Tables of SU(3) Isoscalar Factors

The Clebsch-Gordan coefficients of $SU(3)$ are useful in calculations involving baryons and mesons, as well as in calculations involving arbitrary numbers of quarks. For the latter case, one needs the coupling constants between states of nonintegral hypercharges. The existing published tables are insufficient for many such applications, and therefore we have compiled this collection. This report supplies the isoscalar factors required to reconstruct the Clebsch-Gordan coefficients for a large set of products of representations.Comment: LaTeX, 51 pages, no figures, MACROS INCLUDED IN NEW FIL

D-Meson Mixing in Broken SU(3)

A fit of amplitudes to the experimental branching ratios to two mesons is used to construct a new estimate of neutral $D$ mixing which includes $SU(3)$ breaking. The result is dominated by the experimental uncertainties. This suggests that the charm sector may not be as sensitive to new physics as previously thought and that long-distance calculations may not be useful.Comment: 12 pages, LaTeX, no figure

Program for Generating Tables of SU(3) Coupling Coefficients

A C-Language program which tabulates the isoscalar factors and Clebsch-Gordan coefficients for products of representations in SU(3) is presented. These are efficiently computed using recursion relations, and the results are presented in exact precision as square roots of rational numbers. Output is in LaTeX format.Comment: LaTeX, 29 pages, no figure

Pascal Program for Generating Tables of SU(3) Clebsch-Gordan Coefficients

Pascal routines are provided that generate representations of the group $SU(3)$ and tabulate the Clebsch-Gordan coefficients in the products of representations.Comment: 14 pages, LBL-3573

Nonleptonic Two-Body Decays of D Mesons in Broken SU(3)

Decays of the D mesons to two pseudoscalars, to two vectors, and to pseudoscalar plus vector are discussed in the context of broken flavor SU(3). A few assumptions are used to reduce the number of parameters. Amplitudes are fit to the available data, and predictions of branching ratios for unmeasured modes are made.Comment: LaTeX, 24 page

Comparison of intra-articular injections of Hyaluronic Acid and Corticosteroid in the treatment of Osteoarthritis of the hip in comparison with intra-articular injections of Bupivacaine. Design of a prospective, randomized, controlled study with blinding of the patients and outcome assessors

<p>Abstract</p> <p>Background</p> <p>Although intra-articular hyaluronic acid is well established as a treatment for osteoarthritis of the knee, its use in hip osteoarthritis is not based on large randomized controlled trials. There is a need for more rigorously designed studies on hip osteoarthritis treatment as this subject is still very much under debate.</p> <p>Methods/Design</p> <p>Randomized, controlled trial with a three-armed, parallel-group design. Approximately 315 patients complying with the inclusion and exclusion criteria will be randomized into one of the following treatment groups: infiltration of the hip joint with hyaluronic acid, with a corticosteroid or with 0.125% bupivacaine.</p> <p>The following outcome measure instruments will be assessed at baseline, i.e. before the intra-articular injection of one of the study products, and then again at six weeks, 3 and 6 months after the initial injection: Pain (100 mm VAS), Harris Hip Score and HOOS, patient assessment of their clinical status (worse, stable or better then at the time of enrollment) and intake of pain rescue medication (number per week). In addition patients will be asked if they have complications/adverse events. The six-month follow-up period for all patients will begin on the date the first injection is administered.</p> <p>Discussion</p> <p>This randomized, controlled, three-arm study will hopefully provide robust information on two of the intra-articular treatments used in hip osteoarthritis, in comparison to bupivacaine.</p> <p>Trial registration</p> <p>NCT01079455</p

Subsequent Surgery After Revision Anterior Cruciate Ligament Reconstruction: Rates and Risk Factors From a Multicenter Cohort

BACKGROUND: While revision anterior cruciate ligament reconstruction (ACLR) can be performed to restore knee stability and improve patient activity levels, outcomes after this surgery are reported to be inferior to those after primary ACLR. Further reoperations after revision ACLR can have an even more profound effect on patient satisfaction and outcomes. However, there is a current lack of information regarding the rate and risk factors for subsequent surgery after revision ACLR. PURPOSE: To report the rate of reoperations, procedures performed, and risk factors for a reoperation 2 years after revision ACLR. STUDY DESIGN: Case-control study; Level of evidence, 3. METHODS: A total of 1205 patients who underwent revision ACLR were enrolled in the Multicenter ACL Revision Study (MARS) between 2006 and 2011, composing the prospective cohort. Two-year questionnaire follow-up was obtained for 989 patients (82%), while telephone follow-up was obtained for 1112 patients (92%). If a patient reported having undergone subsequent surgery, operative reports detailing the subsequent procedure(s) were obtained and categorized. Multivariate regression analysis was performed to determine independent risk factors for a reoperation. RESULTS: Of the 1112 patients included in the analysis, 122 patients (11%) underwent a total of 172 subsequent procedures on the ipsilateral knee at 2-year follow-up. Of the reoperations, 27% were meniscal procedures (69% meniscectomy, 26% repair), 19% were subsequent revision ACLR, 17% were cartilage procedures (61% chondroplasty, 17% microfracture, 13% mosaicplasty), 11% were hardware removal, and 9% were procedures for arthrofibrosis. Multivariate analysis revealed that patients aged <20 years had twice the odds of patients aged 20 to 29 years to undergo a reoperation. The use of an allograft at the time of revision ACLR (odds ratio [OR], 1.79; P = .007) was a significant predictor for reoperations at 2 years, while staged revision (bone grafting of tunnels before revision ACLR) (OR, 1.93; P = .052) did not reach significance. Patients with grade 4 cartilage damage seen during revision ACLR were 78% less likely to undergo subsequent operations within 2 years. Sex, body mass index, smoking history, Marx activity score, technique for femoral tunnel placement, and meniscal tearing or meniscal treatment at the time of revision ACLR showed no significant effect on the reoperation rate. CONCLUSION: There was a significant reoperation rate after revision ACLR at 2 years (11%), with meniscal procedures most commonly involved. Independent risk factors for subsequent surgery on the ipsilateral knee included age <20 years and the use of allograft tissue at the time of revision ACLR

