Exploring Potential Signatures of QGP in UHECR Ground Profiles
PPrepared for submission to JCAP
Exploring Potential Signatures of QGPin UHECR Ground Profiles
Danielle LaHurd a and Corbin E. Covault a a Case Western Reserve University10900 Euclid Ave, Cleveland, OH 44106E-mail: [email protected], [email protected]
Abstract.
In this work we explore the possibility that the formation of Quark Gluon Plasma(QGP) during the first interactions of Ultra High Energy Cosmic Rays (UHECRs) may resultin observable signatures in ground profile and shower particle composition that could conceiv-ably be detectable by an air shower array experiment such as the Pierre Auger Observatory.Knowledge of whether QGP formation affects the properties of UHECR development willfurther the understanding of both UHECR behavior and high energy hadronic interactionbehavior. We find that for the vast majority of showers signals of QGP do not manifest them-selves in ways that are observable, but on rare occasion, such as within deeply penetratingshowers, observable signals can be seen. Results show potential for QGP detection at 100PeV initial energy at an initial interaction event height of 12 km through a µ ± excess at 10GeV between 100 - 300 m from the shower core favoring QGP forming events. In contrast,higher initial interaction heights of 24 and 36 km at 100 PeV initial energy show no significantpotential for QGP detection. Unfortunately at present, the 12 km observable signals cannotbe seen with current detectors, such as the Pierre Auger Observatory[1]; however, there maybe potential for detection in future experiments. ArXiv ePrint: a r X i v : . [ a s t r o - ph . H E ] O c t ontents After a UHECR penetrates the atmosphere, it has increasing chances for interaction asit propagates. Upon the inevitable UHECR-Air collision, its center-of-mass energy is ofequivalent or greater magnitude ( √ s NN ∼
100 TeV) to what is currently being run at theLHC. As a result, UHECRs and hadronic interactions are fundamentally linked.It is hypothesized that a new state of matter may exist at very high energy density,where quarks and gluons become asymptotically free. This state is called a Quark GluonPlasma (QGP), in analogy to electromagnetic behavior of high-temperature collections ofcharged particles. A QGP is defined as a local thermal equilibrium, whereby quarks andgluons are deconfined from hadrons and manifest color degrees of freedom on nuclear scalesrather than nucleon scales [3]. The quarks and gluons in a QGP exhibit fluid-like behavior -”flows” - rather than simpler scatterings that occur at lower energy density [12]. Signaturesof “flow” have been reported experimentally from p + P b collisions at √ s NN = 2 .
76 TeVcollisions at the LHC [6] [14], and there has been recent evidence of a small QGP formationin He + Au collisions at RHIC at √ s NN = 200 GeV [4].Since there is recently increasingly strong evidence of QGP formation at collider energiesused at RHIC and the LHC, and UHECR collision energies are an order of magnitude higher( ∼
100 TeV), it stands to reason that, although the interacting hadrons may be lighter, it isplausible that QGP formation may be occurring during the initial UHECR collision.We note that the question of potentially observable effects of QGP in UHECRs has beenasked in prior work [21] using a simplified, two-parton, QGP model, as well as in work [5]done using a String Percolation Model. However, we believe ours is the first study usingup-to-date hadronic interaction models, including hydrodynamic flow behavior, since firstQGP observation in 2005. Knowledge of whether QGP formation affects the properties of– 1 –HECR development will further the understanding of both UHECR behavior and highenergy hadronic interaction behavior.
