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Register a new userAn $X(3872)$-like peak in $Bto (J/psipi^+pi^-) Kpi$ due to triangle singularity
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Satoshi X. Nakamura
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Triangle mechanisms for $B^0to (J/psipi^+pi^-) K^+pi^-$ are studied. Experimentally, an $X(3872)$ peak has been observed in this process. When the final $(J/psipi^+pi^-)pi$ invariant mass is around the $D^*bar D^*$ threshold, one of the triangle mechanisms causes a triangle singularity and generates a sharp $X(3872)$-like peak in the $J/psipi^+pi^-$ invariant mass distribution. The Breit-Wigner mass and width fitted to the spectrum are 3871.68 MeV (a few keV above the $D^{*0}bar{D}^0$ threshold) and $sim$0.4 MeV, respectively.These Breit-Wigner parameters hardly depends on a choice of the model parameters. Comparing with the precisely measured $X(3872)$ mass and width, $3871.69pm 0.17$ MeV and $< 1.2$ MeV, the agreement is remarkable. When studying the $X(3872)$ signal from this process, this non-resonant contribution has to be understood in advance. We also study a charge analogous process $B^0to (J/psipi^0pi^-) K^+pi^0$. A similar triangle singularity exists and generates an $X^-(3876)$-like peak.
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New spectroscopy from the B factories, the advent of CLEO-c and the BES upgrade renewed the interest in charmonia. Among the new measurements, the state X(3872) has received special attention due to its unexpected properties. Its structure has been studied with different theoretical approaches, most of them being able to reproduce the measured mass. A further test for the theoretical descriptions of the X(3872) is to explain its narrow decay width. In this work we address the decays $Xto J/psi pi^+pi^-pi^0$ and $Xto J/psi pi^+ pi^-$, using QCD sum rules with the hypothesis that $X$ is a four quark state.
We perform calculations for the $bar B_s^0 to J/psi pi^0 f_0(980)$ and $bar B_s^0 to J/psi pi^0 a_0(980)$ reactions, showing that the first one is isospin-suppressed while the second one is isospin-allowed. The reaction proceeds via a triangle mechanism, with $bar B_s^0 to J/psi K^* bar K +c.c.$, followed by the decay $K^* to Kpi$ and a further fusion of $Kbar K$ into the $f_0(980)$ or $a_0(980)$. We show that the mechanism develops a singularity around the $pi^0 f_0(980)$ or $pi^0 a_0(980)$ invariant mass of 1420 MeV where the $pi^0 f_0$ and $pi^0 a_0$ decay modes are magnified and also the ratio of $pi^0 f_0$ to $pi^0 a_0$ production. Using experimental information for the $bar B_s^0 to J/psi K^* bar K +c.c.$ decay, we are able to obtain absolute values for the reactions studied which fall into the experimentally accessible range. The reactions proposed and the observables evaluated, when contrasted with actual experiments should be very valuable to obtain information on the nature of the low lying scalar mesons.
A resonance-like structure as narrow as 10 MeV is observed in the $K^-p$ invariant mass distributions in $Lambda_c^+to p K^- pi^+$ at Belle. Based on the large data sample of about 1.5 million events and the small bin width of just 1 MeV for the $K^-p$ invariant mass spectrum, the narrow peak is found precisely lying at the $Lambdaeta$ threshold. While lacking evidence for a quark model state with such a narrow width at this mass region, we find that this narrow structure can be naturally identified as a threshold cusp but enhanced by the nearby triangle singularity via the $Lambda$-$a_0(980)^+$ or $eta$-$Sigma(1660)^+$ rescatterings.
Dalitz-plot analyses of $Brightarrow Kpipi$ decays provide direct access to decay amplitudes, and thereby weak and strong phases can be disentangled by resolving the interference patterns in phase space between intermediate resonant states. A phenomenological isospin analysis of $Brightarrow K^*(rightarrow Kpi)pi$ decay amplitudes is presented exploiting available amplitude analyses performed at the Babar, Belle and LHCb experiments. A first application consists in constraining the CKM parameters thanks to an external hadronic input. A method, proposed some time ago by two different groups and relying on a bound on the electroweak penguin contribution, is shown to lack the desired robustness and accuracy, and we propose a more alluring alternative using a bound on the annihilation contribution. A second application consists in extracting information on hadronic amplitudes assuming the values of the CKM parameters from a global fit to quark flavour data. The current data yields several solutions, which do not fully support the hierarchy of hadronic amplitudes usually expected from theoretical arguments (colour suppression, suppression of electroweak penguins), as illustrated from computations within QCD factorisation. Some prospects concerning the impact of future measurements at LHCb and Belle II are also presented. Results are obtained with the CKMfitter analysis package, featuring the frequentist statistical approach and using the Rfit scheme to handle theoretical uncertainties.
We report the first observation of $B^0 to X(3872) (K^{+}pi^{-})$ and evidence for $B^+ to X(3872) (K^{0}pi^{+})$. We measure the product of branching fractions for the former to be ${cal B}(B^0 to X(3872) (K^+ pi^-)) times {cal B}(X(3872) to J/psi pi^+ pi^-) = (7.9 pm 1.3(mbox{stat.})pm 0.4(mbox{syst.})) times 10^{-6}$ and find that $B^{0}to X(3872) K^{*}(892)^{0}$ does not dominate the $B^{0}to X(3872)K^{+}pi^{-}$ decay mode. We also measure ${cal B}(B^+ to X(3872) (K^0 pi^+)) times {cal B}(X(3872) to J/psi pi^+ pi^-) = (10.6 pm 3.0(mbox{stat.}) pm 0.9(mbox{syst.})) times 10^{-6}$. This study is based on the full data sample of 711~fb$^{-1}$ ($772times 10^6 Bbar B$ pairs) collected at the $Upsilon(4S)$ resonance with the Belle detector at the KEKB collider.
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