new cascade physics program

New Cascade Physics New Cascade Physics ProgramProgram

Yongseok Oh(Univ. of Georgia)

With K. Nakayama (UGA) & H. Haberzettl (GWU)

Cascade Physics Working group: B. Nefkens et al.

Quarks, Nuclei and Universe, Nov. 2006 Yongseok Oh 3UGA

Contents Contents

1. Motivation2. Experiments3. Theories4. Photoproduction process5. Outlook


1. Motivation1. Motivation

Characters of the X hyperons strangeness = -2, baryon number = 1, and isospin = 1/2 Narrow widths: G(X*)/G(N* or D*) ~ 1/10 for pionic decays

G is proportioanl to (# of light quarks)2 Riska, EPJA 17 (2003) Insignificant sea quark contributions to hyperons

Decay Gexp Ratioexp(# of light quark)2

DNp 120 12 9

S*Sp 40 4 4

X*Xp 10 1 1

Decuplet octet + p

expected to have larger effects for excited states

from J. Price


Why Why XX ? ?

What do we know about X baryons? If flavor SU(3) symmetry is exact for the classification of all particles, then

we have N(X) = N(N*) + N(D*) Currently, only a dozen of X have been identified so far.

(cf. more than 20 N*s & more than 20 D*s) Only X(1318) and X(1530) have four-star status. (cf. the rating is based on

the clearness of the peak.) Even the quantum numbers of most X resonances are still to be identified:

practically, no meaningful information for the X resonances.

Particle Data Group (2006)


Advantages Advantages

Easy identification Small decay widths Identifiable in a missing mass plot, e.g.,

missing mass m(K+K+) in + p K+ + K+ + X,invariant mass of decay products such as X p L

Background is less complicated. (+ p K+ + K+ + X* K+ + K+ + p + Xgs)

Isospin ½ (cf. nucleonic resonances have N* & D*; =1/2 and 3/2) No flavor singlet state (unlike L hyperons)

What can we learn from it? Baryon structure from X spectroscopy Properties of S=-1 resonances Exotic particles (penta-quarks & tetra-quarks) New particles (perhaps S=-4 dibaryon?)


Exotic Exotic XX(1860) or (1860) or (1860)(1860)

Isospin-3/2 state: therefore, penta-quark exoticReport from NA49 in pp collision PRL 92 (2004) but never be confirmed by other experiments with higher statistics,

e.g. WA89 in S--nucleus collisions, PRC 70 (2004)(no signal of X(1860) with the 40-year accumulation of Xp spectra)

NA49 WA89


2. Experiments 2. Experiments

Difficulties in searching for X*

Mostly processes through Kp reactions or the S-hyperon induced reactions were used. (initial state has S=-1) No current activity in X physics with hadron beams

They can only produced via indirect processes from the nucleon. (initial state has S=0) In the case of photon-nucleon reaction, we have at least three-body final st

ate. The current CLAS data indicate that the production cross section is less th

an 20 nb at low energies. (cf. KL or KS photoproduction have cross sections of order of a few mb).

Other technical difficulties

Questions What is the third lowest state following X(1320) and X(1530)? Can we confirm the existence of X(1620)?


Earlier experimentsEarlier experiments

WA89 results with S- beam (hep-ex/0406077)

Comments by PDG (2006)

1530 1690 1860(?)


Recent activityRecent activity

CLAS at JLab: initiated new Cascade physics programphotoproduction processes: p K K XMore data with higher statistics are under analyses.

PRC 71 (2005) CLAS preprint (2006)

g6b

g6a


3. Theories 3. Theories

Review on the works before 1975Samlos, Goldberg, and Meadows, Rev. Mod. Phys. 46 (1974) 49

What is the first excited state following X(1320) and X(1530)? What is X(1690)? Even the parity of the ground state X was not directly measured. Model predictions for the X spectrum are needed.Most model builders have not considered X spectrum or the structure of X resonances seriously, except the lowest X’s of octet and decuplet.


Quark model (One-gluon-exchange model)Quark model (One-gluon-exchange model)

Non-relativistic quark model Chao, Isgur, Karl, PRD 23 (1981)Chao, Isgur, Karl, PRD 23 (1981)

First order perturbation calculation in anharmonic terms (linear, Coulomb) and in hyperfine interactions.

from S. Capstick

X(1690) has JP=1/2+ ?

The first negative parity state appears at ~1800 MeV.

Decay widths are not fully calculated by limiting the final state. (but indicates narrow widths)

Relativistic quark model ?


One-boson-exchange model One-boson-exchange model Glozman, Riska, Phys. Rep. 268 (1996)Glozman, Riska, Phys. Rep. 268 (1996)

Exchange of octet pseudoscalar mesons. First order perturbation calculation around harmonic oscillator

spectrum.

Negative parity state seems to have lower mass: but no clear separation between +ve and –ve parity states

Strong decay widths are not calculated.


Comparison of OGE and OBEComparison of OGE and OBE

The two models show very different X hyperon spectrum.The predictions on the candidate for X(1690) are different.


