Structure of Hadrons. quarks d (down) s (strange) c (charm)

Transcription

1 quaks Flavo A t t 0 S B T Q(e) Mc 2 (GeV) u (up) d (down) s (stange) c (cham) b (bottom) t (top) ±12 the least massive ae u- and d-quaks (hence the lightest bayons and mesons must be made exclusively of these two quaks) estimates based on popeties of hadons! stange quak caies a quantum numbe called stangeness S. Stange paticles (such as kaons) cay this quak thee ae also six antiquaks they ae femions; they cay half-intege spins Hadons bayons femions made up of thee quaks must have half-intege spins mesons bosons made up of quak-antiquaks * must have intege spins * Bosons can be annihilated; stong inteactions conseve the # of quaks

2 antipaticles p p Æ g g paticle-antipaticle annihilation paticle and antipaticle have opposite chages, bayon numbes, etc. they must have opposite intinsic paities they must have opposite isospins chage numbe Q = -t 0 A 2 bayon numbe thid component of isospin hage conjugation tansfoms paticles into antipaticles p = a 1/2,-1/2 n = b 1/2,-1/2 0 n = a 1/2,1/2 0 p = b 1/2,1/2 0 0 paticles antipaticles Paticles into antipaticles ae not independent of each othe; they tansfom into each othe though chage conjugation! b t,t0 = (-1) t -t 0 a t,- t0 p æ Æ p n æ Æ - n the same elation holds fo quaks u æ Æ u d æ Æ - d

3 isospin of quaks p = uud n = udd d- and u-quaks fom an isospin doublet t ± (nucleon) Æ t ± (q i ) 3 Â i=1 t u = d t - d = u quak wave functions of pions onside p - (t=1 and t 0 =1). The only possible combination is p - = u d In geneal, it is possible to find seveal linealy independent components coesponding to the same t and t 0. The appopiate combination is given by isospin coupling ules. Futhemoe, the wave function must be antisymmetic among the quaks p 0 = 1 2 t - p - = 1 2 p = - ud ( uu - dd ) T=1 tiplet What about the symmetic combination? ( uu dd ) h 0 = 1 2 T=0 singlet To poduce heavie mesons we have to intoduce excitations in the quak-antiquak system o invoke s- and othe moe massive quaks

4 stange mesons The lightest stange mesons ae kaons o K-mesons. They come in two doublets with t=1/2: { K (us), K 0 (ds)}, K - (u s),k 0 (d s) { } This means that s-quak has zeo isospin (no stange mesons with t=3/2 have been seen), Q = -t ( A S B T ) genealization p - (u d) p(uud) Æ K 0 (ds ) L(uds) stangeness is conseved! Stong inteactions conseve the total numbe of each type of quaks. Howeve, quaks can be tansfomed fom one flavo to anothe though weak inteactions (KM matix!).

5 colo onside a D-paticle. It has isospin 3/2 with fou diffeent chage states: D -,D 0,D,D Since it is nonstange bayon, is has to be made of u- and d-quaks. D has Q=2 and the only possiblity is a (uuu) combination. The intinsic paity of D is known to be positive, its intinsic spin is 3/2, and isospin is also 3/2. How to get the wave function that is untisymmetic with espect to a pemutation of any two of the thee quaks? Is Pauli wong? olo saves the day. It is a popety of quaks. Thee ae thee colos: R (ed), G (geen) and B (blue). The wave function has to be antisymmetic in the colo degee of feedom: the net colo in hadon must vanish! Since colo is an unobseved popety, all hadons must be cololess oblects!

6 static quak model of hadons pseudoscala mesons J = l S, I 3 =I 0 =-T 0 High-enegy physics S = s q s q J total angula momentum l obital angula momentum S total spin S can be eithe 0 o 1. The mesons with the elative zeo obital angula momentum ae lowe in enegy. Fo the pion, S=0, hence J=0. onsequently, pions ae scala paticles. But what about thei paity? The paity of the pion is a poduct of intinsic paities of the quak (1), antiquak (-1) and the paity of the spatial wave function (-1) l =1. Hance the pion has negative paity. It is a pseudoscala meson. With (u,d,s) quaks, one can constuct 9 pseudoscala mesons: 9=8 (octet)1 (singlet) Membes of the octet tansfom into each othe unde otations in flavo space (SU 3 goup!). The emaining meson, h 0, foms a 1-dim iep. p 0 = 1 2 h 8 = 1 6 h 0 = 1 3 ( uu - dd ) ( uu dd - 2 ss ) ( uu dd ss ) nuclea physics (ds ) (us ) (du ) (ud ) (su ) (sd ) masses ae given in MeV/c 2