arXiv subjects

J. A. Oller

Publications and source records attributed to J. A. Oller.

At least 55 records · Page 3Linked to original sources

arXiv2017

Pole structure and compositeness

We present in this talk a series of new results on the nature of a bound state or resonance based on the calculation of the expectation values of the number operators of the free particles in the state of interest. In this way, a new universal criterion for the elementariness of a bound state emerges. In the case of large particle wavelengths compared to the range of their interaction, a new closed formula for the compositeness of a bound state in a two-particle continuum is obtained. The extension of these results to resonances with respect to the open channels can be given by making use in addition of suitable phase-factor transformations as also reviewed here. We end with a discussion on the $X(3872)$ as possible double- or triple-pole virtual state, which would be the first case in particle phenomenology.

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arXiv2017

Different pole structures in line shapes of the $X(3872)$

We introduce a near-threshold parameterization that is more general than the effective-range expansion up to and including the effective-range because it can also handle with a near-threshold zero in the $D^0\bar{D}^{*0}$ $S$-wave. In terms of it we analyze the CDF data on inclusive $p\bar{p}$ scattering to $J/ψπ^+π^-$, and the Belle and BaBar data on $B$ decays to $K\, J/ψπ^+π^-$ and $K D\bar{D}^{*0}$ around the $D^0\bar{D}^{*0}$ threshold. It is shown that data can be reproduced with similar quality for the $X(3872)$ being a bound {\it and/or} a virtual state. We also find that the $X(3872)$ might be a higher-order virtual-state pole (double or triplet pole), in the limit in which the small $D^{*0}$ width vanishes. Once the latter is restored the corrections to the pole position are non-analytic and much bigger than the $D^{*0}$ width itself. The $X(3872)$ compositeness coefficient in $D^0\bar{D}^{*0}$ ranges from nearly 0 up to 1 in the different scenarios.

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arXiv2017

Chiral study of the $a_0(980)$ resonance and $πη$ scattering phase shifts in light of a recent lattice simulation

We investigate the $a_0(980)$ resonance within chiral effective field theory through a three-coupled-channel analysis, namely $πη$, $K\bar{K}$ and $πη'$. A global fit to recent lattice finite-volume energy levels from $πη$ scattering and relevant experimental data on a $πη$ event distribution and the $γγ\toπη$ cross section is performed. Both the leading and next-to-leading-order analyses lead to similar and successful descriptions of the finite-volume energy levels and the experimental data. However, these two different analyses yield different $πη$ scattering phase shifts for the physical masses for the $π, K, η$ and $η'$ mesons. The inelasticities, the pole positions in the complex energy plane and their residues are calculated both for unphysical and physical meson masses.

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arXiv2016

A chiral covariant approach to $ρρ$ scattering

We analyze vector meson - vector meson scattering in a unitarized chiral theory based on a chiral covariant framework. We show that a pole assigned to the the scalar meson $f_0(1370)$ can be dynamically generated from the $ρρ$ interaction, while this is not the case for the tensor meson $f_2(1270)$ as found in earlier works. We show that the generation of the tensor state is untenable due to an artefact of the extreme non-relativistic kinematics used before. We further consider the effects arising from the coupling of channels with different orbital angular momenta. We suggest to use the formalism outlined here to obtain more reliable results for the dynamical generation of resonances in the vector-vector interaction.

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arXiv2016

The N/D method with non-perturbative left-hand-cut discontinuity and the $^1S_0$ $NN$ partial wave

In this letter we deduce an integral equation that allows to calculate the exact left-hand-cut discontinuity for an uncoupled $S$-wave partial-wave amplitude in potential scattering for a given finite-range potential. The results obtained from the $N/D$ method for the partial-wave amplitude are rigorous, since now the discontinuities along the left-hand cut and right-hand cut are exactly known. This solves the open question with respect to the $N/D$ method and the effect on the final result of the non-perturbative iterative diagrams in the evaluation of $Δ(A)$. A big advantage of the method is that short-range physics (corresponding to integrated out degrees of freedom within low-energy Effective Field Theory) does not contribute to $Δ(A)$ and it manifests through the extra subtractions that are implemented within the method. We show the equivalence of the $N/D$ method and the Lippmann-Schwinger (LS) equation for a nonsingular $^1S_0$ $NN$ potential (Yukawa potential). The equivalence between the $N/D$ method with one extra subtraction and the LS equation renormalized with one counter term or with subtractive renormalization also holds for the singular attractive higher-order ChPT potentials. The $N/D$ method also allows to evaluate partial-wave amplitudes with a higher number of extra subtractions, that we fix in terms of shape parameters within the effective range expansion. The result at NNLO shows that the $^1S_0$ phase shifts might be accurately described once the electromagnetic and charge symmetry breaking terms are included. Our present results can be extended to higher partial waves as well as to coupled channel scattering.

