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Experimental motivations for studying few-hadron systems on the - - PowerPoint PPT Presentation

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Experimental motivations for studying few-hadron systems on the lattice Alessandro Pilloni Scattering Amplitudes and Resonances properties from Latticd QCD MITP, Mainz, August 27 th , 2018 Outline Introduction The light sector: the

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Experimental motivations for studying few-hadron systems on the lattice

Alessandro Pilloni

Scattering Amplitudes and Resonances properties from Latticd QCD MITP, Mainz, August 27th, 2018

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Outline

  • A. Pilloni – Experimental motivation for multihadrons on the lattice
  • Introduction
  • The light sector: the 3𝜌 system
  • πœƒβ€², πœ• and 𝜚
  • The 𝑏1(1260)
  • The hybrid 𝜌1
  • The 𝑏1(1420)
  • The heavy sector: XYZ
  • The π‘Œ(3872) and the 𝑍 states
  • Two-body subchannels: π‘Žπ‘‘s and π‘Žπ‘s
  • Complicated Dalitz plots
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Hadron Spectroscopy

Molecule Tetraquark Hybrids

𝑲/𝝎 𝝆 𝝆 𝝆

Hadroquarkonium Glueball Meson Baryon

Data Amplitude analysis Properties, Model building

Interpretations on the spectrum leads to understanding fundamental laws of nature

Experiment Lattice QCD

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Experiment vs. Lattice QCD

Experiment Lattice QCD

  • Higher and higher statistics 
  • Lots of multiparticles

decay channels available οƒΌ

  • Scattering information entangled to

production mechanisms 

  • Experiments happen at the

physical point only 

  • Orthogonal systematics οƒΌ
  • Scattering information separated from

production; unaccessible channels οƒΌ

  • Although QCD is rigid,
  • ne can vary the input parameters

(quark masses, 𝑂𝑑 and π‘œπ‘”) and study the effect on amplitudes οƒΌ

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Experiment vs. Lattice QCD

Experiment Lattice QCD

Intermediate step through a 2-body isobar (partial wave truncation) 𝜌 𝜌 𝜌 𝜌 𝜌 𝜌 𝜍 𝜍 𝑏1(1260) 𝜐 πœ‰ 𝜌 𝜌 𝜍 𝑏1(1260) 𝜌

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Experiment vs. Lattice QCD

Experiment Lattice QCD

Intermediate step through a 2-body isobar (partial wave truncation) 𝜌 𝜌 𝜌 𝜌 𝜌 𝜌 𝜍 𝜍 𝑏1(1260) 𝜌 𝜌 𝜍 𝑏1(1260) 𝜌 IP 𝜌 π‘ž π‘ž

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Light spectrum (1-particle correlators)

  • A. Pilloni – Experimental motivation for multihadrons on the lattice

HadSpec PRD88, 094505 𝑏1(1260) 𝜌1(1600) 𝑏1 1420 ? The higher the mass, the more channels open

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3-body stuff

Unitarity constraints on the Isobar-Spectator amplitude

  • M. Mai, B. Hu, M. Doring,

AP, A. Szczepaniak EPJA53, 9, 177

  • A. Jackura, et al., to appear
  • D. Sadasivan, et al., in progress

β†’ See Michael’s talk on Friday

  • A. Jackura
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The 𝑏1(1260)

  • A. Pilloni – Experimental motivation for multihadrons on the lattice

Despite it has been known since forever, the resonance parameters of the 𝑏1 1260 are poorly determined The production (and model) dependence is affecting their extraction

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The 𝑏1(1260)

  • A. Pilloni – Experimental motivation for multihadrons on the lattice

The extraction of the resonance in the 𝜐 decay should be the cleanest, but the determination of the pole is still unstable

(Lattice simulations with stable 𝜍, Lang, Leskovec, Mohler, Prelovsek, JHEP 1404, 162)

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The 𝑏1(1260)

