arXiv subjects

D. R. Entem

Publications and source records attributed to D. R. Entem.

At least 19 recordsLinked to original sources

arXiv2026

Bootstrapping Two-Nucleon Effective Field Theories

Chiral EFT yields singular potentials that require regularization and renormalization when implemented in a dynamical equation such as the Lippmann--Schwinger equation. We employ two different approaches, renormalization with contact terms -- as is most commonly done in chiral EFT -- and the exact N/D method with multiple subtractions. We start with a toy model in which we can control the finite-range expansion of the potential, treating the full potential as the `exact' theory. To assess the statistical consistency of the approaches with the full theory, we use the bootstrap technique. We apply the same framework to study the consistency of chiral EFT at LO and NLO with the Granada phase-shift analysis in the $^1S_0$ two-nucleon partial wave. Our results show that the NLO potential significantly extends the energy range over which the theory remains valid.

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arXiv2026

Exploring $T_{\Upsilon\Upsilon}$ tetraquark candidates in a coupled-channels formalism

We investigate the spectrum of $T_{\Upsilon\Upsilon}$ tetraquark candidates within a coupled-channels framework. The analysis includes all $L\leq2$ combinations of $\Upsilon(1S)$, $\Upsilon(2S)$, $\eta_b(1S)$, and $\eta_b(2S)$ in the $J^P = 0^\pm, 1^\pm, 2^\pm$ sectors. The meson-meson interaction is derived from an underlying constituent quark model through the resonating group method, and the properties of the states are obtained from poles of the scattering matrix. We find a rich spectrum of resonant, and virtual, states distributed between the $\eta_b(1S)\eta_b(1S)$ and $\Upsilon(2S)\Upsilon(2S)$ thresholds. The pattern of poles exhibits approximate heavy-quark spin symmetry multiplets. Several states are dominated by a single channel and can be associated with threshold-driven structures, while higher-mass resonances show sizable mixing among channels involving radially excited bottomonia. The predicted widths range from tens to several hundred MeV. Branching ratios indicate that many states couple predominantly to final states with at least one excited bottomonium, whereas only a subset of the spectrum is expected to be visible in the $\eta_b(1S)\eta_b(1S)$, $\eta_b(1S)\Upsilon(1S)$ and $\Upsilon(1S)\Upsilon(1S)$ channels. These results provide quantitative guidance for experimental searches of fully heavy tetraquarks and offer a test of coupled-channel dynamics and heavy-quark spin symmetry in the $bb\bar b\bar b$ sector.

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arXiv2025

The Constituent Quark Model

In this chapter we give a pedagogical introduction to the constituent quark model. The explanation of magnetic moments of the nucleons was crucial to introduce an effective quark mass for light quarks that nowadays are understood as an effect of Spontaneous Chiral Symmetry Breaking in QCD. We give an overview of the first applications of the model and an introduction to the most modern developments studying states beyond the naive quark model as tetraquarks and pentaquarks.

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arXiv2024

Revisiting the proton-antiproton scattering using a constituent-quark-model based coupled-channels calculation

Motivated by the last experimental and theoretical advances in the analysis of possible baryonium resonances, the $X(1835)$ and their partners, we perform a constituent-quark-model based coupled-channels calculation of the proton-antiproton scattering in order to analyze the possible existence of bound states or near-threshold structures. The used $N\overline N$ potential is derived from a $G$-parity transformation of the quark-model-based $NN$ interaction which has described well deuteron properties, $NN$ phase shifts, and even hadron-hadron phenomenology. The additional $N\overline N$ annihilation is taken into account by a complex phenomenological potential whose real part is generated by one-pion and one-gluon exchange annihilation potentials and its imaginary part is an energy-independent potential of Gaussian form. Then, all the parameters of the interaction are constrained by the $NN$ sector except those determining the imaginary part of the annihilation potential. Our study concludes that the nucleon-antinucleon dynamics is complex and rich in scattering singularities near the proton-antiproton and neutron-antineutron thresholds.

