arXiv subjects
Publications and source records attributed to J. M. Zanotti.
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.
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.
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.
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.
The renormalized next-to-leading-order (NLO) chiral low-energy constant, $L_{10}^r$, is determined in a complete next-to-next-to-leading-order (NNLO) analysis, using a combination of lattice and continuum data for the flavor $ud$ $V-A$ correlator and results from a recent chiral sum-rule analysis of the flavor-breaking combination of $ud$ and $us$ $V-A$ correlator differences. The analysis also fixes two combinations of NNLO low-energy constants, the determination of which is crucial to the precision achieved for $L_{10}^r$. Using the results of the flavor-breaking chiral $V-A$ sum rule obtained with current versions of the strange hadronic $τ$ branching fractions as input, we find $L_{10}^r(m_ρ)\, =\, -0.00346(32)$. This result represents the first NNLO determination of $L_{10}^r$ having all inputs under full theoretical and/or experimental control, and the best current precision for this quantity.
We present physical results for a variety of light hadronic quantities obtained via a combined analysis of three 2+1 flavour domain wall fermion ensemble sets. For two of our ensemble sets we used the Iwasaki gauge action with beta=2.13 (a^-1=1.75(4) GeV) and beta=2.25 (a^-1=2.31(4) GeV) and lattice sizes of 24^3 x 64 and 32^3 x 64 respectively, with unitary pion masses in the range 293(5)-417(10) MeV. The extent L_s for the 5^th dimension of the domain wall fermion formulation is L_s=16 in these ensembles. In this analysis we include a third ensemble set that makes use of the novel Iwasaki+DSDR (Dislocation Suppressing Determinant Ratio) gauge action at beta = 1.75 (a^-1=1.37(1) GeV) with a lattice size of 32^3 x 64 and L_s=32 to reach down to partially-quenched pion masses as low as 143(1) MeV and a unitary pion mass of 171(1) MeV, while retaining good chiral symmetry and topological tunneling. We demonstrate a significant improvement in our control over the chiral extrapolation, resulting in much improved continuum predictions for the above quantities. The main results of this analysis include the pion and kaon decay constants, f_π=127(3)_{stat}(3)_{sys} MeV and f_K = 152(3)_{stat}(2)_{sys} MeV respectively (f_K/f_π= 1.199(12)_{stat}(14)_{sys}); the average up/down quark mass and the strange-quark mass in the MSbar-scheme at 3 GeV, m_{ud}(MSbar, 3 GeV) = 3.05(8)_{stat}(6)_{sys} MeV and m_s(MSbar, 3 GeV) = 83.5(1.7)_{stat}(1.1)_{sys}; the neutral kaon mixing parameter in the MSbar-scheme at 3 GeV, B_K(MSbar,3 GeV) = 0.535(8)_{stat}(13)_{sys}, and in the RGI scheme, \hat B_K = 0.758(11)_{stat}(19)_{sys}; and the Sommer scales r_1 = 0.323(8)_{stat}(4)_{sys} fm and r_0 = 0.480(10)_{stat}(4)_{sys} (r_1/r_0 = 0.673(11)_{stat}(3)_{sys}). We also obtain values for the SU(2) ChPT effective couplings, \bar{l_3} = 2.91(23)_{stat}(7)_{sys}$ and \bar{l_4} = 3.99(16)_{stat}(9)_{sys}.
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 $\bar{l}_4=4.2(1)$.
Recent analyses of flavor-breaking hadronic-$τ$-decay-based sum rules produce values of $\vert V_{us}\vert$ $\sim 3σ$ low compared to 3-family unitarity expectations. An unresolved systematic issue is the significant variation in $\vert V_{us}\vert$ produced by different prescriptions for treating the slowly converging $D=2$ OPE series. We investigate the reliability of these prescriptions using lattice data for various flavor-breaking correlators and show the fixed-scale prescription is clearly preferred. Preliminary updates of the conventional $τ$-based, and related mixed $τ$-electroproduction-data-based, sum rule analyses incorporating B-factory results for low-multiplicity strange $τ$ decay mode distributions are then performed. Use of the preferred FOPT $D=2$ OPE prescription is shown to significantly reduce the discrepancy between 3-family unitarity expectations and the sum rule results.
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.
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.
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.
A combination of lattice and continuum data for the light-quark V-A correlator, supplemented by results from a chiral sum-rule analysis of the flavor-breaking flavor $ud$-$us$ V-A correlator difference, is shown to make possible a high-precision NNLO determination of the renormalized NLO chiral low-energy constant $L_{10}^r$. Key to this determination is the ability to simultaneously fix the two combinations of NNLO low-energy constants also entering the analysis. With current versions of the strange hadronic $τ$ branching fractions required as input to the flavor-breaking V-A sum rule, we find $L_{10}^r(m_ρ) = -0.00346(29)$. This represents both the best current precision for $L_{10}^r$, and the first NNLO determination having all errors under full control.
We present preliminary results on extractions of the chiral LECs L_10 and C_87 and constraints on the excited pseudoscalar state pi(1300) and pi(1800) decay constants obtained from an analysis of lattice data for the flavor ud light quark V-A correlator. A comparison of the results for the correlator to the corresponding mildly-model-dependent continuum results (based primarily on experimental hadronic tau decay data) is also given
Recent sum rule determinations of |V_us|, employing flavor-breaking combinations of hadronic tau decay data, are significantly lower than either expectations based on 3-family unitarity or determinations from K_ell3 and Gamma[K_mu2]/Gamma[pi_mu2]. We use lattice data to investigate the accuracy/reliability of the OPE representation of the flavor-breaking correlator combination entering the tau decay analyses. The behavior of an alternate correlator combination, constructed to reduce problems associated with the slow convergence of the D = 2 OPE series, and entering an alternate sum rule requiring both electroproduction cross-section and hadronic tau decay data, is also investigated. Preliminary updates of both analyses, with the lessons learned from the lattice data in mind, are also presented.
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.
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.
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.
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.