R. D. Mawhinney

Columbia University, New York City, NY, USA

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Publications (43)29.09 Total impact

  • Article: Chiral transition and U (1) _ {A} symmetry restoration from lattice QCD using domain wall fermions
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    ABSTRACT: We present results on both the restoration of the spontaneously broken chiral symmetry and the effective restoration of the anomalously broken U(1)A symmetry in finite temperature QCD at zero chemical potential using lattice QCD. We employ domain wall fermions on lattices with fixed temporal extent Nτ=8 and spatial extent Nσ=16 in a temperature range of T=139–195 MeV, corresponding to lattice spacings of a≈0.12–0.18 fm. In these calculations, we include two degenerate light quarks and a strange quark at fixed pion mass mπ=200 MeV. The strange quark mass is set near its physical value. We also present results from a second set of finite temperature gauge configurations at the same volume and temporal extent with slightly heavier pion mass. To study chiral symmetry restoration, we calculate the chiral condensate, the disconnected chiral susceptibility, and susceptibilities in several meson channels of different quantum numbers. To study U(1)A restoration, we calculate spatial correlators in the scalar and pseudoscalar channels, as well as the corresponding susceptibilities. Furthermore, we also show results for the eigenvalue spectrum of the Dirac operator as a function of temperature, which can be connected to both U(1)A and chiral symmetry restoration via Banks-Casher relations.
    Phys. Rev. D. 11/2012; 86(9).
  • Article: Domain Wall QCD with Near-Physical Pions
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    ABSTRACT: 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_\pi=127(3)_{stat}(3)_{sys} MeV and f_K = 152(3)_{stat}(2)_{sys} MeV respectively (f_K/f_\pi = 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}.
    08/2012;
  • Article: Lattice determination of the $K \to (\pi\pi)_{I=2}$ Decay Amplitude $A_2$
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    ABSTRACT: We describe the computation of the amplitude A_2 for a kaon to decay into two pions with isospin I=2. The results presented in the letter Phys.Rev.Lett. 108 (2012) 141601 from an analysis of 63 gluon configurations are updated to 146 configurations giving Re$A_2=1.381(46)_{\textrm{stat}}(258)_{\textrm{syst}} 10^{-8}$ GeV and Im$A_2=-6.54(46)_{\textrm{stat}}(120)_{\textrm{syst}}10^{-13}$ GeV. Re$A_2$ is in good agreement with the experimental result, whereas the value of Im$A_2$ was hitherto unknown. We are also working towards a direct computation of the $K\to(\pi\pi)_{I=0}$ amplitude $A_0$ but, within the standard model, our result for Im$A_2$ can be combined with the experimental results for Re$A_0$, Re$A_2$ and $\epsilon^\prime/\epsilon$ to give Im$A_0/$Re$A_0= -1.61(28)\times 10^{-4}$ . Our result for Im\,$A_2$ implies that the electroweak penguin (EWP) contribution to $\epsilon^\prime/\epsilon$ is Re$(\epsilon^\prime/\epsilon)_{\mathrm{EWP}} = -(6.25 \pm 0.44_{\textrm{stat}} \pm 1.19_{\textrm{syst}}) \times 10^{-4}$.
    06/2012;
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    Article: Meson screening masses from lattice QCD with two light quarks and one strange quark
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    ABSTRACT: We present results for screening masses of mesons built from light and strange quarks in the temperature range of approximately between 140MeV to 800MeV. The lattice computations were performed with 2+1 dynamical light and strange flavors of improved (p4) staggered fermions along a line of constant physics defined by a pion mass of about 220MeV and a kaon mass of 500MeV. The lattices had temporal extents N τ =4, 6 and 8 and aspect ratios of N s /N τ ≥4. At least up to a temperature of 140MeV the pseudo-scalar screening mass remains almost equal to the corresponding zero temperature pseudo-scalar (pole) mass. At temperatures around 3T c (T c being the transition temperature) the continuum extrapolated pseudo-scalar screening mass approaches very close to the free continuum result of 2πT from below. On the other hand, at high temperatures the vector screening mass turns out to be larger than the free continuum value of 2πT. The pseudo-scalar and the vector screening masses do not become degenerate even for a temperature as high as 4T c . Using these mesonic spatial correlation functions we have also investigated the restoration of chiral symmetry and the effective restoration of the axial symmetry. We have found that the vector and the axial-vector screening correlators become degenerate, indicating chiral symmetry restoration, at a temperature which is consistent with the QCD transition temperature obtained in previous studies. On the other hand, the pseudo-scalar and the scalar screening correlators become degenerate only at temperatures larger than 1.3T c , indicating that the effective restoration of the axial symmetry takes place at a temperature larger than the QCD transition temperature.
