Single-spin asymmetry ATsin(2ϕ−ϕS) in π−p Drell-Yan process within TMD factorization

We study the single-spin asymmetry ATsin(2ϕ−ϕS) in the pion-induced Drell-Yan process within the transverse momentum dependent factorization (TMD factorization). The asymmetry can be expressed as the convolution of the Boer-Mulders function and the transversity function. We numerically estimate the asymmetry ATsin(2ϕ−ϕS) at the COMPASS kinematics with the model results for the pion meson distributions from the light-cone wave function approach and the available parametrization for the proton distributions. We also include the TMD evolution formalism both proton and pion parton distribution functions by using two different parametrizations on nonperturbative Sudakov form factor. We find that the asymmetry ATsin(2ϕ−ϕS) as functions of xp, xπ, xF and q⊥ is qualitatively consistent with the recent COMPASS measurement.

Bottomonium production and polarization in the NRQCD with $$k_T$$-factorization. III: $$\Upsilon (1S)$$ and $$\chi _b(1P)$$ mesons

The $$\Upsilon (1S)$$ Υ ( 1 S ) meson production and polarization at high energies is studied in the framework of the $$k_T$$ k T -factorization approach. Our consideration is based on the non-relativistic QCD formalism for a bound states formation and off-shell production amplitudes for hard partonic subprocesses. The direct production mechanism, feed-down contributions from radiative $$\chi _b(mP)$$ χ b ( m P ) decays and contributions from $$\Upsilon (3S)$$ Υ ( 3 S ) and $$\Upsilon (2S)$$ Υ ( 2 S ) decays are taken into account. The transverse momentum dependent (TMD) gluon densities in a proton were derived from the Ciafaloni–Catani–Fiorani–Marchesini evolution equation and the Kimber-Martin–Ryskin prescription. Treating the non-perturbative color octet transitions in terms of multipole radiation theory, we extract the corresponding non-perturbative matrix elements for $$\Upsilon (1S)$$ Υ ( 1 S ) and $$\chi _b(1P)$$ χ b ( 1 P ) mesons from a combined fit to transverse momenta distributions measured at various LHC experiments. Then we apply the extracted values to investigate the polarization parameters $$\lambda _\theta $$ λ θ , $$\lambda _\phi $$ λ ϕ and $$\lambda _{\theta \phi }$$ λ θ ϕ , which determine the $$\Upsilon (1S)$$ Υ ( 1 S ) spin density matrix. Our predictions have a reasonably good agreement with the currently available Tevatron and LHC data within the theoretical and experimental uncertainties.

Spin asymmetries in electron-jet production at the future electron ion collider

We study all the possible spin asymmetries that can arise in back-to-back electron-jet production, ep → e + jet + X, as well as the associated jet fragmentation process, ep → e+jet(h)+X, in electron-proton collisions. We derive the factorization formalism for these spin asymmetries and perform the corresponding phenomenology for the kinematics relevant to the future electron ion collider. In the case of unpolarized electron-proton scattering, we also give predictions for azimuthal asymmetries for the HERA experiment. This demonstrates that electron-jet production is an outstanding process for probing unpolarized and polarized transverse momentum dependent parton distribution functions and fragmentation functions.

Quark sivers function at small x: spin-dependent odderon and the sub-eikonal evolution