  • A. Pilloni – Experimental motivation for multihadrons on the lattice
  • M. Mikhasenko, A. Jackura, AP, et al., to appear

We can use these models to fit πœβˆ’ β†’ 2πœŒβˆ’πœŒ+ πœ‰ and describe the 𝑏1(1260) The dispersed improved model describes better the data at threshold

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πœŒπ‘ž β†’ 3𝜌 π‘ž diffractive production

  • A. Pilloni – Experimental motivation for multihadrons on the lattice

COMPASS, PRD95, 032004 (2017) Slide by B. Ketzer

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Deck amplitude

  • A. Pilloni – Experimental motivation for multihadrons on the lattice

π‘†πœŒπœŒ

IP

This production mechanism allows for a nonresonant contribution (Deck effect) Because of the light mass of the pion, the singularity is close to the physical region and generates a peaking background

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𝜌1 1600 β†’ 𝜍𝜌 β†’ 𝜌𝜌𝜌

  • A. Pilloni – Experimental motivation for multihadrons on the lattice

The strength of the Deck effect depends on the momentum transferred 𝑒, but the precise estimates rely on the model for the Deck amplitude

(Deck) (Deck)

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Coupled channel 𝜌1 1600 β†’ πœƒ(β€²)𝜌

  • A. Pilloni – Experimental motivation for multihadrons on the lattice

A strong signal is also observed in πœƒ(β€²)𝜌, consistent with the naive expectation for a hybrid meson Having the 3𝜌 β†’ 3𝜌 scattering data from Lattice will allow for a coupled channel analysis unaffected by the Deck effect

PLB740, 303-311

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  • A. Pilloni – Experimental motivation for multihadrons on the lattice
  • A. Rodas, AP et al. (JPAC), to appear
  • Coupled channel analysis of πœƒπœŒ and πœƒβ€²πœŒ almost completed

𝑏2(1320) 𝑏2

β€² (1700)

𝜌1 1400 ? 𝜌1 1600 ?

Coupled channel 𝜌1 1600 β†’ πœƒ(β€²)𝜌

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  • A. Pilloni – Experimental motivation for multihadrons on the lattice

Coupled channel 𝜌1 1600 β†’ πœƒ(β€²)𝜌

Production amplitude Scattering amplitude 𝐸(𝑑) 𝐸(𝑑) 𝑂(𝑑) π‘œ(𝑑)

𝑒(𝑑) = 𝑂 𝑑 𝐸(𝑑)

The 𝐸(𝑑) has only right hand cuts; it contains all the Final State Interactions constrained by unitarity β†’ universal

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  • A. Pilloni – Experimental motivation for multihadrons on the lattice

Coupled channel 𝜌1 1600 β†’ πœƒ(β€²)𝜌

Production amplitude Scattering amplitude 𝐸(𝑑) 𝐸(𝑑) 𝑂(𝑑) π‘œ(𝑑)

𝑒(𝑑) = 𝑂 𝑑 𝐸(𝑑)

The π‘œ 𝑑 , 𝑂(𝑑) have left hand cuts only, process-dependent, smooth Having access to scattering directly can help reducing systematics

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𝑏1 1420 β†’ 𝑔

0 980 𝜌 β†’ 𝜌𝜌𝜌

  • A. Pilloni – Experimental motivation for multihadrons on the lattice

COMPASS claimed the observation of another 𝑏1 at a slightly higher mass

  • Narrower than the 𝑏1(1260)
  • Unexpected in quark model or lattice spectra
  • Only seen in 𝑔

0 980 𝜌

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𝑏1 1420 β†’ 𝑔

0 980 𝜌 β†’ 𝜌𝜌𝜌

  • A. Pilloni – Experimental motivation for multihadrons on the lattice

Mikhasenko, Ketzer, Sarantsev, PRD91, 094015 If that is the case, the strength

  • f the signal would dramatically

depend on the mass of the exchanges: studying the amplitude at different pion/kaon masses will confirm whether this is true It has been proposed that the peak is due to a triangle singularity i.e. a dynamical enhancement generated by rescattering Triangle Breit-Wigner

