Most of exotic resonances observed in the past decade appear as peak structure near some threshold. These near-threshold phenomena can be interpreted as genuine resonant states or enhanced threshold cusps. Apparently, there is no straightforward way of distinguishing the two structures. In this work, we employ the strength of deep feed-forward neural network in classifying objects with almost similar features. We construct a neural network model with scattering amplitude as input and nature of pole causing the enhancement as output. The training data is generated by an S-matrix satisfying the unitarity and analyticity requirements. Using the separable potential model, we generate a validation data set to measure the network's predictive power. We find that our trained neural network model gives high accuracy when the cut-off parameter of the validation data is within $400$-$800\mbox{ MeV}$. As a final test, we use the Nijmegen partial wave and potential models for nucleon-nucleon scattering and show that the network gives the correct nature of pole.
One of the main issues in hadron spectroscopy is to identify the origin of threshold or near-threshold enhancement. Prior to our study, there is no straightforward way of distinguishing even the lowest channel threshold-enhancement of the nucleon-nucleon system using only the cross-sections. The difficulty lies in the proximity of either a bound or virtual state pole to the threshold which creates an almost identical structure in the scattering region. Identifying the nature of the pole causing the enhancement falls under the general classification problem and supervised machine learning using…
We derive relations for baryon photo-decay amplitudes both for the Breit-Wigner and the pole positions. With an updated SAID partial wave analysis, technically similar to the earliest Virginia Tech analysis of photoproduction data, we compare photo-decay amplitudes at both resonance positions for a few selected nucleon resonances. Comparisons are made and a qualitative similarity, seen between the pole and Breit-Wigner values extracted by the Bonn-Gatchina group, is confirmed in the present study.
A simple heuristic argument to understand the existence of branch points in the unphysical sheet for pi-N scattering amplitude is presented. It is based on a hypothesis that the singularity structure of the pi-N scattering amplitude is a smooth varying function of the pion mass. We find that, in general, multiple poles structure of a resonance is a direct mathematical consequence when additional Riemann surface is included in the study and the two-pole structure found to correspond to the Roper resonance is a good example.
Each and every energy dependent partial-wave analysis is parameterizing the pole positions in a procedure defined by the way how the continuous energy dependence is implemented. These pole positions are, henceforth, inherently model dependent. To reduce this model dependence, we use only one, coupled-channel, unitary, fully analytic method based on the isobar approximation to extract the pole positions from the each available member of the worldwide collection of partial wave amplitudes which are understood as nothing more but a good energy dependent representation of genuine experimental numb…
We develop a robust method to extract the pole configuration of a given partial-wave amplitude. In our approach, a deep neural network is constructed where the statistical errors of the experimental data are taken into account. The teaching dataset is constructed using a generic S-matrix parametrization, ensuring that all the poles produced are independent of each other. The inclusion of statistical error results into a noisy classification dataset which we should solve using the curriculum method. As an application, we use the elastic $πN$ amplitude in the $I(J^P)=1/2(1/2^{-})$ sector where $…
We analyze $ππ-K\bar{K}$ and $πη-K\bar{K}$ couple channel [1,1] matrix Padé amplitudes of $SU(3)\times SU(3)$ chiral perturbation theory. By fitting phase shift and inelasticity data, we determine pole positions in different channels ($f_0(980)$, $a_0(980)$,$f_0(600)$, $K_0^*(800)$, $K^*(892)$, $ρ(770)$) and trace their $N_c$ trajectories. We stress that a couple channel Breit--Wigner resonance should exhibit two poles on different Riemann sheets and meet each other on the real axis when $N_c=\infty$. Poles are hence classified using this criteria and we conclude that $K^*(892)$ and $ρ(770)$ a…
We propose stringy hadronic amplitudes that combine some of the features of sister trajectories and running tension. By summing over string amplitudes with varying Regge trajectories that have integer tension and converging intercept, we obtain parton hard-scattering and Regge soft-scattering behaviors, while preserving discrete poles in both momentum and angular momentum.
We calculate the hadron tensor related to the photon-induced Drell-Yan process, with incoming nucleon being transversally polarised. We predict the new single spin asymmetry which probes gluon poles and which is expressed in terms of photon (both chiral-odd and chiral-even) distribution amplitudes and chiral-odd nucleon function stemming from the nucleon transverse polarization.
