AMS-02 antiprotons, at last! Secondary astrophysical component and immediate implications for Dark Matter

Using the updated proton and helium fluxes just released by the AMS-02 experiment we reevaluate the secondary astrophysical antiproton to proton ratio and its uncertainties, and compare it with the ratio preliminarly reported by AMS-02. We find no unambiguous evidence for a significant excess with respect to expectations. Yet, some preference for a flatter energy dependence of the diffusion coefficient starts to emerge. Also, we provide a first assessment of the room left for exotic components such as Galactic Dark Matter annihilation or decay, deriving new stringent constraints.


Introduction
Since decades, the antiproton component in cosmic rays (CR's) has been recognized as an important messenger for energetic phenomena of astrophysical, cosmological and particle physics nature (see for instance [1,2,3]). In modern times, antiprotons have often been argued to be an important diagnostic tool for cosmic ray sources and propagation properties, and constitute one of the prime channels for indirect searches of Dark Matter (DM) [4,5], which so far has only been detected gravitationally. In DM annihilation (or decay) modes, antiprotons can result either from the hadronization of the primary quarks or gauge bosons or through electroweak radiation for leptonic channels.
The Alpha Magnetic Spectrometer (Ams-02) onboard the International Space Station (ISS), is the most advanced detector for such indirect DM searches via charged cosmic ray flux measurements. The positron fraction has been published earlier [6,7], confirming the rise at energies above 10 GeV detected previously by Pamela [8,9] and Fermi [10]. The sum of electrons and positrons [11] as well as they separate fluxes [12] have also been published, thus drawing a coherent and extremely precise picture of the lepton components of cosmic rays. Despite the fact that DM interpretations of the positron and, more generally, leptonic 'excesses' have been attempted (for a review see [13]), even before the advent of Ams-02 it had been recognized that explanations involving astrophysical sources were both viable and favoured (for a review see [14]), a conclusion reinforced by updated analyses (see [15,16], and references therein, for recent assessments).
In this paper, we will instead focus on cosmic ray antiprotons. Up to now, the so-called secondary antiprotons (originating from collisions of cosmic ray primaries with the interstellar material) have been shown to account for the bulk of the measured flux [18], thus allowing to derive constraints on the DM parameter space and to compute expected sensitivities, respectively based on updated Pamela data [19] and projected Ams-02 data (see e.g. [20,21,22,23,24,25,26,27]). Now that the Ams-02 Collaboration has presented its preliminary measurements of thep/p ratio [28], with an improved statistical precision and energy range extending to 450 GeV, it is crucial and timely to re-examine the situation and update existing results. In addition, Ams-02 has presented the measurement of the proton (p) and helium (α) spectra [28], in qualitative agreement with the previous determinations by Pamela [29], but now with unprecedented precision and detail. This is important for our purposes since the p and α spectra are crucial input ingredients in the computation of the secondary antiproton flux, which is the minimal astrophysical antiproton background, as we will remind later. In other words, with the release of these exquisitely precise datasets, Ams-02 provides a coherent, high-statistics-albeit preliminary-picture in the hadronic component of cosmic rays too, allowing for a scrutiny of possible exotic contributions.
However, the reach of any search for exotic physics is limited by the astrophysical uncertainties affecting the production and the propagation processes of cosmic antiprotons in the Galaxy and in the solar system. Indeed, while the basic processes involved in the production and propagation of cosmic ray antiprotons are rather well understood, the detailed parameters entering in such processes are far from being well determined. Typically,p production, propagation and SOlar modulation uncertainties can have a large impact on both the astrophysical and (in particular) the DM signal. Some sensible ranges for these parameters can and must be determined, e.g. by studying ordinary cosmic-ray fluxes i.e. those that surely have a nonexotic origin. Indeed, this is what leads to the traditional Min-Med-Max schemes [30], and to plausible ranges for the force field parameter of solar modulation (the so-called Fisk potential). However, these ranges are based on past cosmic-ray data and are not necessarily guaranteed to work in describing the current status. We anticipate that this is what we will find in some cases discussed below. For instance, a string of recent papers, based on synchrotron radio emission [31,32,33,34] but also on positrons [15,35] and somewhat also on gamma rays [36], finds that the thin halo predicted by Min is seriously disfavored. More generally, looking for Dark Matter on top of inadequate schemes can lead to non-robust or even wrong conclusions. In other words, one of the most crucial issues in the field is to update the uncertainty ranges of ordinary astrophysics in view of the more recent and precise experimental results, in order to build the DM search on a more solid basis. This will be possible after a careful analysis of accurate secondary over primary data like the boron to carbon (B/C) ratio, soon to be published by Ams-02 (and possibly other experiments), and provided that theoretical uncertainties will be under better control [37]. For the time being, the search for Dark Matter signatures has to be pursued with the utmost care.
