Interpretation of the Q+ as a true pentaquark
• How does pentaquark fit into theoretical view of multi-quark hadrons? • Central theoretical issue: narrow state(s) – well above fall-apart decay threshold(s) • Constituent quark model: masses and widths – Cluster models
– Energies of multi-quark hadrons, Vcolor-spin – “true” pentaquarks
• Isotensor: isoscalar or isovector: Vflavor-spin
• SimonW Capstick,hat canFlorida Statecom Universitye of this? Pentaquark workshop@JLab, Sept. 23 2003-1 Interpretation of Q+, X--
• In the past multi-quark hadron calculations struggled to establish existence of states: – Just bound or slightly unbound relative to (fall- apart) decay thresholds • H di-baryon, uuddss
• Molecular states like • New pentaquark states are significantly above fall-apart decay thresholds! + m(Q ) - (mn + mK+) = 110 MeV -- SimonM Capstick,(X ) Florida- (m StateX- + University mp-) = 1862 -Pentaquark (1321+140) workshop@JLab, = 401 Sept. 23 M 2003-2eV Interpretation of Q+, X--…
• Two central theoretical issues: – Why are these states so narrow? "Q+: G < 25 MeV (LEPS@SPring8), < 21 MeV (CLAS@JLab), < 9 MeV (DIANA/ITEP), < 1 MeV (Arndt, Strakovsky, Workman) "X--: G < 18 MeV (NA49@CERN) – Can we explain why these are the lightest states with these quantum numbers? • Relate masses to those of known hadrons? Simon Capstick, Florida State University Pentaquark workshop@JLab, Sept. 23 2003-3 Pentaquark
• State with baryon number 1, qqqqQ – Note: all baryons qqq contain qqq(q’ q’)! • strong interactions make many qq pairs – q’ can have same flavor as q • p a p p0 or n p+ a p if make uu or dd pair – Or different • p a L K+ a p if make ss pair • If Q has flavor different from the four quarks, no annihilation possible • SimonE.g Capstick,., u Floridaud sStatec Universityis a true pPentaquarkenta workshop@JLab,quark Sept. 23 2003-4 Pentaquark predictions
• History of predictions, like LL di- baryon – Based on magnetic interactions between spinning colored quarks – Lipkin:
– Distinctive signature, hard experiment, not seen so far Simon Capstick, Florida State University Pentaquark workshop@JLab, Sept. 23 2003-5 Need for constituent quark picture?
• Praszalowicz (’87): Diakonov, Petrov & Polyakov (’97) • Mass fixed by assuming N_+(1710) is member of flavor anti-decuplet – But mass, strong decays, EM couplings of N(1710) understood in CQM Simon– Capstick,simple Florida radially State University excited uud,Pentaquark ddu workshop@JLab, state Sept. 23 2003-6 Need constituent quark picture…?
• Width predicted 15 MeV, but G1710 predicted to be ~43 MeV – Particle Data Group “estimate” 100 MeV (50- 250 MeV) • Similarly, width of S(1880) predicted 70 MeV, PDG give 80-260 MeV – Widths in this model all proportional to a calculated constant – If increase to fit widths of 1710 and 1880, width of Z+(1530) = Q+ may be too large to accommodate experimental results Simon Capstick, Florida State University Pentaquark workshop@JLab, Sept. 23 2003-7 Usual vs. fall-apart decays
pair created no pair string broken color/flavor/spin/spatial rearrangement
Simon Capstick, Florida State University Pentaquark workshop@JLab, Sept. 23 2003-8 Fall-apart decays
• Any state, with any flavors: – Possible color configuration is colorless baryon plus colorless meson – Weak forces between them – Non-zero overlap between initial wave function and final state • If isoscalar or isovector, relevant threshold is KN at 1433 MeV – Not the same as with width 16 MeV – No pair creation necessary Simon Capstick, Florida State University Pentaquark workshop@JLab, Sept. 23 2003-9 Fall-apart decays…
• Immeasurably broad if well above threshold to decay: width ~500 MeV? + – The Q is ~ 110 MeV above NK threshold, pcm=270 MeV c.f. typical hadronic scale b~400 MeV
• with JP=1/2- decay is S-wave, no phase space
suppression, G ~ GS ~ 500 MeV P + + • J =1/2 , 3/2 gives P-wave, G ~ 0.2- 0.5 GS - - • 3/2 , 5/2 D-wave: G ~ 0.07 - 0.1 GS • JP=5/2+, 7/2+…, possible F-wave suppression could
entirely account for small width, G~ 0.02 - 0.03 GS – F require lots of orbital L, unlikely to be lightest state! Simon Capstick, Florida State University Pentaquark workshop@JLab, Sept. 23 2003-10 Why are these states so narrow?
