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(1)Indirect Search for Dark Matter and Physics Beyond the Standard Model. Knas Xiao. A Thesis Presented to the Faculty of National Taiwan Normal University for the Degree of Master. Recommended for Acceptance by the Department of Physics Adviser: Chuan-Ren Chen. August 2017.

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(3) Abstract The cosmic ray p¯/p data from 20 to 450 GeV measured by AMS-02 can be interpreted in terms of DM. By using the GALPROP code, the propagation with DM annihilating to anti-protons is calculated based on the conventional model. The b¯b, u¯ u and W + W − final states are considered with different DM masses and annihilating cross-section as free parameters. To see the goodness of fit, the chi-squared test will be used. Once the best-fit parameters are found, the possibility of DM can be discussed. Keywords: Dark matter, Indirect search. iii.

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(5) Acknowledgements I would like to thank my parents, without them this whole thing is not going to happen including my life. And I would like to thank my adviser, the thesis committee, and the group of my adviser. Every suggestion and discussion really helped me a lot.. v.

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(7) To my family.. vii.

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(9) Contents Abstract . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. iii. Acknowledgements . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. v. 1 INTRODUCTION. 2. 2 EVIDENCE. 3. 2.1. The Beginning . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 3. 2.2. Flat Rotation Curve . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 3. 2.3. The Energy Density . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 6. 2.4. The Smoking Gun. 7. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 3 PARTICLE CANDIDATES IN SM?. 8. 4 INDIRECT DETECTION. 10. 5 NUMERICAL RESULTS. 12. 6 SUMMARY. 18. Bibliography. 19. ix.

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(11) Chapter 1 INTRODUCTION Dark Matter is one of mysteries of the Universe. By early observations and researches, there must exist something that does not interact with photon, hence we call it “Dark” matter. We have not directly observed it yet; however, there do have some evidence indicating the existence of dark matter. What we are looking for is a kind of massive particle and it is weakly interacting with ordinary matter, which is composed of the Standard Model particles. In our most successful model, the Standard Model, it does not predict such a particle with these properties, therefore, it is necessary to extend the known theory. At present, the leading candidate constituting dark matter is “WIMPs” (Weakly Interacting Massive Particles). It is generally considered that there are three ways in which we may have the chance to glimpse it: direct detection, indirect detection or through the colliders. All of these three got their own difficulties, but still provide different aspects of constraint. The understanding of dark matter requires certain fields in physics. Accordingly, I will roughly go through as many materials as I can to cover the story. Starting from the first sign that dark matter exists, which is follow by several strong evidences, I discuss if there exists possible candidates within the Standard Model, and finally the detection methods will be introduced. Then the focus of this paper is going to be the indirect detections. 2.

(12) Chapter 2 EVIDENCE 2.1. The Beginning. The first hint was found by Fritz Zwicky in the 1930s. Zwicky studied the Coma Cluster, which was 321 million lightyears from Earth, and calculated the velocity dispersion of galaxies inside it. After knowing the velocity dispersion, Zwicky applied the virial theorem to obtain the cluster’s total mass Mcluster , which was about 4.5 × 1013 M

(13) . This result was inconsistent with the measurement using Mass-to-Luminosity (M/L) ratios for roughly 1000 nebulae in the cluster[1]. It was astonishing due to the huge difference between these two results. The M/L ratio gave only approximately 2% of the value which is using the virial theorem. In other words, galaxies in the cluster only accounted for a small fraction of the total mass; the majority of the mass of the Coma was not ordinary (i.e. visible) matter.. 2.2. Flat Rotation Curve. After Zwicky and the others’ work, Vera Rubin and her collaborators rediscovered the evidence of dark matter in the 1970s. They measured the velocity curves of various galaxies 3.

