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The Next Generation Very Large Array (ngVLA) is a planned radio interferometer providing unprecedented sensitivity at wavelengths between 21 cm and 3 mm. Its 263 antenna element array will be spatially distributed across North America to enable both superb low surface brightness recovery and sub-milliarcsecond angular resolution imaging. The project was developed by the international astronomy community under the lead of the National Radio Astronomy Observatory (NRAO), and is anticipated to be built between 2027 and 2037. Two workshops have been held in 2022 and 2023 with the goal to discuss and consolidate the scientific interests in the ngVLA within the German astronomical community. This community paper constitutes a collection of 48 science ideas which the German community aims to pursue with the ngVLA in the 2030s. This is not a complete list and the ideas are not developed at the level of a "Science Book", such that the present document is mainly meant provide a basis for further discussion within the community. As such, additional contributions are welcome, and will be considered for inclusion in future revisions., Comment: Version 2.0 (status June 18, 2024): 169 pages, comments and future contributions welcome [v2.0: 7 new science cases added, some minor revisions to other chapters]

We have extended our previous computations of the even-N moments of the flavour-singlet four-loop splitting functions to N = 12 for the pure-singlet quark case and N = 10 for all other cases. These results, obtained using physical quantities in inclusive deep-inelastic scattering, have been and will be used to validate conceptionally much more challenging determinations of these splitting functions from off-shell operator matrix elements (OMEs). For the quark-gluon and gluon-gluon splitting functions, which have yet to be computed to higher N using OMEs, we construct approximations based on our moments and endpoint constraints, where we present new large-x results for the gluon-gluon case. These approximations facilitate an approximate N^3LO evolution of parton distributions which are sufficiently accurate outside the region of small momentum fractions x., Comment: 14 pages, 3 figures. Analytical and numerical results in ancillary FORM and Fortran files

We report results for the lowest even-$N$ moments of the flavor-nonsinglet structure functions $F_2$ and $F_L$ in QCD at the fourth order in the perturbative expansion in the strong coupling constant $\alpha_s$. Our results are presented in numerical form and we compare them with the leading and subleading terms of the threshold expansion for large values of $N$, which corresponds to the limit $x \to 1$., Comment: 11 pages, LaTeX, 3 figures; Proceedings "Loops and Legs in Quantum Field Theory - LL2022"

We have carried out exclusive measurements for the photoproduction of an $\eta$ meson from a proton target with an egg-shaped calorimeter made of BGO crystals (BGOegg) and forward charged-particle detectors at the SPring-8 LEPS2 beamline. The differential cross sections and photon beam asymmetries of the $\gamma p \to \eta p$ reaction are measured in a center-of-mass energy ($W$) range of $1.82$-$2.32$ GeV and a polar angle range of $-1.0 < \cos{\theta^{\eta}_{\mathrm{c.m.}}} < 0.6$. The reaction is identified by selecting a proton and two $\gamma$'s produced by an $\eta$-meson decay. The kinematic fit method was employed to select the reaction candidate with the confidence level larger than $1$\%. A bump structure at $W$ = $2.0$-$2.3$ GeV in the differential cross section is confirmed at extremely backward $\eta$ polar angles, where the existing data are inconsistent with each other. This bump structure is likely associated with high-spin resonances that couple with $s\bar{s}$ quarks. The results of the photon beam asymmetries in a wide $\eta$ polar angle range are new for the photon beam energies exceeding $2.1$ GeV. These results are not reproduced by the existing partial wave analyses. They provide an additional constraint to nucleon resonance studies at high energies., Comment: 16 pages, 11 figures

We have computed the four lowest even-N moments of all four splitting functions for the evolution of flavour-singlet parton densities of hadrons at the fourth order in the strong coupling constant alpha_s. The perturbative expansion of these moments, and hence of the splitting functions for momentum fractions x >~ 0.1, is found to be well behaved with relative alpha_s-coefficients of order one and sub-percent effects on the scale derivatives of the quark and gluon distributions at alpha_s ~< 0.2. More intricate computations, including other approaches such as the operator-product expansion, are required to cover the full x-range relevant to LHC analyses. Our results are presented analytically for a general gauge group for detailed checks and validations of such future calculations., Comment: 11 pages, LaTeX, 2 figures. Analytical results in ancillary FORM file

