arXiv subjects

J. A. Oller

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

At least 37 records · Page 2Linked to original sources

arXiv2021

Ladder resummation of spin 1/2 fermion many-body systems with arbitrary partial-wave content

We resum the ladder diagrams for the calculation of the energy density $\cal{E}$ of a spin 1/2 fermion many-body system in terms of arbitrary vacuum two-body scattering amplitudes. The partial-wave decomposition of the in-medium two-body scattering amplitudes is developed, and the expression for calculating $\cal{E}$ in a partial-wave amplitude expansion is also given. The case of contact interactions is completely solved and is shown to provide renormalized results, expressed directly in terms of scattering data parameters, within cutoff regularization in a wide class of schemes. $S$- and $P$-wave interactions are considered up to including the first three-terms in the effective-range expansion, paying special attention to the parametric region around the unitary limit.

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arXiv2021

Insights into the nature of the $P_{cs}(4459)$

We study the nature of the recently observed $P_{cs}(4459)$ by the LHCb collaboration by employing three methods based on the elastic effective-range expansion and the resulting size of the effective-range, the saturation of the compositeness relation and width of the resonance, and a direct fit to data involving the channels $J/ψΛ$, $Ξ'_c\bar{D}$ and $Ξ_c\bar{D}^*$. We have also considered the addition of a CDD pole but this scenario can be discarded. Our different analyses clearly indicate the molecular nature of the $P_{cs}(4459)$ with a clear $Ξ_c\bar{D}^*$ dominant component. In relation with heavy-quark-spin symmetry our results also favor the actual existence of two resonances with $J=1/2$ (the lighter one) and $3/2$ (the heavier one) in the energy region of the $P_{cs}(4459)$. In the scenario of two-resonance for the $P_{cs}(4459)$, the inclusion of the $Ξ_c'\bar{D}$ channel is required for the their mass splitting and it allows one to determine the spin structures of the two resonances.

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arXiv2021

Insights into the inner structures of the fully charmed tetraquark state $X(6900)$

The recently discovered fully charmed tetraquark candidate $X(6900)$ is analyzed within the frameworks of effective-range expansion, compositeness relation and width saturation, and a coupled multichannel dynamical study. By taking into account constraints from heavy-quark spin symmetry, the coupled-channel amplitude including the $J/ψJ/ψ,~ χ_{c0}χ_{c0}$ and $χ_{c1}χ_{c1}$ is constructed to fit the experimental di-$J/ψ$ event distributions around the energy region near $6.9$ GeV. Another dynamical two-coupled-channel amplitude with the $J/ψJ/ψ$ and $ψ(3770) J/ψ$ is also considered to describe the same datasets. The three different theoretical approaches lead to similar conclusions that the two-meson components do not play dominant roles in the $X(6900)$. Our determinations of the resonance poles in the complex energy plane from the refined coupled-channel study are found to be consistent with the experimental analyses. The coupled-channel amplitudes also have another pole corresponding to a narrow resonance $X(6825)$ that we predict sitting below the $χ_{c0}χ_{c0}$ threshold and of molecular origin. We give predictions to the line shapes of the $χ_{c0}χ_{c0}$ and $χ_{c1}χ_{c1}$ channels, which could provide a useful guide for future experimental measurements.

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arXiv2021

A unified description of the hidden-charm tetraquark states $Z_{cs}(3985)$, $Z_c(3900)$ and $X(4020)$

The newly observed hidden-charm tetraquark state $Z_{cs}(3985)$, together with $Z_c(3900)$ and $X(4020)$, are studied in the combined theoretical framework of the effective range expansion, compositeness relation and the decay width saturation. The elastic effective-range-expansion approach leads to sensible results for the scattering lengths, effective ranges and the compositeness coefficients, $i.e.$, the probabilities to find the two-charm-meson molecule components in the tetraquark states. The coupled-channel formalism by including the $J/ψπ$ and $D\bar{D}^*/\bar{D}D^*$ to fulfill the constraints of the compositeness relation and the decay width, confirms the elastic effective-range-expansion results for the $Z_c(3900)$, by using the experimental inputs for the ratios of the decay widths between $D\bar{D}^*/\bar{D}D^*$ and $J/ψπ$. With the results from the elastic effective-range-expansion study as input for the compositeness, we generalize the discussions to the $Z_{cs}(3985)$ by including the $J/ψK^{-}$ and $D_s^{-}D^{*0}/D_s^{*-}D^{0}$, and predict the partial decay widths of the $J/ψK^{-}$. Similar calculations are also carried out for the $X(4020)$ by including the $h_cπ$ and $D^*\bar{D}^*$, and the partial decay widths of the $h_cπ$ is predicted. Our results can provide useful guidelines for future experimental measurements.

