002637588 001__ 2637588
002637588 003__ SzGeCERN
002637588 005__ 20240119044513.0
002637588 020__ $$a9789290835417$$uprint version, paperback
002637588 020__ $$a9789290835424$$belectronic version$$uelectronic version
002637588 0247_ $$2DOI$$a10.23731/CYRM-2019-003$$qebook
002637588 0248_ $$aoai:cds.cern.ch:2637588$$pcerncds:CERN:FULLTEXT$$pcerncds:REPORT$$pcerncds:FULLTEXT$$pcerncds:CERN$$pINIS
002637588 037__ $$9arXiv$$aarXiv:1809.01830$$chep-ph
002637588 037__ $$aCERN-2019-003
002637588 037__ $$9arXiv:reportnumber$$aBU-HEPP-18-04
002637588 037__ $$9arXiv:reportnumber$$aCERN-TH-2018-145
002637588 037__ $$9arXiv:reportnumber$$aIFJ-PAN-IV-2018-09
002637588 037__ $$9arXiv:reportnumber$$aKW 18-003
002637588 037__ $$9arXiv:reportnumber$$aMITP/18-052
002637588 037__ $$9arXiv:reportnumber$$aMPP-2018-143
002637588 037__ $$9arXiv:reportnumber$$aSI-HEP-2018-21
002637588 035__ $$9arXiv$$aoai:arXiv.org:1809.01830
002637588 035__ $$9Inspire$$aoai:inspirehep.net:1692960$$d2024-01-18T01:59:49Z$$h2024-01-19T03:00:22Z$$mmarcxml$$ttrue$$uhttps://inspirehep.net/api/oai2d
002637588 035__ $$9Inspire$$a1692960
002637588 041__ $$aeng
002637588 084__ $$2CERN Yellow Report$$aCERN-2019-003
002637588 100__ $$aBlondel, A.$$uGeneva U.$$vDPNC University of Geneva, Switzerland},
002637588 245__ $$aStandard model theory for the FCC-ee Tera-Z stage$$breport on the Mini Workshop Precision EW and QCD Calculations for the FCC Studies : Methods and Tools, 12–13 January 2018, CERN, Geneva
002637588 246__ $$9arXiv$$aStandard Model Theory for the FCC-ee: The Tera-Z
002637588 269__ $$c2018-09-06
002637588 260__ $$aGeneva$$bCERN$$c2019
002637588 300__ $$a243 p
002637588 490__ $$aCERN Yellow Reports: Monographs$$v3/2019
002637588 500__ $$9arXiv$$a243 pages, Report on the 1st Mini workshop: Precision EW and QCD calculations for the FCC studies: methods and tools, 12-13 January 2018, CERN, Geneva, Switzerland
002637588 520__ $$9arXiv$$aThe future 100-km circular collider FCC at CERN is planned to operate in one of its modes as an electron-positron FCC-ee machine. We give an overview of the theoretical status compared to the experimental demands of one of four foreseen FCC-ee operating stages, which is Z-boson resonance energy physics, FCC-ee Tera-Z stage for short. The FCC-ee Tera-Z will deliver the highest integrated luminosities as well as very small systematic errors for a study the Standard Model (SM) with unprecedented precision. In fact, the FCC-ee Tera-Z will allow to study at least one more quantum field theoretical perturbative order compared to the LEP/SLC precision. The real problem is that the present precision of theoretical calculations of the various observables within the SM does not match that of the anticipated experimental measurements. The bottle-neck problems are specified. In particular, the issues of precise QED unfolding and of the correct calculation of SM pseudo-observables are critically reviewed. In an Executive Summary we specify which basic theoretical calculations are needed to meet the strong experimental expectations at the FCC-ee Tera-Z. Several methods, techniques and tools needed for higher order multi-loop calculations are presented. By inspection of the Z-boson partial and total decay widths analysis, arguments are given that at the beginning of operation of the FCC-ee Tera-Z, the theory predictions may be tuned to be precise enough not to limit the physics interpretation of the measurements. This statement is based on the anticipated progress in analytical and numerical calculations of multi-loop and multi-scale Feynman integrals and on the completion of two-loop electroweak radiative corrections to the SM pseudo-observables this year. However, the above statement is conditional as the theoretical issues demand a very dedicated and focused investment by the community.
