Search

We present recent results based on the IR-improvement of unintegrable singularities in the infrared regime via amplitude-based resummation in $QED \times QCD \subset SU(2)_L \times U_1 \times SU(3)_c$. In the context of precision LHC$/$FCC physics, we focus on specific examples, such as the removal of QED contamination in PDFs evolved from data at ${Q_0}^2 \sim 2\; {\text{GeV}}^2$ and used in the evaluating precision observables in $pp \rightarrow Z + X \rightarrow \ell\bar{\ell} + X'$, in which we discuss new results and new issues., Comment: 6 pages, 4 figures, presented by BFLW at ICHEP 2024, Prague, CZ, July 18, 2024. arXiv admin note: substantial text overlap with arXiv:2410.06226

The LEP precision physics requirements on the theoretical precision tag for the respective luminosity were $0.054 \%$ ($0.061\%$) at $M_Z$, where the former (latter) LEP result has (does not have) the pairs correction. For the contemplated FCC-ee, ILC, and CEPC Higgs/EW factories, one needs improvement at $M_Z$ to at least $0.01\%$ for the theoretical precision tag. We discuss the paths one may take to even exceed this latter goal and present an update on the current expectations for both $M_Z$ and proposed higher energy scenarios., Comment: 3 pages, 3 figures, poster presented by BFLW at ICHEP 2024, Prague, CZ, on 7/18/2024

We improve the YFS IR resummation theory so that it includes all of the attendant collinear contributions which exponentiate. The attendant new resummed contributions are shown to agree with known results from the collinear factorization approach. We argue that they improve the corresponding precision tag for a given level of exactness in the respective YFS hard radiation residuals as the latter are realized in the YFS MC approach to precision high-energy collider physics., Comment: 3 pages, no figures, poster presented by BFLW at ICHEP 2024, Prague, CZ, on 7/19/2024

There is a continuing effort to support and prepare the precision physics programs for the present and planned future colliders such as HL-LHC, FCC, CLIC, CEPC, and CPPC. We discuss new results from IR-improved amplitude-based resummation in quantum field theory relevant to such support and preparation with some emphasis on the interplay between soft and collinear resummation algebras., Comment: 9 pages, 5 figures, presented by BFLW at RADCOR2023, Crieff, Scotland, UK

We extend the YFS IR resummation theory to include all of the attendant collinear contributions which exponentiate. This improves the original YFS formulation in which only a part of these contributions was exponentiated. We show that the new resummed contributions agree with known results from the collinear factorization approach and we argue that they improve the attendant precision tag for a given level of exactness in the respective YFS hard radiation residuals., Comment: 11 pages, 2 figures, improved text, references; typos corrected. arXiv admin note: text overlap with arXiv:2203.12557

KKMChh adapts the CEEX (Coherent Exclusive Exponentiation) formalism of the Monte Carlo Program KKMC for Z boson production and decay to hadron scattering. Amplitude-level soft photon exponentiation of initial and final state radiation, together with initial-final interference, is matched to a perturbative calculation to second order next-to-leading logarithm, and electroweak corrections to the hard process are included via DIZET. The first release of KKMChh included complete initial state radiation calculated with current quark masses. This version assumes idealized pure-QCD PDFs with negligible QED contamination. Traditional PDFs neglect QED evolution but are not necessarily free of QED influence in the data. QED-corrected PDFs provide a firmer starting point for precision QED work. We describe a new procedure for matching KKMChh's initial state radiation to a QED-corrected PDF, and compare this to earlier approaches., Comment: Presented by S. Yost at ICHEP 2022, Bologna Italy, July 6 - 13, 2022; 6 pages with 3 figures. Update adds a hyperlink to one reference. Now matches the published proceedings version exactly

For both the FCC-ee and the ILC, to exploit properly the respective precision physics program, the theoretical precision tag on the respective luminosity will need to be improved from the analogs of the $ 0.054 \% (0.061\%)$ results at LEP at $M_Z$, where the former (latter) LEP result has (does not have) the pairs correction. At the FCC-ee at $M_Z$ one needs improvement to $0.01\%$, for example. We present an overview of the roads one may take to reach the required $0.01\%$ precision tag at the FCC-ee and of what the corresponding precision expectations would be for the FCC-ee$_{350}$, ILC$_{500}$, ILC$_{1000}$, and CLIC$_{3000}$ setups., Comment: 6 pages, 5 tables, talk presented by BFLW at ICHEP2022, Bologna, Italy, 7/7/2022

