Probing the high energy spectrum of neutral pions in ultra-high energy proton-Air interactions
PProbing the high energy spectrum of neutral pionsin ultra-high energy proton-Air interactions
Lorenzo Cazon, Ruben Conceição ∗† , Miguel Martins, Felix Riehn Laboratório de Instrumentação e Física Experimental de Partà culas - LIP and InstitutoSuperior Técnico - IST, Universidade de Lisboa - UL, PortugalE-mail: [email protected]
The interaction of ultra-high energy cosmic rays with the atmosphere nuclei has long been seenas a unique opportunity to study hadronic interactions above energies attainable by accelerators.However, so far the multiparticle production properties of the first interaction have been difficultto assess as they are masked by the many interactions that outline the shower development. Inthis work, we demonstrate, that relevant properties of the ultra-high energy first interaction canbe accessed through the analysis of the shower-to-shower distribution of muons arriving at theground. In particular, it is shown that the slope of the low-tail of the number of muon distributionmeasured at the ground is a direct link to the high energy spectrum of neutral pions produced inthe interaction of the primary protons. In this presentation, it will also address the experimentalfeasibility of such measurements and their connection with physical quantities being currentlymeasured at the Large Hadron Collider. ∗ Speaker. † Acknowledges the financial support of Fundação para a Ciência e Tecnologia, FCT-Portugal(DL57/2016/cP1330/cT0002). c (cid:13) Copyright owned by the author(s) under the terms of the Creative CommonsAttribution-NonCommercial-NoDerivatives 4.0 International License (CC BY-NC-ND 4.0). http://pos.sissa.it/ a r X i v : . [ h e p - ph ] A ug ail of the N µ distribution Ruben Conceição
1. Introduction
Ultra-high energy cosmic rays (UHECRs) have been long seen as an opportunity to study thehigh-energy Universe and access hadronic interactions for center-of-mass energies above the 100TeV scale. However, the degeneracy between the primary composition and hadronic interactions to-gether with the complex behavior of the Extensive Air Shower (EAS) development has underminedour ability to explore the properties of the first interaction, the exception being the measurement ofthe proton-Air cross-section. Muons constitute one of the best links to the hadronic activity withinthe shower, and for that, there has been a large enterprise to understand their behavior both fromthe theoretical (see for instance [1, 2]) and from the experimental point of view, e.g. [3, 4]. In thiswork, we investigate what drives the muon number distribution at the ground. We prove, throughsimulation, that while the average of the distribution depends on the sum of all hadronic interac-tions, its shape depends essentially on what happens in the very first interaction of the shower. Thismanuscript is organized as follows: in section 2 we discuss the origin of the fluctuations of the N µ distribution, while in section 3 we investigate the exponential tail that appears in the distributionfor proton showers; In the sub-section 3.1 we discuss how to use this tail to access the energy flowbetween the hadronic and electromagnetic (e.m.) component in the first interaction unequivocallyand in sec. 3.2 we discuss that the muon tail can also be used to access the high-energy tail of theneutral pion energy spectrum; The obtained results are summarized in section 4.
2. Shower-to-shower distribution of the EAS muon content
It is natural to think that the features of the shower-to-shower distribution of the number ofmuons at the ground, N µ , contain information about the shower development. The distribution ofmuon number recorded at the ground is shown in Fig. 1 (left) for showers initiated by proton withenergy of E = eV and zenith angle of θ = ◦ . The figure is shown for all the most commonlyused hadronic interaction models: QGSJ ET - II.04 [5], EPOS - LHC [6] and S
IBYLL C [7]. Itis interesting to note that this distribution resembles the distribution of the depth of the showermaximum, X max . The most noticeable difference is that for the N µ distribution, the exponential tailappears for low values while for the X max distribution it happens for high X max values. The numberof muons at the ground depends on the shower inclination and observation level. While this canaffect the N µ distribution, it depends solely on the propagation of muons, which can be adequatelytaken into account [1]. Hence, throughout the remaining of this manuscript, N µ at the groundwill be used as a proxy to the EAS muon content. In [8] it has been demonstrated, using EASsimulations that fluctuations of the N µ distribution is substantially related with properties of thevery first interaction, in particular, the ratio of energy that goes into hadronic particles (see schemein Fig. 1 (right)). In fact, it has been observed that for all tested hadronic interaction models, thereis a correlation of about 60% between E had / E and N µ as seen for instance in Fig. 2 (left). Thiscorrelation is stronger for low values of E had / E (and correspondingly for low N µ ). For largervalues, especially above E had / E > .