Microwave transmission measurements were performed for a three-dimensional (3D) layer-by-layer chiral photonic crystal (PhC), whose photonic band structure contains 3D singular points, Weyl points. For the frequency and wavevector in the vicinity of a Weyl point, the transmitted intensity was found to be inversely proportional to the square of the propagation length. In addition, the transmitted wave was well-collimated in the plane parallel to the PhC layers, even for point-source incidence. When a plane wave was incident on the PhC containing metal scatters, the planar wavefront was reconstructed after the transmission, indicating a cloaking effect., Comment: 10 pages, 8 figures

We measured missing mass spectrum of the $^{12}{\rm C}(\gamma,p)$ reaction for the first time in coincidence with potential decay products from $\eta'$ bound nuclei. We tagged an ($\eta+p$) pair associated with the $\eta'N\to\eta N$ process in a nucleus. After applying kinematical selections to reduce backgrounds, no signal events were observed in the bound-state region. An upper limit of the signal cross section in the opening angle $\cos\theta^{\eta p}_{lab}<-0.9$ was obtained to be 2.2 nb/sr at the 90$\%$ confidence level. It is compared with theoretical cross sections, whose normalization ambiguity is suppressed by measuring a quasifree $\eta'$ production rate. Our results indicate a small branching fraction of the $\eta'N\to\eta N$ process and/or a shallow $\eta'$-nucleus potential., Comment: 7 pages, 4 figures

We present the first calculations of next-to-next-to-next-to-next-to-leading order (N^4LO) contributions to anomalous dimensions of spin-N twist-2 operators in perturbative QCD. Specifically, we have obtained the respective non-singlet quark-quark anomalous dimensions at N=2 and N=3 to the fifth order in the strong coupling alpha_s. These results set the scale for the N^4LO contributions to the evolution of the non-singlet quark distributions of hadrons outside the small-x region, and facilitate a first approximate determination of the five-loop cusp anomalous dimension. While the N^4LO coefficients are larger than expected from the lower-order results, their inclusion stabilizes the perturbative expansions for three or more light flavours at a sub-percent accuracy for alpha_s < 0.3., Comment: 11 pages, LaTeX, 2 figures. FORM file of the main results available with the source. v2: Nikhef and DESY numbers added, one very minor text modification. Version to appear in Phys. Lett. B

We report on recent progress on the splitting functions for the evolution of parton distributions and related quantities, the (lightlike) cusp anomalous dimensions, in perturbative QCD. New results are presented for the four-loop (next-to-next-to-next-to-leading order, N^3LO) contributions to the flavour-singlet splitting functions and the gluon cusp anomalous dimension. We present first results, the moments N=2 and N=3, for the five-loop (N^4LO) non-singlet splitting functions., Comment: 10 pages, LaTeX (PoS style), 3 eps-figures. Contribution to the proceedings of `Loops & Legs 2018', St. Goar (Germany), April/May 2018

We have computed the contributions of the quartic Casimir invariants to the four-loop anomalous dimensions of twist-2 spin-N operators at N =< 16. The results provide new information on the structure of the next-to-next-to-next-to-leading order (N^3LO) splitting functions P_{ik}^(3)(x) for the evolution of parton distributions, and facilitate approximate expressions which include the quartic-Casimir contributions to the (light-like) gluon cusp anomalous dimension. These quantities turn out to be closely related, by a generalization of the lower-order `Casimir scaling', to the corresponding quark results. Using these findings, we present an approximate result for the four-loop gluon cusp anomalous dimension in QCD which is sufficient for phenomenological applications., Comment: 12 pages, LaTeX

We sketch how the R*-operation can be used to compute the pole terms of Feynman diagrams. We identify computational difficulties when performing five-loop calculations, and provide four solutions that drastically reduce the number of terms that are generated. Using these methods, we have computed the beta function for Yang-Mills theory with fermions, the R-ratio in electron-positron annihilation, and Higgs decays to quarks and gluons at five-loop accuracy. The results for the beta function and Higgs decay width to gluons in the heavy-top limit are briefly discussed. There is no need for six-loop extensions of these calculations in the near future., Comment: 12 pages, LaTeX (PoS style), 2 eps-figures. Contribution to the proceedings of `RADCOR 2017', St. Gilgen (Austria), September 2017 and (shortened) to the proceedings of `ACAT 2017', Seattle (USA), August 2017