• Within quark model, two types of explanation: – Quarks are in clusters, with a P-wave between the clusters • Angular momentum barrier, necessary rearrangements prevent decay • Widths as small as 10 MeV? – They are in a symmetric (true pentaquark) state • A symmetry largely prevents their decay • Possibly very small widths (fractions of MeV) Simon Capstick, Florida State University Pentaquark workshop@JLab, Sept. 23 2003-11 Cluster models
Jaffe/Wilczek: isoscalar, JP=_+ • Cluster model with: – Two tightly bound (ud) clusters, flavor – Di-quarks coupled to spin zero, isospin zero, color – Must have color coupled to 3, anti-symmetric part – Di-quark(boson) – di-quark wave function must be symmetric • Requires anti-symmetric orbital wave function, negative parity, minimum L=1; – Part of near-ideally mixed
Simon Capstick, Florida --State University Pentaquark workshop@JLab, Sept. 23 2003-12 – Note X3/2 @ 1750 MeV (additive mass formula) Cluster models…
• Jaffe/Wilczek state – Requires: (anti-quark)spin – (di-quark relative)orbit interaction to raise mass of 3/2+ partner • dynamical origin? – Narrow width: • dd in n(ddu) required to come from different di- quarks, in a relative P-wave: angular momentum barrier • Flavor, color and spin rearrangements required
– Could be small enough: G[P_+]/24 ~ 10 MeV (not 1 MeV!)
Simon– Capstick,How Florida tightly State University bound are thePentaquark di-quarks? workshop@JLab, Sept. 23 2003-13 Cluster models…
Karliner/Lipkin: isoscalar, JP=_+, in
part of SU(3)f • Cluster model with: isospin SU(3)f color spin SU(6) color-spin 0 0 21 (AS) (AS) (S) cluster: 0 6 1 21 (S) (S) (S) in cluster 0 3 _ 6 cluster Simon Capstick, Florida State University Pentaquark workshop@JLab, Sept. 23 2003-14 Energies of multi-quark hadrons
• Where does it sit relative to nK+? – Multi-quark hadron calculations based on color-spin (hyperfine) interaction between N quarks (anti-quarks) – Evaluate
a a – In baryons <-Sa l i l j >color singlet = 2/3
a * a – In mesons <-Sa l i l j >color singlet = 4/3 • In multi-quark states requires a little SU(6) (color-spin) group theory: – Jaffe, Hogaasen & Sorba, Lipkin, Leandri & Silvestre- Brac,…
Simon Capstick, Florida State University Pentaquark workshop@JLab, Sept. 23 2003-15 Energies of multi-quark hadrons…
• Trick from quantum mechanics: – E.g. pair-wise spin-spin interaction between N spinors . 2 2 2 2
Simon Capstick, Florida State University Pentaquark workshop@JLab, Sept. 23 2003-16 Energies of multi-quark hadrons…
• Similarly (Jaffe):
– Here C3 [C6] = quadratic Casimir of SU(3)c [SU(6)cs] – tot = representation of multi-quark state – = representation of quark(s) – = representation of antiquark(s)
Simon Capstick, Florida State University Pentaquark workshop@JLab, Sept. 23 2003-17 Cluster models…
Karliner/Lipkin: – assume no interactions between quarks in
