On the possibility of Deeply Bound Hadronic Molecules from single Pion Exchange
Frank Close, Clark Downum
备注：
5 pages, 1 figure. Version accepted to PRL. Equation 3 of v1 of this paper was wrong and has been taken into account in this version. Other minor typos corrected... conclusions unchanged
Pion exchange in S-wave between hadrons that are themselves in a relative S-wave can shift energies by hundreds of MeV. In the case of charmed mesons $D,D^*,D_0,D_1$ a spectroscopy of quasi-molecular states may arise consistent with enigmatic charmonium states observed above 4 GeV in $e^+e^-$ annihilation. A possible explanation of $Y(4260)\to ψππ$ and $Y(4360) \to ψ'ππ$ is found. Searches in $D\bar{D}3π$ channels as well as B decays are recommended to test this hypothesis.
We demonstrate that in calculation, where unitarity constraints are properly imposed, the deeply bound hadronic molecules recently proposed by Close and Downum do not exist.
We show that the s-wave pion-nuclear potential which reproduces the deeply bound pionic states in Pb, recently discovered at GSI, is remarkably close to the one constructed directly from low energy theorems based on chiral symmetry. Converting this information into an effective pion mass we find $m_π^\star/m_π\simeq 1.13$ in the center of the Pb nucleus, and $m_π^\star/m_π\simeq 1.07$ in symmetric nuclear matter.
Diffractive deeply inelastic scattering from a hadron is described in terms of diffractive quark and gluon distributions. If the transverse size of the hadronic state is sufficiently small, these distributions are calculable using perturbation theory. We present such a calculation and discuss the underlying dynamics. We comment on the relation between this dynamics and the pattern of scaling violation observed in the hard diffraction of large-size states at HERA.
The status of the calculation of next-to-leading-order QCD corrections to hadronic final states in deeply inelastic scattering is reviewed, and an overview of the phenomenology (including the measurement of the strong coupling constant and the gluon density via jet rates) is given. We also describe a new universal program (DISASTER++) for the calculation of (2+1)-jet observables.
These are the miniproceedings of the workshop "Exotic hadronic atoms, deeply bound kaonic nuclear states and antihydrogen: present results, future challenges," which was held at the European Centre for Theoretical Nuclear Physics and Related Studies (ECT*), Trento (Italy), June 19-24, 2006. The document includes a short presentation of the topics, the list of participants, and a short contribution from each speaker.
A two-gluon-exchange model incorporating perturbative and non-perturbative effects is presented for rho electroproduction which provides an excellent description of all current data. This is then used to calculate the contribution from the rho to deeply virtual Compton scattering via the vector-meson-dominance transition rho -> gamma. This is found to be sufficiently large to provide a significant contribution through interference with the perturbative QCD term.
Using a soft pion theorem based on chiral symmetry and a $Δ(1232)$ resonance model we propose an estimate for the production cross section of low energy pions in the deeply virtual Compton scattering (DVCS) process. In particular, we express the $e p \to e γπN$ processes in terms of generalized parton distributions. We provide estimates of the contamination of the $e p \to e γp$ DVCS observables due to this associated pion production processes when the experimental data are not fully exclusive, for a set of kinematical conditions representative of present or planned experiments at JLab, HERMES…
We study deeply virtual Compton scattering on a virtual pion that is emitted by a proton. Using a range of models for the generalized parton distributions of the pion, we evaluate the cross section, as well as the beam spin and beam charge asymmetries in the leading-twist approximation. Studying Compton scattering on the pion in suitable kinematics puts high demands on both beam energy and luminosity, and we find that the corresponding requirements will first be met after the energy upgrade at Jefferson Laboratory. As a by-product of our study, we construct a parameterization of pion generaliz…
The study of deeply virtual Compton scattering has shown that electromagnetic gauge invariance requires, to leading order, not only twist two but additional twist three contributions. We apply this analysis and, using the Ellis-Furmanski-Petronzio factorization scheme, compute the single (electron) spin asymmetry arising in the collision of longitudinally polarized electrons with hadrons up to twist 3 accuracy. In order to simplify the kinematics we restrict the actual calculation to pions in the chiral limit. The process is described in terms of the generalized parton distribution functions w…
