arXiv subjects

P. A. Boyle

Publications and source records attributed to P. A. Boyle.

At least 37 records · Page 2Linked to original sources

arXiv2014

Domain Wall QCD with Near-Physical Pions

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}.

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arXiv2013

Lattice Input on the Inclusive $τ$ Decay $V_{us}$ Puzzle

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.

hep-ph↗

arXiv2013

Determination of the $A_2$ amplitude of $K \rightarrow ππ$ decays

We review the status of recent calculations by the RBC-UKQCD collaboration of the complex amplitude $A_2$, corresponding to the decay of a kaon to a two pion state with total isospin 2. In particular, we present preliminary results from two new ensembles: $48^3 \times 96$ with $a^{-1}=1.73$ GeV and $64^3 \times 128$ with $a^{-1}=2.3$ GeV, both at physical kinematics. Both ensembles were generated Iwasaki gauge action and domain wall fermion action with 2+1 flavours. These results, in comparison to our earlier ones on a $32^3$ DSDR lattice with $a^{-1}=1.36$ GeV, enable us to significantly reduce the discretization errors. The partial cancellation between the two dominant contractions contributing to Re($A_2$) has been confirmed and we believe that this cancellation is a major contribution to the $ΔI=1/2$ rule.

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arXiv2013

$L_{10}^r$ From a Combined NNLO Lattice, Continuum Analysis of the Light Quark V-A Correlator

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.

hep-ph↗

arXiv2013

Kaon Mixing Beyond the Standard Model

We report on an ongoing calculation of hadronic matrix elements needed to parameterize K-Kbar mixing in generic BSM scenarios, using domain wall fermions (DWF) at two lattice spacings. Recent work by the SWME collaboration shows a significant disagreement with our previous results for two of these quantities. Since the origin of this disagreement is unknown, it is important to reduce the various uncertainties. In this work, we are using N_f=2+1 DWF with Iwasaki gauge action at inverse lattice spacings of 2.31 and 1.75 GeV, with multiple unitary pions on each ensemble, the lightest being 290 and 330 MeV on the finer and coarser of the two ensembles respectively. This extends previous work by the addition of a second lattice spacing (a^{-1}\approx 1.75 GeV). Renormalization is carried out non-perturbatively in the RI/MOM scheme and converted perturbatively to MSbar.

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arXiv2013

A note on Rome-Southampton Renormalization with Smeared Gauge Fields

We have calculated continuum limit step scaling functions of bilinear and four-fermion operators renormalized in a Rome-Southampton scheme using various smearing prescriptions for the gauge field. Also, for the first time, we have calculated non-perturbative anomalous dimensions of operators renormalized in a Rome-Southampton scheme. The effect of such smearing first enters connected fermionic correlation functions via radiative corrections. We use off-shell renormalisation as a probe, and observe that the upper edge of the Rome-Southampton window is reduced by link smearing. This can be interpreted as arising due to the fermions decoupling from the high momentum gluons and we observe that the running of operators with the scale at large lattice momenta shows enhanced lattice artefacts. We find that the effect is greater for HEX smearing than for Stout smearing, but that in both cases additional care must be taken when using off-shell renormalisation with smeared gauge fields compared to thin link simulations.

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arXiv2013

Emerging understanding of the ΔI = 1/2 Rule from Lattice QCD

There has been much speculation as to the origin of the ΔI = 1/2 rule (Re A_0/Re A_2 \simeq 22.5). We find that the two dominant contributions to the ΔI=3/2, K \to ππ correlation functions have opposite signs leading to a significant cancellation. This partial cancellation occurs in our computation of Re A_2 with physical quark masses and kinematics (where we reproduce the experimental value of A_2) and also for heavier pions at threshold. For Re A_0, although we do not have results at physical kinematics, we do have results for pions at zero-momentum with m_π \simeq 420 MeV (Re A_0/Re A_2=9.1(2.1)) and m_π \simeq 330 MeV (Re A_0/Re A_2=12.0(1.7)). The contributions which partially cancel in Re A_2 are also the largest ones in Re A_0, but now they have the same sign and so enhance this amplitude. The emerging explanation of the ΔI=1/2 rule is a combination of the perturbative running to scales of O(2 GeV), a relative suppression of Re A_2 through the cancellation of the two dominant contributions and the corresponding enhancement of Re A_0. QCD and EWP penguin operators make only very small contributions at such scales.

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arXiv2013

Some continuum physics results from the lattice V-A correlator

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

hep-lat↗

arXiv2013

New results from the lattice on the theoretical inputs to the hadronic tau determination of V_us

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.

hep-ph↗

arXiv2012

Neutral kaon mixing beyond the standard model with nf=2+1 chiral fermions

We compute the hadronic matrix elements of the four-quark operators needed for the study of neutral kaon mixing beyond the Standard Model (SM). We use nf=2+1 flavours of domain-wall fermions (DWF) which exhibit good chiral-flavour symmetry. The renormalization is performed non-perturbatively through the RI-MOM scheme and our results are converted perturbatively to MSbar. The computation is performed on a single lattice spacing a=0.086 fm with a lightest unitary pion mass of 290 MeV. The various systematic errors, including the discretisation effects, are estimated and discussed. Our results confirm a previous quenched study, where large ratios of non-SM to SM matrix elements were obtained.