8, the correlation gets worse due to very high multiplicityevents and diffractive interactions. Therefore, the correlation between E had / E and N µ can befurther improved if one takes into account the first interaction multiplicity. Specifically, this can beachieved by redefining E had / E as 1 ail of the N µ distribution Ruben Conceição
Figure 1: (left) Distribution of the number of muons at the ground in simulated EAS induced by protonswith E = eV and θ = ◦ . The curve were generated with CONEX and so the muon energy thresholdis 1 GeV. (right) Scheme of the energy flow in the first interaction into the electromagnetic and hadroniccomponent of the shower. α = m ∑ i = (cid:18) E had i E (cid:19) β (2.1)where E hadi / E is the fraction of energy carried by each hadronic particle with respect to theprimary energy and m is the number of particles in the hadronic component of the interaction. Theparameter β is the power-law index that weights the growth of the average number of muons withthe primary energy, E . From a simple Heitler-Matthews model [9] it can be shown that β is givenby β = log ( m ) log ( m tot ) (2.2)being m tot the total number of particles that emerge from the hadronic interaction. Hence, thisparameter depends on the interaction multiplicity. The improvement of the correlation of N µ withthis new quantity, α can be seen in Fig. 2 (right). The correlation factor between α and N µ isgreater than 0.7 for all post-LHC hadronic interaction models. It is shown in [8] that α distributionof the first interaction is enough to describe the main features (the width and exponential tail) whilethe rest of the shower contributes only to the overall value of N µ . In fact, being the growth of theshower exponential and being the low-energy hadronic interaction much more numerous than thehigh-energy ones, it becomes evident that any deviation on the expected behavior at low energieswould have a more significant impact on the average of the N µ distribution.While the above findings have been reached using simulation, it can be inferred by takingsome considerations about the shower development. The production of muons in EAS arises nearlyexclusively from the hadronic component of the shower. This means that the number of producedmuons is closely related to the size of the hadronic shower, i.e., the amount of energy that flowsinto this sector. Hence, the relevant quantity is the fraction of energy transmitted to the hadronicsector in each interaction, and not the multiplicity as one could naively think. The distribution second moment. ail of the N µ distribution Ruben Conceição
Figure 2: (left) Distribution of the hadronic energy, E had / E , and N µ and (right) distribution of α versus N µ . Both plots were generated with showers induced by protons having an energy of E = eV and azenith angle of θ = ◦ . Let us now consider that in the first interaction, only a small amount of energy was passed intothe hadronic component. In this case, the size of the hadronic shower would be smaller, regardlessof what might happen in subsequent interactions. Hence, the fluctuation of the number of muonsthat should depend more on the first interactions than on the later stages of the shower development.In fact, as pointed out above the fluctuations of the hadronic energy are so large and the numberof sub-showers (multiplicity) so significant that the fluctuations of N µ can be accounted for by thefirst interaction alone.
3. Accessing the first interaction through the low- N µ distribution tail The possibilities attained to the plot in fig 2 (right) are enormous. For instance, in the case of apure proton composition, the low values of N µ would give access to the fraction of energy flowingto the hadronic component of the shower on the first interaction, while high values would be moresensitive to the interaction multiplicity.As mentioned before, a striking feature of the N µ distribution is its exponential tail at low N µ .This tail is more prominent for proton induced showers, and as the primary composition becomesheavier, the exponential behavior starts to disappear, and the N µ distribution gradually becomeGaussian (see Fig. 3 (right)). This behavior can be explained by a simple superposition model [8].The above feature could be explored to measure the slope of the N µ tail for proton inducedshowers, even in a mixed primary composition scenario, by employing a strategy similar to the oneused to extract the proton-air cross-section analysing the X max distribution tail [10]. E had / E distribution tail of the first interaction In this section, we aim to demonstrate that the measurement of the slope of the tail of the N µ distribution, Λ µ , within current experimental uncertainties, allows to assess a property of themultiparticle production of the first interaction. From Fig. 2 it can be seen that in the N µ tail region,the variable E had / E dominates the behavior of N µ . Hence, given the strong correlation betweenthese two quantities, the ansatz is that the measurement of Λ µ is directly connected to the slope of E had / E , which we will simply address as Λ had . 3 ail of the N µ distribution Ruben Conceição .
