We compute exclusive ${\eta }_c$ production in high-energy electron-nucleon and electron-nucleus collisions that is sensitive to the odderon. In perturbative QCD the odderon is a $C$-odd color singlet consisting of at least three $t$-channel gluons exchanged with the target. By using the Color Glass Condensate effective theory our result describes the odderon exchange at the high-collision energies that would be reached at a future electron-ion collider. The odderon distribution is evolved to small-$x$ using the Balitsky-Kovchegov evolution equation with running coupling corrections. We find that while at low momentum transfers $t$ the cross section off a proton is dominated by the Primakoff process, the odderon becomes relevant at larger momentum transfers of $|t|\ge 1.5{\mathrm{GeV}}^2$. We point that the odderon could also be extracted at low-$t$ using neutron targets since the Primakoff component is strongly suppressed. In the case of nuclear targets, the odderon cross section becomes enhanced thanks to the mass number of the nuclear target. The gluon saturation effect induces a shift in the diffractive pattern with respect to the Primakoff process that could be used as a signal for the odderon.

Motivated by a novel origin of transverse single spin asymmetry (SSA) in semi-inclusive deep inelastic scattering (SIDIS) uncovered by some of us, we quantitatively investigate its impact on the theoretical understanding of the mechanism responsible for SSA. This new contribution from the quark-initiated channel first appears in two-loop perturbation theory and involves the $g_T(x)$ distribution. We point out another entirely analogous piece from the gluon-initiated channel proportional to the gluon helicity distribution $\mathrm{\Delta }G(x)$. Both contributions are solely expressed in terms of twist-two polarized parton distribution functions and twist-two fragmentation functions in the Wandzura-Wilczek approximation, such that they can be unambiguously evaluated without introducing free parameters. We make predictions for measurements of the asymmetries $A_{UT}$ at the future electron-ion collider (EIC), and find that $A_{UT}$ associated with the $\sin ({\varphi }_h-{\varphi }_S)$, $\sin {\varphi }_S$ and $\sin (2{\varphi }_h-{\varphi }_S)$ harmonics can reach up to 1–2% even at the top EIC energy.

The QR factorisation is a cornerstone of numerical linear algebra, essential for solving overdetermined linear systems, eigenvalue problems, and various scientific computing tasks. However, computing it for ill-conditioned tall-and-skinny (TS) matrices on large-scale distributed-memory systems, particularly those with multiple GPUs, presents significant challenges in balancing numerical stability, high performance, and efficient communication. Traditional Householder-based QR methods provide numerical stability but perform poorly on TS matrices due to their reliance on memory-bound kernels. This paper introduces a novel algorithm for computing the QR factorisation of ill-conditioned TS matrices based on CholeskyQR methods. Although CholeskyQR is fast, it typically fails due to severe loss of orthogonality for ill-conditioned inputs. To solve this, our new algorithm, mCQRGSI+, combines the speed of CholeskyQR with stabilising techniques from the Gram–Schmidt process. It is specifically optimised for distributed multi-GPU systems, using adaptive strategies to balance computation and communication. Our analysis shows the method achieves accuracy comparable to Householder QR, even for extremely ill-conditioned matrices (condition numbers up to ${10}^{16}$). Scaling experiments demonstrate speedups of up to $12\times$ over ScaLAPACK and $16\times$ over SLATE’s CholeskyQR2. This work delivers a method that is both robust and highly parallel, advancing the state-of-the-art for this challenging class of problems.

We propose low-virtuality leptoproduction of open-charm, $p^\uparrow l\to D^0+X$, as a probe of the gluon Sivers function (GSF). At leading-order, this process directly probes the gluon content of the proton, making detection of a trasverse single-spin asymmetry in the process a clear indication of a non-zero GSF. Considering the kinematics of the proposed future Electron-Ion Collider (EIC), we present predictions for asymmetry using fits of the GSF available in literature. We also study the asymmetry at the level of muons produced in D-meson decays and find that the asymmetry is preserved therein as well.

We compute the q q ¯ g contribution to the diffractive structure functions in high-energy deep inelastic scattering. The obtained result corresponds to a finite part of the next-to-leading-order contribution to the diffractive cross section. Previous phenomenological applications have included this contribution only in the high- Q 2 or high- M X 2 limits in the case of a soft gluon, and we numerically demonstrate that these existing estimates do not provide a good approximation for the full q q ¯ g contribution. Furthermore, we demonstrate that in addition to the soft gluon contribution, there is an equally important soft quark contribution to the diffractive structure functions at high Q 2 .