We present the {\tt KKMCee 5.00.2} Monte Carlo event generator for lepton and quark pair production for the high energy electron-positron annihilation process. It is still the most sophisticated event generator for such processes. Its entire source code is re-written in the modern C++ language. It reproduces all features of the older \kkmc\ code in Fortran 77. However, a number of improvements in the Monte Carlo algorithm are also implemented. Most importantly, it is intended to be a starting point for the future improvements, which will be mandatory for the future high precision lepton collider projects. As in the older version, in addition to higher order QED corrections, it includes so-called \order{\alpha^{1.5}} genuine weak corrections using a version of the classic {\tt DIZET} library and polarized $\tau$ decays using {\tt TAUOLA} program. Both {\tt DIZET} and {\tt TAUOLA} external libraries are still in Fortran 77. In addition, a {\tt HEPMC3} interface to other MC programs, like parton showers and detector simulation, replaces the older {\tt HepEvt} interface. The {\tt HEPMC3} interface is also exploited in the implementation of the additional photon final state emissions in $\tau$ decays using an external {\tt PHOTOS} library rewritten in C., Comment: To be submitted to Computer Physics Communications

This white paper concerns theoretical and phenomenological aspects relevant to the physics of future $e^+e^-$ colliders, in particular regarding initial-state QED radiation. The contributions each contain key technical aspects, and are formulated in a pedagogical manner so as to render them accessible also to those who are not directly working on these and immediately-related topics. This should help both experts and non-experts understand the theoretical challenges that we shall face at future $e^+e^-$ colliders. Specifically, this paper contains descriptions of the treatment of initial state radiation from several Monte Carlo collaborations, as well as contributions that explain a number of more theoretical developments with promise of future phenomenological impact., Comment: Contribution to: 2022 Snowmass Summer Study

We provide an overview of the status of Monte-Carlo event generators for high-energy particle physics. Guided by the experimental needs and requirements, we highlight areas of active development, and opportunities for future improvements. Particular emphasis is given to physics models and algorithms that are employed across a variety of experiments. These common themes in event generator development lead to a more comprehensive understanding of physics at the highest energies and intensities, and allow models to be tested against a wealth of data that have been accumulated over the past decades. A cohesive approach to event generator development will allow these models to be further improved and systematic uncertainties to be reduced, directly contributing to future experimental success. Event generators are part of a much larger ecosystem of computational tools. They typically involve a number of unknown model parameters that must be tuned to experimental data, while maintaining the integrity of the underlying physics models. Making both these data, and the analyses with which they have been obtained accessible to future users is an essential aspect of open science and data preservation. It ensures the consistency of physics models across a variety of experiments., Comment: 164 pages, 10 figures, contribution to Snowmass 2021

The mini-proceedings of the STRONG2020 Virtual Workshop "Space-like and Time-like determination of the Hadronic Leading Order contribution to the Muon $g-2$", November 24--26 2021, are presented. This is the first workshop of the STRONG2020 WP21: JRA3-PrecisionSM: Precision Tests of the Standard Model (http://www.strong-2020.eu/joint-research-activity/jra3-precisionsm.html). The workshop was devoted to review of the working group activitity on: $(\it i)$ Radiative Corrections and Monte Carlo tools for low-energy hadronic cross sections in $e^+ e^-$ collisions; $(\it ii)$ Annotated database for $e^+e^-$ into hadrons processes at low energy; $(\it iii)$ Radiative Corrections and Monte Carlo tools for $\mu$-$e$ elastic scattering., Comment: 43 pages, 21 contributions. Editors: A. Kup\'s\'c and G. Venanzoni

We describe a new semi-analytical program, KKhhFoam, which provides a simplified framework for testing the amplitude-level exponentiation scheme (CEEX) of the full KKMChh program in the semi-soft limit. The structure of the KKhhFoam integrand is also helpful for elucidating the structure of CEEX. We also discuss the representation of ISR in KKMChh and compare the ISR added by KKMChh to the effect of switching to a QED-corrected PDF, at the individual quark level, and suggest a new approach to running KKMChh with QED-corrected PDFs., Comment: 11 pages, 11 figures, presented at RADCOR/Loopfest 2021, 15th International Symposium on Radiative Corrections: Applications of Quantum Field Theory to Phenomenology, FSU, Tallahassee, FL, USA, 17-21 May 2021

With the advancement of strategies for the precision physics programs for the HL-LHC, FCC-ee, FCC-hh, ILC, CLIC, CEPC, and CPPC, the need for proper control of the attendant theoretical precision tags is manifest. We discuss the role that amplitude-based resummation may play in this regard with examples from the LHC, the proposed new colliders and quantum gravity., Comment: 11 pages, 3 figures, presented by B.F.L. Ward at Radcor-LoopFest2021, Florida State University, Tallahassee, FL, USA, May 2021; improved references; misprints corrected

