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arxiv: 1907.11233 · v1 · pith:LTMYQIC4new · submitted 2019-07-25 · ✦ hep-ex

Studying Transverse Momentum Dependent Distributions in Polarized Proton Collisions Via Azimuthal Single Spin Asymmetries of Charged Pions in Jets

J. Kevin Adkins This is my paper

Pith reviewed 2026-05-24 16:19 UTC · model grok-4.3

classification ✦ hep-ex
keywords Collins asymmetrytransversity distributionsingle spin asymmetrypolarized proton collisionscharged pions in jetshadronic collisionsTMD distributionsazimuthal asymmetries
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The pith

Azimuthal single spin asymmetries of charged pions in jets yield the first statistically significant Collins asymmetries from 200 GeV polarized proton collisions.

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The paper establishes that Collins asymmetries can be isolated and measured in hadronic collisions by examining the spin-dependent azimuthal distributions of charged pions inside jets. This approach matters because it supplies an independent channel for accessing the transversity distribution h1(x), which remains poorly constrained compared to unpolarized and helicity distributions. Prior extractions relied on semi-inclusive deep inelastic scattering and electron-positron data with limited statistics and kinematic coverage. The reported measurement uses 14 inverse picobarns of transversely polarized proton data at 57 percent average polarization and finds the first statistically significant signals at sqrt(s) = 200 GeV.

Core claim

This thesis reports on the first statistically significant Collins asymmetries extracted from sqrt(s)=200 GeV hadronic collisions using 14 pb^{-1} of transversely polarized proton collisions at 57% average polarization. These asymmetries arise when the transversity distribution h1(x) couples to the Collins fragmentation function through spin-dependent azimuthal modulations of charged pions inside jets.

What carries the argument

Azimuthal single spin asymmetries of charged pions in jets, which isolate the product of transversity and the Collins fragmentation function in hadronic collisions.

If this is right

  • The extracted asymmetries provide an independent data set that can be combined with SIDIS and e+e- results to tighten constraints on the transversity distribution h1(x).
  • Hadronic collisions extend the accessible kinematic range in x and z beyond what is currently available from lepton-hadron scattering.
  • The new channel allows direct study of transverse-momentum-dependent effects in a regime dominated by parton-parton scattering rather than virtual-photon exchange.
  • Future higher-luminosity runs can test whether the measured asymmetries scale with beam polarization and integrated luminosity as predicted by the factorization framework.

Where Pith is reading between the lines

These are editorial extensions of the paper, not claims the author makes directly.

  • Global analyses that incorporate these hadronic data points could reveal whether current tensions between different extractions of h1(x) arise from limited statistics or from process-dependent effects.
  • The same jet-based technique could be applied to other final-state particles or to dijet observables to map additional transverse-momentum-dependent distributions.
  • If the asymmetries persist at higher collision energies, they would offer a clean probe for testing the evolution of the Collins function with hard scale.

Load-bearing premise

The spin-dependent azimuthal distributions of charged pions in jets can isolate the Collins asymmetries without significant contamination from other spin-dependent effects or backgrounds in hadronic collisions.

What would settle it

A measurement in which the extracted azimuthal asymmetry is consistent with zero within statistical and systematic uncertainties after all background subtractions and corrections would falsify the claim of first statistically significant Collins asymmetries.

Figures

Figures reproduced from arXiv: 1907.11233 by J. Kevin Adkins.

