AMS-02 ANTIPROTONS ARE CONSISTENT WITH A SECONDARY ASTROPHYSICAL ORIGIN arXiv:1906.07119 M.B, Y. Génolini, L. Derome, J. Lavalle, D. Maurin, P. Salati and P. D. Serpico Table of contents 1. Secondary antiprotons: a new prediction 2. Propagation of uncertainties 3. Prediction vs AMS-02 data 4. Conclusion 1
Secondary antiprotons: a new prediction 2015: AMS-02 antiprotons, at last! Secondary astrophysical component and immediate implications for DM Giesen+(2015) arXiv:1504.04276 2
Secondary antiprotons: a new prediction 2015: AMS-02 antiprotons, at last! Secondary astrophysical component and immediate implications for DM Giesen+(2015) arXiv:1504.04276 New inputs since 2015 DATA MODEL AMS-02 CR transport • pbar flux • H, He, C, N, O fluxes New models from AMS-02 B/C (Génolini et al.) (most abundant CRs ⟹ main pbar parents) • QUAINT: historical model diff/conv/reac • B/C ratio (CR tranport) • SLIM: pure diffusion w/ 2 breaks in the diff. coef. • Systematic errors • BIG: diffusion/convection/reacceleration + 2 breaks in the diffusion coef. AMS-02 collaboration does not provide the covariance matrix of errors (QUAINT, SLIM) ⊂ BIG ⟹ homemade covariance matrix based on the description of systematics in AMS-02 papers Production XS Production XS • Prompt pbar in pp reactions • NA61 : p+p —> pbar + X New parametrisations of the Lorentz invariant √ s = 7.7, 8.8, 12.3 and 17.3 GeV production XS Tp = 31, 40, 80 and 158 GeV σ inv = Ed 3 σ /dp 3 Winkler+(2016), Korsmeier+(2018) • LHCb : p+He —> pbar + X T p = 6.5 TeV • Antihyperons ( Δ 𝛭 ) and isospin asymmetry ( Δ IS ) New energy dependant ( √ s) parametrisations 3
Production XS • Prompt pbar in pp reactions (p + p —> pbar + X) Parametrisation II from Korsmeier+(2018) • functional form of σ inv ( √ s, x R , p T ) from Winkler+(2016) • updated parameters using NA49, NA61, BRAHMS, Dekkers+(1965) Korsmeier+(2018) • Prompt pbar in AA reactions (A 1 + A 2 —> pbar + X) Parametrisation B from Korsmeier+(2018) 0 . 9 • functional form of the nucleon scaling f A1A2 ( √ s, x F ) from Winkler+(2016) median parameters median parameters 0 . 8 median median • updated parameters using LHCb data (p + He —> pbar + X) Korsmeier+(2018) 68% 68% 0 . 7 0 . 6 • Antihyperons correction (p + p —> X + [( 𝛭 bar, Σ bar) —> pbar]) 0 . 5 Λ / ¯ p ¯ Parametrisation of Δ 𝛭 ( √ s) from Winkler+(2016) 0 . 4 BHM NAL MIRABELLE 0 . 3 ∆ Λ ( √ s ) = (0 . 81 ± 0 . 04)(¯ NA49 Λ / ¯ p ) 30-in 0 . 2 ISR STAR 0 . 1 ALICE CMS 0 . 0 10 1 10 2 10 3 10 4 √ s [GeV] • Isospin asymmetry correction (p + p —> X + [nbar—> pbar]) We introduce the following parametrisation to reproduce the results of 0 . 7 starting parameters Winkler+(2016) median 0 . 6 68% ∆ IS ( √ s ) = c 0 ( x + c 2 ) c 3 exp( − x/c 1 ) , x = log( √ s ) 0 . 5 NA49 pC NA49 pC 0 . 4 NA49 np NA49 np ∆ IS Fermilab Fermilab 0 . 3 STAR STAR ALICE ALICE 0 . 2 0 . 1 0 . 0 − 0 . 1 10 1 10 2 10 3 10 4 √ s [GeV] 4