This report presents an investigation of the pion-nucleon elastic scattering in low energy region using a production representation of the partial wave $S$ matrix. The phase shifts are separated into contributions from poles and branch cuts, where the left-hand cut term can be evaluated by tree-level covariant baryon chiral perturbation theory. A comparison between the sum of known contributions and the data in $S$- and $P$- wave channels is made. It is found that the known components in $S_{11}$ and $P_{11}$ channels are far from enough to saturate the corresponding experimental data, indicat…
We extend the double copy picture of scattering amplitudes to a class of matrix elements (so-called form factors) that involve local gauge invariant operators. Both the Bern, Carrasco and Johansson (BCJ) and the Kawai, Lewellen and Tye (KLT) formalisms are considered and novel properties are observed. One remarkable feature is that through the double-copy construction, certain spurious poles hidden in the gauge form factors become physical propagators in gravity. This mechanism also reveals new hidden relations for form factors which can be understood as a generalization of the BCJ relations.
We discuss the relation between the analytic structure of the scattering amplitude and the origin of an eigenstate represented by a pole of the amplitude.If the eigenstate is not dynamically generated by the interaction in the channel of interest, the residue of the pole vanishes in the zero coupling limit. Based on the topological nature of the phase of the scattering amplitude, we show that the pole must encounter with the Castillejo-Dalitz-Dyson (CDD) zero in this limit. It is concluded that the dynamical component of the eigenstate is small if a CDD zero exists near the eigenstate pole. We…
A chiral unitary approach for antikaon-nucleon scattering in on-shell factorization is studied. We find multiple sets of parameters for which the model describes all existing hadronic data similarly well. We confirm the two-pole structure of the $Λ(1405)$. The narrow $Λ(1405)$ pole appears at comparable positions in the complex energy plane, whereas the location of the broad pole suffers from a large uncertainty. In the second step, we use a simple model for photoproduction of $K^+πΣ$ off the proton and confront it with the experimental data from the CLAS collaboration. It is found that only a…
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.
In a previous paper (Commun. Theor. Phys. 57 (2012) 841), we proposed a method to distinguish poles of different dynamical origin, in a unitarized amplitude of $ππ\, K\bar K$ system. That is based on the observation that `A Breit-Wigner resonance should exhibit two poles on different Riemann sheets which meet each other on the real axis when $N_c=\infty$'. In this paper, we extend our previous work (Commun.Theor.Phys. 57 (2012) 841) to the $ππ$-$K\bar K$-$ηη$ three channel system. We reconfirm most of the previous predictions. Especially the $f_0(980)$ is of $K\bar K$ molecule nature. Other po…
Masses, widths, and branching ratios of hadronic resonances are quantified by their pole positions and residues with respect to transition amplitudes on the Riemann sheets of the complex energy-plane. In this study we discuss the analytic structure in the physical energy region of three-body scattering amplitudes on such manifolds. As an application, we determine the pole position of the $a_1(1260)$ meson from the ALEPH experiment by allowing for $πρ$ coupled channels in S- and D-wave. We find it to be $\sqrt{s_0}=(1232^{+15+9}_{-0-11}-i266^{+0+15}_{-22-27})~\text{MeV}$.
We investigate the exclusive two-pion production at the $Z$-pole through the process $e^+e^-\to Z \to ππγ$. In the kinematical region where the invariant mass of the two pions is much smaller than the mass of the $Z$ boson, the process can be factorized into the convolution of a hard coefficient and a soft matrix element, the generalized distribution amplitude of two pions. We calculate the differential cross-section of charged pion pair production and neutral pion pair production and find the former to be much larger than the later. We show that combining the measurements of charged pion pair…
A set of well known once subtracted dispersion relations with imposed crossing symmetry condition is used to modify unitary multichannel $S$ ($ππ$, $K \bar K$, and $ηη$) and $P$ ($ππ$, $ρ2π$, and $ρσ$) wave amplitudes mostly below 1 GeV. Before the modifications, these amplitudes significantly did not satisfy the crossing symmetry condition and did not describe the $ππ$ threshold region. Moreover, the pole of the $S$ wave amplitude related with the $f_0(500)$ meson (former $f_0(600)$ or $σ$) had much smaller imaginary part and bigger real one in comparison with those in the newest Particle Dat…
We derive analytic expressions for high energy $2 \to 2$ off-shell scattering amplitudes of weak vector bosons. They are obtained from six fermion final states in processes of the type $e^+ e^- \to \barν_e + (WW) + ν_e \to \barν_e + (lν)(lν) + ν_e$. As an application we reconsider the unitarity bounds on the Higgs mass. Particular attention is given to the role of the photon exchange which has not been considered in earlier investigations; we find that the photon weakens the bound of the Higgs mass.
