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RADCOR 2023 – 16th International Symposium on Radiative Corrections: Applications of Quantum Field Theory to Phenomenology,
Sunday 28th May - Friday 2nd June,
Crieff, Scotland.
This conference is the 16th in the series of biennial RADCOR conferences on radiative corrections. It is devoted to the applications of quantum field theory to particle physics phenomenology. Subjects will include precision calculations for colliders; progress in higher-loop and higher-multiplicity calculations in the Standard Model; cross sections for new physics; interpretations of experimental data; new techniques for calculations; advances in computer-algebra methods; new theoretical developments.
The conference will be held in Crieff, an attractive old market town in the heart of Perthshire in central Scotland.
The conference will be held in the Crieff Hydro Spa Hotel, which will also be providing an all-inclusive package for the conference participants, where breakfast and dinner are included in the quoted room rate (£165/night per person) while lunch and coffee breaks are covered by the conference fee.
Note that this is an in-person event: all talks will be given locally, and there will be time for informal discussions. Nonetheless, all talks will be recorded and streamed on line, allowing people who cannot travel to follow the conference.
Wednesday afternoon is reserved for social activities; Details will be announced.
Some additional recreation activities in the area can be found here.
As in previous RADCOR editions, talks will be published in the conference proceedings.
A list of confirmed speakers is available here.
The registration deadline is 14th February, 2023.
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In the week preceding RADCOR, we hold our annual Higgs Centre School of Theoretical Physics in the James Clerk Maxwell Building in Edinburgh. This year's school is associated with the RADCOR conference and focuses on radiative corrections.
Local Organising Committee:
International Advisory Board
We study the amplitudes of the light quark mediated Higgs boson production via gluon fusion in the high-energy limit. A complete analytic result is obtained for the three-loop $O(m_q^3)$ double-logarithmic term while and the all-order analysis is performed in the large-$N_c$ limit of QCD and in the abelian approximation.
In the first part of the talk, methods for the calculation of two-loop amplitudes with several mass scales, such as HH, HJ or HZ production in gluon fusion, will be discussed. The second part will focus on Higgs boson pair production, in particular the combination of NLO QCD corrections with anomalous couplings in an Effective Field Theory framework. Predictions for the Higgs boson pair invariant mass spectrum, including leading operators as well as loop-suppressed operators such as 4-top-quark-operators, will be presented.
Kinematic expansions of scattering cross sections provide powerful methods of approximating key LHC observables to a high degree of precision at reduced degree of complexity in comparison to a full computation. I will show several recent advancements and examples in the development and application of collinear expansion techniques.
I critically examine issues that arise when applying modern machine learning techniques in the context of precision collider physics, by specifically considering the case of PDF determinations. Questions that I address include: Can we trust the machine learning model to correctly generalize from known examples? How can we validate results, specifically for uncertainties? Can we detect over- and under-learning? Can a machine learning model detect inconsistencies in the data that it is being shown?
I will review novel developments related to an analytic understanding of power corrections to collider processes in the context of renormalon calculus.
We may associate a geometry to a Feynman integral. Understanding the geometry helps in computing the Feynman integral. In this talk I will discuss how Feynman integrals related to non-trivial geometries like Calabi-Yau manifolds can be computed with the help of the method of differential equations. In particular I will discuss an ansatz, which casts the differential equation into an epsilon-factorised form.
In this talk I will describe the construction of local infrared counterterms to remove all infrared singularities in two-loop amplitudes for gluon-fusion processes to colourless final states. The counterterms are given as form-factor integrands whose integrals are known and the number of such counterterms are very small compared to the number of diagrams involved. This procedure is based on the universality of infrared singularities. Removing ultraviolet counterterms results in a locally finite amplitude, which admits numerical integration in momentum space.
Feynman integrals beyond multiple ploylogarithms are inevitable precision study at colliders. We use the non-planar triangle cross ladder at two loops as an example to show how to obtain the \epsilon-factorised differential equation systematically for elliptic Feynman integrals depending on one dimensionless kinematic variable.
In this talk I will consider signal-background interference effects in Higgs-mediated diphoton production at the LHC. The inclusion of such effects results in a shift of the diphoton invariant mass distribution and in a destructive contribution to the total cross section. As pointed out in earlier works, one can exploit interference studies to put bounds on the Higgs boson decay width. After reviewing the Higgs interferometry framework I will present an extension of this analysis up to NNLO QCD in the soft-virtual approximation.
