Flavor non-singlet parton distribution functions from lattice QCD at physical quark masses via the pseudo-distribution approach
Manjunath Bhat, Krzysztof Cichy, Martha Constantinou, Aurora Scapellato
备注：
Matches journal version. Added an alternative interpolation procedure + analysis of PDF moments + comparison with NNPDF ITDs. Main results and conclusions unchanged. 24 pages, 17 figures
One of the great challenges of QCD is to determine the partonic structure of the nucleon from first principles. In this work, we provide such a determination of the flavor non-singlet ($u-d$) unpolarized parton distribution function (PDF), utilizing the non-perturbative formulation of QCD on the lattice. We apply Radyushkin's pseudo-distribution approach to lattice results obtained using simulations with the light quark mass fixed to its physical value; this is the first ever attempt for this approach directly at the physical point. The extracted coordinate-space matrix elements are used to find the relevant physical Ioffe time distributions from a matching procedure. The full Bjorken-$x$ dependence of PDFs is resolved using several reconstruction methods to tackle the ill-conditioned inverse problem encountered when using discrete lattice data. We consider both the valence distribution $q_v$ and the combination with antiquarks $q_v+2\bar{q}$, related to, respectively, the real and imaginary part of extracted matrix elements. Good agreement is found with PDFs from global fits already within statistical uncertainties and it is further improved by quantifying several systematic effects. The results presented here are the first ever \emph{ab initio} determinations of PDFs fully consistent with global fits in the whole $x$-range. Thus, they pave the way to investigating a wider class of partonic distributions, such as e.g.\ singlet PDFs and generalized parton distributions. Therefore, essential and yet missing first-principle insights can be achieved, complementing the rich experimental programs dedicated to the structure of the nucleon.
$SU(N_c)$ colour-singlet restriction, along with flavour and spin symmetry, on thermal partonic ensemble is shown to recombine the partons with internal colour structure into colour-singlet multi-quark clusters which can be identified with various hadronic modes at a given temperature. This provides a possible basis for recombination model for hadronization of quark-gluon plasma. This also leads to a natural explanation for the ratio of (anti)protons to pions and the quark number scaling of the elliptic flow coefficient in relativistic heavy-ion collisions.
We compute, within the Schrödinger functional scheme, a renormalization group invariant renormalization constant for the first moment of the non-singlet parton distribution function. The matching of the results of our non-perturbative calculation with the ones from hadronic matrix elements allows us to obtain eventually a renormalization group invariant average momentum of non-singlet parton densities, which can be translated into a preferred scheme at a specific scale.
We present a next-to-next-to-leading order (NNLO) calculation of the quasi parton distribution functions (Quasi-PDFs) in the large momentum effective theory (LaMET). We focus on the flavor non-diagonal quark-quark channel and demonstrate the LaMET factorization at the NNLO accuracy in the modified minimal subtraction scheme. The matching coefficient between the quasi-PDF and the light-cone PDF is derived. This provides a first step towards a complete NNLO analysis of quasi-PDFs and to better understand the nucleon structures from the first principle of QCD.
A non perturbative computation of the evolution of singlet parton densities without gauge--fixing requires a gauge invariant gluon source operator. Within the Schrödinger Functional scheme (SF), such a source can be defined in terms of path ordered products of gauge links, connected to the time boundaries. In this paper we adopt this definition and perform a one loop lattice computation of the renormalization constants of the twist--2 operators that correspond to the second moment of singlet parton densities. This calculation fixes the connection between the lattice SF scheme where a non pertu…
We present results on the quark unpolarized, helicity and transversity parton distributions functions of the nucleon. We use the quasi-parton distribution approach within the lattice QCD framework and perform the computation using an ensemble of twisted mass fermions with the strange and charm quark masses tuned to approximately their physical values and light quark masses giving pion mass of 260 MeV. We use hierarchical probing to evaluate the disconnected quark loops. We discuss identification of ground state dominance, the Fourier transform procedure and convergence with the momentum boost.…
We present, for the first time, an \textit{ab initio} calculation of the individual up, down and strange quark helicity parton distribution functions for the proton. The calculation is performed within the twisted mass clover-improved fermion formulation of lattice QCD using one ensemble of dynamical up, down, strange and charm quarks with a pion mass of 260 MeV. The lattice matrix elements are non-perturbatively renormalized and the final results are presented in the $\overline{ \rm MS}$ scheme at a scale of 2 GeV. We give results on the $Δu^+(x)$ and $Δd^+(x)$, including disconnected quark l…
We determine the parton distribution functions (PDFs) in a next-to-next-to-leading order (NNLO) QCD-analysis of the inclusive neutral-current deep-inelastic-scattering (DIS) world data combined with the neutri{-}no-nucleon DIS di-muon data and the fixed-target Drell-Yan data. The PDF-evolution is performed in the $N_f = 3$ fixed-flavor scheme and supplementary sets of PDFs in the 4- and 5-flavor schemes are derived from the results in the 3-flavor scheme using matching conditions. The charm-quark DIS contribution is calculated in a general-mass variable-flavor-number (GMVFN) scheme interpolati…
We present an initiatory study of quark helicity flip generalized parton distributions (GPDs) in n_f=2 lattice QCD, based on clover-improved Wilson fermions for a large number of coupling constants and pion masses. Quark helicity flip GPDs yield essential information on the transverse spin structure of the nucleon. In this work, we show first results on their lowest moments and dipole masses and study the corresponding chiral and continuum extrapolations.