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arXiv2024

Exploring doubly-heavy tetraquarks in constituent-quark-model based meson-meson coupled-channels approach

The LHCb Collaboration announced in 2021 the discovery of a new tetraquark-like state, named $T_{cc}^+$, with minimum quark content $cc\bar u\bar d$, close to the $D^0D^{*+}$ threshold. This has motivated countless theoretical works trying to identify the dynamics which is responsible of the formation of such state; in particular, the one performed by us in Ref. \cite{Ortega:2022efc}, where a $D^0D^{*+}$ molecular candidate whose mass, width, scattering length and effective ranges are in reasonable agreement with experimental measurements. We explore herein the possibility of having $T_{cc}^+$ partners in all doubly-heavy tetraquark sectors, considering doubly represented light antiquarks $u$, $d$ or $s$, and taking into account all possible spin-parity quantum numbers. The computation is done using a constituent-quark-model based meson-meson coupled-channels framework which has been tested many times in the last fifteen years describing conventional heavy mesons and baryons, their coupling with hadron-hadron thresholds but also in exploring its application to compact multiquark structures. The advantage of using an approach with such a relatively large history is that it allows us to make predictions because all the parameters have already been constrained from our previous works. Then, from this perspective, we present a parameter-free model-dependent prediction of doubly-heavy tetraquarks that may be partners of the discovered $T_{cc}^+$ state.

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arXiv2024

Confronting the Lippmann-Schwinger equation and the $N/D$ method for coupled-wave separable potentials

We study a family of separable potentials with and without added contact interactions by solving the associated Lippmann-Schwinger equation with two coupled partial waves. The matching of the resulting amplitude matrix with the effective-range expansion is studied in detail. When a counterterm is included in the potential we also carefully discuss its renormalization. Next, we use the matrix $N/D$ method and study whether the amplitude matrices from the potentials considered admit an $N/D$ representation in matrix form. As a novel result we show that it is typically not possible to find such matrix representation for the coupled partial-wave case. However, a separate $N/D$ representation for each coupled partial wave, a valid option known in the literature, is explicitly implemented and numerically solved in cases where the matrix $N/D$ method is unavailable.

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arXiv2024

An assessment of $\mathbfΥ$-states above $\mathbf{B\bar B}$-threshold using a constituent-quark-model based meson-meson coupled-channels framework

The $Υ(10753)$ state has been recently observed by the Belle and Belle~II collaborations with enough global significance to motivate an assessment of the high-energy spectrum usually predicted by any reasonable \emph{naïve} quark model. In the framework of a constituent quark model which satisfactorily describes a wide range of properties of conventional hadrons containing heavy quarks, the quark-antiquark and meson-meson degrees of freedom have been incorporated with the goal of elucidating the influence of open-bottom meson-meson thresholds into the $Υ$ states whose masses are within the energy range of the $Υ(10753)$'s mass. It is well known that such effects could be relevant enough as to generate dynamically new states and thus provide a plausible explanation of the nature of the $Υ(10753)$ state. In particular, we have performed a coupled-channels calculation in which the bare states $Υ(4S)$, $Υ(3D)$, $Υ(5S)$ and $Υ(4D)$ are considered together with the threshold channels $B\bar{B}$, $B\bar{B}^\ast$, $B^\ast \bar{B}^\ast$, $B_s\bar{B}_s$, $B_s\bar{B}_s^\ast$ and $B_s^\ast \bar{B}_s^\ast$. Among the results we have described, the following conclusions are of particular interest: (i) a richer complex spectrum is gained when thresholds are present and bare bound states are sufficiently non-relativistic; (ii) those poles obtained in the complex energy plane do not have to appear as simple peaks in the relevant cross sections; and (iii) the $Υ(10750)$ candidate is interpreted as a dressed hadronic resonance whose structure is an equally mixture of a conventional $b\bar b$ state and $B^\ast \bar B^\ast$ molecule.

