arXiv subjects

Luka Leskovec

Publications and source records attributed to Luka Leskovec.

At least 19 recordsLinked to original sources

arXiv2026

Electromagnetic form factors and structure of the $T_{bb}$ tetraquark from lattice QCD

We present the first lattice QCD determination of the electromagnetic form factors of the exotic tetraquark $T_{bb} \ (bb \bar u \bar d)$ with quantum numbers $I( J^P ) = 0( 1^+ )$. The extracted form factors encode information about its internal structure, including the charge distribution and the magnetic dipole moments, determined separately for the light and heavy quarks. Our results provide evidence in favor of it being a bound state consisting of a compact heavy diquark $[bb]$ in a color-antitriplet with spin one, and a light antidiquark $[\bar u \bar d]$ in a color-triplet with spin zero. The charge radius of $T_{bb}$ is found to be significantly smaller than the combined charge radii of $B$ and $B^*$ mesons. These two comprise the lowest-lying threshold $BB^*$ in the channel we are considering, and their electric charge form factors are also determined. The computations were performed on a single CLS ensemble with $N_f = 2+1$ dynamical quarks and a lattice spacing of approximately $a \approx0.064 \ \mathrm{fm}$ at the pion mass $m_π\approx 290 \ \mathrm{MeV}$.

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arXiv2026

Electromagnetic form factors and structure of the $T_{bb}$ tetraquark

We present the first lattice QCD calculation of electromagnetic form factors of a tetraquark, focusing on the $T_{bb} = bb\bar u \bar d$ with quantum numbers $I(J^P) = 0(1^+)$. The electromagnetic current probes the charge monopole, magnetic dipole and the electric quadrupole distributions within the tetraquark. From it, we find evidence that its structure consists of a compact heavy diquark $[bb]$ in spin one, color-antitriplet configuration, and a light antidiquark $[\bar u \bar d]$ in spin zero, color-triplet configuration. The computations were performed on a single CLS ensemble with $N_f = 2+1$ dynamical quarks at a lattice spacing $a\approx 0.064$ fm and with a pion mass $m_π\approx 290$ MeV.

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arXiv2025

$B \to ρ\ell \barν$ resonance form factors from $B \to ππ\ell \barν$ in lattice QCD

The decay $B \to ρ\ell \barν$ is an attractive process for determining the magnitude of the smallest CKM matrix element, $|V_{ub}|$, and can provide new insights into the origin of the long-standing exclusive-inclusive discrepancy in determinations of this Standard-Model parameter. This requires a nonperturbative QCD calculation of the $B \to ρ$ form factors $V$, $A_0$, $A_1$, and $A_{12}$. The unstable nature of the $ρ$ resonance has prevented precise lattice QCD calculations of these form factors to date. Here, we present the first lattice QCD calculation of the $B \to ρ$ form factors in which the $ρ$ is treated properly as a resonance in $P$-wave $ππ$ scattering. To this end, we use the Lellouch-Lüscher finite-volume formalism to compute the $B \to ππ$ form factors as a function of both momentum transfer and $ππ$ invariant mass, and then analytically continue to the $ρ$ resonance pole. This calculation is performed with $2+1$ dynamical quark flavors at a pion mass of approximately 320 MeV, and demonstrates a clear path toward results at the physical point.

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arXiv2024

$T_{cc}^+$ via the plane wave approach and including diquark-antidiquark operators

The determination of the $DD^{*}$ scattering amplitude from lattice QCD is complicated by long-range interactions. In particular, the Lüscher method is no longer applicable in the kinematical region close to the left-hand cut. We tackle this problem by adopting plane-wave and effective-field-theoretic methods, which also address partial wave mixing. In addition, we incorporate a diquark-antidiquark interpolator in the operator basis (along with the relevant scattering operators) in order to achieve a better resolution of the energy spectrum. Results show that inclusion of it already has some impact at physical charm quark mass, although it is more significant for larger heavy quark masses, in line with expectations.

