VI. The quark model: hadron quantum numbers, resonances

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1 VI. The qark model: hadron qantm nmbers, resonances Characteristics of a hadron: 1) Mass 2) Qantm nmbers arising from space symmetries : J, P, C. Common notation: J P (e.g. for proton: ), or J PC if a particle is also an eigenstate of C-parity (e.g. for 0 : 0 -+ ) 3) Internal qantm nmbers: Q and B (always conserved), S C B T (conserved in electromagnetic and strong interactions) How do we know what are qantm nmbers of a newly discovered hadron? How do we know that mesons consist of a qark-antiqark pair, and baryons of three qarks? Oxana Smirnova Lnd University 161

2 Some a priori knowledge is needed: Particle Mass (Gev/c2) Qark composition Q B S C B p d n dd K s D dc B b For the lightest 3 qarks (, d, s), possible 3-qark and 2-qark states will be (q i,j,k are - or d- qarks): sss ssq i sq i q j q i q j q k ss sq i sq i q i q i q i q j S Q -1 0; -1 1; 0; -1 2; 1; 0; ; -1 1; 0 0-1; 1 Hence restrictions arise: for example, mesons with S = -1 and Q = 1 are forbidden Oxana Smirnova Lnd University 162

3 Particles which fall ot of above restrictions are called exotic particles (like dds, ds etc.) From observations of strong interaction processes, qantm nmbers of many particles can be dedced: p + p p + n + + p + p p + p + 0 Q= Q= S= S= B= B= p n Q= S= B= Observations of pions confirm these predictions, ensring that pions are non-exotic particles. Oxana Smirnova Lnd University 163

4 Assming that K - is a strange meson, one can predict qantm nmbers of -baryon: K - + p 0 + Q= S= B= And frther, for K + -meson: - + p K Q= S= B= All of the more than 200 hadrons of certain existence satisfy this kind of predictions It so far confirms validity of the qark model, which sggests that only qark-antiqark and 3-qark (or 3-antiqark) states can exist Oxana Smirnova Lnd University 164

5 Pentaqark observation In 1997, a theoretical model predicted pentaqark possibility with mass 1.54 GeV Since 2003, LEPS/SPring-8 experiment in Japan reports observation of a particle with precisely this mass, and having strctre consistent with pentaqark Figre 89: Pentaqark prodction and observation at JLab Reported particle composition: dds, B = +1, S = +1, spin = 1/2 Oxana Smirnova Lnd University 165

6 LEPS/SPring-8 experimental setp: + n (1540) + K - K + + K - + n Laser beam was shot to a target made of liqid deterim Figre 90: New particle signal (the peak) pblished by LEPS in 2009 A reference target of liqid hydrogen (only protons) showed no sch signal Many experiments reported similar observations Still, many dedicated precision experiments show no signal Main problem: how to estimate the backgrond. Search contines... Oxana Smirnova Lnd University 166

7 Even more qantm nmbers... It is convenient to introdce some more qantm nmbers, which are conserved in strong and electromagnetic interactions: Sm of all internal qantm nmbers, except of Q, Instead of Q : hypercharge Y B + S + C + B + T I 3 Q - Y/2...which is to be treated as a projection of a new vector: Isospin I (I 3 ) max so that I 3 takes 2I+1 vales from -I to I I 3 is a good qantm nmber to denote p- and down- qarks, and it is convenient to se notations for particles as: I(J P ) or I(J PC ) Oxana Smirnova Lnd University 167

8 B S C B T Y Q I 3 1/ /3 2/3 1/2 d 1/ /3-1/3-1/2 s 1/ /3-1/3 0 c 1/ /3 2/3 0 b 1/ /3-1/3 0 t 1/ /3 2/3 0 Hypercharge Y, isospin I and its projection I 3 are additive qantm nmbers, ths qantm nmbers for hadrons can be dedced from those of qarks: Y a+ b = Y a + Y b ; Ia + b 3 = Ia 3 + Ib 3 I a + b I a I b I a I b 1 I a I b = + Proton and netron both have isospin of 1/2, and also very close masses: + p(938) = d ; n(940) = dd : I J P 1 = proton and netron are said to belong to isospin doblet Oxana Smirnova Lnd University 168

9 Other examples of isospin mltiplets: K + (494) = s ; K 0 (498) = ds : I J P 1 = (140) = d ; - (140) = d : I J P 10 - = and 0 (135) = (-dd)/ 2 : I J PC = Principle of isospin symmetry: it is a good approximation to treat - and d-qarks as having same masses Particles with I=0 are called isosinglets : (1116) = ds, I J P = By introdcing isospin, we get more criteria for non-exotic particles: sss ssq i sq i q j q i q j q k ss sq i sq i q i q i q i q j S Q -1 0; -1 1; 0; -1 2; 1; 0; ; -1 1; 0 0-1; 1 I 0 1/2 0; 1 3/2; 1/2 0 1/2 1/2 0; 1 0; 1 Oxana Smirnova Lnd University 169

10 In all observed interactions (save pentaqarks) isospin-related criteria are satisfied as well, confirming once again the qark model. This allows predictions of possible mltiplet members: sppose we observe prodction of the + baryon in a strong interaction: which then decays weakly : K - + p n p It follows that + baryon qantm nmbers are: B = 1, Q = 1, S = -1 and hence Y = 0 and I 3 = 1. Since I 3 >0 I 0 and there are more mltiplet members! Oxana Smirnova Lnd University 170