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A host of unexpected resonances have appeared decaying mostly into charmonium + light Hardly reconciled with usual charmonium interpretation

The heavy sector: XYZ states

  • A. Pilloni – Experimental motivation for multihadrons on the lattice

Esposito, AP, Polosa, Phys.Rept. 668

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  • Discovered in

𝐢 β†’ 𝐿 π‘Œ β†’ 𝐿 𝐾/πœ” 𝜌𝜌

  • Quantum numbers 1++
  • Very close to πΈπΈβˆ— threshold
  • Too narrow for an above-

treshold charmonium

  • Isospin violation too big

Ξ“ π‘Œβ†’πΎ/πœ” πœ• Ξ“ π‘Œβ†’πΎ/πœ” 𝜍 ~0.8 Β± 0.3

  • Mass prediction not

compatible with πœ“π‘‘1(2𝑄)

𝑁 = 3871.68 Β± 0.17 MeV π‘π‘Œ βˆ’ π‘πΈπΈβˆ— = βˆ’3 Β± 192 keV Ξ“ < 1.2 MeV @90% 22

π‘Œ(3872)

  • A. Pilloni – Experimental motivation for multihadrons on the lattice
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π‘Œ(3872)

  • A. Pilloni – Experimental motivation for multihadrons on the lattice

Large prompt production at hadron colliders 𝜏𝐢/πœπ‘ˆπ‘ƒπ‘ˆ = 26.3 Β± 2.3 Β± 1.6 % πœπ‘„π‘† Γ— 𝐢(π‘Œ β†’ 𝐾/πœ”πœŒπœŒ) = 1.06 Β± 0.11 Β± 0.15 nb CMS, JHEP 1304, 154

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π‘Œ(3872) on the lattice

  • A. Pilloni – Experimental motivation for multihadrons on the lattice
  • Three body dynamics 𝐸

𝐸𝜌 may play a role. Playing with lighter charm mass?

  • A full amplitude analysis is missing, and is now mandatory

Prelovsek, Leskovec, PRL111, 192001

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Vector 𝑍 states

Lots of unexpected 𝐾𝑄𝐷 = 1βˆ’βˆ’ states found in ISR/direct production (and nowhere else!) Seen in few final states, mostly 𝐾/πœ” 𝜌𝜌 and πœ” 2𝑇 𝜌𝜌 Not seen decaying into open charm pairs Large HQSS violation

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  • A. Pilloni – Experimental motivation for multihadrons on the lattice

Belle J/πœ”πœŒπœŒ BES β„Žπ‘‘πœŒπœŒ

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𝑍(4260)

  • A. Pilloni – Experimental motivation for multihadrons on the lattice

BESIII, PRL118, 092001 (2017) 𝑓+π‘“βˆ’ β†’ 𝐾/πœ” 𝜌𝜌 𝑓+π‘“βˆ’ β†’ β„Žπ‘‘ 𝜌𝜌 BESIII, PRL118, 092002 (2017) New BESIII data show a peculiar lineshape for the 𝑍(4260), and suggest a state narrower and lighter than in the past The state is mature for a coupled channel analysis (on the lattice?) 𝑓+π‘“βˆ’ β†’ 𝜌+𝐸0πΈβˆ—βˆ’ BESIII, arXiv:1808.02847

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𝑓+π‘“βˆ’ β†’ π‘Žπ‘‘ 3900 +πœŒβˆ’ β†’ 𝐾/πœ” 𝜌+πœŒβˆ’ and β†’ πΈπΈβˆ— +πœŒβˆ’ 𝑁 = 3888.7 Β± 3.4 MeV, Ξ“ = 35 Β± 7 MeV 𝑓+π‘“βˆ’ β†’ π‘Žπ‘‘