different clusters, exact SU(3)f (ms - mu,d ~ 0) cluster color C3 spin 8/3 SU(6) C6 Energy S(S+1) (units Vc) 16/3 0 0 21 160/3 -24/3
6 40/3 1 16/3 21 160/3 3 16/3 _ 2 6 70/3 -56/3
– N has hyperfine energy –24/3, D has +24/3, K has –48/3 • Sum of clusters lighter than NK by Simon Capstick,–(8/3)( Florida DState-N)/(4 University8/3) = -5Pentaquark0 MeV workshop@JLab, Sept. 23 2003-18 Cluster models…
• If S-waves between clusters, hyperfine interaction between clusters – repulsion wins, energetically favorable to be K N • If and clusters in a P-wave – No interactions between clusters, angular momentum barrier, parity now positive, JP = 1/2+ or 3/2+ – Costs P-wave excitation energy • estimated ~205 MeV by Karliner and Lipkin
– Puts state at mN+mK – 50 MeV + 205 MeV = 1590 MeV
Simon Capstick, Florida State University Pentaquark workshop@JLab, Sept. 23 2003-19 Cluster models… • Caveats: – Orbital excitation energy an estimate
– SU(3)f breaking (1/mq dependence) required in color-spin – Only color-spin hyperfine energy included: KE, other PE? • Requires spatial wave functions, problem in all models – Spatial extent of clusters? Cluster-cluster interactions? – Source of 1/2+, 3/2+ spin-orbit splitting? • Narrow width: – angular momentum barrier, rearrangements Simon Capstick, Florida State University Pentaquark workshop@JLab, Sept. 23 2003-20 required: small enough? True pentaquark
• What if it had isospin 2? SC, P. Page, W. Roberts – Strong decay to K+n would violate isospin • Width of isospin-violating strong decay? – Decay w a p+p- violates G-parity = isospin (strong decay) – Partial width is 0.14 MeV = 0.1% of r a p+p- – Might expect 0.1% (500 MeV) ~ 0.5 MeV width for isotensor Q+ • Mechanism: isospin impurities in both Q+ (I=0 and 1) and n (I=3/2) allow isospin-violating decay 0 0 0 – E.g. physical L = L 8 – 0.015 S 8 – If I=0 and I=1 in Q+ comparable size (I=3/2 in n known very small) Simon Capstick,• G Florida= 4 (0.015) State University2 500 = 0.45 MeVPentaquark workshop@JLab, Sept. 23 2003-21 Isotensor pentaquark
• Isotensor pentaquark has effectively a raised threshold relative to I=0 or I=1 – Relevant threshold is D K ~ 1730 MeV • Molecular picture unlikely
– 190 MeV binding gives rrms = 0.5 fm
– Molecule candidates f0(980), a0(980) are 10 MeV below threshold • Isotensor likely to be a “true” pentaquark, not molecule – Ground state could, in principle, have JP=1/2-, 3/2-, 5/2-
Simon Capstick, Florida State University Pentaquark workshop@JLab, Sept. 23 2003-22 Isotensor pentaquark…
• True pentaquark: uudds – I=2 is totally symmetric (S) in flavor (e.g. uuuu) – Assume ground state also has four relative S waves – Color x spin must be totally antisymmetric (AS)
• Symmetry group is SU(6)cs • AS representation with 4 objects is
– Made up of Sqqqq=0 color , S=1 color 3 – Can’t have JP=5/2- !
