U-spin analysis of CP violation in B−B^- decays into three charged light pseudoscalar mesons

We carry out a $U$-spin symmetry analysis for CP violation in $B^-$ decays into three light $\pi^-\pi^-\pi^+$, $\pi^- K^-K^+$, $K^-K^-K^+$ and $K^- \pi^-\pi^+$ mesons. We clarify some subtle points in constructing decay amplitudes with $U=0$ formed by the two negatively charged light mesons in the final states. $U$-spin conserving momentum independent and momentum dependent decay amplitudes, and $U$-spin violating decay amplitudes due to quark mass difference are constructed.Comment: RevTex 12 pages wit no figur

The β\beta angle as the CP violating phase in the CKM matrix

The CKM matrix describing quark mixing with three generations can be parameterized by three Euler mixing angles and one CP violating phase. In most of the parameterizations, the CP violating phase chosen is not a directly measurable quantity and is parametrization dependent. In this work, we propose to use the most accurately measured CP violating angle $\beta$ in the unitarity triangleas the phase in the CKM matrix, and construct an explicit $\beta$ parameterization. We also derive an approximate Wolfenstein-like expression for this parameterization.Comment: RevTex 7 pages with one figure. Version to be published in Phys. Lett. B. arXiv admin note: substantial text overlap with arXiv:1204.123

The α\alpha, β\beta and γ\gamma parameterizations of CP violating CKM phase

The CKM matrix describing quark mixing with three generations can be parameterized by three mixing angles and one CP violating phase. In most of the parameterizations, the CP violating phase chosen is not a directly measurable quantity and is parametrization dependent. In this work, we propose to use experimentally measurable CP violating quantities, $\alpha$, $\beta$ or $\gamma$ in the unitarity triangle as the phase in the CKM matrix, and construct explicit $\alpha$, $\beta$ and $\gamma$ parameterizations. Approximate Wolfenstein-like expressions are also suggested.Comment: 14 page, 1 figur

NLO fragmentation functions for a quark into a spin-singlet quarkonium: Same flavor case

In the paper, we calculate the fragmentation functions for $c \to \eta_c$ and $b \to \eta_b$ up to next-to-leading-order (NLO) QCD accuracy. The ultraviolet divergences in the real corrections are removed through operator renormalization under the modified minimal subtraction scheme. We then obtain the fragmentation functions $D_{c \to \eta_c}(z,\mu_F)$ and $D_{b \to \eta_b}(z,\mu_F)$ up to NLO QCD accuracy, which are presented as figures and fitting functions. The numerical results show that the NLO corrections are significant. The sensitives of the fragmentation functions to the renormalization scale and the factorization scale are analyzed explicitly.Comment: 18 pages, 7 figure

The Υ(1S)\Upsilon(1S) leptonic decay using the principle of maximum conformality

In the paper, we study the $\Upsilon(1S)$ leptonic decay width $\Gamma(\Upsilon(1S)\to \ell^+\ell^-)$ by using the principle of maximum conformality (PMC) scale-setting approach. The PMC adopts the renormalization group equation to set the correct momentum flow of the process, whose value is independent to the choice of the renormalization scale and its prediction thus avoids the conventional renormalization scale ambiguities. Using the known next-to-next-to-next-to-leading order perturbative series together with the PMC single scale-setting approach, we do obtain a renormalization scale independent decay width, $\Gamma_{\Upsilon(1S) \to e^+ e^-} = 1.262^{+0.195}_{-0.175}$ keV, where the error is squared average of those from $\alpha_s(M_{Z})=0.1181\pm0.0011$, $m_b=4.93\pm0.03$ GeV and the choices of factorization scales within $\pm 10\%$ of their central values. To compare with the result under conventional scale-setting approach, this decay width agrees with the experimental value within errors, indicating the importance of a proper scale-setting approach.Comment: 6 pages, 4 figure