charm and strangeness production at gsi/fair...

Charm and strangeness production at GSI/FAIR energies

Marcus Bleicher and Jan Steinheimer Frankfurt Institute for Advanced Studies

Institut für Theoretische Physik Goethe Universität - Frankfurt

Marcus Bleicher, THOR 2018

FAIR:FacilityforAn1protonandIonResearch

Location: GSI, Darmstadt, Germany


What is sub-threshold particle production?

And why is it interesting for us?


Production of hadrons below threshold

•  In elementary reactions, e.g. pp, it is not possible to produce a particle with mass mnew , if mP+mP+mnew>ECM,pp (energy conservation)

•  However, in p+A and A+A reaction this is possible

•  The question is, what mechanism allows for the production and are they realized


Mechanisms•  Generally three different mechanisms are available:

1) Fermi motion

(more energy available than we thought) 2) mass reduction/potentials

(lowers the threshold for production) 3) multi-step/multi-particle processes

(collect energy to reach the threshold)


This talk...•  Explores multi-strange particle production

i.e. φ and Ξ production à solves a long standing puzzle at GSI energies

•  Explores charm production

i.e. J/Ψ, Lc and D-mesons à new road for a charm program at FAIR


Motivation: φ


Motivation

Recent measurements on near and below threshold production.

� production

HADES and FOPI reported unexpectedlarge � contribution to the K� yield.

⌅ production

⌅� yield, measured in Ar+KCl much largerthan thermal model.Confirmed in p+Nb ! No Y+Y exchange!!

Both particles are not well described inmicroscopic transport models and thermalfits are also not convincing.

G. Agakishiev et al. [HADES Collaboration], Phys. Rev. C 80, 025209 (2009)

Marcus Bleicher and Jan Steinheimer 2 / 24

Motivation


� production


⌅ production





Motivation


� production


⌅ production



G. Agakishiev et al. [HADES Collaboration], Phys. Rev. Lett. 103, 132301 (2009)


Motivation: Ξ


Motivation


� production


⌅ production





Motivation


� production


⌅ production



G. Agakishiev et al. [HADES Collaboration], Phys. Rev. Lett. 103, 132301 (2009)


5

FIG. 2: Relative ⌅

� yield as a function of the cut value of various ⇤and ⌅

� geometrical distances (see text, abscissa units are mm). Thefull (open) circles display the experimental (simulation) data. Thevertical and horizontal arrows indicate the chosen cut values and theregion of accepted distances, respectively.

of -70 MeV. This allows for comparisons to model calcula-tions (see below). To visualize the energy dependence of theproton-induced data (full curve in Fig. 3), we fitted the corre-sponding ratios with a function f(x) = C(1�(D/x)

µ)

⌫ (withx =

psNN , C = 0.44, D = 2.2GeV, µ = 0.027, ⌫ = 0.78),

a simple parameterization which may be used to estimate theexpected ⌅

�/⇤ ratio in energy regions, where data are not yet

available.

The ⌅

�/(⇤+ ⌃

0) ratio has been investigated within a sta-

tistical approach. We performed a calculation with the pack-age THERMUS [37], using the mixed-canonical ensemble,where strangeness is exactly conserved, while all other quan-tum numbers are conserved only on average by chemical po-tentials. The optimum input parameters for this calculation(i.e. temperature, T = (121 ± 3) MeV, baryon chemical po-tential, µB = (722 ± 85)MeV, charge chemical potential,µQ = (24± 20)MeV, fireball radius, R = (1.05± 0.15) fm,and radius of strangeness-conserving canonical volume, Rc =

(0.8±2.1) fm) follow from the best fit to the available HADESparticle yields (⇡�, ⇡0, ⌘, !, K0, ⇤) in p + Nb collisions at3.5 GeV [29–31]. We obtained a ⌅

� yield of 1.0⇥ 10

�5 anda ⌅

�/(⇤+ ⌃

0) ratio of 8.1 ⇥ 10

�4 (asterisk in Fig. 3). Bothvalues are significantly lower than the corresponding experi-mental data.

