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| CMS-GEN-22-001 ; CERN-EP-2024-216 | ||
| Energy-scaling behavior of intrinsic transverse momentum parameters in Drell-Yan simulation | ||
| CMS Collaboration | ||
| 26 September 2024 | ||
| Submitted to Phys. Rev. Lett. | ||
| Abstract: We present an analysis based on models of the intrinsic transverse momentum of partons in nucleons by studying the dilepton transverse momentum in Drell-Yan events. Using parameter tuning in event generators and existing data from fixed-target experiments, from the Tevatron, and from the LHC, our investigation spans three orders of magnitude in center-of-mass energy and two orders of magnitude in dilepton invariant mass. The results show an energy-scaling behavior of the intrinsic transverse momentum parameters, independent of the dilepton invariant mass at a given center-of-mass energy. | ||
| Links: e-print arXiv:2409.17770 [hep-ex] (PDF) ; CDS record ; inSPIRE record ; CADI line (restricted) ; | ||
| Figures | |
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Figure 1:
Tuned parameter $ q $ values for DY measurements at different center-of-mass energies (points) for various PYTHIA and HERWIG setups (colors). The error bars on the points represent the tuning uncertainties. The tuned values are given in Appendix. For each generator setup, the function $ b \sqrt{s}^a $ is fitted to the points and shown as a line, assuming the same slope $ a $ for all the settings. The $ \chi^2_{\text{lin.}}/\text{NDF} $ and $ p $-value of the combined linear fit is given in the plot. The uncertainty in each fit is shown as a colored band and corresponds to the up and down variations of the fit parameters, propagated from the tune uncertainties. The CASCADE predictions (CAS3) [2,3] are also fitted separately with the function $ b \sqrt{s}^a $ for comparison with PYTHIA and HERWIG. |
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Figure 2:
Tuned parameter $ q $ values for DY measurements at different center-of-mass energies (points) for various generator settings (lines and bands). The error bars on the points represent the tuning uncertainties. The tuned values are given in Appendix. For the PYTHIA CP5 setup, the parameter SPACESHOWER:PT0REF is set to 1 GeV (orange dashed) or its default value of 2 GeV (blue solid). For the HERWIG CH3 setup, the parameter SUDAKOVCOMMON:PTMIN is set to 0.7 GeV (green dotted) or its default value of 1.22 GeV (purple dash-dotted). The function $ b \sqrt{s}^a $ is fitted to the points of each generator setting and shown as a line, allowing free-floating slopes $ a $ and offsets $ \log_{10}(b) $. The uncertainty in each fit is shown as a colored band and corresponds to the up and down variations of the fit parameters, propagated from the tune uncertainties. |
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Figure 3:
Tuned parameter values (points) for DY measurements at four different center-of-mass energies (panels) for the PYTHIA CP5 (blue) and HERWIG CH3 (green) setups. The error bars on the points represent the tuning uncertainties. The tuned values are given in Appendix. For each generator setup, a constant is fitted to the points and shown as a line. The uncertainty in each fit, propagated from the tune uncertainties, is shown as a colored band. |
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Figure A1:
Effects of the variation of the UE parameters on the DY $ p_{\mathrm{T}}(\ell^+\ell^-) $ spectrum (upper), and of the variation of the intrinsic $ k_{\mathrm{T}} $ parameter on the density of the scalar sum of the charged-particle transverse momenta ($ p_{\mathrm{T}}^{\text{sum}} $) on the rapidity ($ \eta $) - azimuthal angle ($ \phi $) space as a function of the transverse momentum of the leading charged particle ($ p_{\mathrm{T}}^{\text{max}} $) in the transMAX region averaged over $ N_\text{events} $ generated events [28] in the minimum bias (MB) process (lower), which is one of the observables used for UE tuning. For each event, the transMAX region is defined by the direction of the leading charged particle in the space transverse to the proton beams. Assuming $ \phi $ as the azimuthal angle of the leading charged particle, the ranges of $ \phi_1 $ satisfying $ 60^{\circ} < |\phi-\phi_1| < 120^{\circ} $ define the two transverse regions, in which transMAX is the one with a higher activity. The red and violet shaded areas represent the predictions from the up and down variations of the UE tune and the intrinsic $ k_{\mathrm{T}} $ tune, respectively. In the upper distribution, both shaded areas are based on the prediction of tuned intrinsic $ k_{\mathrm{T}} $ parameter on top of PYTHIA CP5 (``int.$ k_{\mathrm{T}} $ tune''). In the lower distribution, the red shaded area is based on the prediction of the intrinsic $ k_{\mathrm{T}} $ parameter set to the default 1.8 and the UE tune set to PYTHIA CP5 (``Default int.$ k_{\mathrm{T}} $''), while the violet shaded area is based on the ``int.$ k_{\mathrm{T}} $ tune'' prediction. The error bars represent the statistical uncertainty in the simulated events. The upper distribution also includes the UE prediction of the combined tune of the intrinsic $ k_{\mathrm{T}} $ and the ISR cutoff scale to the DY $ p_{\mathrm{T}}(\ell^+\ell^-) $ distribution (``int.$ k_{\mathrm{T}} $+ISR $ p_{\text{T0Ref}} $ tune''). |
png pdf |
Figure A1-a:
