Production of X(3872) in Ultra- Relativistic Heavy-Ion Collisions Matt Sibila1, Ralf Rapp2, Xiaojian Du2 1Ohio Northern University, 2Texas A&M Cyclotron Institute

1 Presentation Outline

1. Introduction 2. X(3872) background and structure 3. Analysis 1. Simulated URHIC 2. Equilibrium yields 3. Transverse momentum spectra 4. Time evolution yields

5. Extracted PT 4. Conclusion

2 Introduction

• Ultra-relativistic heavy-ion collisions (URHICs) allow us to study QCD matter • Time evolution: • Expanding quark-gluon plasma phase • Chemical freezeout (T=160-170 MeV) • Hadronic medium • Kinetic freezeout (T≈100 MeV) • Studying the hadronic phase can give us an understanding of hadronization mechanisms • We put our focus on X(3872) because of its nontrivial structure and the recent ability to produce it in URHICs 3 X(3872) Background

• Discovered in 2003 by the Belle Collaboration [1] • Observed a state with m=3871.8 MeV decaying into π+π−J/ψ [1]. • LHCb determined quantum numbers JPC to be 1++ in 2012 [2] • In-vacuum production width Γ ≤ 1.2 ��� [3] • Believed to have a quark makeup of ����̅ • Structure has yet to be determined

[1] S.-K. Choi et al. Phys. Rev. Lett., 91:262001, (2003). [2] R. Aaij et al. Phys. Rev. Lett., 110:222001, (2013). [3] M. Tanabashi et al. (Particle Data Group), Phys. Rev. D 98, 030001, (2018). 4 Possible Structures of X(3872)

Tetraquark Model Mesonic Molecule • 2 diquarks (not color neutral) • Bound ��∗ pair • Tightly bound through color • Bound through residual mesonic interactions forces • Small decay width • Large decay width

� � � �̅

� �̅ � � 5 Simulated URHIC

• Use an expanding fireball model [4]

• PbPb collisions at � = 5 ��� • 2 simulations • 0-20% centrality • 20-40% centrality • Gives time evolution of many properties

• temperature (T), charm quark fugacity (γc), radius (R), volume (V), surface velocity (βS)

[4] L. Grandchamp and R. Rapp, Phys. Lett. B523, 60, (2001). 6 Equilibrium Yields

• Use a particle density equation � � � = � � � (2�)

• Fugacity, γc, is constructed from total charm-quark number conservation in the hadronic phase • Quantitatively very important

7 0-20% Equilibrium Yields

• T=170 MeV, Yield of 0.00546 • T=110 MeV, Yield of 0.00122 • Production occurs from t=9 fm to t=16 fm

PbPb ��� = � ���

8 20-40% Equilibrium Yields

• T=170 MeV, Yield of 0.00189012 • T=120 MeV, Yield of 0.0005878 • Production occurs from t=6 fm to t=12 fm

PbPb ��� = � ���

9 Transverse Momentum (PT) Spectra

• Use a thermal blastwave model:

�� �sinh(�) �sinh(�) = � ����� � ��� � � Where… � � = ���ℎ � �

10 Transverse Momentum Spectra

• Factor 4 difference is reflected in spectra • T=110 MeV is flatter, as expected

PbPb ��� = � ���

11 0-20% PT Spectra Comparison

• [5] uses a thermal blastwave model up to 6 GeV • Similar results • Differences due to slightly different choice for temperature and different charm-quark cross-section

PbPb ��� = � ���

[5] A. Andronic et al. arXiv:1901.09200 [nucl-th] 12 Time Evolution Yields

Utilize a kinetic rate equation: �� = −Γ � − � �� ∫ ∫ � Γ��� • Γ is the in-medium reaction rate � � = () ∫ Γ = Γ , n=0,1,2,3,4,5 �

• Γ170=240,200,100,20 MeV [6]

• N(t0)=0

[6]M. Cleven et al. arXiv:1906.06116 [hep-ph] 13 Time Evolution Yields

• Different rates greatly effect the shape • Larger rates have very distinct evolutions, however end with nearly the same final production

PbPb ��� = � ���

14 Extracted PT Spectra

We extract PT Spectra from the production rate by:

∆��

Where � is the normalized blastwave expression

∫ � = � �� ��

15 Extracted PT Spectra

• Higher rates are very similar at low PT however spread out at high PT

0-20% PbPb ��� = � ���

16 Conclusions

• URHICs are an effective means of studying hadronization mechanisms • Due to its nontrivial internal structure, X(3872) is a particularly interesting object to study in URHICs • Modelled URHIC with expanding fireball model with charm-quark number conservation • Computed equilibrium abundance and time evolution of X(3872) production • Reaction rates affect production yields, however effects in PT spectra are more subtle

17 Acknowledgements

This work was supported by the NSF through grant numbers PHY-1659847 and PHY-1913286

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