Femtoscopy of baryonic particles
in heavy-ion collisions
TCHoU WorkShop
2022/03/24 (Thurs)
Moe Isshiki
University of Tsukuba

Baryon-Baryon interaction….
Ø Hyperon-Hyperon (Y-Y) and Hyperon-Nucleon (Y-N) interactions are important for studying exotic hadronicstates such as H-dibaryon as well as to understand the Equation of State of neutron stars.
- Possible bound state of Y-N and Y-Y (S=-2) ?
Ø Also, the identical baryon correlations such as proton-proton are good probe to see the FSI and QS interaction directly.
ØVarious hadrons including hyperons are abundantly produced in Heavy Ion Collisions.
Today, I will talk about ...
In STAR,-The measurement of Λ-Λ in high precision in Au+Au collisions.
-The first measurement of Ξ-Ξ correlation function in Au+Au collisions.
- The first measurement of p−Ξ in Au+Au collisions.
-The first measurement of proton-proton correlation function in 𝑠!! = 3 GeV Au+Au FXT Collisions.
-The measurement of p-Ω correlation in Au+Au collisions.
In ALICE,-The first measurements of p-K interaction in Pb+Pb collisions at 𝑠!! =5.02 TeV and ΛK interaction at 𝑠!! =2.76 TeV-The measurements of p-Ξ and p-Ω interactions in Pb+Pb collisions at 𝑠 = 13 TeV.
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TCHoU workshop Moe Isshiki2What’s femtoscopy?
Ø Technique based on Bose-Einstein/Fermi-Diraccorrelation has been used in heavy-ion collisions toprobe the spatial and temporal extent of particle
emitting source.

Ø Femtoscopic correlations arise due to quantum
statistical effects and final state (strong and Coulomb)interaction (if present) at low relative momentum of twoparticles.

Experiment

Theory!

C(𝑞)=∫ 𝑠 𝑟 |𝜓(𝑞, 𝑟)| 𝑑𝑟&(()"𝐶 𝑞 = *(()

r: relative distance (of pair)
q: relative momentum q=𝑞! " + 𝑞# " + 𝑞$ " − 𝐸% "A: actual pairs from same events
B: background pairs from mixed events𝑠 𝑟 source function 𝜓(𝑞, 𝑟) : wave function of two-particles
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TCHoU workshop Moe Isshiki3Contribution of Each interaction

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Identical correlation

Non-identical correlation

QS+FSI(Strong +Coulomb)

FSI only
TCHoU workshop Moe Isshiki

Hanna Zbroszczyk from STAR(WPCF2018)4

STAR detectors
TOF (Time Of Flight)
Time of flight measurement ofcharged particles, |𝜂| < 0.9

VPD (Vertex Position Detector)
TPC (Time Projection Chamber)
Measure the dE/dx
𝜂 < 1.0 0 < 𝜙 < 2𝜋
2022/04/24

Measure the event start time,
providing the minimum-bias trigger in Au+Au
collisions.
TCHoU workshop Moe Isshiki

5STAR FXT trarget programØ The RHIC-Beam Energy Scan Ⅱ(2019~) program
covered the fixed target mode from 3.0 to 7.7 GeV.
Ø Put the gold target at 210cm from the interaction
region of TPC.

J. Phys.: Conf. Ser. 742 012022
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TCHoU workshop Moe Isshiki

6Lednicky Fit (femtoscopy fit)
11 𝑓 𝑘 *1 𝑑)
𝑅𝑒𝑓 𝑘
𝐼𝑚𝑓 𝑘**𝐶(𝑄)!"#$%&'( = 𝑁[1 + 𝜆 − exp −𝑟) 𝑄 +1−+𝐹𝑄𝑟−𝐹* 𝑄𝑟)+)24 𝑟)*2𝑟)
2 𝜋 𝑟)𝜋𝑟)+ 𝑎,"- exp(−𝑟,"- *𝑄 *)]FSI(Final state interaction) term

Quantum Statistic term

Residual term
(introduced by STAR to account for residual effect)" ""& ' ! #$"
$𝑘 = , 𝐹$ 𝑧 = ∫%𝑑𝑥 … … . . Approximate formula 𝐹$ 𝑧 ≅ 1 − 𝑒 (& ,#&(& "𝐹# (𝑧) = (1 − 𝑒 )/𝑧
𝑁 :Normalization factor
𝜆 :chaotic parameter𝑓% ∶ scattering length
Physical quantity to study a bound state𝑑% ∶ effective range𝑟% ∶source size𝑎)'* ∶ residual amplitude𝑟)'* ∶ width of the Gaussian$$+%#&Scattering Amplitude:𝑓 𝑘 = ( + 𝑑% 𝑘 # − 𝑖𝑘)($2022/04/24