(14) from the analysis of Doppler shift. Intuitively, it was assumed that the orbits of stars in a galaxy would quite likely to follow the same rule as the planets within solar system do: r v(r) =. Gm(r) , r. (2.1). where v is the rotation speed of the star at a radius r, G is the gravitational constant, and m(r) is the total mass contained in r. Hence we have the relation between velocity √ and radius: v(r) ∝ 1/ r. The relation tells us that the velocity of a rotating star should decrease when its distance from the center increases. The observations from Rubin(Figure 2.1), however, show a extremely disagreement to the expectation of Newton’s law of universal gravitation with luminous stars. It is quite obvious that the curves are flat, which means the velocities of stars keep increasing until a limit. The phenomenon can be interpreted by using Gauss’ flux theorem for gravity: Z. ~ = 4πGMencl , ~g · dA. (2.2). S. where the left hand side is the flux of the gravitational field across a closed surface and right hand side is the mass enclosed by the surface. If the enclosed mass increases while the radius of the Gaussian surface is raising, the gravitational field will be enhanced as well, thus the velocity of the rotating object may either increase or remain the same. On the other hand, a decreasing velocity implies the enclosed mass is getting less and less or remain constant as the radius growing. Since the velocities remain the same, and the center of spiral galaxies are luminous, it is concluded that the mass is not concentrated near the center of galaxies, and furthermore the distribution of luminous matters doesn’t represent the distribution of mass.. 4.

(15) Figure 2.1: Rotational velocities with flatness for seven galaxies[2].. 5.

(16) 2.3. The Energy Density. To describe a spatially homogeneous and isotropic universe, we combine the RobertsonWalker(RW) metric and the Einstein’s equation, then there is the Friedmann equation:  2 a˙ 8πG X k H ≡ = ρi − 2 , a 3 a i 2. (2.3). where H is the Hubble parameter, a is a dimensionless scale factor, ρ is the energy density indexes different types of energy in the Universe, and k is a constant describing the curvature of the spatial sections. Furthermore, we may define the critical energy density. ρc ≡. 3H 2 , 8πG. (2.4). which the spatial section is precisely flat (k = 0), and the density parameter Ωtotal > 1 ⇔ k = 1 Ωtotal ≡. ρ , Ωtotal = 1 ⇔ k = 0 ρc Ωtotal < 1 ⇔ k = −1.. (2.5). If Ωtotal equals 1, then the spatial geometry of the Universe is flat; if Ωtotal is larger than 1, the Universe will eventually collapse, and if Ωtotal is less than 1, it will expands forever. Currently, the best estimates for the matter density and the baryon density from Plank Collaboration[3]. Ωm h2 = 0.14170 ± 0.00097, Ωb h2 = 0.02230 ± 0.00014,. (2.6). where h is the reduced Hubble parameter, Ωm is the matter density, and the Ωb is the baryon density. It is quite essential that these two numbers are different, that is, the baryonic matter is not the only form of matter in the Universe, and most of the matter 6.

(17) Figure 2.2: A image of the merging cluster 1E0657-558. The green contours are the weak lensing, and the colorful gradient starting from blue indicates the location of the plasma cloud[4]. density must be in the form of non-baryonic matter. In fact, according to the ΛCDM model, there are three components of Ω due to baryon, cold dark matter and dark energy. We realize that the flatness of the Universe doesn’t come along with baryonic matter only.. 2.4. The Smoking Gun. There is a crushing evidence from the “Bullet Cluster”(Figure 2.2), which is a result of a smaller subcluster colliding with another larger one. During the merger of two clusters, the galaxies inside both clusters behave as collisionless particles passing through each other without interacting, while the hot gas(the majority of baryonic matter) experiences ram pressure. After the collision of clusters, a huge amount of X-ray radiation can be observed because of the compressed and heated gas. If we match the location of the radiation with the location of the majority of the total mass of the clusters, which is measured via weak gravitational lensing, the result shows a discrepancy. We conclude that the majority of the mass is non-barynoic.. 7.

