Future expectations for exotic states Alessandro

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Future expectations for exotic states Alessandro Pilloni Implications and prospects of exotic hadrons at LHCb, October 6th, 2026 2 Spectrum of hadrons A. Pilloni Future expectations for exotic states In the light sector states appear as

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Future expectations for exotic states Alessandro Pilloni Implications and prospects of exotic hadrons at LHCb, October 6th, 2026

2 Spectrum of hadrons A. Pilloni – Future expectations for exotic states In the light sector states appear as broad resonances, harder to disentangle Heavy states are generally narrower and easier to identify

Baryons messier than mesons

Options on the market A. Pilloni – Future expectations for exotic states Quark-level calculations:
Quark models, pNRQCD, Hybrids, ...
Spectrum generally calculated as bound states of some potential
Decay rates as «overlap integrals» between two static configurations

Comprehensive picture  Little scattering dynamics  Hadron level calculations:
Compact states vs. molecules, triangles...
States as poles of scattering amplitudes
Couplings as residues at the poles

Scattering dynamics  More case-by-case 

4 Models for every taste Molecule
Bound or virtual state generated by long-range exchange forces Multiquark
Several (cluster) of valence quarks Hybrids and glueballs
Containing gluonicdegrees of freedom Hadroquarkonium
Heavy core interacting with a light cloud via Van der Waals forces Rescattering effects
Structures generated by cross-channel rescattering, very process-dependent Compact Extended A. Pilloni – Future expectations for exotic states

5 How to proceed? A. Pilloni – Future expectations for exotic states Top-down:you study models,and verify predictions

Bottom-up: you study data(lineshapes), and try and infer the physics

Exotic landscape A. Pilloni – Future expectations for exotic states Scarce consistency between variousproduction mechanisms 6 Pretty much all narrow states appear in the vicinity of some open flavor threshold

7 Broad states: the endgame? A. Pilloni – Future expectations for exotic states Widths from 50 to 230 MeV

Are we at the limits of what we can do? LHCb PRL 127 (2021) 8, 082001

8 Lineshape studies of narrow states A. Pilloni Future expectations for exotic states LHCb, PRD 102 (2020),092005

9 Weinberg’s criterion and lineshapes A. Pilloni Future expectations for exotic states Close to threshold the amplitude can be rewritten as Option b) Option a) Still disagreement on how to deal with isospin breaking though Esposito, Maiani, Pilloni, Polosa, Riquer, 105 (2022) 3, L031503 Baru et al. PLB 833 (2022) 137290

10 A. Pilloni – Theoretical review of exotic states Lineshape selection with NN Model selection is perfect playground for Neural Networks Ng, et al. (JPAC), PRD 105, L091501 The peak region has the largest impact for the decision Highest probability for a virtual state in the IV sheet

11 A. Pilloni – Future expectations for exotic states? More thresholds

12 A. Pilloni – Future expectations for exotic states

13 Any partner for the X? A. Pilloni – Future expectations for exotic states Maiani, et al. PRD89 114010 We need to establish whether there is any relevant interaction or not!

14 Esposito, Guerrieri, AP, PLB 746, 194-201 Kinematics with HQSS, dynamics estimated according to Brodsky et al., PRL113, 112001 If tetraquark Clebsch-Gordan A. Pilloni – Future expectations for exotic states

15 Esposito, Guerrieri, AP, PLB 746, 194-201 If molecule Non-Relativistic Effective Theory, HQET+NRQCD and Hidden gauge Lagrangian
Uncertainty estimated with power counting at NLO Molecule Tetraquark A. Pilloni – Future expectations for exotic states

16 A. Pilloni – Future expectations for exotic states (Slide by P. Ronggang) 1906.00831

A. Pilloni – Future expectations for exotic states The common lore is that the study ofvector quarkonium photoproduction at threshold is directly related to nucleon matrix elements GPD 17

Role of open charm A. Pilloni – Future expectations for exotic states Du et al. Eur.Phys.J.C 80, 11, 1053 The role of intermediate open charm thresholds has been pointed out,
Maybe «all that glitters is not glue» ….

Calculation based on EFT and known couplings, S-wave saturates the cross section Highly off-shellt-channel propagators 18

arXiv:2304.03845 A. Pilloni – Future expectations for exotic states Nature 615, 813 19

20 A. Pilloni – Future expectations for exotic states

21 Central exclusive production A. Pilloni – Future expectations for exotic states

The study of exotic heavy sector is a challenging task
We always want more results and data! Thank you 22 Conclusions & prospects A. Pilloni – Future expectations for exotic states

23 The heavy exotics A. Pilloni – Future expectations for exotic states https://www.youtube.com/watch?v=M8FtUjtevNg

Backup

25 A. Pilloni – Future expectations for exotic states Maiani, Polosa, Riquer PLB 778, 247

26 A. Pilloni – Future expectations for exotic states Maiani, Polosa, Riquer PLB 778, 247

27 A. Pilloni – Future expectations for exotic states Maiani, Polosa, Riquer PLB 778, 247 (Slide by A. Polosa)

Unitary reanalysis A. Pilloni – Future expectations for exotic states The dominant S-wave can include coupled channels,for higher waves cusps are suppressed and there is no point Winney et al. arXiv:2305.01449 28

Total cross section A. Pilloni – Future expectations for exotic states 29

Differential cross section A. Pilloni – Future expectations for exotic states 30 This is realized with the interference of various waves, - constructive in the forward direction - distructive in the backward directionbecause of the Legendre polynomials
Good hierarchy between waves

Contribution of open charm A. Pilloni – Future expectations for exotic states 31

Vector Meson Dominance A. Pilloni – Future expectations for exotic states 32 Since unitary model parametrize separately the production and scattering amplitude,one can compare with the predictions of VMD The value of the scattering amplitude at threshold is called scattering length
According to VMD, a small photoproduction cross sections implies a small scattering length O(1am) With the unitary model, the value of the amplitude at threshold is an unrelated parameter, the scattering length enters with the energy dependence

Vector Meson Dominance A. Pilloni – Future expectations for exotic states 33 VMD badly excluded, except for the poorly constrained 3C-R model

Scattering lengths generally of O(1fm), but smaller onesare not excluded

Crucial to constrain better these fits by measuring open charm final states

Total cross section A. Pilloni – Future expectations for exotic states 34

In a constituent quark model, we can think of a
diquark-antidiquark compact state Maiani, Piccinini, Polosa, Riquer PRD71 014028
same + Faccini, AP, PRD87 111102 35 Tetraquark (2005) Decay pattern mostly driven by HQSS 
Fair understanding of existing spectrum 
A full nonet for each level is expected  Spectrum according to color-spin hamiltonian: A. Pilloni – Future expectations for exotic states

36 Tetraquark: new ansatz (2014) Maiani, Piccinini, Polosa, Riquer PRD89 114010 A. Pilloni – Future expectations for exotic states

37 Tetraquark: new ansatz (2014) Maiani, Piccinini, Polosa, Riquer PRD89 114010 A. Pilloni – Future expectations for exotic states Ali, et al. EPJC78, 1, 29Maiani, Polosa, Riquer, PLB778, 247-251 Two different mass scenarios

cu c̄d̄ Ψ(2S) π+ Z+(4430) Dynamical movie 38 Brodsky, Hwang, Lebed PRL 113 112001 A. Pilloni – Future expectations for exotic states

Future expectations for exotic states Alessandro

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