4. Results 119
4.2. Construction of pp references
4.2.2. pp reference for p
pp Reference Paper The ALICE Collaboration
) c (GeV/
pT
0 10 20 30 40 50
alt. ref. / ref.
0.6 0.8 1 1.2
1.4 Pythia 8 NLO scaled s = 7 TeV CMS Interp. ref. ALICE [171]
Fig. 4: (color online) Ratio of alternative references to the new constructed pp reference at √
s = 2.76 TeV as discussed in the text. The grey band indicates the total p
Tdependent systematic uncertainty as discussed in the text. The overall normalization systematic uncertainties ± 1.9% ( ± 6%) for ALICE (CMS) are not shown.
the upper boundary is fixed to the highest data point measured at p
T= 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 √
s = 2.76 TeV of 6.4% for low p
Tup to 19% at p
T= 50 GeV/c.
The final pp reference for the determination of R
AAat √
s = 2.76 TeV is constructed from the measured data points up to p
T= 5 GeV/c and the parametrization for p
T> 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.
This reference is compared to alternative measurements and approaches. Figure 4 shows the ratio be-tween alternative pp references and the reference at √
s = 2.76 TeV presented in this paper. Above p
T= 20 GeV/c, all references agree within the systematic uncertainties. Simulations with the PYTHIA8 generator [15] agree with the new reference for p
T> 15 GeV/c. Below p
T= 20 GeV/c, the shape of the PYTHIA8 spectrum is similar to the measured reference. A pp reference presented by the CMS collab-oration [16] agrees best for p
T< 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 be-tween measured yields at √
s = 0.9 and 7 TeV as discussed in [4] does not agree with the new reference for p
T> 6 GeV/c. Finally a scaling of the measured differential cross section in INEL pp collisions at
√ s = 7 TeV with the ratio of pQCD calculations (as shown in Figure 2)
d
2σ
chpp/d η dp
T|
2.76TeV= d
2σ
chpp/d η dp
T|
NLO,2.76TeVd
2σ
chpp/d η dp
T|
NLO,7TeV× d
2σ
chpp/d η dp
T|
7TeV(3) agrees well in shape and normalization with the measured data over a wide range in p
T. The systematic uncertainty of the new reference is indicated in Figure 4 as a grey band for comparison.
5 Construction of a pp reference for √
s = 5.02 TeV
Similar to R
AA, a nuclear modification factor R
pAin proton-lead collisions has been studied [17] at
√ s = 5.02 TeV. No measured pp reference is available at this collision energy. Due to the asymmetric p-Pb collision system, the η 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 | η | < 0.3. To construct the pp reference at this energy, different methods for three p
T-ranges are combined.
0.15 < p
T< 5 GeV/c: As NLO-pQCD becomes unreliable for small p
T, the measured differential cross 8
Figure 4.8.: Comparison of alternative pp references atp
s= 2.76 TeV discussed in the text to the chosen one in term of the ratio. The gray band around unity shows thepT de-pendent uncertainty of the reference. Additional normalization uncertainties are not shown. Error-bars shown for the CMS reference are statistical and systematic uncertainties added in quadrature.
Figure published in [178].
is constructed from the data atp
s = 2.76 and 7 TeV assuming a power law behavior of the differential cross section as a function ofp
s for fixedpT: d2σ(p
s) dηd pT ∝p
sn. (4.6)
The pp reference spectrum in the range0.15<pT<5 GeV/cis obtained from this power law interpolation for eachpT bin.
The systematic uncertainty of the pp reference is determined by the maximal relative system-atic uncertainty of the data atp
s= 2.76 and 7 TeV in the rangepT<5 GeV/c. ForpT>5 GeV the uncertainty of the underlyingp
s = 7 TeV measurement is added in quadrature with the uncertainty from a scale variation ofpT/2< µ <2pT in the NLO calculation. In addition, the difference between the power law interpolation and the NLO scaling in the overlap region of 3<pT<5 GeV/cis assigned as an uncertainty of the method and added quadratically. Sta-tistical uncertainties of the measured data atp
s = 2.76 TeV andp
s = 7 TeV are independent and propagated to the pp reference according to Equation (4.6) for pT < 5 GeV/c. Above pT =5 GeV the relative statistical uncertainties are identical to the ones of thep
s = 7 TeV data.
