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I tried to compare data on mult_pi per A_part between HADES, FOPI, TAPS, and KAOS.

But as you know, data require several corrections, so this comparison is alwayd biased, like e.g. in Reisdorf's paper for FOPI,TAPS,KAOS comparison.

The corrections:

The result for m_pi per Apart at 1.23 is (as you can see in detail below):

KAOS * means that it is cross-section was rescaled : 0.86 = 5.9/6.8

We can add then point (if we agree on the procedure of calculation) into Fig.6 on the paper.

One can also compare pt distributions at midrapidity as it is done in Senger&Stroebele review in Fig. 3.2. if we manage to get the exp. points from the three experiments.

Still there will be the same problem with corrections which influence the normalization factor.## Details

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DATA at Au+Au 1 GeV:

KaoS: measured inclusive cross section (CS) at midrapidity,for pi+ and pi-

multiplicity calculated from CS, m_pi = 1.5 * (_pi+ + m_pi-)

m_pi/A_part = 0.09 +-0.01

(Wagner PhD, Senger&Stroebele J Phys G 25 (1999) )

For multiplicity calculation the reaction CS = 5.9+-0.4 barn was used (Wagner PhD, see below).

We have from Glauber 6.8+-0.4 barn, i.e. we can recalculate as mult * 0.86.

TAPS: m_pi0 inclusive measured, m_pi = 3 * m_pi0, m_pi/A_part= 0.069+-0.015 (Averbeck et al, PRC 67 (2003) )

Both experiments measured at midrapidity, then extrapolated data to pi assuming isotropic emission.

FOPI: m_pi+, m_pi- measured at large acceptance, several bins in centrality.

m_pi/A_part=0.118+-0.011

(Reisdorf et al., NPA 781 (2007)

Here is a comparison after 3 corrections (cross section, energy, anisotropy) :

KaoS TAPS FOPI HADES

m_pi/N_part 1 GeV 0.09 +-0.01* 0.069+-0.015** 0.118+-0.011***

anisotropy : 1.25 (A_2) :0.113+-0.013 0.086+-0.019

energy : *1.36 energy 1.23 0.154+-0.018 0.117+-0.026 0.173+-0.016 0.139(8)

cross-section : *0.86 CS 0.132+-0.015

* Senger, Stroebele J Phys G 25 (1999), A. Wagner thesis

* R. Averbeck PHYSICAL REVIEW C67, 024903 2003

***Reisdorf et al., NPA 781 (2007)

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Wagner PhD numbers:

Measured inclusive CS 24.3+-1.0 b for pi-, 12.5+-1.0 b for pi+

sigma_react = 5.9 +- 0.4 b , A_part = 98.5

mult_pi= 1.5*(24.3+12.5)/5.9= 55/5.9 = 9.32

mult_pi/A_part = 9.32/98.5 = 0.09 +- 0.01

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Energy rescaling from 1.0 or 1.2 to 1.23:

KAOS, TAPS: F(1.23/1.00) = 1.36 (from Romain)

And for fopi i rescale from 1.2 GeV, its much closer.

i.e. 0.163*1.06=0.173+-0.016 (this number 0.163 we have from Reisdorf)

FOPI@1.01 AGeV : 0.118 +/- 0.0111

FOPI@1.2 AGeV : 0.163 +/- 0.0154

-------------------------------------------------------------------------- -- GosiaSudol - 27 Jun 2019

But as you know, data require several corrections, so this comparison is alwayd biased, like e.g. in Reisdorf's paper for FOPI,TAPS,KAOS comparison.

The corrections:

- recalculation of KAOS data from cross section to multiplicity. Kaos used sigma_reaction 5.9+-0.4 b, while we in HADES get 6.8+-0.4 b from Glauber. Would be nice to get somewhere some reliable independent value.
- recalculation from energy 1.0 I use here factor 1.36, error is hopefuly small.
- TAPS and KAOS measured at or close to midrapidity, then assumed isotropic distribution.

Knowing that there is quite strong polar asymmetry we can correct it, e.g. by factor 1.25 used by Reisdorf (for A2= 1.0 the correction is 1.33, but at mean p_cm between 100 and 200 MeV A2<1). - determination of centrality (A_part) can be also different in different experiments and influence data for comparison

The result for m_pi per Apart at 1.23 is (as you can see in detail below):

KAOS | KAOS* | TAPS | FOPI | HADES |

0.154+-0.018 | 0.132+-0.015 | 0.117+-0.026 | 0.173+-0.016 | 0.139+-0.008 |

We can add then point (if we agree on the procedure of calculation) into Fig.6 on the paper.

One can also compare pt distributions at midrapidity as it is done in Senger&Stroebele review in Fig. 3.2. if we manage to get the exp. points from the three experiments.

Still there will be the same problem with corrections which influence the normalization factor.

DATA at Au+Au 1 GeV:

KaoS: measured inclusive cross section (CS) at midrapidity,for pi+ and pi-

multiplicity calculated from CS, m_pi = 1.5 * (_pi+ + m_pi-)

m_pi/A_part = 0.09 +-0.01

(Wagner PhD, Senger&Stroebele J Phys G 25 (1999) )

For multiplicity calculation the reaction CS = 5.9+-0.4 barn was used (Wagner PhD, see below).

We have from Glauber 6.8+-0.4 barn, i.e. we can recalculate as mult * 0.86.

TAPS: m_pi0 inclusive measured, m_pi = 3 * m_pi0, m_pi/A_part= 0.069+-0.015 (Averbeck et al, PRC 67 (2003) )

Both experiments measured at midrapidity, then extrapolated data to pi assuming isotropic emission.

FOPI: m_pi+, m_pi- measured at large acceptance, several bins in centrality.

m_pi/A_part=0.118+-0.011

(Reisdorf et al., NPA 781 (2007)

Here is a comparison after 3 corrections (cross section, energy, anisotropy) :

KaoS TAPS FOPI HADES

m_pi/N_part 1 GeV 0.09 +-0.01* 0.069+-0.015** 0.118+-0.011***

anisotropy : 1.25 (A_2) :0.113+-0.013 0.086+-0.019

energy : *1.36 energy 1.23 0.154+-0.018 0.117+-0.026 0.173+-0.016 0.139(8)

cross-section : *0.86 CS 0.132+-0.015

* Senger, Stroebele J Phys G 25 (1999), A. Wagner thesis

*

***Reisdorf et al., NPA 781 (2007)

--------------------------------------------------------------------------

Wagner PhD numbers:

Measured inclusive CS 24.3+-1.0 b for pi-, 12.5+-1.0 b for pi+

sigma_react = 5.9 +- 0.4 b , A_part = 98.5

mult_pi= 1.5*(24.3+12.5)/5.9= 55/5.9 = 9.32

mult_pi/A_part = 9.32/98.5 = 0.09 +- 0.01

--------------------------------------------------------------------------

Energy rescaling from 1.0 or 1.2 to 1.23:

KAOS, TAPS: F(1.23/1.00) = 1.36 (from Romain)

And for fopi i rescale from 1.2 GeV, its much closer.

i.e. 0.163*1.06=0.173+-0.016 (this number 0.163 we have from Reisdorf)

FOPI@1.01 AGeV : 0.118 +/- 0.0111

FOPI@1.2 AGeV : 0.163 +/- 0.0154

-------------------------------------------------------------------------- -- GosiaSudol - 27 Jun 2019

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