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The nuclear equation of state (EOS) is at the center of numerous theoretical and experimental efforts in nuclear physics. With advances in microscopic theories for nuclear interactions, the availability of experiments probing nuclear matter under conditions not reached before, endeavors to develop sophisticated and reliable transport simulations to interpret these experiments, and the advent of multi-messenger astronomy, the next decade will bring new opportunities for determining the nuclear matter EOS, elucidating its dependence on density, temperature, and isospin asymmetry. Among controlled terrestrial experiments, collisions of heavy nuclei at intermediate beam energies (from a few tens of MeV/nucleon to about 25 GeV/nucleon in the fixed-target frame) probe the widest ranges of baryon density and temperature, enabling studies of nuclear matter from a few tenths to about 5 times the nuclear saturation density and for temperatures from a few to well above a hundred MeV, respectively. Collisions of neutron-rich isotopes further bring the opportunity to probe effects due to the isospin asymmetry. However, capitalizing on the enormous scientific effort aimed at uncovering the dense nuclear matter EOS, both at RHIC and at FRIB as well as at other international facilities, depends on the continued development of state-of-the-art hadronic transport simulations. This white paper highlights the essential role that heavy-ion collision experiments and hadronic transport simulations play in understanding strong interactions in dense nuclear matter, with an emphasis on how these efforts can be used together with microscopic approaches and neutron star studies to uncover the nuclear EOS., Comment: White paper prepared for the 2023 Long Range Plan. v3: Updated version as published in Progress in Particle and Nuclear Physics. Note: the published version does not include the executive summary; in the updated arXiv version, the executive summary is included as an appendix. v4: Corrected list of authors

We calculate the next-to-leading order electroweak corrections for Higgs-boson production in gluon fusion and the Higgs-boson decay into two photons or gluons in the real Higgs-singlet extension of the Standard model (HSESM). For the light Higgs-boson of the HSESM the electroweak corrections for these processes are of the same order of magnitude as in the Standard model. For the heavy Higgs-boson of the HSESM the electroweak corrections can become large depending on the considered scenario., Comment: 31 pages, 11 figures

We discuss the first-time calculation of the static gravitational two-body potential up to fifth post-Newtonian(PN) order. The results are achieved through a manifest factorization property of the odd PN diagrams. The factorization property is illustrated also at first and third PN order., Comment: 9 pages, 5 figures, contribution to the 14th International Symposium on Radiative Corrections (RADCOR2019), 9-13 September 2019, Palais des Papes, Avignon, France

We determine the gravitational interaction between two compact bodies up to the sixth power in Newton's constant GN, in the static limit. This result is achieved within the effective field theory approach to General Relativity, and exploits a manifest factorization property of static diagrams which allows to derive static post Newtonian (PN) contributions of (2n+1)-order in terms of lower order ones. We recompute in this fashion the 1PN and 3PN static potential, and present the novel 5PN contribution., Comment: 7 pages, 3 figures. In v2: references added, published on PRL

We have computed the two-loop, electroweak corrections to the production of a light and a heavy neutral, scalar Higgs-boson through the important gluon fusion process in the Two-Higgs-Doublet Model. We provide our results in various renormalization schemes for different scenarios and benchmark points, which will be valuable for experimental studies at the LHC. We describe the technicalities of our two-loop calculation and augment it by a phenomenological discussion. Our results are also applicable to the gluonic neutral, scalar Higgs-boson decays., Comment: 36 pages, 11 figures, 8 tables, v2: version accepted for publication in the journal

We update the experimental moments for the charm quark as computed in arXiv:hep-ph/0702103. and used in arXiv:0907.2110 and arXiv:1010.6157 for the determination of the charm-quark mass. The new value for the MSbar charm-quark mass reads mc(3GeV)=0.993+/-0.008 GeV., Comment: 3 pages

Working within the post-Newtonian (PN) approximation to General Relativity, we use the effective field theory (EFT) framework to study the conservative dynamics of the two-body motion at fourth PN order, at fifth order in the Newton constant. This is one of the missing pieces preventing the computation of the full Lagrangian at fourth PN order using EFT methods. We exploit the analogy between diagrams in the EFT gravitational theory and 2-point functions in massless gauge theory, to address the calculation of 4-loop amplitudes by means of standard multi-loop diagrammatic techniques. For those terms which can be directly compared, our result confirms the findings of previous studies, performed using different methods., Comment: Version accepted for publication in Phys. Rev. D. Appendix C added with details of amplitude computations

