Yongseok Oh Kyungpook National University

Dense 2011, YITP, Kyoto Apr. 19, 2011

Contents

1.  Introduction 2.  Models for hyperon spectrum 3.  Bound state approach to the Skyrme model 4.  Heavy quark baryons 5.  Production process 6.  Outlook

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! p! K +K +"#

INTRODUCTION

I

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Introduction

¤  Baryons with S = -2 ¥  qss (q: light u/d quark) è baryon number = 1, isospin = ½ ¥  Named Ξ

¤  Baryons with S = -3 ¥  sss è baryon number = 1, isospin = 0 ¥  Named Ω

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SU(3) baryons

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Baryon octet Baryon decuplet

Baryons: made of three quarks (!!!)

10881333 ⊕⊕⊕=⊗⊗ :flavor 23

21

21

21

21 ,:spin =⊕⊕ ⨁  "

J P =1 2+ J P = 3 2+

Ξ spectrum

¤  Ξ spectrum ¥  If flavor SU(3) symmetry is good for the classification of hyperon

resonances, then we have ¥  Currently, only a dozen of Ξ baryons have been identified so far.

(cf. more than 20 N* and more than 20 Δ*)

¤  In PDG

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N(!*) = N(N*)+ N(!*)

P is not directly measured

Cf. Spin of Ω- (=3/2) was confirmed only recently

by BaBar Collab. PRL 97 (2006)

Ξ spectrum

¤  Only Ξ(1318) and Ξ(1530) are four-star rated. ¤  Only three states with known spin-parity

¥  The quantum numbers of the other states should be identified.

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Advantages

Difficulties

•  Small decay widths •  Identifiable in missing mass plots •  Isospin is 1/2.

(↔ nonstrange sector: #=1/2 and 3/2) •  No flavor singlet state (unlike Λ hyperons)

•  In most cases, initial state has been used à no hadron beams for Ξ physics

•  With initial state, §  3-body final states at least §  cross section is very small ~ §  other technical difficulties PDG 2010

nb

Ξ spectrum

¤  No meaningful information for Ξ resonances since 1990s ¥  It can open a new window for studying hadron structure.

¦  Baryon structure from Ξ spectroscopy ¦  Properties of S=-1 hyperons (in production mechanisms) ¦  New particles

¤  Recent experiments

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WA89 (CERN-SPS) EPJC, 11 (1999), hep-ex/0406077

1690 Σ--nucleus collisions

CLAS @ JLab

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PRC 71 (2005) PRC 76 (2007)

Questions

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PDG 2008

The 3rd lowest state

1.  Does Ξ(1620) really exist? 2.  Ξ(1620) or Ξ(1690)?

Most recent report on Ξ(1620): NPB 189 (1981) 3.  What are their spin-parity quantum numbers?

↔ comparison with theoretical predictions

Ξ(1530)

CLAS: PRC 76 (2007)

1690  ?

BaBar: JP of Ξ(1690) is ½- PRD 78 (2008)

1620 ?

MODELS FOR HYPERON SPECTRUM

II

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Models

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•  Classify the states as members of octet or decuplet •  Use spin-parity (if known) and Gell-Mann—Okubo mass relation

•  Works before 1975: reviewed by Samlos, Goldberg, Meadows RMP 46 (1974)

•  Recent work along this line Guzey & Polyakov, hep-ph/0512355 (2005)

•  No dynamics

Direct extension of the classification in the quark model

•  Most parameters of models are fixed by the $=0 and $=−1  sector à in principle, no free parameter for the $=−2,  −3

•  Most models give (almost) correct masses for %(1318) and %(1530) ü  Requirement to survive ü  SU(3) group structure

•  But they give very different spectrum for the excited % states!

Hadron models for Ξ baryons

Nonrelativistic quark model

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Chao, Isgur, Karl PRD 23 (1981)

from S. Capstick

The 3rd lowest state at 1695 MeV?

•  Ξ(1690)*** has JP = 1/2+? •  The first negative parity state

appears at ~1800 MeV •  Decay widths are not fully calculated

because of the limited final states (but indicates narrow widths)

Relativistic quark model

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Capstick, Isgur PRD 34 (1986)

from S. Capstick

The 3rd lowest state at 1750 MeV?

NRQM

•  Negative parity states have lower masses

•  The third lowest state has JP = 1/2- at ~1750 MeV

•  Where is Ξ(1690)?

One-boson exchange model

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Glozman, Riska Phys. Rep 268 (1996)

from S. Capstick

Negative states have lower mass

•  Degeneracy pattern appears

•  No clear separation between (+) and (–) parity states

•  Where is %(1690)?