    European Physical Journal C 04/2012; 71(2):1-13. · 3.63 Impact Factor
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    Article: K→(ππ)(I=2) decay amplitude from lattice QCD.
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    ABSTRACT: We report on the first realistic ab initio calculation of a hadronic weak decay, that of the amplitude A(2) for a kaon to decay into two π mesons with isospin 2. We find ReA(2)=(1.436±0.063(stat)±0.258(syst))10(-8) GeV in good agreement with the experimental result and for the hitherto unknown imaginary part we find ImA(2)=-(6.83±0.51(stat)±1.30(syst))10(-13) GeV. Moreover combining our result for ImA(2) with experimental values of ReA(2), ReA(0), and ε'/ε, we obtain the following value for the unknown ratio ImA(0)/ReA(0) within the standard model: ImA(0)/ReA(0)=-1.63(19)(stat)(20(syst)×10(-4). One consequence of these results is that the contribution from ImA(2) to the direct CP violation parameter ε' (the so-called Electroweak Penguin contribution) is Re(ε'/ε)(EWP)=-(6.52±0.49(stat)±1.24(syst))×10(-4). We explain why this calculation of A(2) represents a major milestone for lattice QCD and discuss the exciting prospects for a full quantitative understanding of CP violation in kaon decays.
    Physical Review Letters 04/2012; 108(14):141601. · 7.37 Impact Factor
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    Article: $K$ to $\pi\pi$ Decay amplitudes from Lattice QCD
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    ABSTRACT: We report a direct lattice calculation of the $K$ to $\pi\pi$ decay matrix elements for both the $\Delta I=1/2$ and 3/2 amplitudes $A_0$ and $A_2$ on 2+1 flavor, domain wall fermion, $16^3\times32\times16$ lattices. This is a complete calculation in which all contractions for the required ten, four-quark operators are evaluated, including the disconnected graphs in which no quark line connects the initial kaon and final two-pion states. These lattice operators are non-perturbatively renormalized using the Rome-Southampton method and the quadratic divergences are studied and removed. This is an important but notoriously difficult calculation, requiring high statistics on a large volume. In this paper we take a major step towards the computation of the physical $K\to\pi\pi$ amplitudes by performing a complete calculation at unphysical kinematics with pions of mass 422\,MeV at rest in the kaon rest frame. With this simplification we are able to resolve Re$(A_0)$ from zero for the first time, with a 25% statistical error and can develop and evaluate methods for computing the complete, complex amplitude $A_0$, a calculation central to understanding the $\Delta =1/2$ rule and testing the standard model of CP violation in the kaon system.
    06/2011;
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    Article: Continuum Limit of $B_K$ from 2+1 Flavor Domain Wall QCD
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    ABSTRACT: We determine the neutral kaon mixing matrix element $B_K$ in the continuum limit with 2+1 flavors of domain wall fermions, using the Iwasaki gauge action at two different lattice spacings. These lattice fermions have near exact chiral symmetry and therefore avoid artificial lattice operator mixing. We introduce a significant improvement to the conventional NPR method in which the bare matrix elements are renormalized non-perturbatively in the RI-MOM scheme and are then converted into the MSbar scheme using continuum perturbation theory. In addition to RI-MOM, we introduce and implement four non-exceptional intermediate momentum schemes that suppress infrared non-perturbative uncertainties in the renormalization procedure. We compute the conversion factors relating the matrix elements in this family of RI-SMOM schemes and MSbar at one-loop order. Comparison of the results obtained using these different intermediate schemes allows for a more reliable estimate of the unknown higher-order contributions and hence for a correspondingly more robust estimate of the systematic error. We also apply a recently proposed approach in which twisted boundary conditions are used to control the Symanzik expansion for off-shell vertex functions leading to a better control of the renormalization in the continuum limit. We control chiral extrapolation errors by considering both the NLO SU(2) chiral effective theory, and an analytic mass expansion. We obtain $B_K^{\msbar}(3 GeV) = 0.529(5)_{stat}(15)_\chi(2)_{FV}(11)_{NPR}$. This corresponds to $\hat{B}_K = 0.749(7)_{stat}(21)_\chi(3)_{FV}(15)_{NPR}$. Adding all sources of error in quadrature we obtain $\hat{B}_K = 0.749(27)_{combined}$, with an overall combined error of 3.6%.
    12/2010;
  • Article: η and η' mesons from lattice QCD.