Figure 1.1
Figure 1.1. Figure 1.1: Fundamental Particles in the Standard Model - The fundamental elementary particles arranged nicely into a table. The fermion generations (columns) are in order of discovery and increasing mass from left to right. 1.2.1 Quarks and Leptons Quarks form the foundation for a class of particles called hadrons, which are made up of three valence quarks (baryons) or a quark plus an antiquark (mesons). There are … view at source ↗
Figure 1.2
Figure 1.2. Figure 1.2: Standard Model Forces - The three standard model forces, and which particles experience the force. Particles on each level feel the force on that level, and the force of each level under it. For instance, quarks are subject to the effects of the weak, electromagnetic and strong forces. The weak force is, as one may suspect, the weakest force in the standard model with a strength given by the weak couplin… view at source ↗
Figure 1.3
Figure 1.3. Figure 1.3: π Production in pp Collisions - This cartoon depicts the separation of the non-perturbative functions used to describe the partonic initial and final state, and the perturbative function used to describe the interaction when a pion is produced in a proton-proton collision [7]. process are separated from each other mathematically. The hard scattering cross sec￾tion can be calculated using perturbative QCD… view at source ↗
Figure 1.5
Figure 1.5. Figure 1.5: Unpolarized PDFs - Current results for the unpolarized parton dis￾tribution functions in the proton for up, down, gluon and quark sea contributions [24]. Note that the quark sea and gluon contributions here are scaled by 0.05. This displays the important role of the quark and gluon sea at low x. However, above x ≈ 0.03 the valence quarks begin to dominate the proton. The helicity flip involved with the t… view at source ↗
Figure 1.6
Figure 1.6. Figure 1.6: Helicity PDFs - Current results for the helicity distributions in the proton for up quark (a), down quark (b), and gluon (c) contributions [25]. The red curves from de Florian, Sassot, Stratmann, and Vogelsang (DSSV) presented here are older and have been superseded by a new set of curves found in Ref. [28]. 18 [PITH_FULL_IMAGE:figures/full_fig_p034_1_6.png] view at source ↗
Figure 1.7
Figure 1.7. Figure 1.7: Transversity PDFs - Current results for the transversity distributions in the proton for up and down quark contributions from (a) Kang et al. [26] and (b) Anselmino et al. [27]. to another chiral-odd distribution. This may be accomplished by coupling h1(x) to itself, as in a double spin asymmetry. Otherwise, a chiral-odd fragmentation func￾tion is sought which connects the initial and final state, and re… view at source ↗
Figure 1.8
Figure 1.8. Figure 1.8: SIDIS Collins Asymmetries - Recent SIDIS results for the Collins asymmetry from the COMPASS [31] (a)/(b) and HERMES [32] (c) collaborations. In addition to using outgoing charged pions, HERMES also analyzes the asymmetry for outgoing charged kaons and neutral pions. Similarly, COMPASS computes the asymmetry using outgoing charged and neutral kaons. The asymmetries in (b) show results from (a), only for t… view at source ↗
Figure 1.9
Figure 1.9. Figure 1.9: e +e − Analysis Reference Frames - The two scattering reference frames used in e +e − analyses to extract the A0 (a) and A12 (b) asymmetries [33]. In both reference frames, the unit vector uˆ points along the direction of the e +e − beam [PITH_FULL_IMAGE:figures/full_fig_p039_1_9.png] view at source ↗
Figure 1.10
Figure 1.10. Figure 1.10: e +e − Collins Asymmetries - Recent Collins results from the BaBar [33] (a)/(b) and BELLE [34] (c)/(d) collaborations. Asymmetries are extracted using the two reference frames, A0 and A12. fragmentation have the opposite azimuthal distribution to those coming from favored fragmentation. It is also possible to construct asymmetries in p ↑ + p collisions that are sensitive to the convolution of the transv… view at source ↗
Figure 1.11
Figure 1.11. Figure 1.11: Extracted Collins Fragmentation Function - Current extraction results for the Collins fragmentation function for different values of Q2 [27]. The top plots are for favored fragmentation and the bottom plots are for disfavored fragmen￾tation. transversely polarized p + p data taken at STAR revealed a statistically limited, but tantalizing asymmetry, shown in [PITH_FULL_IMAGE:figures/full_fig_p041_1_11.png] view at source ↗
Figure 1.12
Figure 1.12. Figure 1.12: Preliminary STAR Collins Asymmetry - Preliminary results from 2006 √ s = 200 GeV STAR data for charged pions in jets [35]. The result is statisti￾cally limited, but hints at a separation of charges and possible statistical significance for increased statistics [PITH_FULL_IMAGE:figures/full_fig_p042_1_12.png] view at source ↗
Figure 1.13
Figure 1.13. Figure 1.13: Maximized Quark Collins Asymmetry Prediction - The potential size of the Collins asymmetry for the p ↑ + p → jet + π + + X process at √ s = 200 GeV if the transversity distribution is maximized to the Soffer bound [17]. 26 [PITH_FULL_IMAGE:figures/full_fig_p042_1_13.png] view at source ↗
Figure 1.14
Figure 1.14. Figure 1.14: Sivers Asymmetries from SIDIS - Sivers asymmetry results from the COMPASS [31] (a) and HERMES [37] (b) collaborations as a function of x, z, and p h T . In both cases there is a clear and statistically significant signal for positively charged hadrons, yet nothing for neutral and negatively charged hadrons. to the detected particle2 . Therefore, considering favored and disfavored fragmentation functions… view at source ↗
Figure 1.15
Figure 1.15. Figure 1.15: Extracted Sivers Distributions - Sivers distributions extracted for valence and sea quark contributions by using the asymmetries measured by the HER￾MES and COMPASS collaborations [36] [PITH_FULL_IMAGE:figures/full_fig_p045_1_15.png] view at source ↗
Figure 1.16
Figure 1.16. Figure 1.16: Unpolarized Fragmentation Functions - Unpolarized fragmenta￾tion functions using three different parameterizations [38]. The left column shows the valence favored fragmentation functions, the center column shows the disfavored fragmentation functions, and the right column shows the favored fragmentation func￾tions from the sea. The top is for π + particles and the bottom for K+ particles, although simil… view at source ↗
Figure 1.17
Figure 1.17. Figure 1.17: STAR Inclusive Jet Asymmetry - The single spin inclusive jet asymmetry, as extracted by the STAR collaboration in four bins of pseudorapidity (η) [41]. The STAR collaboration has extracted and published the inclusive jet asymmetry in the past using √ s = 200 GeV proton collisions, and the results are shown in [PITH_FULL_IMAGE:figures/full_fig_p046_1_17.png] view at source ↗
