the measurement of charged particle production in proton  proton collisions at high energy gives insight into the dynamics of soft and hard interactions . parton scattering processes with large momentum transfer are quantitatively described by perturbative quantum chromodynamics ( pqcd ) . measurements at high transverse momenta ( pt ) at lhc - energies can help to constrain parton distribution and fragmentation functions in current next - to - leading - order ( nlo ) pqcd calculations   of charged particle production . as data at various \documentclass[12pt]{minimal } 
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				 \begin{document}$\sqrt{s}$\end{document } become available at the lhc , a systematic comparison with current nlo - pqcd calculations over a large span of \documentclass[12pt]{minimal } 
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				 \begin{document}$\sqrt{s}$\end{document } is now possible . however , most particles are produced at low momentum , where particle production is dominated by soft interactions and only phenomenological approaches can be applied ( e.g. pythia  [ 24 ] , phojet  ) to describe the data . a  systematic comparison to data at different values of \documentclass[12pt]{minimal } 
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				 \begin{document}$\sqrt{s}$\end{document } is an essential ingredient to tune these monte carlo event generators . furthermore , the measurement of charged particle transverse momentum spectra in pp collisions serves as a crucial reference for particle spectra in pb  pb collisions . to quantify final state effects due to the creation of a hot and dense deconfined matter , commonly referred to as the quark gluon plasma ( qgp ) , pt spectra in the two collision systems are compared . the observed suppression   in central pb pb collisions at lhc - energies at high pt relative to an independent superposition of pp collisions is generally attributed to energy loss of the partons as they propagate through the hot and dense qcd medium . to enable this comparison a pp reference pt spectrum at the same \documentclass[12pt]{minimal } 
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				 \begin{document}$\sqrt{s}$\end{document } with the same pt coverage has to be provided . similarly , a pp reference spectrum is also needed for p  pb collisions to investigate possible initial - state effects in the collision . in this paper we present a measurement of primary charged particle transverse momentum spectra in pp collisions at \documentclass[12pt]{minimal } 
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				 \begin{document}$\sqrt{s } = 0.9,\ 2.76 \ \mbox{and}\ 7\ \text{tev}$\end{document}. primary charged particles are considered here as all charged particles produced in the collision and their decay products , except for particles from weak decays of strange hadrons . the measurement is performed in the pseudorapidity range ||<0.8 for particles with pt>0.15 gev / c . pb spectra at \documentclass[12pt]{minimal } 
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				 \begin{document}$\sqrt { s_{\mathrm{nn } } } = 2.76\ \mbox{tev}$\end{document } and p  pb spectra at \documentclass[12pt]{minimal } 
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				 \begin{document}$\sqrt{s_{\mathrm { nn } } } = 5.02\ \mbox{tev}$\end{document } in the corresponding pt range up to pt=50 gev / c are constructed . the data were collected by the alice apparatus   at the cern - lhc in 20092011 . the analysis is based on tracking information from the inner tracking system ( its ) and the time projection chamber ( tpc ) , both located in the central barrel of the experiment . the minimum - bias interaction trigger was derived using signals from the forward scintillators ( vzero ) , and the two innermost layers of the its , the silicon pixel detector ( spd ) . the events are selected based on the minimum - bias trigger mbor requiring at least one hit in the spd or vzero detectors , which are required to be in coincidence with two beam bunches crossing in the alice interaction region . in addition , an offline event selection is applied to reject beam induced ( beam - gas , beam - halo ) background . the vzero counters are used to remove these beam - gas or beam - halo events by requiring their timing signals to be in coincidence with particles produced in the collision . the background events are also removed by exploiting the correlation between the number of the spd hits and the number of the spd tracklets ( short track segments reconstructed in the spd and pointing to the interaction vertex ) . the beam - gas or beam - halo events typically have a large number of hits in the spd compared to the number of reconstructed tracklets ; this is used to reject background events . in total 6.8  m , 65  m and 150  m pp events at \documentclass[12pt]{minimal } 