06 0 .
08 0 .
10 0 .
12 0 .
14 0 . µ . . . . . . . Λ h a d Epos-LHCQGSjetII-04Sibyll 2.3c
Figure 3: (left) Conversion between Λ µ and Λ α . The filled circles indicate the predictions by the differentinteraction models. The lines show how Λ µ changes for each model if Λ had is changed. (right) Number ofshowers with a given number of muons at ground for the nuclear primaries: p, He and N. The vertical barsindicate the fitting range.The total number of events is ≈
200 k.
The measurement of Λ had has two major requirements: it should be possible to select a N µ region where Λ µ can be fitted, independently of the presence of heavier primary elements in thefull distribution; there must exist a universal calibration curve between Λ µ and Λ had .The calibration has been investigated using simulations of proton induced showers for differ-ent hadronic interaction models. The variable Λ had was changed artificially by selecting simulatedshowers from a large ensemble, and the impact on Λ µ was then assessed.The result of such exercise can be seen in Fig. 3 (left). In this figure, the points are the resultfor proton simulation while the curves are the result arising from this test. The results obtainedshow that a relation between Λ µ and Λ had can be derived independently of the hadronic interactionmodels.Now that we can interpret Λ µ as Λ had , it is necessary to prove that Λ µ of the proton can bemeasured. For this, we have used the following mixed mass composition scenario: 25% proton,50% helium, 25% nitrogen, and no iron (or 1:2:1:0). This is one of the most pessimistic scenariosgiven by the analysis of the X max distribution in the Pierre Auger Observatory in the energy rangeof log ( E / eV ) ∈ [ .
5; 19 ] [11]. As the precision on N µ at the ground is highly dependent on theshower energy, we decided, conservatively, to smear it by 20%. This step aims to reproduce themost significant source of experimental uncertainty associated with the measurement of N µ . Withinthis scenario, it is possible to see in Fig. 3 (right) that by choosing the fit region adequately it ispossible to access the proton Λ µ and ultimately measure Λ had .The precision of the measurement of Λ µ in the above-described scenario is shown in Fig. 4(left) for all tested hadronic interaction models. From this plot, it is possible to see that the precisionof the measurement is only bounded to the number of collected shower events. The necessaryprecision to distinguish between hadronic interaction models using Λ µ is marked in the plot as adashed red line ( δ model ). For a N µ distribution made of more than 3000 showers (or around 200events in the fit range), the measurement precision becomes enough to discrimination betweenmodels.Fig. 4 (right) shows the same plot but for different mass composition scenarios. It is inter-esting to note that even in an extreme scenario with a huge amount of helium, such as 1:6:2:0,4 ail of the N µ distribution Ruben Conceição
Figure 4: (left) Relative fluctuation of the reconstructed Λ µ as a function of the number of events in theexperiments for the mass composition scenario 1:2:1:0. The x-bottom scale shows the number of events thatfall in the fit region while the axis on top shows the total number of shower events collected. The differencebetween the predicted slope for the different hadronic interaction models is 20% (red dashed line). This levelof precision is reached with 3000 events. The colored bands show the combined statistical error of the meanand standard deviation in the statistical sample. (right) Same plot as left generated with EPOS-LHC and fordifferent mass composition scenario (see legend). the measurement continues to depend solely on the number of recorded showers (even though onewould have to increase the number of events with respect to the 1:2:1:0 scenario in one order ofmagnitude).The measurement of the slope of the tail of the E had / E distribution, Λ had , is a quantity whichcharacterizes the fluctuations on the energy flow of a hadronic interaction (in this case, the firstone). For each interaction, there is a single E had / E , which means that this it represents the overallbehavior of the multiparticle production resulting from the hadronic interaction.This does not make the quantity less appealing as it could be measured in accelerator experi-ments, for instance, in the forward experiments at the Large Hadron Collider, such as TOTEM [12]and LHCf [13]. Such overlapping measurement between accelerators and cosmic ray experimentsis fundamental to confirm the validity of this analysis. For instance, LHC experiments are operatingat a center-of-mass energy of 13 TeV. The equivalent energy for the cosmic ray interaction with theatmosphere nuclei is about E ∼ eV. This is in an energy region that can be accessed by AMIGAscintillators [14], at the Pierre Auger Observatory and therefore a cross-check could be performed.The above measurement would allow to strengthen the confidence in the measurement of Λ had at E ∼ eV ( √ s ∼
