arXiv subjects

Manuel Pavon Valderrama

Publications and source records attributed to Manuel Pavon Valderrama.

At least 19 recordsLinked to original sources

arXiv2026

Renormalization group evolution and power counting in nuclear matter

In nuclear matter, for interparticle separations larger than the healing distance (a characteristic long-distance scale of finite-density fermionic systems), the in-medium two-body wave function is essentially a free wave function. In terms of the renormalization group (RG), this implies that the running of the effective field theory (EFT) couplings freezes for r-space cutoffs above this distance (or p-space cutoffs below the corresponding healing momentum scale). As a consequence the leading order EFT description of nuclear matter (understood here as the infrared limit of the RG) corresponds to the mean-field approximation and a set of tree-level (i.e. perturbative) leading contact-range couplings. Though the contacts do in principle inherit the power counting they had in the vacuum, their iteration is suppressed in the infrared, explaining why they become perturbative in nuclear matter. In addition to the contact-range potential, RG evolution requires the inclusion of density-dependent terms in the equation of state that can be represented by a pseudo-potential, which (unlike the genuine contacts) should not be iterated. The LO EFT description ends up being a subset of Skyrme forces previously identified by the Orsay group.

nucl-th↗

arXiv2026

Auxiliary counterterms and their role in effective field theory

Effective field theories include contact-range interactions (or counterterms) for two reasons: representing the unknown short-range physics in a model independent manner and ensuring the cutoff independence of observables. Both are intertwined: cutoff independence alone (modulo truncation errors) already generates counterterms encoding physical information not present in the known long-range physics. Yet, there is also residual cutoff dependence, which is smaller than the uncertainties that are achievable within the effective field theory description and thus can be safely neglected in most settings. If one insists on exact cutoff independence though, new counterterms will be required, but they encode no new physical information and are thus what one could call redundant, or auxiliary, counterterms. It happens that auxiliary counterterms are still useful for solving certain inconsistencies that appear during renormalization or for improving the convergence of the effective field theory expansion. Examples of these use cases are discussed, including the interpretation of the improved actions or the relation between perturbative and non-perturbative renormalization.

nucl-th↗

arXiv2026

Reexamining the perturbative renormalizability of the coupled triplets

I reexamine the perturbative renormalizability of chiral two-pion exchange in two-nucleon scattering for coupled triplets when one-pion exchange has been fully iterated at leading order. Improving over previous works, it is shown that only two counterterms are required to obtain cutoff independent results, which is one less than in naive dimensional analysis. The explanation for this reduction is the existence of an attractive and repulsive eigenchannel in the one-pion exchange potential for the coupled triplets: the attractive eigenchannel can be renormalized like a regular attractive uncoupled triplet, while the repulsive eigenchannel is always finite regardless of whether there are counterterms or not. I discuss the implications of this finding for the power counting of the $^3S_1$-$^3D_1$ and $^3P_2$-$^3F_2$ partial waves.

nucl-th↗

arXiv2025

Regulator constraints for the perturbative renormalizability of attractive triplets

Nuclear effective field theory organizes the calculation of observables as a power series in terms of the ratio of soft and hard momentum scales. The rigorous implementation of this idea requires a mixture of perturbative and non-perturbative methods: on the one hand, nuclei are bound states that require the iteration of part of the nuclear potential, while on the other corrections that are small in the aforementioned power series should be perturbative in principle. Recently, it has been noted that these corrections are not cutoff independent as there are a set of exceptional cutoffs for which the couplings cannot be determined, as exemplified with the subleading order $^3P_0$ phase shifts in two-nucleon scattering. Yet, here it is shown by means of concrete calculations that exceptional cutoffs are a regulator-dependent feature. There exists a well-defined limit when the cutoff is removed, which implies that not every regulator choice (understood not only as the regulator itself, but in tandem with renormalization conditions) is acceptable within the effective field theory framework. The practical implications are minor, though: except if one is trying to explicitly probe the cutoff independence of the theory, most sensible regulator and cutoff choices are compatible with the renormalized limit within truncation errors.

