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A steiner tree associated with three quarks

W.A. Beyer, L. Heller
1987 Journal of symbolic computation  
The MIT bag model with three static quarks of the same charge has been discussed by Aerts & Heller. Two different geometries are given for the bag.  ...  , and the energy for this case, denoted Er, is given by the sum of the lengths xt of the Steiner tree associated with the given triangle.  ...  Introduction Aerts & Heller (1981) have discussed the MIT bag model with three static quarks, the three quarks having the same charges.  ... 
doi:10.1016/s0747-7171(87)80006-8 fatcat:s5jzkv6zezer7igvtvoxuvgh3y

Stability of asymmetric tetraquarks in the minimal-path linear potential

Cafer Ay, Jean-Marc Richard, J. Hyam Rubinstein
2009 Physics Letters B  
For tetraquark systems, i.e., two quarks and two antiquarks, this involves the two possible quark--antiquark pairings, and the Steiner tree linking the quarks to the antiquarks.  ...  A novel inequality for this potential demonstrates rigorously that within this model the tetraquark is stable in the limit of large quark-to-antiquark mass ratio.  ...  Asghar, A. Valcarce and J. Vijande for enjoyable discussions on this problem, as well as D. Eberly for useful correspondence. Appendix A. Results on the Steiner problem Three terminals.  ... 
doi:10.1016/j.physletb.2009.03.018 fatcat:a2a34ugrrjgmphmdil25jbuaxa

Stability of the pentaquark in a naive string model

Jean-Marc Richard
2010 Physical Review C  
The ground-state is found to be stable against spontaneous dissociation into a meson and a baryon, both in the case of five equal-mass constituents and for a static quark or antiquark surrounded by four  ...  The pentaquark is studied in a simple model of confinement where the quarks and the antiquark are linked by flux tubes of minimal cumulated length, and the Coulomb-like interaction, the spin-dependent  ...  Acknowledgments It is a pleasure to thank M. Asghar and S. Fleck for fruitful discussions.  ... 
doi:10.1103/physrevc.81.015205 fatcat:rafvmx57ojcdfjsoubqe3xmide

Elusive multiquark spectroscopy

J.-M. Richard
2010 EPJ Web of Conferences  
This includes: coherence in the chromomagnetic interaction, tetraquarks with two heavy quarks, Steiner-tree models of confinement, and hadronic molecules, in particular in the hidden-charm sector.  ...  quarks in a colour singlet.  ...  Acknowledgments It is a pleasure to thank the organisers of this beautiful Conference for giving us the opportunity of many stimulating discussions.  ... 
doi:10.1051/epjconf/20100301015 fatcat:e7krbmr3bvbkxjrmneemghhnv4

Baryon Wilson loop area law in QCD

John M. Cornwall
1996 Physical Review D, Particles and fields  
blades joined along a Steiner line (Y configuration).  ...  ., finite lattice spacing in lattice gauge theory) approximations suggest the form [-KA_Y], where K is the qq̅ string tension and A_Y is the global minimum area, generically a three-bladed area with the  ...  In particular, those graphs formed by attaching an N-leg connected gluon tree with N − 2 three-gluon vertices to N quark lines in a baryon, such that only one gluon is attached to each quark line, vanish  ... 
doi:10.1103/physrevd.54.6527 pmid:10020654 fatcat:l4oihsl5urhdppctqsqibcziq4

Stability of hexaquarks in the string limit of confinement

J. Vijande, A. Valcarce, J.-M. Richard
2012 Physical Review D  
We discuss both six-quark (q^6) and three-quark--three-antiquark (q^3q̅^3) states. The quarks are assumed to be distinguishable and thus not submitted to antisymmetrization.  ...  The investigations are extended to (q^3Q^3) and (Q^3q̅^3) systems with two different constituent masses, and their stability is discussed as a function of the mass ratio.  ...  The interaction is the minimum of flip-flop terms, a meson and a baryon with all permutations, and of connected Steiner trees, as shown in Fig. 2 .  ... 
doi:10.1103/physrevd.85.014019 fatcat:jssk2abpobhivpynbeumhbi5qm

Tetraquarks: relativistic corrections and other issues

Jean Marc Richard, Alfredo Valcarce, Javier Vijande
2022 Suplemento de la Revista Mexicana de Física  
Some other issues associated with exotic hadrons are also briefly discussed.  ...  For a given potential, the use of relativistic kinematics lowers the energy by a larger amount for the threshold made of two mesons than for a tetraquark, so that its binding is weakened.  ...  to a Steiner tree that generalizes the straight string linking the quark and the antiquark inside a meson, and the Y -shape potential à la Fermat-Torricelli joining the three quarks in baryons.  ... 
doi:10.31349/suplrevmexfis.3.0308110 fatcat:34uojsdlhffqthl5mllwyvpvui

Higgs Boson Mass predicted by the Four Color Theorem [article]