Our approach is to use simulation studies of high energy interactions and air shower propa-gation in the atmosphere to explore the feasibility that an observational signature indicatingthe formation of QGP may be detected based on measurements of ground particles. In orderfor a compelling QGP signal to be measured, several steps in sequence need to occur:1. QGP must be created as a result of first interactions between UHECRs and air moleculesat a sufficient rate,2. A sufficient fraction of each QGP must result in child particles with characteristicsuniquely indicative of QGP, for example, multiplicity (N) and flow,3. A sufficient fraction such events must generate a particle cascade where some imprintof the QGP signature remains in some detectable form in the properties of particlesarriving to the ground, and finally,4. The distinguishing signatures of ground particles must be measurable experimentallyand must occur at a rate high enough to be detected against any background due tonon–QGP cosmic ray showers fluctuating so as to mimic the specified signal.Here, we examine in some detail the plausibility for the first three steps indicatedabove. We begin by applying hadronic models to primary interactions which allow for thegeneration of QGP. We then select a subset of these interactions where QGP signaturesin child particles can be most clearly discerned, operating under the assumption that onlyevents that generate clear QGP signatures in the first interaction have any chance to imprinta measurable signature on the resultant ground particles. Only the most promising subsetof interactions are then fed into a full air shower simulations which propagate particles tothe ground. Since the air shower simulations are most time-consuming computationally,we inject selected showers into the atmosphere at discrete depths corresponding to threeheights: 12 km, 24 km and 36 km spanning a range shower penetration. Finally we examinedistributions of ground particles for signatures of QGP in the selected air showers relative toa matched set of non-QGP initiated showers.Our central aim is not to assess the absolute detectability of QGP in the context ofrealistic distributions of cosmic ray and air shower properties, but rather to assess if anydiscernible signal might be seen in ground particles even under optimistic assumptions whereshowers are pre-selected with favorable first interactions taking place deep in the atmosphere.We emphasize that here that we have not completed any study to carefully infer the rateat which QGP signatures might appear in real air shower ground particles generated fromreal UHECRs. Also here we make no attempt to address the extent to which non-QGPinitiated showers can fluctuate so as to yield a background of air showers that mimic QGPsignatures. Such studies will require substantially greater computational resources that havebeen applied here. – 2 – .1 Simulation Models
In order to explore the effects of QGP formation during the initial atmospheric interaction onshower evolution selection criteria are used on simulated events in order to select for promisingQGP candidate events. A discussion [24] was consulted to determine model strengths insimulating and reproducing flow in p + P b . The two high-energy hadronic interaction modelsused for this discussion are QGSJETII-04 [16][13] and EPOS-LHC [25][20][19], both tuned tothe most recent LHC data. QGSJETII-04 does not include hydrodynamic interactions thatmay occur within the initial hadronic collision during a QGP formation. For this reason,we use QGSJETII-04 as the “non-signal” comparison for the purposes of this discussion.Additionally, due to its slightly faster simulation speed, we also use QGSJETII-04 for the airshower propagation portion of the simulation.EPOS-LHC [19] is based on the Parton Gribov-Regge Theory [8] and includes a parametrizedversion of hydrodynamic modeling, replicating QGP effects. A version of EPOS, EPOS3.x [23], exists with full 3D+1 viscous hydrodynamic simulation. However, on consultationwith T. Pierog [18], it was determined the compute time required for simulating initial eventsin EPOS 3 would be too extreme for the purposes of this study, with times estimated onthe order of a month per each initial event and no guarantee that the resulting simulatedevent would have all the features desired for study. Since the full hydrodynamic simulationof EPOS 3 is outside our currently available computing resources, the parametrized hydro-dynamics of EPOS-LHC are instead used for simulating the hydrodynamic, or ‘QGP signal’,initial events.We separate the modeling of the initial event from the atmospheric propagation simula-tion occurring subsequent from the initial interaction. Additionally, we use the same modelfor said atmospheric propagation for both ‘signal’ and ‘non-signal’ events to limit the searchfor differences between the ‘signal’ and ‘non-signal’ to differences within the initial interactionrather than dealing with additional atmospheric propagation differences between models.Specifically, the initial hadronic interactions for both models, EPOS-LHC and QGSJETII-04, are not simulated in the cosmic ray propagation simulation package, CORSIKA [11],but are instead generated in a separate program module called CRMC (Cosmic Ray MonteCarlo) [22], allowing for the simulation of large numbers of initial events. Selection cuts aremade on the CRMC simulated events before continuing simulation in CORSIKA.