β€² 4020 +πœŒβˆ’ β†’ β„Žπ‘‘ 𝜌+πœŒβˆ’ and β†’

πΈβˆ—0πΈβˆ—+πœŒβˆ’ 𝑁 = 4023.9 Β± 2.4 MeV, Ξ“ = 10 Β± 6 MeV

27

Charged π‘Ž states: π‘Žπ‘‘ 3900 , π‘Žπ‘‘

β€²(4020)

In the Dalitz plot projections, two states appear slightly above 𝐸(βˆ—)πΈβˆ— thresholds

  • A. Pilloni – Experimental motivation for multihadrons on the lattice
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Charged π‘Ž states: π‘Žπ‘ 10610 , π‘Žπ‘

β€² (10650)

  • A. Pilloni – Experimental motivation for multihadrons on the lattice

Ξ₯ 5𝑇 β†’ π‘Žπ‘ 10610 +πœŒβˆ’ β†’ Ξ₯ π‘œπ‘‡ 𝜌+πœŒβˆ’, β„Žπ‘ π‘œπ‘„ 𝜌+πœŒβˆ’ and β†’ πΆπΆβˆ— +πœŒβˆ’ 𝑁 = 10607.2 Β± 2.0 MeV, Ξ“ = 18.4 Β± 2.4 MeV Ξ₯ 5𝑇 β†’ π‘Žπ‘

β€² 10650 +πœŒβˆ’ β†’ Ξ₯ π‘œπ‘‡ 𝜌+πœŒβˆ’, β„Žπ‘ π‘œπ‘„ 𝜌+πœŒβˆ’

and β†’ πΆβˆ—0πΆβˆ—+πœŒβˆ’ 𝑁 = 10652.2 Β± 1.5 MeV, Ξ“ = 11.5 Β± 2.2 MeV Anomalous dipion width in Ξ₯ 5𝑇 , 2 orders of magnitude larger than Ξ₯ π‘œπ‘‡ Moreover, observed Ξ₯ 5𝑇 β†’ β„Žπ‘ π‘œπ‘„ 𝜌𝜌 which violates HQSS

2 twin peaks

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π‘Žπ‘‘s on the lattice

  • A. Pilloni – Experimental motivation for multihadrons on the lattice
  • G. Cheung

No calculations have found evidence for a resonance Prelovsek, Leskovec, PLB727, 172-176 HALQCD, PRL117, 242001 HadSpec, JHEP 1711, 033

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One can test different parametrizations of the amplitude, which correspond to different singularities β†’ different natures

Szczepaniak, PLB747, 410 𝑍 𝐸1 𝜌 πΈβˆ— 𝜌 𝐾/πœ” 𝐸

Triangle rescattering, logarithmic branching point (anti)bound state, II/IV sheet pole (Β«moleculeΒ») Resonance, III sheet pole (Β«compact stateΒ»)

Tornqvist, Z.Phys. C61, 525 Swanson, Phys.Rept. 429 Hanhart et al. PRL111, 132003 Maiani et al., PRD71, 014028 Faccini et al., PRD87, 111102 Esposito et al., Phys.Rept. 668

Amplitude analysis for π‘Žπ‘‘(3900)

AP et al. (JPAC), PLB772, 200

  • A. Pilloni – Experimental motivation for multihadrons on the lattice

π‘Žπ‘‘ 3900 ? 𝐸1(2420) 𝑣: 𝐸0(2400) 𝑣: π‘Žπ‘‘ 3900 ? "𝜏, 𝑔

0(980)"

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Amplitude model

π‘Žπ‘‘ 3900 ? 𝐸1(2420) 𝑣: 𝐸0(2400) 𝑣: π‘Žπ‘‘ 3900 ? "𝜏, 𝑔

0(980)"

Khuri-Treiman

  • A. Pilloni – Experimental motivation for multihadrons on the lattice
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Fit: III

  • A. Pilloni – Experimental motivation for multihadrons on the lattice
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Fit: III+tr.

