Lattice QCD Study Research Articles

The negative-parity spin-1/2 Λ baryon spectrum from lattice QCD and effective theory

The spectrum of the negative-parity spin-1/2 Λ baryons is studied using lattice QCD and hadronic effective theory in a unitarized coupled-channel framework. A direct comparison between the two approaches is possible by considering the hadronic effective theory in a finite volume and with hadron masses and mesonic decay constants that correspond to the situation studied on the lattice. Comparing the energy level spectrum and SU(3) flavor decompositions of the individual states, it is found that the lowest two states extracted from lattice QCD can be associated with one of the two Λ(1405)-poles and the Λ(1670) resonance. The quark mass dependences of these two lattice QCD levels are in good agreement with their effective theory counterparts. However, as current lattice QCD studies still rely on three-quark operators to generate the physical states, clear signals corresponding to the meson-baryon scattering states, that appear in the finite volume effective theory calculation, are not yet seen.

Bethe-Salpeter amplitudes of Upsilons

Based on lattice non-relativistic QCD (NRQCD) studies we present results for Bethe-Salpeter amplitudes for $\Upsilon(1S)$, $\Upsilon(2S)$ and $\Upsilon(3S)$ in vacuum as well as in quark-gluon plasma. Our study is based on 2+1 flavor $48^3 \times 12$ lattices generated using the Highly Improved Staggered Quark (HISQ) action and with a pion mass of $161$ MeV. At zero temperature the Bethe-Salpeter amplitudes follow the expectations based on non-relativistic potential models. At non-zero temperatures, the interpretation of Bethe-Salpeter amplitudes turns out to be more nuanced, but consistent with our previous lattice QCD study of excited Upsilons in quark-gluon plasma.

Quarkonium production and suppression: Theory

Heavy quarkonium theory has seen significant progress over the past years. Not only has the community steadily improved the understanding of fully equilibrated quarkonium using first principles lattice QCD studies, but it has taken major steps towards developing a genuine dynamical understanding of quark-antiquark pairs immersed in a hot medium by embracing the paradigm of open quantum systems. We review recent developments, placing an emphasis on quarkonium real-time dynamics.

Lattice QCD Calculations of Transverse-Momentum-Dependent Soft Function through Large-Momentum Effective Theory.

The transverse-momentum-dependent (TMD) soft function is a key ingredient in QCD factorization of Drell-Yan and other processes with relatively small transverse momentum. We present a lattice QCD study of this function at moderately large rapidity on a 2+1 flavor CLS dynamic ensemble with a=0.098 fm. We extract the rapidity-independent (or intrinsic) part of the soft function through a large-momentum-transfer pseudoscalar meson form factor and its quasi-TMD wave function using leading-order factorization in large-momentum effective theory. We also investigate the rapidity-dependent part of the soft function-the Collins-Soper evolution kernel-based on the large-momentum evolution of the quasi-TMD wave function.

Diabatic description of charmoniumlike mesons

We apply the diabatic formalism, first introduced in molecular physics, to the description of heavy-quark mesons. In this formalism the dynamics is completely described by a diabatic potential matrix whose elements can be derived from unquenched lattice QCD studies of string breaking. For energies far below the lowest open flavor meson-meson threshold, the resulting diabatic approach reduces to the well-known Born-Oppenheimer approximation where heavy-quark meson masses correspond to energy levels in an effective quark-antiquark potential. For energies close below or above that threshold, where the Born-Oppenheimer approximation fails, this approach provides a set of coupled Schr\"{o}dinger equations incorporating meson-meson components nonperturbatively, i.e. beyond loop corrections. A spectral study of heavy mesons containing $c\overline{c}$ with masses below $4.1$ GeV is carried out within this framework. From it a unified description of conventional as well as unconventional resonances comes out.

Kaonic hydrogen and deuterium in Hamiltonian effective field theory

The anti-kaon nucleon scattering lengths resulting from a Hamiltonian effective field theory analysis of experimental data and lattice QCD studies are presented. The same Hamiltonian is then used to compute the scattering length for the K−d system, taking careful account of the effects of recoil on the energy at which the K¯N T-matrices are evaluated. These results are then used to estimate the shift and width of the 1S levels of anti-kaonic hydrogen and deuterium. The K−p result is in excellent agreement with the SIDDHARTA measurement. In the K−d case the imaginary part of the scattering length and consequently the width of the 1S state are considerably larger than found in earlier work. This is a consequence of the effect of recoil on the energy of the K¯N energy, which enhances the role of the Λ(1405) resonance.