(18) Chapter 3 PARTICLE CANDIDATES IN SM? According to previous introductions, though there has no clear definition of a WIMP, it is possible to seek if there exists a candidate in a theory due to the gravitational effect and other properties, say,it doesn’t interact with light. The Standard Model is the quantum field theory that describe three of the four fundamental forces in the Universe: the electromagnetic, weak, and strong interactions, also classifying seventeen elementary particles which were confirmed experimentally(see Table 3.1). There are six quarks(up ,down, charm, strange, top, and bottom), six leptons(electron, e neutrino, muon, µ neutrino, tau, and τ neutrino), and five bosons(photon, W ± , Z, gluon, and Higgs). Quarks and leptons are classified as fermions with half-integer spins, where bosons with integer spins. Every particle has its corresponding anti-particle. In SM, the only stable, neutral, and weakly interacting particles are neutrinos. Neutrinos are not the candidate because they are relativistic, that is to say, if the Universe was dominated by neutrinos, then the formation of the Universe would have started from larger structures; however, the “bottom-up” formation seems to be the most possible case since galaxies have been observed to exist less than a billion years after the big bang. Thus, new physics is required to supply the Standard Model.. 8.

(19) Particle u d e− νe. I Mass ≈ 2.2 ≈ 4.7 ≈ 0.511 −. Particle γ W± Z H0. Charge + 32 − 31 −1 0. Fermions II Particle Mass Charge c ≈ 1280 + 32 s ≈ 96 − 31 − µ ≈ 106 −1 νµ − 0. Bosons Participate in Electromagnetic interaction Weak interaction Higgs field. Particle t b τ− ντ. Mass 0 ≈ 80385 ≈ 91188 ≈ 12509. III Mass ≈ 173000 ≈ 4180 ≈ 1777 −. Charge + 23 − 13 −1 0. Charge 0 ±1 0 0. Table 3.1: The particles in the Standard Model. The masses are in units of MeV reported by Particle Data Group[5].. 9.

(20) Chapter 4 INDIRECT DETECTION The products of annihilations or decay of DM can be the SM particles, hence they will become new primary sources of cosmic ray particles; and further changing the spectra of anti-particles such as positron and anti-proton, while they are assumed to be secondaries in the conventional cosmic ray model. Detecting the abundance and the flux of these species offers a good chance to examine the properties of DM. The term “indirect” is because the experiments are detecting the final states of DM(i.e. the SM particles) instead of WIMPs themselves. The Alpha Magnetic Spectrometer (AMS-02) is a module which is mounted on the International Space Station(ISS) for the purpose of measuring anti-matters (anti-particles) in cosmic rays. It is the most sensitive particle detector so far in space. As a magnetic spectrometer, it has the ability to distinguish charged particles. AMS has collected over 90 billion cosmic ray events since its installation on ISS. Protons are the most abundant particles, which has been measured the flux to an accuracy of 1% with 300 million protons and found that the flux deviates from a single power law, as had been assumed for many years[6]. The boron (secondary cosmic ray) to carbon (primary cosmic ray) flux ratio measured by AMS provides significant information on propagation and the average amount of interstellar 10.

(21) material (ISM) through which the cosmic rays travel in the galaxy. Cosmic ray propagation is commonly described as a relativistic gas diffusing through a magnetized plasma. Different models of the magnetized plasma predict different behavior of the B/C flux ratio. Notably, the B/C flux ratio data from AMS does not show any crucial structures in contrast to many cosmic ray models which don’t include DM. In 2016, the AMS collaboration released the latest result of anti-proton to proton flux ratio (¯ p/p). It shows that the flux ratio stays constant or even a little excess from 20 to 450 GeV. This cannot be explained by the secondary anti-proton, which is from the collision of cosmic rays with ISM. In this work, we will discuss the contribution from DM by calculating its propagation and fitting the AMS data.. 11.