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				 \begin{document}$\sqrt{s}=0.9,\ 2.76\ \mbox{and}\ 7\ \text{tev}$\end{document } fulfill the \documentclass[12pt]{minimal } 
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				 \begin{document}$\rm { mb_{{or}}}$\end{document } trigger and offline selection criteria . the average number of interactions per bunch crossing varied from 0.05 to  0.1 . in this analysis the focus is on inelastic ( inel ) pp events originating from single - diffractive , double - diffractive and non - diffractive processes . the inel events are selected with an efficiency \documentclass[12pt]{minimal } 
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				 \begin{document}$\varepsilon _ { \mathrm{mb}_{\mathrm{or}}}$\end{document } of \documentclass[12pt]{minimal } 
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				 \begin{document}$91^{+3.2}_{-1.0}~\%$\end{document } , \documentclass[12pt]{minimal } 
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				 \begin{document}$88.1^{+5.9}_{-3.5}~\%$\end{document } and \documentclass[12pt]{minimal } 
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				 \begin{document}$85.2^{+6.2}_{-3.0}~\%$\end{document } for the three energies . the trigger efficiencies are determined   based on detector simulations with pythia6  [ 24 ] and phojet   event generators . if no vertex is found using tracks in the its and the tpc , it is reconstructed from tracklets in the spd only . tracks or tracklets are extrapolated to the experimental collision region utilizing the averaged measured beam intersection profile in the x  y plane perpendicular to the beam axis . an event is accepted if the z - coordinate of the vertex is within 10  cm of the center of the interaction region along the beam direction . this corresponds to about 1.6 standard deviations from the mean of the reconstructed event vertex distribution for all three energies . in this range , the vertex reconstruction efficiency is independent of  z. the event vertex reconstruction is fully efficient for events with at least one track in the pseudorapidity range ||<1.4 for all three energies . only tracks within a pseudorapidity range of ||<0.8 and transverse momenta pt>0.15  gev / c are selected . a  set of standard cuts based on the number of space points and the quality of the track fit in its and tpc is applied to the reconstructed tracks  . efficiency and purity of the primary charged particle selection are estimated using simulations with pythia6 [ 24 ] and geant3   for particle transport and detector response . the overall pt - dependent efficiency ( tracking efficiency  acceptance ) is 4073  % , 3668  % and 4073  % at \documentclass[12pt]{minimal } 
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				 \begin{document}$\sqrt{s}=0.9,\ 2.76\ \mbox{and}\ 7\ \text{tev}$\end{document}. at \documentclass[12pt]{minimal } 
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				 \begin{document}$\sqrt{s}=2.76~\text{tev}$\end{document } the overall efficiency is lower than at \documentclass[12pt]{minimal } 
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				 \begin{document}$\sqrt { s}=0.9\ \text{and}\ 7\ \text{tev}$\end{document } due to the smaller number of operational channels in the spd . contamination of secondary tracks which passed all selection criteria amounts to 7  % at pt=0.15  gev / c and decreases to 0.6  % for pt>4  gev / c . in addition , the contribution from secondary tracks originating from weak decays of strange hadrons was scaled up by a factor of 11.5 ( pt - dependent ) to match the contribution in data . the secondary tracks were subtracted bin - by - bin from the pt spectra . the pt resolution is estimated from the space point residuals of the track fit . it is verified by the width of the invariant mass peaks of  , \documentclass[12pt]{minimal } 
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				 \begin{document}$\overline{\varlambda}$\end{document } and \documentclass[12pt]{minimal } 
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				 \begin{document}$\mathrm{k}^{0}_{\mathrm{{s}}}$\end{document } , reconstructed from their decays into two charged particles . the relative pt resolution is 3.5  % ,  5.5  %  and  9  % at the highest pt of 20 ,  32  and  50  gev / c at \documentclass[12pt]{minimal } 