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arXiv2016

$P$-wave coupled-channel scattering of $B_sπ,\,B_s^π,\,B\overline K,\,B^{}\overline K$ and the puzzling $X(5568)$

The D0 Collaboration has recently reported a narrow peak structure in the $B_s^0π^\pm$ invariant-mass spectrum, that is called $X(5568)$. Its proposed quantum numbers $J^P=0^+/1^+$ are not determined unambiguously, and we show that one can fit the data assuming $J^P=1^-$ with the same mass and width for the resonance signal. The corresponding isovector $P$-wave coupled-channel scattering involving the states $B_sπ$, $B_s^*π$, $B \overline{K}$ and $B^*\overline K$ is studied employing leading-order Heavy Meson Chiral Perturbation Theory, which is then unitarized making use of standard techniques from Unitary Chiral Perturbation Theory. The subtraction constants that appear in the unitarization process are determined by a $u$-channel crossing symmetry constraint or by naturalness arguments, being the numerical values obtained in both cases quite closed, and no further freedom is left in the model. A crucial point is that if the $X(5568)$ is $1^-$ and decaying into $B_s^0π^\pm$ then it should appear as a pole in the $T$-matrix elements. It finally turns out that no $X(5568)$ pole is found that can be qualified as dynamically generated from the isovector $P$-wave coupled-channel dynamics. This result disfavors the interpretation of the $X(5568)$ within a "molecular" picture.

hep-ph↗

arXiv2016

Probabilistic interpretation of compositeness relation for resonances

Bound, antibound and resonance states are associated to poles in the on-shell partial wave amplitudes. We show here that from the residues of the pole a rank 1 projection operator associated with any of these states can be extracted, in terms of which a sum rule related to the composition of the state can be derived. Although typically it involves complex coefficients for the compositeness and elementariness, except for the bound state case, we demonstrate that one can formulate a meaningful compositeness relation with only positive coefficients for resonances whose associated Laurent series in the variable s converges in a region of the physical axis around Re(s_P), with s_P the pole position of the resonance. It is also shown that this result can be considered as an analytical extrapolation in s_P of the clear narrow resonance case. We exemplify this formalism to study the two-body components of several resonances of interest.

hep-ph↗

arXiv2016

General considerations on the nature of $Z_b(10610)$ and $Z_b(10650)$ from their pole positions

The nature of the bottomonium-like states $Z_b(10610)$ and $Z_b(10650)$ is studied by calculating the $B^{(*)}\overline B^{*}$ compositeness ($X$) in those resonances. We first consider uncoupled isovector $S$-wave scattering of $B^{(*)}\overline B^{*}$ within the framework of effective-range expansion (ERE). Expressions for the scattering length ($a$) and effective range ($r$) are derived exclusively in terms of the masses and widths of the two $Z_b$ states. We then develop compositeness within ERE for the resonance case and deduce the expression $X=1/\sqrt{2r/a-1}$, which is then applied to the systems of interest. Finally, the actual compositeness parameters are calculated in terms of resonance pole positions and their experimental branching ratios into $B^{(*)}\overline{B}^*$ by using the method of Ref.[1]. We find the values $X=0.66\pm 0.11$ and $0.51\pm 0.10$ for the $Z_b(10610)$ and $Z_b(10650)$, respectively. We also compare the ERE with Breit-Wigner and Flatté parameterizations to discuss the applicability of the last two ones for near-threshold resonances with explicit examples.

hep-ph↗

arXiv2016

Resonance on top of thresholds: the $Λ_c(2595)^+$ as an extremely fine-tuned state

A dedicated study of the $πΣ_c$ scattering around its threshold is carried out in this work to probe the nature of $Λ_c(2595)^+$. We first demonstrate that the effective range expansion approach fails to work near the $Λ_c(2595)^+$ pole position, due to the presence of a nearby CDD pole around the $πΣ_c$ thresholds. We then develop a general framework to properly handle the situation with a CDD pole accompanied by nearby thresholds, which is first elaborated for the single-channel case and then generalized to the coupled-channel study. The isospin breaking effects of the three $πΣ_c$ channels with different thresholds are specially taken into account in our study. The finite-width effects from the $Σ_c$ baryons are considered and found to be relevant to give the $Λ_c(2595)^+$ width fully compatible to its experimental value. Through the compositeness analysis, our robust conclusion is that the $π^0Σ_c^+$ component is subdominant inside the $Λ_c(2595)^+$.

