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H. Q. Zheng

Publications and source records attributed to H. Q. Zheng.

33 records · Page 2Linked to original sources
arXiv2006

An improved study of the kappa resonance and the non-exotic $s$ wave $πK$ scatterings up to $\sqrt{s}=2.1$GeV of LASS data

We point out that the dispersion relation for the left hand cut integral presented in one of our previous paper (Nucl. Phys. {\bf A}733(2004)235) is actually free of subtraction constant, even for unequal mass elastic scatterings. A new fit to the LASS data~\cite{Aston} is performed and firm evidence for the existence of $κ$ pole is found. The correct use of analyticity also put strong constraints on threshold parameters -- which are found to be in good agreement with those obtained from chiral theories. We also determined the pole parameters of $K_0^*(1430)$ on the second sheet, and reconfirm the existence of $K_0^*(1950)$ on the third sheet. We stress that the LASS data do not require them to have the twin pole structure of a typical Breit--Wigner resonance.

hep-ph↗
arXiv2006

A unitarity analysis on the I=0 $d$ wave $ππ$ scattering amplitude

We study I=0 $d$ wave $ππ$ scattering phase shift using a proper unitarization approach. It is verified that the $f_2(1270)$ resonance corresponds to a twin pole structure: one on the second sheet, another one on the third sheet. Also we find fair agreement on $f_2(1270)$ pole's mass and width between our results and the PDG values. Besides, our analysis reveals the existence of a virtual state in this channel. Its pole location is determined by fitting experimental data and it is found to be in good agreement with the prediction from chiral perturbation theory. Our analysis demonstrates that partial wave amplitudes calculated in chiral perturbation theory are reliable in the small $|s|$ region, contrary to some unitarization models.

hep-ph↗
arXiv2005

Model dependent analyses on the $N_c$ dependence of the $σ$ pole trajectory

We explore the nature of the$σ$ or $f_0(600)$ meson using large $N_c$ technique, assuming that the $σ$ pole dominates low energy physics in the IJ=00 channel. We trace the $N_c$ dependence of the $σ$ pole position using [1,1] Padé approximation of SU(3) chiral amplitude, [1,2] Padé approximation of SU(2) chiral amplitudes, and the PKU parametrization form. We find that in all 3 cases the $σ$ pole moves to the real axis of the complex $s$-plane. Finally we construct a pedagogical example using the SU(2) Padé amplitude to show that when the analyticity property of the scattering amplitude is violated, it is possible that the $σ$ pole resides on the complex $s$ plane when $N_c$ is large.

hep-ph↗
arXiv2005

Analyticity and the $N_c$ counting rule of $S$ matrix poles

By studying $ππ$ scattering amplitudes in the large $N_c$ limit, we clarify the $N_c$ dependence of the $S$ matrix pole position. It is demonstrated that analyticity and the $N_c$ counting rule exclude the existence of $S$ matrix poles with ${\cal M}, Γ\sim O(1)$. Especially the properties of $σ$ and $f_0(980)$ with respect to the $1/N_c$ expansion are discussed. We point out that in general tetra-quark resonances do not exist.

hep-ph↗
arXiv2005

The pole structure of the unitary, crossing symmetric low energy $ππ$ scattering amplitudes

The pole structure of the low energy $ππ$ scattering amplitudes is studied using a proper chiral unitarization method combined with crossing symmetry and the low energy phase shift data. It is found that the $σ$ pole position is at $M_σ=470\pm 50MeV$, $Γ_σ=570\pm 50MeV$. The existence of the virtual state pole in the IJ=20 channel is reconfirmed. Various threshold parameters are estimated and are found in general in good agreement with the results obtained from the Roy equation analyses.

hep-ph↗
arXiv2004

On the nature of the lightest scalar resonances

We briefly review the recent progresses in the new unitarization approach being developed by us. Especially we discuss the large $N_c$ $ππ$ scatterings by making use of the partial wave $S$ matrix parametrization form. We find that the $σ$ pole may move to the negative real axis on the second sheet of the complex $s$ plane, therefore it raises the interesting question that this `$σ$' pole may be related to the $σ$ in the linear $σ$ model.

hep-ph↗
arXiv2003

The $κ$ resonance in s wave $πK$ scatterings

A new unitarization approach incorporated with chiral symmetry is established and applied to study the $πK$ elastic scatterings. We demonstrate that the $κ$ resonance exists, if the scattering length parameter in the I=1/2, J=0 channel does not deviate much from its value predicted by chiral perturbation theory. The mass and width of the $κ$ resonance is found to be $M_κ=594\pm 79MeV$, $Γ_κ=724\pm 332MeV$, obtained by fitting the LASS data up to 1430MeV. Better determination to the pole parameters is possible if the chiral predictions on scattering lengths are taken into account.

