Interference Between Cabibbo Allowed and Doubly Forbidden Transitions in D\ra K_{S,L} + \pi 's Decays

Both Cabibbo allowed and doubly forbidden transitions contribute coherently to $D\rightarrow K_{S,L}+\pi 's$ decays. This leads to several intriguing and even quantitatively significant consequences, among them: (i) A difference between $\Gamma (D^+\rightarrow K_S \pi ^+)$ and $\Gamma (D^+\rightarrow K_L \pi ^+)$ and between $\Gamma (D^0\rightarrow K_S \pi ^0)$ and $\Gamma (D^0\rightarrow K_L \pi ^0)$ of roughly 10\% ; similarly $\Gamma (D^+\rightarrow [K_S\pi ^0]_{K^*} \pi ^+) \neq \frac{1}{4}\Gamma (D^+\rightarrow [K^-\pi ^+]_{K^*} \pi ^+)$, and more generally $\Gamma (D\rightarrow \bar K^0+\pi 's) \neq 2\Gamma (D\rightarrow K_S+\pi 's)$. (ii) A change in the relative phase between the isospin 3/2 and 1/2 amplitudes as extracted from the observed branching ratios for $D^+\rightarrow K_S\pi ^+$, $D^0\rightarrow K_S\pi ^0 ,\, K^-\pi ^+$. (iii) If New Physics intervenes to provide the required {\em weak} phase, then CP asymmetries of up to a few per cent can arise in $D^+\rightarrow K_S\pi ^+$ vs. $D^-\rightarrow K_S\pi ^-$, $D^0\rightarrow K_S\pi ^0$ vs. $\bar D^0\rightarrow K_S\pi ^0$, $D^+\rightarrow [K_S\pi ^0]_{K^*}\pi ^+$ vs. $D^-\rightarrow [K_S\pi ^0]_{K^*}\pi ^-$, etc.; an asymmetry of the same size, but opposite in sign occurs when the $K_S$ is replaced by a $K_L$ in the final state.Comment: 6 pages, latex, no figure

Understanding I=2 pi-pi Interaction

A correct understanding and description of the I=2 pi-pi S-wave interaction is important for the extraction of the I=0 pi-pi S-wave interaction from experimental data and for understanding the I=0 pi-pi S-wave interaction theoretically. With t-channel rho, f2(1270) exchange and the pi pi -> rho rho -> pi pi box diagram contribution, we reproduce the pi-pi isotensor S-wave and D-wave scattering phase shifts and inelasticities up to 2.2 GeV quite well in a K-matrix formalism.Comment: Talk given at Hadron 03: 10th International Conference on Hadron Spectroscopy, Aschaffenburg, Germany, 31 Aug - 6 Sep 200

D^+_s -> pi^+ pi^+ pi^- decay: the 1^3P_0 s anti-s component in scalar-isoscalar mesons

On the basis of data on the decay D^+_s -> pi^+ pi^+ pi^-, which goes dominantly via the transition D_s -> pi^+ s anti-s, we evaluate the 1^3P_0 s anti-s components in the scalar-isoscalar resonances f0(980), f0(1300), f0(1500) and broad state f0(1200-1600)$. The data point to a large s anti-s component in the f0(980): 40% < s anti-s < 70%. Nearly 30% of the 1^3P_0 s anti-s component flows to the mass region 1300-1500 MeV being shared by f0(1300), f0(1500) and broad state f0(1200-1600): the interference of these states results in a peak near 1400 MeV with the width around 200 MeV.Comment: 17 pages, 4 figures, epsfi

On the role of three functions in the Riemann literatures

In Riemann's paper and Nachlass on the zeta function, $\pi^{-\frac{s}{2}}\Gamma(\frac{s}{2})\zeta(s)$ has three different functional expressions, of which $$\pi^{-\frac{s}{2}}\Gamma(\frac{s}{2})\zeta(s)=2\Re[\pi^{-\frac{s}{2}}\Gamma(\frac{s}{2})f(s)],\qquad\Re(s)=1/2$$ still has no literature to study it so far. Based on its geometric meaning, we obtain the number of zeros of the Riemann zeta function on the critical line is $$\frac{T}{2\pi}\log\frac{T}{2\pi}-\frac{T}{2\pi}+\frac{\arg{f(1/2+iT)}}{\pi}+O(T^{-1}).$$ Research shows that Riemann's assertion about ~"One now finds indeed approximate this number of real roots within these limits" comes from this functional expression of $\pi^{-\frac{s}{2}}\Gamma(\frac{s}{2})\zeta(s)$ which associated with the Jacobi function. Finally, this paper analyzes the reason why these conclusions are neglected.Comment: AMS-LaTeX v2.2, 11 page

ππ\pi\pi scattering S wave from the data on the reaction π−p→π0π0n\pi^-p\to\pi^0\pi^0n

The results of the recent experiments on the reaction $\pi^-p\to\pi^0\pi^0n$ performed at KEK, BNL, IHEP, and CERN are analyzed in detail. For the I=0 $\pi\pi$ S wave phase shift $\delta^0_0$ and inelasticity $\eta^0_0$ a new set of data is obtained. Difficulties emerging when using the physical solutions for the $\pi^0\pi^0$ S and D wave amplitudes extracted with the partial wave analyses are discussed. Attention is drawn to the fact that, for the $\pi^0\pi^0$ invariant mass, m, above 1 GeV, the other solutions, in principle, are found to be more preferred. For clarifying the situation and further studying the $f_0(980)$ resonance thorough experimental investigations of the reaction $\pi^-p\to\pi^0\pi^0n$ in the m region near the $K\bar K$ threshold are required.Comment: 17 pages, 5 figure

The teaching profession in Europe : historical and sociological analysis

A possible effect of direct CP violation in D -> K-S(0)pi(+)pi(-) decay on the gamma measurement from B-+/- -> DK +/-, D -> K-S(0)pi(+)pi(-) Dalitz plot analysis is considered. Systematic uncertainty of gamma coming from the current limits on direct CP violation in D -> K-S(0)pi(+)pi(-) is estimated, and a modified model-independent procedure of B-+/- -> DK +/-, D -> K-S(0)pi(+)pi(-) Dalitz plot analysis is proposed that gives an unbiased gamma measurement even in presence of direct CP violation in charm decays. The technique is applicable to other threebody D decays such as D-0 -> (KSK+K-)-K-0, D-0 -> pi(+)pi(-)pi(0), etc