  • A. Pilloni – Experimental motivation for multihadrons on the lattice
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Fit: IV+tr.

  • A. Pilloni – Experimental motivation for multihadrons on the lattice
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Fit: tr.

  • A. Pilloni – Experimental motivation for multihadrons on the lattice
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Fit summary

III+tr. IV+tr. III tr. Data can hardly distinguish these scenarios. Lattice QCD can actually provide the scattering matrix as an input to this analysis

  • A. Pilloni – Experimental motivation for multihadrons on the lattice
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  • A. Pilloni – Experimental motivation for multihadrons on the lattice

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More complicated Dalitz plots

In the reaction 𝑓+π‘“βˆ’ β†’ πœ”β€²πœŒ+πœŒβˆ’, the situation looks even more obscure Data refused to be fitted with any simple model BESIII, PRD96, 032004

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  • A. Pilloni – Experimental motivation for multihadrons on the lattice

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More complicated Dalitz plots

Very complicated Dalitz plots They can all benefit of the knowledge of the underlying 2 β†’ 2 scattering amplitude LHCb, 𝐢 β†’ 𝐿 𝐾/πœ” 𝜚 LHCb, 𝐢 β†’ 𝐿 πœ”β€² 𝜌 LHCb, Λ𝑐 β†’ 𝐿 𝐾/πœ” π‘ž Belle, 𝐢 β†’ 𝐿 πœ“π‘‘1𝜌

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Outlook

  • A. Pilloni – Experimental motivation for multihadrons on the lattice
  • The light sector: the 3𝜌 system
  • The 𝑏1(1260)
  • The hybrid 𝜌1
  • The 𝑏1(1420)
  • The heavy sector: XYZ
  • The π‘Œ(3872) and the 𝑍 states
  • Two-body subchannels: π‘Žπ‘‘s and π‘Žπ‘s
  • Complicated Dalitz plots

Lattice can disentangle the scattering from the production mechanism Three body dynamics AND coupled channels Lattice can provide the 2 β†’ 2 scattering amplitude that can be used as input in the phenomenological models

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BACKUP

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  • A. Pilloni – Experimental motivation for multihadrons on the lattice

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Pole extraction

III+tr. IV+tr. III Not conclusive at this stage

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Pentaquarks!

LHCb, PRL 115, 072001 LHCb, PRL 117, 082003 Quantum numbers 𝐾𝑄 = 3 2

βˆ’

, 5 2

+

  • r 3

2

+

, 5 2

βˆ’

  • r 5

2

+

, 3 2

βˆ’

Opposite parities needed for the interference to correctly describe angular distributions, low mass region contaminated by Ξ›βˆ— (model dependence?) No obvious threshold nearby Two states seen in Λ𝑐 β†’ 𝐾/πœ” π‘ž πΏβˆ’, evidence in Λ𝑐 β†’ 𝐾/πœ” π‘ž πœŒβˆ’ 𝑁1 = 4380 Β± 8 Β± 29 MeV Ξ“

1 = 205 Β± 18 Β± 86 MeV

𝑁2 = 4449.8 Β± 1.7 Β± 2.5 MeV Ξ“2 = 39 Β± 5 Β± 19 MeV

  • A. Pilloni – Experimental motivation for multihadrons on the lattice
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Pentaquarks!

LHCb, PRL 115, 072001 LHCb, PRL 117, 082003 Quantum numbers 𝐾𝑄 = 3 2

βˆ’

, 5 2

+

  • r 3

2

+

, 5 2

βˆ’

  • r 5

2

+

, 3 2

βˆ’

Opposite parities needed for the interference to correctly describe angular distributions, low mass region contaminated by Ξ›βˆ— (model dependence?) No obvious threshold nearby Two states seen in Λ𝑐 β†’ 𝐾/πœ” π‘ž πΏβˆ’, evidence in Λ𝑐 β†’ 𝐾/πœ” π‘ž πœŒβˆ’ 𝑁1 = 4380 Β± 8 Β± 29 MeV Ξ“

1 = 205 Β± 18 Β± 86 MeV

𝑁2 = 4449.8 Β± 1.7 Β± 2.5 MeV Ξ“2 = 39 Β± 5 Β± 19 MeV

  • A. Pilloni – Experimental motivation for multihadrons on the lattice

MC simul.