Within this broad context, the purpose of this paper is twofold: 1) based on existing propagation models, derive the state-of-the-art astrophysical antiproton background, carefully appraising the related uncertainties; 2) on the basis of such background and fully taking into account such uncertainties, assess what can be said on the room left for a DM signal, and what can not.
The rest of this paper is organized as follows. In Sec. 2, we remind how the computation of the astrophysical antiproton background proceeds, we detail its uncertainties and we compare the result with the measuredp/p. In Sec. 3 we introduce the Dark Matter contribution tō p/p and we derive constraints on the DM annihilation cross section or decay rate, for several annihilation/decay channels and under different DM and astrophysical configurations. Finally in Sec. 4, we conclude with a few final comments.

Re-evaluation of the astrophysical antiproton background
The secondary astrophysical antiproton background 1 is produced in collisions of the cosmic ray high energy protons and helium nuclei on the interstellar medium, mainly constituted of hydrogen and helium, the contributions of heavier nuclei in both projectiles and targets being a few percent correction. The locally measured flux is the result of the diffuse production in the Galactic environment and the subsequent propagation of the antiprotons to the location of the Earth. Hence, the main ingredients of the computation for the '(secondary) astrophysicalp source term' are: i) the injection p and α primary fluxes from Galactic sources, ii) the collision cross sections, iii) the propagation details. While we refer to [21,39] and reference therein for a detailed discussion of all the aspects of the computation, here we just highlight the points of novelty.
For the p and α spectra needed in i), as mentioned above we use the data that have just been released by Ams-02 [28]. The spectra are measured up to a rigidity of 1.8 and 3 TV for p and α nuclei, respectively, and, as already reported by the Pamela Collaboration [29], they cannot be described by a single power law: a hardening at energies higher than ∼300 GV is observed for both. At the practical level, we perform our own fits of the Ams-02 data points. We find that the p spectrum is fitted by a value of the Fisk potential consistent with independent neutron monitor measurements [40]. We choose for definiteness the best fit value of φ p F = 0.62 GV and we will keep it fixed, for p's, in all of the following.The uncertainties on the slope of the p and He spectra at high energies, ∆γ H,He , induce an uncertainty band on the predicted astrophysical p/p ratio. In fig. 1, top left panel 2 , we show the result of our computation of the ratio with such uncertainty band. For the distribution of the sources of primary CR p and α, which can be determined from pulsar and supernova remnant surveys, we use the parameterization of [41], slightly modified as in [42].
For the production processes we need the cross sections σ pH→pX , σ pHe→pX , σ HeH→pX , σ HeHe→pX , where the first index refers to the impingent primary CR while the second one to the target interstellar material. For σ pH we use the new parameterization recently proposed by [43], instead of the traditional fitting relations given in [44,45]. For the cross sections of the other reactions we use the prescription of [39], to which we refer the interested reader. We just remind that the pH reaction largely dominates, providing about 70% of the totalp flux at 1 GeV, while pHe yields about 25% and the reactions involving impinging He contribute the few remaining percentage points. Another element which has only recently been appreciated is related to the contribution of antineutron production: on the basis of isospin symmetry, one would consider the production cross section for antineutrons (e.g. σ pH→nX and the others) as equal to those for antiprotons; the antineutrons then rapidly decay and provide an exact factor of 2 in thep flux. However, as pointed out in [43,46] and as already implemented in [21], it may be that this naïve scaling does not apply and that the antineutron cross section is larger by up to 50% with respect to thep one. All these cumulated effects contribute to an uncertainty band for the astrophysicalp/p ratio which is represented in fig. 8 of [43] and which we will adopt: it varies from about 20% to at most 50% (at large energies and in the most conservative conditions). In fig. 1, top right panel, we show our prediction for thep/p ratio with this uncertainty envelope. There, for the uncertainty of the cross sections involving He, we made the reasonable minimal choice to assume the same relative uncertainty as the pp cross section, lacking actual data to base the estimate on.