We present the soft-gluon resummation for the Higgs boson pair production in the gluon fusion channel to the next-to-next-to-next-to-leading logarithmic(N3LL) accuracy. After matching N3LL to the next-to-next-to-next-to-leading order (N3LO) QCD calculation in the infinite top quark mass approximation, we show that the central values of the inclusive cross sections are quite stable with respect to N3LO, while the conventional renormalisation and factorisation scale uncertainties are reduced by a factor of two, reaching to the subpercent level. After combining with the full top-quark mass dependent next-to-leading order QCD results, our most advanced predictions are presented for both the inclusive total cross sections and the differential invariant mass distributions of the Higgs pair.
We will provide a guided tour through the method of calculating high loop order renormalization functions (7 loops $\phi^4$, 6 loops $\phi^3$) with graphical functions. This tour will lead through graphical functions in even dimensions (for calculating primitive Feynman periods, with M. Borinsky), generalized single-valued hyperlogarithms (GSVHs, a suitable function space), and the extension to non-integer dimensions (dimensional regularization). We will briefly discuss future applications to gauge theories (most notably QED and QCD).
In both single top and VBF Higgs production a structure function approximation can be applied to obtain the leading colour contribution. This approximation contains only so-called factorisable diagrams and is exact at NLO. However, at NNLO non-factorisable contributions come into play. A particular challenge for calculations at this order is the evaluation of two-loop diagrams with several mass scales. In this talk I will present calculations and results for the phenomenological impact of non-factorisable contributions in t-channel single top and VBF Higgs production.
We will discuss how methods developed in the context of perturbation theory can be applied to the computation of lattice correlation functions, in particular in the non-perturbative regime. The techniques we will consider are integration-by-parts identities and the method of differential equations, cast in the framework of twisted Co-Homology. We will report on calculations of correlation functions for phi^4 theory and lattices of small size, both in Euclidean and Minkowskian signature.
Pair production of Z bosons is an essential process at the LHC. It is a significant background to Higgs production, and subsequent decay through the four lepton channel, as well as an important signal process for new physics searches. In this talk, we present our calculation of the next-to-leading order QCD corrections to Z-pair production through gluon fusion with full top quark mass dependence. We discuss the details of the calculation of the challenging two-loop virtual amplitudes. We then present phenomenological results for this process.
The generic 3-loop tetrahedral tadpole, with 6 distinct masses, has elliptic subtructure originating from 12 distinct elliptic curves. I shall show how to evaluate it, at high precision and great speed, by integrating dilogarithms against complete integrals of the third kind, for which there is a proceudre of the arithmetic-geometric mean that is astoundingly fast. The elements of this method go back more 60 years, to Gunnar Kallen and Afaf Sabry. I learnt about them more than 50 years from Gabriel Barton. They deserve to better known.
We propose a Monte Carlo integration algorithm for numerically evaluating Feynman integrals in the physical region of phase space. The algorithm is an extension of the tropical integration algorithm of M. Borinsky. Starting from the projective representation of a Feynman integral, we implement Feynman's i*epsilon prescription via a suitable contour deformation, whereafter tropical sampling is used to approximate the value of the integral. An accompanying public code named 'feyntrop' is introduced, which we use to present examples between 2 and 5 loops. This work is done in collaboration with M. Borinsky and F. Tellander.
We present the first calculation for the production of a W boson in association with massive bottom quarks (Wbb) at hadron colliders at next-to-next-to-leading order (NNLO) in QCD. The use of massive bottom quarks avoids the ambiguities associated with the correct flavour assignment in massless calculations, paving the way to a more realistic comparison with experimental data. The relevant five-point two-loop virtual amplitude with three massive legs required to reach the NNLO accuracy is still not yet available. Exploiting the hierarchy between the bottom quark mass and the characteristic energy scale of the process, a reliable expression has been obtained through a massification procedure applied to the results available for massless bottom quarks. We present phenomenological results considering proton–proton collisions at 13.6 TeV for inclusive Wbb production and within a fiducial region relevant for the associated production of a W boson and a Higgs boson decaying into a bottom-quark pair, for which Wbb production represents one of the most relevant backgrounds. NNLO corrections are substantial and their inclusion is mandatory to obtain reliable predictions.