The pp reference spectrum forp
s = 5.02 TeV and η
<0.3is shown in Figure 4.9 together with the power law parameterization. The ratio DATA/FIT in the bottom panel of Figure 4.7 demonstrates that the highpTpart of the spectrum is well described by the power law function.
While only data points above 20GeV/cin pT are used for the fit, the extrapolation of the fit towards lowerpT is in remarkable agreement with the data (open points in Figure 4.9).
The overall systematic uncertainty (excluding normalization) of the pp reference spectrum amounts to 6.7-8.4% for the full pT range of 0.15 < pT <50 GeV/c and is shown as gray band in the lower panel of Figure 4.9. The publication of RpPb [164] covers only the range 0.5<pT<20 GeV/c, in this range the uncertainty of the reference amounts to 7.7-8.2%. The additional normalization uncertainty of 3.6% is identical to the one in pp atp
s= 7 TeV. Also the statistical uncertainties at high pT are fixed from the 7 TeV pp data. They remain below 5% forpT<20 GeV/cand reach 16% at 50GeV/c.
For the second publication of p–Pb spectra with the extended kinematic range of 0.15 <
pT < 50 GeV/c the power law parameterization of the pp reference has not been adopted to calculate the nuclear modification factor. Instead, the pp reference spectrum for the full acceptance
η
<0.8was used, since only a weak pseudorapidity dependence of thepTspectra for
η
<0.8is observed [173].
132 4. Results
pp Reference Paper The ALICE Collaboration
)2c -2 ) (mb GeV Tp dη)/(dchσ2 ) (d Tp π1/(2
10-9
10-8
10-7
10-6
10-5
10-4
10-3
10-2
10-1
1 10 102
103
ALICE, pp references
| < 0.3 η = 5.02 TeV, | s
> 20 GeV/c) power-law fit (pT
| < 0.8 η = 2.76 TeV, | s
) c (GeV/
pT
10-1 1 10
ref. / fit
0.6 0.7 0.8 0.91 1.1 1.2 1.3
1.4 syst. uncert. reference = 5.02 TeV
s
Fig. 5: (color online) Top: Constructed pp references for√
s = 2.76 and √
s = 5.02 TeV. Bottom: Comparison of NLO-scaled reference and parametrization. The parametrization is used for pT >20 GeV/c. The grey band indicates the total pT dependent systematic uncertainty as discussed in the text.
sections for pp collisions of √
s = 2.76 and 7 TeV are interpolated for a given p
T, assuming a power-law behaviour of the √
s dependence of the cross section. Here the maximum relative systematic uncertainty of the underlying measurements has been assigned as systematic uncertainty.
5 < p
T< 20 GeV/c: The measured differential cross section for pp collisions at √
s = 7 TeV is scaled to
√ s = 5.02 TeV using the NLO-pQCD calculations (Equation 3). Systematic uncertainties are determined by taking into account differences to an interpolated reference as well as to a scaled reference using µ = p
T/2 and µ = 2p
Tas alternative choices for the renormalization and factorization scales.
p
T> 20 GeV/c: The NLO-scaled reference is parametrized in the range 20 < p
T< 50 GeV/c by a power-law function and the parametrization is used.
The constructed pp reference for √ s = 5.02 TeV is shown in Figure 5 together with the reference for
√ s = 2.76 TeV discussed above. For p
T> 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 √
s = 5.02 TeV. In the bottom part of the figure a comparison of the NLO-scaled reference and the parametrization is shown.
6 Summary
Differential cross sections of charged particles in inelastic pp collisions as a function of p
Thave been presented for √
s = 0.9, 2.76 and 7 TeV. Comparisons of the p
Tspectra with NLO-pQCD calculations show that the cross section for an individual value of √
s cannot be described by the calculation. The relative increase of cross section with √
s 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.
9
Figure 4.9.: Top: Constructed pp references for p
s = 2.76 TeV ( η
< 0.8) and 5.02 TeV (
η
< 0.3) as described in the text. The power law parameterization of the reference at p
s = 5.02 TeV is shown for pT > 20 GeV/c. Bottom: Ratio of the reference at p
s = 5.02 TeV obtained from NLO-scaling to the power law parameterization. The band around unity shows the systematic uncertainty of the 5.02 TeV reference.
Figure published in [178].
4.2. Construction of pp references 133