Inclusive-jet and dijet production in polarized deep inelastic scattering

We present the calculation for single-inclusive jet production in (longitudinally) polarized deep-inelastic lepton-nucleon scattering at next-to-next-to leading order (NNLO) accuracy, based on the projection-to-Born method. As a necessary ingredient to achieve the NNLO results, we also introduce the next-to-leading-order (NLO) calculation for the production of dijets in polarized DIS. Our dijet calculation is based on an extension of the dipole subtraction method to account for polarized initial-state partons. We analyze the phenomenological consequences of higher order QCD corrections for the Electron-Ion Collider kinematics.

Figure 1

$\mathcal{O}({\alpha }_S^0)$ Breit frame kinematics for the process $p_1(xp)+{\gamma }^{*}(q)\to p_2(xp+q)$.

Figure 2

Inclusive dijet production distributions as a function of the leading and sub-leading jet transverse momentum, $p_{T,1}^B$ and $p_{T,2}^B$, respectively, for both the polarized and unpolarized cases. The bands reflect the seven point variation in the cross section when independently changing the scales as ${\mu }_R,{\mu }_F=[1/2,2]\frac{1}{2}{\mu }_0$. The lower inset for each plot depicts the $K$-factor, defined as the ratio to the LO cross section.

Figure 3

Inclusive dijet production distributions as a function of the variables $⟨p_T^B{⟩}_2$, $M_{12}$, ${\eta }^{*}$ and ${\log }_{10}({\xi }_2)$. The lower boxes show the $K$-factor for each distribution.

Figure 4

Same as Fig. 3, but for the polarized case. The uncertainty associated the polarized PDFs is depicted with black error bars, in addition to the theoretical uncertainty from scale variations.

Figure 5

Inclusive dijet production unpolarized cross sections in bins of $Q^2$, as a function of ${\log }_{10}({\xi }_2)$. The LO and NLO uncertainty bands are obtained as in Fig. 4. The lower panels display the $K$-factors to the LO calculation.

Figure 6

Same as Fig. 5, but for the polarized case.

Figure 7

Same as Figs. 5 and 6, but separating the contributions initiated by quarks and gluons to the dijet cross section, both at LO (dashed lines) and at NLO (solid lines). The lower insets show the ratio between the gluonic and quark contributions to the cross section.

Figure 8

Double spin asymmetries for dijet production, as a function of $⟨p_T^B{⟩}_2$, $M_{12}$, ${\eta }^{*}$ and ${\xi }_2$. The lower boxes depict the $K$-factors to the LO calculation.

Figure 9

Double spin asymmetry as a function of ${\log }_{10}({\xi }_2)$ and $Q^2$. As in the previous cases, the inset lower boxes show the $K$-factor to the LO asymmetry.

Figure 10

Polarized single-jet cross section, as distributions in transverse momentum $p_T^L$, pseudorapidity $\eta$, photon virtuality $Q^2$ and Bjorken variable $x$ at LO, NLO and NNLO. The bands reflect the seven point variation in the cross section when independently changing the scales as ${\mu }_R,{\mu }_F=[1/2,2]{\mu }_0$. The error bars correspond to the PDF’s errors in the NNLO result. The lower inset shows the corresponding $K$-factors, as defined in the main text.

Figure 11

Same as Fig. 10, but discriminating the contributions to the cross section coming from initial quarks and gluons.

Figure 12

Same as Fig. 11, but for the unpolarized case.

Figure 13

Double spin asymmetries and theoretical uncertainties up to NNLO (upper panels) and separation into partonic channels (lower panels) as distributions of $p_T^L$ and $\eta$. For the upper panels the insets shows the corresponding $K$-factors, as defined in the main text, while for the lower ones, the insets present the ratio between the gluonic and quark contributions to the asymmetry.

Figure 14

NNLO polarized and unpolarized cross sections as a distribution of $p_T^L$ and ${\eta }^L$ for different choices of the jet radius $R$ value.

Figure 15

NNLO double spin asymmetries as a distribution of $p_T^L$ and $\eta$ for different choices of the jet radius $R$ value.

Figure 16

Difference between the $\mathcal{O}({\alpha }_S^2)$ coefficient for the fixed-order Monte Carlo calculation and the expansion of the resummed calculation for the gluonic contribution to ${\tau }_{z_E}$, using disaster, the original version of disent and its fixed version.

Figure 17

Collinear behavior for the n-particle amplitude ${\mathcal{M}}^n$ in the limit $1\parallel 2$.