Exclusive production of <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mrow><mml:mi>ϕ</mml:mi></mml:mrow></mml:math> meson in the <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:msup><mml:mi>γ</mml:mi><mml:mo>*</mml:mo></mml:msup><mml:mi>p</mml:mi><mml:mo stretchy="false">→</mml:mo><mml:mi>ϕ</mml:mi><mml:mi>p</mml:mi></mml:math> reaction at large photon virtualities within <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:msub><mml:mi>k</mml:mi><mml:mi>T</mml:mi></mml:msub></mml:math>-factorization approach
Andrèe Dafne Bolognino, Antoni Szczurek, Wolfgang Schäfer
Abstract
We apply the ${k}_{T}$-factorization approach to the production of $\ensuremath{\phi}$ mesons in deep inelastic scattering. The helicity-conserving ${\ensuremath{\gamma}}^{*}(T,L)\ensuremath{\rightarrow}\ensuremath{\phi}$ impact factor is calculated for longitudinal and transverse photon polarization using $\ensuremath{\phi}$ meson distribution amplitudes. Different unintegrated gluon distributions are used in the calculations. The formalism for massless quarks/antiquarks gives too large transverse and longitudinal cross sections for photon virtualities below ${Q}^{2}\ensuremath{\sim}8\text{ }\text{ }{\mathrm{GeV}}^{2}$. We suggest how to improve the description of the HERA data by introducing effective strange-quark masses into the formalism. We derive the corresponding impact factor for a finite quark mass by comparing to the light-cone wave function representation used in previous ${k}_{T}$-factorization calculations and the color-dipole approaches. As a byproduct we present expressions for higher twist amplitudes as weighted integrals over the light-cone wave function. The quark mass ${m}_{q}\ensuremath{\approx}0.5\text{ }\text{ }\mathrm{GeV}$ allows to improve the description of both longitudinal and transverse cross sections down to ${Q}^{2}\ensuremath{\sim}4\text{ }\text{ }{\mathrm{GeV}}^{2}$ but this depends slightly on the renormalization scale used in the calculation. We also present the polarized cross section ratio ${\ensuremath{\sigma}}_{L}/{\ensuremath{\sigma}}_{T}$ and the behavior of the total cross section ${\ensuremath{\sigma}}_{\text{tot}}={\ensuremath{\sigma}}_{L}+{\ensuremath{\sigma}}_{T}$ as a function of photon virtuality.