100 TeV), at an energy currently inaccessible to accelerator experiments.
While the measurement of Λ had of the first ultra-high energy interaction is already a signif-icant breakthrough, it would be interesting to understand what are the multiparticle productionproperties, or interaction kinematical phase space, that is driving the slope of E had / E .The variable E had has direct relationship with the energy flow to the electromagnetic sector, E em = − E had . Consequently, its fluctuations are the same, σ ( E em ) = σ ( E had ) .The electromagnetic component is mainly fed by neutral pions , whereas the hadronic com- There is only an additional small contribution arising from excited resonances. ail of the N µ distribution Ruben Conceição
Figure 5: (left) Energy spectrum of neutral pions as a function of the lab. energy fraction, x L . The nominalcross-section in Sibyll 2.3c is shown in gray. The yellow curve represents a modified cross-section whereproduction of neutral pions at large x L is suppressed. (right) Distribution of the number of muons at groundin case of the two production spectra shown in the figure at the left. ponent contains equal contributions from other mesons (such as charged pions and kaons ) andbaryons (for instance protons). Therefore, it is natural to think that E had / E is connected with theenergy spectrum of neutral pions.In fact, we have checked, using simulations, that a change on the high-energy tail of the π energy spectrum (inclusive cross-section as a function of the lab. energy), corresponds to a modi-fication to the tail of the N µ distribution, Λ µ , as shown in Fig. 5. The result displayed in this plotstrongly suggests that the measurement of Λ µ gives access to a critical multiparticle productionproperty: the behavior of fast partons in a hadronic interaction (including valence quarks).From this exercise, one concludes that the tail of the N µ distribution is highly dependent onthe amount of energy that is given to the highest energy pions .It has been checked that it is possible to derive a monotonous function that relates the slope ofthe tail of N µ distribution with the high-energy tail of the neutral pions energy spectrum. However,contrary to Λ had , this function has some dependence on the details of the hadronic interactionmodels. These are still preliminary studies, and the calibration might be improved through a moresuitable choice of the energy range. However, it should be noted that even in the presence ofa systematic uncertainty caused by hadronic interaction models, this measurement would allowto exclude new phenomena at the highest energies, namely violations to longitudinal scaling athigh-rapidity, which is shared among all models or any other exotic new physics which would berevealed only at the 100 TeV scale.
4. Conclusions
In this work, it has been shown that the measurement of the features of the muon numberdistribution at the ground can be used to access properties of the first interaction of ultra-highenergy cosmic rays. In particular, it is shown that the exponential slope of the low- N µ distributioncan be used to measure the fraction of energy that flows into the hadronic component.¢aMoreover,the slope of the N µ distribution has also been found to be sensitive to the tail of the inclusive neutralpion production energy spectrum. The highest-energy particle is commonly referred as the leading particle. ail of the N µ distribution Ruben Conceição
It was likewise proved, in this manuscript, that the measurement of the Λ µ slope is possiblewithin the current experimental uncertainties, being its major limitation the number of events. Theanalysis can be done even with an unknown mixed primary composition scenario, provided thatthere is a significant fraction of proton UHECRs.The measurement of hadronic interactions at the highest energies might be relevant for theplanning of future experiments such as the Future Circular Collider. Additionally, it can also pro-vide an important handle to understand the shower development, solve the so-called muon problem,and ultimately get the mass composition of UHECRs unequivocally. References [1] L. Cazon, R. Conceição, M. Pimenta and E. Santos,
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