11 When a baryon has I 3 =1, the only possibility for isospin is I=1, and we have a triplet: S +, S 0, S - Indeed, all sch particles have been observed: K - + p K - + p n Masses and qark composition of -baryons are: + (1189) = s ; 0 (1193) = ds ; - (1197) = dds It indicates that d-qark is heavier than -qark, nder following assmptions: (a) strong interactions between qarks do not depend on their flavor and give contribtion of M o to the baryon mass (b) electromagnetic interactions contribte as e i e j, where e i are qark charges and is a constant Oxana Smirnova Lnd University 171

12 The simplest attempt to calclate mass difference of p- and downqarks: M( - ) = M 0 + m s + 2m d + /3 M( 0 ) = M 0 + m s + m d + m - /3 M( + ) = M 0 + m s + 2m m d - m = [ M( - ) + M( 0 ) -2M( + ) ] / 3 = 3.7 MeV/c 2 NB : this is a very simplified model, as nder these assmptions M( 0 ) = M( ), while their mass difference M( 0 ) - M( ) 77 Mev/c 2. Generally, combining other methods: 2 m d - m 4 ( MeV/c 2 ) which is negligible comparing to hadron masses (bt not if compared to estimated and d masses themselves) Oxana Smirnova Lnd University 172

13 Resonances Resonances are highly nstable particles that decay by strong interaction (lifetimes abot s) L=0 1 S 0 3 S 1 d d I(J P )=1(0 - ) I(J P )=1(1 - ) grond state resonance Figre 91: Example of a qq system in grond and first excited states If a grond state is a member of an isospin mltiplet, then resonant states will form a corresponding mltiplet too Since resonances have very short lifetimes, they can only be detected by registering their decay prodcts: - + p n + X A + B Oxana Smirnova Lnd University 173

14 Invariant mass of a particle is measred via energies and masses of its decay prodcts (see 4-vectors in Chapter I.): W 2 E A + E B 2 p A + p B 2 = E 2 p 2 = M 2 (102) Figre 92: A typical resonance peak in K + K - invariant mass distribtion Oxana Smirnova Lnd University 174

15 Resonance peak shapes are approximated by the Breit-Wigner formla: NW N(W) = K W W (103) N max N max /2 W 0 W Figre 93: Breit-Wigner shape Mean vale of the Breit-Wigner shape is the mass of a resonance: M=W 0 is the width of a resonance, and it has the meaning of inverse mean lifetime of particle at rest: Oxana Smirnova Lnd University 175

16 Internal qantm nmbers of resonances are also derived from their decay prodcts: X for sch X 0 : B = 0 ; S = C = B = T = 0 ; Q = 0 Y=0 and I 3 =0. When I 3 =0, to determine whether I=0 or I=1, searches for isospin mltiplet partners have to be done. Example: 0 (769) and 0 (1700) both decay to + - pair and have isospin partners + and - : + p p By measring anglar distribtion of + - pair, the relative orbital anglar momentm of the pair L can be determined, and hence spin and parity of the resonance X 0 are (S=0): J = L ; P = P2 1 L = 1 L ; C = 1 L Oxana Smirnova Lnd University 176

17 Some excited states of pion: resonance I(J PC ) 0 (769) 1(1 - - ) f 2 0 (1275) 0(2 ++ ) 0 (1700) 1(3 - - ) B=0 : meson resonances, B=1 : baryon resonances. Many baryon resonances can be prodced in pion-ncleon scattering: } X p R N Figre 94: Formation of a resonance R and its decay into a ncleon N Peaks in the observed total cross-section of the p-reaction correspond to resonance formation Oxana Smirnova Lnd University 177

18 Figre 95: Scattering of + and - on proton Oxana Smirnova Lnd University 178

19 All the resonances prodced in pion-ncleon scattering have the same internal qantm nmbers as the initial state: and ths Y=1 and Q=I 3 +1/2 B = 1 ; S = C = B = T = 0 Possible isospins are I=1/2 or I=3/2, since for pion I=1 and for ncleon I=1/2 I=1/2 N-resonances (N 0, N + ) I=3/2 -resonances ( ) Figre 95: peaks at 1.2 GeV/c 2 correspond to ++ and 0 resonances: + + p p - + p p 0 + n Oxana Smirnova Lnd University 179

20 Fits by the Breit-Wigner formla show that both ++ and 0 have approximately same mass of 1232 MeV/c 2 and width 120 MeV/c 2. Stdies of anglar distribtions of decay prodcts show that I J P 3 = Remaining members of the mltiplet are also observed: + and - 2 There is no lighter state with these qantm nmbers is a grond state, althogh observed as a resonance. Qark diagrams Qark diagrams are convenient way of illstrating strong interaction processes Consider an example: ++ p + + The only 3-qark state consistent with ++ qantm nmbers (Q=2) is (), while p=(d) and + =(d) Oxana Smirnova Lnd University 180

21 ++ d d + p Figre 96: Qark diagram of the reaction ++ p + + Analogosly to Feinman diagrams: arrow pointing rightwards denotes a particle, and leftwards antiparticle time flows from left to right Allowed resonance formation process: + d ++ d + p d d p Figre 97: Formation and decay of ++ resonance in + p elastic scattering Oxana Smirnova Lnd University 181

22 Hypothetical exotic resonance: + s ++ s + p d d p Figre 98: Exotic resonance Z ++ in K + p elastic scattering Qantm nmbers of sch a particle Z ++ are exotic. There are no resonance peaks in the corresponding cross-section, bt data are scarce: Center of mass energy (GeV) Figre 99: Cross-section for K + p scattering Oxana Smirnova Lnd University 182

23 Figre 100: Pentaqark searches stats as of October 2005, by Pal Stoler Oxana Smirnova Lnd University 183