Daniel Boer

Time reversal odd distribution functions in leptoproduction

We consider the various asymmetries, notably single spin asymmetries, that appear in leptoproduction as a consequence of the presence of time-reversal odd distribution functions. This could facilitate experimental searches for time-reversal odd phenomena.

Universality of T-odd effects in single spin and azimuthal asymmetries

We analyze the transverse-momentum-dependent distribution and fragmentation functions in space-like and time-like hard processes involving at least two hadrons, in particular, 1-particle inclusive leptoproduction, the Drell–Yan process and two-particle inclusive hadron production in electron–positron annihilation. As is well known, transverse momentum dependence allows for the appearance of unsuppressed single spin azimuthal asymmetries, such as Sivers and Collins asymmetries. Recently, Belitsky, Ji and Yuan obtained fully color-gauge-invariant expressions for the relevant matrix elements appearing in these asymmetries at leading order in an expansion in the inverse hard scale. We rederive these results and extend them to observables at the next order in this expansion. We observe that at leading order one retains a probability interpretation, contrary to a claim in the literature and show the direct relation between the Sivers effect in single spin asymmetries and the Qiu–Sterman mechanism. We also study fragmentation functions, where the process-dependent gauge link structure of the correlators is not the only source of T-odd observables and discuss the implications for universality.

Investigating the origins of transverse spin asymmetries at BNL RHIC

We discuss possible origins of transverse spin asymmetries in hadron-hadron collisions and propose an explanation in terms of a chiral-odd T-odd distribution function with intrinsic transverse momentum dependence, which would signal a correlation between the transverse spin and the transverse momentum of quarks inside an unpolarized hadron. We will argue that despite its conceptual problems, it can account for single spin asymmetries, for example in pp dagger-->pi X, and at the same time for the large cos 2 phi asymmetry in the unpolarized Drell-Yan cross section, which still lacks understanding. We use the latter asymmetry to arrive at a crude model for this function and show explicitly how it relates unpolarized and polarized observables in the Drell-Yan process, as could be measured with the proton-proton collisions at BNL RHIC. Moreover, it would provide an alternative method of accessing the transversity distribution function h(1). For future reference we also list the complete set of azimuthal asymmetries in the unpolarized and polarized Drell-Yan process at leading order involving T-odd distribution functions with intrinsic transverse momentum dependence. [S0556-2821(99)04213-7].

Bessel-weighted asymmetries in semi-inclusive deep inelastic scattering

The concept of weighted asymmetries is revisited for semi-inclusive deep inelastic scattering. We consider the cross section in Fourier space, conjugate to the outgoing hadron’s transverse momentum, where convolutions of transverse momentum dependent parton distribution functions and fragmentation functions become simple products. Individual asymmetric terms in the cross section can be projected out by means of a generalized set of weights involving Bessel functions. Advantages of employing these Bessel weights are that they suppress (divergent) contributions from high transverse momentum and that soft factors cancel in (Bessel-)weighted asymmetries. Also, the resulting compact expressions immediately connect to previous work on evolution equations for transverse momentum dependent parton distribution and fragmentation functions and to quantities accessible in lattice QCD. Bessel-weighted asymmetries are thus model independent observables that augment the description and our understanding of correlations of spin and momentum in nucleon structure.

Initial-State Interactions in the Unpolarized Drell-Yan Process

We show that initial-state interactions contribute to the cos 2phi distribution in unpolarized Drell-Yan lepton pair production pp and p (p) over bar-->l(+)l(-)X, without suppression. The asymmetry is expressed as a product of chiral-odd distributions h(1)(perpendicular to)(x(1),p(perpendicular to)(2))x (h) over bar (perpendicular to)(1)(x(2),k(perpendicular to)(2)), where the quark-transversity function h(1)(perpendicular to)(x,p(perpendicular to)(2)) is the transverse momentum dependent, light-cone momentum distribution of transversely polarized quarks in an unpolarized proton. We compute this (naive) T-odd and chiral-odd distribution function and the resulting cos 2phi asymmetry explicitly in a quark-scalar diquark model for the proton with initial-state gluon interaction. In this model the function h(1)(perpendicular to)(x,p(perpendicular to)(2)) equals the T-odd (chiral-even) Sivers effect function f(1T)(perpendicular to)(x,p(perpendicular to)(2)). This suggests that the single-spin asymmetries in the semi-inclusive deep inelastic scattering and the Drell-Yan process are closely related to the cos 2phi asymmetry of the unpolarized Drell-Yan process, since all can arise from the same underlying mechanism. This provides new insight regarding the role of the quark and gluon orbital angular momentum as well as that of initial- and final-state gluon exchange interactions in hard QCD processes.

Matches and mismatches in the descriptions of semi-inclusive processes at low and high transverse momentum

This talk reports on recent work where we studied the connection between the description of semi-inclusive DIS at high transverse momentum (based on collinear factorization) and low transverse momentum (based on transverse-momentum-dependent factorization). We used power counting to determine the leading behavior of the structure functions at intermediate transverse momentum in the two descriptions. When the power behaviors are different, two distinct mechanisms are present and there can be no matching between them. When the power behavior is the same, the two descriptions must match. An explicit calculation however shows that for some observables this is not the case, suggesting that the transverse-momentum-dependent-factorization description beyond leading twist is incomplete.

Evolution of transverse momentum dependent distribution and fragmentation functions

We use Lorentz invariance and the QCD equations of motion to study the evolution of functions that appear at leading order in a I / Q expansion in azimuthal asymmetries. This includes the evolution equation of the Collins fragmentation function. The moments of these functions are matrix elements of known twist two and twist three operators. We present the evolution in the large N-c limit, restricting to non-singlet for the chiral-even functions

Transverse momentum dependent (TMD) parton distribution functions: Status and prospects*

We review transverse momentum dependent (TMD) parton distribution functions, their application to topical issues in high-energy physics phenomenology, and their theoretical connections with QCD resummation, evolution and factorization theorems. We illustrate the use of TMDs via examples of multi-scale problems in hadronic collisions. These include transverse momentum q(T) spectra of Higgs and vector bosons for low q(T), and azimuthal correlations in the production of multiple jets associated with heavy bosons at large jet masses. We discuss computational tools for TMDs, and present the application of a new tool, TMDLIB, to parton density fits and parameterizations.

Asymmetries in polarized hadron production in

We present the results of the tree-level calculation of inclusive two-hadron production in electron-positron annihilation via one photon up to subleading order in 1/Q. We consider the situation where the two hadrons belong to different, back-to-back jets. We include polarization of the produced hadrons and discuss azimuthal dependences of asymmetries. New asymmetries are found, in particular there is a leading cos(2 phi) asymmetry, which is even present when hadron polarization is absent, since it arises solely due to the intrinsic transverse momenta of the quarks

e^{+}e^{-}

We show that linearly polarized gluons inside unpolarized hadrons can be directly probed in jet or heavy quark pair production in electron-hadron collisions. We discuss the simplest cos2ϕ asymmetries and estimate their maximal value, concluding that measurements of the unknown linearly polarized gluon distribution in the proton should be feasible in future Electron-Ion Collider or Large Hadron electron Collider experiments. Analogous asymmetries in hadron-hadron collisions suffer from factorization breaking contributions and would allow us to quantify the importance of initial- and final-state interactions.