The $\pi f_0(500)$ decay of the $a_1(1260)$

Abstract

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 $\pi \sigma$ channel in recent lattice QCD calculations of the $a_1$.

arXiv comment20 pages, 6 figures and 1 table

References in corpus (53)

• ππscattering
• Chiral Symmetry Amplitudes in the S-Wave Isoscalar and Isovector Channels and the σ, f_0(980), a_0(980) Scalar Mesons
• Chiral symmetry amplitudes in the s-wave isoscalar and isovector channels and the $\sigma ,f_0(980),a_0(980)$ scalar mesons
• N/D Description of Two Meson Amplitudes and Chiral Symmetry
• Hidden Local Symmetry at Loop -- A New Perspective of Composite Gauge Boson and Chiral Phase Transition
• Constituent quark model study of the meson spectra
• From controversy to precision on the sigma meson: a review on the status of the non-ordinary $f_0(500)$ resonance
• Couplings in coupled channels versus wave functions: application to the X(3872) resonance
• Threshold cusps and triangle singularities in hadronic reactions
• Low lying axial-vector mesons as dynamically generated resonances
• On meson resonances and chiral symmetry
• Double-Pionic Fusion of Nuclear Systems and the ABCEffect -- Aproaching a Puzzle by Exclusive and Kinematically Complete Measurements
• A Discussion on Triangle Singularities in the ${\Lambda }_b\to J/\psi K^{-}p$ Reaction
• Three-body Unitarity in the Finite Volume
• Hidden gauge formalism for the radiative decays of axial-vector mesons
• The puzzle of anomalously large isospin violations in $\eta (1405/1475)\to 3\pi$
• Searching for observable effects induced by anomalous triangle singularities
• $B^0$ and $B_s^0$ decays into $J/\psi$ $f_0(980)$ and $J/\psi$ $f_0(500)$ and the nature of the scalar resonances
• On the nature of $a_1(1420)$
• Effective chiral Lagrangians for spin-1 mesons
• Isospin breaking and $f_0(980)$-$a_0(980)$ mixing in the $\eta (1405)\to {\pi }^0{f}_0(980)$ reaction
• Three-body Unitarity with Isobars Revisited
• Clues for the existence of two $K_1(1270)$ resonances
• Chiral extrapolation of light resonances from one and two-loop unitarized Chiral Perturbation Theory versus lattice results
• The "$a_1(1420)$" peak as the $\pi f_0(980)$ decay mode of the $a_1(1260)$
• $f_1(1285)$ decays into $a_0(980){\pi }^0$, $f_0(980){\pi }^0$ and isospin breaking
• Isospin breaking decay $\eta (1405)\to f_0(980){\pi }^0\to 3\pi$
• Strong decays of ${\bar{D}}^{\ast }{K}^{\ast }$ molecules and the newly observed $X_{0,1}$ states
• The $b_1$ resonance in coupled $\pi \omega$, $\pi \varphi$ scattering from lattice QCD
• Molecular states from $D^{(\ast )}{\bar{D}}^{(\ast )}/B^{(\ast )}{\bar{B}}^{(\ast )}$ and $D^{(\ast )}{D}^{(\ast )}/{\bar{B}}^{(\ast )}{\bar{B}}^{(\ast )}$ interactions
• Pseudocalar meson and vector meson interactions and dynamically generated axial-vector mesons
• Unitary coupled-channels model for three-mesons decays of heavy mesons
• Resonant $a_0(980)$ state in triangle rescattering $D_s^{+}\to {\pi }^{+}{\pi }^0\eta$ decays
• Finding the sigma pole by analytic extrapolation of $\pi \pi$ scattering data
• Scattering of unstable particles in a finite volume: the case of pi rho scattering and the a1(1260) resonance
• Axial resonances a1(1260), b1(1235) and their decays from the lattice
• Precise determination of resonance pole parameters through Padé approximants
• Triangle singularities in $B^{-}\to K^{-}{\pi }^{-}{D}_{s0}^{+}$ and $B^{-}\to K^{-}{\pi }^{-}{D}_{s1}^{+}$
• Information on the structure of the a1 from tau decay
• Strong and radiative decays of DΞmolecular state and newly observed ${\Omega }_c$ states
• Strong decay modes $\bar{K}\Xi$ and $\bar{K}\Xi \pi$ of the $\Omega (2012)$ in the $\bar{K}\Xi (1530)$ and $\eta \Omega$ molecular scenario
• Internal particle width effects on the the triangle singularity mechanism in the study of the $\eta (1405)$ and $\eta (1475)$ puzzle
• Can the nature of $a_0(980)$ be tested in the $D_s^{+}\to {\pi }^{+}{\pi }^0\eta$ decay?
• Triangle singularity mechanism for the $pp\to {\pi }^{+}d$ fusion reaction
• Dalitz plots and lineshape of $a_1(1260)$ from a relativistic three-body unitary approach
• Unveiling the $K_1(1270)$ double-pole structure in the $\bar{B}\to J/\psi \rho \bar{K}$ and $\bar{B}\to J/\psi {\bar{K}}^{\ast }\pi$ decays
• Coupled-channel analysis of $D^{+}\to K^{-}{\pi }^{+}{\pi }^{+}$ decay
• On the uncertainty estimates of the $\sigma$-pole determination by Padé approximants
• The $K\bar{K}\pi$ decay of the $f_1(1285)$ and its nature as a $K^{\ast }\bar{K}-cc$ molecule
• Tau decay and the structure of the a1
• Radiative decays of $f_1(1285)$ as the $K^{\ast }\bar{K}$ molecular state
• The three-pion decays of the $a_1(1260)$
• Tau decay into ${\nu }_{\tau }$ and $a_1(1260)$, $b_1(1235)$, and two $K_1(1270)$

Cited by in corpus (4)

• Pole position of the $a_1(1260)$ resonance in a three-body unitary framework
• Three-body dynamics of the $a_1(1260)$ resonance from lattice QCD
• The role of triangle singularity in the decay process $D^0\to {\pi }^{+}{\pi }^{-}{f}_0(980),f_0\to {\pi }^{+}{\pi }^{-}$
• The dynamically generated $h_1$ state by the $K^{\ast }{\bar{K}}^{\ast }$ interaction and its $K_1(1270)\bar{K}$ and $b_1(1235)\pi$ decays