002637588 536__ $$rOpen Access
002637588 540__ $$3preprint$$aCC-BY-4.0$$uhttp://creativecommons.org/licenses/by/4.0/
002637588 540__ $$3publication$$aCC-BY-4.0$$uhttp://creativecommons.org/licenses/by/4.0/
002637588 542__ $$3publication$$dCERN$$g2019
002637588 595__ $$aCERN-TH
002637588 599__ $$aILSSYNC
002637588 599__ $$aILSLINK
002637588 65017 $$2arXiv$$ahep-ph
002637588 65017 $$2SzGeCERN$$aParticle Physics - Phenomenology
002637588 690C_ $$aCERN
002637588 690C_ $$aYELLOW REPORT
002637588 690C_ $$aREPORT
002637588 700__ $$aGluza, J.$$uSilesia U.$$vInstitute of Physics, University of Silesia, 40-007 Katowice, Poland},
002637588 700__ $$aJadach, S.$$uCracow, INP$$vInstitute of Nuclear Physics, PAN, 31-342 Krakow, Poland},
002637588 700__ $$aJanot, P.$$uCERN$$vCERN, CH-1211 Genéve 23, Switzerland},
002637588 700__ $$aRiemann, T.$$uDESY, Zeuthen$$uSilesia U.$$vDeutsches Elektronen-Synchrotron, DESY, 15738 Zeuthen, Germany},$$vInstitute of Physics, University of Silesia, 40-007 Katowice, Poland},
002637588 700__ $$aAkhundov, A.$$uBaku, Inst. Phys.$$uValencia U.$$vDepartamento de Física Teorica, Universidad de València, 46100 València, Spain and Azerbaijan National Academy of Sciences, ANAS,
002637588 700__ $$aArbuzov, A.$$uDubna, JINR$$vBogoliubov Laboratory of Theoretical Physics, JINR, Dubna, 141980 Russia},
002637588 700__ $$aBoels, R.$$uHamburg U., Inst. Theor. Phys. II$$vII. Institut für Theoretische Physik, Universität Hamburg, 22761 Hamburg, Germany},
002637588 700__ $$aBondarenko, S.$$uDubna, JINR$$vBogoliubov Laboratory of Theoretical Physics, JINR, Dubna, 141980 Russia},
002637588 700__ $$aBorowka, S.$$uCERN$$vCERN, CH-1211 Genéve 23, Switzerland},
002637588 700__ $$aCarloni Calame, C.M.$$uINFN, Pavia$$vIstituto Nazionale di Fisica Nucleare, Sezione di Pavia, Pavia, Italy},
002637588 700__ $$aDubovyk, I.$$uDESY, Zeuthen$$uHamburg U., Inst. Theor. Phys. II$$vDeutsches Elektronen-Synchrotron, DESY, 15738 Zeuthen, Germany},$$vII. Institut für Theoretische Physik, Universität Hamburg, 22761 Hamburg, Germany},
002637588 700__ $$aDydyshka, Ya.$$uDubna, JINR$$vDzhelepov Laboratory of Nuclear Problems, JINR, Dubna, 141980 Russia},
002637588 700__ $$aFlieger, W.$$uSilesia U.$$vInstitute of Physics, University of Silesia, 40-007 Katowice, Poland},
002637588 700__ $$aFreitas, A.$$uPittsburgh U.$$vPittsburgh Particle physics, Astrophysics & Cosmology Center (PITT PACC) and Department of Physics & Astronomy, University of Pittsburgh, Pittsburgh, PA 15260, USA},
002637588 700__ $$aGrzanka, K.$$uSilesia U.$$vInstitute of Physics, University of Silesia, 40-007 Katowice, Poland},
002637588 700__ $$aHahn, T.$$uMunich, Max Planck Inst.$$vMax-Planck-Institut für Physik, Föhringer Ring 6, D-80805 München, Germany},
002637588 700__ $$aHuber, T.$$uSiegen U.$$vNaturwissenschaftlich-Technische Fakultät, Universität Siegen, 57068 Siegen, Germany},
002637588 700__ $$aKalinovskaya, L.$$uDubna, JINR$$vDzhelepov Laboratory of Nuclear Problems, JINR, Dubna, 141980 Russia},
