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CMS-PAS-GEN-22-001

Energy scaling behavior of intrinsic transverse momentum in Drell-Yan events

CMS Collaboration

11 April 2024

Abstract: We present an analysis of intrinsic transverse momentum by studying the dilepton transverse momentum in Drell-Yan events. Utilizing widely adopted event generators and data from fixed-target experiments, the Tevatron, and 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 behaviour of the intrinsic transverse momentum. The value is independent of the dilepton invariant mass.

Links: CDS record (PDF) ; CADI line (restricted) ;

Figures
png pdf	Figure 1: Tuned parameter values for DY measurements at different center-of-mass energies (points) for different generator setups (colors). For each generator setup, the function $ b \sqrt{s}^a $ is fitted to the points and shown as a line. 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 2: Tuned parameter values for DY measurements at different center-of-mass energies (points) for different generator settings (colors). For the PYTHIA CP5 setup, the parameter SpaceShower:pT0Ref is set to 1 GeV (red) or its default value of 2 GeV (blue). For the HERWIG CH3 setup, the parameter SudakovCommon:pTmin is set to 0.3 GeV (purple) or its default value of 1.2 GeV (green). For each generator setting, the function $ b \sqrt{s}^a $ is fitted to the points and shown as a line. 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 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. 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 Drell-Yan cross section differential in $ p_{\mathrm{T}}(\ell^+\ell^-) $ at various center-of-mass energies from different hadron-collision processes used as inputs for the intrinsic $ k_{\mathrm{T}} $ tunes. The variable $ Q $ represents the hard-scattering scales of the measurements.

Summary

In summary, generator tunes of the intrinsic transverse momentum $ k_{\mathrm{T}} $ were used as metadata of existing measurements to explore model-independent features of non-perturbative quantum chromodynamics (QCD). The tunes were performed for various underlying-event setups in PYTHIA and HERWIG using the Drell-Yan cross section differential in 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}} $ and $ \log(\sqrt{s}) $ for all generator setups, the intercepts altered by generator-dependent perturbative QCD models such as choices of parton distribution functions or parton shower parameters. The slope was found to be 0.162 $ \pm $ 0.005, independently of the generator setups, and related to pure non-perturbative QCD effects such as non-resolvable low-energy gluon emissions in parton showers. The tunes were also performed to measurements in different dilepton invariant mass regions and demonstrated stable intrinsic $ k_{\mathrm{T}} $ under varying hard-scattering scales at a fixed $ \sqrt{s} $, which indicates the independence of the intrinsic $ k_{\mathrm{T}} $ of the momentum fractions of the quarks in colliding hadrons in Drell-Yan processes.

