Photon-Meson Pair Photoproduction: a New Way to Probe Generalized Parton Distributions

Introduction A new way to access GPDs Non-perturbative ingredients Computation Results: ρ Results: π Conclusion

Photon-meson pair photoproduction: a new way to probe Generalized Parton Distributions

Samuel Wallon

Sorbonne Université and Laboratoire de Physique Théorique CNRS / Université Paris Sud Orsay

Assemblée générale du GDR QCD - 2018 Ecole Polytechnique, 26 - 28 November 2018

27 November 2018 in collaboration with B. Pire (CPhT, Palaiseau), R. Boussarie (LPT Orsay), L. Szymanowski (NCBJ, Warsaw), G. Duplančić, K. Passek-Kumerički (IRB, Zagreb)

based on:

JHEP 1702 (2017) 054 [arXiv:1609.03830 [hep-ph]] (ργ production)

JHEP 18xx (2017) xx [arXiv:1809.08104 [hep-ph]] (πγ production) 1/43 Introduction A new way to access GPDs Non-perturbative ingredients Computation Results: ρ Results: π Conclusion The ultimate picture #$% ) *

' ( ! "

2/43 Introduction A new way to access GPDs Non-perturbative ingredients Computation Results: ρ Results: π Conclusion Extensions from DIS

DIS: inclusive process forward amplitude (t = 0) (optical theorem) → (DIS: Deep Inelastic Scattering) ± ± ex: e p → e X at HERA γ∗ γ∗ 2 2 x 1-dimensional structure Q Q ⇒ CF Structure Function s x x = Coeﬃcient Function ⊗ Parton Distribution Function (hard) (soft) pPDF p

DVCS: exclusive process non forward amplitude ( t s = W 2) → − ≪∗ (DVCS: Deep Vitual Compton Scattering) γ γ Q2 Fourier transf.: t impact parameter (x, t) 3-dimensional↔ structure ⇒ CF Amplitude s x + ξ x ξ − = Coeﬃcient Function ⊗ Generalized Parton Distribution (hard) (soft) ′ pGPD p

Müller et al. ’91 - ’94; Radyushkin ’96; Ji ’97 t 3/43 Introduction A new way to access GPDs Non-perturbative ingredients Computation Results: ρ Results: π Conclusion Extensions from DVCS

Meson production: γ replaced by ρ, π, · · · γ∗ ρ, π 2 Q z DA

CF 1+ z − Amplitude s x + ξ x ξ − = GPD ⊗ CF ⊗ Distribution Amplitude (soft) (hard) (soft) ′ hGPD h

t Collins, Frankfurt, Strikman ’97; Radyushkin ’97 proofs valid only for some restricted cases

4/43 Introduction A new way to access GPDs Non-perturbative ingredients Computation Results: ρ Results: π Conclusion Collinear factorization Meson electroproduction: factorization with a GPD and a DA

The building blocks Q2

H DA M(p,λ) Γ Γ

Γ′

Γ′ Γ, Γ′ : Dirac matrices compatible with quantum numbers: C, P, T, chirality GP D Similar structure for gluon exchange

5/43 Introduction A new way to access GPDs Non-perturbative ingredients Computation Results: ρ Results: π Conclusion Collinear factorization Twist 2 GPDs

Classiﬁcation of twist 2 GPDs For quarks, one should distinguish the exchanges without helicity ﬂip (chiral-even Γ′ matrices): 4 chiral-even GPDs: ξ=0,t=0 ξ=0,t=0 Hq −−−−−−→ PDF q, Eq, H˜ q −−−−−−→ polarized PDFs ∆q, E˜q

1 dz+ + − F q = eixP z hp′| q¯(− 1 z) γ+q( 1 z) |pi 2 2 + 2 Z 2π z =0,z⊥=0 +α 1 i σ ∆α = Hq(x,ξ,t)u ¯(p′)γ+u(p)+ Eq(x,ξ,t)u ¯(p′) u(p) , 2P + 2m 1 dz− + − F˜q = eixP z hp′| q¯(− 1 z) γ+γ q( 1 z) |pi 2 5 2 + 2 Z 2π z =0,z⊥=0 + 1 q ′ + q ′ γ5 ∆ = H˜ (x,ξ,t)u ¯(p )γ γ5u(p)+ E˜ (x,ξ,t)u ¯(p ) u(p) . 2P + 2m with helicity ﬂip ( chiral-odd Γ′ mat.): 4 chiral-odd GPDs: q ξ=0,t=0 q ˜ q ˜q HT −−−−−−→ quark transversity PDFs δq, ET , HT , ET 1 dz− + − eixP z hp′| q¯(− 1 z) i σ+i q( 1 z) |pi 2 2 + 2 Z 2π z =0,z⊥=0