Figure 1.18
Figure 1.18. Figure 1.18: Twist-3 Sivers Prediction - Theoretical constraint placed on the Sivers asymmetry using the twist-3 factorization and STAR data shown in [PITH_FULL_IMAGE:figures/full_fig_p047_1_18.png] view at source ↗
Figure 2.1
Figure 2.1. Figure 2.1: RHIC Complex Layout - The layout of the RHIC accelerator and surrounding complex, including the location of the interaction points, Siberian snakes, and pC/H-jet polarimeters. 2.1.1 Protons on a Collision Course Protons take quite a journey before they finally collide in RHIC. It all begins at the optically pumped polarized H− source (OPPIS) [43], where 300 µs pulses of a 0.5 mA current produces 35 keV t… view at source ↗
Figure 2.2
Figure 2.2. Figure 2.2: STAR Detector - The cutaway cross section of STAR shows the coverage of each subsystem, as well as the overall size of the detector in relation to the human depiction at the bottom [49]. 37 [PITH_FULL_IMAGE:figures/full_fig_p053_2_2.png] view at source ↗
Figure 2.3
Figure 2.3. Figure 2.3: Time Projection Chamber - A schematic of the TPC which shows the central membrane at z = 0, the end pad planes, and the inner and outer field cage [50]. The TPC is filled with a 90% argon and 10% methane gas mixture (commonly called P10) held at 2 mbar above atmospheric pressure, which is continuously being recirculated and resupplied [51]. When a charged particle moves through the gas it leaves a trail … view at source ↗
Figure 2.4
Figure 2.4. Figure 2.4: BEMC Tower Layout - Depiction of how the towers look in half of the BEMC including the η coverage of each tower as well as how all towers project back to the interaction region. A schematic of the top megatile, Sc21, is shown at the top [55]. This schematic of the megatile should not be confused with any physical location. the next event. Because the tiles in each megatile are optically separate, informa… view at source ↗
Figure 2.5
Figure 2.5. Figure 2.5: BEMC Module Construction - End view of the final interior con￾struction of a BEMC module. The first two scintillating layers are thicker for the preshower detector. The SMD is buried at about five radiation lengths from the front plate at η = 0 [55]. 42 [PITH_FULL_IMAGE:figures/full_fig_p058_2_5.png] view at source ↗
Figure 2.6
Figure 2.6. Figure 2.6: EEMC Layout and Construction - On the left, the layout of the towers for half of the EEMC is shown. On the right is how the towers are constructed including the preshower, SMD, and postshower detectors [56]. 2.7. The VPD was designed and constructed to detect far forward particles produced from the primary collision. In proton-proton collisions the hits in the VPD originate from charged pions and π 0 dec… view at source ↗
Figure 2.7
Figure 2.7. Figure 2.7: VPD Front View - Schematic front view of the vertex position detector, showing all 19 of the individual detector positions in the full housing. The housing splits down the middle to clamp directly around the beamline [57]. formation in each of the VPDs. Specifically, the vertex position may be calculated by zV P D = c Teast − Twest 2 (2.2) where Teast and Twest are the times when photons reached the east… view at source ↗
Figure 2.8
Figure 2.8. Figure 2.8: TOF MRPC Module - Side views of an MRPC module, for the long (top) and short (bottom) sides. The color codes on the bottom show the different detector components discussed in the text [58] the mass is calculated by m2 = p 2 [PITH_FULL_IMAGE:figures/full_fig_p063_2_8.png] view at source ↗
Figure 3.1
Figure 3.1. Figure 3.1: Average BEMC Tower ET vs. Run Index - The average BEMC ET before removing any runs due to anomalies or inconsistencies. “Run index” is a label used to number the runs starting from zero and does not reflect the actual run number. This exercise is repeated for each reconstructed value and for all triggers in the plots until all flagged runs have been reviewed and removed or kept based upon a lack of sympt… view at source ↗
Figure 3.2
Figure 3.2. Figure 3.2: Average BEMC Tower ET vs. Run Index - The average BEMC ET after removing problematic runs. 3.4 Jet Reconstruction The proton beams delivered to STAR are at sufficiently high energies that partons are elastically scattered from each other and ejected from the parent protons. Because of confinement, these ejected partons quickly fragment and hadronize into jets of colorless particles. Studying properties o… view at source ↗
Figure 3.3
Figure 3.3. Figure 3.3: Collinear Safety Issue - Multiple low energy particles (left) would fail to produce a seed in a cone-style algorithm, whereas a single high energy particle would (right) [62]. This issue is resolved with the anti-kT algorithm where all particles are grouped by their distances from each other and the beam, where the same jet would be produced regardless of energy deposit in these examples. In the context … view at source ↗
Figure 3.4
Figure 3.4. Figure 3.4: Collinear Safety Issue - Jets in a cone-style algorithm are sensitive to particle ordering. The correct jet (left) would not be formed without the high energy seed in the middle. If this seed were rather two lower energy particles (right), the jet would take on a different shape [62]. in the event are treated equally until all have been grouped into a jet. Thus jets are formed the same with or without so… view at source ↗
Figure 3.5
Figure 3.5. Figure 3.5: Infrared Safety Issue - Two jets correctly formed around two seed tracks (left) may be formed differently in the presence of soft radiation (right) when using a cone-style algorithm. This low energy particle could cause the jets to have enough in common that they are merged rather than saved as two independent jets [62]. For the anti-kT algorithm, the measured distance between particles is what associate… view at source ↗
Figure 3.6
Figure 3.6. Figure 3.6: Number of Jets per Vertex vs. Run Index - The average number of jets per reconstructed vertex for each analysis trigger before removing any runs due to anomalies or inconsistencies. polarization will be a necessity when performing the asymmetry analysis presented in this thesis. Of all the runs removed in both jet and event level quality analyses, 196 of them were removed because of apparent hot towers i… view at source ↗
Figure 3.7
Figure 3.7. Figure 3.7: Number of Jets per Vertex vs. Run Index - The average number of jets per reconstructed vertex for each analysis trigger after the 70 flagged runs were investigated for problems and subsequently removed. the final analysis run list includes 601 runs. These run numbers are documented in the appendix for completeness. 60 [PITH_FULL_IMAGE:figures/full_fig_p076_3_7.png] view at source ↗