(22) Chapter 5 NUMERICAL RESULTS The propagations are calculated using GALPROP[7, 8, 9, 10, 11]. It solves the transport equation with a given source distribution and boundary conditions for all cosmic-ray species. The equation is written in : ∂ψ ~ · (Dxx ∇ψ ~ − V~ ψ) + ∂ p2 Dpp ∂ 1 ψ = q (~r, p) + ∇ ∂t ∂p ∂p p2 ∂ p ~ ~ 1 1 − [pψ ˙ − (∇ · V )ψ] − ψ − ψ, ∂p 3 τf τr. (5.1). where ψ = ψ(~r, p, t) is the number density per unit of total particle momentum, q(~r, p) is the source term, Dxx is the spatial diffusion coefficient taken as Dxx = βD0 (ρ/ρ0 )δ , where ρ = p/Ze is the rigidity of the cosmic ray particle with electric charge Ze, and β(= v/c) is a consequence of a random-walk process. The power index δ can have different values δ = δ1/2 when ρ is below/above rigidity ρ0 . The convection velocity V~ is related to drift of cosmic-ray particles from the galactic disc due to the galactic wind, which implies a constant adiabatic energy loss. The re-acceleration is described as diffusion in momentum space and is determined by the coefficient Dpp . The momentum loss rate p(= ˙ dp/dt) could due to ionization, Coulomb interactions, bremsstrahlung, inverse Compton scattering, and. 12.

(23) Model. R(kpc). Zh (kpc). D0. ρ0. δ1 /δ2. ρs. γp1 /γp2. χ2 (B/C, p¯/p). Conventional χ2 − improved. 20 20. 4.0 4.0. 5.75 5.75. 4.0 4.0. 0.34/0.34 0.34/0.34. 9.0 9.0. 1.82/2.36 1.82/2.33. 204.28,752.77 265.09,438.753. Table 5.1: The parameters in two propagation models. D0 is in units of 1028 cm2 · s−1 , the break rigidities ρ0 and ρs are in units of GV. synchrotron. The parameter τf,r is the time scale for fragmentation/radioactive decay of the cosmic-ray nuclei while they are interacting with interstellar hydrogen and helium. Now we assume that the DM particle is Majorana fermions, which the particle is its own anti-particle. Hence, the primary source term from the annihilation of DM has the form: 1 q(~r, p) = 2. . ρ MDM. 2 hσvi. dN , dE. (5.2). where ρ is the DM density distribution function, hσvi is the thermally averaged crosssection, and dN/dE is the injection spectrum of anti-protons from DM annihilating into different SM final states(b¯b, u¯ u and W + W − will be discussed in this work). First we consider the so-called “conventional” diffusive re-acceleration model as the astrophysical background, then we are going to use another “χ2 -improved” model, which fits the p¯/p data better by using the frequentist χ2 -test, in order to see the limitation without primary sources. The expression of χ2 -test is defined as  X fith − fiexp 2 χ2 = , σi2 i. (5.3). where fith , fiexp , and σi are the theoretical predictions, the central values of experimental data and errors of experimental data, respectively. The index i runs over all data point. A smaller χ2 value means the data is more fit. The p¯/p and the B/C ratio predicted by the conventional and the χ2 -improved models with the latest AMS-02 data[12, 13] are shown in Figure 5.1. Note that the predicted B/C. 13.

(24) Figure 5.1: The predictions for p¯/p and B/C in two propagation models with the latest AMS-02 data. The parameters are listed in Table 5.1. ratio in both model are a bit higher for the energy below 10 GeV, but are consistent with the experiment data for higher energies. Since we don’t see any significant structure in the B/C ratio, the agreement between theoretical expectation and experiment is confirmed. However, this is not the case when we look into the p¯/p flux ratio data. If one wants to get a much better fitting curve, without introducing a new primary source, the B/C ratio gets worse, which is shown in Figure 5.2. Accordingly, a better strategy is to fix the B/C ratio, which can be done by fixing the propagation parameters, and we will pick the improved model as the background, then add the contribution from DM to see the improvement of the χ2 value. Next we consider the contribution from three different DM annihilation channels b¯b, u¯ u, and W + W − . Their injection spectra dN/dE are calculated using the PYTHIA 6.4.14[14] package. Assuming the dark matter halo profile is isothermal expressed by. ρ (r) = ρ

(25). 2 rc2 + r

(26) , rc2 + r 2. (5.4). where the local DM density ρ

(27) = 0.3 GeV·cm−3 , the core radius rc = 3.5 kpc, and ρ

(28) = 8.5 kpc is the distance of the Sun from the galactic center.. 14.