1 P +∆i − ∆+P i γ+∆i − ∆+γi γ+P i − P +γi = u¯(p′) Hq iσ+i + H˜ q + Eq + E˜q 2P + T T m2 T 2m T m

6/43 Introduction A new way to access GPDs Non-perturbative ingredients Computation Results: ρ Results: π Conclusion Collinear factorization Twist 2 GPDs

Classiﬁcation of twist 2 GPDs analogously, for gluons:

4 gluonic GPDs without helicity ﬂip: ξ=0,t=0 Hg −−−−−−→ PDF xg Eg ξ=0,t=0 H˜ g −−−−−−→ polarized PDF x ∆g E˜g

4 gluonic GPDs with helicity ﬂip: g HT g ET ˜ g HT ˜g ET (no forward limit reducing to gluons PDFs here: a change of 2 units of helicity cannot be compensated by a spin 1/2 target)

7/43 Introduction A new way to access GPDs Non-perturbative ingredients Computation Results: ρ Results: π Conclusion Chiral-odd sector: Transversity of the nucleon using hard processes

What is transversity? Transverse spin content of the proton: + | ↑i(x) ∼ |→i | ←i | ↓i(x) ∼ |→i−|←i spin along x helicity states Observables which are sensitive to helicity ﬂip thus give access to transversity ∆T q(x). Poorly known.

Transversity GPDs are completely unknown experimentally.

For massless (anti)particles, chirality = (-)helicity

Transversity is thus a chiral-odd quantity

Since (in the massless limit) QCD and QED are chiral-even (γµ, γµγ5), the chiral-odd quantities (1, γ5, [γµ,γν ]) which one wants to measure should appear in pairs 8/43 Introduction A new way to access GPDs Non-perturbative ingredients Computation Results: ρ Results: π Conclusion Transversity of the nucleon using hard processes: using a two body ﬁnal state process?

How to get access to transversity GPDs? µ ν the dominant DA of ρT is of twist 2 and chiral-odd ([γ ,γ ] coupling) ∗ ↑ ′ unfortunately γ N ρT N = 0 → This cancellation is true at any order : such a process would require a helicity transfer of 2 from a photon.

lowest order diagrammatic argument:

α µ ν γ [γ ,γ ]γα 0 → [Diehl, Gousset, Pire], [Collins, Diehl]

9/43 Introduction A new way to access GPDs Non-perturbative ingredients Computation Results: ρ Results: π Conclusion Transversity of the nucleon using hard processes: using a two body ﬁnal state process?

Can one circumvent this vanishing?

This vanishing only occurs at twist 2

At twist 3 this process does not vanish [Ahmad, Goldstein, Liuti], [Goloskokov, Kroll]

However processes involving twist 3 DAs may face problems with factorization (end-point singularities) can be made safe in the high-energy kT −factorization approach [Anikin, Ivanov, Pire, Szymanowski, S.W.]

One can also consider a 3-body ﬁnal state process [Ivanov, Pire, Szymanowski, Teryaev], [Enberg, Pire, Szymanowski], [El Beiyad, Pire, Segond, Szymanowski, S. W.]

10/43 Introduction A new way to access GPDs Non-perturbative ingredients Computation Results: ρ Results: π Conclusion Probing GPDs using ρ or π meson + photon production

We consider the process γ N γ M N ′ M = meson → Collinear factorization of the amplitude for γ + N γ + M + N ′ 2 → at large MγM t′ t′

2 MγM TH 2 TH MγM φ φ φ → x + ξ x ξ M A B − N N ′ large angle factorization GP D à la Brodsky Lepage

t (small) 11/43 Introduction A new way to access GPDs Non-perturbative ingredients Computation Results: ρ Results: π Conclusion Probing chiral-even GPDs using π meson + photon production

Processes with 3 body ﬁnal states can give access to chiral-even GPDs t′

2 Mγρ TH

φ x + ξ x ξ π± − chiral-even twist 2 DA N N ′ GP D

t (small)

chiral-even twist 2 GPD

12/43 Introduction A new way to access GPDs Non-perturbative ingredients Computation Results: ρ Results: π Conclusion Probing chiral-even GPDs using ρ meson + photon production

Processes with 3 body ﬁnal states can give access to chiral-even GPDs t′

2 Mγρ TH

φ x + ξ x ξ ρ − L chiral-even twist 2 DA N N ′ GP D

t (small)

chiral-even twist 2 GPD

13/43 Introduction A new way to access GPDs Non-perturbative ingredients Computation Results: ρ Results: π Conclusion Probing chiral-odd GPDs using ρ meson + photon production

Processes with 3 body ﬁnal states can give access to chiral-odd GPDs t′

2 Mγρ TH

φ x + ξ x ξ ρ − T chiral-odd twist 2 DA N N ′ GP D

t (small)

chiral-odd twist 2 GPD

14/43 Introduction A new way to access GPDs Non-perturbative ingredients Computation Results: ρ Results: π Conclusion Probing chiral-odd GPDs using ρ meson + photon production

Processes with 3 body ﬁnal states can give access to chiral-odd GPDs How did we manage to circumvent the no-go theorem for 2 2 processes? →

Typical non-zero diagram for a transverse ρ meson

the σ matrices (from DA and GPD sides) do not kill it anymore!

