Corrections to Quark Asymmetries at LEP

The most precise measurement of the weak mixing angle sin^2(theta) at LEP is from the forward-backward asymmetry e+e- --> bbbar at the Z-pole. In this note the QED and electroweak radiative corrections to obtain the pole asymmetry from the measured asymmetry for b- and c-quarks have been calculated using ZFITTER, which has been amended to allow a consistent treatment of partial two-loop corrections for the b-quark final asymmetries. A total correction of dAfbb=0.0019+/-0.0002 and dAfbc=0.0064+/-0.0001 has been found, where the remaining theoretical uncertainty is much too small to explain the apparent discrepancy between sin^2(theta) obtained from Afbb and from the left-right asymmetry at SLD

Forfeiture of Attorney\u27s Fees Under RICO and CCE

We present the matching relations of the variable flavor number scheme at next-to-leading order, which are of importance to define heavy quark partonic distributions for the use at high energy colliders such as Tevatron and the LHC. The consideration of the two-mass effects due to both charm and bottom quarks, having rather similar masses, are important. These effects have not been considered in previous investigations. Numerical results are presented for a wide range of scales. We also present the corresponding contributions to the structure function $F_2(x,Q^2)$

The Role of Differentially Expressed miRNAs and Potential miRNA-mRNA Regulatory Network in Prostate Cancer Progression and Metastasis

Purpose: Aberrant expression of microRNAs (miRNAs) has been discovered in prostate cancer progression however their function is not well understood, thereby further investigation is required to understand the importance of underlying mechanisms and their involvement in multiple signaling pathways, as well as their potential as therapeutic targets. In this study the role and expression levels of three miRNAs were evaluated: miR-21, miR-221 and miR-200c in different prostate cancer cell lines. In addition, based on the latest studies on miRNAs function, their association with other target genes and molecules were analyzed using bioinformatic tools. Methods: Three PCa cell lines PC3, LNCaP and VCaP and normal prostate epithelial cell line PNT1A were screened for miRNA expression levels using qPCR. miRNA target genes and their association with signaling pathways were analyzed through several Network and pathway analysis online tools. Findings: Upregulation of miR-21 and miR-221 was observed in PC3 and VCaP prostate cancer cells, respectively. According to KEGG analysis, we found that Hippo signaling pathway and cytokine-cytokine receptor interactions were affected by miR-21 while miR-221 would interfere with ECM-receptor interaction, Fatty acid elongation and Huntington disease molecular networks. Exposure of PC3 cells to TGF-β (10 µM) caused upregulation of miR-21 with the evidence with increased invasion potential. Discussion and Conclusion: miRNAs could regulate several genes in multiple signaling pathways. Here, we demonstrated that in a panel of PCa cell lines, both mir-21 and miR-221 expressions were upregulated. miR-21 may be a dignostic and prognosticbiomarker for PCa

The Three Loop Two-Mass Contribution to the Gluon Vacuum Polarization

We calculate the two-mass contribution to the 3-loop vacuum polarization of the gluon in Quantum Chromodynamics at virtuality $p^2 = 0$ for general masses and also present the analogous result for the photon in Quantum Electrodynamics.Comment: 5 pages Late

Subleading Logarithmic QED Initial State Corrections to e+e−→γ∗/Z0∗e^+e^- \rightarrow \gamma^*/{Z^{0}}^* to O(α6L5)O(\alpha^6 L^5)