hep-ph↗

arXiv2021

Non-perturbative methods for NN singular interactions

Chiral Effective Field Theory ($χ$EFT) has been extensively used to study the $NN$ interaction during the last three decades. In Effective Field Theories (EFTs) the renormalization is performed order by order including the necessary counter terms. Due to the strong character of the $NN$ interaction a non-perturbative resummation is needed. In this work we will review some of the methods proposed to completely remove cutoff dependencies. The methods covered are renormalization with boundary conditions, renormalization with one counter term in momentum space (or equivalently substractive renormalization) and the exact $N/D$ method. The equivalence between the methods up to one renormalization condition will be checked showing results in the $NN$ system. The exact $N/D$ method allows to go beyond the others, and using a toy model it is shown how it can renormalize singular repulsive interactions.

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arXiv2020

Unitarization Technics in Hadron Physics with Historical Remarks

We review a series of unitarization techniques that have been used during the last decades, many of them in connection with the advent and development of current algebra and later of Chiral Perturbation Theory. Several methods are discussed like the generalized effective-range expansion, K-matrix approach, Inverse Amplitude Method, Padé approximants and the N/D method. More details are given for the latter though. We also consider how to implement them in order to correct by final-state interactions. In connection with this some other methods are also introduced like the expansion of the inverse of the form factor, the Omnés solution, generalization to coupled channels and the Khuri-Treiman formalism, among others.

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arXiv2020

Hyperon resonances and meson-baryon interactions in isospin 1

In this work we extend our formalism to study meson-baryon interactions by including $s$- and $u$-channel diagrams for pseudoscalar-baryon systems. We study the coupled systems with strangeness $-1$ and focus on studying the isospin-1 resonance(s), especially in the energy region around 1400 MeV. By constraining the model parameters to fit the cross section data available on several processes involving relevant channels, we find resonances in the isoscalar as well as the isovector sector in the energy region around 1400 MeV.

hep-ph↗

arXiv2019

Nature of $X(3872)$ from the line shape

Using a general parameterization of two-body scattering amplitude, we systematically analyze the corresponding data on $X(3872)$, more explicitly, 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. We achieve a good reproduction of data and find that the $X(3872)$ can be interpreted as a bound and/or virtual state, or even higher-order (double or triple) virtual sate pole. The latter point was not realized previously in the literature. % The latter point has not been realized in other literatures. As a result, the compositeness of the $X(3872)$ can vary largely from nearly 0 to 1. More higher-precision data is needed to discriminate its pole structure and nature.

hep-ph↗

arXiv2019

Coupled-channel approach in hadron-hadron scattering

Coupled-channel dynamics for scattering and production processes in partial-wave amplitudes is discussed from a perspective that emphasizes unitarity and analyticity. We elaborate on several methods that have driven to important results in hadron physics, either by themselves or in conjunction with effective field theory. We also develop and compare with the use of the Lippmann-Schwinger equation in near-threshold scattering. The final(initial)-state interactions are discussed in detail for the elastic and coupled-channel case. Emphasis has been put in the derivation and discussion of the methods presented, with some applications examined as important examples of their usage.

hep-ph↗

arXiv2019

Hyperon resonances coupled to pseudoscalar- and vector-baryon channels

We study hyperon resonances by solving coupled channel scattering equations. The coupled systems include pseudoscalar- and vector-baryon channels. The parameters of the model are restricted by making a $χ^2$-fit to the cross section data on processes: $K^- p \to K^- p$, $K^- p \to \bar K^0 n$, $K^- p \to ηΛ$, $K^- p \to π^0 Λ$, $K^- p \to π^0 Σ^0$, $K^- p \to π^\pm Σ^\mp$. Data on the energy level shift and width of the $1s$ state of the kaonic hydrogen, as well as some cross-section ratios near the threshold are also considered in the fit. Two types of fits are found as a result. In both cases, the properties of $Λ(1405)$ are well reproduced. In addition to this, a $Σ$ state is also found with mass around 1400 MeV. Cross sections, obtained with one of the two fits, are found to stay close to the data at energies away from the thresholds too, and as a result resonances with higher masses have also been studied.