TCHoU workshop Moe Isshiki

L. Adamczyk for the STAR Collaboration PhysRevLett.114.022301

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Reconstruction of 𝚲 and 𝚵Decay channel

Λ (uds)PΛΞ (𝑑𝑠𝑠)
ΞWMass (from PDG 2018)

Λ −> 𝜋 ( + 𝑝P −> 𝜋 , + 𝑝̅Λ
(63.9%)

1.115683 (GeV/𝑐 # )Ξ −> Λ + 𝜋 ,P + 𝜋(ΞW −> Λ(99.87%)

1.32171 (GeV/𝑐 # )Ø KFParticle package was used.
KFParticle is based on Kalman filter.
Ø Very good Purity for Λ(~88%) and Ξ(~90%).
Daughter particle selection for Λ and Ξ

Invariant massΞΛ

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TCHoU workshop Moe Isshiki

For pion
Ø | n&,( |<3Ø -0.15< Mass " <0.15 (GeV/𝑐 " )"For protonØ | n&,) |<3Ø 0.5 < Mass " <1.5 (GeV/𝑐 " )"For Λ and ΞØ p* ≥ 0.4 GeV/𝑐
Ø |y|<1.08

Result

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TCHoU workshop Moe Isshiki

9Scattering parameters of 𝚲𝚲Phys. Lett. B 797 (2019) 134822
From ALICE’s result..

Ø The HAL QCD from lattice calculation and HKMYY and FG models from hypernuclei data match with ALICE’sexclusion plot’s region of 1 sigma.
Ø Previous STAR data is in the unphysical region.

We revisit Λ-Λ correlation with high statistics data.
2022/04/24

The STAR and ALICE’s result is different largely.
This might be due to feed-down contribution in STARresult.
The paramter is very unstable….

TCHoU workshop Moe Isshiki10𝚲-𝚲 correlation function
Ø New result with high statistics data ~4 times larger than that inprevious study.
- Not corrected for feed-down yet.
Ø Anti-correlation of Λ-Λ is observed in Au+Au at 𝑠++ = 200 GeV.
- New result with better precision is consistent with previous
result within systematic uncertainty.
- There is a long tail of residual correlation in high 𝑄,-. .

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TCHoU workshop Moe Isshiki11𝚵-𝚵 correlation function
Ø First measurement of Ξ-Ξ correlation in Au+Au collisions.
Ø Lattice QCD/chiral EFT calculations indicate an attractive
interaction, but not strong enough to form a bound state [1,2].
Ø The result shows anti-correlation at 𝑄,-. < 0.25 GeV/c.
- qualitatively matched with coulomb strength.
- to cancel quantum statistics (negative correlation),strong interaction needs to be positive correlation.
Ø Feed-down needs to be evaluated and Lednicky- Lyuboshitz
fit will be performed for further discussion.
Ø More events will be taken in 2023(~10B) and 2025(~10B).
[1] J. Haidenbauer et al., Eur. Phys. J. A 51: 17 (2015)[2] T,Doi et al., EPJ Web Conf. 175 (2018) 05009
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TCHoU workshop Moe Isshiki12𝐩-𝚵 correlation function
First measurement of p-Ξ correlation in Au+Au collisions at RHIC

𝑘 ∗ : half of relative
momentum in pair restframe

Ø Feed-down is corrected using Theminator2 model, but residual correlation is not corrected yet.
Ø p-Ξ correlation shows enhancement above Coulomb interaction->Hints presence of strong interaction, and can not be described by sideband background.
Ø Sensitive to system size, more attractive in peripheral collisions (smaller collision system).
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TCHoU workshop Moe Isshiki13𝐩-𝚵 correlation function
𝐶 𝑘 ∗ ratio of small to large systems,𝐶(𝑘 ∗)2%34%%∗
𝐶01 𝑘 =𝐶(𝑘 ∗)%32%%
𝐶./ 𝑘 ∗ is more sensitive to strong interaction with largely
canceled Coulomb interaction[1].
Ø Below 𝑘 ∗ = 0.1 GeV/c, the signal is enhanced beyond theCoulomb interaction and background.
Ø Similar to lattice QCD calculation [2] which suggests anattractive strong interaction between p and Ξ3.
[1] K. Morita et al, Phys. Rev. C94(2016) 031901[2] T.Hatsuda Nuclear Physics A 967 (2017) 856–859
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proton-proton correlation at 3GeV FXTCentralrity dependence
Chuan Fu, QPT 2021(STAR)Ø Significant centrality dependence is observed.
Ø Large correlation in lower collision energy.
Ø The data is very similar to the UrQMD model.

