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M. Napsuciale

Publications and source records attributed to M. Napsuciale.

At least 19 recordsLinked to original sources
arXiv2026

Stationary perturbation theory without sums over intermediate states: Supersymmetric Expansion Algorithm

In this work we show that results of Rayleigh-Schr\"{o}dinger perturbation theory can be easily obtained using the recently proposed supersymmetric expansion algorithm. Our formalism avoids the sums over intermediate states and yield directly corrections to the energy and eigenstates in terms of integrals weighted by the probability densities for the edge states of the involved supersymmetric Hamiltonians.

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arXiv2025

Renormalization of massless fields in the $(1,0)\oplus(0,1)$ representation

We study the one-loop renormalization of self-interacting massless fields in the $(1,0)\oplus(0,1)$ representation of the Restricted Lorentz Group. We work with a general model that represents the entire class of parity-invariant self-interacting massless theories that can be defined in this representation. It consists of a general free Lagrangian that reproduces the massless limit of three theories previously studied in the literature: the Joos-Weinberg, the Shay-Good/Hammer-McDonald-Pursey, and the Klein-Gordon-like one, as particular cases; along with an interacting Lagrangian containing all the independent dimension-4 parity-invariant self-interactions available in this representation. The model is found to be renormalizable.

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arXiv2025

Complete analytical solution to the Cornell potential and heavy quarkonium structure

We use the recently proposed supersymmetric expansion algorithm (SEA) to obtain a complete analytical solution to the Schr\"{o}dinger equation with the Cornell potential. We find that the energy levels $E_{nl}(\lambda)$ depend on $n^{2}$ and $L^{2}=l(l+1)$. For a given $n$, the energy {\emph {decreases}} with $l$ and the radial probabilities have the Coulomb shape but their peaks are shifted toward smaller radius. We study the heavy quarkonium structure on the light of these results, showing that the measured $\bar{b}b$ and $\bar{c}c$ meson masses follow the inverted spectrum pattern predicted by the Cornell potential. Details of the structure of heavy quarkonium like the mean inverse radius and mean squared velocity for the different quarkonium configurations can be obtained from our solution. These details point to significant relativistic corrections for all the configurations of real heavy quarkonium. We calculate relativistic corrections using perturbation theory finding an expansion in $\alpha^{2}_{s}$ for the heavy quarkonium masses. The mass hierarchies in the fine splittings can be qualitatively understood from this expansion. The quantitative analysis of the Bohr-like levels and of the fine splittings in the $l=0$ sector allow us to make well defined predictions for the masses of some of the missing heavy quarkonium states, to identify the $\psi(4040)$ as the $3^{3}S_{1}$ $\bar{c}c$ state and the $\psi(3842)$, $\psi(3823)$ and $\psi(3770)$ as the $3^{3}D_{3}$, $3^{3}D_{2}$ and $3^{3}D_{1}$ $\bar{c}c$ states respectively.

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arXiv2024

Supersymmetric Expansion Algorithm and complete analytical solution for the Hulth\'en and anharmonic potentials

An algorithm for providing analytical solutions to Schr\"{o}dinger's equation with non-exactly solvable potentials is elaborated. It represents a symbiosis between the logarithmic expansion method and the techniques of the superymmetric quantum mechanics as extended toward non shape invariant potentials. The complete solution to a given Hamiltonian $H_{0}$ is obtained from the nodeless states of the Hamiltonian $H_{0}$ and of a set of supersymmetric partners $H_{1}, H_{2},..., H_{r}$. The nodeless states (dubbed "edge" states) are unique and in general can be ground or excited states. They are solved using the logarithmic expansion which yields an infinite systems of coupled first order hierarchical differential equations, converted later into algebraic equations with recurrence relations which can be solved order by order. We formulate the aforementioned scheme, termed to as "Supersymmetric Expansion Algorithm'' step by step and apply it to obtain for the first time the complete analytical solutions of the three dimensional Hulth\'en--, and the one-dimensional anharmonic oscillator potentials.