hep-ph↗

arXiv2014

The strangeness content of the nucleon from effective field theory and phenomenology

We revisit the classical relation between the strangeness content of the nucleon, the pion-nucleon sigma term and the $SU(3)_F$ breaking of the baryon masses in the context of Lorentz covariant chiral perturbation theory with explicit decuplet-baryon resonance fields. We find that a value of the pion-nucleon sigma term of $\sim$60 MeV is not necessarily at odds with a small strangeness content of the nucleon, in line with the fulfillment of the OZI rule. Moreover, this value is indeed favored by our next-to-leading order calculation. We compare our results with earlier ones and discuss the convergence of the chiral series as well as the uncertainties of chiral approaches to the determination of the sigma terms.

hep-ph↗

arXiv2014

Nucleon-Nucleon scattering from dispersion relations: next-to-next-to-leading order study

We study nucleon-nucleon ($NN$) scattering by applying the $N/D$ method in chiral perturbation theory up to next-to-next-to-leading (NNLO) order in the calculation of the imaginary part of the $NN$ partial-wave amplitudes along the left-hand-cut, which is the dynamical input for this approach. A quite good reproduction of the Nijmegen partial-wave analysis phase shifts and mixing angles is obtained, which implies a steady improvement in the accurateness achieved by increasing the chiral order in the calculation of the dynamical input. A power counting for the subtraction constants is established, which is appropriate for those subtractions attached to both the left- and right-hand cuts. We discuss that it is not necessary to modify the $NN$ chiral potential at NNLO to agree with data, but instead one should perform the iteration of two-nucleon intermediate states to finally achieve analytic and unitarity $NN$ partial-wave amplitudes in a well-defined way. We also confirm at NNLO the long-range correlations between the $NN$ $S$-wave effective ranges and scattering lengths, when employing only once-subtracted dispersion relations, that holds up to around 10% when compared with experimental values.

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arXiv2014

Nucleon-Nucleon scattering from the dispersive N/D method: next-to-leading order study

We consider nucleon-nucleon ($NN$) interactions from Chiral Effective Field Theory applying the $N/D$ method. The dynamical input is given by the discontinuity of the $NN$ partial-wave amplitudes across the left-hand cut (LHC) calculated in Chiral Perturbation Theory (ChPT) by including one-pion exchange (OPE), once-iterated OPE and leading irreducible two-pion exchange (TPE). We discuss both uncoupled and coupled partial-waves. We show algebraically that the resulting integral equation has a unique solution when the input is taken only from OPE because it is of the Fredholm type with a squared integrable kernel and an inhomogeneous term. Phase shifts and mixing angles are typically rather well reproduced, and a clear improvement of the results obtained previously with only OPE is manifest. We also show that the contributions to the discontinuity across the LHC are amenable to a chiral expansion. Our method also establishes correlations between the $S$-wave effective ranges and scattering lengths based on unitarity, analyticity and chiral symmetry.

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arXiv2013

Meson-baryon reactions with strangeness -1 within a chiral framework

We study meson-baryon scattering with strangeness -1 in unitary chiral perturbation theory. Ten coupled channels are considered in our work, namely $π^0 Λ$, $π^0 Σ^0$, $π^- Σ^+$, $π^+ Σ^-$, $K^- p$, $\bar{K}^0 n$, $ηΛ$, $ηΣ^0$, $K^0 Ξ^0$ and $K^+ Ξ^-$. A large amount of experimental data are analyzed, including the recent precise measurement by the SIDDHARTA Collaboration of the energy shift and width of the $1s$ state of kaonic hydrogen. This leads to a strong constraint on the free parameters in our theory and of the resulting meson-baryon scattering amplitudes. We also analyze the uncertainty that stems by using several different strategies to perform the fits to data. It is found that large uncertainties in the subthreshold extrapolation of the $K^-p$ scattering amplitude arise by employing either only one common weak pseudoscalar decay constant or distinguishing between $f_π$, $f_K$ and $f_η$. However, in both cases a good reproduction of experimental data is obtained. We also discuss the pole content of the resulting $S$-wave amplitudes, particularly in connection with the two-pole structure of the $Λ(1405)$ resonance.

hep-ph↗

arXiv2013

New insights in \bar{K}N scattering and the Λ(1405)

We discuss in this talk aspects of \bar{K}N plus coupled channels dynamics with special emphasis on the Λ(1405) resonance and isovector resonances in the same energy region. We comment on several experimental reactions giving rise to πΣdistributions with important implications on the spectroscopy. We also discuss recent theoretical models based con NLO SU(3) unitarized chiral perturbation theory.