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				 \begin{document}$\sqrt{s}=0.9,\ 2.76\ \text{and}\ 7~\text{tev}$\end{document } , respectively . from invariant mass distributions minv(pt ) of  and \documentclass[12pt]{minimal } 
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				 \begin{document}$\mathrm{k}^{0}_{\mathrm{{s}}}$\end{document } , the relative uncertainty on the pt resolution is estimated to be 20  % for all three energies . to account for the finite pt resolution of tracks , correction factors to the spectrum for pt>10  gev / c the choice of the unfolding procedure is based on the observation that pt smearing has a small influence on the measured spectrum . as input to the procedure a power - law parametrization of the measured pt spectrum for pt>10 this parametrization is folded with the pt resolution obtained for a given pt from the measured track covariance matrix . the pt dependent correction factors are extracted from the ratio of the input to the folded parametrization and are applied ( bin - by - bin ) to the measured pt spectrum . it was checked that the derived correction factors are the same when replacing the measured with the corrected pt distribution in the unfolding procedure . the correction factors depend on \documentclass[12pt]{minimal } 
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				 \begin{document}$\sqrt{s}$\end{document } due to the change of the spectral shape and reach 2  % ,  4  %  and  6.5  % at \documentclass[12pt]{minimal } 
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				 \begin{document}$\sqrt{s}=0.9,~2.76~\text{and}~7~\text{tev}$\end{document } for the highest pt . the systematic uncertainty of the momentum scale is |(pt)/pt|<0.01 at pt=50  gev / c , as determined from the mass difference between  and \documentclass[12pt]{minimal } 
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				 \begin{document}$\overline{\varlambda}$\end{document } and the ratio of positively to negatively charged tracks , assuming charge symmetry at high pt . the systematic uncertainties on the event selection are determined by changing the lower and upper limits on the z - coordinate of the vertex . track selection criteria   are varied to determine the corresponding systematic uncertainties resulting in a maximal contribution of 4.35.5  % for pt<0.6 gev / c . the systematic uncertainties on the tracking efficiency are estimated from the difference between data and simulation in the tpc - its track matching efficiency . the systematic uncertainties related to the pt resolution correction are derived from the unfolding procedure including a relative uncertainty on the pt resolution , and reach maximum values at the highest pt covered . the systematic uncertainties on the material budget ( 11.5  % x0 , where x0 is the radiation length ) are estimated by changing the material density ( conservatively ) by 10  % in the simulation , contributing mostly at pt<0.2 gev / c . to assess the systematic uncertainties on the tracking efficiency related to the primary particle composition the relative abundance of  , k , p was varied by 30  % in the simulation ; they contribute mostly at pt<0.5 gev / c . the monte carlo ( mc ) event generator dependence was studied using phojet as a comparison , with the largest contribution at pt<0.2 gev / c . the yield of secondary particles from decays of strange hadrons has been varied by 30  % to determine the corresponding uncertainty of maximum 0.3  % at pt1 gev / c . the total pt  dependent systematic uncertainties for the three energies amount to 6.78.2  % , 6.48.0  % and 6.67.9  % and are shown in the bottom panel of fig . there are also comparable contributions related to the track selection ( pt<0.6 gev / c ) and pt resolution correction at the highest pt covered . the systematic uncertainties on the normalization are related to the minimum bias nucleon  nucleon cross section ( \documentclass[12pt]{minimal } 
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				 \begin{document}$\sigma^{\mathrm { nn}}_{\mathrm{mb}}$\end{document } ) determination   and amount to + 5.1/4.0  % , 1.9  % and 3.6  % for pp at \documentclass[12pt]{minimal } 
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				 \begin{document}$\sqrt{s}=0.9~\mbox{tev},\ 2.76~\text{tev}\ \mbox{and}\ 7~\text{tev}$\end{document } , respectively . 1 
 top : differential cross section of charged particles in inel pp collisions at \documentclass[12pt]{minimal } 
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				 \begin{document}$\sqrt{s } = 0.9,\ 2.76\ \text{and}\ 7~\text{tev}$\end{document } as a function of p 
 t compared to a nlo - pqcd calculation   at the same energy . bottom : systematic uncertainties as a function of p 
