arXiv subjects

Raul A. Briceno

Publications and source records attributed to Raul A. Briceno.

18 recordsLinked to original sources

arXiv2021

Constraining $1+\mathcal{J}\to 2$ coupled-channel amplitudes in finite-volume

Whether one is interested in accessing the excited spectrum of hadrons or testing the standard model of particle physics, electroweak transition processes involving multi-hadron channels in the final state play an important role in a variety of experiments. Presently the primary theoretical tool with which one can study such reactions is lattice QCD, which is defined in a finite spacetime volume. In this work, we investigate the feasibility of implementing existing finite-volume formalism in realistic lattice QCD calculation of reactions in which a stable hadron can transition to one of several two-hadron channels under the action of an external current. We provide a conceptual description of the coupled-channel transition formalism, a practical roadmap for carrying out a calculation, and an illustration of the approach using synthetic data for two non-trivial resonant toy models. The results provide a proof-of-principle that such reactions can indeed be constrained using modern-day lattice QCD calculations, motivating explicit computation in the near future.

hep-lat↗

arXiv2019

The quark-mass dependence of elastic $πK$ scattering from QCD

We present a determination of the isospin-1/2 elastic $πK$ scattering amplitudes in S and P partial waves using lattice Quantum Chromodynamics. The amplitudes, constrained for a large number of real-valued energy points, are obtained as a function of light-quark mass, corresponding to four pion masses between 200 and 400 MeV. Below the first inelastic threshold, the P-wave scattering amplitude is dominated by a single pole singularity that evolves from being a stable bound-state at the highest quark mass into a narrow resonance that broadens as the pion and kaon masses are reduced. As in experiment, the S-wave amplitude does not exhibit an obviously resonant behavior, but instead shows a slow rise from threshold, which is not inconsistent with the presence of a $κ$/$K_0^\star(700)$-like resonance at the considered quark masses. As has been found in analyses of experimental scattering data, simple analytic continuations into the complex energy plane of precisely-determined lattice QCD amplitudes on the real energy axis are not sufficient to model-independently determine the existence and properties of this state. The spectra and amplitudes we present will serve as an input for increasingly elaborate amplitude analysis techniques that implement more of the analytic structure expected at complex energies.

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arXiv2017

Isoscalar $ππ, K\overline{K}, ηη$ scattering and the $σ, f_0, f_2$ mesons from QCD

We present the first lattice QCD study of coupled isoscalar $ππ,K\overline{K},ηη$ $S$- and $D$-wave scattering extracted from discrete finite-volume spectra computed on lattices which have a value of the quark mass corresponding to $m_π\sim391$ MeV. In the $J^P=0^+$ sector we find analogues of the experimental $σ$ and $f_0(980)$ states, where the $σ$ appears as a stable bound-state below $ππ$ threshold, and, similar to what is seen in experiment, the $f_0(980)$ manifests itself as a dip in the $ππ$ cross section in the vicinity of the $K\overline{K}$ threshold. For $J^P=2^+$ we find two states resembling the $f_2(1270)$ and $f_2'(1525)$, observed as narrow peaks, with the lighter state dominantly decaying to $ππ$ and the heavier state to $K\overline{K}$. The presence of all these states is determined rigorously by finding the pole singularity content of scattering amplitudes, and their couplings to decay channels are established using the residues of the poles.

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arXiv2017

Scattering processes and resonances from lattice QCD

The vast majority of hadrons observed in nature are not stable under the strong interaction, rather they are resonances whose existence is deduced from enhancements in the energy dependence of scattering amplitudes. The study of hadron resonances offers a window into the workings of quantum chromodynamics (QCD) in the low-energy non-perturbative region, and in addition, many probes of the limits of the electroweak sector of the Standard Model consider processes which feature hadron resonances. From a theoretical standpoint, this is a challenging field: the same dynamics that binds quarks and gluons into hadron resonances also controls their decay into lighter hadrons, so a complete approach to QCD is required. Presently, lattice QCD is the only available tool that provides the required non-perturbative evaluation of hadron observables. In this article, we review progress in the study of few-hadron reactions in which resonances and bound-states appear using lattice QCD techniques. We describe the leading approach which takes advantage of the periodic finite spatial volume used in lattice QCD calculations to extract scattering amplitudes from the discrete spectrum of QCD eigenstates in a box. We explain how from explicit lattice QCD calculations, one can rigorously garner information about a variety of resonance properties, including their masses, widths, decay couplings, and form factors. The challenges which currently limit the field are discussed along with the steps being taken to resolve them.