Influence of hadronic resonances on the chemical freeze-out in heavy-ion collisions

Detailed knowledge of the hadronic spectrum is still an open question, which has phenomenological consequences on the study of heavy-ion collisions. A previous lattice QCD study concluded that additional strange resonances are missing in the currently tabulated lists provided by the Particle Data Group (PDG). That study identified the list labeled PDG2016+ as the ideal spectrum to be used as an input in thermal-model-based analyses. In this work, we determine the effect of additional resonances on the freeze-out parameters of systems created in heavy-ion collisions. These parameters are obtained from thermal fits of particle yields and net-particle fluctuations. For a complete picture, we compare several hadron lists including both experimentally discovered and theoretically predicted states. We find that the inclusion of additional resonances mildly influences the extracted parameters -- with a general trend of progressively lowering the temperature -- but is not sufficient to close the gap in temperature between light and strange hadrons previously observed in the literature.

Zb tetraquark channel from lattice QCD and Born-Oppenheimer approximation

Two Zb hadrons with exotic quark structure b¯bd¯u were discovered by Belle experiment. We present a lattice QCD study of the b¯bd¯u system in the approximation of static b quarks, where the total spin of heavy quarks is fixed to one. The energies of eigenstates are determined as a function of the separation r between b and b¯. The lower eigenstates are related to a bottomonium and a pion. The eigenstate dominated by BB¯⁎ has energy significantly below mB+mB⁎, which points to a sizable attraction for small r. The attractive potential V(r) between B and B¯⁎ is extracted assuming that this eigenstate is related exclusively to BB¯⁎. The Schrödinger equation for BB¯⁎ within the extracted potential leads to one bound state below BB¯⁎ threshold, whose mass depends on the parametrization of the lattice potential. For certain parametrizations, the bound state is very close to the BB¯⁎ threshold and renders a narrow peak in the BB¯⁎ rate above threshold - these features could be related to Zb(10610) in the experiment.

Unpolarized isovector quark distribution function from lattice QCD: A systematic analysis of renormalization and matching

We present a detailed Lattice QCD study of the unpolarized isovector quark Parton Distribution Function (PDF) using large-momentum effective theory framework. We choose a quasi-PDF defined by a spatial correlator which is free from mixing with other operators of the same dimension. In the lattice simulation, we use a Gaussian-momentum-smeared source at $M_\pi=356$ MeV and $P_z \in \{1.8,2.3\}$ GeV. To control the systematics associated with the excited states, we explore {five different source-sink separations}. The nonperturbative renormalization is conducted in a regularization-independent momentum subtraction scheme, and the matching between the renormalized quasi-PDF and $\bar{\rm MS}$ PDF is calculated based on perturbative QCD up to one-loop order. Systematic errors due to renormalization and perturbative matching are also analyzed in detail. Our results for lightcone PDF are in reasonable agreement with the latest phenomenological analysis.

Tetraquark interpolating fields in a lattice QCD investigation of the Ds0*(2317) meson

The authors explore the content of the ${D}_{s0}^{*}(2317)$ meson in a lattice QCD study. Using several local two-quark, local tetraquark, and two-meson, i.e. molecular, interpolating fields, they find that the tetraquark contribution to the ${D}_{s0}^{*}(2317)$ meson is negligible, at least for the pion mass, of about 296 MeV, used in this study.

Lattice QCD study of the rare kaon decay K+→π+νν¯ at a near-physical pion mass

The rare kaon decay $K^+\to\pi^+\nu\bar{\nu}$ is an ideal process in which to search for signs of new physics and is the primary goal of the NA62 experiment at CERN. In this paper we report on a lattice QCD calculation of the long-distance contribution to the $K^+\to\pi^+\nu\bar{\nu}$ decay amplitude at the near-physical pion mass $m_\pi=170$ MeV. The calculations are however, performed on a coarse lattice and hence with a lighter charm quark mass ($m_c^{\bar{\mathrm{MS}}}(\mbox{3 GeV})=750$ MeV) than the physical one. The main aims of this study are two-fold. Firstly we study the momentum dependence of the amplitude and conclude that it is very mild so that a computation at physical masses even at a single kinematic point would provide a good estimate of the long-distance contribution to the decay rate. Secondly we compute the contribution to the branching ratio from the two-pion intermediate state whose energy is below the kaon mass and find that it is less than 1% after its exponentially growing unphysical contribution has been removed and that the corresponding non-exponential finite-volume effects are negligibly small.

Excited bottomonia in quark-gluon plasma from lattice QCD

We present the first lattice QCD study of up to 3S and 2P bottomonia at non-zero temperatures. Correlation functions of bottomonia were computed using novel bottomonium operators and a variational technique, within the lattice non-relativistic QCD framework. We analyzed the bottomonium correlation functions based on simple physically-motivated spectral functions. We found evidence of sequential in-medium modifications, in accordance with the sizes of the bottomonium states.