(29) Figure 5.2: The χ2 -value contour shows a opposite behaviour for fitting the AMS-02 data. The values of x-y axis are the break rigidity indexes γp1 /γp2 . In Figure 5.3, it shows the best χ2 -value cases for every final state. The order of the cross-sections are not the same comes from the very different injection spectrum, which represents how energetic the final state is. Interestingly, we scan the parameter space of the mass from 600 to 3000 GeV and cross-section from 1 ×10−26 to 3 ×10−24 cm3 · s−1 in order to fit the peak around 200 GeV, and it turns out that the smallest χ2 -value curve is not going to reach the highest data point. Although we do have some promising curves, which seem to fit the peak, they don’t fit other data points well with bigger χ2 -values (two examples are shown in Figure 5.4). Since the χ2 -value difference between the best χ2 -value case and other promising curves is so little, we can only conclude that there are some possible masses and cross-sections around certain regions.. 15.

(30) 10-3. �� ->��. 5. × 10-4. AMS-02. DM. 1. × 10-4. DM+background. 5. × 10-5. DM. background. 5. × 10-5. DM. DM. 1. × 10-5. 1. × 10-5. 5. × 10-6. 5. × 10-6. 5. × 10-6. 5. × 10-6. 1. × 10-6 0.1. 1. × 10-6 0.1. 1. × 10-6 0.1. 10. 100. 1000. 10. 100. 1000. 1. 10. 100. 1. × 10-6 0.1. 1000. Energy[GeV]. Energy[GeV]. (a). (b). (c). (d). 10-3. 10-3. �� ->��. 5. × 10-4. AMS-02. background 1. × 10-4. P/P. 5. × 10-5. DM. 1. × 10-4. DM+background. 5. × 10-5. DM. 5. × 10-5. DM. 1. × 10-5. 5. × 10-6. 5. × 10-6. 5. × 10-6. 5. × 10-6. 1. × 10-6 0.1. 100. 1. × 10-6 0.1. 1000. 1. 10. 100. 1. × 10-6 0.1. 1000. Energy[GeV]. (e). (f). (g). (h). 10-3 5. × 10-4. 10-3. �� ->� ±. 5. × 10-4. AMS-02. 1. × 10-4. P/P. DM. 1. × 10-4. DM+background. 5. × 10-5. DM. background 1. × 10-4. DM+background. 5. × 10-5. DM. DM. 1. × 10-5. 1. × 10-5. 1. × 10-5. 5. × 10-6. 5. × 10-6. 5. × 10-6. 5. × 10-6. -6. -6. -6. 10. 100. 1000. 1. × 10. 0.1. 1. 10. 100. 1000. 1. × 10. 0.1. 1. 10. 100. 1000. DM+background. 5. × 10-5. 1. × 10-5. 1. �� ->� ± AMS-02. background. P/P. DM+background. 5. × 10-4. AMS-02. background. 1000. 10-3. �� ->� ±. P/P. �� ->� ±. 5. × 10-5. 0.1. 10. Energy[GeV]. background. 1. × 10. 1. Energy[GeV]. AMS-02. 1. × 10-4. 10. Energy[GeV]. 10-3 5. × 10-4. 1. 100. DM. 1. × 10-5. 1000. DM+background. 5. × 10-5. 1. × 10-5. 100. �� ->��. background 1. × 10-4. DM+background. 1. × 10-5. 10. 1000. AMS-02. background. P/P. DM+background. 5. × 10-4. AMS-02. background. 100. 10-3. �� ->��. P/P. 5. × 10-4. 1. 10. Energy[GeV]. �� ->��. 1. × 10-6 0.1. 1. Energy[GeV]. AMS-02. 1. × 10-4. 1. DM+background. 5. × 10-5. 1. × 10-5. 1. �� ->�� AMS-02. 1. × 10-4. DM+background. 1. × 10-5. 10-3. P/P. 5. × 10-4. background. P/P. P/P. P/P. 1. × 10-4. DM+background. 10-3. �� ->�� AMS-02. background. 5. × 10-5. 5. × 10-4. P/P. 5. × 10-4. AMS-02. background 1. × 10-4. 10-3. �� ->��. P/P. 10-3 5. × 10-4. 1. × 10-6 0.1. 1. 10. Energy[GeV]. Energy[GeV]. Energy[GeV]. Energy[GeV]. (i). (j). (k). (l). 100. 1000. Figure 5.3: Twelve best cases for three different final states. The masses, cross-sections, and χ2 -value are shown in Table 5.2.. Cross-section. χ2 -value. Figure. Mode. Mass(GeV). (a) (b) (c) (d). b¯b b¯b b¯b b¯b. 1200 1100 1000 1300. 1 1 1 1. ×10−24 ×10−24 ×10−24 ×10−24. 390.692 392.562 395.708 396.931. (e) (f) (g) (h). u¯ u u¯ u u¯ u u¯ u. 700 510 600 600. 3 2 2 3. ×10−25 ×10−25 ×10−25 ×10−25. 391.336 392.278 392.531 392.726. (i) (j) (k) (l). W +W − W +W − W +W − W +W −. 3500 3500 3000 2500. 3 4 2 2. ×10−24 ×10−24 ×10−24 ×10−24. 398.255 399.913 401.751 404.056. Table 5.2: The attributes in each figure, which the cross-section is in units of cm3 · s−1 . Every case has approximately 10% improvement in χ2 -value compare to the background. 16.