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arXiv2021

Kinetic mixing, custodial symmetry and a lower bound on the dark $Z^{\prime}$ mass

In this work we consider the extension of the standard model by dark fields with an Abelian $U(1)_{d}$ spontaneously broken gauge symmetry in a hidden dark matter scenario. Considering all the dimension four gauge invariant terms we show that the tree-level relation $M^{2}_{W}=M^{2}_{\tilde Z} \cos^{2} \tilde θ_{w}$ holds and permits to write the mixing angle induced by the kinetic mixing in the neutral massive gauge boson sector, $θ_ζ$, in terms of the values of $M_{Z}$, the weak mixing angle and of the mass of the physical dark gauge $Z^{\prime}$ boson. At the loop level, a similar relation is obtained in the $\overline{MS}$ scheme. Using the result extracted from the global fit to electroweak precision data for the ratio $ρ_{0}=M^{2}_{W}/\hat{c}^{2}_{Z} M^{2}_{Z}\hatρ$, we obtain a lower bound $M_{Z^{\prime}}> M_{Z}$ for the dark $Z^{\prime}$ mass at the $94\%$ confidence level. We argue that this lower bound holds in the general case of theories for physics beyond the standard model with an extra $U(1)$ gauge factor subgroup, whenever the extended Higgs potential respects custodial symmetry.

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arXiv2021

Kinetic mixing, custodial symmetry, $Z$, $Z^{\prime}$ interactions and $Z^{\prime}$ production in hadron colliders

In this work we study the interactions of the $Z$ and $Z^{\prime}$ generated by kinetic mixing in a class of theories for physics beyond the standard model motivated by the dark matter problem, containing a spontaneously broken extra $U(1)_{d}$ gauge factor group in a hidden scenario and a Higgs sector respecting custodial symmetry. It is shown that custodial symmetry allows us to write the $Z$ and $Z^{\prime}$ couplings to standard model fermions in terms of the measured values of $α$, $G_{F}$, $M_{Z}$ and $M_{Z^{\prime}}$. Working at the loop level, we calculate the ratio $ρ_{0}=M^{2}_{W}/\hat{c}^{2}_{Z}M^{2}_{Z}\hatρ$ used in the fit to electroweak precision data (EWPD) and use its value to estimate possible effects of kinetic mixing at the electroweak scale. For the $Z$ sector, we calculate the oblique parameters $S$ and $T$, finding that for $M_{Z^{\prime}}\geq M_{Z}$ our results are in agreement with the values of the oblique parameters extracted from the global fit to EWPD at $1σ$ level. As to the $Z^{\prime}$ sector, we calculate the $Z^{\prime}$ contributions to charged lepton pair production at the Large Hadron Colliderin the well motivated case of dark matter entering particle physics as the matter fields of the $U(1)_{d}$ gauge symmetry with perturbative couplings at the electroweak scale, finding that data reported by the Compact Muon Selenoid Collaboration impose a lower limit $M_{Z^{\prime}}\gtrsim 5.0 ~TeV$.

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arXiv2021

Cosmic-ray antiproton excess from annihilating tensor dark matter

In this paper we calculate the antiproton production in the annihilation of tensor dark matter and explore the possibility that the excess of antiprotons in the range $E_{K}=10-20 ~GeV$ reported by several groups in the analysis of the AMS-02 Collaboration data is due to this production mechanism. We find that these contributions improve the fit to the data on the antiproton to proton ratio for the narrow window $M\in [62.470,62.505] \text{ GeV}$ for the tensor dark matter mass and $g_s \in [0.98,1.01]\times 10^{-3}$ for the Higgs portal coupling in the effective theory. These are precisely the range of values compatible with several experimental constraints, such as dark matter relic density, limits on the spin-independent dark matter-nucleon cross-section from XENON1T, indirect detection limits for the annihilation of dark matter into $\bar{b}b$, $\tau^+ \tau^-$, $\mu^+ \mu^-$ and $\gamma \gamma$, as well as with the gamma-ray excess at the Milky Way galactic center.