We report on recent progress on the flavour non-singlet splitting functions in perturbative QCD. The~exact four-loop (N^3LO) contribution to these functions has been obtained in the planar limit of a large number of colours. Phenomenologically sufficient approximate expressions have been obtained for the parts not exactly known so far. Both cases include results for the four-loop cusp and virtual anomalous dimensions which are relevant well beyond the evolution of non-singlet quark distributions, for which an accuracy of (well) below 1% has now been been reached., Comment: 11 pages, LaTeX (PoS style), 4 eps-figures. Contribution to the proceedings of `RADCOR 2017', St. Gilgen (Austria), September 2017

We present the next-to-next-to-next-to-leading order (N^3LO) contributions to the non-singlet splitting functions for both parton distribution and fragmentation functions in perturbative QCD. The exact expressions are derived for the terms contributing in the limit of a large number of colours. For the remaining contributions, approximations are provided that are sufficient for all collider-physics applications. From their threshold limits we derive analytical and high-accuracy numerical results, respectively, for all contributions to the four-loop cusp anomalous dimension for quarks, including the terms proportional to quartic Casimir operators. We briefly illustrate the numerical size of the four-loop corrections, and the remarkable renormalization-scale stability of the N^3LO results, for the evolution of the non-singlet parton distribution and the fragmentation functions. Our results appear to provide a first point of contact of four-loop QCD calculations and the so-called wrapping corrections to anomalous dimensions in N=4 super Yang-Mills theory., Comment: 73 pages latex, 14 figures, ancillary Form and Fortran files, final version to appear in JHEP

We present the first determination of Higgs-boson decay to hadrons at the next-to-next-to-next-to-next-to-leading order of perturbative QCD in the limit of a heavy top quark and massless light flavours. This result has been obtained by computing the absorptive parts of the relevant five-loop self-energy for a general gauge group and combining the outcome with the corresponding coefficient function already known to this order in QCD. Our new result reduces the uncertainty due to the truncation of the perturbation series to a fraction of the uncertainty due to the present error of the strong coupling constant. We have also performed the corresponding but technically simpler computations for direct Higgs decay to bottom quarks and for the electromagnetic R-ratio in e^+ e^- -> hadrons, thus verifying important fifth-order results obtained so far only by one group., Comment: 26 pages, LaTeX, 2 axodraw2 and 4 eps figures. FORM files of the main results available with the source. v2: version accepted by JHEP: introduction and summary slightly extended, minor other text changes, a few additional references

We explain the construction of Forcer, a FORM program for the reduction of four-loop massless propagator-type integrals to master integrals. The resulting program performs parametric IBP reductions similar to the three-loop Mincer program. We show how one can solve many systems of IBP identities parametrically in a computer-assisted manner. Next, we discuss the structure of the Forcer program, which involves recognizing reduction actions for each topology, applying symmetries, and transitioning between topologies after edges have been removed. This part is entirely precomputed and automatically generated. We give examples of recent applications of Forcer, and study the performance of the program. Finally we demonstrate how to use the Forcer package and sketch how to prepare physical diagrams for evaluation by Forcer., Comment: 43 pages, 6 figures, source code available from https://github.com/benruijl/forcer

We have computed the self-energies and a set of three-particle vertex functions for massless QCD at the four-loop level in the MSbar renormalization scheme. The vertex functions are evaluated at points where one of the momenta vanishes. Analytical results are obtained for a generic gauge group and with the full gauge dependence, which was made possible by extensive use of the Forcer program for massless four-loop propagator integrals. The bare results in dimensional regularization are provided in terms of master integrals and rational coefficients; the latter are exact in any space-time dimension. Our results can be used for further precision investigations of the perturbative behaviour of the theory in schemes other than MSbar. As an example, we derive the five-loop beta function in a relatively common alternative, the minimal momentum subtraction (MiniMOM) scheme., Comment: 50 pages, 4 figures, 15 ancillary files available with the source; v2: minor changes, version accepted by JHEP

