1 Introduction

Measurements of hadron production cross sections in proton–proton (pp) collisions at high energies are important to test our understanding of strong interaction and its underlying theory of quantum chromodynamics (QCD) [1]. Its perturbative treatment (pQCD) becomes feasible for predictions of particle production in hard scattering processes that have a sufficiently high momentum transfer \(Q^2\). This is possible by factorizing [2] the scattering process into three contributions: a QCD matrix element describing the scattering of partons, a parton distribution function (PDF) [3] describing the probability to find a scattering parton within each colliding hadron, and a fragmentation function (FF) [4] that relates the final-state parton momentum to the momentum of an observed hadron. While the QCD matrix element can be calculated in pQCD for sufficiently hard scales, the FFs and PDFs are obtained by global fits of experimental data at various collision energies [5]. However, most particles are produced in soft scattering processes that involve small momentum transfers and therefore can not be calculated within pQCD. In this regime, calculations rely on phenomenological models that also require experimental verification.

Comparison of measured particle spectra with calculations is essential to test their underlying assumptions and provide constraints for the FFs and the PDFs. For example, recent measurements of \(\pi ^0\) and \(\eta \) mesons [6,7,8] at several LHC collision energies constrained gluon fragmentation [9] in a regime not accessible by measurements at lower collision energies. Like the \(\pi ^0\) and \(\eta \) mesons, the \(\omega \) meson is comprised mainly of light valence quarks and hence has similar flavor content. However, it has spin 1 and is heavier than the \(\pi ^0\) and \(\eta \) with a mass of \(782\,\hbox {MeV}/c^2\) [10]. These differences make the \(\omega \) meson an interesting complementary probe to improve our understanding of hadron production in high-energy collisions. Even though there have been several theoretical efforts to describe the fragmentation into pseudoscalar mesons and baryons such as \(\pi \), K, \(\eta \) and protons [11, 12], only a few theoretical models exist to describe the fragmentation into vector mesons, due to a lack of experimental data. Nonetheless, recent efforts [13, 14] have been made to describe the fragmentation into the entire vector meson nonet using a model with broken SU(3) symmetry by analysing RHIC (pp) and LEP (\(e^+e^-\)) data.

This article presents the invariant differential cross section of inclusive \(\omega \) meson production at mid-rapidity (\(|y|<0.5\)) in pp collisions at \(\sqrt{s}=7\,\hbox {TeV}\). The cross section of \(\omega \) production in hadronic interactions has been measured at collision energies of \(\sqrt{s}=62\,\hbox {GeV}\) [15] and \(\sqrt{s}=200\,\hbox {GeV}\) [16,17,18] at ISR and RHIC respectively. At LHC energies, \(\omega \) production has only been measured by ALICE at forward rapidities (\(2.5<y<4.0\)) in pp collision at 7 TeV [19] in a transverse momentum (\(p_{\mathrm {T}}\)) range of \(1<\) \(p_{\mathrm {T}}\) \(<5\,\hbox {GeV}/c\). The results reported here provide the first measurement of \(\omega \) production at mid-rapidity at LHC energies, and in a wide \(p_{\mathrm {T}}\) range of \(2<p_{\mathrm {T}}<17\,\hbox {GeV}/c\), which tests existing calculations in this regime and provides input for future theoretical studies of vector meson fragmentation functions. In addition, the \(\omega /\pi ^0\) production ratio as a function of \(p_{\mathrm {T}}\) is compared to results of measurements at lower collision energies. This ratio also tests the validity of transverse mass (\(m_{\mathrm {T}}\)) scaling [20] for \(\omega \) mesons at LHC energies, which is typically applied to estimate hadronic backgrounds in direct photon or di-electron measurements in situations where no measured hadron spectra are available. The empirical scaling rule, which was established in measurements of identified particle spectra at lower collision energies at ISR and RHIC [21], states that the