Certain selection cuts on initial collision events have been made in order to ensure a decentsample size of potential QGP-positive initial interactions. All initial interaction events weresimulated in 50 event batches using EPOS-LHC and CRMC v1.4 and v1.5.5. The simulationswere of vertical Neon (Ne) primaries at 100 PeV (0.1 EeV) hitting a Carbon (C) targetat rest ( √ s NN = ∼ > <
1% of simulated proton events. The initial energy of 100 PeV wasalso chosen due to compute time restrictions.We are aware that collisions of 100 PeV cosmic rays may probe just the onset of quarkdeconfinement, and air shower signals for the formation of a quark gluon plasma could stillappear at much higher energies. It is important to probe the entire energy parameter spacefrom the onset of deconfinement and higher energies to determine what effects deconfinementhas on shower evolution and development.Before any full
N e + C simulation was done, a small series of test showers were runto compare outputs between EPOS-LHC and QGSJETII-04. Figure 1 shows the azimuthalangular and pseudorapidity difference of pairs of particles produced in hadronic interactionssimulated with and without collective effects. The color code shows the number of particlepairs found for a given difference in azimuthal angle and pseudorapidity. EPOS-LHC eventsshowed signs of collective behavior (1a and 1b), while, as expected, the QGSJETII-04 eventsdid not show the same collective behavior (figure 1c). Similarly, when QGP effects are turnedoff in EPOS, the results are similar to the QGSJETII-04 output [15]. φΔηΔ ηΔ − − − (r ad i an s ) φ Δ − − − − etaphidiff_37_QGP=135_N=3735 Entries 40Mean x 0.9594 − Mean y 0.04305 − RMS x 3.295RMS y 2.305 φΔηΔ (a) EPOS-LHC initial condi-tion with QGP effects present. φΔηΔ ηΔ − − − (r ad i an s ) φ Δ − − − − etaphidiff_26_QGP=122_N=3009 Entries 26Mean x 0.8692 − Mean y 0.007236RMS x 3.32RMS y 2.302 φΔηΔ (b) EPOS-LHC initial condi-tion without full QGP pres-ence. φΔηΔ ηΔ − − − (r ad i an s ) φ Δ − − − − etaphidiff_23_QGP=0_N=3320 Entries 9Mean x 0.0173 − Mean y 0.04892RMS x 3.504RMS y 2.305 φΔηΔ (c) QGSJET initial condition.Note no collective behavior atany ∆ η or ∆ φ . Figure 1 : Simulated particle distributions for pairs of particles produced in under differenthadronic interactions models as a function of both psuedo-rapidity difference ∆ η and azimuthangle difference ∆ φ . The color code shows the number of particle pairs found for a given ∆ η and ∆ φ . All events have ∼ η ∆ φ graphing. Events with lower than 2000 freeze-out particles generally lack sufficient statisticsto discern any flow-like effects. Events with greater than 4000 particles at freeze-out were alsocut, due to both the rarity of these events ( < . η ) cuts via the large number of particlesobscuring the flow effects. In principle, additional η or p T cuts could be made to view floweffects within the high multiplicity candidates; however, for this analysis, these cuts were notmade.The QGSJETII-04 “non-signal” initial events are also given the same multiplicity cut,limiting the events to those with 2000 < N < η = − ln (cid:0) tan θ (cid:1) = ln | p | + p z | p |− p z – 4 – ut Applied Number of Events Percent Remaining Total events simulated 3550 100%Impact Parameter < ≥ < v > .
02 and visible ‘ridges’ 51 1.4%
Table 1 : The number of EPOS-LHC events simulated for potential QGP events and theefficiency of applied selection cuts.induced suppression. We limit the multiplicity of QGSJETII-04 events to ensure similarinitial conditions to those of the QGP ‘signal’ events.The impact parameter, or separation of the centers of the two nuclei when they collide,is provided by the HepMC [7] output of a CRMC simulation. Only QGP candidate eventsthat have a low impact parameter, i.e. high nucleus overlap, are selected for this study as lowimpact parameter correlates strongly with high multiplicity. The impact parameter chosenwas b < φ vs. N graph, then fitted with a Fourier cosine functiondescribing flow: f (∆ φ ) = 1 + (cid:88) n =1 c n cos ( n ∆ φ )It is the v ( n =2) term that is of most interest, as it is a sign of strong collectivebehavior that is influenced positively by the presence of a QGP. Fits were used to select forstrong QGP candidate events. If the v coefficient, corresponding to elliptic flow, was below0.02, the event was rejected, as lower v values correspond to weaker flow effects (low initialanisotropy). This fitting selection process ignores fit errors and is only used as a frameworkfor selecting potential QGP events.The pass rate with all cuts is about 1.4%. Table 1 shows a summary of the selectioncuts applied and the overall efficiency. While EPOS-LHC and QGSJETII-04 are used for the high energy hadronic interaction simu-lations, it is the program CORSIKA [11] that takes these models and uses them to model thepropagation of particles through the atmosphere. The version used for the hadronic interac-tion comparison simulations at the time of the discussion is CORSIKA v74004. CORSKIAtransitions to a lower energy interaction model, FLUKA (v2011.2) [9][10], for particle sim-ulations when the energy of individual particles falls below 100 GeV (configured at time ofsimulation).Thinning in CORSIKA is the process by which computing time is shortened by onlyfollowing one particle from a cascade below a certain energy rather than every particle in-dividually. Thinning does not preserve flavor counts or baryon numbers [18], therefore caremust be taken when deciding the thinning range so as not to lose valuable data. All COR-SIKA showers simulated at 100 PeV were thinned at the 10 GeV level. There is assumed to– 5 –e no discernible signal in the particles below 10 GeV as additional atmospheric interactionsand secondary showers will have clouded the signal.