 t for all three energies . the uncertainty on the normalization ( compare table  1 ) of the spectra is not included ( color figure online)table  1contribution to the systematic uncertainties on the p 
 t  spectra 
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				 \begin{document}$\sqrt{s}$\end{document } 
 0.9  tev2.76  tev7  tevevent vertex selection1.2  % 2.3  % 0.5  % track selection2.55.5  % 2.35.1  % 1.94.3  % tracking efficiency5  % 5  % 5  % 
 p 
 t  resolution correction<1.7  % < 1.9  % < 2.6  % material budget0.21.5  % 0.21.5  % 0.21.5  % particle composition12  % 12  % 12  % mc event generator2.5  % 23  % 23.5  % secondary strange particles<0.3  % < 0.3  % < 0.3  % total p 
 t  dependent6.78.2  % 6.48.0  % 6.67.9  % normalization uncertainty+5.1/4.0  % 1.9  % 3.6  % 
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				 \begin{document}$\sqrt{s } = 0.9,\ 2.76\ \text{and}\ 7~\text{tev}$\end{document } as a function of p 
 t compared to a nlo - pqcd calculation   at the same energy . bottom : systematic uncertainties as a function of p 
 t for all three energies . the uncertainty on the normalization ( compare table  1 ) of the spectra is not included ( color figure online ) contribution to the systematic uncertainties on the p 
 t  spectra the differential cross section dch / d  dpt is calculated as \documentclass[12pt]{minimal } 
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				 \begin{document}$\mathrm{d}^{2}\sigma_{\mathrm{ch } } / { \mathrm{d}}\eta\,\mathrm { d}p_{\mathrm{t } } = \sigma_{\mathrm{mb}_{\mathrm { or}}}^{\mathrm{nn } } \times\mathrm{d}^{2 } { n}^{\mathrm { mb}_{\mathrm{or}}}_{\mathrm{{ch } } } / { \mathrm{{d } } } \eta \,{\mathrm{{d}}}p_{\mathrm{t}}$\end{document } with \documentclass[12pt]{minimal } 
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				 \begin{document}$\mathrm{{d}}^{2 } { { n}}^{\mathrm{{mb_{\mathrm{{or}}}}}}_{\mathrm { { ch } } } / { \mathrm{{d } } } \eta\,{\mathrm{{d}}}p_{\mathrm{t}}$\end{document } being the per event differential yield of charged particles in minimum bias collisions . \documentclass[12pt]{minimal } 
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				 \begin{document}$\sigma_{\mathrm{mb}_{\mathrm{or}}}^{\mathrm{{nn}}}$\end{document } is determined based on van - der - meer scans   as \documentclass[12pt]{minimal } 
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				 \begin{document}$\sigma_{\mathrm{mb}_{\mathrm{or}}}^{\mathrm{nn } } = 55.4 \pm1.0$\end{document } ( 62.22.2 )  mb at \documentclass[12pt]{minimal } 
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				 \begin{document}$\sqrt{s}=2.76~(7)~\mbox{tev}$\end{document}. at \documentclass[12pt]{minimal } 
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				 \begin{document}$\sqrt{s}=0.9~\mbox{tev}$\end{document } van - der - meer scans were not performed and \documentclass[12pt]{minimal } 
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				 \begin{document}$\sigma_{\mathrm{mb}_{\mathrm{or}}}^{\mathrm { { nn}}}=47.8^{+2.5}_{-3.0}~\mbox{mb}$\end{document } is obtained based on detector simulations using the inel cross section \documentclass[12pt]{minimal } 
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				 \begin{document}$\sigma^{\mathrm{{nn}}}_{\mathrm{{inel}}}=52.5^{+2}_{-3.3}~\mbox{mb}$\end{document }  . \documentclass[12pt]{minimal } 
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				 \begin{document}$\sigma^{\mathrm{{nn}}}_{\mathrm{{inel}}}$\end{document } includes the ua5 measurement   and re - analysis of the extrapolation to low diffractive masses . the differential cross section in inel pp collisions as a function of pt is shown in fig .  1 for all three measured collision energies . at high pt a clear evolution of the slope from \documentclass[12pt]{minimal } 
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				 \begin{document}$\sqrt { s}= 0.9\ \mbox{to}\ 7~\text{tev}$\end{document } can be observed . a  nlo - pqcd calculation   for pt>3 gev / c is compared to the spectra . the calculation shows a similar evolution of the high - pt dependence with \documentclass[12pt]{minimal } 
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				 \begin{document}$\sqrt{s}$\end{document } but overpredicts the data by a factor two [ 12 , 15 ] . the low systematic uncertainties demonstrate the accuracy of the measurements for all energies over the full pt range . though the pt dependence of the cross section for a single \documentclass[12pt]{minimal } 
