Measuring the Weizsäcker-Williams distribution of linearly polarized gluons at an electron-ion collider through dijet azimuthal asymmetries

The production of a hard dijet with small transverse momentum imbalance in semi-inclusive DIS probes the conventional and linearly polarized Weizsäcker-Williams (WW) transverse momentum dependent (TMD) gluon distributions. The latter, in particular, gives rise to an azimuthal dependence of the dijet cross section. In this paper we analyze the feasibility of a measurement of these TMDs through dijet production in DIS on a nucleus at an electron-ion collider. We introduce the mcdijet Monte Carlo generator to sample quark-antiquark dijet configurations based on leading-order parton level cross sections with WW gluon distributions that solve the nonlinear small-$x$ QCD evolution equations. These configurations are fragmented to hadrons using PYTHIA, and final-state jets are reconstructed. We report on background studies and on the effect of kinematic cuts introduced to remove beam jet remnants. We estimate that with an integrated luminosity of 20 ${\mathrm{fb}}^{-1}/\mathrm{nucleon}$ one can determine the distribution of linearly polarized gluons with a statistical accuracy of approximately 5%.

Figure 1

$x{G}^{\left(1\right)}(x,q_{\perp }^2)$ and $x{h}^{\left(1\right)}(x,q_{\perp }^2)$ WW gluon distributions versus transverse momentum $q_{\perp }$ at different rapidities $Y=log{x}_0/x$. $Q_s\left(Y\right)$ is the saturation momentum. The curves correspond to evolution at fixed ${\alpha }_s$ [19].

Figure 2

The reference frames: (a) The laboratory frame. In the laboratory frame, the electron and the proton have zero transverse momenta; the energy of the electron (proton) is $E_e$ ($E_p$). (b) The analysis frame. Here, the virtual photon and the proton have zero transverse momenta; the energy of the proton is the same as in the laboratory frame, equal to $E_p$. The energy of the virtual photon is $E_{{\gamma }^{*}}=(q^{+}+q^{-})/\sqrt{2}$, see Eqs. (23) and (24).

Figure 3

Distributions of photon virtuality $Q$ and ${\gamma }^{*}$-nucleon c.m. collision energy $W$ for dijet events subject to the kinematic cuts described in the text.

Figure 4

(a) The contributions of transverse vs. longitudinal photon polarizations as functions of $Q$. (b) The distribution of the quark momentum fraction $z$.

Figure 5

Kinematic range in $q_{\perp }$ vs. $P_{\perp }$ in the correlation limit, $q_{\perp }<P_{\perp }$, for two EIC energies, $\sqrt{s}=40$ and 90 GeV. In (a), lines of constant $x$ for the respective energies are depicted while in (b) we show lines of constant azimuthal anisotropy for longitudinally polarized virtual photons.

Figure 6

$p_T$ and $\eta$ distributions of partons (filled circles) and reconstructed jets (filled squares) in the laboratory frame. The jet spectra are uncorrected.

Figure 7

Comparison of $q_{\perp }$ and $P_{\perp }$ distribution for partons (solid circles) and jets (solid squares).

Figure 8

$d\sigma /d\varphi$ distributions for parton pairs (blue points) generated with the mcdijet generator and corresponding reconstructed dijets (red points) in $\sqrt{s}=90\mathrm{GeV} e$+A collisions for $1.25<q_{\perp }<1.75\mathrm{GeV}/c$ and $3.00<P_{\perp }<3.50\mathrm{GeV}/c$. The error bars reflect an integrated luminosity of $10{\mathrm{fb}}^{-1}$/nucleon. (a) shows the azimuthal anisotropy for all virtual photon polarizations while (b) and (c) correspond to transverse and longitudinal polarized photons, respectively. For details, see text.

Figure 9

$\varphi$, the angle between ${\vec{P}}_{\perp }$ and ${\vec{q}}_{\perp }$, as a function of the pseudorapidity, $\eta$, of each of the partons. The strong correlation indicates the sensitivity of the observed anisotropy in $\varphi$ on the $\eta$ acceptance of potential experimental measurements.

Figure 10

Photon-gluon fusion processes that contributes to the 2+1 jet signal cross section.

Figure 11

$Q^2$ dependence of the signal-to-background ratio derived from PYTHIA6.

Figure 12

Azimuthal asymmetry in reconstructed dijet events from pythia caused by the limited $\eta$ acceptance.

Figure 13

$dN/d\varphi$ distribution of signal and background jets after corrections.

Figure 14

Result of a fit of combined signal and background to a data sample obtained in $\sqrt{s}=90$ GeV $e$+A collisions with an integrated luminosity of 10 ${\mathrm{fb}}^{-1}$/nucleon. For details see text.