Physics Letters B 794 (2019) 29–35

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Physics Letters B

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± From Ds production asymmetry at the LHC to prompt ντ at IceCube ∗ ∗ Victor P. Goncalves a, , Rafał Maciuła b, Antoni Szczurek b, ,1 a Instituto de Física e Matemática, Universidade Federal de Pelotas (UFPel), Caixa Postal 354, CEP 96010-900, Pelotas, RS, Brazil b Institute of , Polish Academy of Sciences, Radzikowskiego 152, PL-31-342 Kraków, Poland a r t i c l e i n f o a b s t r a c t

Article history: The description of the heavy production at large energies and forward rapidities at the LHC Received 18 February 2019 is fundamental to derive realistic predictions of the prompt atmospheric flux at the IceCube Received in revised form 29 April 2019 Observatory. In particular, the prompt neutrino flux is determined by the decay of Ds Accepted 17 May 2019 produced in cosmic ray–air interactions at high energies and large values of the Feynman-xF variable. Available online 21 May 2019 + − Recent data of the LHCb Collaboration indicate a production asymmetry for D and D mesons, which Editor: A. Ringwald s s cannot be explained in terms of the standard modeling of the hadronization process. In this paper we demonstrate that this asymmetry can be described assuming an asymmetric strange sea (s() = s¯(x)) in the wave function and taking into account the dominant charm and subdominant strange fragmentation into Ds mesons. Moreover, we show that the strange fragmentation contribution is dominant at large-xF (≥ 0.3). The prompt ντ flux is calculated and the enhancement associated with the fragmentation contribution, disregarded in previous calculations, is estimated. The considered scenario leads to quite sizable enhancement of the high-energy τ -neutrino flux. © 2019 The Authors. Published by Elsevier B.V. This is an open access article under the CC BY license (http://creativecommons.org/licenses/by/4.0/). Funded by SCOAP3.

1. Introduction tion between the LHC and IceCube results and provide more pre- cise predictions for the Ds production at the LHC and the prompt The experimental results obtained in recent years by the LHC, tau neutrino flux at the IceCube. the Pierre Auger and IceCube Neutrino Observatories have chal- The atmospheric are produced in cosmic-ray inter- lenged and improved our understanding of Physics. The actions with nuclei in Earth’s atmosphere [8]. At low neutrino 5 discovery of the Higgs [1] completed the energies (Eν  10 GeV), these neutrinos arise from the decay of (SM), which is now a self-consistent theory, although, there is still light mesons ( and ), and the associated flux is denoted a small room for Beyond Standard Model (BSM) behavior. On the as the conventional atmospheric neutrino flux [9]. On the other 5 7 other hand, the detection of astrophysical neutrinos by the IceCube hand, in the energy range 10 GeV < Eν < 10 GeV, it is expected Neutrino Observatory sets the beginning of the neutrino astronomy that the prompt atmospheric neutrino flux associated with the de- [2]. In addition, the data from the Pierre Auger Observatory pro- cay of containing heavy flavors become important [10]. In vide an unique opportunity to test at energies well the particular case of the tau neutrino ντ flux, it is dominated at beyond current accelerators [3]. Such results motivated, in par- low energies by the conventional atmospheric flux, via νμ → ντ ticular, the development of new and/or more precise approaches 4 oscillations. On the other hand, for Eν > 10 GeV, this contri- to describe the perturbative and nonperturbative regimes of the bution becomes negligible and the prompt ντ flux is determined Quantum Chromodynamics (QCD). One example is the recent im- by the decay of Ds mesons, which have a leptonic decay channel provement in the description of the heavy meson production in Ds → τντ with a branching ratio of a few percent, with the sub- hadronic collisions at the LHC, directly influenced by the need to sequent τ decay that also contributes to the flux [11]. A precise constrain the magnitude of the prompt neutrino flux, which is cru- determination of the prompt ντ flux is crucial to identify the tau cial for a precise determination of the cosmic neutrino flux at the neutrinos of cosmic origin, which is considered another important IceCube [4–7]. In what follows we will explore this direct connec- signature of the cosmic ray origin of the highest neutrino flux. As demonstrated in Ref. [6], the prompt neutrino flux is determined by the heavy meson production at high energies and very forward Corresponding authors. * rapidities. Therefore, the description of the D production in the E-mail addresses: [email protected] (V.P. Goncalves), [email protected] s (R. Maciuła), [email protected] (A. Szczurek). kinematical region probed by the LHCb Collaboration is a requisite 1 Also at University of Rzeszów, PL-35-959 Rzeszów, Poland. to obtain a precise prediction of the prompt ντ flux. https://doi.org/10.1016/j.physletb.2019.05.026 0370-2693/© 2019 The Authors. Published by Elsevier B.V. This is an open access article under the CC BY license (http://creativecommons.org/licenses/by/4.0/). Funded by SCOAP3. 30 V.P. Goncalves et al. / Physics Letters B 794 (2019) 29–35