Charmonium resonances with JPC=1−− and 3−− from D¯D scattering on the lattice

We present a lattice QCD study of charmonium resonances and bound states with $J^{PC}=1^{--}$ and $3^{--}$ near the open-charm threshold, taking into account their strong transitions to $\bar DD$. Vector charmonia are the most abundant in the experimentally established charmonium spectrum, while recently LHCb reported also the first discovery of a charmonium with likely spin three. The $\bar DD$ scattering amplitudes for partial waves $l=1$ and $l=3$ are extracted on the lattice by means of the L\"uscher formalism, using multiple volumes and inertial frames. Parameterizations of the scattering amplitudes provide masses and widths of the resonances, as well as the masses of bound states. CLS ensembles with 2+1 dynamical flavors of non-perturbatively $O(a)$ improved Wilson quarks are employed with $m_\pi\simeq 280$ MeV, a single lattice spacing of $a\simeq0.086$ fm and two lattice spatial extents of $L=24$ and $32$. Two values of the charm quark mass are considered to examine the influence of the position of the $\bar{D}D$ threshold on the hadron masses. For the lighter charm quark mass we find the vector resonance $\psi(3770)$ with mass $m=3780(7)$ MeV and coupling $g=16.0(^{+2.1}_{-0.2})$ (related to the width), both consistent with their experimental values. The vector $\psi(2S)$ appears as a bound state with $m=3666(10)$ MeV. The charmonium resonance with $J^{PC}=3^{--}$ is found at $m=3831(^{+10}_{-16})$ MeV, consistent with the $X(3842)$ recently discovered by LHCb. At our heavier charm-quark mass the $\psi(2S)$ as well as the $\psi(3770)$ are bound states and the $X(3842)$ remains a resonance. We stress that all quoted uncertainties are only statistical, while lattice spacing effects and the approach to the physical point still need to be explored. This study of conventional charmonia sets the stage for more challenging future studies of unconventional charmonium-like states.

Valence parton distribution function of pion from fine lattice

We present a lattice QCD study of valence parton distribution inside the pion within the framework of Large Momentum Effective Theory. We use a mixed action approach with 1-HYP smeared valence Wilson clover quarks on 2+1 flavor HISQ sea with the valence quark mass tuned to 300 MeV pion mass. We use $48^3 \times 64$ lattice at a fine lattice spacing $a=0.06$ fm for this computation. We renormalize the quasi-PDF matrix element in the non-perturbative RI-MOM scheme. As a byproduct, we test the validity of 1-loop matching procedure by comparing the RI-MOM renormalized quasi-PDF matrix element with off-shell quark external states as computed in the continuum 1-loop perturbation theory with the lattice results at $a=0.04$ and 0.06 fm. By applying the RI-MOM to ${\bar{\rm MS}}$ one-loop matching, implemented through a fit to phenomenologically motivated PDFs, we obtain the valence PDF of pion.

Nucleon isovector charges and twist-2 matrix elements with Nf=2+1 dynamical Wilson quarks

We present results from a lattice QCD study of nucleon matrix elements at vanishing momentum transfer for local and twist-2 isovector operator insertions. Computations are performed on gauge ensembles with non-perturbatively improved $N_f=2+1$ Wilson fermions, covering four values of the lattice spacing and pion masses down to $M_\pi\approx200$MeV. Several source-sink separations (typically ~1.0fm to ~1.5fm) allow us to assess excited-state contamination. Results on individual ensembles are obtained from simultaneous two-state fits across all observables and all available source-sink separations with the energy gap as a common fit parameter. Renormalization has been performed non-perturbatively using the Rome-Southampton method for all but the finest lattice spacing for which an extrapolation has been used. Physical results are quoted in the $\overline{MS}$ scheme at a scale of $\mu=2$GeV and are obtained from a combined chiral, continuum and finite-size extrapolation. For the nucleon isovector axial, scalar and tensor charges we find physical values of $g_A^{u-d}=1.242(25)_\text{stat}(\genfrac{}{}{0pt}{2}{+00}{-31})_\text{sys}$, $g_S^{u-d}=1.13(11)_\text{stat}(\genfrac{}{}{0pt}{2}{+07}{-06})_\text{sys}$ and $g_T^{u-d}=0.965(38)_\text{stat}(\genfrac{}{}{0pt}{2}{+13}{-41})_\text{sys}$, respectively, where individual systematic errors in each direction from the chiral, continuum and finite-size extrapolation have been added in quadrature. Our final results for the isovector average quark momentum fraction and the isovector helicity and transversity moments are given by $\langle x\rangle_{u-d}=0.180(25)_\text{stat}(\genfrac{}{}{0pt}{2}{+14}{-06})_\text{sys}$, $\langle x\rangle_{\Delta u-\Delta d}=0.221(25)_\text{stat}(\genfrac{}{}{0pt}{2}{+10}{-00})_\text{sys}$ and $\langle x\rangle_{\delta u-\delta d}=0.212(32)_\text{stat}(\genfrac{}{}{0pt}{2}{+20}{-10})_\text{sys}$, respectively.