For the “head” or initial interaction, EPOS-LHC and QGSJETII-04 initial events are chosen,as described above in section 2.1.1, and formatted into a CORSIKA readable format.For the air shower simulation, or “body”, the QGSJETII-04 model was chosen foratmospheric simulation of both initial interaction models. This is to allow for only the initialinteraction type to influence the developments within the air shower and allow for moredirect comparisons. QGSJETII-04 was chosen over EPOS-LHC for the “body” simulationas it requires slightly less time for simulation. All showers were simulated using the sameversion of CORSIKA(v74004) and FLUKA to reduce systematic errors.
As the shower is not being generated internally by CORSIKA, an initial height from thedetector plane must be provided for the air shower simulation to begin. Many, very thinned,test showers have been simulated in CORSIKA using proton, carbon, and iron primaries inorder to determine the typical initial collision height. For this discussion, the initial collisionheights have been chosen at discrete values of 12, 24, and 36 kilometers. For detectability,12 km potentially shows the most signal originating from the initial collision due to lessatmosphere attenuation since first interaction. However, as seen in figure 2 with neon primaryinteraction heights, it would be extremely uncommon to see an air shower, especially oneof somewhat heavier composition such as the neon primaries used, originating at such anextreme atmospheric penetration depth. Interactions set to 24 km represent a value closeto the average expected initial height of a shower with a composition near carbon or neonmass, and 36 km represents a high starting-elevation shower. A total of 51 showers have beensimulated for each model (102 total showers) for this discussion, with 17 showers generatedat each of the three initial heights for both models.
The CORSIKA output files are processed, using C++ scripts, into a ROOT format fileconsisting of compact particle data such as position, species, generation, time of impact, andmomentum.During analysis we make an energy cut of all particles below 10 GeV. Most particlesbelow 10 GeV result from secondary showers and decays which can wash out potential signalsfrom initial interactions that we wish to examine. Additionally, making the cut at 10 GeVallows us to eliminate particle weights introduced by CORSIKA though simulation thinning.The removal of the weighted particles can be beneficial as the thinning and weighting ofparticles, while vastly speeding up simulation time, only preserves energy and not baryon orlepton numbers [18]. By not preserving baryon and lepton numbers amongst the weightedparticles, the particle species abundances may be altered in a non-physical way and may hidepotential differences between the evolution of the two initial interaction types.The 17 simulations for each model and height are averaged and normalized before com-parison to obtain a single distribution for initial interaction model comparison purposes.One of the ways we compare the two interaction models is through taking the differencebetween the normalized distributions. This provides a way to look for QGP dependentexcesses or deficiencies, after atmospheric evolution. In order to determine the significance– 6 – eight [m] N
100 PeV Neon First Interaction Height100 PeV Neon First Interaction Height
Figure 2 : Graph initial interaction height of 100 PeV neon primary showers through 10000CORSIKA simulations.of any differences between the QGP and non-QGP results, we divide the differences by thepropagated errors of the difference.