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 vio…
We discuss the structure of infrared singularities in on-shell QCD amplitudes at two-loop order. We present a general factorization formula that controls all the $\ep$-poles of the dimensionally regularized amplitudes. The dependence on the regularization scheme is considered and the coefficients of the $1/\ep^4, 1/\ep^3$ and $1/\ep^2$ poles are explicitly given in the most general case. The remaining single-pole contributions are also explicitly evaluated in the case of amplitudes with a $q{\bar q}$ pair.
We describe the unitarity approach for the numerical computation of two-loop integral coefficients of scattering amplitudes. It is well known that the leading propagator singularities of an amplitude's integrand are related to products of tree amplitudes. At two loops, Feynman diagrams with doubled propagators appear naturally, which lead to subleading pole contributions. In general, it is not known how these contributions can be directly expressed in terms of a product of on-shell tree amplitudes. We present a universal algorithm to extract these subleading pole terms by releasing some of the…
Assessing the role of threshold conditions in the determination of uncertainties in pole extractions using Padé approximants
Universitat Autònoma de Barcelona（巴塞罗那自治大学）；Institut de Física d’Altes Energies (IFAE)（高能物理研究所）；The Barcelona Institute of Science and Technology (BIST)（巴塞罗那科学技术学院）
We study the origin of subleading soft and collinear poles of form factors and amplitudes in dimensionally-regulated massless gauge theories. In the case of form factors of fundamental fields, these poles originate from a single function of the coupling, denoted G(alpha_s), depending on both the spin and gauge quantum numbers of the field. We relate G(alpha_s) to gauge-theory matrix elements involving the gluon field strength. We then show that G(alpha_s) is the sum of three terms: a universal eikonal anomalous dimension, a universal non-eikonal contribution, given by the coefficient B_delta (…
We explore the relation between resummation and explicit multi-loop calculations for QCD hard-scattering amplitudes. We describe how the factorization properties of amplitudes lead to the exponentiation of double and single poles at each order of perturbation theory. For these amplitudes, previously-observed relations between single and double poles in different 2 to 2 processes can now be interpreted in terms of universal functions associated with external partons and process-dependent anomalous dimensions that describe coherent soft radiation. Catani's proposal for multiple poles in dimensio…
Theories with both electric and magnetic charges ("mutually non-local" theories) have several major obstacles to calculating scattering amplitudes. Even when the interaction arises through the kinetic mixing of two, otherwise independent, U(1)'s, so that all low-energy interactions are perturbative, difficulties remain: using a self-dual, local formalism leads to spurious poles at any finite order in perturbation theory. Correct calculations must show how the spurious poles cancel in observable scattering amplitudes. Consistency requires that one type of charge is confined as a result of one o…
A production representation of partial-wave $S$ matrix is utilized to construct low-energy elastic pion-nucleon scattering amplitudes from cuts and poles on complex Riemann sheets. Among them, the contribution of left-hand cuts is estimated using the $\mathcal{O}(p^3)$ results obtained in covariant baryon chiral perturbation theory within the extended-on-nass-shell scheme. By fitting to data on partial-wave phase shifts, it is indicated that the existences of hidden poles in $S_{11}$ and $P_{11}$ channels, as conjectured in our previous paper~\citep{Wang:2017agd}, are firmly established. Speci…
We show how the Regge trajectory of a resonance can be obtained from its pole in a scattering process and analytic constraints in the complex angular momentum plane. The method is suited for resonances that dominate an elastic scattering amplitude. In particular, from the rho(770) resonance pole in pion-pion scattering, we obtain its linear Regge trajectory, characteristic of ordinary quark-antiquark states. In contrast, the f0(500) pole -the sigma meson- which dominates scalar isoscalar pion-pion scattering, yields a non-linear trajectory with a much smaller slope at the f0(500) mass. Convers…
