Applicability of transverse mass scaling in hadronic collisions at energies available at the CERN Large Hadron Collider

We present a study on the applicability of transverse mass scaling for identified particle spectra in proton-proton collisions at $\sqrt{s}=7$ TeV based on data taken by the ALICE experiment at the LHC. The measured yields are parametrized and compared to estimates obtained from a generalized transverse mass scaling approach applied to different reference particle spectra. It is found that generalized transverse mass scaling is not able to describe the measured spectra over the full range in transverse momentum. At low $p_{\text{T}}$, deviations of $20\%$ or more are obtained, in particular, if pions are used as reference particles. A better scaling performance is obtained when kaons are used as reference particles. At high $p_{\text{T}}$ all tested spectra with the possible exception of the charged kaons exhibit a scaling behavior. Investigating the feed-down contributions from resonance decays to the charged pion yields reveals, that using them as reference a general scaling may not be achievable. Our findings imply that for precision measurements of direct photon and di-electron spectra at low transverse momentum one should measure the relevant hadronic background, instead of relying on $m_{\text{T}}$ scaling for its estimate.

Figure 1

Identified, $p_{\text{T}}$ differential particle yields measured by ALICE in pp collisions at $\sqrt{s}=7$ TeV and corresponding parametrizations. Statistical uncertainties are shown as error bars, systematic uncertainties are shown as open boxes. The shown data are ${\pi }^{\pm }$ [19], ${\pi }^0$ [20], $\eta$ [20], $\varphi$ [21], ${\text{K}}^{\pm }$ [19], ${\text{K}}^{*}{\left(892\right)}^0$ [21], $\text{p}/\overline{\text{p}}$ [19], ${\mathrm{\Omega }}^{-}/{\overline{\mathrm{\Omega }}}^{+}$ [22], ${\mathrm{\Xi }}^{-}/{\overline{\mathrm{\Xi }}}^{+}$ [23], and $\mathrm{\Sigma }{\left(1385\right)}^{\pm }/\overline{\mathrm{\Sigma }}{\left(1385\right)}^{\pm }$ [23]. The lines are fits to the data summarized in Table 1.

Figure 2

Ratios of measured yields to the respective parametrizations and reduced ${\chi }^2$ values of the fits. In the case of the $\eta$ meson, the reduced ${\chi }^2$ value of the corresponding $\eta /{\pi }^0$ ratio fit is given. Only statistical uncertainties are shown. For more info see caption of Fig. 1.

Figure 3

The $\eta /{\pi }^0$ ratio measured in pp collisions at $\sqrt{s}=7$ TeV [20], the corresponding parametrization and the ratio between the data and fit. Statistical uncertainties are shown as error bars, systematic uncertainties are shown as open boxes.

Figure 4

The ${\pi }^0/{\pi }^{\pm }$ ratio measured in pp collisions at $\sqrt{s}=7$ TeV [20, 29] and $\sqrt{s}=2.76$ TeV [29, 30]. Statistical uncertainties are shown as error bars, systematic uncertainties are shown as open boxes. The ratios are compared to calculations using PYTHIA 8.2, Monash 2013 tune [31].

Figure 5

Primary charged pion yields (black) in pp collisions at $\sqrt{s}=7$ TeV, according to the primary particle definition in Ref. [32], generated according to the charged pion parametrization given in Table 1. Furthermore, the different feed-down contribution from a particle decay simulation are shown per source. The uncertainties given are related to the statistics of the decay particle simulation and the uncertainties on the parametrization of the sources are not taken into account.

Figure 6

The $\eta /{\pi }^{\pm }$ (left) and ${\mathrm{K}}^{\pm }/{\pi }^{\pm }$ ratio (right) measured in pp collisions at $\sqrt{s}=7$ TeV together with the ratios using the different particles as basis for the scaling of the $\eta$ meson and charged kaon and the parametrization of the charged pion, respectively. The fitted high $p_{\text{T}}$ constant $C$ is reported as well as a blue band in the $p_{\text{T}}$ region, where it was obtained. For comparison the corresponding particle ratios measured in pp collisions at $\sqrt{s}=2.76$ TeV are displayed as well [29, 30].

Figure 7

The $\eta /{\mathrm{K}}^{\pm }$ (left) and $\varphi /{\pi }^{\pm }$ ratio (right) measured in pp collisions at $\sqrt{s}=7$ TeV together with the ratios using the different particles as basis for the scaling of the $\eta$ and $\varphi$ meson and the parametrizations of the charged kaon and pion, respectively. For comparison the corresponding particle ratios measured in pp collisions at $\sqrt{s}=2.76$ TeV are displayed as well [29, 30, 35]. The fitted high $p_{\text{T}}$ constant $C$ is reported as well as a blue band in the $p_{\text{T}}$ region, where it was obtained. The scaling constant for the $\varphi /{\pi }^{\pm }$ is obtained solely on the data obtained for pp collisions at $\sqrt{s}=2.76$ TeV, as the plateau value has not been reached for the results at 7 TeV.

Figure 8

The $\varphi /{\mathrm{K}}^{\pm }$ (left) and $\varphi /\eta$ ratio (right) measured in pp collisions at $\sqrt{s}=7$ TeV together with the ratios using the different particles as basis for the scaling of the $\varphi$ meson and the parametrizations of the charged kaon and $\eta$ meson, respectively. For comparison the corresponding particle ratios measured in pp collisions at $\sqrt{s}=2.76$ TeV are displayed as well [29, 30, 35]. The fitted high $p_{\text{T}}$ constant $C$ is reported as well as a blue band in the $p_{\text{T}}$ region, where it was obtained. Both scaling constants mainly rely on the data obtained for pp collisions at $\sqrt{s}=2.76$ TeV, as the plateau value has not been reached for the results at 7 TeV.

Figure 9

The $\eta /{\pi }^0$ (left) and $\varphi /{\pi }^0$ ratio (right) measured in pp collisions at $\sqrt{s}=7$ TeV together with the ratios using the different particles as basis for the scaling of the $\eta$ and $\varphi$ meson, respectively, and the parametrization of the neutral pions. For comparison the corresponding particle ratios measured in pp collisions at $\sqrt{s}=2.76$ TeV and 8 TeV are displayed as well [28, 30, 35]. The fitted high $p_{\text{T}}$ constant $C$ is reported as well as a blue band in the $p_{\text{T}}$ region, where it was obtained. For the $\varphi /{\pi }^0$ the scaling constant was obtained based on the data measured at $\sqrt{s}=2.76$ TeV, as the plateau value has not been reached for the results at 7 TeV.

Figure 10

Ratio of the measured $\eta$ yield (points) and its fit (lines) to the scaled parametrization obtained from different reference particles. The $p_{\text{T}}$ thresholds for the obtained scaling constants ($C$) are shown as vertical red line and reflect the point at which the ratio between scaled and reference particles is approximately flat.

Figure 11

Ratio of the measured $\varphi$ yield (points) and its fit (lines) to the scaled parametrization obtained from different reference particles. The $p_{\text{T}}$ thresholds for the obtained scaling constants ($C$) are shown as vertical red line and reflect the point at which the ratio between scaled and reference particles is approximately flat.

Figure 12

Ratio of the measured charged kaon yield (points) and its fit (lines) to the scaled parametrization obtained from different reference particles. The $p_{\text{T}}$ thresholds for the obtained scaling constants ($C$) are shown as vertical red line and reflect the point at which the ratio between scaled and reference particles is approximately flat.