CMS-GEN-22-001

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
Phys. Rev. D 111 (2025) 072003
Abstract: An analysis is presented based on models of the intrinsic transverse momentum (intrisic $k_{\mathrm{T}}$ ) 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 and from hadron colliders, 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 $k_{\mathrm{T}}$ 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 ; HepData record ; CADI line (restricted) ;

Figures & Tables	Summary	References	CMS Publications

Figures
png pdf	Figure 1: Effect 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 charged $p_{\mathrm{T}}^{\text{sum}}$ density as a function of $p_{\mathrm{T}}^{\text{max}}$ in the transMAX region of the MB process (lower). 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 areas are 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. $k_{\mathrm{T}}$ ''), and 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 lower 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''). The data are from the CMS measurements on the DY process [22] and the MB process [38] at 13 TeV.
png pdf	Figure 1-a: Effect 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 charged $p_{\mathrm{T}}^{\text{sum}}$ density as a function of $p_{\mathrm{T}}^{\text{max}}$ in the transMAX region of the MB process (lower). 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 areas are 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. $k_{\mathrm{T}}$ ''), and 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 lower 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''). The data are from the CMS measurements on the DY process [22] and the MB process [38] at 13 TeV.
png pdf	Figure 1-b: Effect 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 charged $p_{\mathrm{T}}^{\text{sum}}$ density as a function of $p_{\mathrm{T}}^{\text{max}}$ in the transMAX region of the MB process (lower). 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 areas are 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. $k_{\mathrm{T}}$ ''), and 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 lower 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''). The data are from the CMS measurements on the DY process [22] and the MB process [38] at 13 TeV.
png pdf	Figure 2: 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.
png pdf	Figure 3: 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.
png pdf	Figure 4: Tuned parameter values (points) for DY measurements at four different center-of-mass energies $\sqrt{s} =$ 38.8 GeV [11,12], and 8 [20], 8.16 [21], and 13 TeV [22], for the PYTHIA CP5 (blue dark) and HERWIG CH2 (green light) 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.

Tables
png pdf	Table 1: Measurements of the DY 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 $m(\mathrm{Z})$ .
png pdf	Table A1: Tune results for the BeamRemnants:PrimordialkTHard parameter in PYTHIA 8 and the ShowerHandler:intrinsicpTGaussian parameter in HERWIG 7, taking into account the statistical uncertainty of simulations (MC stat.), the measurement uncertainty in data (data unc.), the uncertainty from choices of tune ranges (range) and the uncerainty from choises of the functions for interpolation (int.).
png pdf	Table A2: Tune results for the BeamRemnants:PrimordialkTHard parameter in PYTHIA8 with the CP5 tune setup, taking into account the statistical uncertainty of simulations (MC stat.), the measurement uncertainty in data (data unc.), the uncertainty from choices of tune ranges (range) and the uncerainty from choises of the functions for interpolation (int.). The parameter SpaceShower:pT0Ref was set to 1 GeV.
png pdf	Table A3: Tune results for the ShowerHandler:intrinsicpTGaussian parameter in HERWIG 7 with the CH3 tune setup, taking into account the statistical uncertainty of simulations (MC stat.), the measurement uncertainty in data (data unc.), the uncertainty from choices of tune ranges (range) and the uncerainty from choises of the functions for interpolation (int.). The parameter SudakovCommon:pTMin was set to 0.7 GeV.
png pdf	Table A4: 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, taking into account the statistical uncertainty of simulations (MC stat.), the measurement uncertainty in data (data unc.), the uncertainty from choices of tune ranges (range) and the uncerainty from choises of the functions for interpolation (int.).

Summary

In summary, generator tunes of the intrinsic transverse momentum

$k_{\mathrm{T}}$ were used to explore model-independent features of nonperturbative quantum chromodynamics (QCD). The tunes were performed for various underlying-event (UE) setups in the generators PYTHIA and HERWIG using the Drell--Yan differential cross section as a function of the dilepton transverse momentum measured in multiple types of hadron collision experiments with

$\sqrt{s}$ ranging from 38.8 GeV to 13 TeV. The results show a linear relation between the logarithm of the intrinsic

$k_{\mathrm{T}}$ parameter and

$\log_{10}(\sqrt{s})$ for all generator tunes, with the intercepts altered by generator-dependent perturbative-QCD models such as choices of parton distribution functions or parton shower parameters. The slope is 0.162

$\pm$ 0.005, independent of the UE tune or generator, and related to nonperturbative-QCD effects such as nonresolvable low-energy gluon emissions in parton showers. The tunes were also performed using experiments that probe different regions of dilepton invariant mass and rapidity, and demonstrate the independence of the intrinsic

$k_{\mathrm{T}}$ parameter with respect to these variables at each

$\sqrt{s}$ . This indicates the independence of the intrinsic

$k_{\mathrm{T}}$ on the longitudinal momentum fractions of the quarks within colliding hadrons in Drell--Yan processes.

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