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arXiv2016

Progress on the three-particle quantization condition

We report progress on extending the relativistic model-independent quantization condition for three particles, derived previously by two of us, to a broader class of theories, as well as progress on checking the formalism. In particular, we discuss the extension to include the possibility of 2->3 and 3->2 transitions and the calculation of the finite-volume energy shift of an Efimov-like three-particle bound state. The latter agrees with the results obtained previously using non-relativistic quantum mechanics.

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arXiv2016

Isoscalar $ππ$ scattering and the $σ$ meson resonance from QCD

We present for the first time a determination of the energy dependence of the isoscalar $ππ$ elastic scattering phase-shift within a first-principles numerical lattice approach to QCD. Hadronic correlation functions are computed including all required quark propagation diagrams, and from these the discrete spectrum of states in the finite volume defined by the lattice boundary is extracted. From the volume dependence of the spectrum we obtain the $S$-wave phase-shift up to the $K\overline{K}$ threshold. Calculations are performed at two values of the $u,d$ quark mass corresponding to $m_π= 236, 391$ MeV and the resulting amplitudes are described in terms of a $σ$ meson which evolves from a bound-state below $ππ$ threshold at the heavier quark mass, to a broad resonance at the lighter quark mass.

hep-ph↗

arXiv2016

Connecting physical resonant amplitudes and lattice QCD

We present a determination of the isovector, $P$-wave $ππ$ scattering phase shift obtained by extrapolating recent lattice QCD results from the Hadron Spectrum Collaboration using $m_π=236$ MeV. The finite volume spectra are described using extensions of Lüscher's method to determine the infinite volume Unitarized Chiral Perturbation Theory scattering amplitude. We exploit the pion mass dependence of this effective theory to obtain the scattering amplitude at $m_π= 140$ MeV. The scattering phase shift is found to be in good agreement with experiment up to center of mass energies of 1.2 GeV. The analytic continuation of the scattering amplitude to the complex plane yields a $ρ$-resonance pole at $E_ρ= \left[755(2)(1)(^{20}_{02})-\frac{i}{2}\,129(3)(1)(^{7}_{1})\right]~{\rm MeV}$. The techniques presented illustrate a possible pathway towards connecting lattice QCD observables of few-body, strongly interacting systems to experimentally accessible quantities.

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arXiv2015

The resonant $π^+γ\toπ^+π^0$ amplitude from Quantum Chromodynamics

We present the first ab initio calculation of a radiative transition of a hadronic resonance within quantum chromodynamics (QCD). We compute the amplitude for $ππ\to πγ^\star$, as a function of the energy of the $ππ$ pair and the virtuality of the photon, in the kinematic regime where $ππ$ couples strongly to the unstable $ρ$ resonance. This exploratory calculation is performed using a lattice discretization of QCD with quark masses corresponding to $m_π\approx 400$~MeV. We obtain a description of the energy dependence of the transition amplitude, constrained at 48 kinematic points, that we can analytically continue to the $ρ$ pole and identify from its residue the $ρ\to πγ^\star$ form factor.

hep-ph↗

arXiv2015

Coupled $ππ, K\overline{K}$ scattering in $P$-wave and the $ρ$ resonance from lattice QCD

We determine elastic and coupled-channel amplitudes for isospin-1 meson-meson scattering in $P$-wave, by calculating correlation functions using lattice QCD with light quark masses such that $m_π= 236$ MeV in a cubic volume of $\sim (4 \,\mathrm{fm})^3$. Variational analyses of large matrices of correlation functions computed using operator constructions resembling $ππ$, $K\overline{K}$ and $q\bar{q}$, in several moving frames and several lattice irreducible representations, leads to discrete energy spectra from which scattering amplitudes are extracted. In the elastic $ππ$ scattering region we obtain a detailed energy-dependence for the phase-shift, corresponding to a $ρ$ resonance, and we extend the analysis into the coupled-channel $K\overline{K}$ region for the first time, finding a small coupling between the channels.

hep-ph↗

arXiv2015

Two-particle multichannel systems in a finite volume with arbitrary spin

The quantization condition for two-particle systems with arbitrary number of two-body open coupled channels, spin, momentum, and masses in a finite volume with either periodic or twisted boundary conditions is presented. Although emphasis is placed in cubic volumes, the result holds for asymmetric volumes. The result is relativistic, holds for all momenta below the three- and four-particle thresholds, and is exact up to exponential volume corrections that are governed by L/r, where L is the spatial extent of the volume and r is the range of the interactions between the particles. For hadronic systems the range of the interaction is set by the inverse of the pion mass, m_pi, and as a result the formalism presented is suitable for m_pi L >> 1. The condition presented is in agreement with all previous studies of two-body systems in a finite volume. Implications of the formalism for the studies of multichannel baryon-baryon systems are discussed.