To exploit properly the precision physics program at the FCC-ee, the theoretical precision tag on the respective luminosity will need to be improved from the 0.054$\%$ (0.061$\%$) results at LEP to 0.01$\%$, where the former (latter) LEP result has (does not have) the pairs correction. We present an overview of the roads one may take to reach the required 0.01$\%$ precision tag at the FCC-ee and we discuss possible synergistic effects of the walk along these roads for other FCC precision theory requirements., Comment: 6 pages, 3 tables, presented by B.F.L. Ward at ICHEP2020, Prague, CZ, July 29, 2020. arXiv admin note: substantial text overlap with arXiv:1902.05912

Since the {\tt KKMC} program was published for the first time over 20 years ago, it has gained popularity and was exploited in a broad spectrum of applications. The core part of the program itself did not change much. In contrast, some of the libraries have evolved substantially. The aim of this publication is to archive four versions, alternative to the one published 20 years ago versions of the electroweak libraries (or just parameter initialization versions), which were instrumental for the precision Standard Model calculation from the end of LEP era till now and for the sake of the future applications/comparisons for the future electron-positron colliders, in particular for the FCC-ee related studies. These electroweak libraries are useful for the hadron collider applications as well, for instance for {\tt KKMC-hh} or {\tt TauSpinner} projects.

The factorisation scheme (FS) abbreviated as KRK FS including a new definition of the PDFs for initial hadrons was formulated while developing KrkNLO scheme of matching QCD NLO corrections for the hard process with the parton shower heavy boson production in hadron-hadron collision and for deep inelastic lepton-hadron scattering. KRK FS (originally called Monte Carlo FS) can be regarded as a variant of the $\overline{MS}$ system. It is therefore trivially universal, that is process independent. The question of its universality is formulated differently: As the basic role of KRK FS is to simplify drastically NLO corrections, the question is now whether the same {\em single} variant of PDFs in the KRK FS is able to achieve the same maximal simplification of the NLO corrections for {\em all processes} with one or two initial hadrons and any number of the final hadrons? Our answer is positive and the proof is elaborated in the present note within the Catani-Seymour subtraction methodology. KRK FS is mandatory in the KrkNLO method of matching NLO calculation and parton shower -- a much simpler alternative of POWHEG and/or MC\@ NLO. However, the use of KRK FS and the corresponding PDFs simplifies NLO calculations for any other method of calculating NLO corrections and for arbitrary processes as well., Comment: Presented at XXV Cracow EPIPHANY Conference, January 7-10, 2020

KKMC-hh is a hadronic event generator for Z boson production and decays, which includes exponentiated multi-photon radiation and first-order electroweak corrections. We have used KKMC-hh to investigate the role of initial sate radiation (ISR) and initial-final interference (IFI) in precision electroweak analyses at the LHC. We compare the effect of this radiation on angular distributions and forward-backward asymmetry, which are particularly important for the measurement of the weak mixing angle. We discuss the relation of the ISR implementation in KKMC-hh to ISR from parton distribution functions with QED corrections., Comment: Presented at 14th International Symposium on Radiative Corrections (RADCOR2019), 9-13 September 2019, Palais des Papes, Avignon, France. 10 pages, 18 figures. Slightly extended relative to published version

Continuing with our investigations of the expected sizes of multiple photon radiative effects in heavy gauge boson production with decay to charged lepton pairs in the context of the precision physics of the LHC, using \KK{MC}-hh 4.22 we consider IFI and ISR effects for specific Z/$\gamma^*$ Drell-Yan observables measured by the ATLAS and CMS Collaborations. With this version of \KK{MC}-hh, we have coherent exclusive exponentiation (CEEX) electroweak (EW) exact ${\cal O}(\alpha^2 L)$ corrections in a hadronic MC and control over the corresponding EW initial-final interference (IFI) effects as well. Specifically, we illustrate the interplay between cuts of the type used in the measurement of $A_{FB}$ and $A_4$ at the LHC and the sizes of the expected responses of the attendant higher order corrections. We find that there are per cent to per mille level effects in the initial-state radiation, fractional per mille level effects in the IFI and per mille level effects in the over-all ${\cal O}(\alpha^2 L)$ corrections that any treatment of EW corrections at the per mille level should consider. Our results are applicable to current LHC experimental data analyses., Comment: 20 pages, 13 figures, 4 tables; updated figures, more discussion, improved references, typos corrected

IR-improvement based on amplitude-level resummation allows one to control unintegrable results in quantum field theory with arbitrary precision in principle. We illustrate such resummation in specific examples in precision LHC and FCC physics and in quantum gravity., Comment: 11 pages, 3 figures, 3 tables, presented by B.F.L. Ward at RADCOR2019, Avignon, FR, 9/12/2019. arXiv admin note: text overlap with arXiv:1811.09509