Effects of the variation of the UE parameters on the DY $ p_{\mathrm{T}}(\ell^+\ell^-) $ spectrum (upper), and of the variation of the intrinsic $ k_{\mathrm{T}} $ parameter on the density of the scalar sum of the charged-particle transverse momenta ($ p_{\mathrm{T}}^{\text{sum}} $) on the rapidity ($ \eta $) - azimuthal angle ($ \phi $) space as a function of the transverse momentum of the leading charged particle ($ p_{\mathrm{T}}^{\text{max}} $) in the transMAX region averaged over $ N_\text{events} $ generated events [28] in the minimum bias (MB) process (lower), which is one of the observables used for UE tuning. For each event, the transMAX region is defined by the direction of the leading charged particle in the space transverse to the proton beams. Assuming $ \phi $ as the azimuthal angle of the leading charged particle, the ranges of $ \phi_1 $ satisfying $ 60^{\circ} < |\phi-\phi_1| < 120^{\circ} $ define the two transverse regions, in which transMAX is the one with a higher activity. The red and violet shaded areas represent the predictions from the up and down variations of the UE tune and the intrinsic $ k_{\mathrm{T}} $ tune, respectively. In the upper distribution, both shaded areas are based on the prediction of tuned intrinsic $ k_{\mathrm{T}} $ parameter on top of PYTHIA CP5 (``int.$ k_{\mathrm{T}} $ tune''). In the lower distribution, the red shaded area is based on the prediction of the intrinsic $ k_{\mathrm{T}} $ parameter set to the default 1.8 and the UE tune set to PYTHIA CP5 (``Default int.$ k_{\mathrm{T}} $''), while the violet shaded area is based on the ``int.$ k_{\mathrm{T}} $ tune'' prediction. The error bars represent the statistical uncertainty in the simulated events. The upper distribution also includes the UE prediction of the combined tune of the intrinsic $ k_{\mathrm{T}} $ and the ISR cutoff scale to the DY $ p_{\mathrm{T}}(\ell^+\ell^-) $ distribution (``int.$ k_{\mathrm{T}} $+ISR $ p_{\text{T0Ref}} $ tune''). |
png pdf |
Figure A1-b:
Effects of the variation of the UE parameters on the DY $ p_{\mathrm{T}}(\ell^+\ell^-) $ spectrum (upper), and of the variation of the intrinsic $ k_{\mathrm{T}} $ parameter on the density of the scalar sum of the charged-particle transverse momenta ($ p_{\mathrm{T}}^{\text{sum}} $) on the rapidity ($ \eta $) - azimuthal angle ($ \phi $) space as a function of the transverse momentum of the leading charged particle ($ p_{\mathrm{T}}^{\text{max}} $) in the transMAX region averaged over $ N_\text{events} $ generated events [28] in the minimum bias (MB) process (lower), which is one of the observables used for UE tuning. For each event, the transMAX region is defined by the direction of the leading charged particle in the space transverse to the proton beams. Assuming $ \phi $ as the azimuthal angle of the leading charged particle, the ranges of $ \phi_1 $ satisfying $ 60^{\circ} < |\phi-\phi_1| < 120^{\circ} $ define the two transverse regions, in which transMAX is the one with a higher activity. The red and violet shaded areas represent the predictions from the up and down variations of the UE tune and the intrinsic $ k_{\mathrm{T}} $ tune, respectively. In the upper distribution, both shaded areas are based on the prediction of tuned intrinsic $ k_{\mathrm{T}} $ parameter on top of PYTHIA CP5 (``int.$ k_{\mathrm{T}} $ tune''). In the lower distribution, the red shaded area is based on the prediction of the intrinsic $ k_{\mathrm{T}} $ parameter set to the default 1.8 and the UE tune set to PYTHIA CP5 (``Default int.$ k_{\mathrm{T}} $''), while the violet shaded area is based on the ``int.$ k_{\mathrm{T}} $ tune'' prediction. The error bars represent the statistical uncertainty in the simulated events. The upper distribution also includes the UE prediction of the combined tune of the intrinsic $ k_{\mathrm{T}} $ and the ISR cutoff scale to the DY $ p_{\mathrm{T}}(\ell^+\ell^-) $ distribution (``int.$ k_{\mathrm{T}} $+ISR $ p_{\text{T0Ref}} $ tune''). |
| Tables | |
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Table 1:
Measurements of the Drell-Yan differential cross section as a function of $ p_{\mathrm{T}}(\ell^+\ell^-) $ at various center-of-mass energies $ \sqrt{s} $ from different hadron-collision processes used as inputs for the intrinsic $ k_{\mathrm{T}} $ tunes. The $ \sqrt{s} $ in $ \mathrm{p}\mathrm{Pb} $ collisions represents the nucleon-nucleon center-of-mass energy. The variable $ Q $ represents the energy scale of the hard scattering, approximated by the dilepton invariant mass. The Z boson mass is denoted as $ m(\mathrm{Z}) $. |
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Table B1:
Tune results for the BEAMREMNANTS:PRIMORDIALKTHARD parameter in PYTHIA 8 and the SHOWERHANDLER:INTRINSICPTGAUSSIAN parameter in HERWIG 7, taking into account the uncertainty from tune ranges (range) and the functions for interpolation (int.). |
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Table B2:
Tune results for the BEAMREMNANTS:PRIMORDIALKTHARD parameter in PYTHIA8 with the CP5 tune setup. The parameter SPACESHOWER:PT0REF was set to 1 GeV. |
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Table B3:
Tune results for the SHOWERHANDLER:INTRINSICPTGAUSSIAN parameter in HERWIG 7 with the CH3 tune setup. The parameter SUDAKOVCOMMON:PTMIN was set to 0.7 GeV. |
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Table B4:
Results of the tune to various ranges of the $ m(\ell^+\ell^-) $ for values of $ \sqrt{s} $ of 38.8 GeV and 8, 8.16, and 13 TeV. |
| Summary |
| In summary, the study assesses the mutual impacts of the variation of the intrinsic $ k_{\mathrm{T}}$ tune on the UE, and that of the UE tune on the DY transverse momentum, and concludes that the impacts are negligible, which supports our approach of tuning the intrinsic $ k_{\mathrm{T}}$ parameters with fixed UE parameters. |
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