Production XS • Prompt pbar in pp reactions (p + p —> pbar + X) Parametrisation II from Korsmeier+(2018) • functional form of σ inv ( √ s, x R , p T ) from Winkler+(2016) • updated parameters using NA49, NA61, BRAHMS, Dekkers+(1965) Korsmeier+(2018) • Prompt pbar in AA reactions (A 1 + A 2 —> pbar + X) Parametrisation B from Korsmeier+(2018) 0 . 9 • functional form of the nucleon scaling f A1A2 ( √ s, x F ) from Winkler+(2016) median parameters median parameters 0 . 8 median median • updated parameters using LHCb data (p + He —> pbar + X) Korsmeier+(2018) 68% 68% 0 . 7 0 . 6 • Antihyperons correction (p + p —> X + [( 𝛭 bar, Σ bar) —> pbar]) 0 . 5 Λ / ¯ p ¯ Parametrisation of Δ 𝛭 ( √ s) from Winkler+(2016) 0 . 4 BHM NAL MIRABELLE 0 . 3 ∆ Λ ( √ s ) = (0 . 81 ± 0 . 04)(¯ NA49 Λ / ¯ p ) 30-in 0 . 2 ISR STAR 0 . 1 ALICE CMS 0 . 0 10 1 10 2 10 3 10 4 √ s [GeV] • Isospin asymmetry correction (p + p —> X + [nbar—> pbar]) We introduce the following parametrisation to reproduce the results of 0 . 7 starting parameters Winkler+(2016) median 0 . 6 68% ∆ IS ( √ s ) = c 0 ( x + c 2 ) c 3 exp( − x/c 1 ) , x = log( √ s ) 0 . 5 NA49 pC NA49 pC 0 . 4 NA49 np NA49 np ∆ IS σ tot Fermilab Fermilab inv = σ inv (2 + ∆ IS + 2 ∆ Λ ) 0 . 3 STAR STAR ALICE ALICE 0 . 2 0 . 1 0 . 0 − 0 . 1 10 1 10 2 10 3 10 4 √ s [GeV] 5
A model for the covariance matrix of AMS-02 errors • Covariance matrix (see David’s talk) Coefficient corresponding to the uncertainty 𝛽 (Acc., Unf., Trig., etc.) (log 10 ( R i /R j ) 2 ✓ − 1 ◆ ( C α ) ij = σ α j exp i σ α 2 ( l α ρ ) 2 • 𝝍 2 calculation Quadratic distance between model and data: X χ 2 = C − 1 � ij x j ≡ x T C − 1 x � x i = data i − model i x i i,j • Visual inspection p z i = x i / • Standard z-score C ii Misleading when correlations between data points • Rotated z-score x i = U ij x j , ˜ ˜ C = U C U T ˜ ˜ σ 2 C C ii = ˜ is diagonal with elements i z i = ˜ x i / ˜ ˜ σ i Rotated rigidity χ 2 = X z 2 ˜ X ˜ ˜ i U 2 R i = ij R j , R i ' R i i j 6
Model of CR transport New models from AMS-02 B/C (see Yoann’s talk) • QUAINT: historical model diff/conv/reac • SLIM: pure diffusion w/ 2 breaks in the diff. coef. • BIG: diffusion/convection/reacceleration + 2 breaks in the diffusion coef. (BASELINE) 0 . 35 BIG 0 . 30 SLIM QUAINT 0 . 25 AMS-02 Data 0 . 20 B/C e − 0.5 p K ( R ) for A/Z = 2 [kpc 2 .Myr − 1 ] 0.3 4 He 0 . 15 0.2 10 0 10 0 10 1 0 . 10 BIG SLIM 10 − 1 0 . 05 QUAINT 10 0 10 1 10 2 10 3 R [GV] 2 Z-score [ σ tot ] 0 − 2 10 0 10 1 10 2 10 3 Rigidity [GV] 7
Antiproton parents Combined fit of AMS-02 H, He, C and O Most abundant CRs ⟹ main pbar parents 0 . 8 BIG BIG BIG 3 3 H Excluded from fit Excluded from fit 0 . 6 tot ] σ eigen z-score [ σ tot ] Distribution He 1 1 z-score [˜ C 0 . 4 O − 1 − 1 0 . 2 H C ˜ − 3 − 3 He O 0 . 0 0 . 8 10 1 10 2 10 3 10 1 10 2 10 3 − 4 − 2 0 2 4 SLIM SLIM SLIM 3 3 σ eigenv ˜ R [GV] ˜ z-score [˜ ] R [GV] H Excluded from fit Excluded from fit tot 0 . 6 tot ] σ eigen z-score [ σ tot ] Distribution He 1 1 z-score [˜ C 0 . 4 O − 1 − 1 0 . 2 H C ˜ − 3 − 3 He O 0 . 0 0 . 8 10 1 10 2 10 3 10 1 10 2 10 3 − 4 − 2 0 2 4 QUAINT QUAINT QUAINT 3 3 σ eigenv ˜ R [GV] ˜ z-score [˜ ] R [GV] H Excluded from fit Excluded from fit tot 0 . 6 tot ] σ eigen z-score [ σ tot ] Distribution He 1 1 z-score [˜ C 0 . 4 O − 1 − 1 0 . 2 H C ˜ − 3 − 3 He O 0 . 0 10 1 10 2 10 3 10 1 10 2 10 3 − 4 − 2 0 2 4 σ eigenv ˜ R [GV] ˜ z-score [˜ ] R [GV] tot 8