15/43 Introduction A new way to access GPDs Non-perturbative ingredients Computation Results: ρ Results: π Conclusion Master formula based on leading twist 2 factorization

The ρ example

1 1 dx dz T (x,ξ,z) H(x,ξ,t)Φρ(z)+ A∝ Z−1 Z0 × · · ·

Both the DA and the GPD can be q k either chiral-even or chiral-odd. At twist 2 the longitudinal ρ DA is zpρ chiral-even and the transverse ρ DA is H ρ chiral-odd. Hence we will need both chiral-even (1 − z)pρ and chiral-odd non-perturbative x + ξ x − ξ building blocks and hard parts.

GPD

p1 p2

16/43 Introduction A new way to access GPDs Non-perturbative ingredients Computation Results: ρ Results: π Conclusion Kinematics

Kinematics to handle GPD in a 3-body ﬁnal state process

q use a Sudakov basis : k hard scale2 2 p⊥ light-cone vectors p, n with 2 p · n = s Mγρ zpρ ∝ assume the following kinematics: H ∆ ≪ p ρ } ⊥ ⊥ 2 2 2 M , mρ ≪ Mγρ (1 − z)pρ x + ξ x − ξ initial state particle momenta: µ µ µ µ M2 µ GPD q = n , p1 = (1+ ξ) p + s(1+ξ) n p1 p2 ﬁnal state particle momenta:

M 2 + ~p 2 ∆ pµ = (1 ξ) pµ + t nµ +∆µ ↓ 2 − s(1 ξ) ⊥ − 2 µ (~pt ∆~ t/2) ∆ kµ = α nµ + − pµ + pµ ⊥ , αs ⊥ − 2 ~ 2 2 µ µ µ (~pt + ∆t/2) + mρ µ µ ∆⊥ pρ = αρ n + p p⊥ , αρs − − 2 17/43 Introduction A new way to access GPDs Non-perturbative ingredients Computation Results: ρ Results: π Conclusion Non perturbative chiral-even building blocks

Helicity conserving GPDs at twist 2 :

− − dz ixP +z 1 − + 1 − e p2,λ2 ψ¯q z γ ψ z p1,λ1 Z 4π h | − 2 2 | i α+ 1 q + q iσ ∆α = u¯(p2,λ2) H (x,ξ,t)γ + E (x,ξ,t) 2P + 2m

− − dz ixP +z 1 − + 5 1 − e p2,λ2 ψ¯q z γ γ ψ z p1,λ1 Z 4π h | − 2 2 | i 5 + 1 q + 5 q γ ∆ = u¯(p2,λ2) H˜ (x,ξ,t)γ γ + E˜ (x,ξ,t) 2P + 2m

We will consider the simplest case when ∆⊥ = 0. In that case and in the forward limit ξ → 0 only the Hq and H˜ q terms survive.

Helicity conserving (vector) DA at twist 2 :

µ 1 µ 0 p −iup·x 0 u¯(0)γ u(x) ρ (p,s) = fρ du e φk(u) h | | i √2 Z0

18/43 Introduction A new way to access GPDs Non-perturbative ingredients Computation Results: ρ Results: π Conclusion Non perturbative chiral-odd building blocks

Helicity ﬂip GPD at twist 2 :

− − dz ixP +z 1 − +i 1 − e p2,λ2 ψ¯q z iσ ψ z p1,λ1 Z 4π h | − 2 2 | i + i + i 1 q +i ˜ q P ∆ ∆ P = + u¯(p2,λ2) HT (x,ξ,t)iσ + HT (x,ξ,t) −2 2P MN + i + i + i + i q γ ∆ ∆ γ ˜q γ P P γ + ET (x,ξ,t) − + ET (x,ξ,t) − u(p1,λ1) 2MN MN

We will consider the simplest case when ∆⊥ = 0. q In that case and in the forward limit ξ → 0 only the HT term survives.

Transverse ρ DA at twist 2 :

1 µν 0 i µ ν ν µ ⊥ −iup·x 0 u¯(0)σ u(x) ρ (p,s) = (ǫρ p ǫρp )fρ du e φ⊥(u) h | | i √2 − Z0

19/43 Introduction A new way to access GPDs Non-perturbative ingredients Computation Results: ρ Results: π Conclusion Models for DAs

Asymptotical DAs

We take the simplistic asymptotic form of the (normalized) DAs (i.e. no evolution):

φπ(z)= φ (z)= φρ⊥(z) = 6z(1 z) . ρk − For the π case, a non asymptotical wave function can be also investigated: 8 φπ(z)= z(1 z) . π − p (under investigation)

20/43 Introduction A new way to access GPDs Non-perturbative ingredients Computation Results: ρ Results: π Conclusion Model for GPDs: based on the Double Distribution ansatz