At the high luminosity electron-positron circular colliders like FCC-ee in CERN and CEPC in China it will possible to measure very precisely $e^+e^-\to Z\gamma$ process with subsequent Z decay into particles invisible in the detector, that is into three neutrina of the Standard Model and possibly into other weakly coupled neutral particles. Apart from the measurement of the total invisible width (which is not the main subject of this work) this process may be used as a source of $Z$ coupling to electron neutrino -- known very poorly. This is possible due to the presence of the $t$-channel $W$ exchange in the $e^+e^-\to \nu_e \bar\nu_e \gamma$ channel which deforms slightly spectrum of the photon. We are going to show experimental investigation of this effect, for $\sim 10$ inverse atobarn accumulated luminosity, which can provide measurement of the $Z-\nu_e$ coupling with statistical error of order 1\%. The estimation of the systematic experimental error will require more work, but most likely it will be of similar size., Comment: Ref. [10] updated

All real and virtual infrared singularities in the standard analysis of the perturbative Quantum Electrodynamics (like that of Yennie-Frautschi-Suura) are associated with photon emissions from the external legs in the scattering process. External particles are stable, with the zero decay width. Such singularities are well understood at any perturbative order and are resummed. The case of production and decay of the semi-stable {\em neutral} particles like $Z$ boson or $\tau$ lepton, with the narrow decay width, $\Gamma/M \ll 1$, is also well understood at any perturbative order and soft photon resummation can be done. For the absent or loose upper cut-off on the total photon energy $\omega$ the production and decay process of the semi-stable (neutral) particles decouples approximately and can be considered quasi-independently. In particular soft photon resummation can be done separately for the production and decay process treating semi-stable (neutral) particle as stable. So far, consistent treatment of the soft photon resummation for semi-stable {\em charged} particles like $W^\pm$ boson is not available in the literature and the aim of this work is to present a solution for this problem. Generally, it should be feasible because the underlying physics is the same as in the case of the neutral semi-stable resonances -- in the limit $\Gamma/M \ll 1$ production and decay processes for charged particles also necessarily decouple due to long lifetime of the particles. The technical problems to be solved in this work are related to the fact that semi-stable charged particle are able to emit photons., Comment: Short version has appeared in conference materials, Symmetry 11, 1389 (2019)

Due to the high anticipated experimental precision at the Future Circular Collider FCC-ee (or other proposed $e^+e^-$ colliders, such as ILC, CLIC, or CEPC) for electroweak and Higgs-boson precision measurements, theoretical uncertainties may have, if unattended, an important impact on the interpretation of these measurements within the Standard Model (SM), and thus on constraints on new physics. Current theory uncertainties, which would dominate the total uncertainty, need to be strongly reduced through future advances in the calculation of multi-loop radiative corrections together with improved experimental and theoretical control of the precision of SM input parameters. This document aims to provide an estimate of the required improvement in calculational accuracy in view of the anticipated high precision at the FCC-ee. For the most relevant electroweak and Higgs-boson precision observables we evaluate the corresponding quantitative impact., Comment: 20 pages, references updated

The Future Circular Collider (FCC) at CERN, a proposed 100-km circular facility with several colliders in succession, culminates with a 100 TeV proton-proton collider. It offers a vast new domain of exploration in particle physics, with orders of magnitude advances in terms of Precision, Sensitivity and Energy. The implementation plan foresees, as a first step, an Electroweak Factory electron-positron collider. This high luminosity facility, operating between 90 and 365 GeV centre-of-mass energy, will study the heavy particles of the Standard Model, Z, W, Higgs, and top with unprecedented accuracy. The Electroweak Factory $e^+e^-$ collider constitutes a real challenge to the theory and to precision calculations, triggering the need for the development of new mathematical methods and software tools. A first workshop in 2018 had focused on the first FCC-ee stage, the Tera-Z, and confronted the theoretical status of precision Standard Model calculations on the Z-boson resonance to the experimental demands. The second workshop in January 2019, which is reported here, extended the scope to the next stages, with the production of W-bosons (FCC-ee-W), the Higgs boson (FCC-ee-H) and top quarks (FCC-ee-tt). In particular, the theoretical precision in the determination of the crucial input parameters, alpha_QED, alpha_QCD, M_W, m_t at the level of FCC-ee requirements is thoroughly discussed. The requirements on Standard Model theory calculations were spelled out, so as to meet the demanding accuracy of the FCC-ee experimental potential. The discussion of innovative methods and tools for multi-loop calculations was deepened. Furthermore, phenomenological analyses beyond the Standard Model were discussed, in particular the effective theory approaches. The reports of 2018 and 2019 serve as white papers of the workshop results and subsequent developments., Comment: Published version