002637588 700__ $$aLee, R.$$uNovosibirsk, IYF$$vThe Budker Institute of Nuclear Physics, 630090, Novosibirsk},
002637588 700__ $$aMarquard, P.$$uDESY, Zeuthen$$vDeutsches Elektronen-Synchrotron, DESY, 15738 Zeuthen, Germany},
002637588 700__ $$aMontagna, G.$$uPavia U.$$vDipartimento di Fisica, Università di Pavia, Pavia, Italy},
002637588 700__ $$aNicrosini, O.$$uINFN, Pavia$$vIstituto Nazionale di Fisica Nucleare, Sezione di Pavia, Pavia, Italy},
002637588 700__ $$aPapadopoulos, C.G.$$uDemocritos Nucl. Res. Ctr.$$vInstitute of Nuclear and Particle Physics, NCSR Demokritos, 15310, Greece},
002637588 700__ $$aPiccinini, F.$$uINFN, Pavia$$vIstituto Nazionale di Fisica Nucleare, Sezione di Pavia, Pavia, Italy},
002637588 700__ $$aPittau, R.$$uGranada U., Theor. Phys. Astrophys.$$uCAFPE, Granada$$vDep. de Física Teórica y del Cosmos and CAFPE, Universidad de Granada,
002637588 700__ $$aPłaczek, W.$$uJagiellonian U.$$vMarian Smoluchowski Institute of Physics, Jagiellonian University, 30-348 Kraków, Poland},
002637588 700__ $$aPrausa, M.$$uFreiburg U.$$vAlbert-Ludwigs-Universität, Physikalisches Institut, Freiburg, Germany},
002637588 700__ $$aRiemann, S.$$uDESY, Zeuthen$$vDeutsches Elektronen-Synchrotron, DESY, 15738 Zeuthen, Germany},
002637588 700__ $$aRodrigo, G.$$uValencia U., IFIC$$vInstituto de Física Corpuscular, Universitat de València - CSIC, 46980 Paterna, València, Spain},
002637588 700__ $$aSadykov, R.$$uDubna, JINR$$vDzhelepov Laboratory of Nuclear Problems, JINR, Dubna, 141980 Russia},
002637588 700__ $$aSkrzypek, M.$$uCracow, INP$$vInstitute of Nuclear Physics, PAN, 31-342 Krakow, Poland},
002637588 700__ $$aStöckinger, D.$$uDresden, Tech. U.$$vInstitut für Kern- und Teilchenphysik, TU Dresden, 01069 Dresden, Germany},
002637588 700__ $$aUsovitsch, J.$$uTrinity Coll., Dublin$$vTrinity College Dublin - School of Mathematics, Dublin 2, Ireland},
002637588 700__ $$aWard, B.F.L.$$uMunich, Max Planck Inst.$$uBaylor U.$$vMax-Planck-Institut für Physik, Föhringer Ring 6, D-80805 München, Germany},$$vBaylor University, Waco, TX, USA},
002637588 700__ $$aWeinzierl, S.$$uU. Mainz, PRISMA$$uMainz U., Inst. Phys.$$vPRISMA Cluster of Excellence, Inst. für Physik, Johannes Gutenberg-Universität, 55099 Mainz, Germany},
002637588 700__ $$aYang, G.$$uBeijing, KITPC$$vCAS Key Laboratory of Theoretical Physics, Chinese Academy of Sciences, Beijing 100190, China},
002637588 700__ $$aYost, S.A.$$uCitadel Military Coll.$$vThe Citadel, Charleston, SC, USA}
002637588 773__ $$wC18-01-12
002637588 8564_ $$81516203$$s5186353$$uhttps://cds.cern.ch/record/2637588/files/89-75-PB.pdf
002637588 8564_ $$81516203$$s6623761$$uhttps://cds.cern.ch/record/2637588/files/89-75-PB.pdf?subformat=pdfa$$xpdfa
002637588 8564_ $$82206711$$s6564885$$uhttps://cds.cern.ch/record/2637588/files/1809.01830.pdf
002637588 8564_ $$82206687$$s4715$$uhttps://cds.cern.ch/record/2637588/files/1706_09852-2.png$$y00007 First integration over momentum $k_1$ in the 3-loop diagram.
