The 3-loop non-singlet heavy flavor contributions to the structure function g1(x,Q2) at large momentum transfer

We calculate the massive flavor non-singlet Wilson coefficient for the heavy flavor contributions to the polarized structure function g1(x,Q2) in the asymptotic region Q2≫m2 to 3-loop order in Quantum Chromodynamics at general values of the Mellin variable N and the momentum fraction x , and derive heavy flavor corrections to the Bjorken sum-rule. Numerical results are presented for the charm quark contribution. Results on the structure function g2(x,Q2) in the twist-2 approximation are also given

The 3-loop non-singlet heavy flavor contributions and anomalous dimensions for the structure function F2(x,Q2) and transversity

We calculate the massive flavor non-singlet Wilson coefficient for the heavy flavor contributions to the structure function F2(x,Q2) in the asymptotic region Q2≫m2 and the associated operator matrix element Aqq,Q(3),NS(N) to 3-loop order in Quantum Chromodynamics at general values of the Mellin variable N . This matrix element is associated with the vector current and axial vector current for the even and the odd moments N , respectively. We also calculate the corresponding operator matrix elements for transversity, compute the contributions to the 3-loop anomalous dimensions to O(NF) and compare to results in the literature. The 3-loop matching of the flavor non-singlet distribution in the variable flavor number scheme is derived. All results can be expressed in terms of nested harmonic sums in N space and harmonic polylogarithms in x -space. Numerical results are presented for the non-singlet charm quark contribution to F2(x,Q2)

ZZ production at hadron colliders in NNLO QCD

We report on the first calculation of next-to-next-to-leading order (NNLO) QCD corrections to the inclusive production of Z -boson pairs at hadron colliders. Numerical results are presented for pp collisions with centre-of-mass energy ( <math altimg="si1.gif" xmlns="http://www.w3.org/1998/Math/MathML"><msqrt><mi>s</mi></msqrt></math> ) ranging from 7 to 14 TeV. The NNLO corrections increase the NLO result by an amount varying from 11% to 17% as <math altimg="si1.gif" xmlns="http://www.w3.org/1998/Math/MathML"><msqrt><mi>s</mi></msqrt></math> goes from 7 to 14 TeV. The loop-induced gluon fusion contribution provides about <math altimg="si2.gif" xmlns="http://www.w3.org/1998/Math/MathML"><mn>60</mn><mtext>%</mtext></math> of the total NNLO effect. When going from NLO to NNLO the scale uncertainties do not decrease and remain at the <math altimg="si3.gif" xmlns="http://www.w3.org/1998/Math/MathML"><mo>±</mo><mn>3</mn><mtext>%</mtext></math> level

The <math altimg="si1.gif" xmlns="http://www.w3.org/1998/Math/MathML"><mi>O</mi><mo stretchy="false">(</mo><msubsup><mrow><mi>α</mi></mrow><mrow><mi>s</mi></mrow><mrow><mn>3</mn></mrow></msubsup><msubsup><mrow><mi>T</mi></mrow><mrow><mi>F</mi></mrow><mrow><mn>2</mn></mrow></msubsup><mo stretchy="false">)</mo></math> contributions to the gluonic operator matrix element

The <math altimg="si2.gif" xmlns="http://www.w3.org/1998/Math/MathML"><mi>O</mi><mo stretchy="false">(</mo><msubsup><mrow><mi>α</mi></mrow><mrow><mi>s</mi></mrow><mrow><mn>3</mn></mrow></msubsup><msubsup><mrow><mi>T</mi></mrow><mrow><mi>F</mi></mrow><mrow><mn>2</mn></mrow></msubsup><msub><mrow><mi>C</mi></mrow><mrow><mi>F</mi></mrow></msub><mo stretchy="false">(</mo><msub><mrow><mi>C</mi></mrow><mrow><mi>A</mi></mrow></msub><mo stretchy="false">)</mo><mo stretchy="false">)</mo></math> contributions to the transition matrix element <math altimg="si3.gif" xmlns="http://www.w3.org/1998/Math/MathML"><msub><mrow><mi>A</mi></mrow><mrow><mi>g</mi><mi>g</mi><mo>,</mo><mi>Q</mi></mrow></msub></math> relevant for the variable flavor number scheme at 3-loop order are calculated. The corresponding graphs contain two massive fermion lines of equal mass leading to terms given by inverse binomially weighted sums beyond the usual harmonic sums. In x -space two root-valued letters contribute in the iterated integrals in addition to those forming the harmonic polylogarithms. We outline technical details needed in the calculation of graphs of this type, which are as well of importance in the case of two different internal massive lines