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Tetraquark: the 𝑑 𝑑𝑑 𝑑 states

Much narrower than LHCb! Look for prompt! Maiani, Polosa and Riquer, PRD 94, 054026

Good description of the spectrum but

  • ne has to assume the axial assignment

for the π‘Œ 4274 to be incorrect (two unresolved states with 0++ and 2++)

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Other beasts

  • A. Pilloni – Experimental motivation for multihadrons on the lattice

π‘Œ(3915), seen in 𝐢 β†’ π‘Œ 𝐿 β†’ 𝐾/πœ” πœ• and 𝛿𝛿 β†’ π‘Œ β†’ 𝐾/πœ” πœ• 𝐾𝑄𝐷 = 0++, candidate for πœ“π‘‘0(2𝑄) But π‘Œ 3915 β†’ 𝐸 𝐸 as expected, and the hyperfine splitting M 2++ βˆ’ M 0++ too small One/two peaks seen in 𝐢 β†’ π‘ŒπΏ β†’ 𝐾/πœ” 𝜚 𝐿, close to threshold

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To exclude any rescattering mechanism, we propose to search the 𝑄

𝑑(4450) state

in photoproduction. Hiller Blin, AP et al. (JPAC), PRD94, 034002

𝑄

𝑑 photoproduction

  • A. Pilloni – Experimental motivation for multihadrons on the lattice

Vector meson dominance relates the radiative width to the hadronic width Hadronic vertex EM vertex Hadronic part

  • 3 independent helicity couplings,

β†’ approx. equal, π‘•πœ‡πœ”,πœ‡π‘žβ€² ∼ 𝑕

  • 𝑕 extracted from total width and (unknown)

branching ratio

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π‘Ÿ π‘Ÿ

Dictionary – Quark model

  • A. Pilloni – Experimental motivation for multihadrons on the lattice

𝑀 = orbital angular momentum 𝑇 = spin π‘Ÿ + π‘Ÿ 𝐾 = total angular momentum = exp. measured spin 𝐽 = isospin = 0 for quarkonia 𝑀 βˆ’ 𝑇 ≀ 𝐾 ≀ 𝑀 + 𝑇 𝑄 = βˆ’1 𝑀+1, 𝐷 = βˆ’1 𝑀+𝑇 𝐻 = βˆ’1 𝑀+𝑇+𝐽

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Charged π‘Ž states: π‘Ž(4430)

π‘Ž 4430 + β†’ πœ”(2𝑇) 𝜌+ 𝐽𝐻𝐾𝑄𝐷 = 1+1+βˆ’ 𝑁 = 4475 Β± 7βˆ’25

+15 MeV

Ξ“ = 172 Β± 13βˆ’34

+37MeV

Far from open charm thresholds If the amplitude is a free complex number, in each bin of π‘›πœ”β€²πœŒβˆ’

2

, the resonant behaviour appears as well

  • A. Pilloni – Experimental motivation for multihadrons on the lattice
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𝑍 4260 β†’ 𝐸𝐸1?