Once produced, antiprotons have to propagate in the local Galactic environment before they are collected at Earth. We deal with this process in the usual way, by solving semi-analytically the full transport equation for a charged species in a 2D cylindrical 'thick halo' model of the Galaxy. We do not reproduce the full treatment here (we refer again to [21] and references therein) but point out that we do include all the relevant processes. In particular, we take  into accountp annihilation, energy losses, 'tertiary production', and diffusive reacceleration. Besides these effects, the propagation parameters governing diffusion and convection are as usual codified in the Min, Med and Max sets [30], which are by definition those that minimize or maximize the primaryp flux at Earth. Note that these have not (yet) been revised on the light of recent secondary data, so the viability of these predictions for thep/p ratio (which extends for instance to higher energies) is not trivially expected to hold. In fig. 1, lower left panel, we show the impact of the propagation uncertainty. The curves which are labelled Min, Med and Max represent the modification which occurs by choosing these standard sets, while the shaded yellow area envelops the results obtained by sampling more widely the propagation parameter space. Notice in passing that the shaded yellow area does not coincide with the Min-Med-Max envelope (see in particular between 50 and 100 GeV): this is not surprising, as it just reflects the fact that the choices of the parameters which minimize and maximize thep/p secondaries are slightly different from those of the primaries. However, the discrepancy is not very large. We also notice for completeness that an additional source of uncertainty that we do not include consists in the uncertainties affecting the energy loss processes. These are however Finally,p's have to penetrate into the heliosphere, where they are subject to the phenomenon of Solar modulation (abbreviated with 'SMod' when needed in the following). We describe this process in the usual force field approximation [47], parameterized by the Fisk potential φ F , expressed in GV. As already mentioned in the Introduction, the value taken by φ F is uncertain, as it depends on several complex parameters of the Solar activity and therefore ultimately on the epoch of observation. In order to be conservative, we let φ F vary in a wide interval roughly centered around the value of the fixed Fisk potential for protons φ p F (analogously to what done in [25], approach 'B'). Namely, φ F = [0.3, 1.0] GV φ p F ± 50%. In fig. 1, bottom right panel, we show the computation of the ratio with the uncertainties related to the value of the Fisk potential in the considered intervals. Notice finally that the force field approximation, even if 'improved' by our allowing for different Fisk potentials for protons and antiprotons, remains indeed an effective description of a complicated phenomenon. Possible departures from it could introduce further uncertainties on the predictedp/p, which we are not including. However it has been shown in the past that the approximation grasps quite well the main features of the process, so that we are confident that our procedure is conservative enough. Fig. 2 constitutes our summary and best determination of the astrophysicalp/p ratio and its combined uncertainties, compared to the new (preliminary) Ams-02 data. The crucial observation is that the astrophysical flux, with its cumulated uncertainties, can reasonably well explain the new datapoints. Thus, our first -and arguably most important-conclusion is that, contrarily to the leptonic case, there is no clear antiproton excess that can be identified in the first place, and thus, at this stage, no real need for primary sources. This also means that,    at least naively, one expects a limited room left for exotic components, such as DM. Indeed in the following section we will proceed to compute the constraints on it.
However, before we can do so, we have to identify specific sets of astrophysical parameters to describe the background, as discussed in the Introduction. We fix in turn Min, Med and Max and we vary the solar modulation potential in the given interval. We model the uncertainties of the source term by allowing a renormalization of the background with an energy dependence and an amplitude A as dictated by the analysis presented above (namely, an uncertainty modulated as the pink band of fig. 1). With this strategy, we look for the best fitting values of the amplitude A of the potential φ F and we trace the correspondingp/p spectra. We show in fig. 3 the different cases.
Even within the limitations of preliminary data like those we are dealing with, we can see that the Min propagation scheme predicts an astrophysical background that can not reproduce the newp/p data points above 30 GeV. The Med scheme provides a barely decent fit (still good up to ∼ 30 GeV but rapidly degrading after) while choosing Max the data can be well explained across the whole range of energies. 3 This is our second conclusion: the preliminaryp/p Ams-02 data seem to prefer a model, such as Max, characterized by a relatively mild energy dependence of the diffusion coefficient at high energies. Although it is too early to draw strong conclusions, this is an interesting observation and it goes in the same direction as the preference displayed by the preliminary B/C Ams-02 data [37].
It would of course be tempting to interpret the room left in the Min and Med cases at large energies as an exotic contribution from DM. However we insist that this would be a wrong deduction in two respects: as long as a model within the uncertainties can fit the data, failure of other models just means a better selection of the background rather than evidence for an extra component; in any case, a new assessment of the viable propagation parameter space would be needed before any conclusion is drawn.

Updated constraints on Dark Matter
Primary antiprotons could originate from DM annihilations, or decays, in each point of the Galactic halo. They then propagate to the Earth subject to the same mechanisms discussed in the previous section, which are in particular described by the canonical sets of parameters Min-Med-Max. Concretely, we obtain thep fluxes at Earth (post-propagation) from the numerical products provided in [49], version 4. Notice that these include the subtle effects of energy losses, tertiaries and diffusive reacceleration which, as discussed at length in [21], are important to reach a detailed prediction.