nucl-th↗

arXiv2025

Scattering amplitudes versus potentials in nuclear effective field theory: search for a potential compromise

In effective field theory physical quantities, in particular observables, are expressed as a power series in terms of a small expansion parameter. For non-perturbative systems, for instance nuclear physics, this requires the non-perturbative treatment of at least part of the interaction (or the potential, if one is dealing with a non-relativistic system), while the rest of the interaction is included as perturbations. This is not entirely trivial and as a consequence different interpretations on how to treat these systems have appeared. A practical approach is to expand the effective potential, where this potential is later fully iterated in the Schroedinger equation for obtaining amplitudes and observables. The expectation is that this will lead to observables that will have an implicit power counting expansion. Here I explicitly check whether the amplitudes (when expanded according to the counting) are actually following the same power counting as the potential. It happens that reality does not necessarily conform to expectations and the amplitudes will sometimes violate the power counting with which the potential has been expanded. A more formal approach is to formulate the expansion directly in terms of amplitudes and observables, which is the original aim of the effective field theory idea. Yet this second approach is technically complicated. I explore here the possibility of constructing potentials that when fully iterated will make sure that amplitudes are indeed expansible in terms of a small expansion parameter.

nucl-th↗

arXiv2025

Molecular $P_ψ$ pentaquarks from light-meson exchange saturation

Theoretical predictions for the spectrum of heavy meson-baryon bound states are a fundamental tool for disentangling the nature of the different pentaquark states that have been observed in experimental facilities. Here we explore this spectrum in a phenomenological model that describes the heavy meson-baryon interaction in terms of a contact-range interaction, where the coupling strength is saturated by the exchange of light scalar and vector mesons, i.e. $σ$, $ρ$ and $ω$ exchanges. Saturation determines the couplings modulo an unknown proportionality constant that can be calibrated from a molecular candidate. If we use the $P_ψ^N(4312)$ as input, we predict a series of molecular pentaquarks including the $P_ψ^N(4440)$ and $P_ψ^N(4457)$, the recent $P_{ψs}^Λ(4338)$ and the $P_{ψs}^Λ(4459)$.

hep-ph↗

arXiv2024

A comparison of two possible nuclear effective field theory expansions around the one- and two-pion exchange potentials

In the effective field theory formalism nuclear forces are organized as a low energy expansion. Usually the lowest order in this expansion corresponds to the non-perturbative iteration of the one-pion exchange potential and a few contact-range operators as to ensure renormalization group invariance. Here we consider an alternative expansion in which two-pion exchange becomes the lowest order finite range interaction and as such is expected to be iterated. A comparison of this new expansion with the standard one shows a better convergence pattern for a few selected partial waves ($^1S_0$, $^3P_0$ and $^3S_1$-$^3D_1$) in two-nucleon scattering, in particular for the $^1S_0$ channel (though both expansions converge well). We briefly comment on the possible theoretical grounds for the expansion around two-pion exchange from the point of view of effective field theory.

nucl-th↗

arXiv2024

Heavy- and light-flavor symmetry partners of the $T_{cc}^+(3875)$, the $X(3872)$ and the $X(3960)$ from light-meson exchange saturation

