Abstract:We compute the differential cross-section for inclusive prompt photon+quark production in deeply inelastic scattering of electrons off nuclei at small x (e + A DIS) in the framework of the Color Glass Condensate effective field theory. The result is expressed as a convolution of the leading order (in the strong coupling αs) impact factor for the process and universal dipole matrix elements, in the limit of hard photon transverse momentum relative to the nuclear saturation scale Qs,A(x). We perform a numerical … Show more
“…The Color Glass Condensate (CGC) is a semi-classical effective field theory (EFT) for small-x gluons in this regime [12][13][14][15][16][17][18][19][20][21][22]. The CGC has been applied for a variety of processes in proton-nucleus collisions as well as DIS: structure functions (inclusive [23,24] and diffractive [25]), semi-inclusive production (photon [26][27][28][29], inclusive single hadron [30][31][32][33][34], dihadron/dijet [35][36][37][38], quarkonia [39][40][41][42]), and exclusive processes (deeply virtual Compton scattering and vector meson [43][44][45][46][47][48][49][50][51], dijet [52][53][54][55], trijet [56][57][58] production) to name a few (for a recent review see ...…”
We compute the differential yield for quark anti-quark dijet production in high-energy electron-proton and electron-nucleus collisions at small x as a function of the relative momentum P⊥ and momentum imbalance k⊥ of the dijet system for different photon virtualities Q2, and study the elliptic and quadrangular anisotropies in the relative angle between P⊥ and k⊥. We review and extend the analysis in [1], which compared the results of the Color Glass Condensate (CGC) with those obtained using the transverse momentum dependent (TMD) framework. In particular, we include in our comparison the improved TMD (ITMD) framework, which resums kinematic power corrections of the ratio k⊥ over the hard scale Q⊥. By comparing ITMD and CGC results we are able to isolate genuine higher saturation contributions in the ratio Qs/Q⊥ which are resummed only in the CGC. These saturation contributions are in addition to those in the Weizsäcker-Williams gluon TMD that appear in powers of Qs/k⊥. We provide numerical estimates of these contributions for inclusive dijet production at the future Electron-Ion Collider, and identify kinematic windows where they can become relevant in the measurement of dijet and dihadron azimuthal correlations. We argue that such measurements will allow the detailed experimental study of both kinematic power corrections and genuine gluon saturation effects.
“…The Color Glass Condensate (CGC) is a semi-classical effective field theory (EFT) for small-x gluons in this regime [12][13][14][15][16][17][18][19][20][21][22]. The CGC has been applied for a variety of processes in proton-nucleus collisions as well as DIS: structure functions (inclusive [23,24] and diffractive [25]), semi-inclusive production (photon [26][27][28][29], inclusive single hadron [30][31][32][33][34], dihadron/dijet [35][36][37][38], quarkonia [39][40][41][42]), and exclusive processes (deeply virtual Compton scattering and vector meson [43][44][45][46][47][48][49][50][51], dijet [52][53][54][55], trijet [56][57][58] production) to name a few (for a recent review see ...…”
We compute the differential yield for quark anti-quark dijet production in high-energy electron-proton and electron-nucleus collisions at small x as a function of the relative momentum P⊥ and momentum imbalance k⊥ of the dijet system for different photon virtualities Q2, and study the elliptic and quadrangular anisotropies in the relative angle between P⊥ and k⊥. We review and extend the analysis in [1], which compared the results of the Color Glass Condensate (CGC) with those obtained using the transverse momentum dependent (TMD) framework. In particular, we include in our comparison the improved TMD (ITMD) framework, which resums kinematic power corrections of the ratio k⊥ over the hard scale Q⊥. By comparing ITMD and CGC results we are able to isolate genuine higher saturation contributions in the ratio Qs/Q⊥ which are resummed only in the CGC. These saturation contributions are in addition to those in the Weizsäcker-Williams gluon TMD that appear in powers of Qs/k⊥. We provide numerical estimates of these contributions for inclusive dijet production at the future Electron-Ion Collider, and identify kinematic windows where they can become relevant in the measurement of dijet and dihadron azimuthal correlations. We argue that such measurements will allow the detailed experimental study of both kinematic power corrections and genuine gluon saturation effects.