Realistic Parametrization of GPDs

GPDs can be represented in terms of Double Distributions [Radyushkin] based on the Schwinger representation of a toy model for GPDs which has the structure of a triangle diagram in scalar φ3 theory

1 1−|β| Hq(x,ξ,t =0)= dβ dα δ(β + ξα x) f q (β, α) Z−1 Z−1+|β| − ansatz for these Double Distributions [Radyushkin]:

chiral-even sector: f q (β, α, t = 0) = Π(β, α) q(β)Θ(β) − Π(−β, α)q ¯(−β) Θ(−β) , f˜q (β, α, t = 0) = Π(β, α)∆q(β)Θ(β)+Π(−β, α) ∆¯q(−β) Θ(−β) . chiral-odd sector: q fT (β, α, t = 0) = Π(β, α) δq(β)Θ(β) − Π(−β, α) δq¯(−β) Θ(−β) , 2 2 3 (1−β) −α : proﬁle function Π(β, α)= 4 (1−β)3 simplistic factorized ansatz for the t-dependence: q q H (x,ξ,t)= H (x,ξ,t = 0) FH (t) × C2 with FH (t)= (t−C)2 a standard dipole form factor (C = .71 GeV) 21/43 Introduction A new way to access GPDs Non-perturbative ingredients Computation Results: ρ Results: π Conclusion Model for GPDs: based on the Double Distribution ansatz

Sets of used PDFs

q(x) : unpolarized PDF [GRV-98] and [MSTW2008lo, MSTW2008nnlo, ABM11nnlo, CT10nnlo]

∆q(x) polarized PDF [GRSV-2000]

δq(x) : transversity PDF [Anselmino et al.]

22/43 Introduction A new way to access GPDs Non-perturbative ingredients Computation Results: ρ Results: π Conclusion Model for GPDs: based on the Double Distribution ansatz

Typical sets of chiral-even GPDs (C = 1 sector) ↔ 2 2 − 2 ξ = .1 SγN = 20 GeV and Mγρ = 3.5 GeV

u(−) 1 4 d(−) H (x,ξ) H (x,ξ) 8 1 2

1 0 6

8 4 6

4 2 2 x x - 1 .0 - 0 .5 0 .0 0 .5 1 .0 - 1 .0 - 0 .5 0 .0 0 .5 1 .0 Hq(−)(x,ξ,t)= Hq(x,ξ,t)+ Hq( x,ξ,t) − ﬁve Ansätze for q(x): GRV-98, MSTW2008lo, MSTW2008nnlo, ABM11nnlo, CT10nnlo

u(−) 3 d(−) H˜ (x,ξ) H˜ (x,ξ) 1 .0 2

0 .5 1

H H - 1 .0 - 0 .5 0 .5 1 .0 - 1 .0 - 0 .5 0 .5 1 .0

- 1 - 0 .5

- 2 - 1 .0 - 3 H˜ q(−)(x,ξ,t)= H˜ q(x,ξ,t) H˜ q( x,ξ,t) − − “valence” and “standard” (ﬂavor-asymmetries in the polarized antiquark sector are neglected): two GRSV Ansätze for ∆q(x) 23/43 Introduction A new way to access GPDs Non-perturbative ingredients Computation Results: ρ Results: π Conclusion Model for GPDs: based on the Double Distribution ansatz

Typical sets of chiral-odd GPDs (C = 1 sector) −

↔ 2 2 2 ξ = .1 SγN = 20 GeV and Mγρ = 3.5 GeV

u(−) d HT (x,ξ) (−) HT (x,ξ) 1 .2 x - 1 .0 - 0 .5 0 .5 1 .0 1 .0

0 .8 - 0 .2

0 .6 - 0 .4

0 .4

0 .2 - 0 .6 x - 1 .0 - 0 .5 0 .0 0 .5 1 .0 - 0 .8 Hq(−)(x,ξ,t)= Hq (x,ξ,t)+ Hq ( x,ξ,t) T T T − “valence” and “standard”: two GRSV Ansätze for ∆q(x) ⇒ two Ansätze for δq(x)

24/43 Introduction A new way to access GPDs Non-perturbative ingredients Computation Results: ρ Results: π Conclusion Computation of the hard part

20 diagrams to compute

The other half can be deduced by q q¯ (anti)symmetry depending on ↔ C-parity in t channel − Red diagrams cancel in the chiral-odd case

25/43 Introduction A new way to access GPDs Non-perturbative ingredients Computation Results: ρ Results: π Conclusion Final computation

Final computation

1 1 dx dz T (x,ξ,z) H(x,ξ,t) Φρ(z) A∝ Z−1 Z0

One performs the z integration analytically q k using an asymptotic DA z(1 z) ∝ − zpρ One then plugs our GPD models into the H ρ formula and performs the integral w.r.t. x

numerically. (1 − z)pρ x + ξ x − ξ Diﬀerential cross section: dσ 2 GPD ′ 2 = 2 |M|2 3 . dtdu dMγρ 32S Mγρ(2π) p1 p2 −t=(−t)min γN