The spectrum of the charmed meson-(anti)meson system is a fundamental tool for disentangling the nature of a few exotic hadrons, including the recently discovered $T_{cc}^+(3875)$ tetraquark, the $X(3960)$, or the $X(3872)$, the nature of which is still not clear after almost two decades of its discovery. Here we consider that the charmed meson-(anti)meson short-range interaction is described by the exchange of light-mesons ($σ$, $ρ$, $ω$). The effects of light-meson exchanges are recast into a simple contact-range theory by means of a saturation procedure, resulting in a compact description of the two-hadron interaction. From this, if the $T_{cc}^+$ were to be an isoscalar $D^* D$ molecule, then there should exist an isoscalar $J=1$ $D^* D^*$ partner, as constrained by heavy-quark spin symmetry. Yet, within our model, the most attractive two charmed meson configurations are the isovector $J=0$ $D^* D^*$ molecule and its sextet $D_s^* D^*$ and $D_s^* D_s^*$ flavor partners. Finally, we find a tension between the molecular descriptions of the $T_{cc}^+$ and that of the $X(3872)$ and $X(3960)$, where most parameter choices suggest that if the $T_{cc}^+$ is purely molecular then the $X(3872)$ overbinds (or conversely, if the $X(3872)$ is a molecule the $T_{cc}^+$ does not bind). This might be consequential for determining the nature of these states.

hep-ph↗

arXiv2024

Molecular charmed baryons and pentaquarks from light-meson exchange saturation

The spectrum of the $c qq$ baryons contains a few states whose nature is not clearly a three-quark composite and which might have a sizable baryon-meson component. Examples include the $Σ_c(2800)$ or the $Λ_c(2940)$. Here we explore the spectrum of two-body systems composed of a light, octet baryon and a charmed meson (or antimeson) within a simple contact-range theory in which the couplings are saturated by light-meson exchanges. This results in the prediction of a series of composite anticharmed pentaquarks ($\bar{c} q qqq $) and singly-charmed baryons ($c \bar{q} qqq $). Among the later we find $J=\tfrac{1}{2}$ $ΞD$ and $J=\tfrac{3}{2}$ $ΞD^*$ bound states with masses matching those of the recently observed $Ω_c(3185)$ and $Ω_c(3327)$ baryons.

hep-ph↗

arXiv2024

Rethinking the $P_c(4457)^+$ as the $P_ψ^{Δ^+}(4457)$ isoquartet $\bar{D}^* Σ_c$ molecule

The nature of the $P_{c}(4312)$, $P_c(4440)$ and $P_c(4457)$ pentaquarks is a fascinating theoretical question. Within the molecular picture their more usual interpretation is that of $I=\tfrac{1}{2}$ $\bar{D} Σ_c$ and $\bar{D}^* Σ_c$ bound states. Here we argue in favor of interpreting the $P_c(4457)$ pentaquark as a $I=\tfrac{3}{2}$ $\bar{D}^* Σ_c$ bound state (with spin $J=\tfrac{1}{2}$) instead. Owing to isospin symmetry breaking effects, with this identification the partial decay width of the $P_c(4457)^+$ into $J/ψp$ will be of the same order of magnitude as the $P_{c}(4312)^+$ and $P_c(4440)^+$, in contrast with the considerably larger partial decay width in the $I=\tfrac{1}{2}$ scenario. In turn, this leads to a different hidden-charm molecular pentaquark spectrum, in which there are only four or five $P_ψ^N$ bound states instead of the usual seven, which might explain why the predicted $J=\tfrac{1}{2}$ and $\tfrac{3}{2}$ ($I=\tfrac{1}{2}$) $\bar{D}^* Σ_c^*$ molecular partners of the $P_c(4312)$ and $P_c(4440)$ have not been observed.

hep-ph↗

arXiv2024

The $P_{ψs}^Λ(4338)$ pentaquark and its partners in the molecular picture

The LHCb collaboration has detected a new hidden-charm pentaquark with the quantum numbers of a $Λ$ baryon: the $P_{ψs}^Λ(4338)$. This pentaquark will be interpreted as a $\bar{D}_s Λ_c$-$\bar{D} Ξ_c$ resonance within a contact-range theory. Here we briefly comment on the relation of the new $P_{ψs}^Λ(4338)$ with the $P^Λ_{ψs}(4459)$. We find that the $P_{ψs}^Λ(4338)$ and $P_{ψs}^Λ(4459)$ both accept a common description in terms of the same parameters, which predicts the existence of a few additional $P_ψ^N$, $P_{ψs}^Λ$, $P_{ψs}^Σ$ and $P_{ψs s}^Ξ$ molecular pentaquarks composed of a charmed antimeson and an antitriplet charmed baryon. The most robust of these predicted pentaquarks is a $P_{ψs}^Λ$ with a mass in the $(4235-4255)\,{\rm MeV}$ range, while other two interesting ones are a $P_ψ^{N}(4150)$ and a $P_ψ^Σ(4335)$, the latter basically at the same mass as the $P_ψ^Λ(4338)$, with which it might mix owing to isospin symmetry breaking effects.