  • A. Pilloni – Experimental motivation for multihadrons on the lattice
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Vector 𝑍 states in BESIII

  • A. Pilloni – Modeling exotic XYZ states

BESIII, 1611.01317 BESIII, 1611.07044 𝑓+π‘“βˆ’ β†’ 𝐾/πœ” 𝜌𝜌 𝑓+π‘“βˆ’ β†’ β„Žπ‘‘ 𝜌𝜌

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Flavored π‘Œ(5568)

  • A. Pilloni – Experimental motivation for multihadrons on the lattice
  • A flavored state seen in 𝐢𝑑

0 𝜌 invariant

mass by D0 (both 𝐢𝑑

0 β†’ 𝐾/πœ” 𝜚

and β†’ πΈπ‘‘πœˆπœ‰),

  • not confermed by LHCb or CMS
  • (different kinematics? Compare differential

distributions) Controversy to be solved

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Hadron Spectroscopy

Molecule Tetraquark Hybrids

𝑲/𝝎 𝝆 𝝆 𝝆

Hadroquarkonium Glueball Meson Baryon

Data Amplitude analysis Properties, Model building

Interpretations on the spectrum leads to understanding fundamental laws of nature

Experiment Lattice QCD

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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

  • A. Pilloni – Experimental motivation for multihadrons on the lattice
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Pole hunting

I sheet II sheet

  • A. Pilloni – Experimental motivation for multihadrons on the lattice

Bound states on the real axis 1st sheet Not-so-bound (virtual) states on the real axis 2nd sheet

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Pole hunting

More complicated structure when more thresholds arise: two sheets for each new threshold

III sheet: usual resonances IV sheet: cusps (virtual states) I sheet II sheet Bound state Virtual state Resonance

  • A. Pilloni – Experimental motivation for multihadrons on the lattice
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𝑓+π‘“βˆ’ β†’ π‘Žπ‘‘ 3900 +πœŒβˆ’ β†’ 𝐾/πœ” 𝜌+πœŒβˆ’ and β†’ πΈπΈβˆ— +πœŒβˆ’ 𝑁 = 3888.7 Β± 3.4 MeV, Ξ“ = 35 Β± 7 MeV

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Example: The charged π‘Žπ‘‘ 3900

A charged charmonium-like resonance has been claimed by BESIII in 2013.

  • A. Pilloni – Experimental motivation for multihadrons on the lattice

Such a state would require a minimal 4q content and would be manifestly exotic

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Amplitude model

π‘Žπ‘‘ 3900 ? 𝐸1(2420) 𝑣: 𝐸0(2400) 𝑣: π‘Žπ‘‘ 3900 ? "𝜏, 𝑔

0(980)"

Khuri-Treiman

  • A. Pilloni – Experimental motivation for multihadrons on the lattice
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Triangle singularity

Szczepaniak, PLB747, 410-416 Szczepaniak, PLB757, 61-64 Guo, Meissner, Wang, Yang PRD92, 071502 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

  • ther channels only!

𝑍(4260) 𝐸1 𝜌 πΈβˆ— 𝜌 𝐾/πœ” 𝐸

  • A. Pilloni – Experimental motivation for multihadrons on the lattice
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Testing scenarios

The scattering matrix is parametrized as π‘’βˆ’1 π‘—π‘˜ = πΏπ‘—π‘˜ βˆ’ 𝑗 πœπ‘— πœ€π‘—π‘˜ Four different scenarios considered:

  • Β«IIIΒ»: the K matrix is

𝑕𝑗 π‘•π‘˜ 𝑁2βˆ’π‘‘, this generates a pole in the closest unphysical sheet

the rescattering integral is set to zero

  • Β«III+tr.Β»: same, but with the correct value of the rescattering integral
  • Β«IV+tr.Β»: the K matrix is constant, this generates a pole in the IV sheet
  • Β«tr.Β»: same, but the pole is pushed far away by adding a penalty in the πœ“2
  • A. Pilloni – Experimental motivation for multihadrons on the lattice
  • 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

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Singularities and lineshapes

Triangle IV sheet pole Triangle III sheet pole Triangle no pole Different lineshapes according to different singularities III+tr. IV+tr. tr.

  • A. Pilloni – Experimental motivation for multihadrons on the lattice
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Guerrieri, AP, Piccinini, Polosa, IJMPA 30, 1530002

  • A. Pilloni – Experimental motivation for multihadrons on the lattice