hep-ph↗
arXiv2003

The properties of the $σ$ and $κ$ resonances in a new unitarization approach

A new unitarization approach is discussed and applied to study the elastic $πK$ scattering process. The existence of the light $κ$ resonance is firmly established if the scattering length in the I=1/2 channel does not deviate too much from its value obtained from chiral perturbation theory, and a precise determination to the mass and width of the $κ$ resonance requires a precise determination of the scattering length parameter.

hep-ph↗
arXiv2003

Canonical Formalism for Lagrangians of Maximal Nonlocality

A canonical formalism for Lagrangians of maximal nonlocality is established. The method is based on the familiar Legendre transformation to a new function which can be derived from the maximally nonlocal Lagrangian. The corresponding canonical equations are derived through the standard procedure in local theory and appear much like those local ones, though the implication of the equations is largely expanded.

hep-th↗
arXiv2003

Evidence of $κ$ particle in $J/ψ\to \bar{K}^*(892)^0 K^+ π^-$

Based on a $J/ψ$ data sample of $7.8 \times 10^6$ events at BESI, the decay of $ J/ψ\to \bar{K}^*(892)^0 K^+ π^-$ is studied and a low mass enhancement, which is believed not coming from the phase space effect or background, is visible in the $K^+ π^-$ invariant mass spectrum recoiling against $\bar{K}^*(892)^0$. Partial wave analysis of this channel favors this low mass enhancement being a broad $0^{+}$ resonance with the mass and width of $771^{+164}_{-221}\pm 55$ MeV/c$^2$ and $220^{+225}_{-169} \pm 97$ MeV/c$^2$, respectively.

hep-ex↗
arXiv2002

The Constraints of Unitary on $ππ$ Scattering Dispersion Relations

A new dispersion relation for the partial wave $ππ$ scattering $S$ matrix is set up. Using the dispersion relation we generalize the single channel unitarity condition, $SS^+=1$, to the entire complex $s$ plane, which is equivalent to the generalized unitarity condition in quantum mechanics. The pole positions of the $σ$ resonance and the $f_0(980)$ resonance are estimated based on the theoretical relations we obtained. The central value of the $σ$ pole position is $M_σ\simeq 410$MeV, $Γ_σ\simeq 550$MeV, obtained after including the the constraint of the Adler zero condition.

hep-ph↗
arXiv2001

Left Hand Singularities, Hadron Form Factors and the Properties of the Sigma Meson

By applying analyticity and single channel unitarity we derive a new formula which is useful to analyze the role of the left-hand singularities in hadron form factors and in the determination of the resonance parameters. Chiral perturbation theory is used to estimate the left-hand cut effects in $ππ$ scattering processes. We find that in the IJ=11 channel the left-hand cut effect is negligible and in the IJ=20 channel the phase shift is dominated by the left-hand cut effect. In the IJ=00 channel the left-hand cut contribution to the phase shift has the wrong sign comparing with the experimental data and therefore it necessitates the $σ$ resonance. The new experimental results from the E865 collaboration is crucial in reducing the uncertainty in the determination of the mass and width of the $σ$ resonance within our scheme.

hep-ph↗
arXiv1998

Structure of f0(980) from a Coupled Channel Analysis of S-wave pi pi Scattering

A coupled channel model is used to study the nature of the f0(980) resonance. It is shown that the existence of two poles close to KKbar threshold, as found in many data fits and confirmed here, can be reconciled with the KKbar molecular origin of the f0(980). Due to a strong coupling between channels the number of the S-matrix poles close to the physical region in the physical case exceeds the number of bare states introduced in the model.

hep-ph↗
arXiv1996

The $ππ$ Final State Interaction in $K\toππ$, $pp\to ppππ$ and Related Processes

Final state interactions in the $S$--wave $ππ$ system (I=0,2) are re-examined on the basis of the Omnès-Mus\-khe\-li\-shvili equation and the coupled channel formalism. The contributions to the pion scalar form factor from $ρ$ and $f_2(1270)$ exchange in the $t$--channel and from the $f_0(980)$ $s$--channel resonance are separately evaluated and the role of the nontrivial polynomial in the Omnès function in a coupled channel situation is elucidated. Applications are made to $K\to ππ$ and $pp\to ppππ$. It is found that the contribution from the $f_0$ resonance to the form-factor is strongly reduced by a nearby zero.

hep-ph↗