The 3rd lowest state at 1760 MeV ?

Large NC (constituent quark model)

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•  Based on quark model •  Expand the mass operator by expansion •  Mass formula (e.g. 70-plet)

•  Fit the coefficients to the known masses and predict.

Large NC quark model

M = cnOnn=0

11

! + dnBnn=1

3

!

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The 3rd lowest state at 1780 MeV?

from J.L. Goity

•  Where is %(1690)?

Model dependence (mass spectrum)

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QM (Pervin, Roberts)

1325 1891 2014

PRC 75

1520 1934 2020 1725 1811 1759 1826

1820 (expt.)

1320 (expt.)

1530 (expt.)

: the 3rd lowest state

Summary

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•  The predicted masses for the third lowest state are higher than 1690 MeV (except NRQM)

•  How to describe %(1690)?

•  The presence of %(1620) is puzzling, if it exits.

Highly model-dependent !

Cf. similar problem in QM: Λ(1405)

BOUND STATE APPROACH TO THE SKYRME MODEL

III

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Skyrme model

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bound kaon

SU(3) is badly broken

Treat light flavors and strangeness on the different footing

L = LSU(2) + LK/K*

Soliton provides background potential which traps K/K* (or heavy) meson

Bound state approach (Callan, Klebanov)

Anomaly terms (i)  Push up the state

to the continuum } no bound state

(ii)  Pull down the state below the threshold } bound state } give hyperons

Bound state model

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•  Renders two bound states with negative strangeness Ø  p-wave: lowest state Ø  s-wave: excited state

•  After quantization

Ø  p-wave: positive parity hyperons Λ(1116) Ø  s-wave: negative parity hyperons Λ(1405)

270 MeV energy difference

•  Includes parameters •  They should be computed with a given Lagrangian (dynamics). •  Or fix them to known masses and then predict.

Mass formula

Hyperon spectrum (expt.)

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289 MeV

290 MeV

285 MeV positive parity

negative parity

parity undetermined

Mass formula

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M (i, j, jm ) =Msol + n1!1 + n2!2 +12I{i(i+1)+ c1c2 jm ( jm +1)+ (c1 ! c1c2 ) j1( j1 +1)+ (c2 ! c1c2 ) j2 ( j2 +1)

!!!!!!!!!!!!!!!!!!!!!+ c1 + c22

j( j +1)! jm ( jm +1)! i(i+1)[ ]+ c1 ! c22!R ! (!J1 !!J2 )}

8 parameters: fit to the available data g  give predictions to the other resonances The last term gives a mixing between the states which have same i, j, jm but different R, J1, J2

Fitted valuesMsol = 866 MeV, I =1.01 fm!1 = 211 MeV, c1 = 0.754,!!!!!!!!!c1 = 0.532!2 = 479 MeV, c2 = 0.641,!!!!!!!!!c2 = 0.821

cf. c1 = c12,!!!c2 = c2

2 in Kaplan, Klebanov, NPB 335 (1990)

Hyperon spectrum (Skyrme model)

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YO, PRD 75 (2007) spin-parity

Recently confirmed by COSY PRL 96 (2006)

Unique prediction of this model. The Ξ(1620) should be there.

still one-star resonance

High precision experiments are required!

Ω’s would be discovered in future.

BaBar: the spin-parity of Ξ(1690) is 1/2- PRD 78 (2008)

NRQM predicts 1/2+

More comments

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Two Ξ states

Other approaches

Unitary extension of chiral perturbation theoryRamos, Oset, Bennhold, PRL 89 (2002): 1 / 2!state at 1606 MeVGarcia-Recio, Lutz, Nieves, PLB 582 (2004): claim tht the "(1620) and "(1690) are 1 / 2!states

Kaons: one in p-wave and one in s-wave!!!!!

!J =!Jsol +

!Jm !!!!!!!(

!Jm =

!J1 +!J2 )

!!!!!!!!!!Jsol : soliton spin (=1/ 2),!!!!!