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arXiv2021

Bound states of the Yukawa potential from hidden supersymmetry

In this work, we present a phenomenological study of the complete analytical solution to the bound eigenstates and eigenvalues of the Yukawa potential obtained previously using the hidden supersymmetry of the system and a systematic expansion of the Yukawa potential in terms of $δ=a_{0}/D$, where $a_{0}$ is the Bohr radius and $D$ is the screening length. The eigenvalues, $ε_{nl}(δ)$, are given in the form of Taylor series in $δ$ which can be systematically calculated to the desired order $δ^{k}$. Coulomb $l$-degeneracy is broken by the screening effects and, for a given $n$, $ε_{nl}(δ)$ is larger for higher values of $l$ which causes the crossing of levels for $n\ge4$. The convergence radius of the Taylor series can be enlarged up to the critical values using the Padé approximants technique which allows us to calculate the eigenvalues with high precision in the whole rage of values of $δ$ where bound states exist, and to reach a precise determination of the critical screening lengths, $δ_{nl}$. Eigenstates have a form similar to the solutions of the Coulomb potential, with the associated Laguerre polynomials replaced by new polynomials of order $δ^{k}$ with $r$-dependent coefficients which, in turn, are polynomials in $r$. In general we find sizable deviations from the Coulomb radial probabilities only for screening lengths close to their critical values. We use these solutions to find the squared absolute value at the origin of the wave function for $l=0$, and their derivatives for $l=1$, for the lowest states, as functions of $δ$, which enter the phenomenology of dark matter bound states in dark gauge theories with a light dark mediator.

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arXiv2021

Complete analytical solution to the quantum Yukawa potential

We present a complete analytical solution to the quantum problem of a particle in the Yukawa potential, using supersymmetry and a systematic expansion of the corresponding super-potentials. Results for the critical screening of the ground state improve in several figures existing results based on both numerical solutions and approximation methods. Our calculation to order $(a_{0}/D)^{2}$ for the squared ground state wavefunction at the origin, which enter in darkonium transitions, yields a correction of $π^{4}/216$ to results based on variational techniques.

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arXiv2020

Spin-one dark matter and gamma ray signals from the galactic center

In this work we study the possibility that the gamma ray excess (GRE) at the Milky Way galactic center come from the annihilation of dark matter with a $(1,0)\oplus(0,1)$ space-time structure (spin-one dark matter, SODM). We calculate the production of prompt photons from initial state radiation, internal bremsstrahlung, final state radiation including the emission from the decay products of the $μ, τ$ or hadronization of quarks. Next we study the delayed photon emission from the inverse Compton scattering (ICS) of electrons (produced directly or in the prompt decay of $μ, τ$ leptons or in the hadronization of quarks produced in the annihilation of SODM) with the cosmic microwave background or starlight. All these mechanisms yield significant contributions only for Higgs resonant exchange, i.e. for $M\approx M_{H}/2$, and the results depend on the Higgs scalar coupling to SODM, $g_{s}$. The dominant mechanism at the GRE bump is the prompt photon production in the hadronization of $b$ quarks produced in $\bar{D}D\to \bar{b}b$, whereas the delayed photon emission from the ICS of electrons coming from the hadronization of $b$ quarks produced in the same reaction dominates at low energies ($ω< 0.3~ GeV$) and prompt photons from $c$ and $τ$, as well as from internal bremsstrahlung, yield competitive contributions at the end point of the spectrum ($ω\ge 30 ~GeV$). Taking into account all these contributions, our results for photons produced in the annihilation of SODM are in good agreement with the GRE data for $g_{s}\in [0.98, 1.01] \times 10^{-3}$ and $M\in [62.470,62.505]~GeV$.