Additional Figures
png pdf	Additional Figure 1: Effects of the variation of the PYTHIA CP5 UE parameters on the DY $ p_{\mathrm{T}} $ spectrum. The red and violet error bands represent the predictions from the up and down variations of the UE tune and the intrinsic $ k_{\mathrm{T}} $ tune, respectively, for the "int.$ k_{\mathrm{T}} $" tune prediction.
png pdf	Additional Figure 2: Effects of the variation of the intrinsic $ k_{\mathrm{T}} $ parameter on the observables of minimum bias (MB) events used for underlying-event tuning: charge particle $ p_{\mathrm{T}}^{sum} $ density in the transMIN region (upper left); charge particle $ p_{\mathrm{T}}^{sum} $ density in the transMAX region (upper right); charge particle density in the transMIN region (lower left); charge particle density in the transMAX region (lower right) as a function of the transverse momentum of the leading charged particle. The red and violet error bands represent the predictions from the up and down variations of the CP5 UE tune and the intrinsic $ k_{\mathrm{T}} $ tune, respectively. The red error band is based on the "CP5+default int.kT" prediction and the violet error band is based on the "CP5+int-kT tune" prediction. The error bars represent the statistical uncertainty of the MC events. The plot also includes the UE prediction of a combined tune of the int-kT and the ISR cutoff scale to the DY $ p_{\mathrm{T}} $ (int-kT+pT0Ref).
png pdf	Additional Figure 2-a: Effects of the variation of the intrinsic $ k_{\mathrm{T}} $ parameter on the observables of minimum bias (MB) events used for underlying-event tuning: charge particle $ p_{\mathrm{T}}^{sum} $ density in the transMIN region (upper left); charge particle $ p_{\mathrm{T}}^{sum} $ density in the transMAX region (upper right); charge particle density in the transMIN region (lower left); charge particle density in the transMAX region (lower right) as a function of the transverse momentum of the leading charged particle. The red and violet error bands represent the predictions from the up and down variations of the CP5 UE tune and the intrinsic $ k_{\mathrm{T}} $ tune, respectively. The red error band is based on the "CP5+default int.kT" prediction and the violet error band is based on the "CP5+int-kT tune" prediction. The error bars represent the statistical uncertainty of the MC events. The plot also includes the UE prediction of a combined tune of the int-kT and the ISR cutoff scale to the DY $ p_{\mathrm{T}} $ (int-kT+pT0Ref).
png pdf	Additional Figure 2-b: Effects of the variation of the intrinsic $ k_{\mathrm{T}} $ parameter on the observables of minimum bias (MB) events used for underlying-event tuning: charge particle $ p_{\mathrm{T}}^{sum} $ density in the transMIN region (upper left); charge particle $ p_{\mathrm{T}}^{sum} $ density in the transMAX region (upper right); charge particle density in the transMIN region (lower left); charge particle density in the transMAX region (lower right) as a function of the transverse momentum of the leading charged particle. The red and violet error bands represent the predictions from the up and down variations of the CP5 UE tune and the intrinsic $ k_{\mathrm{T}} $ tune, respectively. The red error band is based on the "CP5+default int.kT" prediction and the violet error band is based on the "CP5+int-kT tune" prediction. The error bars represent the statistical uncertainty of the MC events. The plot also includes the UE prediction of a combined tune of the int-kT and the ISR cutoff scale to the DY $ p_{\mathrm{T}} $ (int-kT+pT0Ref).
png pdf	Additional Figure 2-c: Effects of the variation of the intrinsic $ k_{\mathrm{T}} $ parameter on the observables of minimum bias (MB) events used for underlying-event tuning: charge particle $ p_{\mathrm{T}}^{sum} $ density in the transMIN region (upper left); charge particle $ p_{\mathrm{T}}^{sum} $ density in the transMAX region (upper right); charge particle density in the transMIN region (lower left); charge particle density in the transMAX region (lower right) as a function of the transverse momentum of the leading charged particle. The red and violet error bands represent the predictions from the up and down variations of the CP5 UE tune and the intrinsic $ k_{\mathrm{T}} $ tune, respectively. The red error band is based on the "CP5+default int.kT" prediction and the violet error band is based on the "CP5+int-kT tune" prediction. The error bars represent the statistical uncertainty of the MC events. The plot also includes the UE prediction of a combined tune of the int-kT and the ISR cutoff scale to the DY $ p_{\mathrm{T}} $ (int-kT+pT0Ref).
png pdf	Additional Figure 2-d: Effects of the variation of the intrinsic $ k_{\mathrm{T}} $ parameter on the observables of minimum bias (MB) events used for underlying-event tuning: charge particle $ p_{\mathrm{T}}^{sum} $ density in the transMIN region (upper left); charge particle $ p_{\mathrm{T}}^{sum} $ density in the transMAX region (upper right); charge particle density in the transMIN region (lower left); charge particle density in the transMAX region (lower right) as a function of the transverse momentum of the leading charged particle. The red and violet error bands represent the predictions from the up and down variations of the CP5 UE tune and the intrinsic $ k_{\mathrm{T}} $ tune, respectively. The red error band is based on the "CP5+default int.kT" prediction and the violet error band is based on the "CP5+int-kT tune" prediction. The error bars represent the statistical uncertainty of the MC events. The plot also includes the UE prediction of a combined tune of the int-kT and the ISR cutoff scale to the DY $ p_{\mathrm{T}} $ (int-kT+pT0Ref).
png pdf	Additional Figure 3: Effects of the variation of the intrinsic $ k_{\mathrm{T}} $ parameter on the observables of minimum bias (MB) events used for underlying-event tuning: charged hadron multiplicity (upper left); charged particle multiplicity in the single-diffractive-enchanced events of MB process (upper right); charged particle multiplicity in the non-single-diffractive-enchanced events MB process (lower center) as a function of rapidity. The red and violet error bands represent the predictions from the up and down variations of the CP5 UE tune and the intrinsic $ k_{\mathrm{T}} $ tune, respectively. The red error band is based on the "CP5+default int.kT" prediction and the violet error band is based on the "CP5+int-kT tune" prediction. The error bars represent the statistical uncertainty of the MC events. The plot also includes the UE prediction of a combined tune of the int-kT and the ISR cutoff scale to the DY $ p_{\mathrm{T}} $ (int-kT+pT0Ref).