002637588 8564_ $$82206688$$s421172$$uhttps://cds.cern.ch/record/2637588/files/loopedia_start.png$$y00052 \textsc{Loopedia}'s landing page.
002637588 8564_ $$82206689$$s4506$$uhttps://cds.cern.ch/record/2637588/files/1706_09852-1.png$$y00032 Example of a 3-loop non-planar integral where \la{} gives a less dimensional \mbr{} integral than \ga{}, though its numerical stability can be worse due to more complicated kinematical factors; even in Euklidean kinematical regions.
002637588 8564_ $$82206690$$s5143$$uhttps://cds.cern.ch/record/2637588/files/chain.png$$y00014 Basic skeleton generating diagrams for 3-loop topologies \cite{Cvitanovic:1974uf}.
002637588 8564_ $$82206691$$s3385$$uhttps://cds.cern.ch/record/2637588/files/ratioPositive.png$$y00040 Scatterplot of the relative error of FIESTA results compared to PSLQ results for the $\epsilon^{\{-6,-5,-4\}}$ coefficients. (Left) Plot of cases ${\textrm{FIESTA error} \over I_{\rm PSLQ} - I_{\rm FIESTA}} > 0$. (Right) Plot of cases ${\textrm{FIESTA error} \over I_{\rm FIESTA} - I_{\rm PSLQ}} > 0$. A logarithmic scale appears on the vertical axis, and all ratios larger than $200$ are not shown in the figures. All ratios are larger than unity, which clearly indicates that the FIESTA errors are conservative estimates. Deviations of FIESTA results from PSLQ results show no tilt to the positive or negative, which supports the conclusion that there is no source of systematic errors.
002637588 8564_ $$82206692$$s4793$$uhttps://cds.cern.ch/record/2637588/files/acollbb.png$$y00011 Comparison between \babayagaNLO\ and \bhwide\ on the acollinearity distribution.
002637588 8564_ $$82206693$$s8000$$uhttps://cds.cern.ch/record/2637588/files/asy-crop.png$$y00039 \it Figure from \cite{Kirsch:1994cf}.The forward-backward asymmetry for the process $e^+ e^- \rightarrow \mu^+ \mu^-$ near the $Z$ peak.
002637588 8564_ $$82206694$$s134251$$uhttps://cds.cern.ch/record/2637588/files/saddle_1.png$$y00016 The real part of the function $f(z)=z^{2}$ with a marked critical value $f(z_{0})=0$ at the critical point $z_{0}=(0,0)$. Below the surface of $Re(z^{2})$ you can see the level set curves of $Im(f(z))=Im(f(z_{0}))$ which correspond to the contour of steepest descent (green) and steepest ascent (blue).
002637588 8564_ $$82206695$$s63950$$uhttps://cds.cern.ch/record/2637588/files/bardin-1980fe-eq421b.png$$y00050 \it Eqns. 4.12 and 4.21 from \cite{Bardin:1980fe} with the contributions of Figs. 4.11 and 4.20 to the general 2$\to$2 matrix element in the unitary gauge.
002637588 8564_ $$82206696$$s17311$$uhttps://cds.cern.ch/record/2637588/files/bardin-1980fe-fig411.png$$y00004 \it Figure 4.11 from \cite{Bardin:1980fe}, showing a generic massive crossed one-loop box diagram of the $ZZ$ and $WW$ box type and Fig. 4.20 with the two photon box diagrams. The latter two diagrams have to be combined with initial-final state interference soft photon bremsstrahlung in order to get a finite result.
002637588 8564_ $$82206697$$s43692$$uhttps://cds.cern.ch/record/2637588/files/bardin-1980fe-eq421a.png$$y00021 \it Eqns. 4.12 and 4.21 from \cite{Bardin:1980fe} with the contributions of Figs. 4.11 and 4.20 to the general 2$\to$2 matrix element in the unitary gauge.
002637588 8564_ $$82206698$$s17692$$uhttps://cds.cern.ch/record/2637588/files/a_el_costh_250.png$$y00018 The left-right asymmetry $A_{LR}$ as a function of the cosine of the electron scattering angle at $\sqrt{s}=250$~GeV (left) and at $\sqrt{s}=500$~GeV (right).