Figure 4.1
Figure 4.1. Figure 4.1: BEMC Hot Tower Spectrum - Number of hits in each BEMC tower that carry a transverse energy greater than 2 GeV. The spikes which have many more counts than the average number of hits are identified as hot tower candidates. method to bring problems to the foreground is to compare the ADC spectrum from a tower in the list of bad ones to a tower which wasn’t tagged as bad. To compare, though, the towers shou… view at source ↗
Figure 4.2
Figure 4.2. Figure 4.2: BEMC Tower Spectrum Comparison - Pedestal shifted ADC spectra for an identified bad, hot tower spectrum (blue) and for a good tower spectrum (green) that is in the same η ring, but at a different value of φ. The good and bad tower both have the same gain constant value (Cgain), thus the deviation in the physics slope is unexpected and shows that the gain constants should be updated. Before 2012, the most… view at source ↗
Figure 4.3
Figure 4.3. Figure 4.3: MIP ADC Spectrum - Resulting MIP ADC spectrum after all cuts from [PITH_FULL_IMAGE:figures/full_fig_p082_4_3.png] view at source ↗
Figure 4.4
Figure 4.4. Figure 4.4: MIP Spectrum Fit - Fit applied to the MIP spectrum is drawn in blue. The red line gives the mean, which is used to calculate the MIP relative calibration constant in Equation 4.2. The same fit is applied to the MIP spectra from all 4800 calorimeter towers. After fitting, each spectrum and fit are reviewed one-by-one to ensure every tower has a good fit and MIP spectrum. Those towers with a bad fit or spe… view at source ↗
Figure 4.5
Figure 4.5. Figure 4.5: BHT2 E/p vs. Track Momentum - This shows the momentum dependence of E/p in the BHT2 triggered events. Also, it is clear to see where the trigger “turns on” around 3.5 GeV/c. First, the BHT2 trigger could be used, so long as the other two lower BHT triggers did not fire, at high enough momentum that it is certain the events are no longer being influenced by the trigger threshold. Then, for the lower momen… view at source ↗
Figure 4.6
Figure 4.6. Figure 4.6: Unbiased E/p vs. Track Momentum - The momentum dependence is removed if we look at the so-called unbiased trigger. The backgrounds at low E/p are much bigger in this triggering setup, though. 0 1 E/p 2 3 0 200 400 600 800 1000 1200 BHT2: 1.5 < p < 2.0 GeV/c 0 1 E/p 2 3 0 100 200 300 400 500 600 BHT2: 2.0 < p < 2.5 GeV/c 0 1 E/p 2 3 0 100 200 300 400 500 BHT2: 2.5 < p < 3.0 GeV/c 0 1 E/p 2 3 0 50 100 150 … view at source ↗
Figure 4.7
Figure 4.7. Figure 4.7: BHT2 E/p Momentum (p) Slices - Above 5 GeV/c, the threshold effects should be gone, and the shoulder at higher E/p has disappeared. 73 [PITH_FULL_IMAGE:figures/full_fig_p089_4_7.png] view at source ↗
Figure 4.8
Figure 4.8. Figure 4.8: Unbiased E/p Momentum (p) Slices - Below 5 GeV/c the peaks are consistent with the peaks in the BHT2 spectra when that momentum is above 5 GeV/c. In these momentum slices, an odd background shoulder below the peak is developing for momentum above 5 GeV/c, which will be difficult to characterize. be applied. This means that either the event was triggered by something other than a high tower trigger, or an… view at source ↗
Figure 4.9
Figure 4.9. Figure 4.9: Sample Ring E/p Spectrum - E/p spectra for the different triggering scenarios once all cuts have been applied, shown here for a midrapidity ring. It is clear that the unbiased spectrum (top) has way more statistics than the BHT2 spectrum (bottom), but exhibits a much more prominent background that will need to be fit correctly. is not possible to know if events were truly triggered by something other tha… view at source ↗
Figure 4.10
Figure 4.10. Figure 4.10: Sample Ring E/p Fits - Example fits applied to the previously shown E/p spectra. The pink curve is the exponential fit applied to the backgrounds, and the blue curve is the Gaussian-only fit applied to the peak. The combination of these two, the final fit, is shown as the red curve. With the fitting procedure finalized, the means from the two triggering schemes may be compared. The fit is applied to eac… view at source ↗
Figure 4.11
Figure 4.11. Figure 4.11: Triggering Fit Mean Comparison - Comparison between the unbi￾ased fit means and the BHT2 fit means. The “Ring ID” value is indexed so that it increases as η goes from −1 to +1. The highest values of |η|, where the mean values diverge, are known as the “outer rings” of the BEMC. The final fitting procedure is applied and example rings are shown in [PITH_FULL_IMAGE:figures/full_fig_p094_4_11.png] view at source ↗
Figure 4.12
Figure 4.12. Figure 4.12: Final Triggering Fit Sample - The final triggering scheme and fits applied to outer ring (top) and midrapidity (bottom) towers. 4.5 Comparing Gain Constant Results With the calibration completed for the 2012 data, it should be compared to the 2009 calibration at the same beam energy to see if the gains fit the expectations of 4.5% yearly tower efficiency degradation. The percent difference is plotted in… view at source ↗
Figure 4.13
Figure 4.13. Figure 4.13: Percent Change Between Calibrations - This shows the size of the change between the 2012 and 2009 gain calibration constants. jected from analysis if they pointed to the tower which fired the high tower. This is problematic because then the E/p values are biased low, forcing the hE/pi to also be too small. If the mean is small, then the absolute gain constants calculated with Equation 4.3 will be too la… view at source ↗
Figure 4.14
Figure 4.14. Figure 4.14: 2009 Triggering E/p Fit Means - The unbiased and high tower Gaussian means from the 2012 data, but restoring the 2009 triggering algorithm. 4.6 Post-Calibration Quality Analysis With such a small change in the calibration constants, the differences in the energies will be minimal. Therefore the issue with the hot towers before are not solved. Regardless, another round of quality analysis with updated ca… view at source ↗
Figure 4.15
Figure 4.15. Figure 4.15: Average BEMC ET with New Gains - Event level quality analysis results using the 196 runs removed previously because of assumed hot towers. both the event and jet levels. With the wild outliers removed, this sample of runs has a stable average value, yielding confidence in the data quality. 82 [PITH_FULL_IMAGE:figures/full_fig_p098_4_15.png] view at source ↗
Figure 4.16
Figure 4.16. Figure 4.16: Average Tower ET with New Gains - Jet level quality analysis results using the updated calibration constants. Seven runs are removed here. 4.7 Systematic Uncertainties The systematic uncertainties assigned to the final gain calibration constants are for the most part data-driven calculations. The goal of these simple analyses is to look for any changes or biases in the constants which may arise from the… view at source ↗