Flavor singlet combinations of quark operators ${\cal{O}}_S^Γ = \bar{u}Γu + \bar{d}Γd + \bar{s}Γs$ contribute to many important physical observables in the low energy region of QCD. Experimentally one finds the values of some of these observables to be in sharp contrast to the naive (perturbative) theoretical expectations. This indicates that non perturbative vacuum properties might play a major role in the comprehension of these phenomena. An example of such a vacuum contribution is the axial anomaly, which appears in the divergence of the flavor singlet axial current and which is connected t…
Accurately calculating the mass of flavor-singlet meson states from numerical lattice simulations is an important milestone for lattice QCD. Careful measurement of the full pseudoscalar flavor-singlet propagator is also a crucial step in understanding the dynamics of the fermion sea on the lattice, in particular for potentially non-trivial formulations such as with 2+1-flavor staggered fermions. We briefly describe details of a dynamical QCD calculation using improved staggered fermions, with 30,000 trajectories, that was run for our studies of flavour singlet mesons.
Studying SU(3) gauge theories with increasing number of light fermions is relevant both for understanding the strong dynamics of QCD and for constructing strongly interacting extensions of the Standard Model (e.g. UV completions of composite Higgs models). In order to contrast these many-flavors strongly interacting theories with QCD, we study the flavor-singlet spectrum as an interesting probe. In fact, some composite Higgs models require the Higgs boson to be the lightest flavor-singlet scalar in the spectrum of a strongly interacting new sector with a well defined hierarchy with the rest of…
Experimentally the charmonium hyperfine splitting is $M_{J/ψ}-M_{η_c}=117$ MeV and current lattice results are generally below this value. The difference could be due to the effects of the disconnected flavor singlet diagrams which have not been included in these calculations. Previous attempts to determine the disconnected flavor singlet corrections have led just to rough estimates in the range of $\pm 20$ MeV. We present preliminary results for these corrections calculated on fine ($a\approx 0.09$ fm) Asqtad 2+1 flavor lattices provided by the MILC Collaboration.
We report on our studies of the renormalization of flavor singlet quark bilinear operators in lattice QCD. The renormalization constants are determined non-perturbatively using gauge field ensembles with Nf=2 dynamical clover improved fermions. The renormalization is performed in the RI'-MOM scheme. The difference between flavor singlet and non-singlet quark bilinear operators is a disconnected contribution, which has to be evaluated by stochastic estimators. We compare our results for the running with perturbation theory.
We present a combined analysis of SESAM and TxL data for the flavor singlet axial coupling G_A^1 of the proton, which is very helpful to stabilize the disconnected signals at small quark masses. From connected and disconnected contributions we use the tadpole improved renormalization constant Z_A and obtain G_A^1=0.21(12).
The strange and flavor-singlet axial form factors of the nucleon from lattice QCD
Helmholtz-Institut Mainz, Johannes Gutenberg-Universität Mainz（美因茨亥姆霍兹研究所）；GSI Helmholtzzentrum für Schwerionenforschung（GSI重离子研究中心）；Theoretical Physics Department, CERN（欧洲核子研究中心理论物理部）；Helmholtz-Institut für Strahlen- und Kernphysik, Universität Bonn（波恩大学辐射与核物理亥姆霍兹研究所）
We report the calculation of the flavor-singlet scalar in the SU(3) gauge theory with the degenerate twelve fermions in the fundamental representation using a HISQ-type action at a fixed $β$. In order to reduce the large statistical error coming from the vacuum-subtracted disconnected correlator, we employ a noise reduction method and a large number of configurations. We observe that the flavor-singlet scalar is lighter than the pion in this theory from the calculations with the fermion bilinear and gluonic operators. This peculiar feature is considered to be due to the infrared conformality o…
We extend our earlier results concerning the breaking of the U_A(1) symmetry in finite temperature QCD. In particular, we use topological arguments to investigate the chiral limit.