Pion exchange in S-wave between hadrons that are themselves in a relative S-wave is shown to shift energies by hundreds of MeV, leading to deeply bound quasi-molecular states. In the case of charmed mesons $D^*,D_1$ a spectroscopy arises consistent with enigmatic charmonium states observed above 4 GeV in $e^+e^-$ annihilation. A possible explanation of $Y(4260)\to ψππ$ and $Y(4360) \to ψ'ππ$ is found. We give results for all isospin and charge-conjugation combinations, and comment on flavor exotic doubly charmed states and bottomonium analogs. A search in $D\bar{D}3π$ is recommended to test th…
Using the approach based on conformal symmetry we calculate the two-loop coefficient function for the axial-vector contributions to two-photon processes in the $\overline{\rm MS}$ scheme. This is the last missing element for the complete next-to-next-to-leading order (NNLO) calculation of the the pion transition form factor $γ^\astγ\to π$ in perturbative QCD. The corresponding high-statistics measurement is planned by the Belle II collaboration and will allow one to put strong constraints on the pion light-cone distribution amplitude. The calculated NNLO corrections prove to be rather large an…
We investigate restrictions on the hadronic contribution to the muon $(g-2)$ factor and to the pion electromagnetic formfactor from the analytical properties of the pion formfactor and the experimental data of the pion formfactor in the space-like [1] region. The values of the pion formfactor of [1] have been improved (see Table 1) and the values of the pion formfactor have been calculated at 20 additional points (see Table 2).
Hadronic transitions of the chi(cj)(1P) states have not been studied yet. We calculate the rate of the hadronic transition chi(c1)(1P) to eta(c) plus two pions in the framework of QCD multipole expansion. We show that this process can be studied experimentally at the upgraded Beijing Spectrometer BES III and the Cornell CLEO-c.
We derive an analytic result for the pion pole contribution to the light-by-light scattering correction to the anomalous magnetic moment of the muon, $a_μ= (g_μ-2)/2$. Using the vector meson dominance model (VMD) for the pion transition form factor, we obtain $a_μ^{{\rm LBL},π^0} = +56 \times 10^{-11}$.
We analyze single transverse-spin asymmetries for hadronic pion production at large transverse momenta using QCD factorization. In the large $x_F$ region, leading contributions to the asymmetries are naturally produced by twist-3 parton correlation functions that couple quark fields and gluon field strengths. With a simple model for these matrix elements, leading-order asymmetries calculated from QCD are consistent with data on pion production from Fermilab, and can be used to predict single-spin asymmetries at RHIC. We argue that our perturbative calculation for the asymmetries is relevant to…
The influence of the hadronic ππinteraction on the wave functions of pionium (the Coulomb bound π^+π^- system) at distances less than 10 fm is calculated for s-states with principal quantum numbers n<5. Hadronic ππpotentials are used that reproduce the scattering phase shifts of two-loop chiral perturbation theory. The pionium wave functions ψ_n (r) are obtained by integrating the coupled Schrödinger equations for the (π^+π^-,π^0π^0) system. We find that, for r<10 fm, n^{3/2} ψ_n (r) is practically independent of n. From this we conclude that the production rates of the s-states of pionium are…
This thesis investigates the Hadronic Light by Light (HLL) scattering contribution to the muon $g-2$, which is one of the most important low energy hadronic effects and consists mainly of the quark loop, the pion pole and the charged pion and kaon loops. In this work the charged pion loop has been investigated more closely. After reviewing the subject a preliminary introduction to Chiral Perturbation Theory (ChPT), Hidden Local Symmetry (HLS) model and the full Vector Meson Dominance (VMD) model is given, and they are used to calculate the pion loop HLL scattering contribution to the muon anom…
A soft photon approximation is used to calculate the rates of lepton pair production through virtual bremsstrahlung from both pions and quarks. Standard assumptions about the evolution of a nuclear system under collision allow pion and quark driven total production to be calculated. Comparisons are made with Dalitz decay of light mesons. These mechanisms are expected to be significant contributors to the soft dilepton mass spectra one might observe in heavy ion collisions at RHIC and LHC energies.