R ≡ (cid:104) N QGP (cid:105) − (cid:104) N noQGP (cid:105) σ Here R is the “residual excess”, a measure of the number of standard deviations the differencedeviates from a null-hypothesis scenario where both QGP and non-QGP initiated air showersproduce the same results, and σ is the RMS uncertainty in the difference between QGP andnon-QGP values.The statistical significance of any one difference is, of course, diluted by the fact thatwe are searching for a range of different potential signatures. Although the “trials factor” isdifficult to estimate, a posteriori , we conservatively expect our study to correspond to severalhundreds of independent searches. For the purposes of initial analysis, we therefore assign an R value greater than 3 σ as a cause for interest, and assign an R value of greater than 5 σ torepresent a likely compelling physical difference between the models. We plot distributions of R for various different measurements. A distribution centered near zero, signifies that bothinitial interaction models evolve similarly, or at least do not display significant differencesafter the initial interaction. If the distribution deviates far from zero, or there are binsresiding significantly outside the central collection, there may be an excess in favor of eitherthe QGP (positive) or non-QGP (negative) events.Additionally, we preform a histogram comparison between 1D variables of QGP andnon-QGP modeled events using the χ test of homogeneity [17]. We examine the resultingnormalized residuals, i.e. the residuals divided by their standard deviation, from the com-parison. If QGP formation has no detectable influence on shower development the residuals– 7 –hould remain distributed at or near zero. Should any residuals bin deviate strongly fromzero, it indicates a potential region where the presence of QGP during the initial collision hasinfluenced shower development. The magnitude of the residuals’ deviation from zero scaleswith, but is not equivalent to, the significance of said deviation. For the presented results we will primarily focus on the 12 km simulated events, as boththe 24 and 36 km events show little differences between QGP (EPOS-LHC) and non-QGP(QGSJETII-04) models with the number of events simulated.
Due to the depth of atmospheric penetration required, a 12 km initial (first interaction)height is an extremely unlikely condition for a Ne, or heavier, primary at 100 PeV. However,examining results at this height provides a informative tool for determining whether viewingQGP effects from the initial interaction is feasible after traversing the atmosphere, or ifany potential signal will be eliminated by the numerous interaction lengths traveled. The12 km sample represents an overly optimist sample which is the most favorable for thedetectability of QGP signature observables. Should no observables be present on the groundafter the comparatively short distance of 12 km there will be little hope of finding detectableobservables at the higher, more realistic, initial interaction heights of 24 and 36 km.We examine the radial distribution of particles from the 12 km events for any differencesbetween the distributions of the QGP and non-QGP ‘headed’ showers. Upon viewing thisradial distribution for all tracked particles (figure 3a) we note that QGP (blue) events demon-strate an excess of particles at a 100 m distance from the core. This is difficult to see in theinitial log-log comparison, however, until we examine the residuals (figure 3b) comparing theQGP results to the non-QGP results. In the residuals, the QGP excess (positive) is clearlyvisible from 50 m up to about 300 m. This difference appears to be significant (figure 3c) asthere are multiple significance bins exceeding 5 σ . Additionally, the significance distributiontrends towards positive significance, indicating a overall QGP excess.Examining a top-down view of the particle distribution, this QGP-favored excess be-tween 50 m and 300 m remains significant when distributed across the azimuthal bins (figure4a). The significance values from this distribution (figure 4b) also exceed 5 σ . There may bean event-to-event azimuthal clustering; however, this was not studied in this discussion.Attempting to untangle which particles are contributing to the QGP-favored excess, weexamine particle distributions separately based on particle species. The muon profile (figure5a) displays an excess in favor of QGP. This excess is once again corroborated by the residuals(figure 5b) exhibiting an excess of µ ± in favor of QGP between 50 and 300 m. This excess isnot as statistically significant (figure 5c) as that seen in the full particle distribution but doescontain a number of bins with 5 σ significance. On examination, the remaining individualparticle species radial distributions show little to no differences between the two models.Therefore, we conclude that the muons dominate the apparent QGP-favored particle excessseen a 50 - 300 m from the core.As there appears to be a potential signal in muons for differentiating QGP and non-QGP showers, we examine particle species abundances within the entire ground profile forother possible difference between the models. A normalized count of particle species (figures6a and 6b) shows a significant difference between the two models for muons and EM. There is– 8 – adius from core [m] N - - - - - - - NonQGP height = 12kmQGP height = 12km
Normalized Radial Distance of Particles with E > 10GeV: 12km (a) Normalized radial distribution: QGP excessnear 100 m.
