Hadron Spectroscopy Alessandro Pilloni Hadronic Physics with Lepton - PowerPoint PPT Presentation

JPAC program for Hadron Spectroscopy Alessandro Pilloni Hadronic Physics with Lepton and Hadron Beams, JLab, September 5 th , 2017

Hadron Spectroscopy Hybrids Tetraquark Meson Baryon Glueball 𝝆 𝑲/𝝎 𝝆 Hadroquarkonium 𝝆 Molecule Experiment ? Fundamental properties, Data Model building Lattice QCD Interpretations on the spectrum leads to understanding fundamental laws of nature 2

Hadron Spectroscopy XYZ states Esposito, AP, Polosa, Phys. Rept. 668 Fundamental ? properties, Data Model building 3

Hadron Spectroscopy XYZ states Esposito, AP, Polosa, Phys. Rept. 668 Fundamental properties, Data Model building 4

Hadron Spectroscopy XYZ states Esposito, AP, Polosa, Phys. Rept. 668 Fundamental properties, Data Model building Improvement needed! With great statistics comes great responsibility! 5

Joint Physics Analysis Center • Joint effort between theorists and experimentalists to work together to make the best use of the next generation of very precise data taken at JLab and in the world • Created in 2013 by JLab & IU agreement • It is engaged in education of further generations of hadron physics practitioners Insight on QCD Effective Field Theories dynamics Analyticity+Unitarity Dispersion Relations Regge Theory Fundamental parameters Resonances, exotic states Experiments CLAS, GlueX, BESIII, COMPASS, LHCb, BaBar, Belle II, KLOE, MAMI Lattice 6 A. Pilloni – JPAC program for Hadron Spectroscopy

Joint Physics Analysis Center L. Bibzrycki, R. Kaminski (Krakow) A. Jackura, N. Sherrill, G. Fox, T. Londergan J. Nys (Ghent U.) (IU), E. Passemar, A. Szczepaniak (IU/JLab) M. Mikhasenko (Bonn U.) L. Dai (FZ Julich) I. Danilkin, R. Workman (GWU), M. Döring (GWU/JLab) A. Hiller Blin (Mainz U.) V. Mathieu, V. Pauk, A. Pilloni, A. Celentano (INFN-GE) V. Mokeev (JLab) P. Guo (Cal. State U.) M. Albaladejo (Valencia U.) J. Castro, C. Fernandez-Ramirez (UNAM) Students, Postdocs, Faculties 7 A. Pilloni – JPAC program for Hadron Spectroscopy

Interactive tools • Completed projects are fully documented on interactive portals • These include description on physics, conventions, formalism, etc. • The web pages contain source codes with detailed explanation how to use them. Users can run codes online, change parameters, display results. http://www.indiana.edu/~jpac/ 8 A. Pilloni – JPAC program for Hadron Spectroscopy

𝑇 -Matrix principles These are constraints the amplitudes have to satisfy, but do not fix the dynamics Resonances (QCD states) are poles in the unphysical Riemann sheets 9 A. Pilloni – JPAC program for Hadron Spectroscopy

Three-Body Unitarity Hu, Mai, Doring, AP, Szczepaniak, EPJA, arXiv:1707.06118 The full implementation of three-body unitarity is a major step for understanding the states appearing in such final states e.g. 𝑏 1 1260 + → 𝜌 + 𝜌 − 𝜌 + , 𝜌 1 1400 + → 𝜌 + 𝜌 − 𝜌 + , 𝑌 3872 → 𝐸 0 𝐸 0 𝜌 0 We completed the proof of the Amado model, based on the isobar approximation and a Bethe-Salpeter ansatz for the amplitude See M. Doring’s talk at 11:30am 10 A. Pilloni – JPAC program for Hadron Spectroscopy

Pole hunting I sheet Bound states on the real axis 1st sheet Not-so-bound (virtual) states on the real axis 2nd sheet II sheet 11 A. Pilloni – JPAC program for Hadron Spectroscopy

Pole hunting I sheet More complicated structure when more thresholds arise: two sheets for each new threshold III sheet: usual resonances IV sheet: cusps (virtual states) Virtual state II sheet Bound state Resonance 12 A. Pilloni – JPAC program for Hadron Spectroscopy

Amplitude analysis for 𝑎 𝑑 (3900) One can test different parametrizations of the amplitude, which correspond to different singularities → different natures AP et al. (JPAC), PLB772, 200 𝑎 𝑑 3900 ? 𝑣: 𝑎 𝑑 3900 ? 𝑣: 𝐸 0 (2400) "𝜏, 𝑔 0 (980)" 𝐸 1 (2420) (anti)bound state, Triangle rescattering, Resonance, II/IV sheet pole logarithmic branching point III sheet pole («molecule») («compact state») 𝜌 𝐸 1 𝐸 ∗ 𝑍 𝜌 𝐸 Tornqvist, Z.Phys. C61, 525 Maiani et al. , PRD71, 014028 𝐾/𝜔 Swanson, Phys.Rept. 429 Faccini et al. , PRD87, 111102 Hanhart et al. PRL111, 132003 Szczepaniak, PLB747, 410 Esposito et al., Phys.Rept. 668 13 A. Pilloni – JPAC program for Hadron Spectroscopy

