The three-loop unpolarized and polarized non-singlet anomalous dimensions from off shell operator matrix elements

We calculate the unpolarized and polarized three–loop anomalous dimensions and splitting functions P$^{+}$$_{NS}$ P$^{-}$$_{NS}$ and P$^{S}$$_{NS}$ n QCD in the $\overline{MS}$ scheme by using the traditional method of space–like off shell massless operator matrix elements. This is a gauge–dependent framework. For the first time we also calculate the three–loop anomalous dimensions P$^{±; tr}$$_{NS}$ for transversity directly. We compare our results to the literature

The two-loop massless off-shell QCD operator matrix elements to finite terms

We calculate the unpolarized and polarized two–loop massless off–shell operator matrix elements in QCD to $O(\varepsilon)$ in the dimensional parameter in an automated way. Here we use the method of arbitrary high Mellin moments and difference ring theory, based on integration-by-parts relations. This method also constitutes one way to compute the QCD anomalous dimensions. The presented higher order contributions to these operator matrix elements occur as building blocks in the corresponding higher order calculations up to four–loop order. All contributing quantities can be expressed in terms of harmonic sums in Mellin–N space or by harmonic polylogarithms in z–space. We also perform comparisons to the literature

The three-loop polarized singlet anomalous dimensions from off-shell operator matrix elements

Future high luminosity polarized deep-inelastic scattering experiments will improve both the knowledge of the spin sub-structure of the nucleons and contribute further to the precision determination of the strong coupling constant, as well as, reveal currently yet unknown higher twist contributions in the polarized sector. For all these tasks to be performed, it is necessary to know the QCD leading twist scaling violations of the measured structure functions. Here an important ingredient consists in the polarized singlet anomalous dimensions and splitting functions in QCD. We recalculate these quantities to three-loop order in the M-scheme by using the traditional method of space-like off-shell massless operator matrix elements, being a gauge-dependent framework. Here one obtains the anomalous dimensions without referring to gravitational currents, needed when calculating them using the forward Compton amplitude. We also calculate the non-singlet splitting function Δ$^{(2),s,NS}$$_{qq}$ and compare the final results to the literature, also including predictions for the region of small values of Bjorken x

The two-loop massless off-shell QCD operator matrix elements to finite terms

We calculate the unpolarized and polarized two–loop massless off–shell operator matrix elements in QCD to $O(\varepsilon)$ in the dimensional parameter in an automated way. Here we use the method of arbitrary high Mellin moments and difference ring theory, based on integration-by-parts relations. This method also constitutes one way to compute the QCD anomalous dimensions. The presented higher order contributions to these operator matrix elements occur as building blocks in the corresponding higher order calculations up to four–loop order. All contributing quantities can be expressed in terms of harmonic sums in Mellin–N space or by harmonic polylogarithms in z–space. We also perform comparisons to the literature

Perturbative dynamics of matrix string for the membrane

Recently Sekino and Yoneya proposed a way to regularize the world volume theory of membranes wrapped around $S^1$ by matrices and showed that one obtains matrix string theory as a regularization of such a theory. We show that this correspondence between matrix string theory and wrapped membranes can be obtained by using the usual M(atrix) theory techniques. Using this correspondence, we construct the super-Poincare generators of matrix string theory at the leading order in the perturbation theory. It is shown that these generators satisfy 10 dimensional super-Poincar\'e algebra without any anomaly.Comment: 23 pages, 1 figur

Perseverance: The Decision-Making Process of the Emergency Triage Nurse

Nursing Scholarship Symposium Event Posters.https://scholarlycommons.libraryinfo.bhs.org/nurs_presentations/1011/thumbnail.jp

Third-order non-Coulomb correction to the S-wave quarkonium wave functions at the origin

We compute the third-order correction to the S-wave quarkonium wave functions |\psi_n(0)|^2 at the origin from non-Coulomb potentials in the effective non-relativistic Lagrangian. Together with previous results on the Coulomb correction and the ultrasoft correction computed in a companion paper, this completes the third-order calculation up to a few unknown matching coefficients. Numerical estimates of the new correction for bottomonium and toponium are given.Comment: 12 pages, v2: matches published version, missing factors in eq. (9), (29) adde