In this paper we study the $J/Ψp$ spectroscopy in the process of $Λ_b\to J/Ψp K^-$. The final state interactions of coupled channel $J/Ψp$ ~-~ $\bar{D} Σ_c$~-~$\bar{D}^{*} Σ_c$ are constructed based on K-matrix with the Chew-Mandelstam function. We build the $Λ_b\to J/Ψp K^-$ amplitude according to the Au-Morgan-Pennington method. The event shape is fitted and the decay width of $Λ_b\to J/Ψp K^-$ is used to constrain the parameters, too. With the amplitudes we extract out the poles and their residues. Our amplitude and pole analysis suggest that the $P_c(4312)$ should be $\bar{D}Σ_c$ molecule,…
A chiral unitary approach for antikaon-nucleon scattering in on-shell factorization is studied. We find multiple sets of parameters for which the model describes all existing hadronic data similarly well. We confirm the two-pole structure of the $Λ(1405)$. The narrow $Λ(1405)$ pole appears at comparable positions in the complex energy plane, whereas the location of the broad pole suffers from a large uncertainty. In the second step, we use a simple model for photoproduction of $K^+πΣ$ off the proton and confront it with the experimental data from the CLAS collaboration. It is found that only a…
We have recently completed the one loop calculation of meson-meson scattering within Chiral Perturbation Theory. Once unitarized, these amplitudes provide simultaneously a remarkable description of the resonance region up to 1.2 GeV as well as the low energy region, respecting the chiral symmetry expansion. The position of the poles in these amplitudes is related to the mass and width of the associated resonances that are generated without being explicitly included in the Lagrangian. The spectroscopic nature of these states can then be deduced by studying the behavior of these poles, through t…
Several theoretical groups describe the antikaon-nucleon interaction at low energies within approaches based on the chiral SU(3) dynamics and including next-to-leading order contributions. We present a comparative analysis of the pertinent models and discuss in detail their pole contents. It is demonstrated that the approaches lead to very different predictions for the $K^{-}p$ amplitude extrapolated to subthreshold energies as well as for the $K^{-}n$ amplitude. The origin of the poles generated by the models is traced to the so-called zero coupling limit, in which the inter-channel couplings…
Particle scattering is a powerful tool to unveil the nature of various subatomic phenomena. The key quantity is the scattering amplitude whose analytic structure carries the information of the quantum states. In this work, we demonstrate our first step attempt to extract the pole configuration of inelastic scatterings using the deep learning method. Among various problems, motivated by the recent new hadron phenomena, we develop a curriculum learning method of deep neural network to analyze coupled channel scattering problems. We show how effectively the method works to extract the pole config…
Within the previously developed Dubna-Mainz-Taipei meson-exchange model, the singularity structure of the pi N scattering amplitudes has been investigated. For all partial waves up to F waves and c.m. energies up to W = 2 GeV, the T-matrix poles have been calculated by three different techniques: analytic continuation into the complex energy plane, speed-plot and the regularization method. For all 4-star resonances, we find a perfect agreement between the analytic continuation and the regularization method. We also find resonance poles for resonances that are not so well established, but in th…
We argue that the evolution of coloured partons into colour-singlet hadrons has approximate factorization into an extended parton-shower phase and a colour-singlet resonance--pole phase. The amplitude for the conversion of colour connected partons into hadrons necessarily resembles Regge-pole amplitudes since qq-bar resonance amplitudes and Regge-pole amplitudes are related by duality. A `Regge-cascade' factorization property of the N-point Veneziano amplitude provides further justification of this protocol. This latter factorization property, in turn, allows the construction of general multi-…
In unitarity cut method, compact input of on-shell tree level amplitudes is crucial to simplify calculations. Although BCFW on-shell recursion relation gives very compact tree level amplitudes, they usually contain spurious poles. In this paper, we present a method to deal with this issue and provide explicit simple algebraic functions for various coefficients in the presence of spurious poles. As an application, we present analytic result (not just rational term) for one-loop five gluon A(-++++) with scalar propagator for the first time.
