Strangeness neutral Kaons Beam of K 0 produced

Strangeness & neutral Kaons � Beam of K 0 produced in an accelerator usually consisted of 2 types of particles with almost same mass (497. 7 Me. V) �They differ in lifetime and mode of decay �Ks 0 : life time = 8. 9 x 10 -11 seconds Decay products : two pions � KL 0 : life time = 5. 2 x 10 -8 seconds Decay products : three particles � m(KL 0)- m(Ks 0 )= 3. 6 X 10 -12 Me. V �Due to these reasons Ks 0 & KL 0 are not particle-antiparticle pair.

Strangeness & neutral Kaons � M Gellmann’s theory K 0 & its antiparticle K 0 (both have exactly same mass , spin (0) and electrical charge(0) but they differ in strangeness) �Most rapid decay mode of each is to two pions (π+π- or π0π0) by weak interaction (strangeness is changed by one unit) �De Broglie : wave nature of material particles �In a beam of K 0 & K 0 , interference occurs between wave functions of the particle and anti particle. �Points where wave functions are added: Decay to two pions (fast process) �Points where wave functions are subtracted: Decay into three particles (complicated and slow process) �Both Ks 0 & KL 0 posses mixed strangeness (+1 and -1)

Strangeness & multiplets �Hadrons can be arranged in groups called ‘multiplets’ �Particles in each group have same strangeness(S), baryon number(A) & spin(s) and only slightly different masses �Proton - neutron: spin=1/2 , A=1, strangeness=0 slightly different masses can be considered as 2 states of one particle(nucleon)

Strangeness & multiplets �Doublets: �Triplets: �Singlet's: �For every multiplets of baryons there is a similar multiplet of antibaryons �Only particles of same S are included in the multiplet : 2 kaon multiplets

Strangeness & multiplets � Multiplets differ from one another in �Number of particles �Average charge � Nucleon doublet: average charge=+1/2 � Xi doublet : average charge= -1/2 (charge: p=1, n=0) (charge: Ξ 0=0, Ξ- = -1) �Relation between average charge & strangeness � Multiplet Average Charge Strangeness 1/2 0 0 -1 - 1/2 -2 -1 -3

Strangeness & multiplets � The more negative the average electric charge, the more negative the strangeness � New quantum number : hypercharge (Y) � Y= S+A valid for all hadrons � Gellmann-Nishijima’s predictions: � Predicted the existence of Ξ 0 by substituting S=-2, A=1 (Y=-1) � Predicted the existence of short lived Σ 0 after analysing the properties of the quantum number ‘isospin’ � Predicted the existence of Ω-

Conservation of isospin I & its component I 3 �By arranging hadrons in multiplets, 2 new quantum no: s are defined � 1) Isotopic spin (isospin I) � 2) I 3 conserved only in strong interactions conserved in strong & electromagnetic interactions

Conservation of isospin I �I-Depends on number of particles in the multiplet � � Isospin is like angular momentum. Isospin conservation corresponds to invariance under rotations in the imaginary space �The strong interactions do not have preferred direction in I-space. �Isospin invariance thus explains the fact that it takes about the same energy to extract a proton or a neutron. Force between n -n, p-p, n-p are the same �i. e strong force acts identically on all particles in a given multiplet �I is not conserved in weak and em interactions (they depend on charge)

Conservation of isospin component I 3 �Different particles in the same multiplets are distinguished by assigning a quantum number called Iz or I 3 � It is the projection of the isospin vector along the z- axis in the imaginary space in which it is defined �I 3 can take 2 I+1 values, between I and -I �I 3 is conserved in both strong and electromagnetic interactions �I & I 3 is meaningful to hadrons only �Charge Q of every hadron (in units of proton charge) �This eqn helped to predict Σ 0

Conservation of isospin component I 3 Multiplet Isospin I 3 1/2 : -1/2 1/2 : -1/2 1 : +1 : 0 : -1 0 0 0