arXiv subjects

P. E. L. Rakow

Publications and source records attributed to P. E. L. Rakow.

At least 73 records · Page 4Linked to original sources

arXiv2014

Connected and disconnected quark contributions to hadron spin

By introducing an external spin operator to the fermion action, the quark spin fractions of hadrons are determined from the linear response of the hadron energies using the Feynman-Hellmann (FH) theorem. At our SU(3)-flavour symmetric point, we find that the connected quark spin fractions are universally in the range 55-70\% for vector mesons and octet and decuplet baryons. There is an indication that the amount of spin suppression is quite sensitive to the strength of SU(3) breaking. We also present first preliminary results applying the FH technique to calculations of quark-line disconnected contributions to hadronic matrix elements of axial and tensor operators. At the SU(3)-flavour symmetric point we find a small negative contribution to the nucleon spin from disconnected quark diagrams, while the corresponding tensor matrix elements are consistent with zero.

hep-lat↗

arXiv2014

Determining Sigma - Lambda mixing

SU2 isospin breaking effects in baryon octet (and decuplet) masses are due to a combination of up and down quark mass differences and electromagnetic effects. These mass differences are small. Between the Sigma and Lambda the mass splitting is much larger, but this is mostly due to their different wavefunctions. However there is now also mixing between these states. We determine the QCD mixing matrix and hence find the mixing angle and mass splitting.

hep-lat↗

arXiv2014

A novel approach to nonperturbative renormalization of singlet and nonsinglet lattice operators

A novel method for nonperturbative renormalization of lattice operators is introduced, which lends itself to the calculation of renormalization factors for nonsinglet as well as singlet operators. The method is based on the Feynman-Hellmann relation, and involves computing two-point correlators in the presence of generalized background fields arising from introducing additional operators into the action. As a first application, and test of the method, we compute the renormalization factors of the axial vector current $A_μ$ and the scalar density $S$ for both nonsinglet and singlet operators for $N_f=3$ flavors of SLiNC fermions. For nonsinglet operators, where a meaningful comparison is possible, perfect agreement with recent calculations using standard three-point function techniques is found.

hep-lat↗

arXiv2014

Renormalization of local quark-bilinear operators for Nf=3 flavors of SLiNC fermions

The renormalization factors of local quark-bilinear operators are computed non-perturbatively for $N_f=3$ flavors of SLiNC fermions, with emphasis on the various procedures for the chiral and continuum extrapolations. The simulations are performed at a lattice spacing $a=0.074$ fm, and for five values of the pion mass in the range of 290-465 MeV, allowing a safe and stable chiral extrapolation. Emphasis is given in the subtraction of the well-known pion pole which affects the renormalization factor of the pseudoscalar current. We also compute the inverse propagator and the Green's functions of the local bilinears to one loop in perturbation theory. We investigate lattice artifacts by computing them perturbatively to second order as well as to all orders in the lattice spacing. The renormalization conditions are defined in the RI$'$-MOM scheme, for both the perturbative and non-perturbative results. The renormalization factors, obtained at different values of the renormalization scale, are translated to the ${\bar{\rm MS}}$ scheme and are evolved perturbatively to 2 GeV. Any residual dependence on the initial renormalization scale is eliminated by an extrapolation to the continuum limit. We also study the various sources of systematic errors. Particular care is taken in correcting the non-perturbative estimates by subtracting lattice artifacts computed to one loop perturbation theory using the same action. We test two different methods, by subtracting either the ${\cal O}(g^2\,a^2)$ contributions, or the complete (all orders in $a$) one-loop lattice artifacts.

hep-lat↗

arXiv2014

A Feynman-Hellmann approach to the spin structure of hadrons

We perform a Nf = 2 + 1 lattice QCD simulation to determine the quark spin fractions of hadrons using the Feynman-Hellmann theorem. By introducing an external spin operator to the fermion action, the matrix elements relevant for quark spin fractions are extracted from the linear response of the hadron energies. Simulations indicate that the Feynman-Hellmann method offers statistical precision that is comparable to the standard three-point function approach, with the added benefit that it is less susceptible to excited state contamination. This suggests that the Feynman-Hellmann technique offers a promising alternative for calculations of quark line disconnected contributions to hadronic matrix elements. At the SU(3)-flavour symmetry point, we find that the connected quark spin fractions are universally in the range 55-70% for vector mesons and octet and decuplet baryons. There is an indication that the amount of spin suppression is quite sensitive to the strength of SU(3) breaking.

