Phenomenological analysis of azimuthal asymmetries in unpolarized semi-inclusive deep inelastic scattering

We present a phenomenological analysis of the $\cos \varphi$ and $\cos 2\varphi$ asymmetries in unpolarized semi-inclusive deep inelastic scattering, based on the recent multidimensional data released by the COMPASS and HERMES collaborations. In the transverse-momentum-dependent framework, valid at relatively low transverse momenta, these asymmetries arise from intrinsic transverse momentum and transverse spin effects, and from their correlations. The role of the Cahn and Boer-Mulders effects in both azimuthal moments is explored up to order $1/Q$. As the kinematics of the present experiments is dominated by the low-$Q^2$ region, higher-twist contributions turn out to be important, affecting the results of our fits.

Figure 1

Kinematical configuration and conventions for SIDIS processes. The initial and final lepton momenta define the $\widehat{x}\text{−}\widehat{z}$ plane.

Figure 2

Best fit curves for $⟨\cos \varphi ⟩$ obtained by fitting COMPASS data on multiplicities, $⟨\cos \varphi ⟩$ and $⟨\cos 2\varphi ⟩$. The Cahn effect in $⟨\cos 2\varphi ⟩$ has been set to zero.

Figure 3

Best fit curves for $⟨\cos 2\varphi ⟩$ obtained by fitting COMPASS data on multiplicities, $⟨\cos \varphi ⟩$ and $⟨\cos 2\varphi ⟩$. The Cahn effect in $⟨\cos 2\varphi ⟩$ has been set to zero.

Figure 4

Best fit curves for $⟨\cos \varphi ⟩$ obtained by fitting HERMES data on multiplicities, $⟨\cos \varphi ⟩$ and $⟨\cos 2\varphi ⟩$. The Cahn effect in $⟨\cos 2\varphi ⟩$ has been set to zero. Here we show only one bin in $z$, as an example, with $⟨z⟩=0.45$.

Figure 5

Best fit curves for $⟨\cos 2\varphi ⟩$ obtained by fitting HERMES data on multiplicities, $⟨\cos \varphi ⟩$ and $⟨\cos 2\varphi ⟩$. The Cahn effect in $⟨\cos 2\varphi ⟩$ has been set to zero. Here we show only one bin in $z$, as an example, with $⟨z⟩=0.45$.