The Polarized Two-Loop Massive Pure Singlet Wilson Coefficient for Deep-Inelastic Scattering

We calculate the polarized massive two--loop pure singlet Wilson coefficient contributing to the structure functions $g_1(x,Q^2)$ analytically in the whole kinematic region. The Wilson coefficient contains Kummer--elliptic integrals. We derive the representation in the asymptotic region $Q^2 \gg m^2$, retaining power corrections, and in the threshold region. The massless Wilson coefficient is recalculated. The corresponding twist--2 corrections to the structure function $g_2(x,Q^2)$ are obtained by the Wandzura--Wilczek relation. Numerical results are presented.Comment: 22 pages Latex, 8 Figure

O(αs3)O(α^3_s) calculations for the inclusive determination of ∣Vcb∣|V_{cb}|

For the determination of the Cabbibo-Kobayashi-Maskawa matrix element $|V_{cb}|$ from inclusive data precise knowledge of the semileptonic $b→c$ decay rate is necessary. Since this observable has a bad convergence behavior when the heavy quark masses are expressed in the on-shell or $\overline{MS}$ scheme the latest determinations have been obtained in the so called kinetic mass scheme. The relation between the different schemes needs to be known to high precision as well. In this proceedings we present our recent calculations which push the precision of both ingredients to $O(α^3_s$). The results can be used to improve the inclusive determination of $|V_{cb}|$

Massive form factors at O(as3^3_s)

We report on our recent calculation of massive quark form factors using a semi-numerical approach based on series expansions of the master integrals around singular and regular kinematic points and numerical matching. The methods allows to cover the whole kinematic range of negative and positive values of the virtuality $s$ with at least seven significant digits accuracy

Double hard scattering without double counting

Double parton scattering in proton-proton collisions includes kinematic regions in which two partons inside a proton originate from the perturbative splitting of a single parton. This leads to a double counting problem between single and double hard scattering. We present a solution to this problem, which allows for the definition of double parton distributions as operator matrix elements in a proton, and which can be used at higher orders in perturbation theory. We show how the evaluation of double hard scattering in this framework can provide a rough estimate for the size of the higher-order contributions to single hard scattering that are affected by double counting. In a numeric study, we identify situations in which these higher-order contributions must be explicitly calculated and included if one wants to attain an accuracy at which double hard scattering becomes relevant, and other situations where such contributions may be neglected.Comment: 80 pages, 20 figures. v2: clarifications in section 4, extended section 8, small changes elsewher

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

Massive form factors at O(αs3)\mathcal{O}(\alpha_s^3)

We report on our recent calculation of massive quark form factors using a semi-numerical approach based on series expansions of the master integrals around singular and regular kinematic points and numerical matching. The methods allows to cover the whole kinematic range of negative and positive values of the virtuality $s$ with at least seven significant digits accuracy.Comment: 9 pages, 3 figures, contribution to the proceedings of Loops and Legs in Quantum Field Theory (LL2022), Ettal, German

Phase-matched few-cycle high-harmonic generation: ionisation gating and half-cycle cutoffs

For the direct exploration of electron dynamics in molecules, e.g. during a chemical reaction, a short pulsed radiation source is required, delivering flashes of duration less than a femtosecond. Due to their wavelengths conventional laser pulses cannot be shortened enough to reach such pulse durations. High-harmonic generation (HHG) is currently the key to the subfemtosecond regime with wavelengths in the extreme-ultraviolet and soft-X-ray range. HHG is a very inefficient process and, therefore, the radiation produced by every atom involved has to be phase-matched to obtain a macroscopic signal. The intrinsic characteristics of phase matching provide the possibility to produce even single attosecond pulses. A simulation will show, how phase matching acts as temporal gate and allows HHG only at the leading-edge of the driving laser pulse. The behaviour of the leading-edge gating will be analysed for different experimental conditions, such as peak intensity of the laser pulse, density of the gaseous generation medium and the distance between focus and generation region. Half-cycle cutoff (HCO) analysis allows an experimental access to observing the leading-edge gate, that will be compared to the simulation. The HCO-analysis can also be used to estimate the duration of the driving laser pulse. In addition the position- and pressure dependence of the HHG process will be analysed, too

Massive form factors at O(as3^3_s)

We report on our recent calculation of massive quark form factors using a semi-numerical approach based on series expansions of the master integrals around singular and regular kinematic points and numerical matching. The methods allows to cover the whole kinematic range of negative and positive values of the virtuality $s$ with at least seven significant digits accuracy

O(αs3)\mathcal{O}(\alpha_s^3) calculations for the inclusive determination of ∣Vcb∣|V_{cb}|

For the determination of the Cabbibo-Kobayashi-Maskawa matrix element |Vcb| from inclusive data precise knowledge of the semileptonic b→c decay rate is necessary. Since this observable has a bad convergence behavior when the heavy quark masses are expressed in the on-shell or MS¯¯¯¯¯¯¯ scheme the latest determinations have been obtained in the so called kinetic mass scheme. The relation between the different schemes needs to be known to high precision as well. In this proceedings we present our recent calculations which push the precision of both ingredients to O(α3s). The results can be used to improve the inclusive determination of |Vcb|

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 $F_2(x,Q^2)$