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arXiv2018

Distinguishing Dirac and Majorana neutrinos with astrophysical fluxes

Massive neutrinos can have helicity $s_{\parallel}\neq -1$. Neutrino helicity changes when the neutrino interacts with an external magnetic field and it is possible that the left-handed neutrinos born inside the Sun or a supernova could leave their sources with a different helicity. Since Dirac and Majorana neutrinos have different cross sections in the scattering on electrons for different neutrino helicities, a change in the final neutrino helicity may generate a different number of events and spectra in terrestrial detectors when astrophysical neutrinos have travelled regions with strong magnetic fields. In this work, we show that looking for these effects in solar neutrinos, it could be possible to set bounds in the neutrino properties such as the neutrino magnetic moment. Furthermore, for neutrinos coming from a supernova, we show that even in the case of an extremely small neutrino magnetic moment, $μ_ν\sim 10^{-19}μ_B$, there will be measurable differences in both the number of events and in the spectra of Majorana and Dirac neutrinos.

hep-ph↗
arXiv2018

Spin portal to dark matter

In this work we study the possibility that dark matter fields transform in the $(1,0)\oplus(0,1)$ representation of the Homogeneous Lorentz Group. In an effective theory approach, we study the lowest dimension interacting terms of dark matter with standard model fields, assuming that dark matter fields transform as singlets under the standard model gauge group. There are three dimension-four operators, two of them yielding a Higgs portal to dark matter. The third operator couple the photon and $Z^0$ fields to the higher multipoles of dark matter, yielding a \textit{spin portal} to dark matter. For dark matter ($D$) mass below a half of the $Z^0$ mass, the decays $Z^0\to \bar{D} D$ and $H\to \bar{D}D$ are kinematically allowed and contribute to the invisible widths of the $Z^0$ and $H$. We calculate these decays and use experimental results on these invisible widths to constrain the values of the low energy constants finding in general that effects of the spin portal can be more important that those of the Higgs portal. We calculate the dark matter relic density in our formalism, use the constraints on the low energy constants from the $Z^0$ and $H$ invisible widths and compare our results with the measured relic density, finding that dark matter with a $(1,0)\oplus(0,1)$ space-time structure must have a mass $M>43 ~ GeV$.

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arXiv2016

Spin one matter fields

Spin-one matter fields are relevant both for the description of hadronic states and as potential extensions of the Standard Model. In this work we present a formalism for the description of massive spin-one fields transforming in the $(1,0)\oplus(0,1)$ representation of the Lorentz group, based on the covariant projection onto parity eigenspaces and Poincaré orbits. The formalism yields a constrained dynamics. We solve the constraints and perform the canonical quantization accordingly. This formulation uses the recent construction of a parity-based covariant basis for matrix operators acting on the $(j,0)\oplus(0,j) $ representations. The algebraic properties of the covariant basis play an important role in solving the constraints and allowing the canonical quantization of the theory. We study the chiral structure of the theory and conclude that it is not chirally symmetric in the massless limit, hence it is not possible to have chiral gauge interactions. However, spin-one matter fields can have vector gauge interactions. Also, the dimension of the field makes self-interactions naively renormalizable. Using the covariant basis, we classify all possible naively renormalizable self-interaction terms.

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arXiv2014

Scattering processes could distinguish Majorana from Dirac neutrinos

It is well known that Majorana neutrinos have a pure axial neutral current interaction while Dirac neutrinos have the standard vector-axial interaction. In spite of this crucial difference, usually Dirac neutrino processes differ from Majorana processes by a term proportional to the neutrino mass, resulting in almost unmeasurable observations of this difference. In the present work we show that once the neutrino polarization evolution is considered, there are clear differences between Dirac and Majorana scattering on electrons. The change of polarization can be achieved in astrophysical environments with strong magnetic fields. Furthermore, we show that in the case of unpolarized neutrino scattering onto polarized electrons, this difference can be relevant even for large values of the neutrino energy.