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arXiv2024

Lattice outlook on $B\toρ\ell\barν$ and $B\to K^\star \ell \ell$

Lattice Quantum Chromodynamics (QCD) has significantly contributed to our understanding of the CKM matrix through precise determinations of hadronic matrix elements. With advancements in theoretical methodologies and computational resources, investigations can now extend to processes involving QCD-unstable hadrons such as the $ρ$ and $K^\star(892)$. These resonances play vital roles in processes such as weak decays of $B$ mesons, opening new avenues for exploration. Finite-volume lattice QCD techniques involving complex computational methods are used to determine the transition amplitudes. Here, we present preliminary results for $B\toρ\ell\barν$.

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arXiv2024

Electroweak Transitions Involving Resonances

The increasing importance of hadronic resonances in our understanding of the Standard Model is underscored by recent advancements in lattice Quantum Chromodynamics (QCD) calculations. We review recent developments, with a particular emphasis on electroweak transitions that result in two-hadron final states. Additionally, we present the finite-volume lattice QCD methodologies that are pivotal in such studies in the context of preliminary results from the $B\to ππ\ell\barν$.

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arXiv2023

Doubly charmed tetraquark: isospin channels and diquark-antidiquark interpolators

We perform a lattice simulation to investigate the doubly charmed tetraquark $T^+_{cc}$ observed by the LHCb collaboration, slightly below the $D^{*+}D^0$ threshold, with flavor content $cc\bar{u}\bar{d}$ and isospin-$0$. Two-meson interpolators are implemented to explore the isospin quantum numbers $I=0$ and $I=1$. We observe attraction near the $DD^*$ threshold for $I=0$ and repulsion for $I=1$. Moreover, we also include diquark-antidiquark interpolators to study their effect on the energy spectrum. There is no significant shift in the ground state energy when adding diquark-antidiquark interpolators to the interpolator basis when the heavy quark mass is close to the physical charm quark mass. However, we observe a non-negligible shift in the second energy level. This effect has to be taken into account to extract the scattering amplitude of the $T^+_{cc}$. Finally, with a higher mass (close to the bottom quark), the ground state is shifted down significantly. The simulation is performed on $N_f=2+1$ CLS ensembles with $m_π\simeq 280$ MeV.

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arXiv2023

A lattice QCD study of the $B \to ππ\ell \barν$ transition

$V_{ub}$ is the smallest and least known of all CKM matrix elements; the community currently determines its magnitude primarily through the exclusive process $B\toπ\ell\barν$. Here we present our progress toward a lattice QCD determination of the $V_{ub}$ matrix element from a novel transition -- $B\toππ\ell\barν$ process, where the $ππ$ system is in a $P$ wave and scattering features the $ρ(770)$ resonance as an enhancement. We perform our calculation on $N_f=2+1$ isotropic clover fermions on a lattice of $L\approx 3.6$ fm and a pion mass of $\approx 320$ MeV; for the $b$-quark we use the anisotropic clover action. After a brief overview of the theoretical framework, we will discuss some preliminary results.

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arXiv2022

The $πγ\to ππ$ transition and the $ρ$ radiative decay width from lattice QCD

We report a lattice QCD determination of the $πγ\to ππ$ transition amplitude for the $P$-wave, $I=1$ two-pion final state, as a function of the photon virtuality and $ππ$ invariant mass. The calculation was performed with $2+1$ flavors of clover fermions at a pion mass of approximately $320$ MeV, on a $32^3 \times 96$ lattice with $L\approx 3.6$ fm. We construct the necessary correlation functions using a combination of smeared forward, sequential and stochastic propagators, and determine the finite-volume matrix elements for all $ππ$ momenta up to $|\vec{P}|= \sqrt{3} \frac{2π}{L}$ and all associated irreducible representations. In the mapping of the finite-volume to infinite-volume matrix elements using the Lellouch-Lüscher factor, we consider two different parametrizations of the $ππ$ scattering phase shift. We fit the $q^2$ and $s$ dependence of the infinite-volume transition amplitude in a model-independent way using series expansions, and compare multiple different truncations of this series. Through analytic continuation to the $ρ$ resonance pole, we also determine the $πγ\to ρ$ resonant transition form factor and the $ρ$ meson photocoupling, and obtain $|G_{ρπγ}| = 0.0802(32)(20)$.