hep-ph↗

arXiv2023

Unitary interaction geometries in few-body systems

We consider few-body systems in which only a certain subset of the particle-particle interactions is resonant. We characterize each subset by a {\it unitary graph} in which the vertices represent distinguishable particles and the edges resonant 2-body interactions. Few-body systems whose unitary graph is connected will collapse unless a repulsive 3-body interaction is included. We find two categories of graphs, distinguished by the kind of 3-body repulsion necessary to stabilize the associated system. Each category is characterized by whether the graph contains a loop or not: for tree-like graphs (graphs containing a loop) the 3-body force renormalizing them is the same as in the 3-body system with two (three) resonant interactions. We show numerically that this conjecture is correct for the 4-body case as well as for a few 5-body configurations. We explain this result in the 4-body sector qualitatively by imposing Bethe-Peierls boundary conditions on the pertinent Faddeev-Yakubovsky~decomposition of the wave function.

cond-mat.quant-gas↗

arXiv2023

Light- and heavy-quark symmetries and the $Y(4230)$, $Y(4360)$, $Y(4500)$, $Y(4620)$ and $X(4630)$ resonances

The heavy hadron spectrum is constrained by symmetries, of which two of the most important ones are heavy-quark spin and SU(3)-flavor symmetries. Here we argue that in the molecular picture the $Y(4230)$ (or $Y(4260)$), the $Y(4360)$ and the recently discovered $Y(4500)$ and $Y(4620)$ vector-like resonances are linked by these two symmetries. By formulating a contact-range effective field theory for the $D \bar{D}_1$ and $D_s \bar{D}_{s1}$ family of S- and P-wave charmed meson-antimeson systems, we find that if the $Y(4230)$ were to be a pure $D \bar{D}_1$ molecular state, there would be a $D^* \bar{D}_1$ partner with a mass similar to the $Y(4360)$, a $D_s \bar{D}_{s1}$ partner with a mass close to the $Y(4500)$ and three $J=1,2$ $D_s^* \bar{D}_{s1}$ and $J=3$ $D_s^* \bar{D}_{s2}^{*}$ bound states with a mass in the vicinity of $4630\,{\rm MeV}$, of which the first one ($J=1$) might correspond with the $Y(4620)$. The previous predictions can in turn be improved by modifying the assumptions we have used to build the effective field theory. In particular, if we consider the closeness of the $D^* \bar{D}_1$-$D^* \bar{D}_2^*$ and $D_s^* \bar{D}_{s1}$-$D_s^* \bar{D}_{s2}^*$ thresholds and include the related coupled channel dynamics, we predict a $J=2$ positive C-parity state with a mass around $4650\,{\rm MeV}$. This hidden-strange and hidden-charm state might in turn be identified with the $X(4630)$ that has been discovered past year by the LHCb in the $J/ψϕ$ invariant mass distribution.

hep-ph↗

arXiv2022

Five-flavor pentaquarks and other light- and heavy-flavor symmetry partners of the LHCb hidden-charm pentaquark