Figure 4.17
Figure 4.17. Figure 4.17: Global vs. Matched Primary Track Momentum - Comparison of the normalized momentum spectra for matched primary tracks and all global tracks to study any potential momentum bias. Both spectra give a very similar mean and shape overall, there seems to be no bias with using the matched primary tracks. E/p 0 0.5 1 1.5 2 2.5 3 1 10 2 10 3 10 Matched Primary Tracks All Global Tracks Note: Primary tracks are ma… view at source ↗
Figure 4.18
Figure 4.18. Figure 4.18: Global vs. Matched Primary Track E/p - Comparison of E/p distributions for matched primary tracks and all global tracks to study any poten￾tial momentum bias. The additional global tracks are clearly concentrated in the background region. 85 [PITH_FULL_IMAGE:figures/full_fig_p101_4_18.png] view at source ↗
Figure 4.19
Figure 4.19. Figure 4.19: e ± Paricle Gain Comparison - Percent difference comparison of gain constants between the total combined sample of final result gains and subsamples of (a) e + and (b) e − particles. The mean of each distribution in [PITH_FULL_IMAGE:figures/full_fig_p102_4_19.png] view at source ↗
Figure 4.20
Figure 4.20. Figure 4.20: Calibration Time Dependence - Gain calibration constant from each run using statistics integrated over all towers. Note that runs which produce less than 100 electrons were removed as they gave nonsensical answers, and the run index is simply a number given to each run for easy plotting. whole range of runs. Again, it is a simple percent difference calculation: 0.9342 − 0.9267 0.9342 × 100% = 0.8028% (4… view at source ↗
Figure 4.21
Figure 4.21. Figure 4.21: Mean E/p vs. ∆R - Mean E/p values extracted as a function of ∆R for the (a) inner 36 towers and the (b) outer two towers on each end. Mean E/p 0.9 0.92 0.94 0.96 0.98 1 1.02 1.04 1.06 1.08 1.1 1 2 3 4 5 Mean = 0.9358 RMS = 0.0067 Inner η rings (a) Mean E/p 0.9 0.92 0.94 0.96 0.98 1 1.02 1.04 1.06 1.08 1.1 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 2 2.2 Mean = 0.9935 RMS = 0.0245 Outer η rings (b) [PITH_FULL_IM… view at source ↗
Figure 4.22
Figure 4.22. Figure 4.22: Mean E/p vs. ∆R Spread - The spread in the mean E/p values from [PITH_FULL_IMAGE:figures/full_fig_p106_4_22.png] view at source ↗
Figure 4.23
Figure 4.23. Figure 4.23: a, where it is clear there is quite a bit of variation in the values. The spread of the values will be used to assign a systematic error [PITH_FULL_IMAGE:figures/full_fig_p108_4_23.png] view at source ↗
Figure 4.24
Figure 4.24. Figure 4.24: Mean E/p vs. η Ring - Mean E/p values extracted for each ring and plotted to look for any dependence as a function of η. points we used previously to determine the time dependence. In this case, rather than plotting versus the run number, we plot as a function of the beam-beam counter (BBC) rate. The BBC at STAR is a two-detector system which wrap around the beam pipe on the east and west sides of the i… view at source ↗
Figure 4.25
Figure 4.25. Figure 4.25: Mean E/p vs. BBC Rate - Mean E/p values integrated over all tower statistics and extracted for each run and plotted as a function of the BBC rate. 4.7.10 Table of Systematic Errors All of the errors calculated and discussed for the BEMC calibration are summarized in [PITH_FULL_IMAGE:figures/full_fig_p111_4_25.png] view at source ↗
Figure 5.1
Figure 5.1. Figure 5.1: Sample nσ(π) Distribution - Plot of nσ(π) for all positively charged tracks that fulfill the JP1 triggering condition. Other track species are also present here and a correction will be applied to account for these contributions. 5.2 Triggering Conditions The analysis triggers are the same as those outlined in Section 3.2. These triggers are subject to several requirements before the events are said to b… view at source ↗
Figure 5.2
Figure 5.2. Figure 5.2: JP2 Trigger Minimum Jet pT Cut - JP2 triggered jet pT spectrum for jets passing all triggering requirements. Data in the red box will be ignored as analysis jets, everything outside of the box are subject to further analysis cuts. If all of the outlined data cuts are met, and a track is identified as a pion, the analysis yields are stored by using an “or” of all of the triggers. This means that if the tr… view at source ↗
Figure 5.3
Figure 5.3. Figure 5.3: STAR Scattering Kinematics - Depiction of the scattering kinematics used for this analysis. The angle φS is the angle between the scattering plane, which intersects the beamline and the jet axis (pjet), and the polarized proton spin (S⊥). The angle φH is the angle between the scattering plane and jT , where jT lies in the plane that intersects the pion momentum (pπ) and pjet. Collins asymmetry not yet co… view at source ↗
Figure 5.4
Figure 5.4. Figure 5.4: Example Asymmetry Fit - An example fit for a particular z bin and Jet pT range. The sinusoidal behavior of the cross ratio is very apparent even without the fit. that event based on the same straight line fit used to extract the parameters: P (t) = P0 + dP dt ∆t (5.15) The polarization values for each good analysis event are stored in a histogram so that once the analysis code has run over all data, all … view at source ↗
Figure 5.5
Figure 5.5. Figure 5.5: Average Polarization vs. Run Index - The average polarization for each run plotted as a function of the run index, which starts from zero and is not the same as the run number. Note that if the polarization for both beams is zero then the run is not shown on this plot, as it would not be included in analysis anyway. 116 [PITH_FULL_IMAGE:figures/full_fig_p132_5_5.png] view at source ↗
Figure 6.1
Figure 6.1. Figure 6.1: Data Invariant Yield Momentum Distribution - The combined 2005 and 2012 invariant yield momentum distribution for π + particles. The charged pion invariant yields were compared to several pure PYTHIA simu￾lation samples, each representing a different tune. This analysis utilized the Perugia 0 tune, which was used in previous √ s = 200 GeV analyses [72], as well as the up￾dated Perugia tunes: Perugia 2012… view at source ↗
Figure 6.2
Figure 6.2. Figure 6.2: Nominal Tunes Comparison - Comparison between the invariant yields from data and from the various PYTHIA tunes with parameters set to their nominal values. The immediate conclusion from the results in [PITH_FULL_IMAGE:figures/full_fig_p138_6_2.png] view at source ↗
Figure 6.3