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arXiv2023

Unraveling the nature of the novel $\mathbf{T_{cs}}$ and $\mathbf{T_{c\bar s}}$ tetraquark candidates

Using proton-proton collisions at centre-of-mass energies $7$, $8$, and $13$ TeV, with a total integrated luminosity of $9\,\text{fb}^{-1}$, the LHCb collaboration has performed amplitude analyses of the $B^+\to D^+D^-K^+$, $B^+\to D^- D_s^+ π^+$ and $B^0\to \bar{D}^0 D_s^+ π^-$ decays, observing that new $T_{cs}$ and $T_{c\bar s}$ resonances are required in order to explain the experimental data. These signals could be the first observation of tetraquark candidates that do not contain a heavy quark-antiquark pair; in fact, they consist of four different flavours of quarks, one of which is a doubly charged open-charm state. We present herein an analysis of the $T_{cs}$ and $T_{c\bar s}$ states, which is an extension of our recently published study of similar $T_{cc}^+$ exotic candidates. Our theoretical framework is a constituent-quark-model-based coupled-channels calculation of $qq^\prime \bar s \bar c$ and $cq\bar s\bar q^{\prime}$ tetraquark sectors for $T_{cs}$ and $T_{c\bar s}$ structures, respectively. We explore the nature, and pole position, of the singularities that appear in the scattering matrix with spin-parity quantum numbers: $J^P=0^\pm$, $1^\mp$, and $2^\pm$. The constituent quark model has been widely used in the heavy quark sector, and thus all model parameters are already constrained from previous works. This makes our predictions robust and parameter-free. We find many singularities in the solution of various scattering-matrix problems which are either virtual states or resonances, but not bound states. Some of them fit well with the experimental observations of the spin-parity, mass and width of $T_{cs}$ and $T_{c\bar s}$ candidates, and thus tentative assignments are made; however, with caution, because the experimental Breit-Wigner parameters are related to the pole characteristics.

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arXiv2023

Local position-space two-nucleon potentials from leading to fourth order of chiral effective field theory

We present local, position-space chiral NN potentials through four orders of chiral effective field theory ranging from leading order (LO) to next-to-next-to-next-to-leading order (N3LO, fourth order) of the Delta-less version of the theory. The long-range parts of these potentials are fixed by the very accurate pi-N LECs as determined in the Roy-Steiner equations analysis. At the highest order (N3LO), the NN data below 190 MeV laboratory energy are reproduced with the respectable chi^2/datum of 1.45. A comparison of the N3LO potential with the phenomenological Argonne v_18 (AV18) potential reveals substantial agreement between the two potentials in the intermediate range ruled by chiral symmetry, thus, providing a chiral underpinning for the phenomenological AV18 potential. Our chiral NN potentials may serve as a solid basis for systematic ab initio calculations of nuclear structure and reactions that allow for a comprehensive error analysis. In particular, the order by order development of the potentials will make possible a reliable determination of the truncation error at each order. Our new family of local position-space potentials differs from existing potentials of this kind by a weaker tensor force as reflected in relatively low D-state probabilities of the deuteron (P_D less or equal 4.0% for our N3LO potentials) and predictions for the triton binding energy above 8.00 MeV (from two-body forces alone). As a consequence, our potentials may lead to different predictions when applied to light and intermediate-mass nuclei in ab initio calculations and, potentially, help solve some of the outstanding problems in microscopic nuclear structure.

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arXiv2022

Kaon spectrum revisited

The European Organization for Nuclear Research (CERN) has recently approved a world-unique QCD facility in which an updated version of the external M2 beam line of the CERN SPS in conjunction with a universal spectrometer of the COMPASS experiment is used. One of its main goals is to use highly intense and energetic kaon beams to map out the complete spectrum of excited kaons with an unprecedented precision; having a broad impact not only on low-energy QCD phenomenology, but also on many high-energy particle processes where excited kaons appear, such as the study of CP violation in heavy-meson decays studied at LHCb and Belle~II. In support of the experimental effort, the kaon spectrum is computed herein using a constituent quark model which has been successfully applied to a wide range of hadronic observables, from light to heavy quark sectors, and thus the model parameters are completely constrained. The model's prediction can be used as a template against which to compare the already collected data and future experimental findings, in order to distinguish between conventional and exotic kaon states. We also compare our results with those available in the literature in order to provide some general statements, common to all calculations.