The discovery of three pentaquark peaks -- the $P_c(4312)$, $P_c(4440)$ and $P_c(4457)$ -- by the LHCb collaboration has a series of interesting consequences for hadron spectroscopy. If these hidden-charm objects are indeed hadronic molecules, as suspected, they will be constrained by heavy-flavor and SU(3)-flavor symmetries. The combination of these two symmetries will imply the existence of a series of five-flavor pentaquarks with quark content $\bar{b} c s d u$ and $b \bar{c} s d u$, that is, pentaquarks that contain each of the five quark flavors that hadronize. In addition, from SU(3)-flavor symmetry alone we expect the existence of light-flavor partners of the three $P_c$ pentaquarks with strangeness $S=-1$ and $S=-2$. The resulting structure for the molecular pentaquarks is analogous to the light-baryon octet -- we can label the pentaquarks as $P_{Q' \bar{Q}}^N$, $P_{Q' \bar{Q}}^Λ$, $P_{Q' \bar{Q}}^Σ$, $P_{Q' \bar{Q}}^Ξ$ depending on their heavy- and light-quark content (with $N$, $Λ$, $Σ$, $Ξ$ the member of the light-baryon octet to which the light-quark structure resembles and $Q'$, $\bar Q$ the heavy quark-antiquark pair). In total we predict $45$ new pentaquarks from heavy- and light-flavor symmetries alone, which extend up to $109$ undiscovered states if we also consider heavy-quark spin symmetry. If an isoquartet ($I={3/2}$) hidden-charm pentaquark is ever observed, this will in turn imply a second multiplet structure resembling the light-baryon decuplet: $P_{Q' \bar{Q}}^Δ$, $P_{Q' \bar{Q}}^{Σ^*}$, $P_{Q' \bar{Q}}^{Ξ^*}$, $P_{Q' \bar{Q}}^Ω$.

hep-ph↗

arXiv2022

Interpretations of the new LHCb $P_c(4337)^+$ pentaquark state

Recently the LHCb collaboration has observed a new pentaquark state, the $P_c(4337)^+$. Owing to its proximity to the $χ_{c0}(1S) p$, $\bar{D}^* Λ_c$, $\bar{D} Σ_c$ and $\bar{D} Σ_c^*$ thresholds, this new pentaquark might very well be a meson-baryon bound state. However its spin and parity have not been determined yet and none of the previous possibilities can be ruled out. We briefly explore a few of these options and the consequences they entail in the present manuscript: (i) the $P_c(4337)^+$ might be a $χ_{c0}(1S) p$ bound state, (ii) the $P_c(4312)^+$ and $P_c(4337)^+$ might be $\bar{D}^* Λ_c$ and $\bar{D} Σ_c$ states close to threshold, respectively, where the Breit-Wigner mass might not correspond to the location of the poles, (iii) the locations of the $P_c(4312)^+$ and $P_c(4337)^+$ might be explained in terms of the $\bar{D}^* Λ_c$-$\bar{D} Σ_c$ and $\bar{D}^* Λ_c$-$\bar{D} Σ_c^*$ coupled channel dynamics. This last option, though not the most probable explanation, is still potentially compatible with the double peak solution of the $P_{cs}(4459)^0$ and with what we know of the $P_c(4312)^+$. As a byproduct of the previous explorations, we conjecture the existence of a series of anticharmed meson - antitriplet charmed baryon bound states and calculate their masses.

hep-ph↗

arXiv2022

Heavy-hadron molecular spectrum from light-meson exchange saturation

If known, the spectrum of heavy-hadron molecules will be a key tool to disentangle the nature of the exotic states that are being discovered in experiments. Here we argue that the general features of the molecular spectrum can be deduced from the idea that the short-range interaction between the heavy hadrons is effectively described by scalar and vector meson exchange, i.e. the $σ$, $ω$ and $ρ$ mesons. By means of a contact-range theory where the couplings are saturated by the aforementioned light mesons we are indeed able to postdict the $X(3872)$ (as a $D^* \bar{D}$ molecule) from the three $P_c(4312)$, $P_c(4440)$ and $P_c(4457)$ pentaquarks (as $\bar{D}Σ_c$ and $\bar{D}^* Σ_c$ molecules). We predict a $J^{PC} = 1^{--}$ $D \bar{D}_1$ molecule at $4240-4260\,{\rm MeV}$ which might support the hypothesis that the $Y(4260)$ is at least partly molecular. The extension of these ideas to the light baryons requires minor modifications, after which we recover approximate SU(4)-Wigner symmetry in the two-nucleon system and approximately reproduce the masses of the deuteron and the virtual state.