Figure 6.3. Figure 6.3: Perugia 0 Reduced kT Ratio - Comparison between the invariant yields from data and from the various PYTHIA tunes with parameters set to their nominal values, except for Perugia 0 where the primordial kT is set to 1 GeV/c. match the data well at lower pT where the UE contributes to the process the most. Fortunately, the UE contributions may be tuned by adjusting either the pT,0 (sref ) or P90 exponent par… view at source ↗
Figure 6.4
Figure 6.4. Figure 6.4: Reduced P90 vs. Increased pT,0 (sref ) - Comparing the effects of reducing the energy exponent vs increasing the pT,0 (sref ) parameter. The result of each change is shown compared to the original out of the box Perugia 2012 tune. In summary, we choose Perugia 2012 because of the excellent “out of the box” agreement for pT > 3 GeV/c and the updated CTEQ6L1 PDF set. Then to get good agreement at low pT wh… view at source ↗
Figure 6.5
Figure 6.5. Figure 6.5: Partonic pT Sepctrum - The full partonic pT spectrum that combines statistics from all pˆT bins. The distribution is smooth at all pˆT bin edges, showing that the weighting scheme for combining bins is correct. One of the input parameters to the simulation is to setup the vertex distribution 126 [PITH_FULL_IMAGE:figures/full_fig_p142_6_5.png] view at source ↗
Figure 6.6
Figure 6.6. Figure 6.6: Vertex Weight Comparison - Comparison of the vertex z-axis posi￾tion distributions for (a) unweighted simulation output and (b) weighted simulation output. Clearly the weighting is producing more accurate simulation distributions than the raw detector reconstructed distribution. that is used by PYTHIA to generate events. From the data, we get the mean position of vertex distribution on the (x, y, z)-axes… view at source ↗
Figure 6.7
Figure 6.7. Figure 6.7: Combined Triggers Jet pT - Comparing the jet pT distributions for the combined triggers in data and embedding. 130 [PITH_FULL_IMAGE:figures/full_fig_p146_6_7.png] view at source ↗
Figure 6.8
Figure 6.8. Figure 6.8: Combined Triggers π + z - Comparing the π + z distributions for the combined triggers in data and embedding. −3 10 −2 10 −1 10 1 2012 Combined Data 2012 Combined Embedding [GeV/c] T j + π 0.5 1 1.5 2 2.5 3 3.5 4 4.5 (Data-Simu)/Data −1 −0.8 −0.6 −0.4 −0.2 0 0.2 0.4 0.6 0.8 1 [PITH_FULL_IMAGE:figures/full_fig_p147_6_8.png] view at source ↗
Figure 6.9
Figure 6.9. Figure 6.9: Combined Triggers π + jT - Comparing the π + jT distributions for the combined triggers in data and embedding. 131 [PITH_FULL_IMAGE:figures/full_fig_p147_6_9.png] view at source ↗
Figure 6.10
Figure 6.10. Figure 6.10: Collins Analysis Jet pT Shift - Calculating the true value of the jet pT for plotting the final Collins asymmetries, with the detector kinematics plotted on the x-axis and the particle level kinematics on the y-axis binned finely. The true value of the jet pT is given by the black bar in each detector level bin. the asymmetry. Smearing of the reconstructed φC about the true value leads to measuring a sm… view at source ↗
Figure 6.11
Figure 6.11. Figure 6.11: Data/MC φC Comparison - Comparison of the values of φC in the data and at the detector level in the simulation for (a) positively and (b) negatively charged identified pion tracks. These plots integrate over all kinematic ranges, and thus represent average values for each bin. triple Gaussian function as in [PITH_FULL_IMAGE:figures/full_fig_p153_6_11.png] view at source ↗
Figure 6.12
Figure 6.12. Figure 6.12: φC Resolution Example Fit - A triple Gaussian fit to the spread in detector minus particle level φC values. smearing for each kinematic bin. The bin-by-bin dilution values are given in the asymmetry result tables in the appendix. 6.4.4 Pion Sample Contamination Correction When performing the Collins analysis, it is important to determine the purity of the signal particle sample. For instance, it is inte… view at source ↗
Figure 6.13
Figure 6.13. Figure 6.13: φC Dilution Example Fit - A sine function is fit to the convolution result. The amplitude of the fit is taken as the dilution parameter for that kinematic bin, in this case it is 0.535. to the π sample is due to K±, p/p¯, and e ± (which carry zero Collins signal) and correct the final asymmetry for it, since each contaminating particle presents some contamination to our true signal. Two detectors are us… view at source ↗
Figure 6.14
Figure 6.14. Figure 6.14: dE/dx Distribution - The dE/dx distribution from the TPC for all track momenta [54]. Clearly, there are different overlaps in the curves as the track momentum changes. These changes need to be addressed in the π contamination study. Region ptrack Range [GeV/c] 1 0.00 − 0.80 2 0.80 − 1.00 3 1.00 − 1.26 4 1.26 − 1.58 5 1.58 − 2.50 6 2.50 − ∞ [PITH_FULL_IMAGE:figures/full_fig_p156_6_14.png] view at source ↗
Figure 6.15
Figure 6.15. Figure 6.15: nσ (K) Mean Fit - A sample fit to extract the peak location of nσ (K) on the nσ (π) distribution for the lowest jet pT bin within the 1.26 GeV/c < ptrack < 1.58 GeV/c bin. 1.58 GeV/c bin, and the final contributions to the total fit which are integrated to calculate the contamination fractions. This procedure is repeated for all track momentum bins within each kinematic bin for both charge states to get… view at source ↗
Figure 6.16
Figure 6.16. Figure 6.16: nσ (π) Sample Fit - A sample fit to the nσ (π) distribution, and the contribution from all particle species to the total combined fit which are used to calculate the contamination fractions. electron mass is very small compared to the pion, it will hover around zero on the m2 distribution and will be engulfed by the π peak. Thus, in this analysis, we get out K and p dilutions, but not for e. The fitting… view at source ↗
Figure 6.17
Figure 6.17. Figure 6.17: m2 Sample Fit - A sample fit to the m2 distribution, and the contri￾bution from all particle species to the total combined fit. With the fractions for our two different regions calculated, but still separated by track momentum, we need to combine the results to get the final fractions for each kinematic bin. Beyond the 1.00 GeV/c < ptrack < 1.26 GeV/c track momentum bin 144 [PITH_FULL_IMAGE:figures/ful… view at source ↗
Figure 6.18
Figure 6.18. Figure 6.18: π Sample Particle Fractions - The signal and background fractions for K + p and π. −1 < nσ (π) 2.5, and Abk meas is the Collins asymmetry measured in the background region outside of the cut. Assuming that the background region is made up of contam￾inating particles, which can only be K and p, then we measure the Collins asymmetry outside of the nσ (π) cut, but we choose particles which satisfy −2 < nσ … view at source ↗
Figure 6.19