We report on our study of flavor-singlet mesons in three-flavor QCD with dynamical overlap quarks. Gauge ensembles are generated on a 16^3 x 48 lattice at a lattice spacing of 0.10 fm with the strange quark masses around its physical value m_s,phys and up and down quark masses down to m_s,phys/5. Connected and disconnected meson correlators are calculated using the all-to-all quark propagator. We present our preliminary results on the spectrum of flavor-singlet pseudoscalar and vector mesons.
Lattice QCD Benchmark of Proton Helicity and Flavor-Dependent Unpolarized Transverse Momentum-Dependent Parton Distribution Functions at Physical Quark Masses
We compute the difference in the renormalization of flavor singlet and nonsinglet fermion bilinear operators, to two loops in perturbation theory. Our results are applicable to a rather wide class of lattice actions with Symanzik improved gluons, stout links and clover fermions, including the Twisted Mass and SLiNC actions. A more detailed presentation of our results, along with relevant references, will appear in a forthcoming publication.
The Asqtad improved staggered fermion formalism has been a valuable tool in successfully calculating the non-singlet parts of the hadronic spectrum. We are engaged in a project to calculate the spectrum of the pseudoscalar singlet mesons with 2+1-flavor Asqtad staggered gauge configurations. Propagators of flavor-singlet states incorporate contributions from both disconnected and connected diagrams, and hence are sensitive to any differences in the actions governing the sea and valence fermions on the lattice. As such, they also present the possibility of a probe of the validity of the ``fourt…
We determine non-perturbatively the anomalous dimensions of the second moment of non-singlet parton densities from a continuum extrapolation of results computed in quenched lattice simulations at different lattice spacings. We use a Schrödinger functional scheme for the definition of the renormalization constant of the relevant twist-2 operator. In the region of renormalized couplings explored, we obtain a good description of our data in terms of a three-loop expression for the anomalous dimensions. The calculation can be used for exploring values of the coupling where a perturbative expansion…
We reconsider the Volume Source Technique (VST) for the determination of flavor singlet quantities on the lattice. We point out a difficulty arising in the case of fermions in real representations of the gauge group and propose an improved version of the method (IVST) based on random gauge transformations of the background configuration. We compare the performance of IVST with the method based on stochastic estimators (SET). We consider the case of the N=1 Supersymmetric Yang-Mills Theory (SYM), where just one fermionic flavor is present, the gluino in the adjoint representation, and only flav…
Information about double parton distributions (DPDs) can be obtained by calculating four-point functions on the lattice. We continue our study on the first DPD Mellin moment of the unpolarized proton by considering interference effects w.r.t. the quark flavor. In our simulation we employ an $n_f = 2 + 1$ ensemble with inverse coupling $β= 3.4$, and pseudoscalar masses of $m_π= 355~\mathrm{MeV}$ and $m_K = 441~\mathrm{MeV}$. The results are converted to the $\overline{\mathrm{MS}}$-scheme at the scale $μ= 2~\mathrm{GeV}$. We analyze the dependence of the considered Mellin moments on the quark p…
We investigate baryon-baryon (BB) interactions in the 3-flavor full QCD simulations with degenerate quark masses for all flavors. The BB potentials in the orbital S-wave are extracted from the Nambu-Bethe-Salpeter wave functions measured on the lattice. We observe strong flavor-spin dependences of the BB potentials at short distances. In particular, a strong repulsive core exists in the flavor-octet and spin-singlet channel(the 8_s representation), while an attractive core appears in the flavor singlet channel (the 1 representation). We discuss the relation of such flavor-spin dependence with …
We present the results of a full QCD lattice calculation of the flavor singlet axial vector coupling $G_A^1$ of the proton. The simulation has been carried out on a $16^3\times 32$ lattice at $β=5.6$ with $n_f=2$ dynamical Wilson fermions. It turns out that the statistical quality of the connected contribution to $G_A^1$ is excellent, whereas the disconnected part is accessible but suffers from large statistical fluctuations. Using a 1st order tadpole improved renormalization constant $Z_A$, we estimate $G_A^1 = 0.20(12)$.
The flavor singlet axial and tensor charges of the nucleon are calculated in lattice QCD. We find $ΔΣ=Δu+Δd+Δs=+0.638(54)-0.347(46)-0.109(30) = +0.18(10)$ for the axial charge and $δΣ=δu+δd+δs=+0.839(60)-0.231(55)-0.046(34) = +0.562(88)$ for the tensor charge. The result for the axial charge shows reasonable agreement with the experiment and that for the tensor charge is the first prediction from lattice QCD before experimental measurements.