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arXiv2013

On the Determination of Elastic and Inelastic Nuclear Observables from Lattice QCD

One of the overarching goals of nuclear physics is to rigorously compute properties of hadronic systems directly from the fundamental theory of the strong interaction, Quantum Chromodynamics (QCD). Currently, lattice QCD (LQCD) provides the only reliable option for performing calculations of low-energy hadronic observables. LQCD calculations are necessarily performed in a finite Euclidean spacetime. As a result, it is necessary to construct formalism that maps the finite-volume observables determined via LQCD to the infinite-volume quantities of interest. This methodology is commonly referred to as the Luscher method, as it was Martin Luscher who first developed such formalism for scalar bosons with zero total momentum below inelastic thresholds. In this work, we review recent progress on the generalization of this formalism. We present a detailed derivation of the extension of Luscher's seminal work for multi-channel two-body scalar systems, two-nucleon non-relativistic systems, and three-body non-relativistic scalar systems. For all of these scenarios we allow for the total momenta of the systems of interest to be nonzero. We also present steps towards being able to study weak processes involving two-nucleon systems, in particular we show how to determine the transition amplitude for proton-proton fusion (pp->e^+ + nu_e) directly from LQCD.

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arXiv2013

Two-Baryon Systems with Twisted Boundary Conditions

We explore the use of twisted boundary conditions in extracting the nucleon mass and the binding energy of two-baryon systems, such as the deuteron, from Lattice QCD calculations. Averaging the results of calculations performed with periodic and anti-periodic boundary conditions imposed upon the light-quark fields, or other pair-wise averages, improves the volume dependence of the deuteron binding energy from ~exp(-kappa*L)/L to ~exp(-sqrt(2)kappa*L)/L. However, a twist angle of pi/2 in each of the spatial directions improves the volume dependence from ~exp(-kappa*L)/L to ~exp(-2kappa*L)/L. Twist averaging the binding energy with a random sampling of twist angles improves the volume dependence from ~exp^(-kappa*L)/L to ~exp(-2kappa*L)/L, but with a standard deviation of ~exp(-kappa*L)/L, introducing a signal-to-noise issue in modest lattice volumes. Using the experimentally determined phase shifts and mixing angles, we determine the expected energies of the deuteron states over a range of cubic lattice volumes for a selection of twisted boundary conditions.

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arXiv2013

Moving Multi-Channel Systems in a Finite Volume with Application to Proton-Proton Fusion

The spectrum of a system with multiple channels composed of two hadrons with nonzero total momentum is determined in a finite cubic volume with periodic boundary conditions using effective field theory methods. The results presented are accurate up to exponentially suppressed corrections in the volume due to the finite range of hadronic interactions. The formalism allows one to determine the phase shifts and mixing parameters of pipi-KK isosinglet coupled channels directly from Lattice Quantum Chromodynamics. We show that the extension to more than two channels is straightforward and present the result for three channels. From the energy quantization condition, the volume dependence of electroweak matrix elements of two-hadron processes is extracted. In the non-relativistic case, we pay close attention to processes that mix the 1S0-3S1 two-nucleon states, e.g. proton-proton fusion (pp -> d+ e^+ + nu_e), and show how to determine the transition amplitude of such processes directly from lattice QCD.

hep-lat↗

arXiv2013

Two-Nucleon Systems in a Finite Volume

I present the formalism and methodology for determining the nucleon-nucleon scattering parameters from the finite volume spectra obtained from lattice quantum chromodynamics calculations. Using the recently derived energy quantization conditions and the experimentally determined scattering parameters, the bound state spectra for finite volume systems with overlap with the 3S1-3D3 channel are predicted for a range of volumes. It is shown that the extractions of the infinite-volume deuteron binding energy and the low-energy scattering parameters, including the S-D mixing angle, are possible from Lattice QCD calculations of two-nucleon systems with boosts of |P| <= 2pi sqrt{3}/L in volumes with spatial extents L satisfying fm <~ L <~ 14 fm.