Using the method of massive operator matrix elements, we calculate the subleading QED initial state radiative corrections to the process $e^+e^- \rightarrow \gamma^*/Z^*$ for the first three logarithmic contributions from $O(\alpha^3 L^3), O(\alpha^3 L^2), O(\alpha^3 L)$ to $O(\alpha^5 L^5), O(\alpha^5 L^4), O(\alpha^5 L^3)$ and compare their effects to the leading contribution $O(\alpha^6 L^6)$ and one more subleading term $O(\alpha^6 L^5)$. The calculation is performed in the limit of large center of mass energies squared $s \gg m_e^2$. These terms supplement the known corrections to $O(\alpha^2)$, which were completed recently. Given the high precision at future colliders operating at very large luminosity, these corrections are important for concise theoretical predictions. The present calculation needs the calculation of one more two--loop massive operator matrix element in QED. The radiators are obtained as solutions of the associated Callen--Symanzik equations in the massive case. The radiators can be expressed in terms of harmonic polylogarithms to weight {\sf w = 6} of argument $z$ and $(1-z)$ and in Mellin $N$ space by generalized harmonic sums. Numerical results are presented on the position of the $Z$ peak and corrections to the $Z$ width, $\Gamma_Z$. The corrections calculated result into a final theoretical accuracy for $\delta M_Z$ and $\delta \Gamma_Z$ which is estimated to be of O(30 keV) at an anticipated systematic accuracy at the FCC\_ee of \sim 100 keV. This precision cannot be reached, however, by including only the corrections up to $O(\alpha^3)$.Comment: 58 pages, 3 Figure

The unpolarized two-loop massive pure singlet Wilson coefficients for deep-inelastic scattering

We calculate the massive two--loop pure singlet Wilson coefficients for heavy quark production in the unpolarized case analytically in the whole kinematic region and derive the threshold and asymptotic expansions. We also recalculate the corresponding massless two--loop Wilson coefficients. The complete expressions contain iterated integrals with elliptic letters. The contributing alphabets enlarge the Kummer-Poincar\'e letters by a series of square-root valued letters. A new class of iterated integrals, the Kummer-elliptic integrals, are introduced. For the structure functions $F_2$ and $F_L$ we also derive improved asymptotic representations adding power corrections. Numerical results are presented.Comment: 42, pages Latex, 8 Figure

The O(α2)O(\alpha^2) Initial State QED Corrections to e+e−e^+e^- Annihilation to a Neutral Vector Boson Revisited

We calculate the non-singlet, the pure singlet contribution, and their interference term, at $O(\alpha^2)$ due to electron-pair initial state radiation to $e^+ e^-$ annihilation into a neutral vector boson in a direct analytic computation without any approximation. The correction is represented in terms of iterated incomplete elliptic integrals. Performing the limit $s \gg m_e^2$ we find discrepancies with the earlier results of Ref.~\cite{Berends:1987ab} and confirm results obtained in Ref.~\cite{Blumlein:2011mi} where the effective method of massive operator matrix elements has been used, which works for all but the power corrections in $m^2/s$. In this way, we also confirm the validity of the factorization of massive partons in the Drell-Yan process. We also add non-logarithmic terms at $O(\alpha^2)$ which have not been considered in \cite{Berends:1987ab}. The corrections are of central importance for precision analyzes in $e^+e^-$ annihilation into $\gamma^*/Z^*$ at high luminosity.Comment: 4 pages Latex, 2 Figures, several style file

The two-mass contribution to the three-loop pure singlet operator matrix element

We present the two-mass QCD contributions to the pure singlet operator matrix element at three loop order in x-space. These terms are relevant for calculating the structure function $F_2(x,Q^2)$ at $O(\alpha_s^3)$ as well as for the matching relations in the variable flavor number scheme and the heavy quark distribution functions at the same order. The result for the operator matrix element is given in terms of generalized iterated integrals that include square root letters in the alphabet, depending also on the mass ratio through the main argument. Numerical results are presented.Comment: 28 papges Latex, 3 figure

The Two-mass Contribution to the Three-Loop Gluonic Operator Matrix Element Agg,Q(3)A_{gg,Q}^{(3)}

We calculate the two-mass QCD contributions to the massive operator matrix element $A_{gg,Q}$ at $\mathcal{O} (\alpha_s^3)$ in analytic form in Mellin $N$- and $z$-space, maintaining the complete dependence on the heavy quark mass ratio. These terms are important ingredients for the matching relations of the variable flavor number scheme in the presence of two heavy quark flavors, such as charm and bottom. In Mellin $N$-space the result is given in the form of nested harmonic, generalized harmonic, cyclotomic and binomial sums, with arguments depending on the mass ratio. The Mellin inversion of these quantities to $z$-space gives rise to generalized iterated integrals with square root valued letters in the alphabet, depending on the mass ratio as well. Numerical results are presented.Comment: 99 pages LATEX, 2 Figure