Recent experimental data on tau decays are used to reconstruct the difference in hadronic spectral densities with vector and axial-vector quantum numbers. The saturation of Das-Mathur-Okubo and Weinberg sum rules is studied. Two methods of improving convergence and decreasing errors are applied, and good agreement with the predictions of current algebra and chiral perturbation theory is observed. The resulting value of the pion polarisability is (2.64 +/- 0.36) 10^-4 fm^3.
We compute the charged pion loop contribution to the light-by-light scattering amplitude for off-shell photons in chiral perturbation theory through next-to-leading order (NLO). We show that NLO contributions are relatively more important due to a fortuitous numerical suppression of the leading-order (LO) terms. Consequently, one expects theoretical predictions for the hadronic light-by-light (HLBL) contribution to the muon anomalous magnetic moment, $a_μ^{HLBL}$, to be sensitive to the choice of model for the higher momentum-dependence of the LBL amplitude. We show that models employed thus f…
A formula for the single transverse spin asymmetry in the large-$p_T$ pion production in the nucleon-nucleon collision is derived. We focuss on the chiral-odd contribution where the transversity distribution and the chiral-odd spin-independent twist-3 distribution contributes. This contribution is expected to give rise to a large effect at $x_F\to -1$.
The interplay of pQCD, pion exchange and FSI effects is studied for the gamma gamma --> pi^+ pi^- reaction in the region of 2 GeV < W_{gamma gamma} < 6 GeV. We find strong interference effects between pQCD and soft pion-exchange amplitudes up to W_{gamma gamma} ~ 4 GeV. We discuss to which extend the conventional hadronic FSI effects could cloud the pQCD effects. We study multipole soft and hard scattering effects as well as the coupling between final state hadronic channels. We show how the perturbative effects in gamma gamma --> rho rho may mix with perturbative effects in gamma gamma --> pi…
The largest error in the theoretical determination of the muon anomalous magnetic moment is due to the low-energy hadronic vacuum polarization, which cannot be calculated by perturbative QCD and requires nonperturbative techniques. Recently, an accurate determination of the low-energy two-pion contribution to muon $g-2$ has been obtained by a parametrization-free analytic continuation of the pion vector form factor from other kinematical regions. In this work we compare the results of the analytic continuation with direct determinations at low momenta from experiment and lattice QCD. We also e…
We present an estimate of a chiral-odd contribution to the single transverse-spin asymmetry in the large-$p_T$ pion production in the nucleon-nucleon collision. In this contribution the transversity distribution and the chiral-odd spin-independent twist-3 distribution appear. Because of the smallness of the corresponding hard cross section, this term turned out to be negligible in all kinematic regions compared with the chiral-even contribution.
The hadronic properties of the pionium ion (Coulomb bound system of three charged pions) are estimated using the results for the positronium ion $P{s}^{-}$. It turns out that the hadronic shift of the ground state energy and the lifetime of the pionium ion are approximately the same as for pionium.
The X(3872) with quantum numbers J(PC) = 1(++) is considered as a composite hadronic state comprised of the dominant molecular D(0) D*(0) component and other hadronic pairs - D(+-) D*(-+), Jpsi omega and Jpsi rho. Applying the compositeness condition we constrain the couplings of the X(3872) to its constituents. We calculate two- and three-body hadronic decays of the X(3872) to charmonium states chi(cJ) and pions using a phenomenological Lagrangian approach. Next using the estimated X-Jpsi-omega and and X-Jpsi-rho couplings we calculate the widths of X(3872) to Jpsi + h, where h = pi(+) pi(-),…
Recent results on prompt photon production in photoproduction, deeply inelastic scattering and hadronic collisions are reviewed and the importance of photons for LHC experiments is briefly discussed.
The pion electromagnetic form factor at finite temperature is studied using an effective chiral lagrangian that includes explicitly vector mesons. We find that in the time-like region around the rho meson resonance it decreases with increasing temperature and leads to a suppression of dilepton production from pion-pion annihilation in a hot hadronic matter. Effects on dilepton production in high energy heavy ion collisions and its relevance to the phase transition in a hot hadronic matter are discussed.
