We present results at one-loop order of perturbation theory for various improvement coefficients in on-shell O(
a) improved lattice QCD. In particular we determine the additive counterterm required ...for on-shell improvement of the isovector vector current. Employing a general mass-independent renormalization scheme we also obtain the coefficients of the O(
a) counterterms which are proportional to the quark mass in the improved isovector pseudo-scalar, axial vector and vector operators. In the latter case a comparison with a recent non-perturbative study is made.
The coefficients multiplying the counterterms required for O(
a) improvement of the action and the isovector axial current in lattice QCD are computed non-perturbatively, in the quenched ...approximation and for bare gauge couplings
g
0 i range 0 ⩽
g
0 ⩽ 1. A finite-size method based on the Schrödinger functional is employed, which enables us to perform all calculations at z nearly zero quark mass. As a by-product the critical hopping parameter
κ
c is obtained at all couplings considered.
The dominant cutoff effects in lattice QCD with Wilson quarks are proportional to the lattice spacing
a. In particular, the isovector axial current satisfies the PCAC relation only up to such ...effects. Following a suggestion of Symanzik, they can be cancelled by adding local O(
a) correction terms to the action and the axial current. We here address a number of theoretical issues in connection with the O(
a) improvement of lattice QCD and then show that chiral symmetry can be used to fix the coefficients multiplying the correction terms.
The COPD Assessment Test (CAT) has been recently developed to quantify COPD impact in routine practice. However, no relationship with other measures in the Global Initiative for Obstructive Lung ...Disease (GOLD) strategy has been evaluated. The present study aimed to evaluate the relationship of the CAT with other GOLD multidimensional axes, patient types, and the number of comorbidities.
This was a cross-sectional analysis of the Clinical presentation, diagnosis, and course of chronic obstructive pulmonary disease (On-Sint) study. The CAT score was administered to all participants at the inclusion visit. A GOLD 2011 strategy consisting of modified Medical Research Council scale (MRC) scores was devised to study the relationship between the CAT, and GOLD 2011 axes and patient types. The relationship with comorbidities was assessed using the Charlson comorbidity index, grouped as zero, one to two, and three or more.
The CAT questionnaire was completed by 1,212 patients with COPD. The CAT maintained a relationship with all the three axes, with a ceiling effect for dyspnea and no distinction between mild and moderate functional impairment. The CAT score increased across GOLD 2011 patient types A-D, with similar scores for types B and C. Within each GOLD 2011 patient type, there was a considerably wide distribution of CAT values.
Our study indicates a correlation between CAT and the GOLD 2011 classification axes as well as the number of comorbidities. The CAT score can help clinicians, as a complementary tool to evaluate patients with COPD within the different GOLD patient types.
In a previous publication we have constructed the Schrödinger functional in Wilson's lattice QCD. It was found that the naive continuum limit leads to a well-defined classical continuum theory. ...Starting from the latter, a formal continuum definition of the Schrödinger functional is given and its saddle point expansion is carried out to one-loop order of perturbation theory. Dimensional regularization and heat kernel techniques are used to determine the one-loop divergences. These are partly canceled by the usual renormalizations of the quark mass and the coupling constant in QCD. An additional divergence can be absorbed in a multiplicative renormalization of the quark boundary fields. The corresponding boundary counterterm is a local polynomial in the fields, so that we confirm a general expectation of Symanzik.
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