Title: Measurement of Two-Point Energy Correlators Within Jets in pp Collisions at Sqrt(s) = 200 GeV

PAs: Helen Caines (Yale), Raghav Kunnawalkam Elayavalli (Vanderbilt)
, Isaac Mooney (Yale), Andrew Tamis (Yale)
GPC:

Target Journal:  PRL

Abstract:

Hard-scattered partons ejected from high-energy proton-proton collisions undergo parton shower and hadronization, resulting in collimated collections of particles that are clustered into jets. A substructure observable that highlights the transition between the perturbative and non-perturbative regimes of jet evolution in terms of the angle between two particles is the two-point energy correlator (EEC). In this letter, the first measurement of the EEC at RHIC is presented, using data taken from 200 GeV pp collisions by the STAR experiment.  The EEC is measured both for all the pairs of particles in jets and separately for pairs with same and opposite electric charges.  These measurements demonstrate that the transition between perturbative and non-perturbative effects occurs within an angular region that is consistent with expectations of a universal hadronization regime that scales with jet momentum.  Additionally, a deviation from Monte-Carlo predictions at small angles in the charge-selected sample could result from mechanics of hadronization not fully captured by current models.

  PWGC Preview : Tamis - PWGC Preview 6_23_23 | The STAR experiment (bnl.gov)

Analysis Note: Link

Paper Draft: Link

Paper Changes, GPC Comments 1: Link
Paper Changes, GPC Comments 2: Link
Paper Changes, GPC Comments 3: Link
Paper Changes, GPC Comments 4: Link

Proposed Figures:

Figure 1: Corrected distributions of the normalized EEC differential in R_L for R_jet = 0.6, with jet transverse momentum selections 15 < p_{T, jet} < 20 GeV/c and 30 < p_{T, jet} < 50 GeV/c (scaled for comparison). Random hadron scaling at small angles and next-to-leading-log-pQCD calculations at large angles are presented alongside Monte-Carlo predictions.

Figure 2: Corrected distributions of the normalized EEC within jets, differential in <p_{T, jet}> R_L  at R_jet = 0.6 for several p_{T, jet} selections. Each distribution is normalized to integrate to one in R_L and fit with the function described in Eq. 2 prior to shifting.  The resulting fit is also shifted and compared with data within the range 1 < p_{T, jet} > R_L < 6 GeV/c.

Figure 3: Corrected distributions of the charge-selected EEC compared with the inclusive case (top panel) and charged ratio (bottom panel) for R_jet = 0.6 with a jet transverse momentum selection of 20  < p_{T, jet} < 30 GeV/c.  Comparisons with the PYTHIA 8 Detroit Tune and the default tune of HERWIG 7 are given.

Appendix:

Figure 4: Corrected distributions of the normalized EEC differential in R_L for R_jet = 0.4, with jet transverse momentum selections 15 < p_{T, jet} < 20 GeV/c and 30 < p_{T, jet} < 50 GeV/c (scaled for comparison). Random hadron scaling at small angles and next-to-leading-log-pQCD calculations at large angles are presented alongside Monte-Carlo predictions.

Figure 5: Corrected distributions of the normalized EEC within jets, differential in <p_{T, jet}> R_L  at R_jet = 0.4 for several p_{T, jet} selections. Each distribution is normalized to integrate to one in R_L and fit with the function described in Eq. 2 prior to shifting.  The resulting fit is also shifted and compared with data within the range 1 < p_{T, jet} > R_L < 6 GeV/c.

Figure 6: Corrected distributions of the charge-selected EEC compared with the inclusive case (top panel) and charged ratio (bottom panel) for R_jet = 0.4 with a jet transverse momentum selection of 20  < p_{T, jet} < 30 GeV/c.  Comparisons with the PYTHIA 8 Detroit Tune and the default tune of HERWIG 7 are given.