I will discuss the use of intersection numbers computed in relative cohomologies for the manipulation of Feynman integrals in Dimensional Regularization. This approach has the potential to revolutionize integral reductions, which with current techniques are a significant bottleneck for phenomenologically relevant scattering amplitude computations.
We compute the two-loop master integrals relevant for the NNLO QCD correction to heavy pseudo-scalar quarkonium production and decay both analytically and numerically. The analytic expressions involve elliptic multiple polylogarithms and iterated integrals of modular forms. We discuss the master integral computation and the form-factors obtained. We briefly discuss their phenomenological importance.
In this talk, we present the mixed QCD-EW two-loop virtual corrections for the charged current Drell-Yan production. The presence of one additional mass compare to the neutral current case makes the computation of the two-loop amplitudes extremely challenging, specially the two-loop Feynman integrals. Our approach to evaluate the relevant two-loop Feynman integrals using semi-analytical method, allows us to obtain the renormalized two-loop amplitudes. We perform the subtraction of the universal infrared singularities mostly analytically and present the numerical evaluation of the hard function as a grid.
In this talk, I will introduce new tools towards the evaluation of Feynman integrals, including AMFlow and Blade. AMFlow, based on auxiliary mass flow method, which can numerically evaluate Feynman integrals in an efficient and systematic way, have proved to be very useful in the past year. Another tool named Blade, which is based on block-triangular relations among Feynman integrals, can perform much faster samling in finite field than traditional integration-by-parts system and as a result, much more efficient reduction of Feynman integrals.
The associated production of a Higgs boson with a top–antitop quark pair is a crucial process at the LHC since it allows for a direct measurement of the top-quark Yukawa coupling. In this talk we will present the computation of the radiative corrections to this process at the next-to-next-to-leading order (NNLO) in QCD perturbation theory. This represents the very first computation for a 2 → 3 process with massive coloured particles at this perturbative order. In order to overcome the bottleneck of the missing two-loop amplitudes (which are at the frontier of current techniques), we developed a soft Higgs boson approximation, which enabled us to reliably quantify the impact of the yet unknown two-loop contribution. The IR-singularities are treated within the well-established qT-subtraction framework, properly extended to the case of heavy-quark production in association with a colourless system.
In multiloop computations, choosing an integral basis that minimizes infrared divergences holds the promise of simplifying results. I describe a procedure based on analysis of Landau equations for finding sets of finite integrals. The same technique can also be applied to finding integrals which are manifestly O(ϵ). These integrals can give rise to special relations between integrals beyond those arising from integration by parts.
I will present flow oriented perturbation theory (FOPT), a coordinate space analogue of time-ordered perturbation theory and loop-tree duality. Within this approach, a generic Feynman graph is mapped to a sum of all its possible different energy-flows respecting energy conservation at each vertex (strongly connected directed graphs). In the FOPT framework, the integrals associated with virtual and real corrections turn out to have the same integral measure. Hence, FOPT shows promising potential in the context of explicit phase-space integration with manifest cancellation of real and virtual singularities. Additionally, I will present a FOPT representation of the S-matrix that exhibits manifest infrared singularity factorization on a per-diagram level.
The hybrid kT-factorization formula, for which one initial-state parton momentum is space-like and carries non-vanishing transverse components while the other is on-shell, is promoted to NLO for arbitrary processes. We identify all soft and collinear divergencies in the partonic cross section, and recognize that the non-cancelling ones can be attributed to PDF evolution, evolution kernel, and target impact factors. Furthermore, we present expressions for one-loop amplitudes for 2->2 processes, and a strategy to calculate the real corrections.
The rho parameter is an important Standard Model precision observable. It is currently known to four-loop order in QCD in the limit of vanishing bottom quark mass. When the rho parameter was calculated at three-loop order with exact bottom quark mass dependence, it was discovered that elliptic integrals enter the results. In this talk, we report on the status of our calculation of the rho parameter at four-loop order in QCD with exact dependence on the bottom quark mass with a particular emphasis on the mathematical structure of the integrals that enter the results.