+ − During the last years, the LHCb Collaboration released a large identical amount of Ds and Ds mesons, which implies that the set of data associated with the D and production. The charge asymmetry defined by data for the transverse momentum and rapidity distributions are, + − in general, quite well described by theoretical approaches. On the + σ (D ) − σ (D ) A (D ) = s s (1) other hand, the description of the experimental data for the charge P s + + − σ (Ds ) σ (Ds ) production asymmetries [12,13]is still a challenge for the great majority of the theoretical approaches. In general, these production will be zero at this approximation. Consequently, the asymme- asymmetry are interpreted as arising during the nonperturbative tries are expected to be generated by subleading partonic subpro- process of hadronization as implemented e.g. in the PYTHIA Monte cesses, initial state asymmetries and/or a distinct description of the hadronization process. Here we extend the approach proposed in Carlo, which is based on the Lund string fragmentation model. + − However, this approach fails to describe the recent LHCb data for Ref. [14], which explains the D /D asymmetry in terms of the ± unfavored fragmentation functions, which are responsible for light the Ds production asymmetries, which have found evidence for a nonzero asymmetry. In particular, in contrast with PYTHIA that quark/antiquark fragmentation to D mesons, for Ds production. predicts a positive value, the experimental data indicate that the The fact that u = d in the incident , naturally leads to the + − asymmetry is negative. Very recently, two of us have proposed D /D asymmetry when the subleading contribution for the frag- in Ref. [14]an alternative approach to describe the asymmetry mentation is taken into account. In contrast, in the case of Ds pro- + − present in the D and D production [12]. The basic idea is that duction, the inclusion of the subleading fragmentation, associated → − ¯ → + + = subleading contributions for the parton fragmentation are nonneg- to the s Ds and s Ds transformations, implies A P (Ds ) 0if = ¯ ± ligible at the LHC energies and that the asymmetry comes from the s s. Therefore, our interpretation of the LHCb data is that the Ds asymmetry of the u and d valence distributions inherent in the in- asymmetry arises due to an asymmetry in the strange quark sea. ± As explained before, such a behavior is predicted by some theoreti- cident protons. In this paper we extend the approach for the Ds production and demonstrate that the LHCb data can be described cal models and is not excluded by the recent QCD global analysis of if we assume that the strange quark sea in the proton is asym- the experimental data. In fact, the global fits do not include the re- metric, with s = s¯. Such asymmetry is predicted e.g. by the Meson cent LHCb experimental data. In particular, the CTEQ Collaboration Cloud Model (see. e.g. Refs. [15–19]) and is not excluded by the has performed a dedicated study of the strange parton distribu- recent data and by QCD global analyses. In reality, the strange sea tion of the proton in Ref. [24]and obtained that the experimental in the proton is only poorly known, with its behavior being deter- data is quite well described also assuming s = s¯. In our analysis mined in a great extent by the neutrino and antineutrino-induced we use rather old CTEQ6 PDF parametrization, however, the most DIS data on charm production obtained by the CCFR/NuTeV and recent analyzes published by the various PDF collaborations use, NOMAD experiments [20,21], which are characterized by the pres- as input for their fits, symmetric strange/antistrange quark dis- + − ence of μ μ in the final state. In particular, these experiments tributions. In several papers related to PDFs, it was shown that have studied the difference between the neutrino and antineutrino different data seem to point towards different values of the asym- induced dimuon differential cross sections, which is sensitive to metry. In particular, data from some experiments seemed to prefer the strange quark/antiquark asymmetry s(x) − s¯(x), and found a negative asymmetries, whereas those from other ones seemed to non-zero value for the asymmetry, which could partially explain prefer positive asymmetries. For the LHCb experiment [13]typical the anomaly seen by the NuTeV experiment in their measurement longitudinal momentum fractions of s or s¯ belong to the interval of the Weinberg angle [22]. Recent analysis of the LHC data for x ∈ (0.1, 0.3). There both the CTEQ6 parametrization and meson ± the W production improved our understanding of the strange cloud models suggests s(x) > s¯(x) [25–27]. distribution, especially at small-x, but the existence or not of an In the present paper we shall include the dominant g + g → asymmetric strange sea is still an open question [23]. As a con- c + c¯ subprocess as well as the s/s¯ + g → s/s¯ + g and g + s/s¯ → sequence, assuming that our approach for the subleading parton g + s/s¯ terms with the strange partons from Ref. [24]. Moreover, ± ¯ → ± fragmentation is correct, the results for the Ds asymmetry can be we will include the subleading s/s Ds fragmentation, which considered as a first signature that s = s¯ in the proton. Finally, the is described in terms of the probability of transition of a strange results presented in Ref. [14] and in what follows indicate that the quark into a Ds meson (P s→Ds ). Of course, the leading fragmen- → + ¯ → − subleading contributions to the parton fragmentation are nonneg- tation is associated with the c Ds and c Ds transitions ligible and have a large impact on the Feynman-xF distributions with an associated transition branching of about 5-9 % [28]. As of the heavy mesons produced in hadronic collisions. As discussed in Ref. [14]the –gluon channel will be calculated within the e.g. in Refs. [5,6], this distribution determines the prompt neutrino kT -factorization approach, with the cross section being expressed flux. Therefore, it is expected that the prompt ντ flux will be en- in terms of the unintegrated gluon distribution function (UGDF) hanced by these subleading contributions. One of the goals of this and off-shell matrix element for the gg → cc¯ subprocess. In the paper is to estimate this enhancement and provide realistic predic- present paper we use the Kimber-Martin-Ryskin (KMR) prescrip- tions for the tau neutrino flux that are based on a formalism that tion for UGDF [29] which was shown many times to allow a good is in agreement with the recent LHCb data. Although the formalism description of experimental data for different final states, including may seem rather simplistic it was successfully applied to explain open charm [30], quarkonia [31]dijet [32]and electroweak gauge ± the D asymmetry [14]. The predictions for the tau neutrinos are boson [33,34]production at the LHC. In contrast, the s(s¯)g → s(s¯)g directly connected to our approach for the Ds meson production. If and gs(s¯) → gs(s¯) processes are calculated within a leading-order ± our explanation for the Ds asymmetry is correct, the tau neutrino collinear approach, with the regulation of small transverse mo- flux will be amplified in comparison to previous analyses. menta region being done as in Ref. [14]. Moreover, the c → Ds fragmentation is described using the Peterson model (with ε = 2. D production at the LHC → − ¯ → + s 0.05), while the s Ds and s Ds fragmentation functions are parametrized as in Ref. [14]using the reversed-Peterson and tri- At high energies the charm are produced dominantly angular fragmentation functions. The only free parameter in our by gluon–gluon interactions via the gg → cc¯ subprocess and are approach is P s→Ds . In principle, it is expected to be larger than believed to hadronize to Ds-mesons mainly through the c → Ds the value obtained in Ref. [14]for the u/d → D transition, due fragmentation process. Therefore, at leading order, we expect an to the larger mass of the strange quark. However, as this quantity V.P. Goncalves et al. / Physics Letters B 794 (2019) 29–35 31