Ashay Dharwadker, Vladimir Khachatryan
2009 arXiv   pre-print
We specify well-defined rules to match the Standard Model in a one-to-one correspondence with the topological and algebraic structure of the particle frame.  ...  In this paper, we concentrate on explicitly specifying the quarks, gauge vector bosons, the Standard Model scalar Higgs H^0 boson and the weak force field.  ...  tree-level.  ... 
arXiv:0912.5189v1 fatcat:yvfhtk4jorfe7htxgj3zab7nfa

Adiabaticity and color mixing in tetraquark spectroscopy

J. Vijande, A. Valcarce, J.-M. Richard
2013 Physical Review D  
We revisit the role of color mixing in the quark-model calculation of tetraquark states, and compare simple pairwise potentials to more elaborate string models with three- and four-body forces.  ...  However, the Steiner-tree with two junctions, that plays a marginal role, is neglected. Hence, this is the pure flip-flop model. • Model B is a smooth version of the adiabatic approximation.  ...  There are multi-Y connected diagrams in which the * javier.vijande@uv.es † valcarce@usal.es ‡ j-m.richard@ipnl.in2p3.fr string interaction links all quarks and antiquarks as a Steiner tree whose cumulated  ... 
doi:10.1103/physrevd.87.034040 fatcat:eegyzvmltndkpcc5ljjyq6ryae

πKscattering in full QCD with domain-wall valence quarks

Silas R. Beane, Paulo F. Bedaque, Thomas C. Luu, Kostas Orginos, Elisabetta Pallante, Assumpta Parreño, Martin J. Savage
2006 Physical Review D  
We calculate the pi+ K+ scattering length in fully-dynamical lattice QCD with domain-wall valence quarks on MILC lattices with rooted staggered sea-quarks at a lattice spacing of b=0.125 fm, lattice spatial  ...  Edwards for help with the QDP =Chroma programming environment [34] with which the calculations discussed here were performed.  ...  We have performed a hybrid mixed-action calculation with domain-wall valence quarks tuned to the staggered sea-quark masses of the MILC configurations.  ... 
doi:10.1103/physrevd.74.114503 fatcat:kpilwhjfcbatbkjqawlembd4y4

Tetraquarks: relativistic corrections and other issues [article]

Jean-Marc Richard, Alfredo Valcarce, Javier Vijande
2021 arXiv   pre-print
Some other issues associated with exotic hadrons are also briefly discussed.  ...  For a given potential, the use of relativistic kinematics lowers the energy by a larger amount for the threshold made of two mesons than for a tetraquark, so that its binding is weakened.  ...  to a Steiner tree that generalizes the straight string linking the quark and the antiquark inside a meson, and the Y -shape potential la Fermat-Torricelli joining the three quarks in baryons.  ... 
arXiv:2112.04300v2 fatcat:33ln7op6lvglzpsxtd7v5zttrq

The Role of Flavor in Multiquark Spectroscopy [article]

Jean-Marc Richard
2012 arXiv   pre-print
In several mechanisms proposed for multiquark binding, the flavor content of the quark configuration plays a very important role.  ...  We shall review some past or recent results on multiquarks dealing with the chromomagnetic interaction and with the spin-independent potential among quarks.  ...  Acknowledgments I would like to thank the organizers for the pleasant and stimulating atmosphere of this workshop, and A. Valcarce and J.  ... 
arXiv:1212.4955v1 fatcat:yx5t4qp2drghtcka3mkuihijve

An introduction to the quark model [article]

Jean-Marc Richard
2012 arXiv   pre-print
This document contains a review on the quark model, prepared for lectures at the Niccolo Cabeo School at Ferrara in May 2012.  ...  The analogies between few-charge systems and few-quark bound states will be underlined.  ...  A slightly shortened version will be included in the Proceedings. It is a pleasure to thanks M. Asghar for several constructive comments on an early version of this review.  ... 
arXiv:1205.4326v2 fatcat:vzrjnsomibawrkkymyvktdngf4

Page 4369 of Mathematical Reviews Vol. , Issue 88h [page]

1988 Mathematical Reviews  
A. (1-LANL-TD); Heller, L. (1-LANL-TD) A Steiner tree associated with three quarks. J. Symbolic Comput. 3 (1987), no. 3, 283-289.  ...  Summary: “The MIT bag model with three static quarks of the same charge has been discussed by Aerts and Heller. Two different geometries are given for the bag.  ... 

Measurement of Leading Particle Effects in Decays ofZ0Bosons into Light Flavors

K. Abe, K. Abe, T. Akagi, N. J. Allen, W. W. Ash, D. Aston, K. G. Baird, C. Baltay, H. R. Band, M. B. Barakat, G. Baranko, O. Bardon (+215 others)
1997 Physical Review Letters  
Charged hadrons were identified with a Cherenkov ring imaging detector.  ...  A polarized electron beam was used to tag quark and antiquark jets, and a vertex detector was employed to reject heavy-flavor events.  ...  jets initiated by a specific light flavor and with separating quark jets from antiquark jets.  ... 
doi:10.1103/physrevlett.78.3442 fatcat:2kpnu5p4trft7mfyr33owgmlxu
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