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Register a new userDecay rates $f_{1}(1285)to rho^{0}pi^{+} pi^{-}$ and $a_{1}(1260)toomegapi^{+}pi^{-}$ in the Nambu -- Jona-Lasinio model
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The anomalous decays $f_1(1285)torho^0pi^+pi^-$ and $a_1(1260)toomegapi^+pi^-$ violating natural parity for vectors and axial-vectors are studied in the framework of the Nambu -- Jona-Lasinio model. We consider the Lagrangian with $U(2)_Ltimes U(2)_R$ chiral symmetric four quark interactions. The theory is bosonized and corresponding effective meson vertices are obtained in the leading order of $1/N_c$ and derivative expansions. The uncertainties related with the surface terms of anomalous quark triangle diagrams are fixed by the corresponding symmetry requirements. We make a numerical estimate of the decay widths $Gamma (f_1(1285)torho^0pi^+pi^-)=2.78, mbox{MeV}$ and $Gamma (a_1(1260)toomegapi^+pi^-)=87, mbox{keV}$. Our result on the $f_1(1285)torho^0pi^+pi^-$ decay rate is in a good agreement with experiment. It is shown that a strong suppression of the $a_1(1260)toomega pipi$ decay is a direct consequence of destructive interference between box and triangle anomalies.
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Using the Nambu--Jona-Lasinio model with the $U(2)times U(2)$ chiral symmetric effective four-quark interactions, we derive the amplitude of the radiative decay $f_1(1285) topi^+pi^-gamma$, find the decay width $Gamma (f_1topi^+pi^-gamma)=346,mbox{keV}$ and obtain the spectral di-pion effective mass distribution. It is shown that in contrast to the majority of theoretical estimates (which consider the $a_1(1260)$ meson exchange as the dominant one), the most relevant contribution to this process comes out from the $rho^0$-resonance exchange related with the triangle $f_1rho^0gamma$ anomaly. The spectral function is obtained to be confronted with the future empirical data.
Within the framework of the extended Nambu -- Jona-Lasinio model, we calculate the matrix element of the $tau to f_1(1285) pi^{-} u_{tau}$ decay, obtain the invariant mass distribution of the $f_1pi$ -system and estimate the branching ratio Br$(tau to f_1 pi^{-} u_{tau})=4.0times 10^{-4}$. The two types of contributions are considered: the contact interaction, and the axial-vector $I^G(J^{PC})=1^-(1^{++})$ resonance exchange. The latter includes the ground $a_1(1260)$ state, and its first radially excited state, $a_1(1640)$. The corrections caused by the $pi -a_1$ transitions are taken into account. Our estimate is in a good agreement with the latest empirical result Br$(tau to f_1 pi^{-} u_{tau})=(3.9pm 0.5)times 10^{-4}$. The distribution function obtained for the decay $tau to f_1(1285) pi^{-} u_{tau}$ shows a clear signal of $a_1(1640)$ resonance which should be compared with future experimental data including our estimate of the decay width $Gamma (a_1(1640) to f_1 pi )=14.1,mbox{MeV}$.
We calculate the thermal evolution of $pi-pi$ scattering lengths, in the frame of the Nambu--Jona-Lasinio model. The thermal corrections were calculated at the one loop level using Thermofield Dynamics. We present also results for the pion thermal mass. Our procedure implies the modeling of a propagating scalar meson as a resumation of chains of quark bubbles, which is presented explicitly. We compare our results with previous analysis of this problem in the frame of different theoretical approaches.
Proton-proton collision data recorded in 2011 and 2012 by the lhcb experiment, co-rres-pon-ding to an integrated luminosity of 3.0invfb, are a-na-lysed to search for the charmless ${B^0 to rho^0 rho^0}$ decay. More than 600 ${B^0 to (pi^+pi^-)(pi^+pi^-)}$ signal decays are selected and used to perform an amplitude analysis from which the ${B^0 to rho^0 rho^0}$ decay is observed for the first time with 7.1 standard deviations significance. The fraction of ${B^0 to rho^0 rho^0}$ decays yielding a longitudinally polarised final state is measured to be $fL = 0.745^{+0.048}_{-0.058} ({rm stat}) pm 0.034 ({rm syst})$. The ${B^0 to rho^0 rho^0}$ branching fraction, using the ${B^0 to phi K^*(892)^{0}}$ decay as reference, is also reported as ${BF(B^0 to rho^0 rho^0) = (0.94 pm 0.17 ({rm stat}) pm 0.09 ({rm syst}) pm 0.06 ({rm BF})) times 10^{-6}}$.
Using the close relationship between the low--energy constants of chiral perturbation theory and the chiral invariant interactions of the vector meson resonances with the pseudoscalar mesons, we investigate the process $rho^0 ra pi^+ pi^- gamma$. Compared with the contribution from the pure bremsstrahlung mechanism, we find an enhancement of the decay rate near the endpoint of the photon energy spectrum. Such a particular shape of the differential decay rate has indeed been observed experimentally and turns out to be an important confirmation of the theoretical concept of chiral vector meson dominance.
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