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TCHoU workshop Moe Isshiki

STAR Sebastian Siejka QuarkMatter2018
Nucl. Phys. A 982 (2019), 359-362
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proton-𝜴 correlation

STAR, arXiv:1808.02511

In 40~80% centrality, enhancement due to Coulomb interaction
is not visible.
discussing about bound state….
Models from lattice QCD
VⅠ:without bound state
It’s difficult which one is the best fit
VⅡ:shallow bound state->more statistics needed…
VⅢ:deep bound state2022/04/24

Ø potentials VI and VII are 3σ larger than the dataat 𝑘 ∗ = 20 MeV/c.
Ø VIII with expanding source and static source arewithin 1σ of the data at 𝑘 ∗ = 20 MeV/c.

TCHoU workshop Moe Isshiki

Deep bound state???
16p-𝚵 and p-𝛀 correlations from ALICE
Nature volume 588, pages232–238 (2020)

High multiplicity p-p collisions at 𝑠 = 13 TeV.
Ø p-Ξ and p-Ω were measured with goodprecision and have attractive interactions.
Comparison with HAL QCDØ p-Ω correlation is twice bigger than p-Ξ. This
caused by the large difference in the strong
attractive interaction predicted thecalculations by the HAL QCD
Ø The depletion around k*= 150 MeV/c in HAL
QCD model caused by the p-Ω bound state.
àthe data is not matched…
There is no bound state of p-Ω ???

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+α

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Recent study of hadron correlations

TCHoU workshop Moe Isshiki18p-K Correlation function
ALICE, Phys. Lett. B 822 (2021) 136708
The first mesurement of p-K in Pb-Pb at 𝑠!! = 5.02 TeVThere are attractive Coulomb interactions in low 𝑘 ∗ .
Ø In 20 <𝑘 ∗ < 50MeV/c, the repulsive strong interaction
in more peripheral (small system), it’s stronger

ALICE Phys. Lett. B 822 (2021) 136708
2021/12/13

Ø The result is consistent with result fromscattering and exotic kaonic atom experiments and model
calculations.
Journal Club in 2021 Autumn

19𝜦-𝑲 Correlation Function
ALICE,Phys. Rev. C 103, 055201 (2021)
The first mesurements of 𝛬-𝐾 correlations.
dotted curve…the primary (ΛK) contribution to the fit
dashed curve…the non-femtoscopic backgroundsolid curve …the final fit
Ø primary ΛK component(dot curve) have the largest
differences between solid curve in the 30–50%.
The contribution from non-femtoscopic backgroundis biggest in 30-50%.
ΛK+…..replusive interaction
ΛK-……attractive interaction
Λ𝐾%. ….attractive interaction2022/04/24

TCHoU workshop Moe Isshiki

Caused by the different
quark-antiquarkinteractions orfrom different net
strangeness20

Summary
Recently, new results of baryon-baryon correlations were reported in the STAR.
ØΛ-Λ correlation function- New result with high statistics data is consistent with previous result.
- Anti-correlation is observed.
ØΞ-Ξ correlation function- Anti-correlation seems to be observed for the first time, which is almost matched with Coulombinteraction. It seems that quantum statistics and strong interaction are canceled.
Ø p-Ξ correlation- Attractive interaction is observed.
- Similar to lattice QCD calculation which suggests an attractive strong interaction between p and Ξ( .
Ø p-p correlation-Attractive interaction is also observed in the 3 GeV FXT.
-There is clear energy dependence.
Ø p-𝛀 correlation-Deep bound state ??
ALICE’s result- p-Ξ and p-𝛺 correlations are attractive interactions.
- p-K is matched with the results scattering and exotic kaonic atom experiments.
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Future plansFor Λ-Λ and Ξ-Ξ correlation,-Apply the feed-down effect and momentum resolution corrections to the correlation functions.
-Fit the correlation functions using models including different interaction mechanisms to understandhyperons.
-More events of Au+Au s66 = 200 GeV will be taken in 2023(10B~events) and 2025(10B~events).

For other Correlations,
From STAR,-Study on p-Λ in 𝑠66 = 3GeV the Fixed target and 19.6 GeV will be reported in QM2022.
-The proton-light-nuclei correlation in Fixed target will be reported in QM2022.
V and Ξ-ΞW correlation functions are ongoing.
−Λ-Λ-If more statistics…. the Ω-Ω study is coming????A new study about most strangeness barons (di-omega).

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