We present a consistent renormalization scheme for the CP-conserving Two-Higgs-Doublet Model based on $\overline{MS}$ renormalization of the mixing angles and the soft-$Z_2$-symmetry-breaking scale $M_{sb}$ in the Higgs sector. This scheme requires to treat tadpoles fully consistently in all steps of the calculation in order to provide gauge-independent $S$-matrix elements. We show how bare physical parameters have to be defined and verify the gauge independence of physical quantities by explicit calculations in a general $R_{\xi}$-gauge. The procedure is straightforward and applicable to other models with extended Higgs sectors. In contrast to the proposed scheme, the $\overline{MS}$ renormalization of the mixing angles combined with popular on-shell renormalization schemes gives rise to gauge-dependent results already at the one-loop level. We present explicit results for electroweak NLO corrections to selected processes in the appropriately renormalized Two-Higgs-Doublet Model and in particular discuss their scale dependence., Comment: 52 pages, PDFLaTeX, PDF figures, JHEP version with Eq. (5.23) corrected

A brief discussion of massive tadpole diagrams and their phenomenological consequences is presented. This includes predictions of the $\rho$ parameter and, as a consequence, the mass of the $W$ boson, implications on the charm and bottom quark masses from the moments, i.e. the derivatives of the current correlators, and the Higgs boson decay rate. A fairly consistent picture emerges, with $m_c(3 {GeV})=0.986\pm0.013$ GeV and $m_b(m_b)=3.610\pm0.016$ GeV. Furthermore, fairly stringent predictions for the Higgs decay rate into photons and gluons are obtained, which will be interesting in increasingly precise experiments., Comment: 12 pages, Contribution to the Proceedings of the Final Meeting of the Collaborative Research Centre / Transregio 9 "Computational Particle Physics", Durbach, Germany, September 2014, to appear in Nucl. Phys. (Proc. Suppl.), v2: Fig.10 updated, reference added

We compute the decoupling function of the MSbar renormalized fine-structure constant up to four-loop order in perturbative QCD. The results are used in order to determine the related top-quark contributions to the Higgs-boson decay into two photons in the heavy top-quark mass limit to order alpha_s^4., Comment: 19 pages, 4 figures

The running of the effective electromagnetic coupling is for many electroweak observables the dominant correction. It plays an important role for deriving constraints on the Standard Model in the context of electroweak precision measurements. We compute the four-loop QED corrections to the running of the effective electromagnetic coupling and perform a numerical evaluation of the different gauge invariant subsets., Comment: 26 pages, 4 figures

Measurements of kaon production at subthreshold energies in heavy-ion collisions point to a soft nuclear equation-of-state for densities up to 2-3 times nuclear matter saturation density. We apply these results to study the implications on compact star properties, especially in the context of the recent measurement of the two solar mass pulsar PSR J1614-2230. The implications are two-fold: Firstly, the heavy-ion results constrain nuclear matter at densities relevant to light neutron stars. Hence, a radius measurement could provide information about the density dependence of the symmetry energy which is a crucial quantity in nuclear physics. Secondly, the information on the nucleon potential obtained from the analysis of the heavy-ion data can be combined with restrictions from causality on the nuclear equation-of-state. From this we can derive a limit for the highest allowed compact star mass of three solar masses., Comment: 7 pages, 4 figures, version accepted for publication in Phys. Rev. C

Complete electroweak two-loop corrections to the process $gg \to H$ are presented and discussed in a Standard Model with a fourth generation of heavy fermions. The latter is studied at the LHC to put exclusion limits on a fourth generation of heavy fermions. Therefore also a precise knowledge of the electroweak(EW) next-to-leading-order(NLO) corrections is important. The corrections due to the fourth generation are positive and large for a light Higgs boson, positive but relatively small around the $\bar{t}-t$ threshold and start to become negative for a Higgs boson mass around $M_H = 450 GeV$. Increasing further the value of the Higgs boson mass, the EW NLO effects tend to become huge and negative, ${\cal O}(-100%)$, around the heavy-fermion threshold, assumed at $1.2 TeV$, so that $gg$-fusion becomes non-perturbative. Above that threshold they start to grow again and become positive around $M_H= 1.75 TeV$. The behaviour at even larger values of $M_H$ shows a positive enhancement, ${\cal O}(+100%)$ at $M_H= 3 TeV$., Comment: 7 pages, 5 figures