2 = averaged amplitude squared |M| Kinematical parameters: S2 , M 2 and u′ γN γρ − 26/43 Introduction A new way to access GPDs Non-perturbative ingredients Computation Results: ρ Results: π Conclusion

Fully diﬀerential cross section: ρL Chiral even cross section at t =( t)min − − dσ dσeven −6 even (pb GeV−6) (pb GeV ) 2 ′ dM 2 d( u′)d( t) · dMγρd( u )d( t) · γρ − − − − 2 0 1 4 0

1 2 0 1 5 1 0 0

8 0 1 0

6 0

4 0 5

2 0

0 0 1 2 3 4 5 1 2 3 4 5

u′ (GeV2) u′ (GeV2) − − proton target neutron target

2 SγN = 20 GeV 2 2 Mγρ = 3, 4, 5, 6 GeV solid: “valence” model

dotted: “standard” model 27/43 Introduction A new way to access GPDs Non-perturbative ingredients Computation Results: ρ Results: π Conclusion

Fully diﬀerential cross section: ρT Chiral odd cross section at t =( t)min − − dσ dσ odd (pb GeV−6) odd (pb GeV−6) dM 2 d( u′)d( t) · dM 2 d( u′)d( t) · γρ − − γρ − − 3 .5 2 .0 3 .0

2 .5 1 .5 2 .0 1 .0 1 .5

1 .0 0 .5 0 .5

0 .0 0 .0 1 2 3 4 5 1 .0 1 .5 2 .0 2 .5 3 .0 3 .5 4 .0 4 .5 5 .0 u′(GeV2) u′(GeV2) − − proton target neutron target “valence” and “standard” models, “valence“ model only each of them with ±2σ [S. Melis]

2 SγN = 20 GeV 2 2 Mγρ = 3, 4, 5, 6 GeV

28/43 Introduction A new way to access GPDs Non-perturbative ingredients Computation Results: ρ Results: π Conclusion Phase space integration

Evolution of the phase space in ( t, u′) plane − − large angle scattering: M 2 u′ t′ γρ ∼− ∼− ′ 2 ′ 2 2 in practice: u > 1 GeV and t > 1 GeV and ( t)min 6 t 6 .5 GeV − 2 − − − this ensures large Mγρ

2 example: SγN = 20 GeV u′ u′ u′ 1 .2 2 .0 − − 1 .4 − 1 .0 1 .2 1 .5 0 .8 1 .0 0 .8 0 .6 1 .0 0 .6 0 .4 0 .4 0 .5 0 .2 0 .2 0 .0 0 .0 0 .0 0 .0 0 .1 0 .2 0 .3 0 .4 0 .5 0 .0 0 .1 0 .2 0 .3 0 .4 0 .5 0 .0 0 .1 0 .2 0 .3 0 .4 0 .5 t t t − 2 2 − 2 −2 Mγρ = 2.2 GeV Mγρ = 2.5 GeV Mγρ = 3 GeV u′ u′ u′

− 4 − 7 − 8 6 3 6 5

4 2 4 3

2 1 2 1

0 0 0 0 .0 0 .1 0 .2 0 .3 0 .4 0 .5 0 .0 0 .1 0 .2 0 .3 0 .4 0 .5 0 .0 0 .1 0 .2 0 .3 0 .4 0 .5 t t t −2 −2 −2 Mγρ = 5 GeV Mγρ = 8 GeV Mγρ = 9 GeV 29/43 Introduction A new way to access GPDs Non-perturbative ingredients Computation Results: ρ Results: π Conclusion

Variation with respect to SγN

Mapping (SγN , Mγρ) (S˜γN , M˜ γρ) 7→ One can save a lot of CPU time: (α, ξ) and GPDs(ξ,x) M In the generalized Bjorken limit: ′ −u α = 2 Mγρ 2 Mγρ ξ = 2 2 2(SγN −M )−Mγρ 2 2 Given SγN (= 20 GeV ), with its grid in Mγρ, choose another S˜γN . One can get the corresponding grid in M˜ γρ by just keeping the same ξ’s:

˜ 2 ˜ 2 2 SγN M Mγρ = Mγρ − 2 , SγN M − From the grid in u′, the new grid in u˜′ is given by just keeping the same α’s: − − ˜ 2 ′ Mγρ ′ u˜ = 2 ( u ) . − Mγρ −

2 a single set of numerical computations is required (we take SγN = 20 GeV ) ⇒ 30/43 Introduction A new way to access GPDs Non-perturbative ingredients Computation Results: ρ Results: π Conclusion

