This report summarizes the proceedings of the 2014 Mainz Institute for Theoretical Physics (MITP) scientific program on High precision fundamental constants at the TeV scale. The two outstanding parameters in the Standard Model dealt with during the
MITP scientific program are the strong coupling constant $alpha_s$ and the top-quark mass $m_t$. Lacking knowledge on the value of those fundamental constants is often the limiting factor in the accuracy of theoretical predictions. The current status on $alpha_s$ and $m_t$ has been reviewed and directions for future research have been identified.
We have calculated the complete matrix of three-loop helicity-difference (`polarized) splitting functions Delta P_ik^(2), i,k = q,g, in massless perturbative QCD. In this note we briefly discuss some properties of the polarized splitting functions an
d our non-standard determination of the hitherto missing lower-row quantities Delta P_gq^(2) and Delta P_gg^(2). The resulting next-to-next-to-leading order (NNLO) corrections to the evolution of polarized parton distributions are illustrated and found to be small even at rather large values of the strong coupling constant alpha_s.
The ATLAS and CMS experiments observed a particle at the LHC with a mass $approx 126$ GeV, which is compatible with the Higgs boson of the Standard Model. A crucial question is, if for such a Higgs mass value, one could extrapolate the model up to hi
gh scales while keeping the minimum of the scalar potential that breaks the electroweak symmetry stable. Vacuum stability requires indeed the Higgs boson mass to be $M_H gsim 129 pm 1$ GeV, but the precise value depends critically on the input top quark pole mass which is usually taken to be the one measured at the Tevatron, $m_t^{rm exp}=173.2 pm 0.9$ GeV. However, for an unambiguous and theoretically well-defined determination of the top quark mass one should rather use the total cross section for top quark pair production at hadron colliders. Confronting the latest predictions of the inclusive $p bar p to tbar t +X$ cross section up to next-to-next-to-leading order in QCD to the experimental measurement at the Tevatron, we determine the running mass in the $bar{rm MS}$-scheme to be $m_t^{bar{rm MS}}(m_t) = 163.3 pm 2.7$ GeV which gives a top quark pole mass of $m_t^{rm pole}= 173.3 pm 2.8$ GeV. This leads to the vacuum stability constraint $M_H geq 129.8 pm 5.6$ GeV to which a $approx 126$ GeV Higgs boson complies as the uncertainty is large. A very precise assessment of the stability of the electroweak vacuum can only be made at a future high-energy electron-positron collider, where the top quark pole mass could be determined with a few hundred MeV accuracy.
We report on the first calculation of the structure function g_1 in polarised deep-inelastic scattering to the third order in massless perturbative QCD. The calculation follows the dispersive approach already used for the corresponding unpolarised ca
ses of F_2,L, but additionally involves higher tensor integrals and the Dirac matrix gamma_5 in D unequal 4 dimensions. Our results confirm all known two-loop expressions including the coefficient functions of Zijlstra and van Neerven not independently verified before. At three loops we extract the helicity-difference next-to-next-to-leading order (NNLO) quark-quark and gluon-quark splitting functions Delta P_qq and Delta P_qg. The results exhibit interesting features concerning sum rules and the momentum-fraction limits x to 1 and x to 0.
Second- and third-order results are presented for the structure functions of charged-current deep-inelastic scattering in the framework of massless perturbative QCD. We write down the two-loop differences between the corresponding crossing-even and -
odd coefficient functions, including those for the longitudinal structure function not covered in the literature so far. At three loops we compute the lowest five moments of these differences for all three structure functions and provide approximate expressions in Bjorken-$x$ space. Also calculated is the related third-order coefficient-function correction to the Gottfried sum rule. We confirm the conjectured suppression of these quantities if the number of colours is large. Finally we derive the second- and third-order QCD contributions to the Paschos-Wolfenstein ratio used for the determination of the weak mixing angle from neutrino-nucleon deep-inelastic scattering. These contributions are found to be small.
We report on our recent results for deep-inelastic neutrino-proton scattering. We have computed the perturbative QCD corrections to three loops for the harged current structure functions F_2, F_L and F_3 for the combination nu P - nubar P. In leading
twist approximation we have calculated the first six odd-integer Mellin moments in the case of F_2 and F_L and the first six even-integer moments in the case of F_3. As a new result we have obtained the coefficient functions to O(alpha_s^3) and we have found the corresponding anomalous dimensions to agree with known results in the literature.
We derive for deep-inelastic neutrino-proton scattering in the combination nu P - nubar P the perturbative QCD corrections to three loops for the charged current structure functions F_2, F_L and F_3. In leading twist approximation we calculate the fi
rst five odd-integer Mellin moments in the case of F_2 and F_L and the first five even-integer moments in the case of F_3. As a new result we obtain the coefficient functions to O(alpha_s^3) while the corresponding anomalous dimensions agree with known results in the literature.