002637588 8564_ $$82206699$$s6880$$uhttps://cds.cern.ch/record/2637588/files/delta_el_costh_NN_500.png$$y00019 The differential cross section (left) [in pb] and the relative correction $\delta$ (right) [in \%] vs. the cosine of the electron scattering angle for $\sqrt{s}=500$~GeV.
002637588 8564_ $$82206700$$s3266$$uhttps://cds.cern.ch/record/2637588/files/mu-massive.png$$y00051 IR divergent splitting regulated by $\mu$-massive (thick) unobserved particles. The cut on the left represents the virtual part. The two-particle cut on the right contributes to the real radiation. The sum of the two is free of IR divergences.
002637588 8564_ $$82206701$$s6987$$uhttps://cds.cern.ch/record/2637588/files/delta_el_costh_NN_1000.png$$y00025 The differential cross section (left) [in pb] and the relative correction $\delta$ (right) [in \%] vs. the cosine of the electron scattering angle for $\sqrt{s}=1000$~GeV.
002637588 8564_ $$82206702$$s7935$$uhttps://cds.cern.ch/record/2637588/files/el_costh_NN_1000.png$$y00023 The differential cross section (left) [in pb] and the relative correction $\delta$ (right) [in \%] vs. the cosine of the electron scattering angle for $\sqrt{s}=1000$~GeV.
002637588 8564_ $$82206703$$s1075$$uhttps://cds.cern.ch/record/2637588/files/mbbrackets_ex.png$$y00026 Two-loop non-planar vertex-type Feynman integral.
002637588 8564_ $$82206704$$s26115$$uhttps://cds.cern.ch/record/2637588/files/mersennetwister.png$$y00005 Comparison of sequences.
002637588 8564_ $$82206705$$s8048$$uhttps://cds.cern.ch/record/2637588/files/el_costh_NN_500.png$$y00033 The differential cross section (left) [in pb] and the relative correction $\delta$ (right) [in \%] vs. the cosine of the electron scattering angle for $\sqrt{s}=500$~GeV.
002637588 8564_ $$82206706$$s8753$$uhttps://cds.cern.ch/record/2637588/files/a_el_costh_1000.png$$y00006 The left-right asymmetry $A_{LR}$ as a function of the cosine of the electron scattering angle at $\sqrt{s}=1000$~GeV.
002637588 8564_ $$82206707$$s165867$$uhttps://cds.cern.ch/record/2637588/files/EWPO-LEP.png$$y00010 Scheme of construction of the EWPOs in data analysis of LEP
002637588 8564_ $$82206708$$s8006$$uhttps://cds.cern.ch/record/2637588/files/el_costh_NN_250.png$$y00035 The differential cross section (left) [in pb] and the relative correction $\delta$ (right) [in \%] vs. the cosine of the electron scattering angle for $\sqrt{s}=250$~GeV.
002637588 8564_ $$82206709$$s197059$$uhttps://cds.cern.ch/record/2637588/files/EWPO-FCC.png$$y00047 Possible scheme of construction of the EWPPs in data analysis of FCC-ee
002637588 8564_ $$82206710$$s1505$$uhttps://cds.cern.ch/record/2637588/files/ll.png$$y00034 3-loop topologies generated from the left skeleton diagram in Fig.~\ref{fig:skel}.
002637588 8564_ $$82206712$$s2054$$uhttps://cds.cern.ch/record/2637588/files/contour.png$$y00028 The black dots are the poles of the integrand in Eq.~\eqref{eq:MB0h0w14finitelinearTransformation} in the $z_{1}$ complex plane. The dashed line is the integration contour parallel to the imaginary axis.
002637588 8564_ $$82206713$$s2794$$uhttps://cds.cern.ch/record/2637588/files/int99.png$$y00044 Example of a planar four-loop diagram.
002637588 8564_ $$82206714$$s2180$$uhttps://cds.cern.ch/record/2637588/files/llnp.png$$y00012 3-loop topologies generated from the right skeleton diagram in Fig.~\ref{fig:skel}.