Single diﬀerential cross section: ρL

Chiral even cross section

dσeven −2 dσeven −2 2 (pb GeV ) dMγρ · 2 (pb GeV ) dMγρ ·

1 .0 8

0 .8 6 0 .6 4 0 .4

2 0 .2

3 4 5 6 7 8 9 3 4 5 6 7 8 9

2 2 2 2 Mγρ (GeV ) Mγρ (GeV ) proton target neutron target “valence” scenario

2 SγN vary in the set 8, 10, 12, 14, 16, 18, 20 GeV (from left to right)

typical JLab kinematics

31/43 Introduction A new way to access GPDs Non-perturbative ingredients Computation Results: ρ Results: π Conclusion

Single diﬀerential cross section: ρT Chiral odd cross section

dσodd −2 2 (pb GeV ) dMγρ ·

0 .2 0

0 .1 5

0 .1 0

0 .0 5

0 .0 0 2 4 6 8 1 0

2 2 Mγρ (GeV ) 2 SγN = 20 GeV

Various ansätze for the PDFs ∆q used to build the GPD HT : dotted curves: “standard” scenario solid curves: “valence” scenario deep-blue and red curves: central values light-blue and orange: results with 2σ. ± 32/43 Introduction A new way to access GPDs Non-perturbative ingredients Computation Results: ρ Results: π Conclusion

Single diﬀerential cross section: ρT Chiral odd cross section

dσodd −2 2 (pb GeV ) dMγρ ·

0 .3 0

0 .2 5

0 .2 0

0 .1 5

0 .1 0

0 .0 5

3 4 5 6 7 8 9

2 2 Mγρ(GeV )

proton target, “valence” scenario

2 SγN vary in the set 8, 10, 12, 14, 16, 18, 20 GeV (from left to right)

typical JLab kinematics 33/43 Introduction A new way to access GPDs Non-perturbative ingredients Computation Results: ρ Results: π Conclusion

Integrated cross-section: ρL

Chiral even cross section

σeven (pb) σeven (pb)

3 .0 2 0 2 .5

1 5 2 .0

1 .5 1 0 1 .0 5 0 .5

5 1 0 1 5 2 0 5 1 0 1 5 2 0

2 2 SγN (GeV ) SγN (GeV )

proton target neutron target

solid red: “valence” scenario dashed blue: “standard” one

34/43 Introduction A new way to access GPDs Non-perturbative ingredients Computation Results: ρ Results: π Conclusion

Integrated cross-section: ρT

Chiral odd cross section

σodd (pb) σodd (pb)

0 .6 0 .4

0 .5 0 .3 0 .4

0 .3 0 .2

0 .2 0 .1 0 .1

5 1 0 1 5 2 0 5 1 0 1 5 2 0

2 2 SγN (GeV ) SγN (GeV ) proton target neutron target

solid red: “valence” scenario dashed blue: “standard” one

35/43 Introduction A new way to access GPDs Non-perturbative ingredients Computation Results: ρ Results: π Conclusion Counting rates for 100 days: ρ

example: JLab Hall B untagged incoming γ Weizsäcker-Williams distribution ⇒ With an expected luminosity of = 100 nb−1s−1, for 100 days of run: L 5 Chiral even case : ≃ 1.9 10 ρL .

3 Chiral odd case : ≃ 7.5 10 ρT

36/43 Introduction A new way to access GPDs Non-perturbative ingredients Computation Results: ρ Results: π Conclusion Fully diﬀerential cross section: π±

Chiral even sector: π± at t =( t)min − − dσγπ+ −6 dσγπ− −6 2 ′ (pb GeV ) 2 ′ (pb GeV ) dM d( u )d( t) · dM − d( u )d( t) · γπ+ − − γπ − − 20 20

15 15

10 10

5 5

0 0 1.0 1.5 2.0 2.5 3.0 3.5 1.0 1.5 2.0 2.5 3.0 3.5

u′ (GeV2) u′ (GeV2) − − π+ photoproduction (proton target) π− photoproduction (neutron target) 2 2 2 SγN = 20 GeV Mγρ = 4 GeV vector GPD / axial GPD / total result

solid: “valence” model dotted: “standard” model 37/43 Introduction A new way to access GPDs Non-perturbative ingredients Computation Results: ρ Results: π Conclusion Fully diﬀerential cross section: π±

Chiral even sector: π± at t =( t)min − −

dσγπ+ −6 dσγπ− −6 2 ′ (pb GeV ) 2 ′ (pb GeV ) dM d( u )d( t) · dM − d( u )d( t) · γπ+ − − γπ − − 3 0 3 0 2 5 2 5 2 0 2 0

1 5 1 5

1 0 1 0

5 5

0 0 1 2 3 4 5 1 2 3 4 5 u′ (GeV2) u′ (GeV2) − − π+ photoproduction (proton target) π− photoproduction (neutron target)

2 SγN = 20 GeV 2 2 Mγρ = 3, 4, 5, 6 GeV solid: “valence” model

dotted: “standard” model 38/43 Introduction A new way to access GPDs Non-perturbative ingredients Computation Results: ρ Results: π Conclusion Single diﬀerential cross section: π±