hep-ph↗

arXiv2019

Investigation of $J/ψ\to γ\, π^0 η(π^+π^-, π^0π^0)$ radiative decays including final-state interactions

We revisit the coupled channel $K\bar{K}$ interactions and dynamically generate the resonances $f_0(980)$ and $a_0(980)$ within both the isospin and the physical bases. The $f_0(980)-a_0(980)$ mixing effects are generated in the scattering amplitudes of the coupled channels with the physical basis, which exploits the important role of the $K\bar{K}$ channel in the dynamical nature of these resonances. With the scattering amplitudes obtained, we investigate the $f_0(980)$ and $a_0(980)$ contributions to the $J/ψ\to γηπ^0$, $J/ψ\to γπ^+π^-$ and $J/ψ\to γπ^0π^0$ radiative decays through the final-state interactions. We obtain the corresponding branching fractions $Br(J/ψ\to γa_0(980) \to γηπ^0) = (0.47\pm0.05) \times 10^{-7}$, $Br(J/ψ\to γf_0(980) \to γπ^+π^-) = 0.37 \times 10^{-7} - 1.98 \times 10^{-6}$, $Br(J/ψ\to γf_0(980) \to γπ^0π^0) = 0.18 \times 10^{-7} - 9.92 \times 10^{-7}$, and predict $Br(J/ψ\to γa_0(980)) = 1.72 \times 10^{-8} - 3.07\times 10^{-7}$ and $Br(J/ψ\to γf_0(980)) = 1.86 \times 10^{-8} - 1.89\times 10^{-5}$. These fractions are within the upper limits of the experimental measurements.

hep-ph↗

arXiv2019

Effective-range-expansion study of near threshold heavy-flavor resonances

In this work we study the resonances near the thresholds of the open heavy-flavor hadrons using the effective-range-expansion method. The unitarity, analyticity and compositeness coefficient are also taken into account in our theoretical formalism. We consider the $Z_c(3900)$, $X(4020)$, $χ_{c1}(4140)$, $ψ(4260)$ and $ψ(4660)$. The scattering lengths and effective ranges from the relevant elastic $S$-wave scattering amplitudes are determined. Tentative discussions on the inner structures of the aforementioned resonances are given.

hep-ph↗

arXiv2019

Anatomy of the newly observed hidden-charm pentaquark states: $P_c(4312)$, $P_c(4440)$ and $P_c(4457)$

We study the newly reported hidden-charm pentaquark candidates $P_c(4312)$, $P_c(4440)$ and $P_c(4457)$ from the LHCb Collaboration, in the framework of the effective-range expansion and resonance compositeness relations. The scattering lengths and effective ranges from the $S$-wave $Σ_c\bar{D}$ and $Σ_c\bar{D}^*$ scattering are calculated by using the experimental results of the masses and widths of the $P_c(4312)$, $P_c(4440)$ and $P_c(4457)$. Then we calculate the couplings between the $J/ψp,\,Σ_c\bar{D}$ channels and the pentaquark candidate $P_c(4312)$, with which we further estimate the probabilities of finding the $J/ψp$ and $Σ_c\bar{D}$ components inside $P_c(4312)$. The partial decay widths and compositeness coefficients are calculated for the $P_c(4440)$ and $P_c(4457)$ states by including the $J/ψp$ and $Σ_c\bar{D}^*$ channels. Similar studies are also carried out for the three $P_c$ states by including the $Λ_c\bar{D}^{*}$ and $Σ_c\bar{D}^{(*)}$ channels.