Physics Messages:

-Figure 1

• Transition from geometrical random hadron scaling into the perturbative quark and gluon region, corresponding to onset of hadronization, is observed.
• Two regions determined via their scaling behavior: increasing linearly with angle at small angles and a downward trend predicted by perturbative QCD at large angles. 

This figure shows the ability of the EEC to separate angular scales out into both the non-perturbative and perturbative scales.  At small angles a prediction corresponding to uniformly distributed hadrons in phase-space is given, with a next-to-leading-log pQCD calculation given at large angles.  Comparisons with both HERWIG7.2 and PYTHIA8 Detroit Tune are given.  The observed EEC behavior is well described by the model prediction at low angles and the theory calculation at large angles: which highlights the non-perturbative transition region associated with hadronization.  The Monte-Carlo models, however, capture the location of this region well, showing that previous tuning to jet fragmentation allows them to describe energy flow in jets well.  The EEC with jet resolution parameter R_jet = 0.6 is given for two selections on jet momentum: showing that the distribution shifts to smaller angles for higher momenta jets.

-Figure 2:

• Scaling the x axis by jet transverse momentum collapses the transition region to the same location regardless of momentum selection shows that transition region moves as a function of 1/jet momentum.

This shows the EEC for three different momentum selections scaled on the x-axis by the average p_{T, jet} within that momentum bin.  This is observed to collapse the transition region to a single point for each momentum selection, which supports a universal transition region that occurs at an angular scale inversely proportional to jet momentum.  This is reinforced by a curve-fit to a functional description of the transition region, which produces fit values consistent with each other within errors regardless of jet momentum.

-Figure 3:

• The general behavior of the EEC is recovered for both like-charge and opposite-charge correlations, with a larger contribution of like-charge correlations than expected at small angles.
• Comparisons with HERWIG and PYTHIA  test effects of different hadronization models, showing an agreement at angles larger than the transition region, but both models fail below the transition region, showing that hadronization effects are not fully captured in these models. An expected shift in the transition region location between like-charge and opposite-charge correlations predicted by Monte-Carlo models is also not observed in data.

This figure shows the ratio of the charge-correlated EEC over the nominal EEC for  R_jet = 0.6.  This observable explores how the hadronization differences of like-sign and opposite-sign sign pairs differ as a function of angular scale.  An increased correlation moving from larger to smaller angles consistent with theory predictions is observed, however an increased de-correlation compared to Monte-Carlo models is observed at extremely small angles.

Conclusions:
In this letter, the first measurement of the two-point energy correlator (EEC) at RHIC has been presented using STAR data from pp collisions at $\sqrt{s}$ = 200 GeV, showing clear separation of the jet evolution into three regimes. Agreement is observed with theoretical predictions in the region dominated by perturbative effects as well as with scaling expectations of the free hadron regime, allowing for identification of a transition regime between the two.
 When scaled by jet momentum, the peak of the transition region can be characterized by a scale <p_{T, jet}>² T ~ 15.5 (GeV/c)² independent of jet momentum. This is in line with the expectation: a universal hadronization scale that causes higher energy jets to hadronize at later times.  Comparisons with other experiments, such as the studies performed by CMS and ALICE, will allow for studying the effects of changing initiator flavor due to different collision energies.  Additional studies performed across experiments that directly involve the initiating parton, such as photon-jet measurements or heavy flavor tagging, will therefore be informative about the commonality of this transition against collision energies.  Additionally, separating the track pairs with like-charge and opposite-charge correlations allows for increased sensitivity to hadronization.  At angles below the transition regime, predictions from both PYTHIA and HERWIG fail to fully describe the charge-weighted EEC. This provides an opportunity for further development of Monte-Carlo generators in modeling the hadronization process.  Since the EEC allows for time-scale separation in jets, it could prove useful in probing the modifications of jet evolution in the quark gluon plasma created in heavy-ion collisions. This study, therefore, could serve as a baseline in future measurements of the EEC in heavy-ion collisions at RHIC.