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Register a new usereta - eta Mixing -- From Electromagnetic Transitions to Weak Decays of Charm and Beauty Hadrons (presented at Hadron 2011)
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It has been realized for a long time that knowing the eta and eta wave functions in terms of quark and gluon components probes our understanding of non-perturbative QCD dynamics. Great effort has been given to this challenge -- yet no clear picture has emerged even with the most recent KLOE data. We point out which measurements would be most helpful in arriving at a more definite conclusion. A better knowledge of these wave functions will significantly help to disentangle the weight of different decay subprocesses in semi-leptonic decays of D^+, D_s^+ and B^+ mesons. The resulting insights will be instrumental in treating even non-leptonic B transitions involving $eta$ and $eta^{prime}$ and their CP asymmetries; thus they can sharpen the case for or against New Physics intervening there.
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First observations of the decays $Lambda_b^0 to Lambda_c^+ D_{(s)}^-$ are reported using data corresponding to an integrated luminosity of $3,{rm fb}^{-1}$ collected at 7 and 8 TeV center-of-mass energy in proton-proton collisions with the LHCb detector. In addition, the most precise measurement of the branching fraction ${mathcal{B}(B_s^0 to D^+D_s^-)}$ is made and a search is performed for the decays $B^0_{(s)} to Lambda_c^+ Lambda_c^-$. The results obtained are begin{eqnarray*} mathcal{B}(Lambda_b^0 to Lambda_c^+ D^-)/mathcal{B}(Lambda_b^0 to Lambda_c^+ D_{s}^-) &=& 0.042 pm 0.003({rm stat}) pm 0.003({rm syst}), left[frac{mathcal{B}(Lambda_b^0 to Lambda_c^+ D_{s}^-)}{mathcal{B}({kern 0.2em}overline{kern -0.2em B}_d^0 to D^+D_s^-)}right]big/left[frac{mathcal{B}(Lambda_b^0 to Lambda_c^+pi^-)}{mathcal{B}({kern 0.2em}overline{kern -0.2em B}_d^0 to D^+pi^-)}right] &=& 0.96 pm 0.02({rm stat}) pm 0.06({rm syst}), mathcal{B}(B_s^0 to D^+D_s^-)/mathcal{B}({kern 0.2em}overline{kern -0.2em B}_d^0 to D^+D_s^-) &=& 0.038pm0.004({rm stat})pm0.003({rm syst}), mathcal{B}({kern 0.2em}overline{kern -0.2em B}^0 to Lambda_c^+ Lambda_c^-)/mathcal{B}({kern 0.2em}overline{kern -0.2em B}_d^0 to D^+D_s^-) & < & 0.0022; [95% ; {rm C.L.}], mathcal{B}(B^0_{s} to Lambda_c^+ Lambda_c^-)/mathcal{B}(B_s^0 to D^+D_s^-) & < & 0.30; [95% ; {rm C.L.}]. end{eqnarray*} Measurement of the mass of the $Lambda_b^0$ baryon relative to the $B^0$ meson gives ${M(Lambda_b^0) -M(B^0) = 339.72pm 0.24({rm stat}) pm 0.18({rm syst})}$ MeV$/c^2$. This result provides the most precise measurement of the mass of the $Lambda_b^0$ baryon to date.
A value for the $eta$-$eta^prime$ mixing angle is extracted from the data on $VPgamma$ transitions using simple quark-model ideas. The set of data covers {it all} possible radiative transitions between the pseudoscalar and vector meson nonets. Two main ingredients of the model are the introduction of flavour-dependent overlaps for the various $qbar{q}$ wave functions and the use of the quark-flavour basis to describe the $eta$-$eta^prime$ system. In this basis the mixing angle is found to be $phi_P=(37.7pm 2.4)^circ$.
We present a lattice QCD computation of $eta$ and $eta^prime$ masses and mixing angles, for the first time controlling continuum and quark mass extrapolations. The results for the eta mass 551(8)(6) MeV (first error statistical, second systematic) and the eta mass 1006(54)(38)(+61) MeV (third error from our method) are in excellent agreement with experiment. Our data show that the mixing in the quark flavour basis can be described by a single mixing angle of 46(1)(3) degree indicating that the eta is mainly a flavour singlet state.
We have revisited glueball mixing with the pseudoscalar mesons in the MIT bag model scheme. The calculation has been performed in the spherical cavity approximation to the bag using two different fermion propagators, the cavity and the free propagators. We obtain a very small probability of mixing for the eta at the level of $0.04-0.1% and a bigger for the eta at the level of 4-12%. Our results differ from previous calculations in the same scheme but seem to agree with the experimental analysis. We discuss the origin of our difference which stems from the treatment of our time integrations.
Since the discovery of CP violation more than 5 decades ago, this phenomenon is still attracting a lot of interest. Among the many fascinating aspects of this subject, this review is dedicated to direct CP violation in non-leptonic decays. The advances within the last decade have been enormous, driven by the increasingly large samples of b- and c-hadron decays, and have led to very interesting results such as large CP asymmetries in charmless B decays and the observation of direct CP violation in the charm sector. We address the quest for understanding the origin of strong phases, the importance of final state interactions and the relation with CPT symmetry, and different approaches to measure direct CP violation in these decays. The main experimental results and their implications are then discussed.
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