(31) Figure 5.4: (LEFT) A DM to u¯ u curve seems to reach the peak, but not the smallest 2 χ -value with 400 GeV and hσvi = 3 ×10−25 cm3 · s−1 . (RIGHT) Same story goes to the b¯b case with MDM = 1100 GeV and hσvi = 2 ×10−24 cm3 · s−1 .. 17.

(32) Chapter 6 SUMMARY We have seen the indications of DM from different scale of the Universe. Even though there are several theories claiming that the unexpected observations can be described without DM(i.e. MOND1 ), the story only goes if DM is included in every aspect. Besides lacking a DM candidate, the Standard Model has other issues (i.e. baryon asymmetry, the non-zero masses of neutrinos, etc.), thus the expansion of SM is greatly desired. To explore the essential of DM, we need to check its every footprint. In particular, we are trying to find some clues by studying the AMS p¯/p data. Though we are not going to have a strong conclusion for the properties of DM, we do find that it is possible to improve the agreement to the AMS-02 p¯/p data by introducing a DM contribution.. 1. Modified of Newtonian Dynamics[15]. 18.

(33) Bibliography [1] F. Zwicky. “On the Masses of Nebulae and of Clusters of Nebulae”. In: Astrophysical Journal 86 (1937), p. 217. doi: 10.1086/143864. [2] V. Rubin, N. Thonnard, and W. K. Ford Jr. “Extended rotation curves of highluminosity spiral galaxies. IV - Systematic dynamical properties, SA through SC”. In: Astrophysical Journal, Part 2 - Letters to the Editor 225 (1978), pp. 107–111. doi: 10.1086/182804. [3] P. A. R. Ade et al. “Planck 2015 results. XIII. Cosmological parameters”. In: Astron. Astrophys. 594 (2016), A13. doi: 10.1051/0004- 6361/201525830. arXiv: 1502. 01589 [astro-ph.CO]. [4] Douglas Clowe et al. “A direct empirical proof of the existence of dark matter”. In: Astrophys. J. 648 (2006), pp. L109–L113. doi: 10 . 1086 / 508162. arXiv: astro ph/0608407 [astro-ph]. [5] C. Patrignani and Particle Data Group. “Review of Particle Physics”. In: Chinese Physics C 40.10 (2016), p. 100001. url: http://stacks.iop.org/1674-1137/40/ i=10/a=100001. [6] M. Aguilar et al. “Precision Measurement of the Proton Flux in Primary Cosmic Rays from Rigidity 1 GV to 1.8 TV with the Alpha Magnetic Spectrometer on the International Space Station”. In: Phys. Rev. Lett. 114 (17 Apr. 2015), p. 171103. doi: 