Erratum to: Determination of the strong coupling constant $${{\varvec{\alpha _{\mathrm{s}} (m_{\mathrm{Z}})}}}$$ in next-to-next-to-leading order QCD using H1 jet cross section measurements

The determination of the strong coupling constant $$\alpha _{\mathrm{s}} (m_{\mathrm{Z}})$$ α s ( m Z ) from H1 inclusive and dijet cross section data [1] exploits perturbative QCD predictions in next-to-next-to-leading order (NNLO) [2–4]. An implementation error in the NNLO predictions was found [4] which changes the numerical values of the predictions and the resulting values of the fits. Using the corrected NNLO predictions together with inclusive jet and dijet data, the strong coupling constant is determined to be $$\alpha _{\mathrm{s}} (m_{\mathrm{Z}}) =0.1166\,(19)_{\mathrm{exp}}\,(24)_{\mathrm{th}}$$ α s ( m Z ) = 0.1166 ( 19 ) exp ( 24 ) th . Complementarily, $$\alpha _{\mathrm{s}} (m_{\mathrm{Z}})$$ α s ( m Z ) is determined together with parton distribution functions of the proton (PDFs) from jet and inclusive DIS data measured by the H1 experiment. The value $$\alpha _{\mathrm{s}} (m_{\mathrm{Z}}) =0.1147\,(25)_{\mathrm{tot}}$$ α s ( m Z ) = 0.1147 ( 25 ) tot obtained is consistent with the determination from jet data alone. Corrected figures and numerical results are provided and the discussion is adapted accordingly.

On next to soft threshold corrections to DIS and SIA processes

We study the perturbative structure of threshold enhanced logarithms in the coefficient functions of deep inelastic scattering (DIS) and semi-inclusive e+e− annihilation (SIA) processes and setup a framework to sum them up to all orders in perturbation theory. Threshold logarithms show up as the distributions ((1−z)−1 logi(1−z))+ from the soft plus virtual (SV) and as logarithms logi(1−z) from next to SV (NSV) contributions. We use the Sudakov differential and the renormalisation group equations along with the factorisation properties of parton level cross sections to obtain the resummed result which predicts SV as well as next to SV contributions to all orders in strong coupling constant. In Mellin N space, we resum the large logarithms of the form logi(N) keeping 1/N corrections. In particular, the towers of logarithms, each of the form $$ {a}_s^n/{N}^{\alpha }{\log}^{2n-\alpha }(N),{a}_s^n/{N}^{\alpha }{\log}^{2n-1-\alpha }(N)\cdots $$ a s n / N α log 2 n − α N , a s n / N α log 2 n − 1 − α N ⋯ etc for α = 0, 1, are summed to all orders in as.

Dark matter detection, Standard Model parameters and Intermediate Scale Supersymmetry

The vanishing of the Higgs quartic coupling at a high energy scale may be explained by Intermediate Scale Supersymmetry, where supersymmetry breaks at (109-1012) GeV. The possible range of supersymmetry breaking scales can be narrowed down by precise measurements of the top quark mass and the strong coupling constant. On the other hand, nuclear recoil experiments can probe Higgsino or sneutrino dark matter up to a mass of 1012 GeV. We derive the correlation between the dark matter mass and precision measurements of standard model parameters, including supersymmetric threshold corrections. The dark matter mass is bounded from above as a function of the top quark mass and the strong coupling constant. The top quark mass and the strong coupling constant are bounded from above and below respectively for a given dark matter mass. We also discuss how the observed dark matter abundance can be explained by freeze-out or freeze-in during a matter-dominated era after inflation, with the inflaton condensate being dissipated by thermal effects.

Determination of $$\alpha _{S}$$ beyond NNLO using event shape averages

We consider a method for determining the QCD strong coupling constant using fits of perturbative predictions for event shape averages to data collected at the LEP, PETRA, PEP and TRISTAN colliders. To obtain highest accuracy predictions we use a combination of perturbative $${{{\mathcal {O}}}}(\alpha _{S}^{3})$$ O ( α S 3 ) calculations and estimations of the $${{{\mathcal {O}}}}(\alpha _{S}^{4})$$ O ( α S 4 ) perturbative coefficients from data. We account for non-perturbative effects using modern Monte Carlo event generators and analytic hadronization models. The obtained results show that the total precision of the $$\alpha _{S}$$ α S determination cannot be improved significantly with the higher-order perturbative QCD corrections alone, but primarily requires a deeper understanding of the non-perturbative effects.

2S and 3S State Masses and decay constants of heavy-flavour mesons in a non-relativistic QCD potential model with three-loop effects in V-scheme

We make an analysis of three -loop effects of the strong coupling constant in the study of masses and decay constants of the heavy-flavour pseudo-scalar mesons (PSM) D, $$D_s$$ D s , B, $$B_s,$$ B s , $$B_c$$ B c , $$\eta _c$$ η c and $$\eta _b$$ η b in a non-relativistic QCD potential model using Dalgarno’s perturbation theory (DPT). The first order mesonic wavefunction is obtained using Dalgarno’s perturbation theory. The three-loop effects of strong coupling constant are included in the wave function in co-ordinate space and then used to examine the static and dynamic properties of the heavy-flavour mesons for 2S and 3S higher states. The results are compared with the other models available and are found to be compatible with available experimental values. In V-scheme, the three-loop effects on masses and decay constants of heavy-flavour mesons show a significant result.

Tree-level splitting amplitudes for a gluon into four collinear partons

We compute in conventional dimensional regularisation the tree-level splitting amplitudes for a gluon parent which splits into four collinear partons. This is part of the universal infrared behaviour of the QCD scattering amplitudes at next-to-next-to-next-to-leading order (N3LO) in the strong coupling constant. Combined with our earlier results for a quark parent, this completes the set of tree-level splitting amplitudes required at this order. We also study iterated collinear limits where a subset of the four collinear partons become themselves collinear.