We consider four primary annihilation (or decay) channels: DM DM → bb, W + W − , µ + µ − and γγ. These, for all practical purposes, cover very well the range of possible spectra. Indeed, annihilation (or decay) into tt or hh (with h the Higgs boson) would give spectra practically indistinguishable from those from DM DM → bb, and ZZ from those of W + W − . The µ + µ − channel represents leptonic channels, in which a small yield of antiprotons is obtained thanks to ElectroWeak corrections (namely, the radiation from the final state leptons of a weak boson which decays hadronically). Similarly, the γγ channel produces some subdominantp flux via electromagnetic corrections 4 .
We also consider two representative DM Galactic profiles: Einasto and Burkert, with the precise functional forms and definitions of the parameters as in [49]. The former possesses a peaked distribution towards the Galactic Center and hence typically results in a more abundant yield of antiprotons with respect to the latter, which features a core in the inner few kpc.
With the astrophysical background discussed in the previous section and the fluxes from Dark Matter as just presented, we can now compute the constraints in the usual planes 'mass m DM vs. thermally averaged annihilation cross section σv ' or 'mass m DM vs. decay rate Γ'. We refer to [21] for a detailed discussion of the practical procedure. On the basis of the discussion in the previous section, it makes sense to derive constraints only within the propagation schemes that provide a decent explanation of the background. Max is the favored scheme. Med provides overall a worse but still reasonable fit to the data, so that we will employ it. In addition, (see     The results that we obtain with this strategy are presented in fig. 4 for the DM annihilation case and in fig. 5 for the DM decay case. In the left panels we fix a benchmark DM profile (Einasto) and the Med propagation model, and show the constraints for the different particle physics channels introduced above. We see for example that the thermal annihilation cross section σv = 3 · 10 −26 cm 3 /s is now excluded for m DM 150 GeV for thebb channel. In the right panels we explore the impact of changing the propagation parameters or the DM distribution. As already highlighted several times in the literature, the effect is sizable and can reach a factor of up to an order of magnitude. For instance, the previously quoted limit for the mass of a thermal relic can vary between 90 and 250 GeV for the range of models explored here. Of course, as Max maximizes by definition the DMp yield, its constraints are much stronger than those of the Med case. Turning the argument around, if the preference for Max-like propagation schemes hinted at by preliminary Ams-02 data is confirmed, Ams-02 itself has the unprecedented possibility to exclude m DM 250 GeV for thermal annihilation cross section in thebb channel.

Final remarks
In the light of the preliminary results presented by Ams-02 on p and α fluxes, as well as thep/p ratio, we have re-evaluated the secondary astrophysical predictions for thep/p ratio, accounting for the different sources of uncertainties: namely on the injection fluxes, on the production cross sections, on the propagation process and those connected to Solar modulation. Our first and main result is that there is no unambiguous antiproton excess that can be identified in the first place, and thus, at this stage, no real need for primary sources of antiprotons. Within errors, secondary astrophysical production alone can account for the data.
Next, we enter in the merit of which propagation schemes do account for the data, taking into account the other uncertainties. We find that the data seem to prefer a model, such as Max, characterized by a relatively mild energy dependence of the diffusion coefficient at high energies. If confirmed, this would go in the same direction as other indications already obtained in different channels, as discussed above.
Finally, an important application concerns updated constraints on DM: within the framework of the propagation schemes that it is sensible to use, we derive bounds that are more stringent by about one order of magnitude with respect to the previous ones (based on Pamela data).
Of course, this analysis is very preliminary and there is still room for improvements. First and foremost, the release of the finalp/p measurement with systematic and statistical errors fully accounted for. Yet, even a preliminary analysis allows to show that antiprotons confirm themselves as a very powerful probe for cosmic-ray physics and for DM in particular. Actually, considering the puzzling excesses of undetermined origin in the electron and positron fluxes, considering the complicated background of most gamma-ray searches and considering the challenges of neutrino detection,p's might arguably still be the most promising avenue in DM indirect searches. In this respect, the Ams-02 experiment can play a crucial role. So far it has essentially confirmed the results of previous experiments (most notably Pamela), but it has done so with an impressively improved accuracy: the qualitative picture in DM indirect searches has been left largely unchanged by it, but Ams-02 has allowed improved pinning down of the parameters and tightening of the constraints. In this context, while follow-up releases of antiproton data (e.g. pure fluxes, extended energy range or enlarged statistics) will obviously be welcome, it is urgent to address first one of the main current limitations in the field of charged CRs, namely the determination of the propagation parameters. In this respect, analyzing the upcoming reliable and accurate light nuclei measurements from Ams-02 will provide the community with a very powerful leverage for any search of exotics in cosmic-rays. At that point it will be possible to assess whether or not excesses are present in antiproton data (although identifying their origin will remain very challenging [50]).