymax

sπmin+Q2min

s ; s cannot be too small

Þ Neglecting the dependence of the eπ cross section on the pion virtuality t

d4σ(ep → eγπn)

dy dQ2 dtπ dφπ≈Z

dxπ Π(xπ, |t|max)d4σ(eπ → eγπ)

dyπ dQ2 dtπ dφπ

(for |t|max = 0.3 GeV2 (solid) and |t|max = 0.5 GeV2 (dashed))




π+

neutron

e e′

proton

γ?

TDA + GPD

γ

π+

Þ e(`) + p(p)→ e(`′) + γ(q′) + π+(p′π) + n(p′) q = `− `′pπ = p − p′ xB = Q2

2p·q y = p·qp·` t = (p − p′)2 xπ = pπ·`




2pπ·q




N

1−xπ)


sπmin+Q2min



d4σ(ep → eγπn)



dyπ dQ2 dtπ dφπ





π+

neutron

e e′

proton

γ?

TDA + GPD

γ

π+


2p·q y = p·qp·` t = (p − p′)2 xπ = pπ·`




2pπ·q




N

1−xπ)


sπmin+Q2min



d4σ(ep → eγπn)



dyπ dQ2 dtπ dφπ





π+

neutron

e e′

proton

γ?

TDA + GPD

γ

π+


2p·q y = p·qp·` t = (p − p′)2 xπ = pπ·`




2pπ·q




N

1−xπ)


sπmin+Q2min



d4σ(ep → eγπn)



dyπ dQ2 dtπ dφπ





π+

neutron

e e′

proton

γ?

TDA + GPD

γ

π+


2p·q y = p·qp·` t = (p − p′)2 xπ = pπ·`




2pπ·q




N

1−xπ)


sπmin+Q2min



d4σ(ep → eγπn)



dyπ dQ2 dtπ dφπ





π+

neutron

e e′

proton

γ?

TDA + GPD

γ

π+


2p·q y = p·qp·` t = (p − p′)2 xπ = pπ·`




2pπ·q




N

1−xπ)


sπmin+Q2min



d4σ(ep → eγπn)



dyπ dQ2 dtπ dφπ





π+

neutron

e e′

proton

γ?

TDA + GPD

γ

π+


2p·q y = p·qp·` t = (p − p′)2 xπ = pπ·`




2pπ·q




N

1−xπ)


sπmin+Q2min



d4σ(ep → eγπn)



dyπ dQ2 dtπ dφπ





D. Amrath, M. Diehl, JPL, EPJC58:179-192,2008.

Þ Finally, we want to avoid the effect of πn resonances: M2nπ (mN + mπ)2

Þ M2nπ ' x−1

π [...] + m2N + m2

π: we prefer low xπ, and tπ away for its min value.

Þ Not so easy

Þ In brief, all those conditions imposes to wait for JLab-12 GeV






Þ M2nπ ' x−1

π [...] + m2N + m2


Þ Not so easy







Þ M2nπ ' x−1

π [...] + m2N + m2


Þ Not so easy







Þ M2nπ ' x−1

π [...] + m2N + m2


Þ Not so easy




A few words on DVCS on virtual-pion targetD. Amrath, M. Diehl, JPL, EPJC58:179-192,2008.

Defining the weighted differences

ScosφπC

=

Zdφπ cosφπ

»dσ(e` = +1)

dφπ−

dσ(e` = −1)

dφπ

–S

sinφπL

=

Zdφπ sinφπ

»dσ(P` = +1)

dφπ−

dσ(P` = −1)

dφπ

–

of cross sections for different beam charge or beam polarization.

Q2min sπmin |t|max |tπ|max ymax M2

πn min σBH σVCS σINT ScosφπC

SsinφπL

2 4 0.3 0.7 0.85 — 18.4 0.88 −0.18 0.39 7.57

2 4 0.3 0.7 0.8 — 5.12 0.29 −0.09 0.17 2.17

2 4 0.3 0.7 0.9 — 45.6 1.86 −0.27 0.64 17.9

2 4 0.2 0.7 0.85 — 0.41 0.016 −0.002 0.004 0.16

2 4 0.5 0.7 0.85 — 105 6.52 −2.32 5.00 46.2

2.5 4 0.3 0.7 0.85 — 2.55 0.103 −0.010 0.018 0.96

2 5 0.3 0.7 0.85 — 0.30 0.013 −0.003 0.008 0.12

2 4 0.3 0.5 0.85 — 16.2 0.69 −0.09 0.18 6.30

2 4 0.3 0.7 0.85 1.5 13.4 0.67 −0.19 0.42 5.72

2 4 0.3 0.7 0.85 1.8 5.08 0.31 −0.14 0.30 2.46

(Limiting values of Q2, sπ , t, tπ , and M2πn are given in units of GeV2, and cross sections in units of fb.)


Part V

Outlooks


Perspectives

Perspectives (for the TDAs)

Þ Further quantitative predictions require modelsß Soft pion limit: OKß 4-ple distribution (spectral representation: double distr. for GPD):

to be doneß etc.

Þ Experimental data are necessary to test the pictureand then to extract physics

Þ ...expected from

ß JLab-6 GeV: Backward electroproduction of π, ηß GSI: pp → γ?π0, pp → J/ψπ0, pp → γ?γ, . . .ß JLab-12 GeV: e.g. DVCS on pionß B-factories (γ?γ → MM) possible: TDA γ → Mß COMPASS: γ?p → pJ/ψ ... EIC ?


Perspectives



to be doneß etc.


Þ ...expected from



Perspectives



to be doneß etc.


Þ ...expected from



Documents

Looking at hadrons in the backward direction with hard ...Looking at hadrons in the backward direction with hard photons: the Transition Distribution Amplitudes & DVCS on virtual pions