Motivated by the recent extraction of the helicity amplitudes for the D+ -> K*0bar mu+ nu decay, done by the FOCUS collaboration, we determine helicity amplitudes for the D+ -> K*0bar l nu, D+ -> rho0 l nu and Ds -> phi l nu semileptonic decays using the knowledge of the relevant form factors. The vector and axial form factors for D -> V l nu decays are parameterized by including contributions of charm meson resonances and using the HQET and SCET limits. In the case that the vector form factor receives contributions from two poles while axial form factors are dominated by a single pole for D+ …
In the framework of quantum gravity propagating in large extra dimensions, the effects of virtual Kaluza-Klein gravitons on the imaginary part of the amplitude of the process e+ e- --> f f-bar are analyzed at the Z-pole. Notably, the interference of the almost-continuous spectrum of the KK gravitons with the standard model resonant amplitude is finite and predictable in terms of the fundamental D-dimensional Plank scale M_D. We find that, while the virtual-gravitons effect on total cross sections vanishes at tree-level, both angular and polarization asymmetries are modified by terms whose rela…
We present a strategy to extract the position of the two $Λ(1405)$ poles from experimental photoproduction data measured recently at different energies in the $γp \to K^+ π^0 Σ^0 $ reaction at Jefferson Lab. By means of a chiral dynamics motivated potential but with free parameters, we solve the Bethe Salpeter equation in the coupled channels $\bar K N$ and $πΣ$ in isospin I=0 and parameterize the amplitude for the photonuclear reaction in terms of a linear combination of the $πΣ\to πΣ$ and $\bar K N \to πΣ$ scattering amplitudes in I=0, with a different linear combination for each energy. Goo…
The doubly charm tetraquark with flavor $cc\bar u\bar d$ and isospin $I\!=\!0$ is investigated by calculating the $DD^*$ scattering amplitude with lattice QCD. The simulation is done on CLS ensembles with dynamical $u/d,s$ quarks and $m_π\simeq 280~$MeV for two charm quark masses, one slightly larger and one slightly lower than the physical value. The scattering amplitudes for partial waves $l=0,1$ are extracted near-threshold via the Lüscher's method by considering systems with total momenta $PL/(2π)=0,1,\sqrt{2},2$ on two spatial volumes. A virtual bound state pole in the $DD^*$ scattering a…
We make use of a unitarized coupled-channel model to analyze the mass distribution data of final states in production processes of $X(4260)$. By analyzing the analytical structures of the decay amplitudes, we find that the line shape of $Z_c(3900)$ signal is related to the combined effect of a pair of near-threshold "shadow" poles and the $(D\bar{D}^*)^\pm$ thresholds, in which the third-sheet pole might provide a dominant contribution. As all the coupled channels effects are tuning off, the trajectories of these two poles suggest that the $Z_c(3900)$ might originate from the attractive intera…
Independent of assumptions about the form of the quark-quark scattering kernel, K, we derive the explicit relation between the flavour-nonsinglet pseudoscalar meson Bethe-Salpeter amplitude, Gamma_H, and the dressed-quark propagator in the chiral limit. In addition to a term proportional to gamma_5, Gamma_H necessarily contains qualitatively and quantitatively important terms proportional to gamma_5 gamma.P and gamma_5 gamma.k k.P, where P is the total momentum of the bound state. The axial-vector vertex contains a bound state pole described by Gamma_H, whose residue is the leptonic decay cons…
We present a chiral model for the $J=0, I=1/2,$ elastic $K\p$ amplitude, suited to be employed in $D^+ \rar K^- \p^+ \p^+$ data analyses and valid between threshold and $1.5 $GeV. Although not as precise as other versions available in the literature, it is rather simple and incorporates the essential physics in this energy domain. In the case of the $K$-matrix approximation, the model allows the pole structure of the $K\p$ amplitude to be understood by solving a quadratic equation in $s$. We show that the solutions to this equation can be well approximated by polynomials of masses and coupling…
In this paper we propose a dispersive method to describe two-body scattering with unitarity imposed. This approach is applied to elastic $ππ$ scattering. The amplitudes keep single-channel unitarity and describe the experimental data well, and the low-energy amplitudes are consistent with that of chiral perturbation theory. The pole locations of the $σ$, $f_0(980)$, $ρ(770)$ and $f_2(1270)$ and their couplings to $ππ$ are obtained. A virtual state appearing in the isospin-two S-wave is confirmed. The correlations between the left (and right) hand cut and the poles are discussed. Our results sh…
The pion - nucleon scattering phase shifts in $s$ and $p$ waves are analyzed using PKU unitarization approach that can separate the phase shifts into different contributions from poles and branch cuts. It is found that in $S_{11}$ and $P_{11}$ channels, there exist large and positive missing contributions when one compares the phase shift from known resonances plus branch cuts with the experimental data, which indicates that those two channels may contain sizable effects from $N^*(1535)$ and $N^*(1440)$ shadow poles. Those results are obtained using tree level results of the $πN$ amplitude.