The azimuthal distributions around the jet axis of leading pions produced in the jet fragmentation process in pp collisions are studied within the framework of the so-called generalized parton model. The observable leading-twist azimuthal asymmetries are estimated in kinematic configurations presently investigated at RHIC. It is shown how the main contributions coming from the Collins and Sivers effects can be disentangled. In addition, a test of the process dependence of the Sivers function is provided.
The anomalously large rates of some hadronic transitions from quarkonium are studied using QCD multipole expansion (QCDME) in the framework of a constituent quark model which has been successful in describing hadronic phenomenology. The hybrid intermediate states needed in the QCDME method are calculated in a natural extension of our constituent quark model based on the Quark Confining String (QCS) scheme. Some of the anomalies are explained due to the presence of an hybrid state with a mass near the mass of the decaying resonance whereas other are justified by the presence of molecular compon…
Using a generalized parton model approach including spin and intrinsic parton motion effects, and assuming the validity of factorization for large pT jet production in hadronic collisions, we study the azimuthal distribution around the jet axis of leading pions, produced in the jet fragmentation process. We identify the observable leading-twist azimuthal asymmetries, which are generated by all the physically allowed combinations of transverse momentum dependent (TMD) parton distribution and fragmentation functions. In particular, we show how one can isolate the Collins and Sivers contributions…
We extend the multi-purpose Monte-Carlo event generator Sherpa to include processes in deeply inelastic lepton-nucleon scattering. Hadronic final states in this kinematical setting are characterised by the presence of multiple kinematical scales, which were up to now accounted for only by specific resummations in individual kinematical regions. Using an extension of the recently introduced method for merging truncated parton showers with higher-order tree-level matrix elements, it is possible to obtain predictions which are reliable in all kinematical limits. Different hadronic final states, d…
We summarize our recent new evaluation of the pion-exchange contribution to hadronic light-by-light scattering in the muon g-2. We first derive a new short-distance constraint on the off-shell pion-photon-photon form factor at the external vertex in a_μwhich relates the form factor to the quark condensate magnetic susceptibility in QCD. We then evaluate the pion-exchange contribution in the framework of large-N_C QCD using an off-shell form factor which fulfills all short-distance constraints and obtain the new estimate a_μ(LbyL;π^0) = (72 \pm 12) x 10^{-11}. Updating our earlier results for t…
The role of intrinsic transverse momentum both in unpolarized and polarized processes is discussed. We consider inclusive cross sections for pion production in hadronic collisions and for Drell-Yan processes. We reanalyze transverse single spin asymmetries (SSA) in inclusive pion production, p(transv. polarized) p --> pion + X, in terms of Sivers effect and show its contribution to A_{UL} in semi-inclusive DIS (SIDIS).
Single spin asymmetry (SSA) is a twist-3 observable in the collinear factorization approach. We present a twist-3 single-spin-dependent cross section formula for the pion production in pp-collision, p^\uparrow p\toπX, relevant to RHIC experiment. In particular, we calculate the soft-fermion-pole (SFP) contribution to the cross section from the quark-gluon correlation functions. We show that its effect can be as large as the soft-gluon-pole (SGP) contribution owing to the large SFP partonic hard cross section, even though the derivative of the SFP function does not participate in the cross sect…
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.
In most experiments aimed at determining the masses and mixing parameters for neutrino oscillations in different energy regimes there are strong backgrounds to neutrino interactions with matter that can confuse the expected small signals. One particular set of backgrounds is due to neutrino production of mesons, particularly pions, from nucleon or nuclear targets. It is especially important and theoretically interesting in itself to study $coherent$ neutrino production of pions, i.e. wherein the target does not break up. Preserving the target requires that the meson produced in the reaction wi…
Tau decays into hadrons have a twofold interest: On the one hand, they are a clean environment for studying the hadronization of the left-handed current of QCD, while, on the other side, provide relevant dynamical information of the resonances that mediate these processes. Within an effective field theory-like framework, namely Resonance Chiral Theory, we analyse the decays ot the tau into K K pion modes and compare the results with CLEO and BaBar data. In this way, we provide bounds on the couplings entering our Lagrangian and predict the corresponding spectral functions. As a main result -an…
Recently it was pointed out that for the evaluation of the numerically dominant pion-exchange contribution to the hadronic light-by-light scattering correction in the muon g-2, a fully off-shell pion-photon-photon form factor should be used. Following this proposal, we first derive a new short-distance constraint on the off-shell form factor which enters at the external vertex for the muon g-2 and show that it is related to the quark condensate magnetic susceptibility in QCD. We then evaluate the pion-exchange contribution in the framework of large-N_C QCD using an off-shell form factor which …
We propose a model-independent parametrization for the one-pion-to-vacuum matrix elements of the vector and axial vector hadronic currents in the presence of an external uniform magnetic field. It is shown that, in general, these hadronic matrix elements can be written in terms of several gauge covariant Lorentz structures and form factors. Within this framework we obtain a general expression for the weak decay $π^- \to l\,\barν_l$ and discuss the corresponding limits of strong and weak external magnetic fields.