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arXiv2022

Towards the discovery of novel $B_c$ states: radiative and hadronic transitions

The properties of the $B_c$-meson family ($c\bar b$) are still not well determined experimentally because the specific mechanisms of formation and decay remain poorly understood. Unlike heavy quarkonia, i.e. the hidden heavy quark-antiquark sectors of charmonium ($c\bar c$) and bottomonium ($b\bar b$), the $B_c$-mesons cannot annihilate into gluons and they are, consequently, more stable. The excited $B_c$ states, lying below the lowest strong-decay $BD$-threshold, can only undergo through radiative decays and hadronic transitions to the $B_c$ ground state, which then decays weakly. As a result of this, a rich spectrum of narrow excited states below the $BD$-threshold appear, whose total widths are two orders of magnitude smaller than those of the excited levels of charmonium and bottomonium. In a different article, we determined bottom-charmed meson masses using a non-relativistic constituent quark model which has been applied to a wide range of hadron physical observables, and thus the model parameters are completely constrained. Herein, continuing to our study of the $B_c$ sector, we calculate the relevant radiative decay widths and hadronic transition rates between $c\bar b$ states which are below $BD$-threshold. This shall provide the most promising signals for discovering excited $B_c$ states that are below the lowest strong-decay $BD$-threshold. Finally, our results are compared with other models to measure the reliability of the predictions and point out differences.

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arXiv2021

Nucleon-nucleon potentials from Delta-full chiral effective-field-theory and implications

We closely investigate NN potentials based upon the Delta-full version of chiral effective field theory. We find that recently constructed NN potentials of this kind, which (when applied together with three-nucleon forces) were presented as predicting accurate binding energies and radii for a range of nuclei from A=16 to A=132 and providing accurate equations of state for nuclear matter, yield a chi^2/datum of 60 for the reproduction of the pp data below 100 MeV laboratory energy. This chi^2 is more than three times what the Hamada-Johnston potential of the year of 1962 achieved already some 60 years ago. We perceive this historical fact as concerning in view of the current emphasis on precision. We are able to trace the very large chi^2 as well as the apparent success of the potentials in nuclear structure to unrealistic predictions for P-wave states, in which the Delta-full NNLO potentials are off by up to 40 times the NNLO truncation errors. In fact, we show that, the worse the description of the P-wave states, the better the predictions in nuclear structure. Thus, these potentials cannot be seen as the solution to the outstanding problems in current miscroscopic nuclear structure physics.

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arXiv2021

Renormalization of NN Chiral EFT, my personal mixed feelings

We are celebrating thirty-years from the seminal papers from Weinberg proposing to use the rules of Chiral Perturbation Theory to nucleon systems. His proposal was to build an Effective Field Theory (EFT) with Chiral symmetry as a key property. A big effort on this line have been made during these three decades, however the issue of renormalization of the theory is not settled. I will briefly review my path on this issue and give my personal view.

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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

Weak B Decays into Orbitally Excited Charmed Mesons

The BaBar Collaboration has recently reported branching fractions for semileptonic decays of the $B$ meson into final states with charged and neutral $D_{1}(2420)$ and $D_{2}^{\ast}(2460)$, two narrow orbitally excited charmed mesons. We evaluate these branching fractions within the framework of a constituent quark model in two steps, one which involves a semileptonic decay and the other one mediated by a strong process. Our results are in agreement with the experimental data.

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arXiv2020

Microscopic Model of Charmonium Strong Decays

Although the spectra of heavy quarkonium systems has been successfully explained by certain QCD motivated potential models, their strong decays are difficult to deal with. We perform a microscopic calculation of charmonium strong decays using the same constituent quark model which successfully describes the $c\bar{c}$ meson spectrum. We compare the numerical results with the $^{3}P_{0}$ and the experimental data. Comparison with other predictions from similar models are included.

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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.

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arXiv2018

Heavy mesons in the Quark Model

Since the discovery of the $J/ψ$, the quark model was very successful in describing the spectrum and properties of heavy mesons including only $q\bar q$ components. However since 2003, with the discovery of the $X(3872)$, many states that can not be accommodated on the naive quark model have been discovered, and they made unavoidable to include higher Fock components on the heavy meson states. We will give an overview of the success of the quark model for heavy mesons and point some of the states that are likely to be more complicated structures such as meson-meson molecules.

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