We re-examine the jet probes of the nucleon spin and flavor structures. We find for the first time the time-reversal odd (T-odd) component of a jet, conventionally thought to vanish, can survive due to the non-perturbative fragmentation and hadroniza
tion effects and could be testable. This additional contribution of a jet will lead to novel jet phenomena relevant for unlocking the access to several spin structures of the nucleon, which were thought to be impossible by using jets. As examples, we show how the T-odd constituent can couple to the proton transversity at the Electron Ion Collider (EIC) and can give rise to the anisotropy in the jet production in $e^+e^-$ annihilations. We expect the T-odd contribution of the jet to have broad applications in high energy nuclear physics.
Jets constructed via clustering algorithms (e.g., anti-$k_T$, soft-drop) have been proposed for many precision measurements, such as the strong coupling $alpha_s$ and the nucleon intrinsic dynamics. However, the theoretical accuracy is affected by mi
ssing QCD corrections at higher orders for the jet functions in the associated factorization theorems. Their calculation is complicated by the jet clustering procedure. In this work, we propose a method to evaluate jet functions at higher orders in QCD. The calculation involves the phase space sector decomposition with suitable soft subtractions. As a concrete example, we present the quark-jet function using the anti-$k_T$ algorithm with E-scheme recombination at next-to-next-to-leading order.
We study factorization in single transverse spin asymmetries for dijet production in proton-proton collisions, by considering soft gluon radiation at one-loop order. We show that the associated transverse momentum dependent (TMD) factorization is val
id at the leading logarithmic level. At next-to-leading-logarithmic (NLL) accuracy, however, we find that soft gluon radiation generates terms in the single transverse spin dependent cross section that differ from those known for the unpolarized case. As a consequence, these terms cannot be organized in terms of a spin independent soft factor in the factorization formula. We present leading logarithmic predictions for the single transverse spin dijet asymmetry for $pp$ collisions at RHIC, based on quark Sivers functions constrained by semi-inclusive deep inelastic scattering data. We hope that our results will contribute to a better understanding of TMD factorization breaking effects at NLL accuracy and beyond.
We study the lepton-jet correlation in deep inelastic scattering. We perform one-loop calculations for the spin averaged and transverse spin dependent differential cross sections depending on the total transverse momentum of the final state lepton an
d the jet. The transverse momentum dependent (TMD) factorization formalism is applied to describe the relevant observables. To show the physics reach of this process, we perform a phenomenological study for HERA kinematics and comment on an ongoing analysis of experimental data. In addition, we highlight the potential of this process to constrain small-$x$ dynamics.
We calculate the next-to-leading order (NLO) radiative correction to the color-octet $h_c$ inclusive production in $e^+e^-$ annihilation at Super $B$ factory, within the nonrelativistic QCD factorization framework. The analytic expression for the NLO
short-distance coefficient (SDC) accompanying the color-octet production operator $mathcal{O}_8^{h_c}(^1S_0)$ is obtained after summing both virtual and real corrections. The size of NLO correction for the color-octet production channel is found to be positive and substantial. The NLO prediction to the $h_c$ energy spectrum is plagued with unphysical endpoint singularity. With the aid of the soft-collinear effective theory, those large endpoint logarithms are resummed to the next-to-leading logarithmic (NLL) accuracy. Consequently, further supplemented with the non-perturbative shape function, we obtain the well-behaved predictions for the $h_c$ energy spectrum in the entire kinematic range, which awaits the examination by the forthcoming Belle II experiment.
Given data in $mathbb{R}^{p}$, a Tukey $kappa$-trimmed region is the set of all points that have at least Tukey depth $kappa$ w.r.t. the data. As they are visual, affine equivariant and robust, Tukey regions are useful tools in nonparametric multivar
iate analysis. While these regions are easily defined and interpreted, their practical use in applications has been impeded so far by the lack of efficient computational procedures in dimension $p > 2$. We construct two novel algorithms to compute a Tukey $kappa$-trimmed region, a na{i}ve one and a more sophisticated one that is much faster than known algorithms. Further, a strict bound on the number of facets of a Tukey region is derived. In a large simulation study the novel fast algorithm is compared with the na{i}ve one, which is slower and by construction exact, yielding in every case the same correct results. Finally, the approach is extended to an algorithm that calculates the innermost Tukey region and its barycenter, the Tukey median.