Radius from core [m] N o r m a li z e d r es i du a l s - - c Radial Distance of Particles with E > 10GeV: (b) Normalized residuals: QGP excess up to 300m.
Mean 0.3977 – – s - - - N Mean 0.3977 – – Radial Distance of Particles with E > 10GeV: QGP - NonQGP 12km Significance Distribution (c) Significance values: Centered on the positiveaxis; multiple bins are above 5 σ . Figure 3 : Radial distribution comparison ofall particles with energy exceeding 10 GeVbetween QGP and non-QGP events with aninitial interaction height of 12 km.
X Distance from core [m] - - - - - Y D i s t a n ce f r o m c o r e [ m ] - - - - - D i ff e r e n ce - - - (a) Significance( σ ) of the difference of normalizedcounts by ( x, y ). Mean 0.03984 – – s - - - N Mean 0.03984 – – Ground particle distribution: QGP - NonQGP 12km Significance Distribution (b) Distribution of significance values of the dif-ference of normalized counts.
Figure 4 : Particle distribution ( x, y ) with energy exceeding 10 GeV and an initial interactionheight of 12 km. Significance favoring QGP is positive(blue) and non-QGP is negative(red)little difference between QGP and non-QGP for the other tracked particle species. The EM( γ, e ± ) excess strongly favors non-QGP events and µ ± excess strongly favors QGP events.– 9 – adius from core [m] N - - - - - - NonQGP height = 12kmQGP height = 12km with E > 10GeV: 12km – m Normalized Radial Distance of (a) Normalized radial distribution: QGP eventsare in blue and non-QGP events are in red.
Radius from core [m] N o r m a li z e d r es i du a l s - - - - c with E > 10GeV: – m Radial Distance of (b) Normalized residuals: QGP-favored excessbetween 50 and 300 m.
Mean 0.3848 – – s - - - N Mean 0.3848 – – with E > 10GeV: QGP - NonQGP 12km Significance Distribution – m Radial Distance of (c) Significance values
Figure 5 : Radial distribution comparison of µ ± with energy exceeding 10 GeV betweenQGP and non-QGP events with an initialinteraction height of 12 km. Particle ID g + e - e + m - m p + p + p L0 K + K - K n p p S0 K h N - - - - - NonQGP height = 12kmQGP height = 12km
Normalized Particle Abundance with E > 10GeV: 12km (a) Normalized counts of particle species. QGPevents are in blue and non-QGP events are inred.
Particle ID g + e - e + m - m p + p + p L0 K + K - K n p p S0 K h L N o r m a li z e d r es i du a l s - - - c Particle Abundance with E > 10GeV: (b) Normalized residuals comparing particlespecies.
Figure 6 : Comparison of particle species counts and significance with energy exceeding10 GeV and an initial interaction height of 12 km.
There appears to be a significant difference, especially in the radial particle distribution,in the muon and EM output between the QGP and non-QGP ‘heads’ at 12 km. For thenon-QGP ‘headed’ events, there is a e ± excess seen within the core region when compared to– 10 –GP headed events. However, there is no current detector capable of measuring the directshower core output due to the required fine-grain surface detector spacing of ∼
100 m −
300 m.As such, an e ± core excess or deficiency cannot be used as a signature to determine whetheran initial event has formed QGP using previously collected data from experiments past orexisting, such as Auger.As for muons, there is a significant difference between the initial interaction modeloutputs when viewing the area between 50 and 300 m from the core. However, this is onlyapparent when comparing the discrepancy to the outer regions of the ground profile, whereboth models are identical. While the spacing of currently existing detectors is not ideal,this signature is potentially detectable if one uses a tightly clustered detector with ∼
100 mspacing. To search for a QGP signature, one would have to compare the peripheral of theshower’s ground profile with the profile of the 50 to 300 m region and find an anomalousexcess of particles in comparison to other shower profiles. This could be made easier withthe addition of scintillation panels to water Cherenkov surface detectors to better separatemuon particle detections from electron detections.
For 24 km initial heights, looking at the top-down view of the particle distribution (figure7a) there appears to be no evidence of excess. In fact, the ( x, y ) distribution of all particlesexceeding 10 GeV, with a 24 km initial height, appears to show no difference between thetwo models in particle count. This is confirmed by the near-Gaussian distribution of thesignificance values in figure 7b.