We examine the taste structure of eigenvectors of the staggered-fermion Dirac operator. We derive a set of conditions on the eigenvectors of modes with small eigenvalues (near-zero modes), such that staggered fermions reproduce the 't Hooft vertex in the continuum limit. We also show that, assuming these conditions, the correlators of flavor-singlet mesons are free of contributions singular in $1/m$, where $m$ is the quark mass. This conclusion holds also when a single flavor of sea quark is represented by the fourth root of the staggered-fermion determinant. We then test numerically, using th…
We investigate baryon-baryon (BB) interactions in the 3-flavor full QCD simulations with degenerate quark masses for all flavors. The BB potentials in the orbital S-wave are extracted from the Nambu-Bethe-Salpeter wave functions measured on the lattice. We observe strong flavor-spin dependences of the BB potentials at short distances. In particular, a strong repulsive core exists in the flavor-octet and spin-singlet channel (the 8_s representation), while an attractive core appears in the flavor singlet channel (the 1 representation). We discuss a relation of such flavor-spin dependence with t…
We compute the screening correlators in the sigma and eta' flavor singlet channels in finite temperature QCD with 2 light quark flavors. Together with the correlators in the pi and delta channels, these are used to discuss several issues related to symmetry restoration and the nature of the QCD phase transition. Our calculations span a range of temperature extending from approximately 125 MeV to 170 MeV and are carried out in the context of a staggered fermion formulation on a 16^3x8 lattice. In addition to the computation at a fixed quark mass (am_q=0.00625), we discuss the issue of the chira…
A discussion of methods for reducing the noise variance of flavor singlet quantities ("disconnected diagrams") in lattice QCD is given. After an introduction, the possible advantage of partitioning the Wilson fermion matrix into disjoint spaces is discussed and a numerical comparison of the variance for three possible partitioning schemes is carried out. The measurement efficiency of lattice operators is examined and shown to be strongly influenced by the Dirac and color partitioning choices. Next, the numerical effects of an automated subtraction algorithm on the noise variance of various dis…
We report on progress in measuring disconnected correlators associated with pseudoscalar flavor-singlet mesons. This will eventually allow us to compute the masses of the eta and eta' mesons. Flavor-singlet physics also presents an interesting test of the staggered fermion formulation, as disconnected correlators are sensitive to whether the same action governs both sea quarks and valence quarks. It can also help test the validity of the ``fourth-root trick'' used in unquenched lattice calculations where the number of flavors $N_f<4$.
A novel view of the flavor-singlet spectrum from multi-flavor QCD on the lattice
RIKEN Center for Computational Science（理化学研究所计算科学中心）；Institute for Solid State Physics, University of Tokyo（东京大学固体物理研究所）；Swansea Academy of Advanced Computing, Swansea University（斯旺西大学高级计算学院）；Kobayashi-Maskawa Institute for the Origin of Particles and the Universe, Nagoya University（名古屋大学小林-益川粒子宇宙起源研究所）；Institute of Particle and Nuclear Studies, High Energy Accelerator Research Organization (KEK)（高能加速器研究机构粒子核研究部）；Department of Physics, Nara Women’s University（奈良女子大学物理学系）；Interdisciplinary Theoretical & Mathematical Science (iTHEMS) Program, RIKEN（理化学研究所交叉理论与数学科学项目）；Computing Research Center, High Energy Accelerator Research Organization (KEK)（高能加速器研究机构计算研究中心）；Institute of Pure and Applied Sciences, University of Tsukuba（筑波大学理学院）；Center for Computational Sciences, University of Tsukuba（筑波大学计算科学中心）
We present results for the mass of the eta-prime meson in the continuum limit for two-flavor lattice QCD, calculated on the CP-PACS computer, using a renormalization-group improved gauge action, and Sheikholeslami and Wohlert's fermion action with tadpole-improved csw. Correlation functions are measured at three values of the coupling constant beta corresponding to the lattice spacing a approx. 0.22, 0.16, 0.11 fm and for four values of the quark mass parameter kappa corresponding to mpi over mrho approx. 0.8, 0.75, 0.7 and 0.6. For each beta, kappa pair, 400-800 gauge configurations are used.…
I discuss minimally doubled fermions fermions as an ultra-local formulation on the lattice for sea quarks that realize a non-singlet chiral symmetry. I introduce a non-singlet mass term for Karsten-Wilczek fermions and identify the appropriate representation of the SU(2) flavor group at finite lattice spacing. I present an algebraic proof that the symmetry of the quark determinant under charge conjugation and reflections of the Euclidean axes is preserved for Karsten-Wilczek fermions as sea quarks. Finally, I discuss how the flavor components in meson correlation functions with Karsten-Wilczek…
We study negative-parity baryon spectra in quenched anisotropic lattice QCD. The negative-parity baryons are measured as the parity partner of the ground-state baryons. In addition to the flavor octet and decuplet baryons, we pay much attention to the flavor-singlet negative-parity baryon as a three-quark state and compare it with the Lambda(1405) baryon. Numerical results of the flavor octet and decuplet negative-parity baryon masses are close to experimental values of lowest-lying negative-parity baryons, while the flavor-singlet baryon is much heavier than Lambda(1405). This indicates that …
