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that, for this input, the generated SystUnc is similar to or larger than the StatUnc . 

– The transport parameters are very sensitive to the low- energy spectral shape of the source parameter η$_{S}$ , but not to the source slope α . Both parameters can be de- termined by including data of a primary flux in the fit. When doing so, the SystUnc and StatUnc are of the same order. 

– If we let η$_{T}$ —which parameterises the low-energy shape of the diffusion coefficient— free in the range [ − 2 ., 1 . ], the SystUnc completely dominate the StatUnc . Diffusion coefficients with a sharp turn-off at low-energy are possible, as shown in Fig. 1 of Ptuskin et al. 2006 (their dashed line corresponds to our η$_{T}$ = − 2). 

– For the cross sections, as seen in Fig. 4, the SystUnc can also be larger than the StatUnc for some of the transport coefficients. The use of other secondary-to- primary ratios, such as Li/C and Be/C, could help to cross-check the consistency of each cross-section set, and thus decrease the SystUnc . 

These conclusions hold for all classes of models (0, I, II, and III). 

## 9.2. Which value of δ should we trust? 

The two key ingredients for determinaning δ are i) the low- energy spectral shape of the diffusion coefficient as parame- terised by η$_{T}$ [see Eq. (10)], and ii) the presence or absence of a wind. These two effects allow δ to reach values as low as 0.2 up to 0.9. Such a wide range is also found in Jones et al. (2001), depending on the model they consider (convection, turbulent diffusion, stochastic reacceleration). 

We recover δ ≈ 0 . 3 in the pure reacceleration case (no convection), as in other propagation codes (Strong & Moskalenko 1998; Jones et al. 2001). As soon as a convective wind is included, the diffusion slope is large ( δ ≈ 0 . 8), as obtained in other studies (Jones et al. 2001; Maurin et al. 2001). The effect of the low-energy shape of the diffusion coefficient is illustrated by the fact that stan- dard LBM and standard diffusion models lead to different δ (more details are given in Putze, Derome & Maurin, ICRC 2009). For LBM, which are equivalent to diffusion models if K ( E ) = K$_{0}$ R $^{δ}$, we recover δ ≈ 0 . 5 − 0 . 6 (Webber et al. 2003, Paper I. 

It is reassuring to see that the results of the various propagation codes used in the literature are consistent. However, this does not settle the question of which value of δ we should trust. In principle, one advantage of our anal- ysis is that it should clearly point to a preferred value for δ , by a mere comparison of the best χ 2 values. Indeed, in almost all settings considered, Model III (convection and reacceleration) performs better than any other, the second best being Model II (no convection). This behaviour is il- lustrated by the χ 2 min dependence as a function of δ , as shown in Fig. 6. For a standard diffusion coefficient (black- solid curve), there is a clear minimum at high δ , and a less marked local minimum at low δ . This second minimum matches the χ 2 min of Model II (black-dashed curve). The value of the χ 2 min slightly decreases when η$_{T}$ decreases (red curves), then increases for η$_{T}$ ≲ 0 (grey and violet curves). In the process, the best-fit value for δ is displaced to smaller values, the local minimum at low δ overtaking and merging with the high δ one. 

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† Best-fit transport parameters for standard Model II and III. 

‡ Best-fit parameters with η$_{T}$ free (no reacceleration). 

Note 10. Standard models refer to SA diffusion coefficients (see Table 5). Alternative models show their different values for η$_{T}$ , as parameterised from Eq. (10). 

For standard diffusion schemes (SA), the best class of models is Model III. The main problem is that whatever ingredients are changed in this model, we are always left with δ ≳ 0 . 6, and most of the time with even higher values, ∼ 0 . 9. Such high values, always associated to the presence of the constant convective wind, are difficult to explain. Should we choose to discard this Model III, we would be left with the task of explaining why the statistical analysis fails in the context of CR physics. A way out is provided, as seen in Fig. 6, if we let free η$_{T}$ (low-energy shape of the diffusion coefficient). Indeed, the only case where Model II (reacceleration only) performs as Model III is for η$_{T}$ in the range − 3 ≲ η$_{T}$ ≲ − 1 . 5. In such a configuration, the best- fit value for the convective velocity of Model III drops to zero, so that the best model only has reacceleration (i.e. equivalent to Model II): we term this class of models III/II. The next best-fit class of models is obtained if we discard reacceleration (Model I-like) and again let η$_{T}$ go free. As for the previous case, the best-fit value for the convective velocity drops to zero: we denote this class I/0. In terms of the best χ 2 $_{min}$, the standard diffusion Model II has only the fourth-best χ 2 value. The best-fit values for these four classes of models are gathered in Table 10, sorted according to their figure of merit. 

⋆ Best-fit parameters for fixed η$_{T}$ . 

