Complete flavor decomposition of the spin and momentum fraction of the proton using lattice QCD simulations at physical pion mass

We evaluate the gluon and quark contributions to the spin of the proton using an ensemble of gauge configuration generated at physical pion mass. We compute all valence and sea quark contributions to high accuracy. We perform a non-perturbative renormalization for both quark and gluon matrix elements. We find that the contribution of the up, down, strange and charm quarks to the proton intrinsic spin is $\frac{1}{2}\sum_{q=u,d,s,c}\Delta\Sigma^{q^+}=0.191(15)$ and to the total spin $\sum_{q=u,d,s,c}J^{q^+}=0.285(45)$. The gluon contribution to the spin is $J^g=0.187(46)$ yielding $J=J^q+J^g=0.473(71)$ confirming the spin sum. The momentum fraction carried by quarks in the proton is found to be $0.618(60)$ and by gluons $0.427(92)$, the sum of which gives $1.045(118)$ confirming the momentum sum rule. All scale and scheme dependent quantities are given in the $\mathrm{ \overline{MS}}$ scheme at 2 GeV

Nucleon axial, tensor and scalar charges and σ\sigma-terms in lattice QCD

We determine the nucleon axial, scalar and tensor charges within lattice Quantum Chromodynamics including all contributions from valence and sea quarks. We analyze three gauge ensembles simulated within the twisted mass formulation at approximately physical value of the pion mass. Two of these ensembles are simulated with two dynamical light quarks and lattice spacing $a=0.094$~fm and the third with $a=0.08$~fm includes in addition the strange and charm quarks in the sea. After comparing the results among these three ensembles, we quote as final values our most accurate analysis using the latter ensemble. For the nucleon isovector axial charge we find $1.286(23)$ in agreement with the experimental value. We provide the flavor decomposition of the intrinsic spin $\frac{1}{2}\Delta\Sigma^q$ carried by quarks in the nucleon obtaining for the up, down, strange and charm quarks $\frac{1}{2}\Delta\Sigma^{u}=0.431(8)$, $\frac{1}{2}\Delta\Sigma^{d}=-0.212(8)$, $\frac{1}{2}\Delta\Sigma^{s}=-0.023(4)$ and $\frac{1}{2}\Delta\Sigma^{c}=-0.005(2)$, respectively. The corresponding values of the tensor and scalar charges for each quark flavor are also evaluated providing valuable input for experimental searches for beyond the standard model physics. In addition, we extract the nucleon $\sigma$-terms and find for the light quark content $\sigma_{\pi N}=41.6(3.8)$~MeV and for the strange $\sigma_{s}=45.6(6.2)$~MeV. The y-parameter that is used in phenomenological studies we find $y=0.078(7)$.Comment: Expanded version as accepted in Phys. Rev. D.20 pages and 20 figure

Isospin-0 ππ\pi\pi s-wave scattering length from twisted mass lattice QCD

We present results for the isospin-0 $\pi\pi$ s-wave scattering length calculated with Osterwalder-Seiler valence quarks on Wilson twisted mass gauge configurations. We use three $N_f = 2$ ensembles with unitary (valence) pion mass at its physical value (250$\sim$MeV), at 240$\sim$MeV (320$\sim$MeV) and at 330$\sim$MeV (400$\sim$MeV), respectively. By using the stochastic Laplacian Heaviside quark smearing method, all quark propagation diagrams contributing to the isospin-0 $\pi\pi$ correlation function are computed with sufficient precision. The chiral extrapolation is performed to obtain the scattering length at the physical pion mass. Our result $M_\pi a^\mathrm{I=0}_0 = 0.198(9)(6)$ agrees reasonably well with various experimental measurements and theoretical predictions. Since we only use one lattice spacing, certain systematics uncertainties, especially those arising from unitary breaking, are not controlled in our result.Comment: 21 pages, 5 figures, 6 table

Pion transition form factor from twisted-mass lattice QCD and the hadronic light-by-light π 0 -pole contribution to the muon g − 2

The neutral pion generates the leading pole contribution to the hadronic light-by-light tensor, which is given in terms of the nonperturbative transition form factor $\mathcal{F}_{\pi^0\gamma\gamma}(q_1^2,q_2^2)$. Here we present an ab-initio lattice calculation of this quantity in the continuum and at the physical point using twisted-mass lattice QCD. We report our results for the transition form factor parameterized using a model-independent conformal expansion valid for arbitrary space-like kinematics and compare it with experimental measurements of the single-virtual form factor, the two-photon decay width, and the slope parameter. We then use the transition form factors to compute the pion-pole contribution to the hadronic light-by-light scattering in the muon $g-2$, finding $a_\mu^{\pi^0\text{-pole}} = 56.7(3.2) \times 10^{-11}$.Comment: 21 pages, 17 figures, 4 tables, updated to published versio