We have computed the five-loop corrections to the scale dependence of the renormalized coupling constant for Quantum Chromodynamics (QCD), its generalization to non-Abelian gauge theories with a simple compact Lie group, and for Quantum Electrodynamics (QED). Our analytical result, obtained using the background field method, infrared rearrangement via a new diagram-by-diagram implementation of the R* operation and the Forcer program for massless four-loop propagators, confirms the QCD and QED results obtained by only one group before. The numerical size of the five-loop corrections is briefly discussed in the standard MSbar scheme for QCD with n_f flavours and for pure SU(N) Yang-Mills theory. Their effect in QCD is much smaller than the four-loop contributions, even at rather low scales., Comment: 19 pages, LaTex, 4 figures. FORM file of the main results available with the source. v2: version accepted by JHEP: minor text changes, a few additional references, typos corrected

We have computed the fourth-order nf^2 contributions to all three non-singlet quark-quark splitting functions and their four nf^3 flavour-singlet counterparts for the evolution of the parton distributions of hadrons in perturbative QCD with nf effectively massless quark flavours. The analytic form of these functions is presented in both Mellin N-space and momentum-fraction x-space; the large-x and small-x limits are discussed. Our results agree with all available predictions derived from lower-order information. The large-x limit of the quark-quark cases provides the complete nf^2 part of the four-loop cusp anomalous dimension which agrees with two recent partial computations., Comment: 29 pages, Latex, 8 figures. FORM files of the main results available with the source

We present a new FORM program for analytically evaluating four-loop massless propagator-type Feynman integrals in an efficient way. Our program Forcer implements parametric reductions of the aforementioned class of Feynman integrals into a set of master integrals and can be considered as a four-loop extension of the three-loop Mincer program. Since the program structure at the four-loop level is highly complicated and the equations easily become lengthy, most of the code was generated in an automatic way or with computer-assisted derivations. We have checked correctness of the program by recomputing already-known quantities in the literature., Comment: 10 pages, 2 figures, to appear in the proceedings of Loops and Legs in Quantum Field Theory, 24-29 April 2016, Leipzig, Germany

We present results on the fourth-order splitting functions and coefficient functions obtained using Forcer, a four-loop generalization of the Mincer program for the parametric reduction of self-energy integrals. We have computed the respective lowest three even-N and odd-N moments for the non-singlet splitting functions and the non-singlet coefficient functions in electromagnetic and nu+nu(bar) charged-current deep-inelastic scattering, and the N=2 and N=4 results for the corresponding flavour-singlet quantities. Enough moments have been obtained for an LLL-based determination of the analytic N-dependence of the nf^3 and nf^2 parts, respectively, of the singlet and non-singlet splitting functions. The large-N limit of the latter provides the complete nf^2 contributions to the four-loop cusp anomalous dimension. Our results also provide additional evidence of a non-vanishing contribution of quartic group invariants to the cusp anomalous dimension., Comment: 11 pages, LaTeX (PoS style), 4 eps-figures. To appear in the proceedings of `Loops & Legs 2016', Leipzig (Germany), April 2016

We present Forcer, a new FORM program for the calculation of four-loop massless propagators. The basic framework is similar to that of the Mincer program for three-loop massless propagators: the program reduces Feynman integrals to a set of master integrals in a parametric way. To overcome an ineludible complexity of the program structure at the four-loop level, most of the code was automatically generated or made with computer-assisted derivations. Correctness of the program has been checked with the recomputation of some quantities in the literature., Comment: 5 pages, 2 figures, to appear in the proceedings of ACAT 2016

Intense electromagnetic evanescent fields are thermally excited in near fields on material surfaces (at distances smaller than the wavelength of peak thermal radiation). The property of the fields is of strong interest for it is material-specific and is important for understanding a variety of surface-related effects, such as friction forces, Casimir forces, near-field heat transfer, and surface-coupled molecular dynamics. On metal surfaces, relevance of surface plasmon polaritons (SPlPs), coupled to collective motion of conduction electrons, has attracted strong interest, but has not been explicitly clarified up to the present time. Here, using a passive terahertz (THz) near-field microscope with unprecedented high sensitivity, we unveil detailed nature of thermally generated evanescent fields (wavelength:lamda0~14.5micron) on metals at room temperature. Our experimental results unambiguously indicate that the thermal waves are short-wavelength fluctuating electromagnetic fields, from which relevance of SPlPs is ruled out., Comment: 16pages, 4figures