Figure 6.19. Figure 6.19: Quark and Gluon Fractions vs. Jet pT - Detector and particle level quark and gluon fractions. These fractions go into the ratio, Rquark to calculate the systematic error due to trigger bias. these use the same statistics, so identical errors will be assigned for both plotting arrangements. Jet pT Range [GeV/c] Trigger Bias Error (%) 6.0 - 8.4 1.362 8.4 - 9.9 2.682 9.9 - 11.7 1.959 11.7 - 16.3 0.955 16.3… view at source ↗
Figure 6.20
Figure 6.20. Figure 6.20: Rquark vs. Jet pT - The ratio of the detector to particle level quark fractions as a function of jet pT that can be found as the red lines in [PITH_FULL_IMAGE:figures/full_fig_p170_6_20.png] view at source ↗
Figure 6.21
Figure 6.21. Figure 6.21: Rquark vs. z in Jet pT Ranges - The ratio of the detector to particle level quark fractions as a function of z, given for the final kinematic ranges of jet pT . The errors are calculated as a percentage of the actual asymmetry point for each kinematic bin. The errors are assigned as follows: • If Rquark > 1 then an asymmetric error bar will be applied to each asymmetry point on the side of decreasing ma… view at source ↗
Figure 6.22
Figure 6.22. Figure 6.22: Rquark vs. jT in Jet pT Ranges - The ratio of the detector to particle level quark fractions as a function of jT , given for the final kinematic ranges of jet pT . should have more gluon events which would dilute the asymmetry value down. In the example of jet pT above, the error will be applied towards a decreasing asymmetry value by the amount of 8.34% of each asymmetry point, thus the error bar grows… view at source ↗
Figure 6.23
Figure 6.23. Figure 6.23: Rquark vs. jT in Pion z Ranges - The ratio of the detector to particle level quark fractions as a function of jT , given for the final kinematic ranges of pion z. number of RHIC fills worth of data used for analysis is not the total number used for the polarization determination, and for the error in the beam intensity profile. The calculation of the adjustment factor is straightforward and is outlined … view at source ↗
Figure 7.1
Figure 7.1. Figure 7.1: Inclusive Jet AN vs. Jet pT - The inclusive jet asymmetry plotted as a function of the jet pT for both jet scattering states. 7.2 Collins Asymmetries The Collins asymmetry, A sin(φS−φH) UT , is sensitive to contributions from the transversity parton distribution function and the Collins fragmentation function. Results for the Collins asymmetry for the 2012 STAR √ s = 200 GeV p ↑ + p data are shown for al… view at source ↗
Figure 7.2
Figure 7.2. Figure 7.2: A sin(φS−φH) UT vs. Jet pT - The Collins asymmetry plotted as a function of the jet pT , for xF > 0 and xF < 0. This result integrates over the entire range of z and jT [PITH_FULL_IMAGE:figures/full_fig_p178_7_2.png] view at source ↗
Figure 7.3
Figure 7.3. Figure 7.3: Accessed x Distributions - Distributions of the values of x accessed in the analysis. On average, the forward scattered jets access a slightly higher value of x than the backward scattered jets. These two kinematic variables are positively correlated, so it would seem that they are driving each other’s shape. We will explore this concept more in the following section. The Collins fragmentation function d… view at source ↗
Figure 7.4
Figure 7.4. Figure 7.4: A sin(φS−φH) UT vs. z - The Collins asymmetry plotted as a function of z, for xF > 0 and xF < 0 and six average values of jet pT to map out the dependence of the fragmentation function on z and the hard scale. Once the fragmentation is mapped out well as a function of the hard scale, then the last piece of the puzzle is to gain an understanding of the transversity distribution. Going back to the hard sca… view at source ↗
Figure 7.5
Figure 7.5. Figure 7.5: A sin(φS−φH) UT vs. jT - The Collins asymmetry plotted as a function of jT , for xF > 0 and xF < 0 and six average values of jet pT to map out the dependence of the fragmentation function on jT and the hard scale. 166 [PITH_FULL_IMAGE:figures/full_fig_p182_7_5.png] view at source ↗
Figure 7.6
Figure 7.6. Figure 7.6: A sin(φS−φH) UT vs. jT - The Collins asymmetry plotted as a function of jT , for xF > 0 and xF < 0 and four average values of z to help disentangle the fragmentation function kinematic dependencies. 167 [PITH_FULL_IMAGE:figures/full_fig_p183_7_6.png] view at source ↗
Figure 7.7
Figure 7.7. Figure 7.7: A sin(φS−φH) UT Comparison at √ s = 200 GeV and 500 GeV - The Collins asymmetry from the 2011 √ s = 500 GeV and 2012 √ s = 200 GeV analyses. The results are plotted for identical kinematics by applying appropriate ∆Rmin cuts and for the same value of xT . The results for √ s = 200 GeV and 500 GeV match each other very well in [PITH_FULL_IMAGE:figures/full_fig_p185_7_7.png] view at source ↗
Figure 7.8
Figure 7.8. Figure 7.8: Theory Comparison Without TMD Evolution - Results from the theoretical Collins asymmetry calculations compared to the √ s = 200 GeV and 500 GeV STAR preliminary result [66]. The TMD functions in this calculation include no evolution. 171 [PITH_FULL_IMAGE:figures/full_fig_p187_7_8.png] view at source ↗
Figure 7.9
Figure 7.9. Figure 7.9: Theory Comparison With TMD Evolution - Results from the theo￾retical Collins asymmetry calculations compared to the √ s = 200 GeV and 500 GeV STAR preliminary result [66]. The TMD functions in this calculation include effects from TMD evolution. 172 [PITH_FULL_IMAGE:figures/full_fig_p188_7_9.png] view at source ↗
Figure 8.1
Figure 8.1. Figure 8.1: Combined Triggers Jet Rt - Comparing the jet Rt distributions for the combined triggers in data and embedding. 175 [PITH_FULL_IMAGE:figures/full_fig_p191_8_1.png] view at source ↗
Figure 8.2
Figure 8.2. Figure 8.2: Combined Triggers Jet φ - Comparing the jet φ distributions for the combined triggers in data and embedding. 0 0.01 0.02 0.03 0.04 0.05 2012 Data 2012 Embedding Jet η −1 −0.5 0 0.5 1 (Data-Simu)/Data −0.8 −0.6 −0.4 −0.2 0 0.2 0.4 0.6 0.8 [PITH_FULL_IMAGE:figures/full_fig_p192_8_2.png] view at source ↗
Figure 8.3
Figure 8.3. Figure 8.3: Combined Triggers Jet η - Comparing the jet η distributions for the combined triggers in data and embedding. 176 [PITH_FULL_IMAGE:figures/full_fig_p192_8_3.png] view at source ↗
Figure 8.4
Figure 8.4. Figure 8.4: Combined Triggers Tower ET - Comparing the tower ET distributions for the combined triggers in data and embedding. −9 10 −8 10 −7 10 −6 10 −5 10 −4 10 −3 10 −2 10 −1 10 1 2012 Data 2012 Embedding Charge = +1 [GeV/c] T Jet Track p 0 5 10 15 20 25 (Data-Simu)/Data −0.8 −0.6 −0.4 −0.2 0 0.2 0.4 0.6 0.8 [PITH_FULL_IMAGE:figures/full_fig_p193_8_4.png] view at source ↗
Figure 8.5
Figure 8.5. Figure 8.5: Combined Triggers Track pT - Comparing the track pT distributions for the combined triggers in data and embedding. 177 [PITH_FULL_IMAGE:figures/full_fig_p193_8_5.png] view at source ↗
read the original abstract

