Ⅱ-4. Hadron Physics

RIKEN Accel. Prog. Rep. 56 (2023)
RIKEN
Accel. Prog. Rep. 56 (2023)

Signature of the gluon orbital angular momentum†
S. Bhattacharya,∗1 R. Boussarie,∗2 and Y. Hatta∗1,∗3
The Relativistic Heavy Ion Collider (RHIC) spin
program at Brookhaven National Laboratory has revealed that the gluon helicity contribution ∆G to theproton spin sum rule1
1= ∆Σ + ∆G + Lq + Lg ,2
2

the gluon helciity GPD, respectively. We observe aninteresting interplay between the gluon OAM and thegluon helicity. The latter contribution was missed in
the previous calculation of a related observable.1)
In Fig. 1, we show our numerical result for the crosssection for the EIC kinematics at δϕ = ϕl⊥ − ϕ∆⊥ = 0for Q2 = 2.7 GeV2 plotted as a function of skewness
ξ (longitudinal momentum fraction the proton loses inscattering). We see that the OAM and helicity contributions are comparable in magnitude, but with opposite signs. This is consistent with the theoreticalprediction3) that the gluon OAM and gluon helicity
parton distributions cancel in the small-x region. Forlarger values of Q2 , our result (3) predicts that the twocontributions add up. This can be tested in experimentby varying Q2 .

(1)

is nonvanishing and likely sizable. Together with theknown quark helicity contribution ∆Σ ∼ 0.3, the result
indicates that parton helicities account for a signiﬁcant
fraction of the proton spin. Yet, there still remainhuge uncertainties
about the small-x contribution to∫1∆G = 0 dx∆G(x). Resolving this issue is one of themajor goals of the future Electron-Ion Collider (EIC).
Another obvious goal of the EIC is to measure the orbital angular momentum (OAM) of quarks and gluons
Lq,g . However, progress in this direction is relatively
slow, although there have been a few suggestions1) for
experimental observables in recent years. In this report we propose a new and promising observable forthe gluon OAM in Deep Inelastic Scattering and makea quantitative prediction for the EIC.
Speciﬁcally, we calculate longitudinal double spin
asymmetry (DSA) in exclusive dijet production inelectron-proton collisions ep → γ ∗ p → jjp′ where boththe incoming electron and proton are longitudinallypolarized. The part of the cross section which depends
on the proton and electron polarizations takes the formdσ hp hl ∼ hp hl cos(ϕl⊥ − ϕ∆⊥ )Re(A2 A∗3 ),d (pb/ GeV 2)

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24q⊥

2 + µ2q⊥}

∗1
∗2
∗340
20
00.0004

0.00060.00080.00100.0012(2)Fig. 1. Spin-dependent part of the cross section at Q2 =2.7 GeV2 as a function of the skewness variable ξ. The‘OAM’ and ‘Helicity’ contributions come from the Lgand H̃g terms in (3), respectively.

In conclusion, we have made the ﬁrst quantitative
prediction for an observable sensitive to the parton
OAM at the EIC. Our result adequately demonstrates
the feasibility of accessing the gluon OAM from DSA.
It also emphasizes that, due to the admixture of thegluon helicity contribution, in order to extract theOAM reliably, one needs an accurate determinationof ∆G(x) down to x ∼ 10−3 .

(3)]

Hg(2)∗ Lg − Hg(1)∗ H̃g ,where q⊥ is the transverse momentum of the two jets
which are assumed to be symmetric and 4µ2 = Q2
(1,2)
is the photon virtuality. Hg , Lg and H̃g are theCompton form factors of the unpolarized gluon generalized parton distribution (GPD), the gluon OAM and†

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20

where hl , hp = ±1 are the electron and proton helicities. ϕl⊥ and ϕ∆⊥ are the azimuthal angles of the outgoing lepton and the proton, respectively. A2 is theknown2) twist-2 amplitude for dijet production. A3
is a twist-3 amplitude which contains the OAM andwhich is calculated for the ﬁrst time in this work. Thedetails can be found in the published letter. Here weshow the ﬁnal result after certain approximations
Re(A2 A∗3 )[{∝ Re Hg(1)∗ +OAM
Helicity
Total

References
1) X. Ji et al., Phys. Rev. Lett. 118, 192004 (2017),
arXiv:1612.02438.
2) V. M. Braun et al., Phys. Rev. D 72, 034016 (2005),
arXiv:hep-ph/0505263.
3) Y. Hatta et al., Phys. Lett. B 781, 213 (2018),
arXiv:1802.02716.

Condensed from the article in Phys. Rev. Lett. 128, 182002(2022)
Department of Physics, Brookhaven National Laboratory
Ecole Polytechnique
RIKEN BNL Research Center- 60 -