Transverse Momentum Dependent Observables from Low to High Energy: Factorization, Evolution, and Global Analyses

Transverse momentum dependent (TMD) observables in high-energy particle collisions allow one to study the motion of hadron constituents (partons) in three dimensions. The intense theoretical, phenomenological, and experimental work over the last several decades has seen great progress in modeling and extracting TMD parton distribution functions (PDFs) and fragmentation functions (FFs) [1, 2]. The wealth of experimental data, both current and future [3–6], across various reactions and energy ranges, along with substantial progress in other approaches, such as Lattice QCD [7], has increased the demand to rigorously study the intrinsic transverse motion of hadrons. Such issues currently being addressed include factorization, evolution, and operator definitions of TMD distributions, as well as how they influence phenomenological and Lattice QCD studies. Therefore, in this special issue we attempt to further the effort of understanding TMD structure through a series of review articles that address some of the significant areas of ongoing research.

Lattice QCD study of doubly charmed strange baryons

We present the energy spectra of the low lying doubly-charmed baryons using lattice quantum chromodynamics. We precisely predict the ground state mass of the charmed-strange Omega(cc) (1/2+) baryon to be 3712(11)(12) MeV which could well be the next doubly-charmed baryon to be discovered at the LHCb experiment at CERN. We also predict masses of other doubly-charmed strange baryons with quantum numbers 3/2+, 1/2-, and 3/2-.

Identifying spin and parity of charmonia in flight with lattice QCD

The spectrum of charmonium resonances contains a number of unanticipated states along with several conventional quark-model excitations. The hadrons of different quantum numbers $J^P$ appear in a fairly narrow energy band, where $J^P$ refers to the spin-parity of a hadron at rest. This poses a challenge for Lattice QCD studies of (coupled-channel) meson-meson scattering aimed at the determination of scattering amplitudes and resonance pole positions. A wealth of information for this purpose can be obtained from the lattice spectra in frames with nonzero total momentum. These are particularly dense since hadrons with different $J^P$ contribute to any given lattice irreducible representation. This is because $J^P$ is not a good quantum number in flight, and also because the continuum symmetry is reduced on the lattice. In this paper we address the assignment of the underlying continuum $J^P$ quantum numbers to charmonia in flight using a $N_f = 2 + 1$ CLS ensemble. As a first step, we apply the single-hadron approach, where only interpolating fields of quark-antiquark type are used. The approach follows techniques previously applied to the light meson spectrum by the Hadron Spectrum Collaboration. The resulting spectra of charmonia with assigned $J^P$ will provide valuable information for the parameterization of (resonant) amplitudes in future determinations of resonance properties with lattice QCD.

Some hadronic parameters of charmonia in varvec{N_{text {f}}=2} lattice QCD

The phenomenology of leptonic decays of quarkonia holds many interesting features: for instance, it can establish constraints on scenarios beyond the Standard Model with the Higgs sector enriched by a light CP-odd state. In the following paper, we report on a two-flavor lattice QCD study of the eta _c and J/psi decay constants, f_{eta _c}=387(3)(3), {mathrm{MeV}} and f_{J/psi }=399(4)(2), {mathrm{MeV}}. We also examine some properties of the first radial excitation eta _c(2S) and psi (2S).

Discussion of thermodynamic features within the PNJL model**Supported by National Natural Science Foundation of China (11475085, 11535005, 11690030, 11805097), National Major state Basic Research and Development of China (2016YFE0129300) and Jiangsu Provincial Natural Science Foundation of China (BK20180323)

We discuss some thermodynamical features of a QCD system within the two-flavor Polyakov loop extended Nambu–Jona-Lasinio (PNJL) model. Several thermodynamical quantities of interest (pressure, energy density, specific heat, speed of sound, etc.) are investigated and discussed in detail with two different forms of Polyakov loop potential. The effective coupling strength G incorporating a quark feedback (quark condensate) through operator product expansion is also discussed, as well as the relationship between color deconfinement and chiral phase crossover. We find that some thermodynamical quantities have quite different behavior for different Polyakov loop potentials. By changing the characteristic temperature T0 of the pure Yang-Mills field, we find that when T0 becomes small, color deconfinement might happen earlier than chiral phase crossover, while their relationship can be determined via some thermodynamical quantities. Furthermore, the behavior of the thermodynamical quantities is quite different in the two different forms of Polyakov loop potential studied. Especially, one of the potentials, specific heat, has two peaks, which correspond to color deconfinement and chiral phase crossover respectively. This interesting phenomenon may shed some light on whether the inflection points of the chiral condensate and deconfinement transitions happen at the same temperature or not for lattice QCD and experimental studies.