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    ABSTRACT: The large mass of the ninth pseudoscalar meson, the η', is believed to arise from the combined effects of the axial anomaly and the gauge field topology present in QCD. We report a realistic, 2+1-flavor, lattice QCD calculation of the η and η' masses and mixing which confirms this picture. The physical eigenstates show small octet-singlet mixing with a mixing angle of θ=-14.1(2.8)°. Extrapolation to the physical light quark mass gives, with statistical errors only, mη=573(6) MeV and mη'=947(142) MeV, consistent with the experimental values of 548 and 958 MeV.
    Physical Review Letters 12/2010; 105(24):241601. · 7.37 Impact Factor
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    Article: Continuum Limit Physics from 2+1 Flavor Domain Wall QCD
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    ABSTRACT: We present physical results obtained from simulations using 2+1 flavors of domain wall quarks and the Iwasaki gauge action at two values of the lattice spacing $a$, ($a^{-1}$=\,1.73\,(3)\,GeV and $a^{-1}$=\,2.28\,(3)\,GeV). On the coarser lattice, with $24^3\times 64\times 16$ points, the analysis of ref.[1] is extended to approximately twice the number of configurations. The ensembles on the finer $32^3\times 64\times 16$ lattice are new. We explain how we use lattice data obtained at several values of the lattice spacing and for a range of quark masses in combined continuum-chiral fits in order to obtain results in the continuum limit and at physical quark masses. We implement this procedure at two lattice spacings, with unitary pion masses in the approximate range 290--420\,MeV (225--420\,MeV for partially quenched pions). We use the masses of the $\pi$ and $K$ mesons and the $\Omega$ baryon to determine the physical quark masses and the values of the lattice spacing. While our data are consistent with the predictions of NLO SU(2) chiral perturbation theory, they are also consistent with a simple analytic ansatz leading to an inherent uncertainty in how best to perform the chiral extrapolation that we are reluctant to reduce with model-dependent assumptions about higher order corrections. Our main results include $f_\pi=124(2)_{\rm stat}(5)_{\rm syst}$\,MeV, $f_K/f_\pi=1.204(7)(25)$ where $f_K$ is the kaon decay constant, $m_s^{\bar{\textrm{MS}}}(2\,\textrm{GeV})=(96.2\pm 2.7)$\,MeV and $m_{ud}^{\bar{\textrm{MS}}}(2\,\textrm{GeV})=(3.59\pm 0.21)$\,MeV\, ($m_s/m_{ud}=26.8\pm 1.4$) where $m_s$ and $m_{ud}$ are the mass of the strange-quark and the average of the up and down quark masses respectively, $[\Sigma^{\msbar}(2 {\rm GeV})]^{1/3} = 256(6)\; {\rm MeV}$, where $\Sigma$ is the chiral condensate, the Sommer scale $r_0=0.487(9)$\,fm and $r_1=0.333(9)$\,fm.
    11/2010;
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    Article: Meson screening masses from lattice QCD with two light and the strange quark
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    ABSTRACT: We present results for screening masses of mesons built from light and strange quarks in the temperature range of approximately between 140 MeV to 800 MeV. The lattice computations were performed with 2+1 dynamical light and strange flavors of improved (p4) staggered fermions along a line of constant physics defined by a pion mass of about 220 MeV and a kaon mass of 500 MeV. The lattices had temporal extents Nt = 4, 6 and 8 and aspect ratios of Ns / Nt \geq 4. At least up to a temperature of 140 MeV the pseudo-scalar screening mass remains almost equal to the corresponding zero temperature pseudo-scalar (pole) mass. At temperatures around 3Tc (Tc being the transition temperature) the continuum extrapolated pseudo-scalar screening mass approaches very close to the free continuum result of 2 \pi T from below. On the other hand, at high temperatures the vector screening mass turns out to be larger than the free continuum value of 2 \pi T. The pseudo-scalar and the vector screening masses do not become degenerate even for a temperature as high as 4Tc. Using these mesonic spatial correlation functions we have also investigated the restoration of chiral symmetry and the effective restoration of the axial symmetry. We have found that the vector and the axial-vector screening correlators become degenerate, indicating chiral symmetry restoration, at a temperature which is consistent with the QCD transition temperature obtained in previous studies. On the other hand, the pseudo-scalar and the scalar screening correlators become degenerate only at temperatures larger than 1.3Tc, indicating that the effective restoration of the axial symmetry takes place at a temperature larger than the QCD transition temperature.
