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Text: −0.048 nb , where the first uncertainties are statistical , the second systematic and the third are due to the unknown polarisation of the three Υ states . The integrated Υ ( 1S ) cross - section is about a factor one hundred smaller than the integrated J / ψ cross - section in the identical region of p T and y [ 26 ] , and a factor three smaller than the integrated Υ ( 1S ) cross - section in the central region , as measured by CMS [ 16 ] and ATLAS [ 15 ] . Figure 4 compares the LHCb measurement of the differential Υ ( 1S ) → µ + µ − production cross - section with several theory predictions in the LHCb acceptance region . In Fig . 4(a ) the data are compared to direct production as calculated from a NNLO * colour - singlet model [ 29 ] , where the notation NNLO * denotes an evaluation that is not a complete next - to - next leading order computation and that can be affected by logarithmic corrections , which are not easily quantifiable . Direct production as calculated from NLO CSM is also represented . In Fig . 4(b ) the data are compared to two model predictions for the Υ ( 1S ) production : the calculation from NRQCD at NLO , including contributions from χ b and higher Υ states decays , summing the colour - singlet and colour - octet contributions [ 30 ] , and the calculation from the NLO CEM , including contributions from χ b and higher Υ states decays [ 11 ] . Note that the NNLO * theoretical model computes the direct Υ ( 1S ) production , whereas the LHCb measurement includes Υ ( 1S ) from χ b , Υ ( 2S ) and Υ ( 3S ) decays . However , taking into account the feed - down contribution , which has been measured to be of the order of 50 % [ 31 ] , a satisfactory agreement is found with the theoretical predictions . Figure 5 compares the LHCb measurement of the differential Υ ( 2S ) and Υ ( 3S ) production cross - sections times branching fraction with the NNLO * theory predictions of direct production . It can be seen that the agreement with the theory is better for the Υ ( 3S ) , which is expected to be less affected by feed - down . At present there is no measurement of the contribution of feed - down to the Υ ( 2S ) and Υ ( 3S ) inclusive rate . The cross - sections times the dimuon branching fractions for the three Υ states are compared in Fig . 6 as a function of rapidity and transverse momentum . The cross - section results are used to evaluate the ratios R iS/1S of the Υ ( 2S ) to Υ ( 1S ) and Υ ( 3S ) to Υ ( 1S ) cross - sections times the dimuon branching fractions . Most of the systematic uncertainties on the cross - sections cancel in the ratio , except those due to the size of the data sample , the choice of fit function and the unknown polarisation of the different states . The polarisation uncertainty has been evaluated for the scenarios in which one of the two Υ states is completely polarised ( either transversely or longitudinally ) and the other is not polarised . The maximum difference of these two cases ranges between 15 % and 26 % . The ratios R iS/1S , i = 2 , 3 , are given in Table 5 Figure 4 : Differential Υ ( 1S ) → µ + µ − production cross - section times dimuon branching fraction as a function of p T integrated over y in the range 2.0 - 4.5 , compared with the predictions from ( a ) the NNLO * CSM [ 29 ] for direct production , and ( b ) the NLO NRQCD [ 30 ] and CEM [ 11 ] . The error bars on the data correspond to the total uncertainties for each bin , while the bands indicate the uncertainty on the theory prediction .    [ 29 ] . The error bars on the data correspond to the total uncertainties for each bin , while the bands indicate the uncertainty on the theory prediction . uncertainty is not included in these figures . The results agree well with the corresponding ratio measurements from CMS [ 16 ] in the p T range common to both experiments .   Figure 7 : Ratios of Υ ( 2S ) → µ + µ − and Υ ( 3S ) → µ + µ − with respect to Υ ( 1S ) → µ + µ − as a function of p T of the Υ in the range 2.0 < y < 4.5 , assuming no polarisation . The error bars on the data correspond to the total uncertainties for each bin except for that due to the unknown polarisation .<|eot_id|><|start_header_id|>assistant<|end_header_id|>

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