arXiv subjects

Gumaro Rendon

Publications and source records attributed to Gumaro Rendon.

27 records · Page 2Linked to original sources

arXiv2021

$Λ_b \to Λ^*(1520)\ell^+\ell^-$ form factors from lattice QCD

We present the first lattice QCD determination of the $Λ_b \to Λ^*(1520)$ vector, axial vector, and tensor form factors that are relevant for the rare decays $Λ_b \to Λ^*(1520)\ell^+\ell^-$. The lattice calculation is performed in the $Λ^*(1520)$ rest frame with nonzero $Λ_b$ momenta, and is limited to the high-$q^2$ region. An interpolating field with covariant derivatives is used to obtain good overlap with the $Λ^*(1520)$. The analysis treats the $Λ^*(1520)$ as a stable particle, which is expected to be a reasonable approximation for this narrow resonance. A domain-wall action is used for the light and strange quarks, while the $b$ quark is implemented with an anisotropic clover action with coefficients tuned to produce the correct $B_s$ kinetic mass, rest mass, and hyperfine splitting. We use three different ensembles of lattice gauge-field configurations generated by the RBC and UKQCD collaborations, and perform extrapolations of the form factors to the continuum limit and physical pion mass. We give Standard-Model predictions for the $Λ_b \to Λ^*(1520)\ell^+\ell^-$ differential branching fraction and angular observables in the high-$q^2$ region.

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arXiv2021

$I=1/2$ $S$-wave and $P$-wave $Kπ$ scattering and the $κ$ and $K^*$ resonances from lattice QCD

We present a lattice-QCD determination of the elastic isospin-$1/2$ $S$-wave and $P$-wave $Kπ$ scattering amplitudes as a function of the center-of-mass energy using Lüscher's method. We perform global fits of $K$-matrix parametrizations to the finite-volume energy spectra for all irreducible representations with total momenta up to $\sqrt{3}\frac{2π}{L}$; this includes irreps that mix the $S$- and $P$-waves. Several different parametrizations for the energy dependence of the $K$-matrix are considered. We also determine the positions of the nearest poles in the scattering amplitudes, which correspond to the broad $κ$ resonance in the $S$-wave and the narrow $K^*(892)$ resonance in the $P$-wave. Our calculations are performed with $2+1$ dynamical clover fermions for two different pion masses of $317.2(2.2)$ and $175.9(1.8)$ MeV. Our preferred $S$-wave parametrization is based on a conformal map and includes an Adler zero; for the $P$-wave we use a standard pole parametrization including Blatt-Weisskopf barrier factors. The $S$-wave $κ$-resonance pole positions are found to be $\left[0.86(12) - 0.309(50)\,i\right]\:{\rm GeV}$ at the heavier pion mass and $\left[0.499(55)- 0.379(66)\,i\right]\:{\rm GeV}$ at the lighter pion mass. The $P$-wave $K^*$-resonance pole positions are found to be $\left[ 0.8951(64) - 0.00250(21)\,i \right]\:{\rm GeV}$ at the heavier pion mass and $\left[0.8718(82) - 0.0130(11)\,i\right]\:{\rm GeV}$ at the lighter pion mass, which corresponds to couplings of $g_{K^* Kπ}=5.02(26)$ and $g_{K^* Kπ}=4.99(22)$, respectively.

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arXiv2019

$K π$ scattering and the $K^*(892)$ resonance in 2+1 flavor QCD

In this project, we will compute the form factors relevant for $B \to K^*(\to K π)\ell^+\ell^-$ decays. To map the finite-volume matrix elements computed on the lattice to the infinite-volume $B \to K π$ matrix elements, the $K π$ scattering amplitude needs to be determined using Lüscher's method. Here we present preliminary results from our calculations with $2+1$ flavors of dynamical clover fermions. We extract the $P$-wave scattering phase shifts and determine the $K^*$ resonance mass and the $K^* K π$ coupling for two different ensembles with pion masses of $317(2)$ and $178(2)$ MeV.

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arXiv2018

Towards the P-wave nucleon-pion scattering amplitude in the $Δ(1232)$ channel

We use lattice QCD and the Lüscher method to study elastic pion-nucleon scattering in the isospin $I = 3/2$ channel, which couples to the $Δ(1232)$ resonance. Our $N_f=2+1$ flavor lattice setup features a pion mass of $m_π\approx 250$ MeV, such that the strong decay channel $Δ\rightarrow πN$ is close to the threshold. We present our method for constructing the required lattice correlation functions from single- and two-hadron interpolating fields and their projection to irreducible representations of the relevant symmetry group of the lattice. We show preliminary results for the energy spectra in selected moving frames and irreducible representations, and extract the scattering phase shifts. Using a Breit-Wigner fit, we also determine the resonance mass $m_Δ$ and the $g_{Δ-πN}$ coupling.

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arXiv2018

Calculating the $ρ$ radiative decay width with lattice QCD

We present the results of our lattice QCD study of the $πγ\toππ$ process, where the $ρ$ resonance appears as an enhancement in the transition amplitude. We use $N_f=2+1$ clover fermions on a lattice of $L=3.6$ fm and a pion mass of $320$ MeV. Using a combination of forward, stochastic, and sequential propagators, we calculate the two-point and three-point functions that allow us to determine the $πγ\toππ$ matrix elements for several values of the invariant mass $s$ and momentum transfer $q^2$. To fit the $q^2$ and $s$ dependence of the $πγ\toππ$ amplitude, we explore a set of general parametrizations based on a Taylor expansion. By analytic continuation to the complex pole corresponding to the $ρ$ resonance, we determine the resonant form factors and calculate the radiative decay width of the $ρ$.