√ √ + − − Fig. 1. Ds Ds asymmetry obtained with our approach for s = 7 TeV (left panel) and s = 8 TeV (right panel) together with the LHCb experimental data [13]. is associated with a nonperturbative process, it is not possible to for both considered, 7 and 8TeV, data sets. In other words, a calculate its value from first principles. In what follows, we will small value of P s→Ds for the unfavored fragmentation function constrain P s→Ds using the LHCb data for the charge production is sufficient to describe the LHCb data. The statistics of the ex- + asymmetry A P (Ds ). perimental data is still too low to perform a more detailed fit + − − In√ Fig. 1 we present our results√ for the Ds Ds asymmetry and/or to discriminate between the two models for the subleading for s = 7 TeV (left panels) and s = 8 TeV (right panels) us- fragmentation. However, the results indicate that the asymmetry ing the reversed-Peterson and triangular fragmentation functions of strangeness in the proton wave function, as described in the for the s → Ds transition. Rather reasonable agreement with the CTEQ6 parametrization, is able to generate the correct sign for · −2 + LHCb data is obtained assuming P s→Ds = 7 10 . As can be A P (Ds ), in contrast to PYTHIA [13], as well as the enhancement seen from Fig. 2, this value leads to a minimal χ 2/N with N = 12 of the asymmetry at larger rapidities. In these calculations, the 32 V.P. Goncalves et al. / Physics Letters B 794 (2019) 29–35