002637588 8564_ $$82206715$$s70210$$uhttps://cds.cern.ch/record/2637588/files/figtrans2.png$$y00024 HCuba/figtrans2
002637588 8564_ $$82206716$$s2935$$uhttps://cds.cern.ch/record/2637588/files/contour2.png$$y00029 The original contour $C_{1}$ is shifted by $n_{1}=-2$ to a contour $C_{2}$. The third contour $C_{3}$ encircles the poles to correct the shift.
002637588 8564_ $$82206717$$s22499$$uhttps://cds.cern.ch/record/2637588/files/I39OTE0movederr3.png$$y00045 The I39 Integral calculated at $\mathcal{O}(\epsilon^0)$ with a fourth order series expansion. The scale $s$ is over the $4m_1^2$ threshold, with $u=-59858 \text{GeV}^2$, $m_2=\frac{1}{\sqrt{2}}m_1$ and $m_1=173~\text{GeV}$. The lower plots show the relative \textsc{TayInt} and \textsc{SecDec} uncertainties, respectively.
002637588 8564_ $$82206718$$s2916$$uhttps://cds.cern.ch/record/2637588/files/anomaly.png$$y00027 The two diagrams generating the ABJ anomaly.
002637588 8564_ $$82206719$$s1487$$uhttps://cds.cern.ch/record/2637588/files/I39.png$$y00031 The box-type integral I39 is so far unknown analytically. Dashed lines indicate massless and solid lines massive propagators.
002637588 8564_ $$82206720$$s7721$$uhttps://cds.cern.ch/record/2637588/files/hggdiagrams.png$$y00049 Virtual and real diagrams contributing to $H \to g g (g)$ at ${\cal O}(\alpha_S^3)$.
002637588 8564_ $$82206721$$s1675$$uhttps://cds.cern.ch/record/2637588/files/mxnp.png$$y00037 Transforming five propagators of the chosen 2-loop sub-diagram into an effective propagator leading directly to the one-loop topology.
002637588 8564_ $$82206722$$s12266$$uhttps://cds.cern.ch/record/2637588/files/rhodiag2.png$$y00008 Heavy-quark corrections to the $W$ and $Z$ propagator contributing to the $\rho$ parameter at ${\cal O}(G_F\alpha_S)$ (from \cite{Zirke:2015spg}).
002637588 8564_ $$82206723$$s1820$$uhttps://cds.cern.ch/record/2637588/files/mxpl.png$$y00020 Transforming propagators of the one-loop box at the left side into an effective propagator which changes the whole diagram into a two-loop topology.
002637588 8564_ $$82206724$$s1641$$uhttps://cds.cern.ch/record/2637588/files/planar-pentabox-P3_withp-eps-converted-to.png$$y00030 The three planar pentaboxes of the families $P_1$ (left), $P_2$ (middle) and $P_3$ (right) with one external massive leg.
002637588 8564_ $$82206725$$s8603$$uhttps://cds.cern.ch/record/2637588/files/a_el_costh_500.png$$y00042 The left-right asymmetry $A_{LR}$ as a function of the cosine of the electron scattering angle at $\sqrt{s}=250$~GeV (left) and at $\sqrt{s}=500$~GeV (right).
002637588 8564_ $$82206726$$s1699$$uhttps://cds.cern.ch/record/2637588/files/planar-pentabox-P1_withp-eps-converted-to.png$$y00017 The three planar pentaboxes of the families $P_1$ (left), $P_2$ (middle) and $P_3$ (right) with one external massive leg.
002637588 8564_ $$82206727$$s26570$$uhttps://cds.cern.ch/record/2637588/files/bardin-1980fe-fig420.png$$y00046 \it Figure 4.11 from \cite{Bardin:1980fe}, showing a generic massive crossed one-loop box diagram of the $ZZ$ and $WW$ box type and Fig. 4.20 with the two photon box diagrams. The latter two diagrams have to be combined with initial-final state interference soft photon bremsstrahlung in order to get a finite result.
002637588 8564_ $$82206728$$s1598$$uhttps://cds.cern.ch/record/2637588/files/planar-pentabox-P2_withp-eps-converted-to.png$$y00022 The three planar pentaboxes of the families $P_1$ (left), $P_2$ (middle) and $P_3$ (right) with one external massive leg.
