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Register a new userThree-pion decays of the tau lepton, the a_1(1260) properties, and the a_1-rho-pi Lagrangian
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We show that the a_1-rho-pi Lagrangian is a decisive element for obtaining a good phenomenological description of the three-pion decays of the tau lepton. We choose it in a two-component form with a flexible mixing parameter sin(theta). In addition to the dominant a_1-> pho pi intermediate states, the a_1->pi sigma ones are included. When fitting the three-pion mass spectra, three data sets are explored: (1) ALEPH 2005 pi-pi-pi+ data, (2) ALEPH 2005 pi-pi0pi0 data, and (3) previous two sets combined and supplemented with the ARGUS 1993, OPAL 1997, and CLEO 2000 data. The corresponding confidence levels are (1) 28.3%, (2) 100%, and (3) 7.7%. After the inclusion of the a_1(1640) resonance, the agreement of the model with data greatly improves and the confidence level reaches 100% for each of the three data sets. From the fit to all five experiments [data set (3)] the following parameters of the a_1(1260) are obtained m_{a_1}=(1233+/-18) MeV, Gamma_{a_1}=(431+/-20) MeV. The optimal value of the Lagrangian mixing parameter sin(theta)= 0.459+/-0.004 agrees with the value obtained recently from the e+e- annihilation into four pions.
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We evaluate the $a_1(1260) to pi sigma (f_0(500))$ decay width from the perspective that the $a_1(1260)$ resonance is dynamically generated from the pseudoscalar-vector interaction and the $sigma$ arises from the pseudoscalar-pseudoscalar interaction. A triangle mechanism with $a_1(1260) to rho pi$ followed by $rho to pi pi$ and a fusion of two pions within the loop to produce the $sigma$ provides the mechanism for this decay under these assumptions for the nature of the two resonances. We obtain widths of the order of $13-22$ MeV. Present experimental results differ substantially from each other, suggesting that extra efforts should be devoted to the precise extraction of this important partial decay width, which should provide valuable information on the nature of the axial vector and scalar meson resonances and help clarify the role of the $pisigma$ channel in recent lattice QCD calculations of the $a_1$.
It is found that in presence of electroweak interactions the gauge covariant diagonalization of the axial-vector -- pseudoscalar mixing in the effective meson Lagrangian leads to a deviation from the vector meson and the axial-vector meson dominance of the entire hadronic electroweak current. The essential features of such a modification of the theory are investigated in the framework of the extended Nambu-Jona-Lasinio model with explicit breaking of chiral $U(2) times U(2)$ symmetry. The Schwinger-DeWitt method is used as a major tool in our study of the real part of the relevant effective action. Some straightforward applications are considered.
The axial-vector $a_1(1260)$-meson longitudinal twist-2 distribution amplitude $phi_{2;a_1}^| (x,mu )$ within the framework of QCD sum rules under the background field theory is investigated. By considering the vacuum condensates up to dimension-six and the perturbative part up to next-to-leading order QCD corrections, the moments at initial scale $mu_0=1~{rm GeV}$ are $langle xi_{2;a_1}^{|;2}rangle |_{mu_0} = 0.210 pm 0.018$, $langle xi_{2;a_1}^{|;4}rangle |_{mu_0} = 0.091 pm 0.007$, and $langle xi_{2;a_1}^{|;6}rangle |_{mu_0} = 0.052 pm 0.004$ respectively. Secondly, the transition form factors (TFFs) for $Dto a_1(1260)$ under the light-cone sum rules are given. When taking squared momentum transfer to zero, we obtain $ A(0) = 0.130_{ - 0.015}^{ + 0.013}$, $V_1(0) = 1.899_{ - 0.127}^{ + 0.119}$, $V_2(0) = 0.211_{ - 0.020}^{ + 0.018}$, and $V_0(0) = 0.235_{ - 0.025}^{ + 0.026}$. With the extrapolated TFFs for the physically allowable region, the differential decay widths and total branching ratios for the processes $D^{0(+)} to a_1^{-(0)}(1260)ell^+ u_ell$ can be obtained, i.e. ${cal B}(D^0to a_1^-(1260) e^+ u_e) = (5.421_{-0.697}^{+0.702}) times 10^{-5}$, ${cal B}(D^+to a_1^0(1260) e^+ u_e) = (6.875_{-0.884}^{+0.890}) times 10^{-5}$, ${cal B}(D^0to a_1^-(1260) mu^+ u_mu)=(4.864_{-0.641}^{+0.647}) times 10^{-5}$, ${cal B}(D^+ to a_1^0(1260) mu^+ u_mu)=(6.169_{-0.821}^{+0.813}) times 10^{-5}$.
Tau decays into hadrons foresee the study of the hadronization of vector and axial-vector QCD currents, yielding relevant information on the dynamics of the resonances entering into the processes. We analyse tau -> (3 pion) nu_tau decays within the framework of the Resonance Chiral Theory, comparing this theoretical scheme with the experimental data, namely ALEPH spectral function and branching ratio. Hence we get values for the mass and on-shell width of the a_1(1260) resonance, and provide the structure functions that have been measured by OPAL and CLEO-II.
Using a recently proposed gauge covariant diagonalization of $pi a_1$-mixing we show that the low energy theorem $F^{pi}=e f_pi^2 F^{3pi}$ of current algebra, relating the anomalous form factor $F_{gamma to pi^+pi^0pi^-} = F^{3pi}$ and the anomalous neutral pion form factor $F_{pi^0 to gammagamma}=F^pi$, is fulfilled in the framework of the Nambu-Jona-Lasinio (NJL) model, solving a long standing problem encountered in the extension including vector and axial-vector mesons. At the heart of the solution is the presence of a $gamma pi {bar q} q $ vertex which is absent in the conventional treatment of diagonalization and leads to a deviation from the vector meson dominance (VMD) picture. It contributes to a gauge invariant anomalous tri-axial (AAA) vertex as a pure surface term.
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