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arXiv2013

Finite volume treatment of $ππ$ scattering in the $ρ$ channel

We make a theoretical study of $ππ$ scattering with quantum numbers $J^{PC}=1^{--}$ in a finite box. To calculate physical observables for infinite volume from lattice QCD, the finite box dependence of the potentials is not usually considered. We quantify such effects by means of two different approaches for vector-isovector $ππ$ scattering based on Unitarized Chiral Perturbation Theory results: the Inverse Amplitude Method and another one based on the $N/D$ method. We take into account finite box effects stemming from higher orders through loops in the crossed $t,u-$channels as well as from the renormalization of the coupling constants. The main conclusion is that for $ππ$ phase shifts in the isovector channel one can safely apply Lüscher based methods for finite box sizes of $L$ greater than $2 m_π^{-1}$.

hep-lat↗

arXiv2013

Low energy analysis of $πN$ scattering and the pion-nucleon sigma term with covariant baryon chiral perturbation theory

The pion-nucleon sigma term ($σ_{πN}$) is an observable of fundamental importance because embodies information about the internal scalar structure of the nucleon. Nowadays this quantity has triggered renewed interest because it is a key input for a reliable estimation of the dark matter-nucleon spin independent elastic scattering cross section. In this proceeding we present how this quantity can be reliably extracted by employing only experimental information with the use covariant baryon chiral perturbation theory. We also contrast our extraction with updated phenomenology related to $σ_{πN}$ and show how this phenomenology favours a relatively large value of $σ_{πN}$. Finally, we extract a value of $σ_{πN}=59(7)$ MeV from modern partial wave analyses data.

hep-ph↗

arXiv2012

Improved description of the $πN$-scattering phenomenology in covariant baryon chiral perturbation theory

We present a novel analysis of the $πN$ scattering amplitude in covariant baryon chiral perturbation theory up to ${\cal O}(p^3)$ within the extended-on-mass-shell renormalization scheme and including the $Δ(1232)$ explicitly in the $δ$-counting. We take the hadronic phase shifts provided by partial wave analyses as basic experimental information to fix the low-energy constants. Subsequently, we study in detail the various observables and low-energy theorems related to the $πN$ scattering amplitude. In particular, we discuss the results and chiral expansion of the phase shifts, the threshold coefficients, the Goldberger-Treiman relation, the pion-nucleon sigma term and the extrapolation onto the subthreshold region. The chiral representation of the amplitude in the theory with the $Δ$ presents a good convergence from very low energies in the subthreshold region up to energies well above threshold, leading also to a phenomenological description perfectly consistent with the one reported by the respective partial wave analyses and independent determinations. We conclude that a model-independent and systematic framework to analyze $πN$-scattering observables using directly experimental data shall be possible in covariant baryon chiral perturbation theory.

hep-ph↗

arXiv2012

Nucleon-Nucleon Interactions from Dispersion Relations: Coupled Partial Waves

We consider nucleon-nucleon interactions from chiral effective field theory applying the N/D method. The case of coupled partial waves is now treated, extending Ref. [1] where the uncoupled case was studied. As a result three N/D elastic-like equations have to be solved for every set of three independent partial waves coupled. As in the previous reference the input for this method is the discontinuity along the left-hand cut of the nucleon-nucleon partial wave amplitudes. It can be calculated perturbatively in chiral perturbation theory because it involves only irreducible two-nucleon intermediate states. We apply here our method to the leading order result consisting of one-pion exchange as the source for the discontinuity along the left-hand cut. The linear integral equations for the N/D method must be solved in the presence of L - 1 constraints, with L the orbital angular momentum, in order to satisfy the proper threshold behavior for L>= 2. We dedicate special attention to satisfy the requirements of unitarity in coupled channels. We also focus on the specific issue of the deuteron pole position in the 3S1-3D1 scattering. Our final amplitudes are based on dispersion relations and chiral effective field theory, being independent of any explicit regulator. They are amenable to a systematic improvement order by order in the chiral expansion.

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