Chiral even sector: π±

dσγπ+ −2 dσγπ− −2 2 (pb GeV ) 2 (pb GeV ) dMγπ+ · dMγπ− · 3.0 2.5 2.5 2.0 2.0 1.5 1.5

1.0 1.0

0.5 0.5

2 4 6 8 2 4 6 8

2 2 2 2 Mγπ+ (GeV ) Mγπ− (GeV ) π+ photoproduction (proton target) π− photoproduction (neutron target)

2 SγN vary in the set 8, 10, 12, 14, 16, 18, 20 GeV (from left to right)

solid: “valence” model dotted: “standard” model

39/43 Introduction A new way to access GPDs Non-perturbative ingredients Computation Results: ρ Results: π Conclusion Integrated cross-section: π±

Chiral even sector: π±

σγπ+ (pb) σγπ− (pb)

7 7 6 6

5 5

4 4

3 3

2 2

1 1

5 1 0 1 5 2 0 5 1 0 1 5 2 0

2 2 SγN (GeV ) SγN (GeV )

π+ photoproduction (proton target) π− photoproduction (neutron target)

solid red: “valence” scenario dashed blue: “standard” one

40/43 Introduction A new way to access GPDs Non-perturbative ingredients Computation Results: ρ Results: π Conclusion Counting rates for 100 days: π±

example: JLab Hall B untagged incoming γ Weizsäcker-Williams distribution ⇒ With an expected luminosity of = 100 nb−1s−1, for 100 days of run: L π+ : ≃ 104

π− : ≃ 4 × 104

41/43 Introduction A new way to access GPDs Non-perturbative ingredients Computation Results: ρ Results: π Conclusion Conclusion Results and experimental perspectives

High statistics for the chiral-even components: enough to extract H (H˜ ?) and test the universality of GPDs in ρ0, ρ± (not shown) and π± channels In this chiral-even sector: analogy with Timelike Compton Scattering, the γρ or γπ pair playing the role of the γ∗. ρ-channel: chiral-even component w.r.t. the chiral-odd one: σodd/σeven 1/25. ∼ possible separation ρL/ρT through an angular analysis of its decay products Future: study of polarization observables ⇒ sensitive to the interference of these two amplitudes: very sizable eﬀect expected, of the order of 20%

The Bethe Heitler component (outgoing γ emitted from the incoming lepton) is: zero for the chiral-odd case suppressed for the chiral-even case Possible measurement at JLab (Hall B, C, D) A similar study could be performed at COMPASS. EIC, LHC in UPC?

42/43 Introduction A new way to access GPDs Non-perturbative ingredients Computation Results: ρ Results: π Conclusion Conclusion Future For γπ± photoproduction: Eﬀect of non asymptotical π DA? 8 φπ(z)= z(1 − z) π p AdS/QCD correspondence, dynamical chiral symmetry breaking on the light-front, etc. Eﬀect of twist 3 contributions? presumably important for π electroproduction Observables sensitive to quantum interferences: γ beam asymmetry Target polarization asymmetries For ρ0γ photoproduction: built from the π+π− decay product angular distribution ⇒ chiral odd versus chiral even Loop corrections: in progress Accessing GPDs in light nuclei: spin-0 case using an 4He target

Crossed-channel: using the J-PARC π beam (spallation reaction of a proton beam): πN γγN → The processes γN γπ0N ′ and γN γη0N ′ are of particular interest: → → they give an access to the gluonic GPDs at Born order. Our result can also be applied to electroproduction (Q2 = 0) after adding 6 Bethe-Heitler contributions and interferences. New release of PARTONS platform 43/43 Restrictions and further studies Details on various contributions (ρ case) Eﬀects of an experimental angular restriction for the produced γ

Angular distribution of the produced γ ρL photoproduction

after boosting to the lab frame

1 dσeven 1 dσeven 1 dσeven σeven dθ σeven dθ σeven dθ

0 .1 0 0 .1 5 0 .2 0

0 .0 8 0 .1 5 0 .1 0 0 .0 6 0 .1 0 0 .0 4 0 .0 5 0 .0 5 0 .0 2

0 .0 0 0 .0 0 0 .0 0 0 1 0 2 0 3 0 4 0 0 5 1 0 1 5 2 0 2 5 3 0 3 5 0 5 1 0 1 5 2 0 2 5 3 0

θ θ θ

2 2 2 SγN = 10 GeV SγN = 15 GeV SγN = 20 GeV

2 2 2 2 2 2 Mγρ = 3, 4 GeV Mγρ = 3, 4, 5 GeV Mγρ = 3, 4, 5 GeV JLab Hall B detector equipped between 5◦ and 35◦

this is safe! ⇒ 1/6 Restrictions and further studies Details on various contributions (ρ case) Eﬀects of an experimental angular restriction for the produced γ