    10/2010;
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    Article: The $\eta$ and $\eta^\prime$ mesons from Lattice QCD
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    ABSTRACT: The large mass of the ninth pseudoscalar meson, the $\eta^\prime$, is believed to arise from the combined effects of the axial anomaly and the gauge field topology present in QCD. We report a realistic, 2+1 flavor, lattice QCD calculation of the $\eta$ and $\eta^\prime$ masses and mixing which confirms this picture. The physical eigenstates show small octet-singlet mixing with a mixing angle of $\theta = -14.1(2.8)^\circ$. Extrapolation to physical light quark mass gives, with statistical errors only, $m_\eta=573(6)$ MeV and $m_{\eta^\prime}=947(142)$ MeV, consistent with the experimental values of 548 MeV and 958 MeV. Comment: 4 pages, 5 figures
    02/2010;
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    Article: The finite temperature QCD using 2+1 flavors of domain wall fermions at N_t = 8
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    ABSTRACT: We study the region of the QCD phase transition using 2+1 flavors of domain wall fermions (DWF) and a $16^3 \times 8$ lattice volume with a fifth dimension of $L_s = 32$. The disconnected light quark chiral susceptibility, quark number susceptibility and the Polyakov loop suggest a chiral and deconfining crossover transition lying between 155 and 185 MeV for our choice of quark mass and lattice spacing. In this region the lattice scale deduced from the Sommer parameter $r_0$ is $a^{-1} \approx 1.3$ GeV, the pion mass is $\approx 300$ MeV and the kaon mass is approximately physical. The peak in the chiral susceptibility implies a pseudo critical temperature $T_c = 171(10)(17)$ MeV where the first error is associated with determining the peak location and the second with our unphysical light quark mass and non-zero lattice spacing. The effects of residual chiral symmetry breaking on the chiral condensate and disconnected chiral susceptibility are studied using several values of the valence $L_s$. Comment: 41 pages, 10 tables, 13 figures
    11/2009;
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    Article: Equation of State for physical quark masses
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    ABSTRACT: We calculate the QCD equation of state for temperatures corresponding to the transition region with physical mass values for two degenerate light quark flavors and a strange quark using an improved staggered fermion action (p4-action) on lattices with temporal extent N_tau=8. We compare our results with previous calculations performed at twice larger values of the light quark masses as well as with results obtained from a resonance gas model calculation. We also discuss the deconfining and chiral aspects of the QCD transition in terms of renormalized Polyakov loop, strangeness fluctuations and subtracted chiral condensate. We show that compared to the calculations performed at twice larger value of the light quark mass the transition region shifts by about 5 MeV toward smaller temperatures Comment: 7 pages, LaTeX, 6 figures; minor corrections, typos corrected, references added
    11/2009;
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    Article: Equation of state and QCD transition at finite temperature
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    ABSTRACT: We calculate the equation of state in 2+1 flavor QCD at finite temperature with physical strange quark mass and almost physical light quark masses using lattices with temporal extent Nτ=8. Calculations have been performed with two different improved staggered fermion actions, the asqtad and p4 actions. Overall, we find good agreement between results obtained with these two O(a2) improved staggered fermion discretization schemes. A comparison with earlier calculations on coarser lattices is performed to quantify systematic errors in current studies of the equation of state. We also present results for observables that are sensitive to deconfining and chiral aspects of the QCD transition on Nτ=6 and 8 lattices. We find that deconfinement and chiral symmetry restoration happen in the same narrow temperature interval. In an appendix we present a simple parametrization of the equation of state that can easily be used in hydrodynamic model calculations. In this parametrization we include an estimate of current uncertainties in the lattice calculations which arise from cutoff and quark mass effects.
    Phys. Rev. D. 07/2009; 80(1).