best fit set of the CTEQ6 parametrization was assumed. However, in Ref. [24], the authors also have obtained two other fits of the data, assuming different magnitudes for the strangeness asymme- try. For completeness, in Fig. 3 we show the results obtained with these three different strangeness asymmetry fits from the CTEQ6 PDF. The high-, low- and best-asymmetry fits lead to a quite dif- ferent predictions for the Ds production asymmetry, especially, at larger rapidities. The two limiting cases correspond to the lower and upper bounds of the magnitude of strangeness asymmetry in the CTEQ6 parametrization. In Fig. 4 (left panel) we present the resulting predictions for the + + − transverse momentum distributions of Ds Ds for the different ranges of the meson rapidity (yD ) probed by the LHCb Collabora- tion [35]. A quite good agreement with the LHCb data is achieved without free parameters. We use BR(c → Ds) = 6% which gives the best fit of the LHCb open charm data, in terms of χ 2 test, within the central value of our model. We have verified that the contri- bution of the subleading fragmentation for the pT -spectra is small 2 → ≤ √Fig. 2. The χ /N distribution√ as a function of P s Ds fragmentation probability for ( 5%) in the kinematical range probed by the LHCb Collaboration. s = 7 TeV (dashed) and s = 8 TeV (solid). For the statistical test we include all In contrast, the behavior of the rapidity and Feynman-xF distri- of the twelve data points for each of the two energies reported by the LHCb [13]. butions are significantly modified at large values of yD and xF .

√ + − − Fig. 3. Ds Ds asymmetry obtained with our approach for s = 7 TeV together with the LHCb experimental data [13]for different rapidity bins (left and right panel). Here, three different fits of the strangeness asymmetry from the CTEQ6 PDF set are used.

+ + − Fig. 4. Left: Transverse momentum distributions of Ds Ds for different ranges of rapidity. The LHCb data [35]are shown for comparison. Right: ± Feynman-xF distribution for the Ds production. V.P. Goncalves et al. / Physics Letters B 794 (2019) 29–35 33

Fig. 5. Left: The prompt atmospheric tau neutrino (ντ + ντ ) flux as a function of the neutrino energy for three different models for the primary flux (top, middle and bottom panels). Right: Ratio between the full calculation (conventional + subleading contributions) and the conventional one.

In Fig. 4 (right panel) we demonstrate that the asymmetry in the disregarded in the analysis of the Ds production, are dominant. strange sea imply different behaviors for the xF -distributions of the Such values of xF correspond to rapidities larger than those probed + − Ds and Ds mesons at intermediate xF . More important, while at by the LHCb detector. However, as demonstrated in Ref. [6], this is small-xF the conventional contribution dominates, at large-xF the exactly the kinematical region that determines the behavior of the situation is reversed. One has that the contribution associated to prompt neutrino flux. Consequently, the presence of the sublead- the sg¯ → sg¯ channel becomes dominant for xF ≥ 0.05. In particu- ing contributions for the Ds production is expected to have direct lar, for xF  0.3, the channels initiated by strange quarks, usually impact on the predictions of the prompt tau neutrino flux. 34 V.P. Goncalves et al. / Physics Letters B 794 (2019) 29–35

