Hadronic Resonances

Evgeni Kolomeitsev, Matej Bel University

ResonancesResonances

Scattering,K-matrix, PWA

Scattering,K-matrix, PWA

PentaquarkPentaquark

QCDQCD

HadrogenesisHadrogenesis

Particle Data Group publishes every two years Review of Particles Physics.

The main part of review is devoted to the Particle Properties Tables. Their current form stems directly from a 1957 article in the Annual review of nuclear science, by Gell-Mann and Rosenfeld.

Till 1963 the data surveys were provided by two periodic compilations: Univ. of California Radiation Lab. Report UCRL-8030 by Barkas and Rosenfeld (Rosenfeld’s Tables) and by Matts Roos from NORDITA. As Roos saw the Rosenfeld et al.'s computerized draft of the 1964 edition, he suggested combining efforts.

There were only 27 pages!

Rev. Mod. Phys. 36 (1965) 977

Review of Particle Physics 2004:

• 53 authors + 97 additional contributors• more than 1000 pages

Mesons Baryons

C=B=0 72+28(s) 44+59(s)

C,B=1 22 17C,B=2 28 1

Total: 150 123

6 quark, 4 gauge bosons

QCD is trying to explain 273 hadronic states in terms of u,d,s,c,b quarks

• electrons, protons and neutrons

All others particles only on photographs

• pions

K-

-

e+ e+ e-

e-

• kaons

0

lead sheet

+

+

+

-

-

-

-

K- +

K-

• hyperons

n

n

• - hyperons

-

K+

K-

-

-

e-

e-

e+

e+

K0 0

p

• D mesons

2 mm

D0

D+

Resonaneces live too short 10-24 s to be seen on photographs

first subatomic resonance seen at BNL in 1953 in N ! N reaction

The graph was drawn by Luke Yuan who with colleague Sam Lindenbaum, made the discovery.

Excite !

Resonance measurement at home

geometry and elastisitydefine a resonating eigenmode

resonating system

Listen and enjoy!

Target

Detector

phase shift

partial wave amplitudes

Non-relativistic resonance scattering

[K. Peräjärvi et al, Phys. Rev. C 74, 024306 (2006)]

suppression of outgoing wave

@wave function in 11C+p

Re T

Im T

22

1

N (1220MeV)

N (1534MeV)

Manley, Saleski, PRD 45, 4002

momentum can be precisely measured only at t->1

momentum can be precisely measured only at t->1

coordinate of a relativistic particle has no meaning

coordinate of a relativistic particle has no meaning

Zeitschrift für Physik 69

interaction zonefree particles free particles

introduced by J.A. Wheeler Phys. Rev. 52 (1937) 1107

interaction vanishes at §1

reaction amplitude

scattered wave function

Transition probability in the unit of time:

discrete spectrum

continous spectrum

smooth function of energy

Conservation of probability

for scattering amplitude on the energy shell

Breit-Wigner amplitude

Re T

Im T1

phase shift goes th

rough /2

anticlockwise arcs

pronounced peaks in cross sectionsRe T=0 and Im T peaks

Valid for narrow and isolated resonance!

K is real and symmetric and can be diagonalized by the an orthogonal transformation. T and S=1+2iT are diagonalized by the same transformation.

resonance in channel a :

resonance in channel a :

partial widths in incoming

and outgoing channels

background

Background (non-resonant) part distorts a resonance signalBackground (non-resonant) part distorts a resonance signal

Reliable identification of the resonance becomes artReliable identification of the resonance becomes art

NN

resonances listed in PDGresonances listed in PDG

Arndt, SP06

N (I=0)N (I=0)

Giacomelli, NPB 71, 138 Giacomelli (74)

Martin (75)

THEORY IS NEEDED

But how to build hadrons out of quarks?But how to build hadrons out of quarks?

Portrait gallery of the Nucleon

© Ed Shuryak NPA 606

quark modelbag model

chiral bag

Skyrmion

Excitations?

What is a suitable language for the description of hadronic states?

Weinberg's Third Law of Progress in Theoretical Physics

You may use any degrees of freedom you like to describe a physical system, but if you use the wrong ones, you'll be sorry!

Weinberg's Third Law of Progress in Theoretical Physics

You may use any degrees of freedom you like to describe a physical system, but if you use the wrong ones, you'll be sorry!

production

final state interactions!

scattering

Resonances are seen through their decay products

in reactions resonance

mass shift

+

open the closed system

width analiticity

fluctuations: closed channel dynamics

mass shift due to coupling to closed channels

U. Fano, Phys. Rev. 124 (1961) 1866

+ background

effective kernel: smooth dependence on energy s1/2

the heavier channel, the less attraction we need

Lippmann-Schwinger, Bethe-Salpeter equationattractive potential generates a bound state

dialing the interaction one can always generate a resonance in one channel

“3 quark bound states” are seen on the Lattice

Bern-Graz-Regensburg Collab. PRD 74

unquenching = let quarks fluctuate!open questions: extrapolation to small quark masses

hadron loops

mass shift can be substential

Morel, Capstick, nucl-th/0204014

physical mass

bare potential from quark model

Found. Phys. 31 (2001)

known from mid 60s(1405), N(1535),…

to be tested

Phys.Lett. B582,49; Phys. Lett. B585, 243

[10]

[10]

[10]

[10]

[8]

[8]

[8]

[8]

[27]?

f0(980), …

to be tested

Nucl. Phys A730, 392

beyond quark model

Phys. Lett. B582, 39similar pattern in 1+ spectrum shifted by 140 MeV

Resonances are “seen” in reactions, i.e, only when they couple to some initial and final states

“Final state interaction” can be strong and can “generate” the resonance

Hadrogenesis conjecture:

Hadronic resonances can be constructed from lowest 0-, 1-, and 1/2+, 3/2+ states

Chiral SU(3) at leading order: parameter-free prediction for baryon and meson resonances in light and heavy-light quark sectors

Chiral SU(3) at leading order: parameter-free prediction for baryon and meson resonances in light and heavy-light quark sectors

Meson-nucleon scatteringMeson-nucleon scattering

Q:

Q2 :

Q3 :

Nucl. Phys. A700 (2002) 193

Nucl. Phys. A700 (2002) 193

Nucl. Phys. A700 (2002) 193