“…of order Q s , or smaller) even for relatively large virtualities Q 2 Q 2 s [3][4][5][6]. The "golden probe" which attracted most attention over the last years is the production of a pair of hadrons (or jets) in "dilute-dense" collisions (eA or pA) at forward rapidities (in the fragmentation region of the dilute projectile) [5][6][7][8][9][10][11][12][13][14][15][16][17][18][19][20][21][22][23]. Even when the final particles/jets have relatively large transverse momenta (k 2 ⊥ ∼ Q 2 Q 2 s ), the physics of saturation is still visible in the broadening of the back-to-back peak in their azimuthal angle distribution.…”
Using the dipole picture for electron-nucleus deep inelastic scattering at small Bjorken x, we study the effects of gluon saturation in the nuclear target on the cross-section for SIDIS (single inclusive hadron, or jet, production). We argue that the sensitivity of this process to gluon saturation can be enhanced by tagging on a hadron (or jet) which carries a large fraction z ≃ 1 of the longitudinal momentum of the virtual photon. This opens the possibility to study gluon saturation in relatively hard processes, where the virtuality Q2 is (much) larger than the target saturation momentum $$ {Q}_s^2 $$
Q
s
2
, but such that z(1 − z)Q2 ≲ $$ {Q}_s^2 $$
Q
s
2
. Working in the limit z(1 − z)Q2 ≪ $$ {Q}_s^2 $$
Q
s
2
, we predict new phenomena which would signal saturation in the SIDIS cross-section. For sufficiently low transverse momenta k⊥ ≪ Qs of the produced particle, the dominant contribution comes from elastic scattering in the black disk limit, which exposes the unintegrated quark distribution in the virtual photon. For larger momenta k⊥ ≳ Qs, inelastic collisions take the leading role. They explore gluon saturation via multiple scattering, leading to a Gaussian distribution in k⊥ centred around Qs. When z(1 − z)Q2 ≪ Q2, this results in a Cronin peak in the nuclear modification factor (the RpA ratio) at moderate values of x. With decreasing x, this peak is washed out by the high-energy evolution and replaced by nuclear suppression (RpA< 1) up to large momenta k⊥ ≫ Qs. Still for z(1 − z)Q2 ≪ $$ {Q}_s^2 $$
Q
s
2
, we also compute SIDIS cross-sections integrated over k⊥. We find that both elastic and inelastic scattering are controlled by the black disk limit, so they yield similar contributions, of zeroth order in the QCD coupling.
“…Motivated by the studies in pp and dAu collisions at RHIC and the LHC (c.f. Section 3.3.3), this process has received considerable attention in recent years and it is considered a promising channel for gluon saturation searches at the EIC (see also in [197] for photonhadron azimuthal correlations).…”
Quantum chromodynamics (QCD) is the theory of strong interactions of quarks and gluons collectively called partons, the basic constituents of all nuclear matter. Its non-abelian character manifests in nature in the form of two remarkable properties: color confinement and asymptotic freedom. At high energies, perturbation theory can result in the growth and dominance of very gluon densities at small-x. If left uncontrolled, this growth can result in gluons eternally growing violating a number of mathematical bounds. The resolution to this problem lies by balancing gluon emissions by recombinating gluons at high energies: phenomena of gluon saturation. High energy nuclear and particle physics experiments have spent the past decades quantifying the structure of protons and nuclei in terms of their fundamental constituents confirming predicted extraordinary behavior of matter at extreme density and pressure conditions. In the process they have also measured seemingly unexpected phenomena. We will give a state of the art review of the underlying theoretical and experimental tools and measurements pertinent to gluon saturation physics. We will argue for the need of high energy electron-proton/ion colliders such as the proposed EIC (USA) and LHeC (Europe) to consolidate our knowledge of QCD knowledge in the small x kinematic domains.
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