Measurement of the distribution of hadronic energy in the final state in deeply inelastic electron scattering at HERA can provide a good test of our understanding of perturbative QCD. For this purpose, we consider the energy distribution function, which can be computed without needing final state parton fragmentation functions. We compute this distribution function for finite transverse momentum q_T at order alpha_s, and use the results to sum the perturbation series to obtain a result valid for both large and small values of transverse momentum.
As noticed by Fadin, Kuraev and Lipatov in 1975 incorporation of asymptotic freedom into the BFKL equation splits the QCD pomeron into a series of isolated poles in complex angular momentum plane. Following our earlier work on the proton structure function we explore the phenomenological consequences of the emerging BFKL-Regge factorized expansion for the small-$x$ structure function of the pion $F_{2π}(x,Q^2)$. We calculate $F_{2π}$ in a small-$x$ region and find good agreement with the recent H1 determination of $F_{2π}(x,Q^2)$. We also present the BFKL-Regge factorization based evaluation o…
The role of intrinsic transverse momentum both in unpolarized and polarized processes is discussed. We consider inclusive cross sections for pion production in hadronic collisions and for Drell-Yan processes; the results are compared with available experimental data in several different kinematical situations. We reanalyze transverse single spin asymmetries (SSA) observed in inclusive pion production, p(transv. polarized) p --> pion + X, in terms of Sivers effect and show how it can be disentangled in polarized Drell-Yan processes by suitably integrating over some final configurations. Estimat…
A model for the $p(e,e'π^+)n$ reaction which combines an improved treatment of gauge invariant meson--exchange currents and hard deep--inelastic scattering (DIS) of virtual photons off nucleons is proposed. It is shown that DIS dominates and explains the transverse response at moderate and high photon virtualities $Q^2$ whereas the longitudinal response is dominated by hadronic degrees of freedom and the pion electromagnetic form factor. This leads to a combined description of the longitudinal and transverse components of the cross section in a wide range of photon virtuality $Q^2$ and momentu…
A model independent expression for the electromagnetic corrections to a phenomenological hadronic pion-nucleon scattering length, extracted from pionic hydrogen, is obtained. In a non-relativistic approach and using an extended charge distribution, these corrections are derived up to terms of order (alpha)**2 log(alpha) in the limit of a short-range hadronic interaction. We infer a charged pion-proton scattering length of 0.0870(5) in units of inverse pion mass, which gives for the charged pion-proton-neutron coupling, through the GMO relation, a value of 14.04(17).
In this paper a measure of complexity of the system of angle-angular momentum quantum states produced in hadronic scattering is introduced in terms of the scattering entropies. We presented strong experimental evidence for the saturation of the entropic optimal limits in the pion-nucleon and kaon-nucleon scatterings. The validity of a principle of minimum complexity in hadronic interaction is supported with high accuracy (CL>99%) by the experimental data on pion-nucleon especially at energies higher than 2 GeV.
