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Register a new userA Note on CP Invariance and Rephasing Invariance
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T. Kurimoto
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CP invariance condition and rephasing invariance in KM scheme of CP violation is discussed. The CP violation measures in B physics, corresponding to the three angles of unitarity triangle are given in rephasing invariant form. With the obtained results it is shown that the sum of the three CP angles to be measured at B factories becomes $pi$ even if the Kobayashi-Maskwa matrix is not a $3times 3$ unitary matrix under reasonable assumptions.
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We identified a set of four rephasing invariant parameters of the CKM matrix. They are found to exhibit hierarchies in powers of $lambda^2$, from $lambda^2$ to $lambda^8$. It is shown that, at the present level of accuracy, only the first three parameters are needed to fit all available data on flavor physics.
The most general lagrangian describing spin 2 particles in flat spacetime and containing operators up to (mass) dimension 6 is carefully analyzed, determining the precise conditions for it to be invariant under linearized (transverse) diffeomorphisms, linearized Weyl rescalings, and conformal transformations.
We present the joint helicity amplitudes for $J/psi to Lambda bar{Lambda}$, $Lambda(barLambda)$ decays to different final states in the helicity frame. Two observables to search for $CP$ violation in $J/psitoLambdabarLambda$ can be expressed with the information of helicity angles of baryon and antibaryon. Four decay parameters of $Lambda$ and $barLambda$, namely, $alpha_-,alpha_+,alpha_0$ and $baralpha_0$, can be obtained with the joint helicity amplitude equations by the likelihood fit method. With the data sample of $10^{10}$ $J/psi$ decays accumulated by BESIII, the precision of the measurements is estimated to be about $10^{-3}$.
Several rotational invariant quantities for the lepton angular distributions in Drell-Yan and quarkonium production were derived several years ago, allowing the comparison between different experiments adopting different reference frames. Using an intuitive picture for describing the lepton angular distribution in these processes, we show how the rotational invariance of these quantities can be readily obtained. This approach can also be used to determine the rotational invariance or non-invariance of various quantities specifying the amount of violation for the Lam-Tung relation. While the violation of the Lam-Tung relation is often expressed by frame-dependent quantities, we note that alternative frame-independent quantities are preferred.
The strong coupling constant $1/g^2$ and the vacuum angle $theta$ of the SU(3) Yang-Mills theory are investigated in the infrared limit under the renormalization group flow. It is shown that the theory has an infrared attractive fixed point at $1/g^2 = theta = ,0$, which leads to linear confinement and naturally solves the strong CP problem. In particular, any initial value of $theta eq 0$ is found to be driven to $theta = 0$ at macroscopic distances, where quarks and gluons freeze into hadrons by the confinement mechanism.
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