Investigations into the flavor dependence of partonic transverse momentum

TL;DR

This study probes whether unpolarized TMD PDFs and FFs exhibit flavor-dependent transverse momenta by fitting a flavor-dependent Gaussian ansatz to Hermes SIDIS multiplicities within a LO, evolution-free framework. The analysis finds convincing evidence that unfavored fragmentation into pions and kaons carries larger transverse momentum than favored fragmentation, while flavor dependence in PDFs is weaker but not absent. The results reveal a clear anti-correlation between the widths of distributions and fragmentations and highlight the significant role of kaon data in disentangling flavor effects. Limitations include the absence of TMD evolution and reliance on Gaussian ansatz; future work should incorporate evolution, broader data sets, and more flexible functional forms. Overall, the work lays a foundational step toward flavor-resolved TMDs with clear directions for refinement and extension.

Abstract

Recent experimental data on semi-inclusive deep-inelastic scattering from the HERMES collaboration allow us to discuss for the first time the flavor dependence of unpolarized transverse-momentum dependent distribution and fragmentation functions. We find convincing indications that favored fragmentation functions into pions have smaller average transverse momentum than unfavored functions and fragmentation functions into kaons. We find weaker indications of flavor dependence in the distribution functions.

Figures (8)

• Figure 1: Diagram describing the relevant momenta involved in a semi-inclusive DIS event: a virtual photon (defining the reference axis) strikes a parton inside a proton. The parton has a transverse momentum $\bm{k}_\perp$ (not measured). The struck parton fragments into a hadron, which acquires a further transverse momentum $\bm{P}_\perp$ (not measured). The total measured transverse-momentum of the final hadron is $\bm{P}_{hT}$. When $Q^2$ is very large, the longitudinal components are all much larger than the transverse components. In this regime, $\bm{P}_{hT} \approx z \bm{k}_\perp + \bm{P}_\perp$ (see also Ref. Rajotte:2010).
• Figure 2: Distribution of the values of $\chi^2/{\rm d.o.f.}$ for the default fit. On the vertical axis, the number of replicas with $\chi^2/{\rm d.o.f.}$ inside the bin. The bin width is $0.1$.
• Figure 3: Data points: Hermes multiplicities $m_p^h(x,z,\bm{P}_{hT}^2; Q^2)$ for pions and kaons off a proton target as functions of $\bm{P}^2_{hT}$ for one selected $x$ and $Q^2$ bin and few selected $z$ bins. Shaded bands: 68% confidence intervals obtained from fitting 200 replicas of the original data points in the scenario of the default fit. The bands include also the uncertainty on the collinear fragmentation functions. The lowest $\bm{P}^2_{hT}$ bin has not been included in the fit.
• Figure 4: Same content and notation as in the previous figure, but for a deuteron target.
• Figure 5: (a) Distribution of the values of the ratios $\langle \bm{k}^2_{\perp, d_v} \rangle / \langle \bm{k}^2_{\perp, u_v}\rangle$ vs. $\langle \bm{k}^2_{\perp, {\rm sea}}\rangle / \langle \bm{k}^2_{\perp, u_v}\rangle$ obtained from fitting 200 replicas of the original data points in the scenario of the default fit. The white squared box indicates the center of the 68% confidence interval for each ratio. The shaded area represents the two-dimensional 68% confidence region around the white box. The dashed lines correspond to the ratios being unity; their crossing point corresponds to the result with no flavor dependence. For most of the points, $\langle \bm{k}^2_{\perp, d_v}\rangle < \langle \bm{k}^2_{\perp, u_v}\rangle < \langle \bm{k}^2_{\perp, {\rm sea}}\rangle$. (b) Same as previous panel, but for the distribution of the values of the ratios $\langle \bm{P}^2_{\perp, {\rm unf}}\rangle / \langle \bm{P}^2_{\perp, {\rm fav}}\rangle$ vs. $\langle \bm{P}^2_{\perp, u K}\rangle / \langle \bm{P}^2_{\perp, {\rm fav}}\rangle$. For all points, $\langle \bm{P}^2_{\perp, {\rm fav}}\rangle < \langle \bm{P}^2_{\perp, {\rm unf}}\rangle \sim \langle \bm{P}^2_{\perp, u K}\rangle$.