We apply the formalism developed earlier [1, 2] for studying transverse momentum dependent parton distribution functions (TMDs) at small Bjorken x to construct the small-x asymptotics of the quark Sivers function. First, we explicitly construct the complete fundamental “polarized Wilson line” operator to sub-sub-eikonal order: this object can be used to study a variety of quark TMDs at small x. We then express the quark Sivers function in terms of dipole scattering amplitudes containing various components of the “polarized Wilson line” and show that the dominant (eikonal) term which contributes to the quark Sivers function at small x is the spin-dependent odderon, confirming the re- cent results of Dong, Zheng and Zhou [3]. Our conclusion is also similar to the case of the gluon Sivers function derived by Boer, Echevarria, Mulders and Zhou [4] (see also [5]). We also analyze the sub-eikonal corrections to the quark Sivers function using the constructed “polarized Wilson line” operator. We derive new small-x evolution equations re-summing double-logarithmic powers of αs ln2(1/x) with αs the strong coupling constant. We solve the corresponding novel evolution equations in the large-Nc limit, obtaining a sub-eikonal correction to the spin-dependent odderon contribution. We conclude that the quark Sivers function at small x receives contributions from two terms and is given by$$ {f}_{1T}^{\perp q}\left(x,{k}_T^2\right)={C}_O\left(x,{k}_T^2\right)\frac{1}{x}+{C}_1\left({k}_T^2\right){\left(\frac{1}{x}\right)}^0+\cdots $$ f 1 T ⊥ q x k T 2 = C O x k T 2 1 x + C 1 k T 2 1 x 0 + ⋯ with the function CO(x,$$ {k}_T^2 $$ k T 2 ) varying slowly with x and the ellipsis denoting the subasymptotic and sub-sub-eikonal (order-x) corrections.

A new approach to semi-inclusive deep-inelastic scattering with QED and QCD factorization

We present the details of a new factorized approach to semi-inclusive deep-inelastic scattering which treats QED and QCD radiation on equal footing, and provides a systematically improvable approximation to the extraction of transverse momentum dependent parton distributions. We demonstrate how the QED contributions can be well approximated by collinear factorization, and illustrate the application of the factorized approach to QED radiation in inclusive scattering. For semi-inclusive processes, we show how radiation effects prevent a well-defined “photon-nucleon” frame, forcing one to use a two-step process to account for the radiation. We illustrate the utility of the new method by explicit application to the spin-dependent Sivers and Collins asymmetries.

General helicity formalism for two-hadron production in e+e− annihilation within a TMD approach

We present the complete leading-order results for the azimuthal dependences and polarization observables in e+e−→ h1h2 + X processes, where the two hadrons are produced almost back-to-back, within a transverse momentum dependent (TMD) factorization scheme. We consider spinless (or unpolarized) and spin-1/2 hadron production and give the full set of the corresponding quark and gluon TMD fragmentation functions (TMD-FFs). By adopting the helicity formalism, which allows for a more direct probabilistic interpretation, single- and double-polarization cases are discussed in detail. Simplified expressions, useful for phenomenological analyses, are obtained by assuming a factorized Gaussian-like dependence on intrinsic transverse momenta for the TMD-FFs.

The diphoton $$q_T$$ spectrum at N$$^3$$LL$$^\prime $$ + NNLO

We present a $$q_T$$ q T -resummed calculation of diphoton production at order N$$^3$$ 3 LL$$^\prime $$ ′ + NNLO. To reach the primed level of accuracy we have implemented the recently published three-loop $${\mathcal {O}}(\alpha _s^3)$$ O ( α s 3 ) virtual corrections in the $$q\bar{q}$$ q q ¯ channel and the three-loop transverse momentum dependent beam functions and combined them with the existing infrastructure of , a code performing resummation at order N$${}^3$$ 3 LL. While the primed predictions are parametrically not more accurate, one typically observes from lower orders and other processes that they are the dominant effect of the next order. We include in both the $$q\bar{q}$$ q q ¯ and loop-induced gg channel the hard contributions consistently together at order $$\alpha _s^3$$ α s 3 and find that the resummed $$q\bar{q}$$ q q ¯ channel without matching stabilizes indeed. Due to large matching corrections and large contributions and uncertainties from the gg channel, the overall improvements are small though. We furthermore study the effect of hybrid-cone photon isolation and hard-scale choice on our fully matched results to describe the ATLAS $$\text {8}$$ 8 TeV data and find that the hybrid-cone isolation worsens agreement at small $$q_T$$ q T compared to smooth-cone isolation.