The Drell-Yan mechanism for the production of lepton pairs is one of the most basic processes for physics studies at hadron colliders. It is therefore important to have accurate theoretical predictions. In this work we compute the two-loop virtual mixed QCD x QED corrections to Drell-Yan production. We evaluate the Feynman diagrams by decomposing the amplitudes into a set of known master integrals and their coefficients, which allows us to derive an analytical result. We also perform a detailed study of the ultraviolet and infrared structure of the two-loop amplitude and the corresponding poles in epsilon., Comment: 20 pages, 3 figures

The non-perturbative renormalization of four-quark operators plays a significant role in lattice studies of flavor physics. For this purpose, we define regularization-independent symmetric momentum-subtraction (RI/SMOM) schemes for Delta S=1 flavor-changing four-quark operators and provide one-loop matching factors to the MS-bar scheme in naive dimensional regularization. The mixing of two-quark operators is discussed in terms of two different classes of schemes. We provide a compact expression for the finite one-loop amplitudes which allows for a straightforward definition of further RI/SMOM schemes., Comment: 22 pages, 5 figures

Light quark masses can be determined through lattice simulations in regularization invariant momentum-subtraction(RI/MOM) schemes. Subsequently, matching factors, computed in continuum perturbation theory, are used in order to convert these quark masses from a RI/MOM scheme to the MS-bar scheme. We calculate the two-loop corrections in quantum chromodynamics(QCD) to these matching factors as well as the three-loop mass anomalous dimensions for the RI/SMOM and RI/SMOM_gamma_mu schemes. These two schemes are characterized by a symmetric subtraction point. Providing the conversion factors in the two different schemes allows for a better understanding of the systematic uncertainties. The two-loop expansion coefficients of the matching factors for both schemes turn out to be small compared to the traditional RI/MOM schemes. For nf=3 quark flavors they are about 0.6-0.7% and 2%, respectively, of the leading order result at scales of about 2 GeV. Therefore, they will allow for a significant reduction of the systematic uncertainty of light quark mass determinations obtained through this approach. The determination of these matching factors requires the computation of amputated Green's functions with the insertions of quark bilinear operators. As a by-product of our calculation we also provide the corresponding results for the tensor operator., Comment: 24 pages, 2 figures; v2: version accepted for publication in the journal

The relation between physical observables measured at LHC and Tevatron and standard model Higgs pseudo-observables (production cross section and partial decay widths) is revised by extensively using the notion of the Higgs complex pole on the second Riemann sheet of the $S $-matrix. The extension of their definition to higher orders is considered, confronting the problems that arise when QED(QCD) corrections are included in computing realistic observables. Numerical results are presented for pseudo-observables related to the standard model Higgs boson decay and production. The relevance of the result for exclusion plots of the standard model Higgs boson for high masses (up to $600 $GeV) is discussed. Furthermore, a recipe for the analytical continuation of Feynman loop integrals from real to complex internal masses and complex Mandelstam invariants is thoroughly discussed., Comment: 36 pages, 19 figures, 4 Tables

We discuss the concepts and the framework of the renormalization procedure in regularization-invariant momentum subtraction schemes. These schemes are used in the context of lattice simulations for the determination of physical quantities like light quark masses. We focus on the renormalization procedure with a symmetric subtraction point of a quark mass and discuss its conversion from the RI/SMOM scheme to the MSbar scheme. A symmetric subtraction point allows for a lattice calculation with a reduced contamination from infrared effects. The perturbative series for the resulting matching factor at next-to-leading order is better behaved for the symmetric momentum configuration than for the exceptional one which can decrease the uncertainty in light quark mass determinations., Comment: 5 pages, 3 figures, to be published in the proceedings of DPF-2009, Detroit, MI, July 2009, eConf C090726