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				 \begin{document}$\sqrt{s}$\end{document } is not well described by nlo - pqcd , the relative dependence on pt of cross sections of two collision energies is described much better . figure  2 shows the ratio between the differential cross section in inel pp collisions at \documentclass[12pt]{minimal } 
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				 \begin{document}$\sqrt{s } = 2.76\ \mbox{to}\ 7~\mbox{tev},\ 0.9\ \mbox{to}\ 2.76~\mbox{tev}\ \mbox{and}\ 0.9\ \mbox{to}\ 7~\mbox{tev}$\end{document } as a function of pt in comparison to the same ratio calculated with nlo - pqcd . the total pt dependent systematic uncertainties on the ratios are evaluated taking into account correlated contributions , and amount to 8.19.8  % , 7.89.8  % and 7.99.9  % for 0.9  tev/2.76  tev , 0.9  tev/7  tev and 2.76  tev/7  tev . the corresponding normalization uncertainties amount to + 5.4  % /4.4  % , + 6.2  % /5.4  % and 4.1  % , and are calculated assuming that the normalization uncertainties on the pt spectra ( table  1 ) are uncorrelated . in all three ratios good agreement between data and nlo - pqcd calculations is found , which can be seen in the double ratio of data and nlo - pqcd for the three energy ratios in the lower panel of fig .  2 . 2 
 top : ratio of differential cross sections of charged particles in inel pp collisions at different collision energies as a function of p 
 t. gray boxes denote p 
 t dependent systematic uncertainties . a  variation of the renormalization and factorization scale of the nlo calculation gives a systematic uncertainty on the double ratio of 0.523.6  % for 0.9  tev/2.76  tev , 1.037.8  % for 0.9  tev/7  tev and 2.412.3  % for 2.76  tev/7  tev ( color figure online ) 
 top : ratio of differential cross sections of charged particles in inel pp collisions at different collision energies as a function of p 
 t. gray boxes denote p 
 t dependent systematic uncertainties . a  variation of the renormalization and factorization scale of the nlo calculation gives a systematic uncertainty on the double ratio of 0.523.6  % for 0.9  tev/2.76  tev , 1.037.8  % for 0.9  tev/7  tev and 2.412.3  % for 2.76  tev/7  tev ( color figure online ) for the determination of the nuclear modification factor 
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				 \begin{document}$$ r_{\mathrm{aa } } ( p_{\mathrm{t } } ) = \frac { \mathrm{d}^2 { n } _ { \mathrm{ch}}^{\mathrm{aa}}/ { \mathrm{d } } \eta\,{\mathrm { d}}p_{\mathrm{t } } } { \langle t_{\mathrm{aa } } \rangle\ , \mathrm{d}^2 \sigma_{\mathrm { ch}}^{\mathrm{pp } } / { \mathrm{d } } \eta\,{\mathrm{d}}p_{\mathrm{t } } } $ $ \end{document } in heavy - ion collisions a well described pp reference \documentclass[12pt]{minimal } 
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				 \begin{document}$\mathrm{d}^{2 } \sigma_{\mathrm { ch}}^{\mathrm{pp } } / { \mathrm{d } } \eta\,{\mathrm{d}}p_{\mathrm{t}}$\end{document } at the same center - of - mass energy up to high pt is essential . \documentclass[12pt]{minimal } 
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				 \begin{document}${n}_{\mathrm{ch}}^{\mathrm{aa}}$\end{document } describes the charged particle yield per event in nucleus nucleus collisions and taa is the average nuclear overlap function  [ 6 , 10 ] . the statistics in the measurement of \documentclass[12pt]{minimal } 
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				 \begin{document}$\mathrm{d}^{2 } \sigma_{\mathrm { ch}}^{\mathrm{pp } } / { \mathrm{d } } \eta\,{\mathrm{d}}p_{\mathrm{t}}$\end{document } for \documentclass[12pt]{minimal } 
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				 \begin{document}$\sqrt{s } = 2.76\ \mbox{tev}$\end{document } reported in this paper allows pt=32 gev / c to be reached . in order to extrapolate to higher pt , the measured cross section needs to be parametrized . as can be seen in fig . 1 for pt>10 gev / c the pp spectrum at \documentclass[12pt]{minimal } 
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				 \begin{document}$\sqrt{s } = 2.76\ \mbox{tev}$\end{document } shows a clear power - law dependence on pt . to constrain the parametrization better by including data points at lower pt , \documentclass[12pt]{minimal } 
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				 \begin{document}$\mathrm{d}^{2 } \sigma_{\mathrm{ch}}^{\mathrm{pp } } / { \mathrm{d } } \eta\,{\mathrm{d}}p_{\mathrm{t}}$\end{document } has been parametrized by a so - called modified hagedorn function  
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				 \begin{document}$$ \frac{1}{2\pi p_{\mathrm{t}}}\frac{\mathrm{d}^2 \sigma_{\mathrm { ch}}^{\mathrm{pp}}}{\mathrm{d } \eta\,{\mathrm{d}}p_{\mathrm{t } } } = a \frac{p_{\mathrm{t}}}{m_{\mathrm{t } } } \biggl(1 + \frac{p_{\mathrm { t}}}{p_{\mathrm{t,0 } } } \biggr)^{-n } $ $ \end{document } where mt denotes the transverse mass \documentclass[12pt]{minimal } 