The expected experimental precision of the rates and asymmetries in the Future Circular Collider with electron positron beams (FCC-ee) in the centre of the mass energy range 88-365GeV considered for construction in CERN, will be better by a factor 5-200. This will be thanks to very high luminosity, factor up to $10^5$ higher than in the past LEP experiments. This poses the extraordinary challenge of improving the precision of the Standard Model predictions by a comparable factor. In particular the perturbative calculations of the trivial QED effects, which have to be removed from the experimental data, are considered to be a major challenge for almost all quantities to be measured at FCC-ee. The task of this paper is to summarize on the "state of the art" in this class of the calculations left from the LEP era and to examine what is to be done to match the precision of the FCC-ee experiments -- what kind of technical advancements are necessary. The above analysis will be done for most important observables of the FCC-ee like the total cross sections near $Z$ and $WW$ threshold, charge asymmetries, the invisible width of $Z$ boson, the spin asymmetry from $\tau$ lepton decay and the luminosity measurement., Comment: Corrected author's name in ref. [106]

We present pathways to the required theoretical precision for the luminosity targeted by the FCC-ee precision studies. We put the discussion in context by reviewing briefly the situation at the time of LEP. We then present the current status and routes to the desired 0.01\% targeted by the FCC-ee (as well as by the ILC)., Comment: 6 pages, 2 tables; talk presented at the International Workshop on Future Linear Colliders (LCWS2018), Arlington, Texas, 22-26 October 2018. C18-10-22; typos corrected; misprint corrected

The current status of the theoretical precision for the Bhabha luminometry is critically reviewed and pathways are outlined to the requirement targeted by the FCC-ee precision studies. Various components of the pertinent error budget are discussed in detail -- starting from the context of the LEP experiments, through their current updates, up to prospects of their improvements for the sake of the FCC-ee. It is argued that with an appropriate upgrade of the Monte Carlo event generator BHLUMI and/or other similar MC programs calculating QED effects in the low angle Bhabha process, the total theoretical error of $0.01\%$ for the FCC-ee luminometry can be reached. A new study of the $Z$ and $s$-channel $\gamma$ exchanges within the angular range of the FCC-ee luminometer using the BHWIDE Monte Carlo was instrumental in obtaining the above result. Possible ways of BHLUMI upgrade are also discussed., Comment: This work is based on the material presented at the FCC-ee-Z Theory Miniworkshop at CERN, January 2018", see Section C6 in arxiv:1809.018

${\cal KK}$MC-hh is a precision event-generator for Z production and decay in hadronic collisions, which applies amplitude-level resummation to both initial and final state photon radiation, including perturbative residuals exact through ${\cal O}(\alpha^2L)$, together with exact ${\cal O}(\alpha)$ EW matrix element corrections. We present some comparisons to other programs and results showing the effect of multi-photon radiation for cuts motivated by a recent ATLAS W mass analysis. We also show preliminary untuned comparisons of the electroweak corrections of ${\cal KK}$MC-hh to those of HORACE, which includes exact ${\cal O}(\alpha)$ corrections with resummed final-state photon radiation., Comment: 6 pages, 3 figures, presented by B.F.L. Ward at ICHEP2018, Seoul, S. Korea, 7/5/2018

The 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 comparing the theoretical status to the experimental demands of one of four foreseen FCC-ee operating stages, Z-boson resonance energy physics, called the 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 of the Standard Model (SM) with unprecedented precision. In fact, the FCC-ee Tera-Z will allow the study of at least one more perturbative order in quantum field theory compared to the LEP/SLC precision. The real problem is that the present precision of theoretical calculations of the various SM observables does not match that of the anticipated experimental measurements. The bottle-necks to overcoming this situation are identified. In particular, the issues of precise QED unfolding and 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 width analyses, it is argued 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 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., Comment: Published version

KKMC-hh is a precision event-generator for Z production and decay in hadronic collisions, which applies amplitude-level exponentiation to both initial and final state photon radiation, including perturbative residuals through order $\alpha^2 L$, together with electroweak matrix element corrections. We present results showing the effect of multi-photon radiation for cuts motivated by a recent ATLAS W-mass analysis. We also show preliminary untuned comparisons of the electroweak corrections of KKMC-hh to those of HORACE, which includes order $\alpha$ corrections with exponentiated final-state photon radiation., Comment: 10 pages, 18 figures. Presented by S.A. Yost at RADCOR 2017, the 13th International Symposium on Radiative Corrections, 24-29 September, 2017 in St. Gilgen, Austria