We also estimated the ⌅ production probability within twodifferent transport approaches, both having implemented theaforementioned strangeness-exchange channels. The first ap-

FIG. 3: The yield ratio ⌅

�/(⇤+ ⌃

0) as a function of

psNN orp

sNN �psthr (inset). The arrows indicate the threshold in free NN

collisions. The open symbols represent data for symmetric heavy-ioncollisions measured at LHC [1, 34] (cross), RHIC [2, 3] (stars), SPS[4, 5] (triangles), AGS [6] (square), and SIS18 [12] (circle). Thefilled cross depicts p + p collisions at LHC [35], while the downwardand upward pointing filled triangles are for p +A reactions at DESY[36] and SPS [18], respectively. The filled circle shows the presentratio (2) for p (3.5 GeV) + Nb reactions (statistical error within ticks,systematic error as bar). The full curve is a parameterization (seetext) of the proton-induced reaction data. The asterisk, diamondand filled star display the predictions of the statistical-model pack-age THERMUS [37], the GiBUU [38, 39], and the UrQMD [16, 17]transport approaches, respectively.

proach is the UrQMD model [16, 17] (version2 3.4). For ⌅�

hyperons, we derived a yield of (6.9± 2.8)⇥ 10

�7 per eventwhich is more than two orders of magnitude lower than theexperimental yield (1) and decreases only by a factor of two,if the channels YY ! ⌅N (with cross sections from [13])are deactivated; i.e. in the model hyperon-hyperon fusionis of minor importance for ⌅ production in proton-nucleusreactions at 3.5 GeV. The ⇤ rapidity distribution, however,was fairly well reproduced by UrQMD [31]. The resulting⌅

�/(⇤+ ⌃

0) ratio amounts to (3.1 ± 1.2) ⇥ 10

�5 (filledstar in Fig. 3). The second transport approach we used is theGiBUU model [38, 39] (release3 1.6). We estimated a ⌅

�

yield of (6.2±0.9)⇥10

�6, a value being considerably higherthan the prediction by the UrQMD model, but still signifi-cantly lower than the experimental yield (1). Also here, the

2 http://urqmd.org3 https://gibuu.hepforge.org

p+Nb

Au+AuTHERMUSGiBUU

UrQMD (old)

Threshold for p+pàp+p+φ ≈ 2.895 GeVThreshold for p+pàN+Ξ+K+K ≈ 3.24 GeV

Subthreshold production:Two paradigms

Multi-step processes

•  Increase the available energy above threshold by creation of heavy resonances

•  NNàNN*, N*N*àNN**, a) N**N**à stringàX b) N**àNφ�c) N**àΞKK

In-medium modifications

•  Decrease the needed energy by in-medium modifications

Marcus Bleicher, THOR 2018 600 800 1000 1200

q0 [MeV]

0

1

2

3

4

5

6

7

8

9

S K*(q

=0,q

0 ) [G

eV-2

]

ρ=0ρ=0.5ρ

0ρ=ρ

0ρ=1.5ρ

0

FIG. 7: The K̄∗ spectral function as function of the meson energy q0 for different densities and zero

momentum.

These results are better visualized in the K̄∗ meson spectral function, which is displayed in

Fig. 7 as a function of the meson energy q0, for zero momentum and different densities up to

1.5ρ0. The dashed line refers to the calculation in free space, where only the K̄π decay channel

contributes, while the other three lines correspond to fully self-consistent calculations, which also

incorporate the process K̄∗ → K̄π in the medium.

We observe a rather pronounced peak at the quasiparticle energy

ωqp(q⃗ = 0 )2 = m2 +ReΠ(ωqp(q⃗ = 0 ), q⃗ = 0 ) , (26)

which moves to lower energies with respect to the free K̄∗ mass position as density increases. The

Λ(1783)N−1 and Σ(1830)N−1 excitations are also clearly visible on the right-hand side of the

quasiparticle peak. In spite of the fact that the real part of the optical potential, ReΠ(mK̄∗ , q⃗ =

0 )/(2mK̄∗), acquires a moderate value of −50 MeV at ρ0 (see Fig. 5), interferences with the

resonant-hole modes, which appear at energies close to the K̄∗ mass, push the quasiparticle peak

to a substantially lower energy. Note, however, that the properties of the quasiparticle peak will

15

L. Tolos et al., Phys.Rev.C82:045210,2010

Anti-K*

Subthreshold particle production

How does it work?

•  Fermi momenta can lift the collision energy above threshold

•  Secondary interactions accumulate energy

•  Ar+KCl at Elab=1.76 AGeV Is there enough energy for φ and Ξ production?

Resonance mass distribution

Yes! But for Ξ, only in the tails. à Introduce branching ratio for decay into Nφ cdf


On the probability of sub threshold production

How does sub-threshold production work?

Fermi momenta lift the collision energy above the threshold.

Secondary interactions accumulate energy.