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arXiv2013

Covariant basis induced by parity for the $(j,0)\oplus (0,j)$ representation

In this work, we build a covariant basis for operators acting on the $(j,0)\oplus(0,j)$ Lorentz group representations. The construction is based on an analysis of the covariant properties of the parity operator, which for these representations transforms as the completely temporal component of a symmetrical tensor of rank $2j$. The covariant properties of parity involve the Jordan algebra of anti commutators of the Lorentz group generators which unlike the Lie algebra is not universal. We make the construction explicit for $j=1/2,1$ and $3/2$, reproducing well-known results for the $j=1/2$ case. We provide an algorithm for the corresponding calculations for arbitrary $j$. This covariant basis provides an inventory of all the possible interaction terms for gauge and non-gauge theories of fields for these representations. In particular, it supplies a single second rank antisymmetric structure, which in the Poincaré projector formalism implies a single Pauli term arising from gauge interactions and a single (free) parameter $g$, the gyromagnetic factor. This simple structure predicts that for an elementary particle in this formalism all multipole moments, $Q^{l}_{E}$ and $Q^{l}_{M}$, are dictated by the complete algebraic structure of the Lorentz generators and the value of $g$. We explicitly calculate the multipole moments, for arbitrary $j$ up to $l=8$. Comparing with results in the literature we find that only the electric charge and magnetic moment of a spin $j$ particle are independent of the Lorentz representation under which it transforms, all higher multipoles being representation dependent. Finally we show that the propagation of the corresponding spin $j$ waves in a electromagnetic background is causal.

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arXiv2013

Parity-based formalism for high spin matter fields

Using the recent parity-based construction of a covariant basis for operators acting on the $(j,0)\oplus(0,j)$ representation of the HLG, we propose a formalism for the description of high spin matter fields, based on the projection over subspaces of well-defined parity. We identify two possibilities for the projection, on-shell and off-shell projection. For all $j$ except for $j=1/2$, we find that the projection does not completely fix the properties of the interacting theory. This freedom is related to the fact that the covariant form of parity can be written in terms of one of the symmetric traceless tensors in the covariant basis and in general allows for a free magnetic dipole term in the lagrangian. We gauge the theory and construct the charge conjugation operator. In the case of bosons, the parity invariant subspaces are also invariant under charge conjugation and time reversal and the formulation of a quantum field theory can be done using only these subspaces. As a first exhaustive example we work out the electrodynamics for $j=1$ matter bosons, rewrite the theory in terms of an antisymmetric tensor field and compare our results with existing formalisms in the literature. We find that there are three essentially different formalisms: i) formalisms equivalent to the on-shell parity projection, ii) formalisms equivalent to the off-shell parity projection and iii) the Poincaré projector formalism which describes a degenerate parity doublet. We perform a chiral decomposition of these theories and show that chiral symmetry can be realized linearly only for the theory based on the on-shell projection. Chiral symmetry forbids mass and anomalous magnetic dipole terms and in general admits six self-interaction terms. We conclude that this is the appropriate framework to attempt the incorporation of spin 1 matter bosons in chiral theories like the standard model.

hep-ph↗
arXiv2013

Compton scattering off massive fundamental bosons of pure spin 1

Relativistic particles with spins $J>0$ are described by means of multicomponent wave functions which transform covariantly according to Lorentz-group representations that contain at rest the spin of interest. The symmetry group of space-time provides not one but an infinity of such representations which are equivalent for free particles but yield different electromagnetic couplings upon gauging; thus the challenge is to develop criteria which allow us to select those of them which relate to physically detectable particles. We here take the position that the unitarity of the Compton scattering cross sections in the ultrarelativistic limit, when predicted by a consistent method for a spin-$1$ description, could provide such a criterion. We analyze the properties of massive fundamental spin-$1$ bosons transforming as antisymmetric tensors of second rank, $(1,0)\oplus(0,1)$. For this purpose, we employ the Poincaré covariant projector method, which provides consistent, causal, and representation specific Lagrangians. This formalism yields a twofold extension of the Proca Lagrangian for the description of spin-$1$ bosons, first from an in-built $g=1$ value of the gyromagnetic ratio to an unspecified $g\not=1$, and from, single-parity, to parity-doublet degrees of freedom. We find different results for Compton scattering in these theories and track the differences to the lack of universality of the vector-antisymmetric-tensor equivalence theorem which is specific only to Proca's framework, and valid for $g=1$, while it is violated within the covariant projector formalism. Our main result is that a finite Compton scattering differential cross section in the ultrarelativistic limit requires us to consider the contributions of both parities in $(1,0)\oplus(0,1)$. On that basis, we conclude that massive spin-$1$ bosons transforming as antisymmetric tensors are physical parity doublets.

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