Improved OBE modelImproved OBE model

Semi-relativistic OBE model Glozman et al., PRD 58 (1998)

OBE + OGE Valcarce, Garcilazo, Vijande, PRC 72 (2005)

Glozman et al. Valcarce et al.MN


1/N1/Ncc (constituent quark model) (constituent quark model)

Expand the mass operator by 1/Nc expansion

Basically O(3) X SU(6) quark modelMass formula (e.g. 70-plet: L=1, p=-1)

Fit the coefficients to the known particle masses and then predict.

11 3

0 1

ˆ ˆn n n n

n m

c d

M O B

from J.L. Goity

Where is X(1690)?

Schat, Scoccola, Goity, PRL 88 (2002) and other groups


QCD sum rulesQCD sum rules

Mass splitting between 1/2+ and1/2- baryons. Jido & Oka, hep-ph/9611322 (unpublished) Interpolating field (with a parameter t)

X(1/2+) = 1320 MeV and X(1/2-) = 1630 MeV. So, X(1690) would be X(1/2-).

Sum rules for 1/2+, 1/2-, and 3/2-. F.X. Lee & X. Liu, PRD 66 (2002) Three-parameter calculation (similar interpolating field)

X(1/2+) = 1320 MeV, X(1/2-) = 1550 MeV, X(3/2-) = 1840 MeV (exp. 1820 MeV)

X(1820) is well reproduced, but where is X(1690)?

5 5( ) ( ) ( ) ( ) ( ) ( )abc a b c a b cJ s x Cd x s x t s x C d x s x


Other hadron modelsOther hadron models

No rigorous calculation for X spectrum was done in other hadron models in the market. NJL model, Skyrme model, bag models(?), …

This is a good place to test and improve hadron models.Various model calculations are highly desirable.


Lattice calculationLattice calculation F.X. Lee et al., Nucl. Phys. B (PS) 119 (2003)F.X. Lee et al., Nucl. Phys. B (PS) 119 (2003)

Quenched approx. with Bayesian statisticsLevel cross-over in the physical region?Results for 1/2+ and 1/2- statesHigher-spin states?


Lattice calculation Lattice calculation Bern-Graz-Regensburg Coll., PRD 74 Bern-Graz-Regensburg Coll., PRD 74 (2006)(2006)

Quenched approx. (variational method)The first excited state seems to have negative parity.Higher-spin states?

X octet with J = 1/2


S=-4 dibaryon?S=-4 dibaryon?

A new dibaryon (possibly at JLab & J-PARC)Feasibility of an 1S0 di-Cascade bound state? A simple estimate G.A. Miller, nucl-th/0607006 Both NN and XX are in the same 27-plet representation of SU(3).

N and X iso-doublets occupy analogous positions. Use 4-point interactions (meson-exchange is ignored)

Invariant under NN XX Maybe good for 1S0

0

0

0

2 6

2 6

2

3

p

B n


di-Cascadedi-Cascade

NR Schroedinger equation with a potential whose parameters are fixed by n-n/p-p or n-p system. Square well potential, non-local separable potential, delta-shell po

tential. Obtained results for XX system

Scattering length: 8~11 fm Binding energy: 0.5 ~ 7.5 MeV

Deuteron binding energy ~ 2.2 MeV With Nijmegen potential (6 versions of it) Binding energy: 0.1 ~ 16 MeV

Suggests the existence of a XX bound state.Needs other model predictions.Possible reactions: D (JLab) or KD (J-PARC)


4. Photoproduction4. Photoproduction

CLAS at JLab succeeded to produce X by photon-induced reactions. So far, only a few inclusive X photoproduction were reported. Tag

ged Photon Spectrometer Collab., NPB 282 (1987)

No theoretical work on X photoproduction Except one for pentaquark X photoproduction Liu, Ko, PRC 69 (2004)

Our strategy Investigate the production mechanism using the currently availabl

e information only. Then consider other possible (and important) mechanisms. Final-state interactions & coupled channel?

Ideal, but practically impossible at this stage. Use the tree-level approximation as the first attempt to understand th

e production mechanism.

Nakayama, Oh, HaberzettlNakayama, Oh, HaberzettlPRC 74 (2006) 035205PRC 74 (2006) 035205


Forbidden or suppressed mechanismsForbidden or suppressed mechanisms

In kaon—anti-kaon production , meson production processes, especially f meson production, are important.In X photoproduction, such processes are suppressed since the produced meson should be exo

tic having strangeness S=+2 in order to decay into two kaons. By the same reason, t-channel meson-exchange for KN KX is also suppr

essed as the exchange meson should have S=+2.

E: exotic meson with S=+2

N K K N( )


Considered diagramsConsidered diagrams

Consider K and K* exchange only. Axial-vector K1 mesons: lack of information

& heavy mass Scalar k or K0 mesons: not allowed since k

K coupling is forbidden by angular momentum and parity conservation.

Consider N’ = N and D Y, Y’ = low-lying L and S hyperons X’ = X(1320) and X(1530)

+ exchanged diagrams q1 q2


Strategy Strategy

Problems There are many hyperon resonances of S=-1, which can

contribute to the production process. We start with a very simple model for the production

mechanism by choosing only a few intermediate hyperon states.