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    Article: Physical results from 2+1 flavor domain wall QCD and SU(2) chiral perturbation theory
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    ABSTRACT: We have simulated QCD using 2+1 flavors of domain wall quarks and the Iwasaki gauge action on a (2.74 fm)3 volume with an inverse lattice scale of a-1=1.729(28) GeV. The up and down (light) quarks are degenerate in our calculations and we have used four values for the ratio of light quark masses to the strange (heavy) quark mass in our simulations: 0.217, 0.350, 0.617, and 0.884. We have measured pseudoscalar meson masses and decay constants, the kaon bag parameter BK, and vector meson couplings. We have used SU(2) chiral perturbation theory, which assumes only the up and down quark masses are small, and SU(3) chiral perturbation theory to extrapolate to the physical values for the light quark masses. While next-to-leading order formulas from both approaches fit our data for light quarks, we find the higher-order corrections for SU(3) very large, making such fits unreliable. We also find that SU(3) does not fit our data when the quark masses are near the physical strange quark mass. Thus, we rely on SU(2) chiral perturbation theory for accurate results. We use the masses of the Ω baryon, and the π and K mesons to set the lattice scale and determine the quark masses. We then find fπ=124.1(3.6)stat(6.9)syst MeV, fK=149.6(3.6)stat(6.3)syst MeV, and fK/fπ=1.205(0.018)stat(0.062)syst. Using nonperturbative renormalization to relate lattice regularized quark masses to regularization independent momentum scheme masses, and perturbation theory to relate these to MS̅ , we find mudMS̅ (2 GeV)=3.72(0.16)stat(0.33)ren(0.18)syst MeV, msMS̅ (2 GeV)=107.3(4.4)stat(9.7)ren(4.9)syst MeV, and m˜ud∶m˜s=1∶28.8(0.4)stat(1.6)syst. For the kaon bag parameter, we find BKMS̅ (2 GeV)=0.524(0.010)stat(0.013)ren(0.025)syst. Finally, for the ratios of the couplings of the vector mesons to the vector and tensor currents (fV and fVT, respectively) in the MS̅ scheme at 2 GeV we obtain fρT/fρ=0.687(27); fK*T/fK*=0.712(12), and fϕT/fϕ=0.750(8).
    Phys. Rev. D. 12/2008; 78(11).
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    Article: Baryon Number, Strangeness and Electric Charge Fluctuations in QCD at High Temperature
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    ABSTRACT: We analyze baryon number, strangeness and electric charge fluctuations as well as their correlations in QCD at high temperature. We present results obtained from lattice calculations performed with an improved staggered fermion action (p4-action) at two values of the lattice cut-off with almost physical up and down quark masses and a physical value for the strange quark mass. We compare these results, with an ideal quark gas at high temperature and a hadron resonance gas model at low temperature. We find that fluctuations and correlations are well described by the former already for temperatures about 1.5 times the transition temperature. At low temperature qualitative features of the lattice results are quite well described by a hadron resonance gas model. Higher order cumulants, which become increasingly sensitive to the light pions, however show deviations from a resonance gas in the vicinity of the transition temperature. Comment: 11 pages, 8 figures; revised and published version
    11/2008;
  • Article: Nonperturbative renormalization of quark bilinear operators and B_ {K} using domain wall fermions
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    ABSTRACT: We present a calculation of the renormalization coefficients of the quark bilinear operators and the K-K̅ mixing parameter BK. The coefficients relating the bare lattice operators to those in the RI/MOM scheme are computed nonperturbatively and then matched perturbatively to the MS̅ scheme. The coefficients are calculated on the RBC/UKQCD 2+1 flavor dynamical lattice configurations. Specifically we use a 163×32 lattice volume, the Iwasaki gauge action at β=2.13 and domain wall fermions with Ls=16.
    Phys. Rev. D. 09/2008; 78(5).
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    Article: The Spatial String Tension and Dimensional Reduction in QCD
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    ABSTRACT: We calculate the spatial string tension in (2+1) flavor QCD with physical strange quark mass and almost physical light quark masses using lattices with temporal extent N_tau=4,6 and 8. We compare our results on the spatial string tension with predictions of dimensionally reduced QCD. This suggests that also in the presence of light dynamical quarks dimensional reduction works well down to temperatures 1.5T_c.
    07/2008;
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    Article: Neutral-kaon mixing from (2+1)-flavor domain-wall QCD.
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    ABSTRACT: We present the first results for neutral-kaon mixing using (2+1)-flavors of domain-wall fermions. A new approach is used to extrapolate to the physical up and down quark masses from our numerical studies with pion masses in the range 240-420 MeV; only SU(2)_{L}xSU(2)_{R} chiral symmetry is assumed and the kaon is not assumed to be light. Our main result is B_{K};{MS[over ]}(2 GeV)=0.524(10)(28) where the first error is statistical and the second incorporates estimates for all systematic errors.
    Physical Review Letters 02/2008; 100(3):032001. · 7.37 Impact Factor
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    Article: Non-perturbative renormalization of quark bilinear operators and B_K using domain wall fermions
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    ABSTRACT: We present a calculation of the renormalization coefficients of the quark bilinear operators and the K-Kbar mixing parameter B_K. The coefficients relating the bare lattice operators to those in the RI/MOM scheme are computed non-perturbatively and then matched perturbatively to the MSbar scheme. The coefficients are calculated on the RBC/UKQCD 2+1 flavor dynamical lattice configurations. Specifically we use a 16^3 x 32 lattice volume, the Iwasaki gauge action at beta=2.13 and domain wall fermions with L_s=16.
    01/2008;