X Distance from core [m] - - - - - Y D i s t a n ce f r o m c o r e [ m ] - - - - - - - - (a) Plot of the significance of the difference inparticle count on an x − y plane. There is nofavoring of either model present. Mean 0.02043 – – s - - - N Mean 0.02043 – – Ground particle distribution: QGP - NonQGP 24km Significance Distribution (b) Plot of significance value distribution. Thevalues are centered on zero with no deviationsoutside 3 σ favoring one side over the other. Figure 7 : Significance of the difference in distribution of all particles with E >
10 GeVbetween QGP and non-QGP events with initial height of 24 km. Positive (blue) signifies adistribution in favor of QGP, while negative (red) signifies a distribution in favor of non-QGP.
Any differences between QGP and non-QGP events as measured from the ground particleprofile (figures 8a and 8b) at a 36 km initial height appear to be statistically negligible andsimilar to the 24 km radial distribution discussed previously. Neither figure demonstratesa favoring of one model over the other but rather display an extreme similarity between a– 11 –GP initiated shower and a non-QGP initiated shower. This may be a result of too muchtime, and/or too many interaction lengths, since first interaction eliminating any perceivabledifferences.Unfortunately, the lack of statistically significant effects at 36 km is discouraging forprospects of detecting QGP in real UHECR air showers as a 36 km initial height is many timesmore likely to occur than one at 12 km. This is especially true with the penetration potentialof heavier primaries at 100 PeV, which would be more likely to have QGP formation duringinitial collision due to containing more interacting nucleons. Ironically, the most favorableconditions for QGP formation occur with the least likely ability for detection, as neon andsimilar weighted primaries are most likely to interact at a higher elevations.
X Distance from core [m] - - - - - Y D i s t a n ce f r o m c o r e [ m ] - - - - - - - - (a) ( x, y ) plot of the significance ( σ ) of the dif-ference in distribution. Note the randomness ofthe distribution, signifying no favoring of eithermodel. Mean 0.0206 – – s - - - N Mean 0.0206 – – Ground particle distribution: QGP - NonQGP 36km Significance Distribution (b) Plot of the significance distribution. Thereare no outliers and the significance is centerednear zero, implying similar distributions.
Figure 8 : Significance of the difference in distribution of all particles with E >
10 GeVbetween QGP and non-QGP events with initial height of 36 km. Positive (blue) signifies adistribution in favor of QGP, while negative (red) signifies a distribution in favor of non-QGP.
The aim of this discussion is to determine if there exist effects on the ground profile andparticle composition of a UHECR air shower due to the formation of QGP during the initialinteraction of the UHECR on the atmosphere. The knowledge of whether QGP formationaffects the properties of UHECR development would enhance understanding of both UHECRand high energy hadronic interaction behaviors.Based on the results, the conclusion we reach is, in all practicality, detecting whetherQGP has formed within a UHECR is extremely challenging. While there is potential in the 12km results, more simulated events are needed to verify the extent to which the features seenin the 12 km results remain both present and detectable. With 102 total events simulated,and only 34 at each height, a statistical anomaly within in a single event can alter theperceived results. A more reasonable number of simulations for review would on the orderof 100 simulated events per model at each height, thereby limiting the effects of anomaliesto 10% or less rather than a 25% effect with the current number of events. Simulating onthe order of 1000 events per height and model would only be feasible with supercomputingresources, but would limit the effects of any outlier or anomalous events to ∼ ∼ would yieldapproximately 100,000 events during a 5-year operating window. At a 0.0021% rate, thiswould result in about 2 QGP-detectable events based on selection cuts. Although this is inprinciple a detectable number of events, the rarity of QGP means that selection cuts againstnon-QGP showers must have very high rejection factors. Acknowledgments
This discussion was made possible by NSF grant PHY-1207523. D. LaHurd acknowledgesthe support of the Timken Fellowship at Case Western Reserve University. Data analysiswas made possible in part by CRMC[22]. We acknowledge very helpful discussions withand guidance from T. Pierog. We are grateful for editorial and scientific comments andsuggestions on the manuscript from J. Matthews and other members of the Pierre AugerCollaboration. – 13 – eferences [1] Alexander Aab et al. The Pierre Auger Cosmic Ray Observatory.
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