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				 \begin{document}$m_{\mathrm{t } } = \sqrt{m_{0}^{2 } + p_{\mathrm{t}}^{2}}$\end{document } , with m0=140 mev / c assumed for all tracks . for small pt , the term \documentclass[12pt]{minimal } 
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				 \begin{document}$(1 + \frac { p_{\mathrm{t}}}{p_{\mathrm{t,0 } } } ) ^{-n}$\end{document } behaves like an exponential function with an inverse slope parameter of \documentclass[12pt]{minimal } 
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				 \begin{document}$p_{\mathrm{t,0}}/n$\end{document } while for large pt the hagedorn function behaves like a power - law function . to determine the extrapolation to high pt , \documentclass[12pt]{minimal } 
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				 \begin{document}$\mathrm { d}^{2 } \sigma_{\mathrm{ch}}^{\mathrm{pp } } / { \mathrm{d } } \eta \,{\mathrm{d}}p_{\mathrm{t}}$\end{document } is parametrized for pt>5 gev / c . for 5 gev / c < pt<10  gev / c the exponential part of the hagedorn function acts as a correction term to the power - law part in the function . figure  3 shows the differential cross section in inel pp collisions as a function of pt for \documentclass[12pt]{minimal } 
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				 \begin{document}$\sqrt{s } = 2.76~\mbox{tev}$\end{document } together with the parametrization for pt>5 gev / c . the ratio between data and parametrization in the lower panel demonstrates the good agreement of the parametrization with the data . the gray band indicates the total pt dependent systematic uncertainty of the measured spectrum as presented in table  1 . 3 
 top : differential cross section of charged particles in inel pp collisions at \documentclass[12pt]{minimal } 
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				 \begin{document}$\sqrt{s } = 2.76\ \mbox{tev}$\end{document } as a function of p 
 t together with the parametrization ( p 
 t>5 gev / c ) described in the text . the gray band indicates the total p 
 t dependent systematic uncertainty of the data , open circles show data points only used for the evaluation of the systematic uncertainty of the parametrization ( color figure online ) 
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				 \begin{document}$\sqrt{s } = 2.76\ \mbox{tev}$\end{document } as a function of p 
 t together with the parametrization ( p 
 t>5 gev / c ) described in the text . the gray band indicates the total p 
 t dependent systematic uncertainty of the data , open circles show data points only used for the evaluation of the systematic uncertainty of the parametrization ( color figure online ) to estimate the systematic uncertainty of the parametrization and extrapolation , the lower boundary of the fit range of the hagedorn parametrization is varied between pt=3 gev / c and pt=7 gev / c , while the upper boundary is fixed to the highest data point measured at pt=32 gev / c . together with the systematic uncertainties on the measured differential cross section as shown in table  1 this results in a total systematic uncertainty on the reference at \documentclass[12pt]{minimal } 
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				 \begin{document}$\sqrt{s } = 2.76\ \mbox{tev}$\end{document } of 6.4  % for low pt up to 19  % at pt=50  gev / c . the final pp reference for the determination of raa at \documentclass[12pt]{minimal } 
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				 \begin{document}$\sqrt{s } = 2.76\ \mbox{tev}$\end{document } is constructed from the measured data points up to pt=5 gev / c and the parametrization for pt>5 gev / c . statistical uncertainties in the extrapolated part of the reference are obtained from the covariance matrix of the parametrization . the systematic uncertainties on the spectrum are propagated to the reference by application of the full extrapolation procedure using the measured data points shifted up and down by the total systematic uncertainty . figure  4 shows the ratio between alternative pp references and the reference at \documentclass[12pt]{minimal } 
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				 \begin{document}$\sqrt{s } = 2.76\ \mbox{tev}$\end{document } presented in this paper . above pt=20  gev / c simulations with the pythia8 generator   agree with the new reference for pt>15 gev / c . below pt=20  gev / c , the shape of the pythia8 spectrum is similar to the measured reference . a  pp reference presented by the cms collaboration   agrees best for pt<6 gev / c . the overall normalization systematic uncertainties 1.9  % ( 6  % ) for alice ( cms ) are not included in the comparison . a  reference based on an interpolation between measured yields at \documentclass[12pt]{minimal } 