Intermediate hyperonsIntermediate hyperons

Particle Data Group

Decay widths and couplings are in a very wide range. No information for the other couplings.


Strategy Strategy

Problems There are many hyperon resonances of S=-1, which can contribute

to the production process. We start with a very simple model for the production mechanism b

y choosing only a few intermediate hyperon states.

Lots of unknown coupling constants and ambiguities. We make use of the experimental (PDG) or empirical data (like Nij

megen potential) if available. Or we use model predictions for the unknowns: SU(3) relations, qu

ark model, ChPT, Skyrme model, chiral quark model etc. The details are in nucl-th/0605169.

Preliminary CLAS data (of Weygand and Guo) The total cross sections data (hep-ex/0601011) is used to determine

the cutoff parameter of the form factors.


Model (A)Model (A)

First, consider only the low mass hyperons:L(1116), L(1405), L(1520), S(1190), S(1385) Their couplings are rather well-known.

The cross sections for the two non-identical kaon productions are larger than those for two identical kaon productions: isospin factors

The dominant contribution to p K+K+X- comes from the spin-1/2 hyperon resonances.

spin-1/2baryons

spin-3/2baryons


Invariant mass distributionsInvariant mass distributions

Invariant mass distributions of K+X- and K+K+. No structure for K+K+ distribution as expected: absence of S=+2 exotic mes

ons in this calculation. No structure for K+X-distribution since we are considering the low-lying hype

rons only whose masses are below 1.6 GeV, while the minimum value for m(K+X-) is > 1.8 GeV

pv coupling ps coupling


Higher-mass resonancesHigher-mass resonances

As the K+X-mass distribution covers the energy larger than 1.8 GeV, it is natural to expect important role from the higher-mass hyperon resonances around 1.8 GeV and above. The properties of higher-mass hyperons are poorly known.We first consider the hyperons of spin-1/2 and 3/2 only.What we know are The broad range of the NYK couplings: from (YNK) of PDG The photoproduction amplitudes at the hyperon on-shell point have

So 1/2 and 3/2+ hyperon resonances around M = 1.8 GeV are expected to be important.

1/ 2 3/ 2

,Y N Y Y N YM m m m m M m m m m


Intermediate hyperonsIntermediate hyperons

Particle Data Group

Decay widths and couplings are in a very wide range. No information for the other couplings.


Model (B)Model (B)

Assumptions. In order to reduce the number of unknown couplings, we consider

two hyperon resonances only, L(1800)1/2 and L(1890)3/2+ in addition to the low mass hyperons.

Neglect their magnetic moments and radiative transitions. Then the only unknown is the product of the coupling constants, g

NLKgXLK. We take gNLKgXLK = 2 for simplicity.

Form factors are readjusted to fit the total cross section data.


Results (I)Results (I)

Total cross sections

Nearly the same results as before.

total cross section alone cannot distinguish the contributions from the low-mass and the high-mass resonances.

Other quantities should be measured.

Spin -1/2

Spin -3/2


Results (II)Results (II)

Invariant mass distributions of K+X and K+K+. No structure for K+K+ distribution as before. Two bump structure for K+X-distribution is seen.

L(1800) bump cannot be seen.: below thresholdThe first bump at lower mass is due to L(1890).The second bump is not from a resonance at higher mass.

» The position depends on the energy. » So-called kinematic reflections of the three-body final states.


Model (C)Model (C)

What happens if we have (unknown) hyperon resonance at a mass around 2 GeV which couples strongly enough to the nucleon and X?In fact, the preliminary CLAS data do not show a sharp peak in K+X channel.Some well-established L and S resonances of spin-5/2 and 7/2 at around 2 GeV.Consider a fictitious spin-3/2+ hyperon at around 2 GeV, so we consider three high-mass resonances in addition to the low-lying resonances.L(1800)1/2, L(1890)3/2+, and L(2050)3/2+ (fictitious particle)Adjust the parameters so that we have similar total cross sections.


Results (IV)Results (IV)

But we have very different K+X invariant mass distribution. The bump structure disappears. The valley between the two peaks is now filled up by the additional reson

ance. This shows that the higher-mass resonance at around 2 GeV should be exami

ned.


5. Outlook 5. Outlook

CLAS at JLab initiated Cascade Physics Program. Opens the door to many avenues of research for X

hyperons.

More data are coming! Does X(1620) exist? Should confirm other X resonances in PDG.

Role of L and S resonances in X photoproduction. Offers a chance to study those hyperons. Higher mass and high spin resonances: under progress

Theoretical models for X spectrum Only a few model gives the X spectrum. Where is the low-lying X resonances? Possible di-baryon? Etc …


Cascade Physics Working GroupCascade Physics Working Group

Members

B. Nefkens, D.S. Carman, S. Capstick, J.L. Goity, L. Guo, H. Haberzettl, N. Marthur, K. Nakayama, Y. Oh, J. Price, D.G. Richards, S. Stepanyan, D.P. Weygand, and more.

new cascade physics program

Documents

x physics

x resonances

x spectrum

structure of x

priceugawhy x

x hyperonsstrangeness

x baryons

dozen of x