Study of tau- --> V P- nu(tau) in the framework of resonance chiral theory

In this paper we study two kinds of tau decays: (a) tau- --> (rho pi-,omega pi-, phi pi-, K*0 K-) nu(tau), which belong to Delta S=0 processes and (b) Delta S = 1 processes, like tau- --> (rho K-, omega K-, phi K-, \bar{K*0} pi-) nu(tau), in the framework of resonance chiral theory. We fit the tau- --> omega pi- nu(tau) spectral function and the invariant mass distribution of omega K in the process of tau- --> omega K- nu(tau) to get the values of unknown resonance couplings. Then we make a prediction for branching ratios of all channels.Comment: Published version; References added. 20 pages, 3 figures, 2 table

One meson radiative tau decays

We have studied the one meson radiative tau decays: tau- -> nu(tau) pi-(K-) gamma, computing the structure dependent contributions within a Lagrangian approach based on the large-N(C) limit of QCD that ensures the proper low-energy limit dictated by chiral symmetry. Upon imposing the short-distance QCD constraints to the form-factors we are able to predict without any free parameter the structure dependent radiation and, therefore, the relevant observables for the decay tau- -> nu(tau) pi- gamma: the photon energy spectrum, the invariant mass spectrum of the meson-photon system and the integrated decay rate. We also discuss the remaining uncertainties in these observables for the tau- -> nu(tau) K- gamma decay. According to our results, the present facilities could detect these rare decays for the first time in the near future allowing for a stringent test of our predictions.Comment: 40 pages, 13 figures, 2 tables. Published version: discussion on the QCD short distance behavior added in Section VI and corresponding references included too; numerical results and conclusions not change

Some congruences involving binomial coefficients

Binomial coefficients and central trinomial coefficients play important roles in combinatorics. Let $p>3$ be a prime. We show that $$T_{p-1}\equiv\left(\frac p3\right)3^{p-1}\ \pmod{p^2},$$ where the central trinomial coefficient $T_n$ is the constant term in the expansion of $(1+x+x^{-1})^n$. We also prove three congruences modulo $p^3$ conjectured by Sun, one of which is $$\sum_{k=0}^{p-1}\binom{p-1}k\binom{2k}k((-1)^k-(-3)^{-k})\equiv \left(\frac p3\right)(3^{p-1}-1)\ \pmod{p^3}.$$ In addition, we get some new combinatorial identities.Comment: 9 pages, final published versio

Pi pi scattering lengths at O(p^6) revisited

This article completes a former work where part of the O(p^6) low-energy constants entering in the pi pi scattering were estimated. Some resonance contributions were missed in former calculations and slight differences appeared with respect to our outcome. Here, we provide the full results for all the contributing O(p^6) couplings. We also perform a reanalysis of the hadronic inputs used for the estimation (resonance masses, widths...). Their reliability was checked together with the impact of the input uncertainties on the determinations of the chiral couplings and the scattering lengths a^I_J. Our outcome is found in agreement with former works though with slightly larger errors. However, the effect in the final values of the a^I_J is negligible after combining them with the other uncertainties. Based on this consistency, we conclude that the previous scattering length determinations seem to be rather solid and reliable, with the cO(p^6) low-energy constants quite under control. Nevertheless, the uncertainties found in the present work point out the limitation on further improvements unless the precision of the O(p^6) couplings is properly increased.Comment: 19 pages. Improved treatment of the a0 decay width and update of the numerical outcomes. Final version published in Phys. Rev. D (10.1103/PhysRevD.79.096006

The Strong Decays of Orbitally Excited BsJ∗B^{*}_{sJ} Mesons by Improved Bethe-Salpeter Method

We calculate the masses and the strong decays of orbitally excited states $B_{s0}$, $B'_{s1}$, $B_{s1}$ and $B_{s2}$ by the improved Bethe-Salpeter method. The predicted masses of $B_{s0}$ and $B'_{s1}$ are $M_{B_{s0}}=5.723\pm0.280 {\rm GeV}$, $M_{B'_{s1}}=5.774\pm0.330 {\rm GeV}$. We calculate the isospin symmetry violating decay processes $B_{s0}\to B_s \pi$ and $B'_{s1}\to B_s^* \pi$ through $\pi^0-\eta$ mixing and get small widths. Considering the uncertainties of the masses, for $B_{s0}$ and $B'_{s1}$, we also calculate the OZI allowed decay channels: $B_{s0}\to B\bar K$ and $B'_{s1}\to B^*\bar K$. For $B_{s1}$ and $B_{s2}$, the OZI allowed decay channels $B_{s1}\to B^{*}\bar K$, $B_{s2}\to B\bar K$ and $B_{s2}\to B^{*}\bar K$ are studied. In all the decay channels, the reduction formula, PCAC relation and low energy theorem are used to estimate the decay widths. We also obtain the strong coupling constants $G_{B_{s0}B_s\pi}$, $G_{B_{s0}B\bar K}$, $G_{B'_{s1}B_s^*\pi}$, $F_{B'_{s1}B_s^*\pi}$, $G_{B'_{s1}B^*\bar K}$, $F_{B'_{s1}B^*\bar K}$, $G_{B_{s1}B^{*}\bar K}$, $F_{B_{s1}B^{*}\bar K}$, $G_{B_{s2}B\bar K}$ and $G_{B_{s2}B^{*}\bar K}$.Comment: 21 pages, 1 figure, 4 table