002637588 8564_ $$82206729$$s3410$$uhttps://cds.cern.ch/record/2637588/files/planar-pentabox-P1_withpx-eps-converted-to.png$$y00015 The parametrization of external momenta in terms of $x$ for the planar pentabox of the family $P_1$. All external momenta are incoming.
002637588 8564_ $$82206730$$s152155$$uhttps://cds.cern.ch/record/2637588/files/250px-DYuBardin-2.png$$y00043 s'-M_Z^2
002637588 8564_ $$82206731$$s2319$$uhttps://cds.cern.ch/record/2637588/files/JU-5liner-crop.png$$y00001 Two-loop vertex Feynman integral with two internal massive lines and the kinematics are $p^{2}_{1,2}=0$ and $2p_{1}p_{2}=s$. The $Z$-boson mass $M_{Z}$ indicates massive propagators.
002637588 8564_ $$82206732$$s26184$$uhttps://cds.cern.ch/record/2637588/files/sobol.png$$y00003 Comparison of sequences.
002637588 8564_ $$82206733$$s6701$$uhttps://cds.cern.ch/record/2637588/files/pysecdec_workflow-eps-converted-to.png$$y00038 Flowchart showing the main building blocks of \textsc{pySecDec}. Steps 1 to 6 are executed in python. \textsc{FORM} is used in step 7 to produce optimized C++ code.
002637588 8564_ $$82206734$$s2555$$uhttps://cds.cern.ch/record/2637588/files/ratioNegative.png$$y00048 Scatterplot of the relative error of FIESTA results compared to PSLQ results for the $\epsilon^{\{-6,-5,-4\}}$ coefficients. (Left) Plot of cases ${\textrm{FIESTA error} \over I_{\rm PSLQ} - I_{\rm FIESTA}} > 0$. (Right) Plot of cases ${\textrm{FIESTA error} \over I_{\rm FIESTA} - I_{\rm PSLQ}} > 0$. A logarithmic scale appears on the vertical axis, and all ratios larger than $200$ are not shown in the figures. All ratios are larger than unity, which clearly indicates that the FIESTA errors are conservative estimates. Deviations of FIESTA results from PSLQ results show no tilt to the positive or negative, which supports the conclusion that there is no source of systematic errors.
002637588 8564_ $$82206735$$s6577$$uhttps://cds.cern.ch/record/2637588/files/delta_el_costh_250.png$$y00000 The differential cross section (left) [in pb] and the relative correction $\delta$ (right) [in \%] vs. the cosine of the electron scattering angle for $\sqrt{s}=250$~GeV.
002637588 8564_ $$82206736$$s8218$$uhttps://cds.cern.ch/record/2637588/files/correlators.png$$y00013 Irreducible QCD Green's functions. The gray blobs denote the sum of all possible two-loop Feynman diagrams.
002637588 8564_ $$82206737$$s2220$$uhttps://cds.cern.ch/record/2637588/files/top26.png$$y00009 \tt FindIntegerNullVector
002637588 8564_ $$82206738$$s4903$$uhttps://cds.cern.ch/record/2637588/files/invmassbb.png$$y00036 Comparison between \babayagaNLO\ and \bhwide\ on the final-state invariant mass distribution.
002637588 8564_ $$82206739$$s122882$$uhttps://cds.cern.ch/record/2637588/files/bardin-1980fe-eq412.png$$y00041 \it Eqns. 4.12 and 4.21 from \cite{Bardin:1980fe} with the contributions of Figs. 4.11 and 4.20 to the general 2$\to$2 matrix element in the unitary gauge.
002637588 8564_ $$82206740$$s4913$$uhttps://cds.cern.ch/record/2637588/files/hppdiagrams.png$$y00002 Feynman diagrams contributing to the QCD corrections of the top-loop-mediated Higgs decay into two photons. The same diagrams with the electric charge flowing counterclockwise also contribute.
002637588 8564_ $$82223716$$s121001$$uhttps://cds.cern.ch/record/2637588/files/Front cover.png
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002637588 962__ $$b2637701$$ngeneva20180112
002637588 960__ $$a21
002637588 980__ $$aConferencePaper
002637588 980__ $$aBOOK
002637588 980__ $$aREPORT
002637588 980__ $$aPREPRINT