Hadron excitations as resonant particles in hadron reactions

  • Slides: 16
Download presentation
Hadron excitations as resonant particles in hadron reactions Hiroyuki Kamano (RCNP, Osaka Univ. )

Hadron excitations as resonant particles in hadron reactions Hiroyuki Kamano (RCNP, Osaka Univ. ) Crossover workshop@Nagoya U. , July 12 -13, 2012

Introduction: Hadron spectrum and reaction dynamics ü Various static hadron models have been proposed

Introduction: Hadron spectrum and reaction dynamics ü Various static hadron models have been proposed to calculate hadron spectrum and form factors. Ø Quark models, Bag models, Dyson-Schwinger approaches, Holographic QCD, … Ø Excited hadrons are treated as stable particles. The resulting masses are real. ü In reality, excited hadrons are “unstable” and can exist “molecule-like” states only as resonance states in hadron reactions. “Mass” becomes complex !! “pole mass” u u d core (bare state) + meson cloud Constituent quark model resonance bare state meson cloud

Definitions of hadron parameters Definitions of ü Masses (spectrum) of hadrons Pole positions of

Definitions of hadron parameters Definitions of ü Masses (spectrum) of hadrons Pole positions of the amplitudes ü Coupling constants of hadrons Residues 1/2 at the pole Decay vertex Consistent with the resonance theory based on Gamow vectors G. Gamow (1928), R. E. Peierls (1959), … A brief introduction of Gamov vectors: de la Madrid et al, quant-ph/0201091 (complex) energy eigenvalues transition matrix elements = = pole values pole position 1/2 of ( Im(E 0 )poles (residue) the 0) =<

) (E Im Resonance pole in complex-E plane and peak in cross section (Breit-Wigner

) (E Im Resonance pole in complex-E plane and peak in cross section (Breit-Wigner formula) Cross section σ ~ |T|2 Conditions: ü Pole is isolated. ü Small background. ü Amplitudes between the pole and real energy axis are analytic. Re (E )

f 0(980) in pi-pi scattering π π From M. Pennington’s talk f 0 (980)

f 0(980) in pi-pi scattering π π From M. Pennington’s talk f 0 (980) π σ (ππ ππ) π f 0 (980) Im(E) (Ge. V) 0. 4 0. 8 1. 2 ~ 980 – 70 i (Me. V) 1. 6 ? Re(E) (Ge. V)

Multi-layer structure of the scattering amplitudes e. g. ) single-channel two-body scattering physical sheet

Multi-layer structure of the scattering amplitudes e. g. ) single-channel two-body scattering physical sheet Scattering amplitude is a double-valued function of complex E !! Essentially, same analytic structure as square-root function: f(E) = (E – Eth)1/2 unphysical sheet Im (E) Re(E) + iε =“physical world” 0 × Eth (branch point) Re (E) × 0 Eth × (branch point) × Re (E)

f 0(980) in pi-pi scattering, Cont’d f 0(980) is barely contributed f 0(980) pole

f 0(980) in pi-pi scattering, Cont’d f 0(980) is barely contributed f 0(980) pole CANNOT produce a “clean” peak in the cross section because of discontinuity induced by KK channel !! Relations + Im (E ) Not only the resonance poles, but also the KK analytic structure of the scattering amplitudes in the complex E-plane plays. Re a crucial role (E) f for the shape of cross sections on the real energy axis (=ofreal world) !! Just slope the peak requires “clean” peak in cross section. f 0(980) produced by f 0(980) pole is seen. This is the reason why we need the third condition: “Amplitudes between the pole and real energy axis are analytic. ” ππ unphysical & KK physical sheet KK ππ unphysical & KK unphysical sheet

Delta(1232) : The 1 st P 33 resonance Suzuki, Julia-Diaz, Kamano, Lee, Matsuyama, Sato,