For Ar+KCl at E1.76 A GeV:

Is there enough energy availablefor � and ⌅?

Yes but for ⌅ in the ”tails”

Why not introduce these decays forthe less known resonances?

For our model that would be the N⇤(1990), N⇤(2080), N⇤(2190),N⇤(2220) and N⇤(2250).

Jan Steinheimer (FIAS) 26.03.2015 5 / 12

Probabilities


On the probability of sub threshold production

Sub-threshold production baseline

Fermi momenta lift the collision energy above the threshold.

Secondary interactions accumulate energy.

Why not introduce these decays for the less known resonances?


New resonances


Strangeness Production in UrQMD

Strange particle production goesONLY viaResonance excitation:

N+N! X

N+M! X

M+M! X

N*(1650) �(1232)N*(1710) �(1600)N*(1720) �(1620)N*(1875) �(1700)N*(1900) �(1900)N*(1990) �(1905)N*(2080) �(1910)N*(2190) �(1920)N*(2220) �(1930)N*(2250) �(1950)N*(2600) �(2440)N*(2700) �(2750)N*(3100) �(2950)N*(3500) �(3300)N*(3800) �(3500)N*(4200) �(4200)


Strangeness Production in UrQMD

Strange particle production goesONLY viaResonance excitation:

N+N! X

N+M! X

M+M! X

N+N Cross section

�1,2!3,4(ps) / (2S3 + 1)(2S4 + 1)

hp3,4ihp1,2i

|M(m3,m4)|2

with

|M(m3,m4)|2 =A

(m4 �m3)2(m4 +m3)2


Important: New resonances replace the strings,no additional pp cross section is introduced

Fixing the branching ratio


Fixing the N ⇤ ! �+N decay with p+p data

We use ANKE data on the � production cross section to fix theN⇤ ! N + � branching fraction.

Only 1 parameter

�N

⇤!N�

/�tot

= 0.2%1 parameter fits all 3 points!

Y. Maeda et al. [ANKE Collaboration], Phys. Rev. C 77, 015204 (2008) [arXiv:0710.1755[nucl-ex]].


The φ+N cross section


The notorious �+N cross section

Does the � have a small hadronic cross section?

The idea that the � has a small hadronic cross section is not new.A. Shor, Phys. Rev. Lett. 54, 1122 (1985).

The � would be an important probe of hadronization.

COSY and LEPS experiments have found large nuclear absorptioncross sections

ANKE SPring-8

14-21 mb 35 mbM. Hartmann et al., Phys. Rev. C 85, 035206 (2012)T. Ishikawa et al., Phys. Lett. B 608, 215 (2005)


Cross sections


� suppression in nuclear medium

Detailed balance ! absorption cross section

d�b!a

d⌦=

⌦p2a

↵

hp2bi(2S1 + 1)(2S2 + 1)(2S3 + 1)(2S4 + 1)

J+X

J=J�

hj1m1j2m2| |JMi2

hj3m3j4m4| |JMi2d�a!b

d⌦

�+ p cross section from detailed balanceis very small.

Still the transparency ratio is wellreproduced. Remember: this is what leadto the 20 mb cross section from ANKE.

Cross section from transparency ratio ismodel dependent!




d�b!a

d⌦=

⌦p2a

↵

hp2bi(2S1 + 1)(2S2 + 1)(2S3 + 1)(2S4 + 1)

J+X

J=J�

hj1m1j2m2| |JMi2


d⌦







d�b!a

d⌦=

⌦p2a

↵

hp2bi(2S1 + 1)(2S2 + 1)(2S3 + 1)(2S4 + 1)

J+X

J=J�

hj1m1j2m2| |JMi2


d⌦






φ transparency ratios I

6

0.5 1.0 1.5

0.4

0.6

0.8Cu/C

0.51

2

4

)C φ

σ/A φ

σR

=(12

/A)(

0.2

0.4

0.6Ag/C

0.5

1

2

4

0.5 1.0 1.5

0.2

0.4

Au/C0.5

1

2

4

0.5 1.0 1.5

0.4

0.6

0.8Cu/C

30

73120200

0.2

0.4

0.6Ag/C

30

73120200

[GeV/c]φ

p0.5 1.0 1.5

0.2

0.4

Au/C

30

73120

0.5 1.0 1.5

0.4

0.6

0.8Cu/C

102030

0.2

0.4

0.6Ag/C

1015

30

0.5 1.0 1.5

0.2

0.4

Au/C

101525

FIG. 3: (Color online) The transparency ratio R for the three different nuclear combinations as a function of the φ laboratorymomentum. The experimental data, shown in red, are connected with lines to guide the eye. The predictions of the threetheoretical approaches are shown for model 1 (left), model 2 (center), model 3 (right). For the rest of the notations, see thetext.