Simon Capstick, Florida State University Pentaquark workshop@JLab, Sept. 23 2003-23 Isotensor pentaquark mass • What about mass of isotensor? – Specialize Jaffe formula to Q+ pentaquark:
where
– Here v is hyperfine strength in hadron of interest
• e.g. D = 8 vB, N = -8 vB, K = -16 vM
– Can correct for ms (Lipkin)
Simon Capstick, Florida State University Pentaquark workshop@JLab, Sept. 23 2003-24 Isotensor pentaquark
• SU(6)cs: – 70 = (S=3/2)x8 + (S=1/2)x8’ + (S=1/2)x10 + (S=1/2)x1 • This is our S=1/2 color singlet – 20 = (S=1/2)x8 + (S=3/2)x1 • This is our S=3/2 color singlet
– Isotensor hyperfine energy (mu,d= ms): Lipkin, SC P - • J = 1/2 : + 88/3 vP P - • J = 3/2 : + 40/3 vP • Both unbound relative to D K threshold
Simon(also Capstick, true Florida State with University ms correPentaquarkction workshop@JLab,s) Sept. 23 2003-25 True pentaquark… • What about isoscalar or isovector (symmetric) pentaquarks? – Hogaasen & Sorba (’78): SC, Lipkin, Robson – uu and dd in 15 of SU(6)cs – uudd must be in • States in the 105 are isoscalar (exchange P - - symmetry), with S4q=1: gives J =1/2 , 3/2 with orbital S-waves – JP=1/2- state has attraction • H&S (1978): “…we have very strong attraction in the state |V> that has J^P=1/2- and contains a flavor octet and an antidecuplet. This open the possibility that we can expect fairly low lying exotic states with S=+1, I=0 and S=-2, I=3/2” • Light, but no mechanism to prevent fall-apart decay! Simon– Capstick,JP=3/2 Florida- state State Universityrepulsive Pentaquark workshop@JLab, Sept. 23 2003-26 True pentaquark…
• States in the 105’ are isovector (exchange
symmetry), with S4q=0,1,2: many states! • gives JP=1/2-, 3/2-, 5/2- (orbital S-waves) – There is an attractive JP=3/2-
~ -10 vP with SU(3)f breaking, mixing from color-spin interaction (H&S) • What about decays? Jennings & Maltman – Recall fall-apart decay operator is 1 – Spin scalar, Q(3/2-) to n(1/2+) K(0-) forbidden – J&M argue that if Q(3/2-) ~ 1540 MeV, lighter Q(1/2-) below NK
Simon Capstick,• Needs Florida Statefurther University study Pentaquark workshop@JLab, Sept. 23 2003-27 • Is isovector(tensor) ruled out experimentally? GBE interactions between quarks
• Used as model of short range interactions in baryons • Robson, Glozman & Riska, Plessas,… – May coexist with color-spin (CM) interactions • Buchmann & Faessler,… • Flavor-spin interactions possibly more important in multi-quark systems – Colorless clusters allowed • Examined by several groups • Carlson, Carone, Kwee, Nazaryan (also do CM) • Stancu and Riska
Simon Capstick,• M aFloridaltma Staten & UniversityJennings: RobsoPentaquarkn & SC workshop@JLab, Sept. 23 2003-28 GBE interactions between quarks…
• Light isoscalar 3/2- state – Fall apart decay forbidden by spin… • with GBE, is lightest state P-wave (JP=1/2+)? • Stancu & Riska, Jennings & Maltman • J&M point out such a state dominated by Jaffe/Wilczek configurations • Lightest with GBE if neglect interactions between clusters • Subject of on-going investigation(s)…
Simon Capstick, Florida State University Pentaquark workshop@JLab, Sept. 23 2003-29 Summary • Hadron spectrum should be richer than simple baryon and meson states – Until recently multi-quark states either: • didn’t exist (experimental point of view) • eluded detection (theorist point of view) • Central theoretical problem: simultaneously explain small width and mass relative to existing hadrons – Due to clustering? Simon– Capstick,Due toFlorida breaking State University of a symmetryPentaquark workshop@JLab, (isospin, Sept. spin,… 23 2003-30) Summary…
• To understand nature of Q+, X—:
– Need to know the spin and parity! – Need definitive exclusion/discovery of other charge states of Q+
• Potential pay-off: – New information about nature of short- distance interactions between quarks – Entirely new hadron spectrum Simon Capstick, Florida State University Pentaquark workshop@JLab, Sept. 23 2003-31