Antiproton parents Combined fit of AMS-02 H, He, C and O Most abundant CRs ⟹ main pbar parents 0 . 8 BIG BIG BIG 3 3 H Excluded from fit Excluded from fit 0 . 6 tot ] σ eigen z-score [ σ tot ] Distribution He 1 1 z-score [˜ C 0 . 4 O − 1 − 1 0 . 2 H C ˜ − 3 − 3 He O 0 . 8 0 . 0 10 1 10 2 10 3 10 1 10 2 10 3 − 4 − 2 0 2 4 SLIM SLIM SLIM 3 3 σ eigenv ˜ R [GV] ˜ z-score [˜ ] R [GV] H Excluded from fit Excluded from fit tot 0 . 6 tot ] σ eigen z-score [ σ tot ] Distribution He scores distribution close to 1 1 z-score [˜ C Gaussian ( 𝜈 =0, 𝜏 =1) as expected from 0 . 4 O − 1 − 1 statistical fluctuations 0 . 2 H C ˜ − 3 − 3 He O 0 . 0 0 . 8 10 1 10 2 10 3 10 1 10 2 10 3 − 4 − 2 0 2 4 QUAINT QUAINT QUAINT 3 3 σ eigenv ˜ R [GV] ˜ z-score [˜ ] R [GV] H Excluded from fit Excluded from fit tot 0 . 6 tot ] σ eigen z-score [ σ tot ] Distribution He 1 1 z-score [˜ C 0 . 4 O − 1 − 1 0 . 2 H C ˜ − 3 − 3 He O 0 . 0 10 1 10 2 10 3 10 1 10 2 10 3 − 4 − 2 0 2 4 σ eigenv ˜ R [GV] ˜ z-score [˜ ] R [GV] tot 9
Ranking parents contributions 10
Heavy parents, heavy species in the ISM Fast calculation (ref) Full (slow) calculation • pbar and B/C parents: H … 30 Si • pbar and B/C parents: H … 58 Fe • ISM species: H, He • ISM species: H…Fe 1 . 04 58 Fe 58 Fe BIG BIG H , He H ... Fe 58 Fe 58 Fe (BIG & ¯ p ) 1 . 03 (BIG & ¯ p ) H ... Fe H , He 1 . 02 p ref ) TOA 1 . 01 1 . 00 p / ¯ 0 . 99 ( ¯ 0 . 98 0 . 97 0 . 96 10 − 1 10 0 10 1 10 2 10 3 10 4 R [GV] We rescale our pbar prediction by the black solid line to account for heavy species in the ISM 11
Propagation of uncertainties Uncertainties on parameters entering: • Production XS (fit collider data) • Transport (fit B/C) • Parents (fit H, He, C and O) Assume parameter distribution is Gaussian ⟹ use the covariance matrix of errors to propagate uncertainties and their correlations In practice 1. Draw randomly 10000 pbar predictions from the covariance matrix for each source of uncertainties (XS, Transport, Parents) 2. Determine the 1 𝜏 confidence intervals 1 10 100 1000 1 10 100 1000 R [GV] R [GV] 12
Covariance matrix of model uncertainties • For the source of uncertainty a ∈ (XS, Transport, Parents) N ij = 1 X C a � Φ a i,n − µ a � � Φ a j,n − µ a � µ a mean prediction at the energy bin i i j i N n =1 C α ij c α • Associated correlation matrix: ij = p p C α C α ii jj 1 . 0 1 XS Transport 3 0 . 9 10 R [GV] 30 0 . 8 100 1 Parents Total 0 . 7 3 10 R [GV] 0 . 6 30 0 . 5 100 1 3 10 30 100 1 3 10 30 100 R [GV] R [GV] 13
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