hep-ph↗

arXiv2019

An in-medium chiral power counting for nuclear matter and some applications

We review on a chiral power counting for in-medium chiral perturbation theory with nucleons and pions as explicit degrees of freedom coupled to external sources. It allows for a systematic expansion including both local and pion-mediated inter-nucleon interactions. One can identify from this power counting classes of non-perturbative diagrams that require resummation. A non-perturbative method based on Unitary Chiral Perturbation Theory was also developed for performing those resummations. This power counting and non-perturbative techniques were firstly applied to calculate the pion self-energy, the pion-decay constants and the quark condensate in nuclear matter up-to-and-including next-to-leading order (NLO) contributions. The cancellation of the contributions at NLO to the pion self-energy and decay constants from in-medium nucleon-nucleon (NN) interactions was derived. Some NLO NN contributions survive for the quark condensate due to the quark-mass dependence of the pion mass. Next, we discuss the calculation of the energy density in the nuclear medium by employing the in-medium NN scattering amplitudes. For symmetric and neutron matter it reproduces in good agreement, and without fine tuning, calculations from realistic NN potentials with a model for the three-nucleon interaction. These results are applied to derive the equation of state (EOS) for neutron stars and obtain an upper limit for a neutron mass slightly above 2 solar masses. Our results also fulfill other constraints from the detection of the gravitational waves in the event GW170817, like the upper bound on the maximal mass of a neutron star and the allowed interval for the radius of a 1.4-solar-mass neutron star. The knowledge of the neutron-matter EOS is also employed to give an upper bound of the gravitational constant within the strong gravitational field of a 2 solar-mass neutron star.

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arXiv2018

Resonance properties from lattice energy levels using chiral effective field theory

We use the chiral effective field theory to study the lattice finite-volume energy levels from the meson-meson scattering. The hadron resonance properties and the scattering amplitudes at physical masses are determined from the lattice energy levels calculated at unphysically large pion masses. The results from the $πη, K\bar{K}$ and $πη'$ coupled-channel scattering and the $a_0(980)$ resonance are explicitly given as a concrete example.

hep-lat↗

arXiv2018

Towards a precise determination of the scattering amplitudes of the charmed and light-flavor pseudoscalar mesons

We study the scattering of the light-flavor pseudoscalar mesons ($π, K, η$) off the ground-state charmed mesons ($D,D_s$) within chiral effective field theory. The recent lattice simulation results on various scattering lengths and the finite-volume spectra both in the moving and center-of-mass frames, most of which are obtained at unphysical meson masses, are used to constrain the free parameters in our theory. Explicit formulas to include the $S$- and $P$-wave mixing to determine the finite-volume energy levels are provided. After a successful reproduction of the lattice data, we perform a chiral extrapolation to predict the quantities with physical meson masses, including phase shifts, inelasticities, resonance pole positions and the corresponding residues from the scattering of the light pseudoscalar and charmed mesons.

hep-ph↗

arXiv2018

The exact discontinuity of a partial wave along the left-hand cut and the exact $N/D$ method in non-relativistic scattering

We first deduce the analytical continuation in the complex planes of the initial and final three-momenta of the Lippmann-Schwinger equation in coupled or uncoupled partial-wave amplitudes. This result allows us to deduce a master equation whose solution is the exact discontinuity of the on-shell partial-wave amplitudes along the left-hand cut. This equation is always a linear non-singular integral equation whose solution is fixed exclusively by the knowledge of the potential, applicable to either regular or singular potentials. The capability of calculating exactly this discontinuity allows one to settle the exact $N/D $ method in two-body non-relativistic scattering for coupled and uncoupled waves. We exemplify this new advance in scattering theory by explicitly checking the agreement between the Lippmann-Schwinger equation with the corresponding solutions of the exact $N/D$ method for some examples that involve regular and singular potentials, either attractive or repulsive.

hep-ph↗

arXiv2018

New results from a number operator interpretation of the compositeness of bound and resonant states

A novel theoretical approach to the problem of the compositeness ($X$) of a resonance or bound state is developed on the basis of the expectation values of the number operators of the free particles in the continuum. This formalism is specially suitable for effective field theories in which the bare elementary states are integrated out but that give rise to resonance and bound states when implemented in nonperturbative calculations. We demonstrate that $X=1$ for finite-range energy-independent potentials, either regular or singular. A non-trivial example for an energy-dependent potential is discussed where it is shown that $X$ is independent of any type of cutoff regulator employed. The generalization of these techniques to relativistic states is developed. We also explain how to obtain a meaningful compositeness with respect to the open channels for resonances, even if it is complex in a first turn, by making use of suitable phase-factor transformations. Defining elementariness as $X=0$, we derive a new universal criterion for the elementariness of a bound state. Along the same lines, a necessary condition for a resonance to be qualified as elementary is given. The application of the formalism here developed might be of considerable practical interest.

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