Any momentum dependence in the results of model 2is much more moderate but it is clear that in neithercase can the variation of the Cu/C, Ag/C and Au/Ctransparency ratios be described with a single value of theφ width. The results from model 3 are more promisingin this respect, since the steady fall in the data can bereproduced with a constant φN absorption cross sectionof about 15 - 20 mb.

By comparing the calculated and measured values ofthe transparency ratio for the three target combinations,it is possible to determine the weighted average of the φwidth Γφ in the nuclear rest frame for density ρ0 for eachmomentum bin. The results of applying this procedureare shown in Fig. 4(a) for both model 1 and 2. Model 3, aswell as the SPring-8 [15] and JLab [16] data, are directlysensitive to the values of the φN absorption cross sectionthat are noted in Fig. 4(b). The values of Γφ shown inFig. 4(a) were, in these cases, deduced in the low-density

approximation, Γφ = pφρ0σφN/Eφ.

Figure 5 shows the measured differential cross sectionsfor φ production as functions of pφ. The result on thelight C nucleus increases much faster with the φ momen-tum than for heavier targets, and this is reflected in thevariation of the transparency ratio in Fig. 2. The ex-perimental results are compared with the predictions ofthe models 2 and 3 that use the values of the φ widthand φN absorption cross section shown in Fig. 4. Theagreement of both models with the data generally im-proves for larger pφ though, in the highest momentumbin, the results of model 3 lie closer to experiment. Onepossible reason for this is the introduction of a greaternumber of φ production channels in this model. On theother hand, both models underestimate strongly the ex-perimental data at low pφ.

The models are, of course, sensitive to the relativestrength of φ production in pp and pn collisions [25].

Model 1: The eikonal approximation of the Valencia group.

Model 2: Paryev developed the spectral function approach for φ production in both the primary proton- nucleon and secondary pion-nucleon channels.

Model 3: BUU transport calculation of the Rossendorf group. Accounts for baryon- baryon and meson-baryon φ production processes.

Model 1 Model 2 Model 3

Transparency ratios II




d�b!a

d⌦=

⌦p2a

↵

hp2bi(2S1 + 1)(2S2 + 1)(2S3 + 1)(2S4 + 1)

J+X

J=J�

hj1m1j2m2| |JMi2


d⌦





New explanation





Cross section from trabsparency ratio is

model dependent!

Not ’absorption’ of the �, but of themother resonance.

Reactions of the type:N⇤ +N ! N 0⇤ +N 0⇤

N⇤ +N ! N 0⇤ +N 0⇤

where the mass of N 0⇤ < N⇤ so no � can

be produced.


Extrapolation to AA


� production in nuclear collisions below the p+p threshold

When applied to nuclear collisions:

Qualitative behavior nicelyreproduced

Predicted maximum at 1.25A GeV

High energies: too low dueto string production

HADES preliminary resultsfor 1.23 A GeV, see HADEStalks by R. Holzmann and T.Scheib.

Even centrality dependence is very well reproduced: Signal for multi stepprocesses.


Centrality


� production in nuclear collisions below the p+p threshold

Even centrality dependence works well:

Centrality dependence nicelyreproduced.

Good indicator for multistep production.

Data from: K. Piasecki et al., arXiv:1602.04378 [nucl-ex].


Plain Kaon yields


Backup


Good description of the Kaon data

Comparison to other model studies


The Kaon-Nuclear potential

0

1

2

3

4

5

0.1 0.15 0.2

K- /K+ (%

)

UK+(ρ0)=40 MeVUK-(ρ0,p=0)≈-50 MeVNO Pot.

a)

0.1 0.15 0.2

UK+(ρ0)=40 MeV, no K- Pot.

Al+Al1.9A GeV

ECMkin (GeV)

b)

P. Gasik et al. [FOPI Collaboration], arXiv:1512.06988 [nucl-ex].

An exampleThe K

�/K

+ ratio is used to determine the Kaon nuclear potentials.

Quantitative result relies on the baseline of non-potential case.

� contribution to the K

� found to be important.


A word on the K potential


About the Kaon potential

Kaon PotentialsTo constrain the Kaonpotentials from kaon spectra oneneeds to understand the baseline

For example the � contributionto the K�.