10.1103/PhysRevLett.114.171103. url: https://link.aps.org/doi/10.1103/ PhysRevLett.114.171103. [7] A. W. Strong and I. V. Moskalenko. “Propagation of cosmic-ray nucleons in the galaxy”. In: Astrophys. J. 509 (1998), pp. 212–228. doi: 10.1086/306470. arXiv: astro-ph/9807150 [astro-ph]. [8] Igor V. Moskalenko et al. “Secondary anti-protons and propagation of cosmic rays in the galaxy and heliosphere”. In: Astrophys. J. 565 (2002), pp. 280–296. doi: 10. 1086/324402. arXiv: astro-ph/0106567 [astro-ph]. [9] A. W. Strong and I. V. Moskalenko. “Models for galactic cosmic ray propagation”. In: Adv. Space Res. 27 (2001), pp. 717–726. doi: 10.1016/S0273-1177(01)00112-0. arXiv: astro-ph/0101068 [astro-ph]. [10] Igor V. Moskalenko et al. “Challenging cosmic ray propagation with antiprotons. Evidence for a fresh nuclei component?” In: Astrophys. J. 586 (2003), pp. 1050–1066. doi: 10.1086/367697. arXiv: astro-ph/0210480 [astro-ph]. 19.

(34) [11] V. S. Ptuskin et al. “Dissipation of magnetohydrodynamic waves on energetic particles: impact on interstellar turbulence and cosmic ray transport”. In: Astrophys. J. 642 (2006), pp. 902–916. doi: 10.1086/501117. arXiv: astro-ph/0510335 [astro-ph]. [12] M. Aguilar et al. “Precision Measurement of the Boron to Carbon Flux Ratio in Cosmic Rays from 1.9 GV to 2.6 TV with the Alpha Magnetic Spectrometer on the International Space Station”. In: Phys. Rev. Lett. 117 (23 Nov. 2016), p. 231102. doi: 10.1103/PhysRevLett.117.231102. url: https://link.aps.org/doi/10.1103/ PhysRevLett.117.231102. [13] M. Aguilar et al. “Antiproton Flux, Antiproton-to-Proton Flux Ratio, and Properties of Elementary Particle Fluxes in Primary Cosmic Rays Measured with the Alpha Magnetic Spectrometer on the International Space Station”. In: Phys. Rev. Lett. 117 (9 Aug. 2016), p. 091103. doi: 10.1103/PhysRevLett.117.091103. url: https: //link.aps.org/doi/10.1103/PhysRevLett.117.091103. [14] Torbjorn Sjostrand, Stephen Mrenna, and Peter Z. Skands. “PYTHIA 6.4 Physics and Manual”. In: JHEP 05 (2006), p. 026. doi: 10.1088/1126-6708/2006/05/026. arXiv: hep-ph/0603175 [hep-ph]. [15] Mordehai Milgrom. “MOND theory”. In: Can. J. Phys. 93.2 (2015), pp. 107–118. doi: 10.1139/cjp-2014-0211. arXiv: 1404.7661 [astro-ph.CO].. 20.

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