hep-lat↗

arXiv2014

Nucleon axial charge and pion decay constant from two-flavor lattice QCD

The axial charge of the nucleon $g_A$ and the pion decay constant $f_π$ are computed in two-flavor lattice QCD. The simulations are carried out on lattices of various volumes and lattice spacings. Results are reported for pion masses as low as $m_π=130\,\mbox{MeV}$. Both quantities, $g_A$ and $f_π$, suffer from large finite size effects, which to leading order ChEFT and ChPT turn out to be identical. By considering the naturally renormalized ratio $g_A/f_π$, we observe a universal behavior as a function of decreasing quark mass. From extrapolating the ratio to the physical point, we find $g_A^R=1.29(5)(3)$, using the physical value of $f_π$ as input and $r_0=0.50(1)$ to set the scale. In a subsequent calculation we attempt to extrapolate $g_A$ and $f_π$ separately to the infinite volume. Both volume and quark mass dependencies of $g_A$ and $f_π$ are found to be well decribed by ChEFT and ChPT. We find at the physical point $g_A^R=1.24(4)$ and $f_π^R=89.6(1.1)(1.8)\,\mbox{MeV}$. Both sets of results are in good agreement with experiment. As a by-product we obtain the low-energy constant $\bar{l}_4=4.2(1)$.

hep-lat↗

arXiv2013

SU(3) flavour symmetry breaking and charmed states

By extending the SU(3) flavour symmetry breaking expansion from up, down and strange sea quark masses to partially quenched valence quark masses we propose a method to determine charmed quark hadron masses including possible QCD isospin breaking effects. Initial results for some open charmed pseudoscalar meson states and singly and doubly charmed baryon states are encouraging and demonstrate the potential of the procedure. Essential for the method is the determination of the scale using singlet quantities, and to this end we also give here a preliminary estimation of the recently introduced Wilson flow scales.

hep-lat↗

arXiv2013

SU(3) flavour breaking and baryon structure

We present results from the QCDSF/UKQCD collaboration for hyperon electromagnetic form factors and axial charges obtained from simulations using Nf=2+1 flavours of O(a)-improved Wilson fermions. We also consider matrix elements relevant for hyperon semileptonic decays. We find flavour-breaking effects in hyperon magnetic moments which are consistent with experiment, while our results for the connected quark spin content indicates that quarks contribute more to the spin of the Xi baryon than they do to the proton.

hep-lat↗

arXiv2013

Electromagnetic splitting of quark and pseudoscalar meson masses from dynamical QCD + QED

Lattice QCD simulations are now reaching a precision where electromagnetic corrections from QED become important. In investigating the effects of SU(3) breaking due to quark mass differences within QCD, a group-theoretical analysis of the mass dependence greatly helped us organize our results. We now do the same with electromagnetic charge effects by extending the calculations to dynamical 1+1+1 flavor QCD + QED.

hep-lat↗

arXiv2013

The SU(3) Beta Function from Numerical Stochastic Perturbation Theory

The SU(3) beta function is computed from Wilson loops to 20th order numerical stochastic perturbation theory. An attempt is made to include massless fermions, whose contribution is known analytically to 4th order. The question whether the theory admits an infrared stable fixed point is addressed.

hep-lat↗

arXiv2013

Perturbatively improving renormalization constants

Renormalization factors relate the observables obtained on the lattice to their measured counterparts in the continuum in a suitable renormalization scheme. They have to be computed very precisely which requires a careful treatment of lattice artifacts. In this work we present a method to suppress these artifacts by subtracting one-loop contributions proportional to the square of the lattice spacing calculated in lattice perturbation theory.