!J1(!J2 ) : spin of the p(s)-wave kaon !(=1/ 2)

!!!!!!!!!Jm = 0 or 1: both of them can lead to J P =1/ 2" !#!states Therefore, two J P =1/ 2" !#!states and one J P = 3 / 2" !#!statesIn this model, it is natural to have two J P =1/ 2" !#!states at 1616 MeV & 1658 MeVClearly, different from quark models

Sum rules

¤  Mass sum rules ¥  Modified GMO and equal spacing rules

¥  The hyperfine relation

¥  The same relations hold for

¤  Magnetic moments

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3! +"# 2(N +$) = "*#%# (&#$*)(&#$*)# ($*#"*) = ($*#"*)# ("*#%)

!*"!+ 32(!"#) = $" N

!(1 / 2" ),!!#(1 / 2" ),!!#(3 / 2" ),!!$(1 / 2+ ),!!!$(3 / 2+ ),!!!%(3 / 2" )

µ(!,1 / 2" ) = 43µ(#1116 )"

13µ(#1405 ),

µ(!,3 / 2" ) = 2µ(#1116 )+µ(#1405 ),!!!etc YO, PRD 75 (2007)

HEAVY QUARK BARYONS

IV

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Heavy quark baryons

¤  A dog wagging a tail? ¥  Large NC vs. Large M

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Large NC: Y.O. & B.Y. Park, PRD 51 (1995)

Large M: Y.O. & B.Y. Park, ZPA 359 (1997) Fewer bound states

300 MeV

Charm baryon spectrum

Λc Σc Ξc Ωc Ξcc

1/2+ 2287 1/2+ 2454 1/2+ 2470 1/2+ 2695 ?? 3519 1/2- 2595 3/2+ 2518 1/2+ 2577 3/2+ 2766 3/2- 2628 ?? 2800 3/2+ 2646 5/2+ 2882 1/2- 2790 ?? 2939 3/2- 2817

?? 2931 ?? 2971 ?? 3054 ?? 3077 ?? 3123

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in MeV Under analysis in the Skyrme model

PRODUCTION PROCESSES

V

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Ξ photoproduction

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!

"N #KK$Dominance of the intermediate S=-1 hyperon states

M1/2±

2, M

5/2±2! EN !M N( ) E"

!M"( )

M3/2±

2, M

7/2±2! EN ±M N( ) E"

±M"( )

Nakayama, YO, Haberzettl, PRC 74

Man, YO, Nakayama, arXiv:1103.1699

Ξ photoproduction

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If we include spin-1/2 and 3/2 hyperon resonances in the intermediate state, then we fail.

Nakayama, YO, Haberzettl, PRC 74

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p2 +m2( )!!1!2!!s= 0

! !"+m( )#!1!2!!n$1= 0

Propagator

¤  propagators

¤  General expressions

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S(p) = ip2 !M 2 " for a boson

S(p) = ip2 !M 2 p #! +M( )" for a fermion

For integer spin n

!!1!!n"1!!n (n, p) = 1

n!"

#$

%

&'

2

"#i!i + a1"#1#2

" !1!2 "#i!i

i=3

n

( +!i=1

n

()

*+

,

-.

P(! ),P(" )/

for even nwith

ar(n) = 0

12

"

#$

%

&'r n!r!(n0 2r)!

1(2n01)(2n03)!(2n0 2r +1)

,

etc

RNπ Lagrangian

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!

JP =12

±

case

L1/ 2 = g"NR N i#$(±)" !1% #

MR ± MN

$µ(±)& µ"

'

( )

*

+ , R + H.c.

JP =32

±

case

L3 / 2 =g"NRM"

N$(! )& µ"Rµ + H.c.

JP =52

±

case

L5 / 2 = i g"NRM"

2 N$(±)& µ&-"Rµ- + H.c.

JP =72

±

case

L7 / 2 =g"NRM"

3 N$(! )& µ&-&."Rµ-. + H.c.

!± =!51

"

#$$

%

&'',!!!!!!!µ

± =!µ!5!µ

"

#

$$

%

&

''

!

"(R#N$) =3g$NR

2

4$2n (n!)2

n(2n)!k$

2n%1

MRM$2(n%1) EN ± MN( )

for (%1)n Ps = ±1 with Ps being the parity of the spin - s resonance R

Ξ photoproduction

¤  inclusion of spin-7/2 Σ(2030)

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OUTLOOK

VI

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Outlook

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¤  Study on the spectrum of Ξ hyperons ¥  Opens a new window for understanding baryon structure

¤  Theoretical models for Ξ spectrum ¥  Different and even contradictory predictions ¥  What is the third lowest Ξ resonance?

And the quantum numbers? ¥  Soliton model: Ξ(1620) and Ξ(1690): analogue to Λ(1405)

¤  Experimentally, more data are required! ¥  Does Ξ(1620) exist? ¥  Should confirm other poorly established Ξ resonances in PDG as well as th

eir quantum numbers ¥  Almost no information on the Ω baryon resonances

¤  Role of Λ and Σ resonances in Ξ photoproduction. ¥  Offers a chance to study those hyperons. ¥  Higher mass and high spin resonances