A complete, fundamental understanding of the proton must include knowledge of the underlying spin structure. The transversity distribution, $h_1\left(x\right)$, which describes the transverse spin structure of quarks inside of a transversely polarized proton, is only accessible through channels that couple $h_1 \left(x\right)$ to another chiral odd distribution, such as the Collins fragmentation function ($\Delta^N D_{\pi/q^\uparrow}\left(z,j_T\right)$). Significant Collins asymmetries of charged pions have been observed in semi-inclusive deep inelastic scattering (SIDIS) data. These SIDIS asymmetries combined with $e^+e^-$ process asymmetries have allowed for the extraction of $h_1\left(x\right)$ and $\Delta^N D_{\pi/q^\uparrow}\left(z,j_T\right)$. However, the current uncertainties on $h_1\left(x\right)$ are large compared to the corresponding quark momentum and helicity distributions and reflect the limited statistics and kinematic reach of the available data. In transversely polarized hadronic collisions, Collins asymmetries may be isolated and extracted by measuring the spin dependent azimuthal distributions of charged pions in jets. This thesis will report on the first statistically significant Collins asymmetries extracted from $\sqrt{s}=200$ GeV hadronic collisions using $14$ pb$^{-1}$ of transversely polarized proton collisions at 57% average polarization.

Editorial analysis

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Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit. Tearing a paper down is the easy half of reading it; the pith above is the substance, this is the friction.

Referee Report

2 major / 1 minor

Summary. The manuscript reports the first extraction of statistically significant Collins asymmetries from azimuthal single-spin asymmetries of charged pions in jets produced in transversely polarized proton-proton collisions at √s=200 GeV. The analysis uses 14 pb^{-1} of data collected with an average beam polarization of 57% and isolates the asymmetries via spin-dependent azimuthal distributions to access the product of transversity h1(x) and the Collins fragmentation function.

Significance. If the central extraction holds, the result supplies the first Collins asymmetry data from hadronic collisions, extending the kinematic reach beyond existing SIDIS and e+e− measurements and offering new constraints on the transversity distribution with reduced uncertainties.

major comments (2)
  1. [Abstract] Abstract: the claim of the 'first statistically significant' extraction is stated without any reported asymmetry values, statistical significances, error bars, or systematic uncertainties. The results section must supply these quantities to substantiate the central claim of statistical significance.
  2. [Analysis] Analysis of azimuthal distributions: the isolation of the Collins contribution requires explicit quantitative demonstration that other spin-dependent effects and backgrounds do not produce significant contamination in the selected pion-in-jet sample; without such tests the interpretation remains vulnerable.
minor comments (1)
  1. [Abstract] The abstract would benefit from a concise statement of the observed asymmetry magnitudes to allow immediate assessment of the result's scale.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for the careful reading and constructive comments on our manuscript. We address each major comment below.

read point-by-point responses

  1. Referee: [Abstract] Abstract: the claim of the 'first statistically significant' extraction is stated without any reported asymmetry values, statistical significances, error bars, or systematic uncertainties. The results section must supply these quantities to substantiate the central claim of statistical significance.

    Authors: The results section presents the extracted Collins asymmetries for charged pions in jets, including central values, statistical and systematic uncertainties, and significances derived from the 14 pb^{-1} data set at 57% average polarization. To make the abstract claim self-contained and directly substantiated, we will revise the abstract to quote the key measured asymmetries and their significances. revision: yes

  2. Referee: [Analysis] Analysis of azimuthal distributions: the isolation of the Collins contribution requires explicit quantitative demonstration that other spin-dependent effects and backgrounds do not produce significant contamination in the selected pion-in-jet sample; without such tests the interpretation remains vulnerable.

    Authors: The analysis isolates the Collins term via the spin-dependent azimuthal modulation in the pion-in-jet sample and includes consistency checks across kinematic bins and comparisons to unpolarized reference samples to constrain other contributions. To meet the request for explicit quantitative demonstration, we will add a dedicated subsection with numerical estimates (including upper limits) on residual contamination from other spin-dependent effects and backgrounds. revision: yes

Circularity Check

0 steps flagged

No significant circularity in experimental measurement report

full rationale

This document is an experimental thesis reporting the extraction of Collins asymmetries from 14 pb^{-1} of √s=200 GeV transversely polarized p+p collision data. The abstract and described content contain no derivation chain, no fitted parameters renamed as predictions, no self-citation load-bearing uniqueness theorems, and no ansatz smuggling. The central claim rests on direct analysis of collected collision data rather than any reduction of outputs to inputs by construction. No load-bearing steps reduce to self-referential definitions or prior fitted quantities.

Axiom & Free-Parameter Ledger

0 free parameters · 1 axioms · 0 invented entities

Only abstract available; no explicit free parameters or invented entities identified. The analysis implicitly relies on standard assumptions about the applicability of the Collins mechanism in pp collisions.

axioms (1)
  • domain assumption The Collins fragmentation function couples to transversity in hadronic collisions in the same way as in SIDIS
    The paper assumes the azimuthal asymmetry in jets isolates the same chiral-odd correlation without additional hadronic effects.

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