# Presentation: 816236

## Variational Monte Carlo studies of pentaquark states

- Status of +(1540) and non-relativistic constituent quark model calculations
- Thanks for discussions with: Jo Dudek (quark model/expt’l), Ross Young (lattice calculations),
- Bob Wiringa (VMC wave functions)
- nucl-th/0507061, *PRL, In press*

## Organizing principle:
Fix parameters of HNRCQM from 3q,6q
Narrow resonance approximation
What is m5q?

Outline
Pentaquark states
negative or positive parity

Isospin T=0
Define H
Non-relativistic constituent quark flux-tube model
Variational wave function & Monte Carlo

Results
                Masses
diquark—diquark pair distributions

- Fix parameters of HNRCQM from 3q,6q
- Narrow resonance approximation
- What is m5q?
**Outline**
- Pentaquark states
- negative or positive parity
- Isospin T=0
- Define H
- Non-relativistic constituent quark flux-tube model
- Variational wave function & Monte Carlo
- Results
-                 Masses
- diquark—diquark pair distributions

- Overview

## Pentaquark Taxonomy

-                     minimal quark content
- SU(3)F:

- Flavor

- Exotics

**Notes:**
3 animations

## Constituent quark model Hamiltonian

- Dynamical Hamiltonian model
- non-relativistic kinetic energy
- many-body confining term
- flux tube model
- two-body potential interactions
- strong state dependence T=0,1 isospin
- 			           S=0,1 spin
- 			           C=**3***,**6 **color
- just about any configuration
- 	space potential can be handled
- use one-gluon exchange + one-pion exchange
- constant term
- scales with number of quarks
- flux tube ends
- constant term

## Confinement potential: flux tube model

- Motivated by lattice Hamiltonian (at strong coupling)
- Kogut & Susskind
- Strong coupling: eigenstates for static quarks are definite paths of flux links; plaquettes induce configuration mixing
- VMB={string tension} £ {flux tube length}
- Configurations:

-   color electric field

- color magnetic field “plaquette”;
- Wilson loop

## Many body confinement

- Flux tube confinement
- 	-consistent with gauge invariance
- 	-Kogut & Susskind Hamiltonian
- 	-Lattice potential studies Suganuma, et. al.

- Many-body/2b decomposition

- FT topologies

- color
- states

## Model parameters

- Constituent quark mass
- light quark mass mq = mN/3
- fixed by non-relativistic form
- strange quark mass ms=550 MeV
- parameter
- string tension
- N and trajectories
- E2 vs. J for “stringlike” configurations E2=21/2J
-  1/2=0.88 GeV/fm
- perturbative gluon coupling constant
- m – mN ) s=0.61
- pion quark coupling – fit from elastic NN data
- RNN!1 ) f qq=3f NN/5
- quark form factor
-  =5 fm-1; parameter
- constant term fitted to mN ) v01⁄4130 MeV (per flux tube end)

- RNN!1

## +(“1540”) Quantum numbers

- +(“1540”) Quantum numbers

- 4q totally antisymm:
- Antiquark coupling:
- [4q]:
- Isospin:
- Spin/orbital:
- Total parity =§1, either!

- Total Spin:

## Solution of the Schrödinger equation

- Variational Monte Carlo
- Correlated many-body wave function
- Correlation operator
- Ansätz
- Two-body correlation
- Solve two-body Schrodinger-like equation, eg.

## Uncorrelated [4q] states

- Classification
- Inner products on
- Overlaps
- Jaffe-Wilczek
- Karliner-Lipkin

- symmetry index for given total parity

## Masses

Short range diquark structure

- Masses
- Short range diquark structure

- Results

- Notes:
- Negative parity lightest
- Positive parity
- lower V
- higher T

- Notes:
- Uncorrelated:
- SS=VV=1/6
- Correlated
- SS+VV . 1/3
- SS>>VV

- scalar—scalar(SS)

- vector—vector(VV)

## Concluding remarks:pentaquark in NRCQM

- pentaquark masses & 2 GeV
- Hamiltonian fit to 3q & 6q properties
- solve 5q Schrodinger equation (almost) exactly
- inconsistent with chiral quark soliton model &
- 	JW—correlated quark model
- negative parity < positive parity for J=1/2
- potential is reduced for
- but not enough to compensate for kinetic energy increase due to orbital angular momentum
- short-range structure
- significant JW component 1⁄4 1/3
- other structures important
- existence at 1540 MeV?
- Yes: what’s been overlooked?  symm? ...?
- No: could it be elsewhere? why doesn’t it exist?