Angular distribution of the produced γ ρL photoproduction

dσeven −2 dσeven −2 dσeven −2 2 (pb GeV ) 2 (pb GeV ) 2 (pb GeV ) dMγρ · dMγρ · dMγρ ·

7 8 6 8

5 6 6 4 4 3 4

2 2 2 1

0 0 0 2 .0 2 .5 3 .0 3 .5 4 .0 2 3 4 5 6 7 2 3 4 5 6 7 8 9

2 2 2 2 2 2 Mγρ (GeV ) Mγρ (GeV ) Mγρ (GeV )

2 2 2 SγN = 10 GeV SγN = 15 GeV SγN = 20 GeV

◦ ◦ ◦ ◦ ◦ ◦ θmax = 35 , 30 , 25 , 20 , 15 , 10

JLab Hall B detector equipped between 5◦ and 35◦

this is safe! ⇒ 2/6 Restrictions and further studies Details on various contributions (ρ case) Eﬀects of an experimental angular restriction for the produced γ

Angular distribution of the produced γ ρT photoproduction

after boosting to the lab frame

1 dσodd 1 dσodd 1 dσodd σodd dθ σodd dθ σodd dθ

0 .2 0 0 .3 5 0 .2 5 0 .3 0 0 .1 5 0 .2 0 0 .2 5

0 .1 5 0 .2 0 0 .1 0 0 .1 5 0 .1 0 0 .1 0 0 .0 5 0 .0 5 0 .0 5

0 .0 0 0 .0 0 0 .0 0 0 1 0 2 0 3 0 4 0 0 1 0 2 0 3 0 4 0 0 1 0 2 0 3 0 4 0

θ θ θ

2 2 2 SγN = 10 GeV SγN = 15 GeV SγN = 20 GeV

2 2 2 2 2 2 Mγρ = 3, 4 GeV Mγρ = 3.5, 5, 6.5 GeV Mγρ = 4, 6, 8 GeV JLab Hall B detector equipped between 5◦ and 35◦

this is safe! ⇒ 3/6 Restrictions and further studies Details on various contributions (ρ case) Eﬀects of an experimental angular restriction for the produced γ

Angular distribution of the produced γ ρT photoproduction

dσodd −2 dσodd −2 dσodd −2 2 (pb GeV ) 2 (pb GeV ) 2 (pb GeV ) dMγρ · dMγρ · dMγρ ·

0 .3 0 0 .2 0 0 .1 2

0 .2 5 0 .1 0 0 .1 5 0 .2 0 0 .0 8

0 .1 5 0 .1 0 0 .0 6

0 .1 0 0 .0 4 0 .0 5 0 .0 5 0 .0 2

0 .0 0 0 .0 0 0 .0 0 2 .0 2 .5 3 .0 3 .5 4 .0 2 3 4 5 6 7 2 3 4 5 6 7 8 9

2 2 2 2 2 2 Mγρ (GeV ) Mγρ (GeV ) Mγρ (GeV )

2 2 2 SγN = 10 GeV SγN = 15 GeV SγN = 20 GeV

◦ ◦ ◦ ◦ ◦ ◦ θmax = 35 , 30 , 25 , 20 , 15 , 10

JLab Hall B detector equipped between 5◦ and 35◦

this is safe! ⇒ 4/6 Restrictions and further studies Details on various contributions (ρ case) Chiral-even cross section

Contribution of u versus d ρL photoproduction

dσeven −6 dσeven −6 (pb GeV ) 2 ′ (pb GeV ) dM 2 d( u′)d( t) · dMγρd( u )d( t) · γρ − − − − 1 0 0 3 0

2 5 8 0

2 0 6 0 1 5 4 0 1 0

2 0 5

0 0 1 .0 1 .5 2 .0 2 .5 1 .0 1 .5 2 .0 2 .5

u′(GeV2) u′(GeV2) − − proton neutron

2 2 Mγρ = 4 GeV . Both vector and axial GPDs are included. u + d quarks u quark d quark

Solid: “valence” model dotted: “standard” model u-quark contribution dominates due to the charge eﬀect

the interference between u and d contributions is important and negative. 5/6 Restrictions and further studies Details on various contributions (ρ case) Chiral-even cross section

Contribution of vector versus axial amplitudes ρL photoproduction

dσeven dσeven −6 −6 (pb GeV ) 2 ′ (pb GeV ) dM 2 d( u′)d( t) · dMγρd( u )d( t) · γρ − − − −

7 0 8

6 0

5 0 6

4 0 4 3 0

2 0 2 1 0

0 0 1 .0 1 .5 2 .0 2 .5 1 .0 1 .5 2 .0 2 .5

u′(GeV2) u′(GeV2) − − proton neutron

2 2 Mγρ = 4 GeV . Both u and d quark contributions are included. vector + axial amplitudes / vector amplitude / axial amplitude

solid: “valence” model dotted: “standard” model dominance of the vector GPD contributions no interference between the vector and axial amplitudes 6/6