Combining the recent lattice calculation of $a_0(1450)$ and $\sigma(600)$ mesons with the overlap fermion in the chiral regime with the pion mass less than $300 {\rm MeV}$, the quenched lattice calculation of the scalar glueball, and the phenomenological s

PatternofLightScalarMesons3

vectormesonsK1(1270)andK1(1400).Thisisasituationwhichparallelsthecaseofnon-strangemesonswherea0(1450)ishigherthana1(1260)anda2(1320)andiscontrarytotheconventionalwisdominthequarkmodelasfarastheorderofspin-orbitsplittingisconcerned. (1430),havingonestrangequark,isalmostdegenerate ItisnotclearwhyK0√¯)/witha0(1450),assumingthelateris(uu¯ dd

2,ss¯andglueball.Whichiswhich?Is

themixingmorelikethatof√thepseudoscalarsectorwherethereissubstantial¯)/mixingbetween(uu¯+dd

=0,±1,±2...)

andcheckifthereexistsaboundstatewhichisseparatedfromthediscretescatteringstates.Inthecontextoftheexistenceofσ(600),oneneedsto rstworkinthechiralregionwheremπ<300MeVinrecognitionofthefactthattheoccurrenceofσisonthebasisof‘currentalgebra,spontaneoussymmetrybreakdown,andunitarity’.8)Secondly,oneneedstoidentifyboththetetraquarkmesoniumandthecollateralππscatteringstates.Thirdly,itisnecessarytoworkonalatticewherethescatteringstatesandtheboundstatearewellseparated(e.g.furtherapartthanhalfofthe‘wouldbe’resonancewidth)inordertodiscernthenatureofthesestatesseparatelytomakesurethatσisindeedaone-particlestateandnotatwo-particlescatteringstate.Tothisend,arecentlatticeQCDcalculationwascarriedouton123×32and163×32latticeswitha=0.2fmand300con gurationstoexaminethespectrumwiththeΨγ5Ψtypeoffour-quarkinterpolationoperators.Althoughaquenchedcalculation,itincorporatesthechiralfermion(overlapfermion)inthechiralregionwiththepionmassaslowas182MeV.Resultsonthe123×28latticearepresentedinFig.2asafunctionofm2πforthepionmassrangefrom182MeVLa,n