## Additional slides

## Negative paritypentaquark results

- Negative paritypentaquark results

- Two types of pair correlation operators
- lq-lq:
- lq-sq:

## +(1540) is a WMD(Weird Multiquark Demon)*

- After: Jaffe & Wilczek
- Remarkably narrow
- m–(mn+mK)1⁄4+100 MeV
- COM threshold ~270 MeV ) not-very-relativistic
- short range interaction)only s- or p-wave likely
- no annihilation (“exotic”)
- Potential scattering
- s-wave resonance not possible
- p-wave:
- range of potential ~ 1 fm gives width ~ 102 MeV !!!
- some other mechanism (dynamical) needed to get ~10 MeV

- *F. Close

## Flux tube exchange/CND matrix elements

## Production mechanisms

- photoproduction: p/A ! +X
- hadroproduction:
- pp/pA ! +X
- K+p/K+A ! +X
- AA ! +X
- leptoproduction:
- e+e- ! +X
- eN/N ! +X

## Experimental status (I) – Positive signal

- Dzierba, Meyer, & Szczepaniak ~ 6 months ago  hep-ex/0412077
- Impressive array of experimental evidence – on the surface
- statistical significance ~ 4—8 

- Photoproduction

- Hadroproduction

- Leptoproduction

## Experimental status (II) – positive signal – cross sections

- Sampling of experimental cross sections
- counts vs. invariant mass recoiling against K+n/KSp
- Error bars are statistical only
- Low statistics
- 10 – 100 peak events

## Experimental status (III) – Negative signal

- DMS (continued)
- Published and unpublished results
- generally high statistics
- fine resolution,
-     1—2 MeV
- benchmark resonances seen:
- (1020),K*(890),
- (1520),(1320),
- (1530)

## Experimental status (IV) -- Jefferson Lab g2

- 43 events above bg in peak
- bg cuts:
-  p! X
- 		 ! YX: M(K+K-)<1.07 GeV2
-  p! K+:
-       1.485<M(pK-)<1.551GeV2
- M = 1542(5) MeV
- FWHM = 21 MeV

- Gaussian bg

- MC sim bg

## Experimental status (V) -- Jefferson Lab g11

- Exclusive process
- High statistics – 120k events

- g11 data courtesy R. diVita

## Experimental analysis – possible problems

- Low statistics
- statistical significance estimators:
- often quoted
- Harsh angular cuts
- capable of producing peaks
- Final state interaction effects
- effects on cross section not studied
- Two masses?
- 1530 MeV
- 1540 MeV
- Low energy vs. high energy
- production mechanism “exotic”?
- fragmentation production
- constituent counting rules +
- 	high energy prod. suppressed
- 	Titov et.al. PRC,70,042202(R)
- If + doesn’t exist,
- 	what implications on expt’l
- 	analysis?

- 4!8 

- 2!6 

## Alternative explanations

- Kinematic reflections Dzierba, Meyer, Szczepaniak hep-ex/0412077
- a2, f2, 3, ... ! K+K- ) stucture in K+n
- decay angular distribution ~
-  1⁄40) mK+n small; 1⁄4) mK+n large
- amplitude
- 	~ t-channel Regge £ decay ang. dist.
- generated distributions ~ 20% have peak
- model specifics wrong
-  0 Regge doesn’t contribute
- physics may be correct
- 	 	Oh, Nakayama, & Lee hep-ph/0412363; Hicks et.al. hep-ph/0411265
- Spurious peaks
-  (1115)!-p ghost tracks
- track “doubling” mimics +
- kinematic cuts
- peak only seen after
- 	angular cuts on K+

- not seen

## (Quenched) Lattice QCDafter Lasscock, et.al. CSSM Lattice Collaboration hep-lat/0503008

- Interpolating functions  [ ̈ T=0,1]
- color-singlet form
- color-fused form
- Jaffe-Wilczek
- Lattice baryon resonance signature
- all N, resonance states lie *below *sum of decay products

