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 evolution in vacuum and hadronization, resulting in collimated sprays of particles that are clustered into jets. A substructure observable that highlights the transition between the perturbative and non-perturbative regimes of jet evolution as a function of angle between two particles is the two-point energy correlator (EEC). In this letter, the first measurement of the EEC, both inclusive and separated by relative charge of the particles, at RHIC is presented, using data taken from 200 GeV $pp$ collisions by STAR.  These measurements show a transition between perturbative and non-perturbative effects mapped to an angular scale that is consistent with expectations of a universal hadronization scale that scales with jet momentum.  Additionally, a deviation from Monte-Carlo predictions at low angles in the charge-selected sample could result from mechanics of hadronization not 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

Proposed Figures:

Requesting final figure status to show at Hard Probes 2024

Figure 1: Corrected distributions of the normalized EEC plotted differential in $R_{L}$ for $R_{jet}=$ 0.6, with jet transverse momentum selections 15 $< p_{\rm T, jet} <$ 20 GeV/c and 30 $< p_{\rm T, jet} <$ 50 GeV/c (scaled for comparison). Random hadron scaling at low 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, plotted differential in $ \left\langle p_{\rm T,jet} \right\rangle R_{L} $ at $R_{jet} =$ 0.6 for several jet transverse momentum selections.

Figure 3: Corrected Distribution 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_{\rm T, jet} <$  30 GeV/c.  Comparisons with PYTHIA8: Detroit Tune and HERWIG7 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.

-Figure 3:

• Distribution is shifted when selecting on opposite or like sign charged pairs, with opposite sign correlations moving to smaller angles and like sign moving to larger angles in general.
• 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.

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 2-point energy correlator at STAR has been presented in pp collisions at sqrt(s) = 200 GeV, showing clear separation of the jet evolution into three regimes. Agreement with theoretical predictions seen in the region dominated by perturbative effects as well as scaling expectations of the free hadron regime: allowing for identification of a transition regime between the two. This transition region is seen to propagate at a scale inversely proportional to jet momentum, showing a universal hadronization scale that causes higher energy jets to hadronize at later times. Additionally, separating the track pairs with like-sign and opposite-sign correlations shifts the relative magnitude of perturbative and non-perturbative effects, implying that hadronization dynamics differ between the two samples. This study could also serve as a baseline in future measurements of the EEC in heavy-ion collisions. This result, particularly the collapse of the transition region, can only be compared reliably between experiments when taking into account the difference between momenta of full and charged jets as well as the previously mentioned quark/gluon fraction difference.  For example, due to the higher sqrt(s) at which the ALICE measurement was taken, 5 TeV, the fraction of jets that were gluon initiated increases significantly relative to this measurement due to being reported at a comparable p_{T, jet}, which would result in a transition present at a higher p_{T, jet}R_L.  However, within each experiment, the trend of the transition region being collapsed to a single point is recovered. These measurements, therefore, provide evidence for a universal transition from non-perturbative to perturbative effects for a given initiator flavor.  Additional studies done across experiments that directly involve the initiating parton, such as heavy flavor tagging, will then be extremely informative about the commonality of this transition between collision energies.  Since the EEC allows for time-scale separation in jets, proving useful in discriminating the evolution of a jet being modified by interactions with the QGP.