png pdf	Additional Figure 3-a: Effects of the variation of the intrinsic $ k_{\mathrm{T}} $ parameter on the observables of minimum bias (MB) events used for underlying-event tuning: charged hadron multiplicity (upper left); charged particle multiplicity in the single-diffractive-enchanced events of MB process (upper right); charged particle multiplicity in the non-single-diffractive-enchanced events MB process (lower center) as a function of rapidity. The red and violet error bands represent the predictions from the up and down variations of the CP5 UE tune and the intrinsic $ k_{\mathrm{T}} $ tune, respectively. The red error band is based on the "CP5+default int.kT" prediction and the violet error band is based on the "CP5+int-kT tune" prediction. The error bars represent the statistical uncertainty of the MC events. The plot also includes the UE prediction of a combined tune of the int-kT and the ISR cutoff scale to the DY $ p_{\mathrm{T}} $ (int-kT+pT0Ref).
png pdf	Additional Figure 3-b: Effects of the variation of the intrinsic $ k_{\mathrm{T}} $ parameter on the observables of minimum bias (MB) events used for underlying-event tuning: charged hadron multiplicity (upper left); charged particle multiplicity in the single-diffractive-enchanced events of MB process (upper right); charged particle multiplicity in the non-single-diffractive-enchanced events MB process (lower center) as a function of rapidity. The red and violet error bands represent the predictions from the up and down variations of the CP5 UE tune and the intrinsic $ k_{\mathrm{T}} $ tune, respectively. The red error band is based on the "CP5+default int.kT" prediction and the violet error band is based on the "CP5+int-kT tune" prediction. The error bars represent the statistical uncertainty of the MC events. The plot also includes the UE prediction of a combined tune of the int-kT and the ISR cutoff scale to the DY $ p_{\mathrm{T}} $ (int-kT+pT0Ref).
png pdf	Additional Figure 3-c: Effects of the variation of the intrinsic $ k_{\mathrm{T}} $ parameter on the observables of minimum bias (MB) events used for underlying-event tuning: charged hadron multiplicity (upper left); charged particle multiplicity in the single-diffractive-enchanced events of MB process (upper right); charged particle multiplicity in the non-single-diffractive-enchanced events MB process (lower center) as a function of rapidity. The red and violet error bands represent the predictions from the up and down variations of the CP5 UE tune and the intrinsic $ k_{\mathrm{T}} $ tune, respectively. The red error band is based on the "CP5+default int.kT" prediction and the violet error band is based on the "CP5+int-kT tune" prediction. The error bars represent the statistical uncertainty of the MC events. The plot also includes the UE prediction of a combined tune of the int-kT and the ISR cutoff scale to the DY $ p_{\mathrm{T}} $ (int-kT+pT0Ref).
png pdf	Additional Figure 4: The ratio between the contributions from individual uncertainty sources to the total tuning uncertainties in the intrinsic $ k_{\mathrm{T}} $ tunings under the UE tunes: HERWIG CH2 (upper left); HERWIG CH3 (upper right); PYTHIA CP3 (lower left); PYTHIA CP4 (lower center); PYTHIA CP5 (lower right).
png pdf	Additional Figure 4-a: The ratio between the contributions from individual uncertainty sources to the total tuning uncertainties in the intrinsic $ k_{\mathrm{T}} $ tunings under the UE tunes: HERWIG CH2 (upper left); HERWIG CH3 (upper right); PYTHIA CP3 (lower left); PYTHIA CP4 (lower center); PYTHIA CP5 (lower right).
png pdf	Additional Figure 4-b: The ratio between the contributions from individual uncertainty sources to the total tuning uncertainties in the intrinsic $ k_{\mathrm{T}} $ tunings under the UE tunes: HERWIG CH2 (upper left); HERWIG CH3 (upper right); PYTHIA CP3 (lower left); PYTHIA CP4 (lower center); PYTHIA CP5 (lower right).
png pdf	Additional Figure 4-c: The ratio between the contributions from individual uncertainty sources to the total tuning uncertainties in the intrinsic $ k_{\mathrm{T}} $ tunings under the UE tunes: HERWIG CH2 (upper left); HERWIG CH3 (upper right); PYTHIA CP3 (lower left); PYTHIA CP4 (lower center); PYTHIA CP5 (lower right).
png pdf	Additional Figure 4-d: The ratio between the contributions from individual uncertainty sources to the total tuning uncertainties in the intrinsic $ k_{\mathrm{T}} $ tunings under the UE tunes: HERWIG CH2 (upper left); HERWIG CH3 (upper right); PYTHIA CP3 (lower left); PYTHIA CP4 (lower center); PYTHIA CP5 (lower right).
png pdf	Additional Figure 4-e: The ratio between the contributions from individual uncertainty sources to the total tuning uncertainties in the intrinsic $ k_{\mathrm{T}} $ tunings under the UE tunes: HERWIG CH2 (upper left); HERWIG CH3 (upper right); PYTHIA CP3 (lower left); PYTHIA CP4 (lower center); PYTHIA CP5 (lower right).
png pdf	Additional Figure 5: MC and data comparison for the intrinsic $ k_{\mathrm{T}} $ after tuning. The tune uncertainty comes from the choice of $ p_{\mathrm{T}} $ range and the interpolation function in the tune. The last panel corresponds to MC prediction compared to the CMS data measured at 13 TeV.
png pdf	Additional Figure 6: The tune results to the DY measurements at various center-of-mass energies and the fit for all the generator setups for PYTHIA and HERWIG, compared to the intrinsic $ k_{\mathrm{T}} $ tunes in CASCADE, in which more soft gluon emissions are included using the Parton Branching method in describing the transverse-momentum-dependent parton distributions, and weaker dependence of the intrinsic $ k_{\mathrm{T}} $ on the $ \sqrt{s} $ is observed.

Additional Tables
png pdf	Additional Table 1: The RIVET plugins corresponding to the data histograms used in the tune, as well as the ranges for calculating and minimizing the goodness of fit.
png pdf	Additional Table 2: The 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).
png pdf	Additional Table 3: Tune results to the $ p_{\mathrm{T}}(\ell^+\ell^-) $ in various dilepton ranges for the 38.8 GeV, 8 TeV, 8.16 TeV and 13 TeV collisions.

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