We propose a non-perturbative calculation scheme which is based on the semi-classical approximation of QCD and can be used to evaluate quantities of interest in hadronic physics. As a first application, we evaluate the mass of the pion and of the nucleon. Such masses are related to a particular combination of Green functions which, in some limit, is dominated by the contribution of \emph{very small-sized} instantons. The size distribution of these pseudo-particles is determined by the 't Hooft tunneling amplitude formula and therefore our calculation is free from any model parameters. We prove…
We discuss selected and important features of hadronic molecules as one of promising forms of exotic hadrons near thresholds. Using examples of $D \bar D^*$ systems such as $X(3872)$ and $Z_c$, emphasis is put on the roles of the one pion exchange interaction between them and their coupling to intrinsic quark states. Thus hadronic molecules emerge as admixtures of the dominant long-range hadron structure and short-range quark structure. For the pion exchange interaction, properties of the tensor force are analyzed in detail. More coupled channels supply more attractions, and heavier constituen…
A realistic model for the free rho meson with coupling to two-pion states is employed to calculate the rho propagator in a hot and dense hadron gas. The medium modifications are based on hadronic rescattering processes: intermediate two-pion states are renormalized through interactions with surrounding nucleons and deltas, and rho meson scattering is considered off nucleons, deltas, pions and kaons. Constraints from gauge invariance as well as the full off-shell dynamics of the interactions are accounted for. Within the vector dominance model we apply the resulting in-medium rho spectral funct…
The two-pion contribution to hadronic vacuum polarization can be extracted from tau decay data when isospin violating and radiative corrections are taken into account. When the dominant corrections are applied to the photon-inclusive decay of the tau into two pions, one obtains a shift (-12.0 +/- 2.6).10^{-10} for the anomalous magnetic moment of the muon. The shift appears to be too small to reconcile the determinations of hadronic vacuum polarization from existing tau and e+ e- data. The reliability of electromagnetic corrections in the photon-inclusive tau decay is examined.
We briefly review the current status of the hadronic light-by-light scattering correction to the muon g-2. Then we present our semi-analytical evaluation of the pion-pole contribution, using a description of the pion-photon-photon form factor based on large-N_C and short-distance properties of QCD. We also sketch an effective field theory approach to hadronic light-by-light scattering. In view of several still unsolved problems, our conservative estimate for the full hadronic light-by-light scattering contribution is a_{mu}(LbyL;had) = + 8 (4) x 10^{-10}.
In the real-time thermal field theory, the pion self-energy at finite temperature and density is evaluated where the different mesonic and baryonic loops are considered. The interactions of pion with the other mesons and baryons in the medium are governed by the effective hadronic Lagrangian densities whose effective strength of coupling constants have been determined from the experimental decay widths of the mesons and baryons. The detail branch cut structures of these different mesonic and baryonic loops are analyzed. The Landau cut contributions of different baryon and meson loops become on…
In a perturbative QCD approach, with inclusion of spin and transverse momentum effects, experimental data on azimuthal asymmetries observed in polarized semi-inclusive deeply inelastic scattering and e+ e- annihilations can be used to determine the Sivers, transversity and Collins soft functions. By using these functions, within the same scheme, we predict p(transv. polarized) p -> h + X single spin asymmetries in remarkable agreement with RHIC experimental data.
We perform a new calculation of the hadronic contributions, $a({\rm Hadronic})$ to the anomalous magnetic moment of the muon, $a_μ$. For the low energy contributions of order $α^2$ we carry over an analysis of the pion form factor $F_π(t)$ using recent data both on $e^+e^-\toπ^+π^-$ and $τ^+\to \barν_τπ^+π^0$. In this analysis we take into account that the phase of the form factor is equal to that of $ππ$ scattering. This allows us to profit fully from analyticity properties so we can use also experimental information on $F_π(t)$ at spacelike $t$. At higher energy we use QCD to supplement expe…
Pion-Kaon femtoscopy as a probe of the space-time emission anisotropies due to interactions at the hadronic stage of matter evolution in relativistic heavy-ion collisions
Warsaw University of Technology（华沙理工大学）；Bogolyubov Institute for Theoretical Physics（博戈柳博夫理论物理研究所）；Indian Institute of Technology Bombay（孟买印度理工学院）
A short review of both theoretical and experimental aspects of the radiative return method is presented. It is emphasised that the method gives not only possibility of the independent from the scan method measurement of the hadronic cross section, but also can provide information concerning details of the hadronic interactions. New developments in the PHOKHARA event generator are also reviewed. The 3 pion and kaon pair production is implemented within the version 5.0 of the program, together with contributions of the radiative phi decays to the 2 pion final states. Missing NLO radiative correc…