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arXiv2012

Lattice determination of the $K \to (ππ)_{I=2}$ Decay Amplitude $A_2$

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 $K\to(ππ)_{I=0}$ 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 $ε^\prime/ε$ 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 $ε^\prime/ε$ is Re$(ε^\prime/ε)_{\mathrm{EWP}} = -(6.25 \pm 0.44_{\textrm{stat}} \pm 1.19_{\textrm{syst}}) \times 10^{-4}$.

hep-lat↗

arXiv2012

Opening the Rome-Southampton window for operator mixing matrices

We show that the running of operators which mix under renormalization can be computed fully non-perturbatively as a product of continuum step scaling matrices. These step scaling matrices are obtained by taking the "ratio" of Z matrices computed at different energies in an RI-MOM type scheme for which twisted boundary conditions are an essential ingredient. Our method allows us to relax the bounds of the Rome-Southampton window. We also explain why such a method is important in view of the light quark physics program of the RBC-UKQCD collaborations. To illustrate our method, using n_f=2+1 domain-wall fermions, we compute the non-perturbative running matrix of four-quark operators needed in K->pipi decay and neutral kaon mixing. Our results are then compared to perturbation theory.

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arXiv2011

Non-perturbative running and renormalization of kaon four-quark operators with nf=2+1 domain-wall fermions

We compute the renormalization factors of four-quark operators needed for the study of $K\toππ$ decay in the $ΔI=3/2$ channel. We evaluate the Z-factors at a low energy scale ($μ_0=1.145 \GeV$) using four different non-exceptional RI-SMOM schemes on a large, coarse lattice ($a\sim 0.14\fm$) on which the bare matrix elements are also computed. Then we compute the universal, non-perturbative, scale evolution matrix of these renormalization factors between $μ_0$ and $3\GeV$. We give the numerical results for the different steps of the computation in two different non-exceptional lattice schemes, and the connection to $\msbar$ at $3\GeV$ is made using one-loop perturbation theory.

hep-lat↗

arXiv2011

The $K\to(ππ)_{I=2}$ Decay Amplitude from Lattice QCD

We report on the first realistic \emph{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 Re$A_2=(1.436\pm 0.063_{\textrm{stat}}\pm 0.258_{\textrm{syst}})\,10^{-8}\,\textrm{GeV}$ in good agreement with the experimental result and for the hitherto unknown imaginary part we find {Im}$\,A_2=-(6.83 \pm 0.51_{\textrm{stat}} \pm 1.30_{\textrm{syst}})\,10^{-13}\,{\rm GeV}$. Moreover combining our result for Im\,$A_2$ with experimental values of Re\,$A_2$, Re\,$A_0$ and $ε^\prime/ε$, we obtain the following value for the unknown ratio Im\,$A_0$/Re\,$A_0$ within the Standard Model: $\mathrm{Im}\,A_0/\mathrm{Re}\,A_0=-1.63(19)_{\mathrm{stat}}(20)_{\mathrm{syst}}\times10^{-4}$. One consequence of these results is that the contribution from Im\,$A_2$ to the direct CP violation parameter $ε^{\prime}$ (the so-called Electroweak Penguin, EWP, contribution) is Re$(ε^\prime/ε)_{\mathrm{EWP}} = -(6.52 \pm 0.49_{\textrm{stat}} \pm 1.24_{\textrm{syst}}) \times 10^{-4}$. 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.

hep-lat↗

arXiv2011

Continuum Limit Physics from 2+1 Flavor Domain Wall QCD

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 $π$ and $K$ mesons and the $Ω$ 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 $f_π=124(2)_{\rm stat}(5)_{\rm syst}$\,MeV, $f_K/f_π=1.204(7)(25)$ 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, $[Σ^{\msbar}(2 {\rm GeV})]^{1/3} = 256(6)\; {\rm MeV}$, where $Σ$ is the chiral condensate, the Sommer scale $r_0=0.487(9)$\,fm and $r_1=0.333(9)$\,fm.

hep-lat↗

arXiv2011

$K$ to $ππ$ Decay amplitudes from Lattice QCD

We report a direct lattice calculation of the $K$ to $ππ$ decay matrix elements for both the $ΔI=1/2$ 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 $K\toππ$ 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 $Δ=1/2$ rule and testing the standard model of CP violation in the kaon system.

hep-lat↗

arXiv2011

Step Scaling with off-shell renormalisation

We make use of twisted boundary conditions for off-shell Rome-Southampton renormalisation. This allows to define the vertex function precisely, at a fixed physical momentum that need not be one of the Fourier modes of a simulation. This definition includes choosing the orientation with respect to lattice axes, and so lattice artefacts including ${\cal O}(4)$ breaking then have a valid Symanzik expansion. Excellent statistical precision is afforded by volume plane-wave sources, enabling both a theoretically and statistically clean continuum limit to be taken. Thereafter all $p^2$ dependence can be unambiguously identified as continuum anomolous running. The use of non-exceptional momenta has been found to greatly reduce the dependence of non-perturbative vertex functions on both mass and $p^2$. We illustrate how this can be developed into a practical scheme for step-scaling the RI/SMOM approach with initial results. The size of the possible steps is continuous, rather than discrete allowing one to take arbitrarily small steps, and the scheme inherits from RI/MOM the property that it is easy to implement for general operators.

hep-lat↗

arXiv2010

Continuum Limit of $B_K$ from 2+1 Flavor Domain Wall QCD

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 $B_K^{\msbar}(3 GeV) = 0.529(5)_{stat}(15)_χ(2)_{FV}(11)_{NPR}$. This corresponds to $\hat{B}_K = 0.749(7)_{stat}(21)_χ(3)_{FV}(15)_{NPR}$. Adding all sources of error in quadrature we obtain $\hat{B}_K = 0.749(27)_{combined}$, with an overall combined error of 3.6%.

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