Evanescent integrals are those whose integrands vanish when considered on loop momentum configurations that are strictly four-dimensional. They naturally span the space of dimensionally-regulated integrals that are missed when performing four-dimensional unitarity cuts. Such integrals are well understood at one loop, where they give rise to the so-called "rational part" of the amplitude. In this talk, we discuss a new approach to computing evanescent integrals that generalizes to the two-loop level. Our method makes use of the local counterterm formalism of Anastasiou and Sterman, which we use to show that these integrals can be broken down into contributions from soft, collinear and ultra-violet regions. These contributions are much simpler than the original two-loop integral: they take the form of products of one-loop integrals, or one-fold integrals over one-loop integrals. To demonstrate the power of our approach, we apply it to the two-loop five-point all-plus amplitude and find that at both one and two loops the finite remainder is given by only ultra-violet contributions.
I will discuss the recent progress that has been made towards the computation of 3-loop non-planar master integrals relevant to N3LO corrections to processes such as H+jet production at the LHC. I will describe the analytic structure of these integrals as well as several technical issues regarding their analytic computation using canonical differential equations. Finally I will comment on the remaining steps towards the computation of all relevant 3-loop topologies and their application to amplitude calculations.
Massive form factors in QCD are important building blocks in higher order corrections to various observables like heavy quark production, top quark decays or muon-electron scattering, where they describe the virtual contributions. Furthermore, they show universal infrared behaviour which makes them interesting to study also in the context of the infrared structure of QCD amplitudes. In this talk I will present our recent calculation of singlet and anomaly contributions to the massive quark form factors, which is based on expansions around singular and regular points of the master integrals and numerical matching. This completes the calculation of the massive form factors for external vector, axial-vector, scalar and pseudo-scalar currents up to three-loop order.
I will discuss the two-loop computation of massless QCD helicity amplitudes with five external states and full colour dependence.
We present recent analytic results on the 3-loop heavy flavor corrections to deep-inelastic scattering.
Multi-jet rates at hadron colliders provide a unique possibility for probing Quantum Chromodynamics (QCD), the theory of strong interactions. By comparing theory predictions with collider data, one can directly test perturbative QCD, extract fundamental parameters like the strong coupling and search for physics beyond the Standard Model. Recent developments enabled lifting three-jet cross-sections to next-to-next-to-leading order (NNLO) in QCD. I will present numerical results for three-to-two jet ratios and event shapes at the Large Hadron Collider (LHC). Then, I will discuss the first extraction of the strong coupling constant from event shapes at the LHC with NNLO QCD accuracy.
We present recent results on the computation of the splitting functions in quantum chromodynamics at four loops.
I discuss the recent advances in the computation of two-loop scattering amplitudes for five-particle processes. The latter are fundamental ingredients to obtain predictions at the next-to-next-to-leading order (NNLO) in QCD for many interesting LHC processes. I discuss the state-of-the-art technology for computing scattering amplitudes analytically, and present new results relevant for the LHC phenomenology.
The most general renormalizable quantum field theory one can write down for a finite spectrum of spin-0, 1/2, and 1 particles is a gauge theory, with possible spontaneously broken symmetries. The existence of Lie group structures in such a theory is determined by perturbative unitarity of the on-shell scattering amplitudes. Armed with new tools developed for scattering amplitudes, we demonstrate very explicitly how broken symmetries emerge from the constraints of tree unitarity. Such constraints result in relations dictating the couplings to be invariant tensors of the gauge group, and each of these relations has a counterpart for kinematic numerators of on-shell amplitudes. This facilitates the extension of color-kinematics duality to spontaneously broken gauge theories.
Multi-loop Feynman integrals are the cornerstone of modern perturbative approaches to quantum field theory and a pillar of precision computations for colliders as well as gravitational wave experiments. It is therefore essential to develop efficient method to evaluate them. A big bottleneck in that direction is the necessity to deal with integrals depending on many scales. In this talk, I will present a new method designed to handle such problem, namely a loop-by-loop approach to the computation of differential equation for (dual) Feynman integrals. As a proof of concept example, I will discuss how one can obtain a 'ready to integrate’ differential equation for the unequal mass elliptic sunrise integral near 4-dimension.
The knowledge of infrared singularities of gauge-theory amplitudes enables us to systematically resum large logarithmic corrections to many important observables. In this talk, I will present the structure of anomalous dimensions governing infrared singularities of QCD amplitudes with one massive and an arbitrary number of massless external partons. The analytical expression of tripole correlations involving one massive parton is obtained at three loops for the first time. The results are essential to improve the theoretical predictions of single top and top quark pair productions at hadron colliders.