Time windows of the muon HVP from twisted-mass lattice QCD

We present a lattice determination of the leading-order hadronic vacuum polarization (HVP) contribution to the muon anomalous magnetic moment, aHVPμ , in the so-called short and intermediate time-distance windows, aSDμ and aWμ . We employ gauge ensembles produced by the Extended Twisted Mass Collaboration (ETMC) with Nf=2+1+1 flavours of Wilson-clover twisted-mass quarks with masses of all the dynamical quark flavours tuned close to their physical values. The simulations are carried out at three values of the lattice spacing equal to ≃0.057,0.068 and 0.080 fm with spatial lattice sizes up to L≃7.6 ~fm. For the short distance window we obtain aSDμ=69.27(34)⋅10−10 , in agreement with the dispersive determination based on experimental e+e− data. For the intermediate window we get instead aWμ=236.3(1.3)⋅10−10 , which is consistent with recent determinations by other lattice collaborations, but disagrees with the dispersive determination at the level of 3.6σ

Pseudoscalar-pole contributions to the muon g−2g-2 at the physical point

Pseudoscalar-pole diagrams are an important component of estimates of the hadronic light-by-light (HLbL) contribution to the muon g−2. We report on our computation of the transition form factors P→γ∗γ∗ for the neutral pseudoscalar mesons P=π0 and η . The calculation is performed using twisted-mass lattice QCD with physical quark masses. On the lattice, we have access to a broad range of (space-like) photon four-momenta and therefore produce form factor data complementary to the experimentally accessible single-virtual direction, which directly leads to an estimate of the pion- and η -pole components of the muon g−2 . For the pion, our result for the g−2 contribution in the continuum is comparable with previous lattice and data-driven determinations, with combined relative uncertainties below 10% . For the η meson, we report on a preliminary determination from a single lattice spacing

Optical Absorption of an Interacting Many-Polaron Gas

The optical absorption of a many (continuum) polaron gas is derived in the framework of a variational approach at zero temperature and weak or intermediate electron-phonon coupling strength. We derive a compact formula for the optical conductivity of the many-polaron system taking into account many-body effects in the electron or hole system. Within the method presented here, these effects are contained completely in the dynamical structure factor of the electron or hole system. This allows to build on well-established studies of the interacting electron gas. Based on this approach a novel feature in the absorption spectrum of the many-polaron gas, related to the emission of a plasmon together with a phonon, is identified. As an application and illustration of the technique, we compare the theoretical many-polaron optical absorption spectrum as derived in the present work with the `d-band' absorption feature in Nd$_{2}$CuO$_{2}$. Similarities are shown between the theoretically and the experimentally derived first frequency moment of the optical absorption of a family of differently doped Nd$_{2-x}$Ce$_{x}$CuO$_{4-y}$ materials.Comment: 24 pages, 5 figures; revised and expanded versio

Isospin-0 ππ scattering from twisted mass lattice QCD

We present results for the isospin-0 $pipi$ s-wave scattering length calculated in twisted mass lattice QCD. We use three $N_f = 2$ ensembles with unitary pion mass at its physical value, 240~MeV and 330~MeV respectively. We also use a large set of $N_f = 2 + 1 +1$ ensembles with unitary pion masses varying in the range of 230~MeV - 510~MeV at three different values of the lattice spacing. A mixed action approach with the Osterwalder-Seiler action in the valence sector is adopted to circumvent the complications arising from isospin symmetry breaking of the twisted mass quark action. Due to the relatively large lattice artefacts in the $N_f = 2 + 1 +1$ ensembles, we do not present the scattering lengths for these ensembles. Instead, taking the advantage of the many different pion masses of these ensembles, we qualitatively discuss the pion mass dependence of the scattering properties of this channel based on the results from the $N_f = 2 + 1 +1$ ensembles. The scattering length is computed for the $N_f = 2$ ensembles and the chiral extrapolation is performed. At the physical pion mass, our result $M_pi a^mathrm{I=0}_0 = 0.198(9)(6)$ agrees reasonably well with various experimental measurements and theoretical predictions

The Role of CO2-EOR for the Development of a CCTS Infrastructure in the North Sea Region: A Techno-Economic Model and Application

Scenarios of future energy systems attribute an important role to Carbon Capture, Transport, and Storage (CCTS) in achieving emission reductions. Using captured CO2 for enhanced oil recovery (CO2-EOR) can improve the economics of the technology. This paper examines the potential for CO2-EOR in the North Sea region. UK oil fields are found to account for 47% of the estimated additional recovery potential of 3739 Mbbl (1234 MtCO2 of storage potential). Danish and Norwegian fields add 28% and 25%, respectively. Based on a comprehensive dataset, the paper develops a unique techno-economic market equilibrium model of CO2 supply from emission sources and CO2 demand from CO2-EOR to assess implications for a future CCTS infrastructure. A detailed representation of decreasing demand for fresh CO2 for CO2-EOR operation is accomplished via an exponential storage cost function. In all scenarios of varying CO2 and crude oil price paths the assumed CO2-EOR potential is fully exploited. CO2-EOR does add value to CCTS operations but the potential is very limited and does not automatically induce long term CCTS activity. If CO2 prices stay low, little further use of CCTS can be expected after 2035