At the future high luminosity electron-positron collider FCC-ee proposed for CERN, the precise measurement of the charge asymmetry in $e^+ e^- \to \mu^+ \mu^-$ near the Z resonance is of special interest. In particular, such a measurement at $M_Z \pm 3.5$ GeV may provide a very precise measurement of the electromagnetic coupling at the scale $\sim M_Z$, a fundamental constant of the Standard Model. However, this charge asymmetry is plagued by a large trivial contribution from the interference of photon emission from initial state electrons and final state muons. We address the question whether this interference can be reliably calculated and subtracted with the help of a resummed QED calculation., Comment: 7 pages, 5 figures. Presented by S. Jadach at the "Matter To The Deepest" Conference, Podlesice, Poland, 3-8 September 2017. Updated version adds graphics labels for monochrome viewing. No content changes

With an eye toward the precision physics of the LHC, such as the recent measurement of $M_W$ by the ATLAS Collaboration, we present here systematic studies relevant to the assessment of the expected size of multiple photon radiative effects in heavy gauge boson production with decay to charged lepton pairs. We use the new version 4.22 of ${\cal KK}$MC-hh so that we have CEEX EW exact ${\cal O}(\alpha^2 L)$ corrections in a hadronic MC and control over the corresponding EW initial-final interference (IFI) effects as well. In this way, we illustrate the interplay between cuts of the type used in the measurement of $M_W$ at the LHC and the sizes of the expected responses of the attendant higher order corrections. We find that there are per cent to per mille level effects in the initial-state radiation, fractional per mille level effects in the IFI and per mille level effects in the over-all ${\cal O}(\alpha^2 L)$ corrections that any treatment of EW corrections at the per mille level should consider. Our results have direct applicability to current LHC experimental data analyses., Comment: 14 pages, 2 tables, 9 figures; typos corrected; modified to 21 pages, 14 figures

This document provides a writeup of contributions to the FCC-ee mini-workshop on "Physics behind precision" held at CERN, on 2-3 February 2016., Comment: https://indico.cern.ch/event/469561/

This document collects the proceedings of the "Parton Radiation and Fragmentation from LHC to FCC-ee" workshop (http://indico.cern.ch/e/ee\_jets16) held at CERN in Nov. 2016. The writeup reviews the latest theoretical and experimental developments on parton radiation and parton-hadron fragmentation studies --including analyses of LEP, B-factories, and LHC data-- with a focus on the future perspectives reacheable in $e^+e^-$ measurements at the Future Circular Collider (FCC-ee), with multi-ab$^{-1}$ integrated luminosities yielding 10$^{12}$ and 10$^{8}$ jets from Z and W bosons decays as well as 10$^5$ gluon jets from Higgs boson decays. The main topics discussed are: (i) parton radiation and parton-to-hadron fragmentation functions (splitting functions at NNLO, small-$z$ NNLL resummations, global FF fits including Monte Carlo (MC) and neural-network analyses of the latest Belle/BaBar high-precision data, parton shower MC generators), (ii) jet properties (quark-gluon discrimination, $e^+e^-$ event shapes and multi-jet rates at NNLO+N$^{n}$LL, jet broadening and angularities, jet substructure at small-radius, jet charge determination, $e^+e^-$ jet reconstruction algorithms), (iii) heavy-quark jets (dead cone effect, charm-bottom separation, gluon-to-$b\bar{b}$ splitting), and (iv) non-perturbative QCD phenomena (colour reconnection, baryon and strangeness production, Bose-Einstein and Fermi-Dirac final-state correlations, colour string dynamics: spin effects, helix hadronization)., Comment: 181 pages, 120 figures. Proceedings "Parton Radiation and Fragmentation from LHC to FCC-ee" Workshop (CERN, Nov. 2016), David d'Enterria, Peter Z. Skands (eds.)

We present an improvement of the MC event generator Herwiri2, where we recall the latter MC was a prototype for the inclusion of CEEX resummed EW corrections in hadron-hadron scattering at high cms energies. In this improvement the new exact ${\cal O}(\alpha^2L)$ resummed EW generator ${\cal{KK}}$ MC 4.22, featuring as it does the CEEX realization of resummation in the EW sector, is put in union with the Herwig parton shower environment. The {\rm LHE} format of the attendant output event file means that all other conventional parton shower environments are available to the would-be user of the resulting new MC. For this reason (and others -- see the text) we henceforth refer to the new improvement of the Herwiri2 MC as ${\cal{KK}}\text{MC-hh}$. Since this new MC features exact ${\cal O}(\alpha)$ pure weak corrections from the DIZET EW library and features the CEEX and the EEX YFS-style resummation of large multiple photon effects, it provides already the concrete path to 0.05\% precision on such effects if we focus on the EW effects themselves. We therefore show predictions for observable distributions and comparisons with other approaches in the literature. This MC represents an important step in the realization of the exact amplitude-based $QED\otimes QCD$ resummation paradigm. Independently of this latter observation, the MC rigorously quantifies important EW effects in the current LHC experiments., Comment: 22 pages, 13 figures, 2 tables; updated funding credits; fixed typo