We discuss the Padé approximation to the $ππ$ scattering amplitudes in 1--loop chiral perturbation theory. The approximation restores unitarity and can reproduce the correct resonance poles, but the approximation violates crossing symmetry and produce spurious poles on the complex $s$ plane and therefore plagues its predictions on physical quantities at quantitative level. However we find that one virtual state in the IJ=20 channel may have physical relevance.
Gluonic pole matrix elements explain the appearance of single spin asymmetries (SSA) in high-energy scattering processes. They involve a combination of operators which are odd under time reversal (T-odd). Such matrix elements appear in principle both for parton distribution functions and parton fragmentation functions. We show that for parton fragmentation functions these gluonic pole matrix elements vanish as a consequence of the analytic structure of scattering amplitudes in Quantum Chromodynamics. This result is important in the study of the universality of transverse momentum dependent (TM…
We provide a new set of on-shell recursion relations for tree-level scattering amplitudes, which are valid for any non-trivial theory of massless particles. In particular, we reconstruct the scattering amplitudes from (a subset of) their poles and zeroes. The latter determine the boundary term arising in the BCFW-representation when the amplitudes do not vanish as some momenta are taken to infinity along some complex direction. Specifically, such a boundary term can be expressed as a sum of products of two on-shell amplitudes with fewer external states and a factor dependent on the location of…
By dealing with the evaluation of string theory correlators of $<V_C V_T V_{\barΨ} V_Ψ>$, the complete and closed form of the amplitude of two fermion fields, one tachyon and one closed string Ramond-Ramond field in type IIB superstring theory is found. Specifically by comparing infinite tachyon poles in field theory amplitude with infinite tachyon poles of the S-matrix of string amplitude (for $p+1=n$ case), all the infinite higher derivative corrections of two tachyons and two fermions (in type IIB) to all orders of $α'$ have been discovered. Using these new couplings, we are able to produce…
The $S$- and $P$- wave phase shifts of low-energy pion-nucleon scatterings are analysed using Peking University representation, in which they are decomposed into various terms contributing either from poles or branch cuts. We estimate the left-hand cut contributions with the help of tree-level perturbative amplitudes derived in relativistic baryon chiral perturbation theory up to $\mathcal{O}(p^2)$. It is found that in $S_{11}$ and $P_{11}$ channels, contributions from known resonances and cuts are far from enough to saturate experimental phase shift data -- strongly indicating contributions f…
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 …
We show that t-channel unitarity constraints make it possible to obtain the photon-photon cross sections from the photon-proton and proton-proton cross sections, for Q2<150 GeV2. In order to do so, one must postulate the existence of double-pole or triple-pole singularities in the complex j plane.
We consider the Olsson sum rule, i.e., the forward dispersion relation for pion-pion scattering with exchange of isospin unity at threshold. We show that, if using the S0, S2 and P wave expressions of Colangelo, Gasser and Leutwyler, then either the sum rule is not satisfied or, if adjusting the residue of the rho exchange Regge amplitude to have the sum rule satisfied (as recently proposed by Caprini, Colangelo and Leutwyler) then the subsequent high energy amplitude is in disagreement with experimental pi-pi cross sections.
We suggest a simple analytical description of the S-wave isoscalar $ππ$ amplitude, which corresponds to a joint dressing of the bare resonance and background contributions. The amplitude describes well the experimental data on the $δ^0_0$ phase shift in the energy region below 900 MeV and has two poles in the $Re s > 0$ half-plane. Besides the well-known pole of $σ(600)$-meson with $Re s \sim m_π^2$, there exists a more distant pole with $Re s \sim 0.6 GeV^2$. Our analysis indicates for the dynamical origin of the $σ(600)$ pole, while the second pole should be associated with lowest $q\bar{q}$…