hep-ph↗

arXiv2022

Subleading contributions to the decay width of the $T_{cc}^+$ tetraquark

Recently the LHCb collaboration has announced the discovery of the $T_{cc}^+$ tetraquark. Being merely a few hundred ${\rm keV}$ below the $D^{*+} D^0$ threshold, the $T_{cc}^+$ is expected to have a molecular component, for which there is a good separation of scales that can be exploited to make reasonably accurate theoretical predictions about this tetraquark. Independently of its nature, the most important decay channels will be $D^+ D^0 π^0$, $D^0 D^0 π^+$ and $D^+ D^0 γ$. Its closeness to threshold suggests that the mass and particularly the width of the $T_{cc}^+$ tetraquark depend on the resonance profile. While the standard Breit-Wigner parametrization generates a $T_{cc}^+$ that is too broad for current theoretical calculations to reproduce, a three-body unitarized Breit-Wigner shape reveals instead a decay width ($Γ_{\rm pole} = 48\pm 2\,{}^{+0}_{-12}\,{\rm keV}$) consistent with theoretical expectations. Here we consider subleading order contributions to the decay amplitude, which though having at most a moderate impact in the width still indicate potentially significant differences with the experimental width that can be exploited to disentangle the nature of the $T_{cc}^+$. Concrete calculations yield $Γ^{\rm LO} = 49 \pm 16\,{\rm keV}$ and $Γ^{\rm NLO} = 58^{+7}_{-6}\,{\rm keV}$, though we expect further corrections to the ${\rm NLO}$ decay widths from asymptotic normalization effects. We find that a detailed comparison of the ${\rm NLO}$ total and partial decay widths with experiment suggests the existence of a small (but distinguishable from zero) non-molecular component of the $T_{cc}^+$.

hep-ph↗

arXiv2021

Axial meson exchange and the $Z_c(3900)$ and $Z_{cs}(3985)$ resonances as heavy hadron molecules

Early speculations about the existence of heavy hadron molecules were grounded on the idea that light-meson exchanges forces could lead to binding. In analogy to the deuteron, the light-mesons usually considered include the pion, sigma, rho and omega, but not the axial meson $a_1(1260)$. Though it has been argued in the past that the coupling of the axial meson to the nucleons is indeed strong, its mass is considerably heavier than that of the vector mesons and thus its exchange ends up being suppressed. Yet, this is not necessarily the case in heavy hadrons molecules: we find that even though the contribution to binding from the axial meson is modest, it cannot be neglected in the isovector sector where vector meson exchange cancels out. This might provide a natural binding mechanism for molecular candidates such as the $Z_c(3900)$, $Z_c(4020)$ or the more recently observed $Z_{cs}(3985)$. However the $Z_{cs}(3985)$ is more dependent on a mixture of different factors, which (besides axial meson exchange) include $η$ exchange and the nature of scalar meson exchange. Together they point towards the existence of two $Z_{cs}(3985)$-like resonances instead of one, while the observations about the role of scalar meson exchange in the $Z_{cs}(3985)$ might be relevant for the $P_{cs}(4459)$. Finally, the combination of axial meson exchange and flavor symmetry breaking effects indicates that the isovector $J^{PC} = 0^{++}$ $D^*\bar{D}^*$ and the strange $J^P = 2^{+}$ $D^*\bar{D}_s^*$ molecules are the most attractive configurations and thus the most likely molecular partners of the $Z_c(3900)$, $Z_c(4020)$ and $Z_{cs}(3985)$.

hep-ph↗