Triangle singularity 𝜌 𝐸 1 𝐸 ∗ 𝑍(4260) 𝜌 𝐸 𝐾/𝜔 • Logarithmic branch points due to exchanges in the cross channels can simulate a resonant behavior, only in very special kinematical conditions (Coleman and Norton, Nuovo Cim. 38, 438) • However, this effects cancels in Dalitz projections, no peaks (Schmid, Phys.Rev. 154, 1363) • But the cancellation can be spread in different channels, you might still see peaks in other channels! 14 A. Pilloni – JPAC program for Hadron Spectroscopy

Testing scenarios • We approximate all the particles to be scalar – this affects the value of couplings, which are not normalized anyway – but not the position of singularities. This also limits the number of free parameters The scattering matrix is parametrized as 𝑢 −1 𝑗𝑘 = 𝐿 𝑗𝑘 − 𝑗 𝜍 𝑗 𝜀 𝑗𝑘 Four different scenarios considered: 𝑕 𝑗 𝑕 𝑘 • «III»: the K matrix is 𝑁 2 −𝑡 , this generates a pole in the closest unphysical sheet the rescattering integral is set to zero • «III+tr.»: same, but with the correct value of the rescattering integral • «IV+tr.»: the K matrix is constant, this generates a pole in the IV sheet • «tr.»: same, but the pole is pushed far away by adding a penalty in the 𝜓 2 15 A. Pilloni – JPAC program for Hadron Spectroscopy

Singularities and lineshapes Different lineshapes according to different singularities III+tr. III sheet pole Triangle IV+tr. tr. IV sheet pole no pole Triangle Triangle 16 A. Pilloni – JPAC program for Hadron Spectroscopy

Fit: III 17 A. Pilloni – JPAC program for Hadron Spectroscopy

Fit: III+tr. 18 A. Pilloni – JPAC program for Hadron Spectroscopy

Fit: IV+tr. 19 A. Pilloni – JPAC program for Hadron Spectroscopy

Fit: tr. 20 A. Pilloni – JPAC program for Hadron Spectroscopy

Fit summary III IV+tr. tr. III+tr. Naive loglikelihood ratio test give a ∼ 4𝜏 significance of the scenario III+tr. over IV+tr., looking at plots it looks too much – better using some more solid test 21 A. Pilloni – JPAC program for Hadron Spectroscopy

Pole extraction IV+tr. III III+tr. 22 A. Pilloni – JPAC program for Hadron Spectroscopy Not conclusive at this stage

Pentaquark photoproduction To exclude any rescattering mechanism, we propose to search the 𝑄 𝑑 (4450) state in photoproduction We use the (few) existing data and VMD + pomeron inspired bkg to estimate the cross section GlueX data coming soon! 𝐾 𝑄 = 3/2 − Hiller Blin, AP et al. (JPAC), PRD94, 034002 23 A. Pilloni – JPAC program for Hadron Spectroscopy

Higher energies: Regge exchange Resonances are poles in 𝑡 for fixed 𝑚 Reggeons are poles in 𝑚 for fixed 𝑡 dominate low energy region dominate high energy region 𝐵 𝑚 ∼ 𝑕 1 𝑕 2 𝐵 ∼ ∑ 𝑡 𝑚 ∼ 𝛾 𝑢 𝑡 𝛽(𝑢) 𝑡 𝑞 − 𝑡 24 A. Pilloni – JPAC program for Hadron Spectroscopy

Finite energy sum rules See J. Nys talk at 12pm PWA in the low energy region Regge exchanges Analytically Resonance at high energy connected extraction 25 A. Pilloni – JPAC program for Hadron Spectroscopy

Searching for resonances in 𝜃𝜌 The 𝜃𝜌 system is one of the golden modes for hunting hybrid mesons • We build the partial waves amplitude according to the 𝑂/𝐸 method • ′ show up We test against the 𝐸 -wave data, where the 𝑏 2 and the 𝑏 2 • Resonant content A. Jackura, AP et al. (JPAC & COMPASS), 1707.02848 The denominator 𝐸(𝑡) contains all the Final State Interactions constrained by unitarity → universal The numerator 𝑜(𝑡) depends on the exchanges → process-dependent, smooth 26 A. Pilloni – JPAC program for Hadron Spectroscopy

Searching for resonances in 𝜃𝜌 Smooth «background» Precise determination of pole position

Searching for resonances in 𝜃𝜌 • We implemented the two-channel fit to estimate the systematic dependence on coupled-channel effects • Other systematic uncertainties include the variation of the number of terms in 𝑜(𝑡) , and in the barrier factor radius 𝑡 𝑆 • The coupled channel analysis involving the exotic 𝑄 -wave is ongoing, as well as the extention to the GlueX production mechanism and kinematics 28 A. Pilloni – JPAC program for Hadron Spectroscopy