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arXiv2021

Existence and Non-Existence of Doubly Heavy Tetraquark Bound States

In this work we investigate the existence of bound states for doubly heavy tetraquark systems $ \bar{Q}\bar{Q}'qq' $ in a full lattice-QCD computation, where heavy bottom quarks are treated in the framework of non-relativistic QCD. We focus on three systems with quark content $ \bar{b}\bar{b}ud $, $ \bar{b}\bar{b}us $ and $ \bar{b}\bar{c}ud $. We show evidence for the existence of $ \bar{b}\bar{b}ud $ and $ \bar{b}\bar{b}us $ bound states, while no binding appears to be present for $ \bar{b}\bar{c}ud $. For the bound four-quark states we also discuss the importance of various creation operators and give an estimate of the meson-meson and diquark-antidiquark percentages.

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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.

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arXiv2021

P-wave nucleon-pion scattering amplitude in the $Δ(1232)$ channel from lattice QCD

We determine the $Δ(1232)$ resonance parameters using lattice QCD and the Lüscher method. The resonance occurs in elastic pion-nucleon scattering with $J^P=3/2^+$ in the isospin $I = 3/2$, $P$-wave channel. Our calculation is performed with $N_f=2+1$ flavors of clover fermions on a lattice with $L\approx 2.8$ fm. The pion and nucleon masses are $m_π=255.4(1.6)$ MeV and $m_N=1073(5)$ MeV, and the strong decay channel $Δ\rightarrow πN$ is found to be above the threshold. To thoroughly map out the energy-dependence of the nucleon-pion scattering amplitude, we compute the spectra in all relevant irreducible representations of the lattice symmetry groups for total momenta up to $\vec{P}=\frac{2π}{L}(1,1,1)$, including irreps that mix $S$ and $P$ waves. We perform global fits of the amplitude parameters to up to 21 energy levels, using a Breit-Wigner model for the $P$-wave phase shift and the effective-range expansion for the $S$-wave phase shift. From the location of the pole in the $P$-wave scattering amplitude, we obtain the resonance mass $m_Δ=1378(7)(9)$ MeV and the coupling $g_{Δ\text{-}πN}=23.8(2.7)(0.9)$.

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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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arXiv2020

Investigation of Doubly Heavy Tetraquark Systems using Lattice QCD

We search for possibly existent bound states in the heavy-light tetraquark channels with quark content $ \bar{b}\bar{b}ud $, $ \bar{b}\bar{b}us $ and $ \bar{b}\bar{c}ud $ using lattice QCD. We carry out calculations on several gauge link ensembles with $ N_f=2+1 $ flavours of domain-wall fermions and consider a basis of local and non-local interpolators. Besides extracting the energy spectrum from the correlation matrices, we also perform a Lüscher analysis to extrapolate our results to infinite volume.

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arXiv2019

Lattice QCD investigation of a doubly-bottom $\bar{b} \bar{b} u d$ tetraquark with quantum numbers $I(J^P) = 0(1^+)$

We use lattice QCD to investigate the spectrum of the $\bar{b} \bar{b} u d$ four-quark system with quantum numbers $I(J^P) = 0(1^+)$. We use five different gauge-link ensembles with $2+1$ flavors of domain-wall fermions, including one at the physical pion mass, and treat the heavy $\bar{b}$ quark within the framework of lattice nonrelativistic QCD. Our work improves upon previous similar computations by considering in addition to local four-quark interpolators also nonlocal two-meson interpolators and by performing a Lüscher analysis to extrapolate our results to infinite volume. We obtain a binding energy of $(-128 \pm 24 \pm 10) \, \textrm{MeV}$, corresponding to the mass $(10476 \pm 24 \pm 10) \, \textrm{MeV}$, which confirms the existence of a $\bar{b} \bar{b} u d$ tetraquark that is stable with respect to the strong and electromagnetic interactions.

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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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