But also the general shape ofthe spectra may depend on themodel.

UrQMD results

K�/K+ ratio as function of Kaon energy.

With and without the � the ratio is much closer to the data alreadyas in a comparable study with K� potential.

Can we make robust quantitative statements?


Now for the Ξ


How to fix the N ⇤ ! ⌅� +K +K decay?

No elementary measurements near threshold.We use p+Nb at Elab = 3.5 GeV data ! �

N

⇤!⌅+K+K

/�tot

= 3.0%

HADES data

h⌅�i ⌅�/⇤(2.0± 0.3± 0.4)⇥ 10�4 (1.2± 0.3± 0.4)⇥ 10�2

UrQMD

h⌅�i ⌅�/⇤(1.44± 0.05)⇥ 10�4 (0.71± 0.03)⇥ 10�2

Table: ⌅� production yield and ⌅�/⇤ ratio for minimum bias p+Nb collision ata beam energy of Elab = 3.5 GeV, compared with recent HADES results

G. Agakishiev et al., Phys.Rev.Lett. 114 (2015) no.21, 212301.


Comparison to data for Ξ


⌅� production in nuclear collisions below the p+pthreshold

⌅� yield in Ar+KCl collisions isnicely reproduced

Consistent with the p+Nb data.

Indication for ⌅ production fromnon-thermal ’tails’ of particleproduction.

All other strange particle ratiosare also in line with experiment


Can we also use this for charm?

Bold..., but possible...


Can we make predictions about

sub-threshold charm production?

J. Steinheimer, A. Botvina and M. Bleicher, arXiv:1605.03439 [nucl-th].


Why is charm interesting?


Why is a sub threshold charm prediction interesting?

Charm at high baryon densities

Study properties of charmed hadrons in dense nuclear matter.

Study hadronic charm rescattering.

Study charm in cold nuclear matter.

Big part of CBM program...but that was SIS300!


Fixing the branching ratio


Fixing the N ⇤ ! J/ +N decay with p+p data

We use data from p+p atps = 6.7 GeV to fix the N⇤ ! N + J/

branching fraction.

Only 1 parameter

�N

⇤!NJ /�tot = 2.5 · 10�5

Assumptions

We assume the associatedproduction of N⇤ ! ⇤

c

+D tobe a factor 15 larger at thatbeam energy and to contributeabout the half of the totalcharm production.

We neglect D +D pairproduction as it has asignificantly higher threshold

We neglect string production

All the contributions shouldeven increase the expected yield.


J/Ψ cross section


J/ suppression in nuclear medium

Detailed balance ! absorptioncross section

J/ + p cross section from detailedbalance is very small.

Not ’absorption’ of the J/ , but ofthe mother resonance.

Reactions of the type:N⇤ +N ! N 0⇤ +N 0⇤

N⇤ +N ! N 0⇤ +N 0⇤

where the mass of N 0⇤ < N⇤ so no

J/ can be produced.Comparable to: D. Kharzeev and H. Satz,Phys. Lett. B 334, 155 (1994).


Predictions for SIS-100


J/ and open charm production in nuclear collisions belowthe p+p threshold

When applied to central nuclear collisions (min. bias: divide by 5):

Elab = 11 A GeV

1.5 · 10�6 J/ per event

2 · 10�5 ⇤c

per event

⇡ 3� 4 · 10�5 D per event


Comparison to others I


Comparisons to HSD

Parametrized cross section for J/

�NN

i

(s) = fi

a

✓1� m

ips

◆↵

✓ps

mi

◆�

✓(ps�

ps0i)

HSD results taken from:O. Linnyk, E. L. Bratkovskaya and W. Cassing, Int. J. Mod. Phys. E 17, 1367 (2008)


Comparison to others II


Comparisons to hadronic Lagrangian

Cross section for p+ p ! p+D0+ ⇤

c

Taken from:W. Liu, C. M. Ko and S. H. Lee, Nucl. Phys. A 728, 457 (2003)


Hadronic Lagrangian

Summary•  A new mechanism for the production of Ξ and φ is

introduced and validated in elementary collisions

•  This new branching ratio of high mass resonances is fitted to available data and extrapolated to AA

•  It allows for the first time to describe the sub-threshold multi-strange particle production

•  If this mechanism is also be applicable to charm production it may open a new road for charm studies at FAIR-SIS 100


charm and strangeness production at gsi/fair...

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