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				 \begin{document}$\sqrt { s } = 0.9\ \text{and}\ 7~\text{tev}$\end{document } as discussed in   does not agree with the new reference for pt>6 gev / c . finally a scaling of the measured differential cross section in inel pp collisions at \documentclass[12pt]{minimal } 
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				 \begin{document}$\sqrt{s } = 7\ \mbox{tev}$\end{document } with the ratio of pqcd calculations ( as shown in fig . 2 ) 
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				 \begin{document } $ $ \begin{aligned } { \mathrm{d}}^2 \sigma_{\mathrm{ch}}^{\mathrm{pp } } / { \mathrm{d } } \eta\,{\mathrm{d}}p_{\mathrm{t } } |_{2.76\ \mathrm{tev } } & = \frac { \mathrm{d}^2 \sigma_{\mathrm{ch}}^{\mathrm{pp } } / { \mathrm{d } } \eta\,{\mathrm{d}}p_{\mathrm{t}}| _ { \mathrm{nlo } , 2.76\ \mathrm{tev } } } { \mathrm{d}^2 \sigma_{\mathrm{ch}}^{\mathrm{pp } } / { \mathrm{d } } \eta\,{\mathrm{d}}p_{\mathrm{t } } |_{\mathrm{nlo},\ 7\ \mathrm{tev } } } \\ & \quad \times \mathrm{d}^2 \sigma_{\mathrm{ch}}^{\mathrm{pp } } / { \mathrm{d } } \eta\ , { \mathrm{d}}p_{\mathrm{t}}|_{7\ \mathrm{tev } } \end{aligned}$$ \end{document } agrees well in shape and normalization with the measured data over a wide range in pt . the systematic uncertainty of the new reference is indicated in fig .  4 as a gray band for comparison 4ratio of alternative references to the new constructed pp reference at \documentclass[12pt]{minimal } 
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				 \begin{document}$\sqrt{s } = 2.76\ \mbox{tev}$\end{document } as discussed in the text . the gray band indicates the total p 
 t dependent systematic uncertainty as discussed in the text . the overall normalization systematic uncertainties 1.9  % ( 6  % ) for alice ( cms ) are not shown ( color figure online ) ratio of alternative references to the new constructed pp reference at \documentclass[12pt]{minimal } 
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				 \begin{document}$\sqrt{s } = 2.76\ \mbox{tev}$\end{document } as discussed in the text . the gray band indicates the total p 
 t dependent systematic uncertainty as discussed in the text . the overall normalization systematic uncertainties 1.9  % ( 6  % ) for alice ( cms ) are not shown ( color figure online ) similar to raa , a nuclear modification factor rpa in proton - lead collisions has been studied   at \documentclass[12pt]{minimal } 
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				 \begin{document}$\sqrt{s } = 5.02\ \mbox{tev}$\end{document}. no measured pp reference is available at this collision energy . due to the asymmetric p pb collision system , the  coverage of the detector is shifted with respect to the symmetric pp or pb  pb collisions . to obtain a maximum overlap between the pp and p  pb systems , a pp reference is needed for ||<0.3 . to construct the pp reference at this energy , different methods for three 0.15<pt<5 gev / c : as nlo - pqcd becomes unreliable for small pt , the measured differential cross sections for pp collisions of \documentclass[12pt]{minimal } 
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				 \begin{document}$\sqrt{s } = 2.76\ \mbox{and}\ 7~\text{tev}$\end{document } are interpolated for a given pt , assuming a power - law behavior of the \documentclass[12pt]{minimal } 
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				 \begin{document}$\sqrt{s}$\end{document } dependence of the cross section . here the maximum relative systematic uncertainty of the underlying measurements has been assigned as systematic uncertainty . 5<pt<20 gev / c : the measured differential cross section for pp collisions at \documentclass[12pt]{minimal } 
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				 \begin{document}$\sqrt{s } = 7\ \mbox{tev}$\end{document } is scaled to \documentclass[12pt]{minimal } 
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				 \begin{document}$\sqrt{s } = 5.02\ \mbox{tev}$\end{document } using the nlo - pqcd calculations ( eq .  ( 3 ) ) . systematic uncertainties are determined by taking into account differences to an interpolated reference as well as to a scaled reference using =pt/2 and =2pt as alternative choices for the renormalization and factorization scales . pt>20 gev / c : the nlo - scaled reference is parametrized in the range 20<pt<50 gev / c by a power - law function and the parametrization is used . the constructed pp reference for \documentclass[12pt]{minimal } 