We present numerical tests and predictions of the KrkNLO method for matching of NLO QCD corrections to hard processes with LO parton shower Monte Carlo generators (NLO+PS). This method was described in detail in our previous publications, where it was also compared with other NLO+PS matching approaches (MC@NLO and POWHEG) as well as fixed-order NLO and NNLO calculations. Here we concentrate on presenting some numerical results (cross sections and distributions) for $Z/\gamma^*$ (Drell-Yan) and Higgs-boson production processes at the LHC. The Drell--Yan process is used mainly to validate the KrkNLO implementation in the Herwig 7 program with respect to the previous implementation in Sherpa. We also show predictions for this process with the new, complete, MC-scheme parton distribution functions and compare them with our previously published results. Then, we present the first results of the KrkNLO method for Higgs production in gluon-gluon fusion at the LHC and compare them with MC@NLO and POWHEG predictions from Herwig 7 fixed-order results from HNNLO and a resummed calculation from HqT, as well as with experimental data from the ATLAS collaboration., Comment: 21 pages, 9 figures, version published in EPJC

Next steps in development of the KrkNLO method of implementing NLO QCD corrections to hard processes in parton shower Monte Carlo programs are presented. This new method is a simpler alternative to other well-known approaches, such as MC@NLO and POWHEG. The KrkNLO method owns its simplicity to the use of parton distribution functions (PDFs) in a new, so-called Monte Carlo (MC), factorization scheme which was recently fully defined for the first time. Preliminary numerical results for the Higgs-boson production process are also presented., Comment: 8 pages, 5 JPG figures, conference: "Loops and Legs in Quantum Field Theory", 24-29 April 2016, Leipzig, Germany

This report was prepared in the context of the LPCC "Electroweak Precision Measurements at the LHC WG" and summarizes the activity of a subgroup dedicated to the systematic comparison of public Monte Carlo codes, which describe the Drell-Yan processes at hadron colliders, in particular at the CERN Large Hadron Collider (LHC). This work represents an important step towards the definition of an accurate simulation framework necessary for very high-precision measurements of electroweak (EW) observables such as the $W$ boson mass and the weak mixing angle. All the codes considered in this report share at least next-to-leading-order (NLO) accuracy in the prediction of the total cross sections in an expansion either in the strong or in the EW coupling constant. The NLO fixed-order predictions have been scrutinized at the technical level, using exactly the same inputs, setup and perturbative accuracy, in order to quantify the level of agreement of different implementations of the same calculation. A dedicated comparison, again at the technical level, of three codes that reach next-to-next-to-leading-order (NNLO) accuracy in quantum chromodynamics (QCD) for the total cross section has also been performed. These fixed-order results are a well-defined reference that allows a classification of the impact of higher-order sets of radiative corrections. Several examples of higher-order effects due to the strong or the EW interaction are discussed in this common framework. Also the combination of QCD and EW corrections is discussed, together with the ambiguities that affect the final result, due to the choice of a specific combination recipe., Comment: 92 pages, report of the working group on precision calculations for Drell-Yan processes

We show that already at the NLO level the DGLAP evolution kernel Pqq starts to depend on the choice of the evolution variable. We give an explicit example of such a variable, namely the maximum of transverse momenta of emitted partons and we identify a class of evolution variables that leave the NLO Pqq kernel unchanged with respect to the known standard MS-bar results. The kernels are calculated using a modified Curci-Furmanski-Petronzio method which is based on a direct Feynman-graphs calculation., Comment: 16 pages, 4 figures

A next step in development of the KrkNLO method of including complete NLO QCD corrections to hard processes in a LO parton-shower Monte Carlo (PSMC) is presented. It consists of generalisation of the method, previously used for the Drell-Yan process, to Higgs-boson production. This extension is accompanied with the complete description of parton distribution functions (PDFs) in a dedicated, Monte Carlo (MC) factorisation scheme, applicable to any process of production of one or more colour-neutral particles in hadron-hadron collisions., Comment: 26 pages, 6 figures, minor corrections