Tables of SU(3) isoscalar factors

Abstract The Clebsch-Gordan coefficients of SU (3) are useful in calculations involving baryons and mesons, as well as in calculations involving arbitrary numbers of quarks. For the latter case, one needs the coupling constants between states of nonintegral hypercharges. The existing published tables are insufficient for many such applications, and therefore we have compiled this collection. This report supplies the isoscalar factors required to reconstruct the Clebsch-Gordan coefficients for a large set of products of representations. * This work was supported by the Director, Office of Energy Research, Office of High Energy and Nuclear Physics, Division of High Energy Physics of the U.S. Department of Energy under Contract DE-AC03-76SF00098. † Electronic address: [email protected]. Disclaimer This document was prepared as an account of work sponsored by the United States Government. While this document is believed to contain correct information, neither the United States Government nor any agency thereof, nor The Regents of the University of California, nor any of their employees, makes any warranty, express or implied, or assumes any legal liability or responsibility for the accuracy, completeness, or usefulness of any information, apparatus, product, or process disclosed, or represents that its use would not infringe privately owned rights. Reference herein to any specific commercial products process, or service by its trade name, trademark, manufacturer, or otherwise, does not necessarily constitute or imply its endorsement, recommendation, or favoring by the United States Government or any agency thereof, or A few things must be discussed. Our phase conventions are explained in Section 1. In Section 2 we show the notation of the tables and explain how to reconstruct the ClebschGordan coefficients from the isoscalar factors. There we also present some symmetry relations that allow us to omit some tables. Finally, the tables themselves are presented. The tables of Clebsch-Gordan tables that were reduced to the present set of isoscalar tables were generated by computer. Most of the routines are described in Conventions The representations of SU (3) can be thought of as consisting of SU (2) multiplets (henceforth called isomultiplets), each at a specific hypercharge. We have adopted the Condon-Shortley phase convention For the relative phases between isomultiplets in a given representation, we have adopted the de Swart phase convention In a few cases, there is an arbitrary choice in the construction of representations that are multiply degenerate. By this we mean that two or more of the same representation occur in the same Clebsch-Gordan series. In these cases, we follow the prescription of 1 The Clebsch-Gordan coefficients are also called vector coupling coefficients or Wigner coefficients in the literature; the isoscalar factors are also called Racah coefficients. 1 The highest outer degeneracy in this work is two, and is only present when one of the factors is an octet. The prescription of It remains to specify the overall phases of representations in the decomposition of the product of two irreducible representations. Representations are named as in With these phase conventions, the Clebsch-Gordan coefficients and isoscalar factors are real. Reconstruction of Clebsch-Gordan Coefficients from Isoscalar Factors The isoscalar factors depend of the identity of the representations, and on the hypercharges and isospins of the isomultiplets that are coupled. We will denote them by F (R, Y, I; r, y, i, r ′ , y ′ , i ′ ). The SU (3) Clebsch-Gordan coefficients are found as products of isoscalar factors and SU (2) Clebsch-Gordan coefficients: The SU (2) tables can be reconstructed from Tables 1 3 , 2 3 , 3 3 , and 4 3 of There are two symmetry relations among the isoscalar factors that will allow us to omit many tables from our exposition. Those tables can be reconstructed from those that are present, with the help of the phase factors involved in these symmetry relations. Both 2 relations come from [1], but we rewrite them in our notation. 2 The first involves the order of the factor representations. If the order is reversed, then a phase ξ may enter: The factor (−1) I−i−i ′ comes from Equation 3. The phase ξ(R; r, r ′ ) does not depend on the quantum numbers of the states, but only on the identity of the representations r, r ′ , and R, and on the phase conventions described in the previous section. The second symmetry relation involves the conjugation of the representations: Here ζ(R; r, r ′ ) also does not depend on the quantum numbers of the states involved, but only on the identities of the representations and on our phase conventions. For these relations, we naturally define 1 ≡ 1, 8 ≡ 8, 27 ≡ 27, and 64 ≡ 64. It is easy to show from Equations 4 and 5 that ξ(R; r, r ′ ) = ξ(R; r, r ′ ). Then it can be shown (using Equation 6) that The ξ and ζ needed to construct the omitted tables are presented in If in the reversed product r ′ ⊗ r the highest-isospin state in r ′ that couples to I h in R has quantum numbers y ′rev h and i ′rev h , and the highest isospin in r that couples to these two has y rev h and i rev h . Then ξ(R; r, r ′ ) = (−1) where sign(x) = x/|x|