Delta(1232) : The 1 st P 33 resonance Suzuki, Julia-Diaz, Kamano, Lee, Matsuyama, Sato, PRL 104 065203 (2010) Complex E-plane (E ) P 33 Im Im (T) Real energy axis “physical world” p. N physical & p. D physical sheet p. N Re (E) p. D 1211 -50 i ü Small background ü Isolated pole ü Simple analytic structure E-plane p. N unphysicalof&the p. D complex unphysical sheet p. N unphysical & p. D physical sheet In this case, BW mass & width can be a good approximation of the pole position. pole BW 1211 , 50 1232 , 118/2=59 Riemann-sheet for other channels: (h. N, r. N, s. N) = (-, p, -)

Two-pole structure of the Roper P 11(1440) Suzuki, Julia-Diaz, Kamano, Lee, Matsuyama, Sato, PRL

Two-pole structure of the Roper P 11(1440) Suzuki, Julia-Diaz, Kamano, Lee, Matsuyama, Sato, PRL 104 065203 (2010) Complex E-plane Im (E ) P 11 Re (T) Real energy axis pole A: D unphys. sheet p. N physical & p. D physical sheet “physical world” Two-pole structure of the Roper is found pole B: D phys. sheet from several groups, on the basis of completely different approaches: p. N Im (T) Re (E) Pole A cannot generate a resonance shape on “physical” real E axis. 1356 -78 i p. D A 1364 -105 i B p. N unphysical & p. D physical sheet In this case, BW mass & width has NO clear relation with the resonance poles: Two 1356 , 78 poles 1364 , 105 D branch point prevents pole B from generating a resonance shape on “physical” real E axis. p. N unphysical & p. D unphysical sheet BW ? 1440 , 300/2 = 150 Riemann-sheet for other channels: (h. N, r. N, s. N) = (p, p, p)

Dynamical origin of nucleon resonances Suzuki, Julia-Diaz, Kamano, Lee, Matsuyama, Sato, PRL 104 065203

Dynamical origin of nucleon resonances Suzuki, Julia-Diaz, Kamano, Lee, Matsuyama, Sato, PRL 104 065203 (2010) Corresponds to hadrons of static hadron models Pole positions and dynamical origin of P 11 resonances Multi-channel reactions can generate many resonance poles from a single bare state !! Eden, Taylor, Phys. Rev. 133 B 1575 (1964) For evidences in hadron and nuclear physics, see e. g. , in Morgan and Pennington, PRL 59 2818 (1987)

Summary ü Analytic structure of the scattering amplitudes plays crucial role in the extraction

Summary ü Analytic structure of the scattering amplitudes plays crucial role in the extraction of resonance parameters (mass, width, …) from the data. Ø Shape of cross sections depend not only on resonance poles but also the analytic structure of the amplitudes in the complex E-plane. Ø Breit-Wigner formula sometimes (often? ) fails to describe resonance parameters, particularly in the light hadron spectroscopy. ü Non-trivial multichannel reaction dynamics in hadron spectroscopy Ø Naïve one-to-one correspondence between physical resonances and static hadrons does not exist in general, regardless of the existence of molecule-like states. Ø Reaction dynamics can produce sizable mass shift.

back up

back up

N-N* transition form factors at resonance poles Extracted from analyzing the p(e, e’ )N

N-N* transition form factors at resonance poles Extracted from analyzing the p(e, e’ )N data (~ 20000) from CLAS Nucleon - 1 st D 13 e. m. transition form factors Coupling to meson-baryon continuum states makes N* form factors complex !! Fundamental nature of resonant particles (decaying states) Real part Imaginary part Julia-Diaz, Kamano, Lee, Matsuyama, Sato, Suzuki PRC 80 025207 (2009) Suzuki, Sato, Lee, PRC 82 045206 (2010)

Meson cloud effect in gamma N N* form factors GM(Q 2) for g N

Meson cloud effect in gamma N N* form factors GM(Q 2) for g N D (1232) transition N, N* Full Bare Note: Most of the available static hadron models give GM(Q 2) close to “Bare” form factor.

g N D(1232) form factors compared with Lattice QCD data ours

g N D(1232) form factors compared with Lattice QCD data ours

A clue how to connect with static hadron models g p Roper e. m.

A clue how to connect with static hadron models g p Roper e. m. transition “Static” form factor from DSE-model calculation. (C. Roberts et al) “Bare” form factor determined from our DCC analysis.