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arXiv2018

A Lattice QCD study of the $ρ$ resonance

We present a lattice QCD study of the $ρ$ resonance with $N_f=2+1$ clover fermions at a pion mass of approximately $320$ MeV and lattice size $3.6$ fm. We consider two processes involving the $ρ$. The first process is elastic scattering of two pions in P-wave with isospin $1$. Using the Lüscher method we determine the scattering phase shift, from which we obtain the $ρ$ resonance mass and decay width $Γ(ρ\toππ)$. The second process is the radiative transition $πγ\toππ$, where we follow the Briceño-Hansen-Walker-Loud approach to determine the transition amplitude in the invariant mass region near the $ρ$ resonance and for both space- and time-like photon momentum. This allows us to determine the coupling between the $ρ$, the pion and the photon, and the resulting $ρ$ radiative decay width.

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arXiv2017

$P$-wave $ππ$ scattering and the $ρ$ resonance from lattice QCD

We calculate the parameters describing elastic $I=1$, $P$-wave $ππ$ scattering using lattice QCD with $2+1$ flavors of clover fermions. Our calculation is performed with a pion mass of $m_π\approx 320\:\:{\rm MeV}$ and a lattice size of $L\approx 3.6$ fm. We construct the two-point correlation matrices with both quark-antiquark and two-hadron interpolating fields using a combination of smeared forward, sequential and stochastic propagators. The spectra in all relevant irreducible representations for total momenta $|\vec{P}| \leq \sqrt{3} \frac{2π}{L}$ are extracted with two alternative methods: a variational analysis as well as multi-exponential matrix fits. We perform an analysis using Lüscher's formalism for the energies below the inelastic thresholds, and investigate several phase shift models, including possible nonresonant contributions. We find that our data are well described by the minimal Breit-Wigner form, with no statistically significant nonresonant component. In determining the $ρ$ resonance mass and coupling we compare two different approaches: fitting the individually extracted phase shifts versus fitting the $t$-matrix model directly to the energy spectrum. We find that both methods give consistent results, and at a pion mass of $am_π=0.18295(36)_{stat}$ obtain $g_{ρππ} = 5.69(13)_{stat}(16)_{sys}$, $am_ρ= 0.4609(16)_{stat}(14)_{sys}$, and $am_ρ/am_{N} = 0.7476(38)_{stat}(23)_{sys} $, where the first uncertainty is statistical and the second is the systematic uncertainty due to the choice of fit ranges.

hep-lat↗

arXiv2017

Lattice QCD calculation of form factors for $Λ_b \to Λ(1520) \ell^+ \ell^-$ decays

Experimental results for mesonic $b \to s μ^+ μ^-$ decays show a pattern of deviations from Standard-Model predictions, which could be due to new fundamental physics or due to an insufficient understanding of hadronic effects. Additional information on the $b \to s μ^+ μ^-$ transition can be obtained from $Λ_b$ decays. This was recently done using the process $Λ_b \to Λμ^+ μ^-$, where the $Λ$ is the lightest strange baryon. A further interesting channel is $Λ_b \to p^+ K^- μ^+ μ^-$, where the $p^+ K^-$ final state receives contributions from multiple higher-mass $Λ$ resonances. The narrowest and most prominent of these is the $Λ(1520)$, which has $J^P=\frac32^-$. Here we present an ongoing lattice QCD calculation of the relevant $Λ_b \to Λ(1520)$ form factors. We discuss the choice of interpolating field for the $Λ(1520)$, and explain our method for extracting the fourteen $Λ_b \to Λ(1520)$ helicity form factors from correlation functions that are computed in the $Λ(1520)$ rest frame. We present preliminary numerical results at a pion mass of 340 MeV and a lattice spacing of 0.11 fm. This calculation uses a domain-wall action for the $u$, $d$, and $s$ quarks and a relativistic heavy-quark action for the $b$ quark, and is based on gauge-field configurations generated by the RBC and UKQCD Collaborations.

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arXiv2016

A study of the radiative transition $ππ\to πγ^{*}$ with lattice QCD

Lattice QCD calculations of radiative transitions between hadrons have in the past been limited to processes of hadrons stable under the strong interaction. Recently developed methods for $1\to2$ transition matrix elements in a finite volume now enable the determination of radiative decay rates of strongly unstable particles. Our lattice QCD study focuses on the process $ππ\to πγ^{*}$, where the $ρ$ meson is present as an enhancement in the cross-section. We use $2+1$ flavors of clover fermions at a pion mass of approximately $320$ MeV and a lattice size of approximately $3.6$ fm. The required $2$-point and $3$-point correlation functions are constructed from a set of forward, sequential and stochastic light quark propagators. In addition to determining the $ρ$ meson resonance parameters via the Lüscher method, the scattering phase shift is used in conjunction with the $1\to2$ transition matrix element formalism of Briceño, Hansen and Walker-Loud to compute the $ππ\toπγ^{*}$ amplitude at several values of the momentum transfer and $ππ$ invariant mass.

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