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arXiv2013

Two-Nucleon Systems in a Finite Volume: (II) 3S1-3D1 Coupled Channels and the Deuteron

The energy spectra of two nucleons in a cubic volume provide access to the two phase shifts and one mixing angle that define the S-matrix in the 3S1-3D1 coupled channels containing the deuteron. With the aid of recently derived energy quantization conditions for such systems, and the known scattering parameters, these spectra are predicted for a range of volumes. It is found that extractions of the infinite-volume deuteron binding energy and leading scattering parameters, including the S-D mixing angle at the deuteron pole, are possible from Lattice QCD calculations of two-nucleon systems with boosts of |P| <= 2pi sqrt{3}/L in volumes with 10 fm <~ L <~ 14 fm. The viability of extracting the asymptotic D/S ratio of the deuteron wavefunction from Lattice QCD calculations is discussed.

hep-lat↗

arXiv2013

Two-Nucleon Systems in a Finite Volume: (I) Quantization Conditions

The quantization condition for interacting energy eigenvalues of the two-nucleon system in a finite cubic volume is derived in connection to the nucleon-nucleon scattering amplitudes. This condition is derived using an auxiliary (dimer) field formalism that is generalized to arbitrary partial waves in the context of non-relativistic effective field theory. The quantization condition presented gives access to the scattering parameters of the two-nucleon systems with arbitrary parity, spin, isospin, angular momentum and center of mass motion, from a lattice QCD calculation of the energy eigenvalues. In particular, as it includes all non-central interactions, such as the two-nucleon tensor force, it makes explicit the dependence of the mixing parameters of nucleon-nucleon systems calculated from lattice QCD when there is a physical mixing among different partial-waves, e. g. S-D mixing in the deuteron channel. We provide explicit relations among scattering parameters and their corresponding point group symmetry class eigenenergies with orbital angular momentum l smaller than or equal to 3, and for center of mass boost vectors of the form 2π(2n_1, 2n_2, 2n_3)/L, 2π(2n_1, 2n_2, 2n_3+1)/L and 2π(2n_1+1, 2n_2+1, 2n_3)/L. L denotes the special extent of the cubic volume and n_1,n_2,n_3 are integers. Our results are valid below inelastic thresholds up to exponential volume corrections that are governed by the pion mass.

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arXiv2012

Three-particle scattering amplitudes from a finite volume formalism

We present a quantization condition for the spectrum of a system composed of three identical bosons in a finite volume with periodic boundary conditions. This condition gives a relation between the finite volume spectrum and infinite volume scattering amplitudes. The quantization condition presented is an integral equation that in general must be solved numerically. However, for systems with an attractive two-body force that supports a two-body bound-state, a diboson, and for energies below the diboson breakup, the quantization condition reduces to the well-known Luscher formula with exponential corrections in volume that scale with the diboson binding momentum. To accurately determine infinite volume phase shifts, it is necessary to extrapolate the phase shifts obtained from the Luscher formula for the boson-diboson system to the infinite volume limit. For energies above the breakup threshold, or for systems with no two-body bound-state (with only scattering states and resonances) the Luscher formula gets power-law volume corrections and consequently fails to describe the three-particle system. These corrections are nonperturbatively included in the quantization condition presented.

hep-lat↗

arXiv2012

Charmed-Baryon Spectroscopy from Lattice QCD with N_f=2+1+1 Flavors

We present the results of a calculation of the positive-parity ground-state charmed-baryon spectrum using 2+1+1 flavors of dynamical quarks. The calculation uses a relativistic heavy-quark action for the valence charm quark, clover-Wilson fermions for the valence light and strange quarks, and HISQ sea quarks. The spectrum is calculated with a lightest pion mass around 220 MeV, and three lattice spacings (a \approx 0.12 fm, 0.09 fm, and 0.06 fm) are used to extrapolate to the continuum. The light-quark mass extrapolation is performed using heavy-hadron chiral perturbation theory up to O(m_pi^3) and at next-to-leading order in the heavy-quark mass. For the well-measured charmed baryons, our results show consistency with the experimental values. For the controversial J=1/2 Xi_{cc}, we obtain the isospin-averaged value M_{Xi_{cc}}=3595(39)(20)(6) MeV (the three uncertainties are statistics, fitting-window systematic, and systematics from other lattice artifacts, such as lattice scale setting and pion-mass determination), which shows a 1.7 sigma deviation from the experimental value. We predict the yet-to-be-discovered doubly and triply charmed baryons Xi_{cc}^*, Omega_{cc}, Omega_{cc}^* and Omega_{ccc} to have masses 3648(42)(18)(7) MeV, 3679(40)(17)(5) MeV, 3765(43)(17)(5) MeV and 4761(52)(21)(6) MeV, respectively.

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