- N*(1535) vs. N

- 1232) vs. N

## Lattice signature

- Look for q5 state with mass smaller than N+K
- Isoscalar
- Positive and negative parity

- Standard lattice resonance signature not observed for any of the spin—1/2 pentaquark states
- Negative parity mass < positive parity (for m large)

## Chiral quark soliton model

- Baryons are solitons of the pion (chiral) field
- Hedgehog
- T=J
- Successes
- Gell-Mann—Okubo	relations
- Guadagnini formula
- Anti-decuplet
- Fix zero by fitting N*1/2-(1710)
- Capstick, Page, and Roberts hep-ph/0307019
- point out that N(1710) identification is arbitrary, using
- 	N(1440) )  stable

- within 8 and 10

- between 8 and 10

## Model calculations(in no particular order)

- Diakonov, Petrov, & Polyakov (-Quark Soliton Model)
- Jaffe & Wilczek (Constituent Quark Model (CQM) – diquark)
- Carlson et. al. (CQM-uncorrelated)
- Close & Dudek (CQM-variational)
- Karliner & Lipkin (CQM-uncorrelated)
- Praszalowicz (Skyrme)
- Huang, Zhang, Yu, & Zou (SU(3))
- Hosaka ( bag model)
- Zhu (QCD sum rules)
- Stancu (CQM-variational)
- Kanada-En'yo et.al. (CQM-AMD)
- Oh, Nakayama, & Lee (CQM+phen.)
- Hiyama (CQM-variational)
- Takeuchi & Shimizu (CQM-variational)
- Capstick (CQM)
- Gerasyuta & Kochkin (Relativistic CQM)

- why do another?
- 	-QMC methods exact
- 	-anti-symmetrized WF
- 	-fully correlated WF
- 	-any/all TSL structures
- 	-investigate SR (2Q?)

## T=0,S=0,C=3* strongest attraction

- T=0,S=0,C=**3********* **strongest attraction
- 	     due to pion and gluon
- 	     exchange

## Single hadron wave function

- S- and P-wave N &  states
- uncorrelated |qqqi states
- color singlet ) Ti¢ Tj = -2/3 8 i,j
- spin—isospin
- Apply correlation operator:

## Single hadron results

- s- & p-wave spectra
- Neutron quark & charge densities

- T=S=0 diquark

## Flux tube dynamics

- Strong coupling: gs!1
- different quark configurations have orthogonal flux tube configurations
- Finite coupling:
-  FT – flux tube overlap parameter
- More complicated quark position dependence possible
- eg. Green, Micheal, Paton NPA 554, 701 (1993)

## Quark pair distribution function

- 2£Single nucleon pdf

## Deuteron properties

- Add V2-type interaction
- Distortion of the nucleon?
- let FT!1
-  ) given q$N
- finite FT

- Rcavity

## Pentaquark states -- |qqqqsi          

- Treat pentaquark as a bound state
- narrow resonance approximation
- Variational wave function
- Uncorrelated states
- Take appropriate inner products of these to obtain a state which is totally anti-symmetric w.r.t. the four light quarks

## Negative parity pentaquark

- Color-orbital: C£L
- Flavor-spin: T£S

- No inner product with CL yields (1)4

- states of 4q
- T=0
- S=0,1,2
- C=**3** * anti-quark **** **3***
- parity even ) L=0

- yields singlet

## Negative parity pentaquark results

- Two types of pair correlation operators
- lq-lq:
- lq-sq:

## Comparisons

- with uncorrelated variational
- M() decreased by ~40 MeV
- compare with M()-(mK+mn)1⁄4100 MeV
- Carlson, et. al.
- uncorrelated negative parity state; bag model wave functions

## Pending results

- Positive parity mass: higher or lower??
- lattice: m-<m+
- CQM: m->m+
- (increased symmetry of state compensates for L=1)
- Widths
- Flux tube model predict narrow states?
- Overlap of fully antisymmetrized states with
- 	favorite flavors:
- Jaffe-Wilczek diquark
- nK molecular
- etc.
- Short range structures
- diquark size, shape, distributions
- TO BE CONTINUED...
- 		(but not for much longer)

## Frank Close’s observation