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The Weak Interaction in the Framework of Grand Unification Theories
Published in K Grotz, H V Klapdor, S S Wilson, The Weak Interaction in Nuclear, Particle and Astrophysics, 2020
K Grotz, H V Klapdor, S S Wilson
The fact that the gluons themselves also carry colour charges leads to two important (particularly as far as grand unification theories are concerned) properties of the QCD, namely the confinement and the asymptotic freedom of quarks. Confinement means that quarks may physically exist only in bound systems which form colour singlets. An attempt to remove an individual quark from such a system requires so much potential energy that eventually a new quark–antiquark pair is formed. Together with the quarks already in existence, we then have two colour singlet states. This strong increase in the potential energy once a critical separation between the quarks is exceeded is caused by the gluon–gluon interaction due to the colour charge of the gluons (Figure 6.1b,c). Each gluon thus becomes the source of new gluons, and so the space between two quarks is filled by a gluon field, whose strength is more or less independent of the separation. Thus the potential energy increases roughly proportionally to the separation of the quarks. We recall that the potential energy in an interaction obeying Coulomb’s law grows increasingly weakly with the separation and finally attains a saturation value. On the other hand, the behaviour of the colour interaction for large separations may also be described by a Coulomb-type interaction, if we define an effective coupling constant geff which is not constant but increases with the separation.
Accurate determination of the enhancement factor X for the nuclear Schiff moment in 205TlF molecule based on the four-component relativistic coupled-cluster theory
Published in Molecular Physics, 2020
Minori Abe, Takashi Tsutsui, Jörgen Ekman, Masahiko Hada, Bhanu Das
The effective Hamiltonian due to the NSM can be written as follows [11] where, σN is the nucleus spin axis and λ is the inter-nuclear molecular axis of a diatomic system. Q is the magnitude of the Schiff moment of the nucleus, and is calculated as an expectation value using the nucleon wave function Ψn, perturbed by the P, T odd interactions [11]. At the particle physics level, the dominant contributions to the nuclear Schiff moment are the interaction of the chromo EDM of the quark with the gluon field and the interaction of the gluon field with its dual characterised by the parameter θ [12,13]. n and rn denote the nucleon index and coordinates. X is the electronic enhancement parameter given by, Here is the electronic density [11], and the z-axis is taken to be the molecular axis. X is the electronic enhancement factor also for the intrinsic nucleon EDMs, and this interaction is called the volume effect [11]. The effective Hamiltonian for the volume effect of 205TlF can be written as where dp is the value of the proton EDM and R is a parameter with the dimension of square of length calculated using the nuclear wave function [11].