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				 \begin{document}$\sqrt{s } = 5.02\ \mbox{tev}$\end{document } is shown in fig .  5 together with the reference for \documentclass[12pt]{minimal } \usepackage{amsmath } 
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				 \begin{document}$\sqrt{s}=2.76~\mbox{tev}$\end{document } discussed above . for pt>20 gev / c the data points show the nlo - scaled reference which is parametrized by a power - law function ( line ) to obtain the final reference at \documentclass[12pt]{minimal } 
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				 \begin{document}$\sqrt { s } = 5.02\ \mbox{tev}$\end{document}. in the bottom part of the figure a comparison of the nlo - scaled reference and the parametrization is shown . 5 
 top : constructed pp references for \documentclass[12pt]{minimal } 
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				 \begin{document}$\sqrt{s } = 2.76\ \text{and } \ \sqrt{s } = 5.02\ \mbox{tev}$\end{document}. bottom : comparison of nlo - scaled reference and parametrization . the gray band indicates the total p 
 t dependent systematic uncertainty as discussed in the text ( color figure online ) 
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				 \begin{document}$\sqrt{s } = 2.76\ \text{and } \ \sqrt{s } = 5.02\ \mbox{tev}$\end{document}. bottom : comparison of nlo - scaled reference and parametrization . the gray band indicates the total p 
 t dependent systematic uncertainty as discussed in the text ( color figure online ) differential cross sections of charged particles in inelastic pp collisions as a function of pt have been presented for \documentclass[12pt]{minimal } 
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				 \begin{document}$\sqrt{s } = 0.9,\ 2.76\ \text{and}\ 7~\text{tev}$\end{document}. comparisons of the pt spectra with nlo - pqcd calculations show that the cross section for an individual value of \documentclass[12pt]{minimal } 
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				 \begin{document}$\sqrt{s}$\end{document } can not be described by the calculation . the relative increase of cross section with \documentclass[12pt]{minimal } 
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				 \begin{document}$\sqrt{s}$\end{document } is well described by nlo - pqcd , however . the systematic comparison of the energy dependence can help to tune the model dependent ingredients in the calculation . utilizing these observations and measurements procedures are discussed to construct pp reference spectra at \documentclass[12pt]{minimal } 
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				 \begin{document}$\sqrt{s } = 2.76$\end{document } ( ||<0.8 ) and 5.02  tev ( ||<0.3 ) in the corresponding pt range of charged particle pt spectra in pb  pb and p  pb collisions measured by the alice experiment . the reference spectra are used for the calculation of the nuclear modification factors raa   and rpa  . the systematic uncertainties related to the pp reference were significantly reduced with respect to the previous measurement by using the pt distribution measured in pp collisions at \documentclass[12pt]{minimal } 
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				 \begin{document}$\sqrt{s}=2.76~\mbox{tev}$\end{document}.
differential cross sections of charged particles in inelastic pp collisions as a function of pt have been measured at \documentclass[12pt]{minimal } 
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				 \begin{document}$\sqrt{s } = 0.9,\ 2.76\ \text{and}\ 7\ \text{tev}$\end{document } at the lhc . 
 the pt spectra are compared to nlo - pqcd calculations . 
 though the differential cross section for an individual \documentclass[12pt]{minimal } 
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				 \begin{document}$\sqrt{s}$\end{document } can not be described by nlo - pqcd , the relative increase of cross section with \documentclass[12pt]{minimal } 
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				 \begin{document}$\sqrt{s}$\end{document } is in agreement with nlo - pqcd . 
 based on these measurements and observations , procedures are discussed to construct pp reference spectra at \documentclass[12pt]{minimal } 
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				 \begin{document}$\sqrt{s } = 2.76\ \text{and}\ 5.02~\text{tev}$\end{document } up to pt=50 gev / c as required for the calculation of the nuclear modification factor in nucleus  nucleus and proton  nucleus collisions .