hep-lat↗

arXiv2013

Perturbatively improving RI-MOM renormalization constants

The determination of renormalization factors is of crucial importance in lattice QCD. They relate the observables obtained on the lattice to their measured counterparts in the continuum in a suitable renormalization scheme. Therefore, they have to be computed as precisely as possible. A widely used approach is the nonperturbative Rome-Southampton method. It requires, however, a careful treatment of lattice artifacts. In this paper we investigate a method to suppress these artifacts by subtracting one-loop contributions to renormalization factors calculated in lattice perturbation theory. We compare results obtained from a complete one-loop subtraction with those calculated for a subtraction of contributions proportional to the square of the lattice spacing.

hep-lat↗

arXiv2012

Octet baryon mass splittings from up-down quark mass differences

Using an SU(3) flavour symmetry breaking expansion in the quark mass, we determine the QCD component of the neutron-proton, Sigma and Xi mass splittings of the baryon octet due to up-down (and strange) quark mass differences. Provided the average quark mass is kept constant, the expansion coefficients in our procedure can be determined from computationally cheaper simulations with mass degenerate sea quarks and partially quenched valence quarks. Full details and numerical results are given in ref 1.

hep-lat↗

arXiv2012

Isospin breaking in octet baryon mass splittings

Using an SU(3) flavour symmetry breaking expansion in the quark mass, we determine the QCD component of the nucleon, Sigma and Xi mass splittings of the baryon octet due to up-down (and strange) quark mass differences in terms of the kaon mass splitting. Provided the average quark mass is kept constant, the expansion coefficients in our procedure can be determined from computationally cheaper simulations with mass degenerate sea quarks and partially quenched valence quarks. Both the linear and quadratic terms in the SU(3) flavour symmetry breaking expansion are considered; it is found that the quadratic terms only change the result by a few percent, indicating that the expansion is highly convergent.

hep-lat↗

arXiv2012

The effects of flavour symmetry breaking on hadron matrix elements

By considering a flavour expansion about the SU(3)-flavour symmetric point, we investigate how flavour-blindness constrains octet baryon matrix elements after SU(3) is broken by the mass difference between the strange and light quarks. We find the expansions to be highly constrained along a mass trajectory where the singlet quark mass is held constant, which proves beneficial for extrapolations of 2+1 flavour lattice data to the physical point. We investigate these effects numerically via a lattice calculation of the flavour-conserving and flavour-changing matrix elements of the vector and axial operators between octet baryon states.

hep-lat↗

arXiv2012

Perturbative and Nonperturbative Renormalization in Lattice QCD

We investigate the perturbative and nonperturbative renormalization of composite operators in lattice QCD restricting ourselves to operators that are bilinear in the quark fields (quark-antiquark operators). These include operators which are relevant to the calculation of moments of hadronic structure functions. The nonperturbative computations are based on Monte Carlo simulations with two flavors of clover fermions and utilize the Rome-Southampton method also known as the RI-MOM scheme. We compare the results of this approach with various estimates from lattice perturbation theory, in particular with recent two-loop calculations.

hep-lat↗

arXiv2012

Perturbative subtraction of lattice artifacts in the computation of renormalization constants

The determination of renormalization factors is of crucial importance. They relate the observables obtained on finite, discrete lattices to their measured counterparts in the continuum in a suitable renormalization scheme. Therefore, they have to be computed as precisely as possible. A widely used approach is the nonperturbative Rome-Southampton method. It requires, however, a careful treatment of lattice artifacts. They are always present because simulations are done at lattice spacings $a$ and momenta $p$ with $ap$ not necessarily small. In this paper we try to suppress these artifacts by subtraction of one-loop contributions in lattice perturbation theory. We compare results obtained from a complete one-loop subtraction with those calculated for a subtraction of $O(a^2)$.

hep-lat↗

arXiv2012

Scattering phases for meson and baryon resonances on general moving-frame lattices

A proposal by Lüscher enables one to compute the scattering phases of elastic two-body systems from the energy levels of the lattice Hamiltonian in a finite volume. In this work we generalize the formalism to S--, P-- and D--wave meson and baryon resonances, and general total momenta. Employing nonvanishing momenta has several advantages, among them making a wider range of energy levels accessible on a single lattice volume and shifting the level crossing to smaller values of $m_πL$.

hep-lat↗