3. Prompt ντ flux at the IceCube 4. Conclusions

One of the current goals of the IceCube Observatory is the In the present paper we propose, for the first time, the descrip- + − measurement of tau-neutrinos [36], which are considered an in- tion of the production asymmetry for Ds and Ds mesons in terms dependent probe of the cosmic neutrinos. Such an expectation is of an asymmetry in the strange sea of the proton associated to the → − strongly motivated by the fact that for cosmic neutrinos the de- inclusion of the subleading fragmentation mechanisms s Ds or → + − ¯ cay of charged pions generated in astrophysical sources implies a s Ds . We have used asymmetric s s distributions obtained ratio νe : νμ : ντ = 1 : 1 : 1 at the Earth, while for atmospheric by the CTEQ group and derived in a global analysis of different neutrinos this ratio is expected to be typically νe : νμ : ντ = 1 : 1: experimental data and which is consistent with meson cloud pic- 0.1 [5,11]. As a consequence, the background associated to atmo- ture of the nucleon.2 Different sets from that analysis have been spheric tau neutrinos is usually predicted to be strongly reduced used to demonstrate uncertainties. We have demonstrated that a in comparison to the other flavors, with the measurement of a small value of the P s→Ds probability for the strange fragmentation tau neutrino being considered a direct probe of cosmic neutrinos. function into Ds mesons is sufficient to describe the LHCb data. However, previous analyses have disregarded the subleading con- 2 A similar value of P s→√Ds was obtained by√ minimizing χ for the tributions discussed in this paper. It is the aim of the present study LHCb asymmetry for s = 7TeV and for s = 8TeV. Such a new to make a realistic estimate of the prompt ντ +ντ flux when using contribution, disregarded in previous studies, becomes dominant the current information from the LHC. at large values of xF , that is the kinematical range that deter- + In order to estimate the prompt ντ ντ flux, we will closely mines the prompt atmospheric ντ flux at the IceCube Observatory. follow the procedure described in detail in Refs. [6,7]. We will We have estimated the impact of this contribution and demon- calculate the prompt tau neutrino flux using the semi-analytical strated that it implies an enhancement by a factor larger than 3 Z-moment approach [10], where a set of coupled cascade equa- in the kinematical range probed by the IceCube Observatory. Our tions for the , heavy mesons and (and their an- results indicate that a future experimental analysis of prompt tau tiparticles) fluxes is solved, with the equations being expressed neutrinos at the IceCube can be useful to probe the underlying in terms of the nucleon-to- (Z NH), nucleon-to-nucleon mechanism of Ds production at high energies and forward rapidi- (Z NN), hadron-to-hadron (Z HH) and hadron-to-neutrino (Z Hν ) ties at the LHC. Z-moments. These moments are inputs in the calculation of the The production of τ -neutrinos was discussed very recently in prompt tau neutrino flux associated with the production of Ds the context of intrinsic charm in the nucleon [38] and the beam mesons and their decay into a ντ in the low- and high-energy dump fixed target experiment SHiP at CERN [39]. No reference to regimes. We will focus on vertical fluxes and will consider three the LHCb asymmetry was done there. different models for the cosmic ray incident flux φN , i.e. as de- scribed by the H3a and H3p spectra proposed in Ref. [37]as well Acknowledgements as for the Broken Power Law (BPL) model. As in Ref. [11]we will include in our calculations the contribution of neutrinos produced We are indebted to Maria Garzelli and Pavel Nadolsky for in- → in the direct Ds ντ decay as well as those generated in the teresting discussion on s/s¯ symmetry/asymmetry. This study was → → chain decay Ds τ ντ . The contribution for the prompt ντ partially supported by the Polish National Science Center grant flux associated to the decay of mesons heavier than Ds is negli- DEC-2014/15/B/ST2/02528, by the Center for Innovation and Trans- gible [5] and will not be included in our analysis. In Fig. 5 (left fer of Natural Sciences and Engineering Knowledge in Rzeszów and + 3 panels) we show the flux of the prompt ντ ντ flux scaled by Eν . by the Brazilian funding agencies CNPq, FAPERGS and INCT-FNA In addition to the conventional component, associated to heavy (process number 464898/2014-5). quark production by a gluon-gluon fusion and represented by the solid black line, we show the results which includes in addition the References subleading fragmentation assuming a symmetric (dashed red line) or an asymmetric (dot-dashed blue line) strange sea in the proton [1] G. Aad, et al., ATLAS Collaboration, Phys. Lett. B 716 (2012) 1; wave function. The subleading mechanism leads to a significant S. Chatrchyan, et al., CMS collaboration, Phys. Lett. B 716 (2012) 30. enhancement of the high-energy prompt τ -neutrino flux, which [2] M.G. Aartsen, et al., IceCube Collaboration, Science 342 (2013) 1242856. can be quantified calculating the ratio between the full prediction [3] A. 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This is 2 Recent fits to the LHC data for W /W or W c¯/W c production. assume expected from previous studies about the prompt neutrino flux at rather s(x) = s¯(x), which is rather caused by the fact that the data is not precise enough to allow independent parametrization for s and s¯. We wish to note, how- high energies. However, the results also show that the presence of + − ever, that separate χ 2 values for W and W are quite different as discussed e.g. the subleading fragmentation generates a larger flux, with the am- in [40]and [41]. We hope that LHC Run3 data will allow for fits relaxing the tech- plification factor being almost independent of the model used for nical condition s(x) = s¯(x). Also future DUNE ν/ν¯ data [42]will be helpfull in this the primary flux. respect. V.P. Goncalves et al. / Physics Letters B 794 (2019) 29–35 35

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