Simple software for Monte Carlo(MC) calculation of the Higgs boson lineshape and its beam broadening effect by the beam energy dispersion was described. The software bases on FOAM [4] adaptive MC integrator from ROOT library [2]. The software is intended for those who want to reproduce results from paper [3] and experiment with different parameters for the lineshapes and QCD correction factors. Parallel version of the software based on MPI [10] is also described., Comment: 11 pages, 4 figures

The effect of the photon emission (bremsstrahlung) in the cross section of the process of direct production of the Higgs boson in the future high luminosity electron and muon colliders is calculated. It was found that cross section at the top of the Higgs boson resonance peak is reduced by factor 0.347 for the electron collider and 0.548 for the muon collider. Machine spread of the centre of the mass energy of 4.2MeV (equal to the Higgs width) would reduce peak cross section further, by factor 0.170 and 0.256 (QED and energy spread) for electron and muon beams respectively. Possible uncertainties in the resummed QED calculations are discussed. Numerical results for the lineshape cross section including QED and many values of the machine energy spread are provided., Comment: 18 pages, 7 figures; added new references

We report on re-calculation of the next-to-leading order DGLAP evolution kernels performed in a scheme suited for Monte Carlo simulations of parton cascades (parton showers)., Comment: Presented at Cracow Epiphany Conference, 8-10 January 2015

A new method of including the complete NLO QCD corrections to hard processes in the LO parton-shower Monte Carlo (PSMC) is presented. This method, called KrkNLO, requires the use of parton distribution functions in a dedicated Monte Carlo factorization scheme, which is also discussed in this paper. In the future, it may simplify introduction of the NNLO corrections to hard processes and the NLO corrections to PSMC. Details of the method and numerical examples of its practical implementation, as well as comparisons with other calculations, such as MCFM, MC@NLO, POWHEG, for single $Z/\gamma^*$-boson production at the LHC, are presented., Comment: 50 pages, 14 figures. Version published in JHEP: added a comparison of krkNLO results and the fixed-order NNLO result from the DYNNLO program and addressed several points raised by the referee

With an eye toward the precision physics of the LHC, FCC-ee and possible high energy muon colliders, we present the extension of the CEEX (coherent exclusive exponentiation) realization of the YFS approach to resummation in our KK MC to include the processes f\bar{f}\rightarrow f'\bar{f'}, f=\mu,\tau, q,\nu_\ell, f'=e, \mu,\tau, q, \nu_\ell, q=u,d,s,c,b,t, \ell =e,\mu,\tau with f \ne f'. After giving a brief summary of the CEEX theory with reference to the older EEX (exclusive exponentiation) theory, we illustrate theoretical results relevant to the LHC, FCC-ee, and possible muon collider physics programs., Comment: 4 pages, one figure, 2 tables; accepted as a poster in ICHEP14, Valencia, ES

In this note we outline the Monte Carlo project {\tt KrkMC}. The goal of this project is to construct a QCD Parton Shower accurate to NLO level in both coefficient function and splitting function (shower) parts. We discuss in detail one of its aspects --- the evolution kernels. The kernels had to be recalculated in a new regularisation scheme, called NPV. In this scheme all the singularities in the plus component of the integration momenta are regularised by means of principal value prescription. This is in contrast to the standard approach, in which only the spurious axial singularities are regularised by principal value. As a result, the triple poles in the dimensional regularisation parameter $\epsilon$ are replaced by a combination of $\epsilon$-poles and logarithms of geometrical cut-off $\delta$. The resulting exclusive parton densities are more suitable for stochastic applications in four dimensions. Simultaneously, at the inclusive level, the standard and new prescriptions give the same results provided appropriate real and virtual contributions are added., Comment: 8 pages, 1 figure; Contribution to Loops and Legs in Quantum Field Theory 2014

We report on the progress in calculating NLO DGLAP splitting functions for $x<1$ using the New Principal Value prescription, which is a modification of the standard Principal Value approach proposed by Curci, Furmanski and Petronzio in 1980. The new prescription reproduces the standard results on the inclusive (integrated) level, but simplifies individual contributions and restricts the cancellations between real and virtual diagrams which makes it useful for Monte Carlo simulations., Comment: Presented by O.Gituliar at XX Cracow Epiphany Conference, Cracow (Poland), 8--10 Jan 2014

We propose a modified use of the Principal Value prescription for regularizing the infrared singularities in the light-cone axial gauge by applying it to all singularities in the light-cone plus component of integration momentum. The modification is motivated by and applied to the re-calculation of the QCD NLO splitting functions for the purpose of Monte Carlo implementations. The final results agree with the standard PV prescription whereas contributions from separate graphs get simplified., Comment: 11 pages, 1 figure, updated to match published version