The full $\mathcal{O}(\alpha)$ electroweak radiative corrections to $t \bar{t} \gamma$ and $e^-e^+\gamma$ productions at the International Linear Collider (ILC) are presented in this paper. The computation is performed with the help of GRACE-Loop system. In the physical results, we discuss on the cross section, electroweak corrections, and the top quark forward-backward asymmetry ($A_{FB}$) which are the function of the center-of-mass energy., Comment: 4 pages, Proceedings of ICISE2013 - Rencontres du Vietnam, Windows on the Universe. 11-17 Aug 2013. Quy Nhon, Vietnam

By using the GRACE-Loop system, we calculate the full $\mathcal{O}(\alpha)$ electroweak radiative corrections to the process $e^+e^- \rightarrow e^+e^- \gamma$, which is important for future investigations at the International Linear Collider (ILC). With the GRACE-Loop system, the calculations are checked numerically by three consistency tests: ultraviolet finiteness, infrared finiteness, and gauge-parameter independence. The results show good numerical stability when quadruple precision is used. In the phenomenological results, we find that the electroweak corrections to the total cross section range from $\sim -4\%$ to $\sim -21\%$ when $\sqrt{s}$ varies from $250$ GeV to $1$ TeV. The corrections also significantly affect the differential cross sections, which are a function of the invariant masses and angles and the final-particle energies. Such corrections will play an important role for the high-precision program at the ILC., Comment: 15 pages, 7 figures, Talk presented at the International Workshop on Future Linear Colliders (LCWS13), Tokyo, Japan, 11-15 November 2013

We describe the implementation of output code optimization in the open source computer algebra system FORM. This implementation is based on recently discovered techniques of Monte Carlo tree search to find efficient multivariate Horner schemes, in combination with other optimization algorithms, such as common subexpression elimination. For systems for which no specific knowledge is provided it performs significantly better than other methods we could compare with. Because the method has a number of free parameters, we also show some methods by which to tune them to different types of problems., Comment: 31 pages

We present a new QCD description of the ATLAS jet veto measurement, using the Banfi-Marchesini-Smye equation to constrain the inter-jet QCD radiation. This equation resums emissions of soft gluons at large angles, at leading-logarithmic accuracy, and accounts for both the so-called Sudakov and non-global logarithms. We show that this approach is able to reproduce, with no fitting parameters, the fraction of high-pT forward/backward di-jet events which do not contain additional hard emissions in the inter-jet rapidity range. We also compute the gap fraction in fixed-order perturbation theory to O(alpha_s^2) and show that the perturbative series is unstable at large rapidity intervals., Comment: 10 pages, 5 figures

We present the full $\mathcal{O}(\alpha)$ electroweak radiative corrections to the process $e^+e^- \rightarrow t \bar{t} \gamma$ at the International Linear Collider (ILC). The computation is performed with the help of the GRACE-Loop system. We present the total cross-section and the top quark forward-backward asymmetry ($A_{FB}$) as a function of the center-of-mass energy and compare them with the process $e^+e^- \rightarrow t \bar{t}$. We find that the value of $A_{FB}$ in $t \bar{t} \gamma$ production is larger than $A_{FB}$ in $t\bar{t}$ production. It is an important result for the measurement of the top quark forward-backward asymmetry at the ILC. Applying a structure function method, we also subtract the QED correction to gain the genuine weak correction in both the $\alpha$ scheme and the $G_{\mu}$ scheme ($\delta_{W}^{G_{\mu}}$). We obtain numerical values for $\delta_{W}^{G_{\mu}}$ which are changing from 2% to -24% when we vary the center-of-mass energy from 360 GeV to 1 TeV., Comment: 13 pages, 9 figures

We present version 4.0 of the symbolic manipulation system FORM. The most important new features are manipulation of rational polynomials and the factorization of expressions. Many other new functions and commands are also added; some of them are very general, while others are designed for building specific high level packages, such as one for Groebner bases. New is also the checkpoint facility, that allows for periodic backups during long calculations. Lastly, FORM 4.0 has become available as open source under the GNU General Public License version 3., Comment: 26 pages. Uses axodraw