I will discuss recent progress concerning the factorization of physical observables and the resummation of large logarithms at next-to-leading power, focusing on the loop calculation of the universal functions in which physical observables factorize.
Amplitude are geometric objects and we have ambitions to classify them. As functions of discrete indices of color, charge, helicity, ..., and spin, they are tensors on the Fock spaces of elementary particles. Linear spaces, like the Fock spaces, they have automorphisms under which a given tensor is transformed into another in the equivalent class. In this sense, equivalent classes of tensors are orbits under the action of linear automorphism groups, it is thus natural to represent each equivalent class of tensors by normal forms composed of `invariants'. E.g., matrices under congruence they classify $(0,2)$-type bilinear forms, while under similarity they classify $(1,1)$-type linear endomorphisms, two such $(1,1)$ forms are equivalent if and only if their corresponding characteristic matrices share the same set of Smith invariant factors over a polynomial PID (principal ideal domain). On the other hand, amplitude in massive theory is quite often associated with families of elliptic curves parameterized by the Mandelstam variables. Just like automorphisms of linear spaces leads to the transformation between equivalent tensors, isomorphisms of elliptic curves lead to the modular transformation of the symbol letters. Just like equivalent classes of tensors are represented by normal forms, the space of equivalent classes of elliptic curves are represented by fundamental domains of moduli curves (spaces) $\Gamma\backslash\mathbb{H}$. In this spirit, we are aimed at a classification of different scattering processes according to the underlying moduli space, deriving potential dimension formulas and function bases for the symbol letters. In this talk, I report a first step towards the land of amplitude beyond genus one -- the complete analytic computation of the 2-loop Bhabha scattering in Quantum Electrodynamics. I will start from the correspondence between modular curves $\Gamma\backslash\mathbb{H}$ and elliptic moduli space with level structures, and then use the sunrise family to show how we parameterize the punctured Riemann sphere through principal modular function, and eventually jump over to modular parameterization of elliptic K3 surface through the universal curves $\mathcal{E}_{\Gamma_1(4)\backslash\mathbb{H}}$. I will highlight the choice of a \emph{universal rational marked point} inspired by \textrm{Mordell–Weil theorem}, and show that Bhabha scattering and planar top quark production at sector 79 are described by the same moduli space of $\mathscr{M}_{1;2}[4]$ with $4$-level structures, thus should be represented by the same class of function space.
The Energy Correlator observables probe the geometric distributions of energy flow in the final states of particle scattering experiments. They provide valuable data for studies ranging from conformal field theories to jet substructure. We present an analytic formula for the three-point energy correlator (EEEC) at leading order (LO) in N = 4 super Yang Mills theory, which exhibits unexplored simplicity and novel features in its function space. In addition we introduce a new approach to obtaining higher-point correlators in the small-angle limit from the super form factor of protected scalar operators. These results provide tools and experience for QCD, which is phenomenologically relevant for the cutting-edge studies at LHC.
We report on recent progress for the QCD corrections to top-quark pair plus jet production. In particular, we discuss a recent computation for the two-loop master integrals associated to a two-loop five-point pentagon-box integral configuration with one internal massive propagator, that contributes to top-quark pair production in association with a jet in the QCD planar limit.
In this talk we present the calculation of NLO QCD corrections to $pp \to t\bar{t}jj$ in the dilepton decay channel. The narrow width approximation is used to model the decays of the top quark pair preserving spin correlations. Jet radiation and QCD corrections are consistently included in the production and decay of the top quarks. We discuss the size of NLO QCD corrections and the main theoretical uncertainties of fiducial cross sections at the integrated and differential level. In addition, we examine the contributions of jet radiation in the production and decay of the top quark pair, as well as the mixed contribution, in which jet radiation is simultaneously present in the production and decay stage.
The associated production of a single top quark with a Z boson (tZj) represents an important probe of the EW sector of the Standard Model. Since differential measurements of tZj are expected to enhance the sensitivity to new-physics effects, and the experimental interest in this direction is growing in the light of upcoming LHC runs, it is crucial to improve the off-shell modelling of this process for realistic fiducial regions. We present the first Standard-Model calculation of the off-shell tZj production in the multi-lepton decay channel including NLO EW and QCD corrections to the LO EW signal. All off-shell effects and spin correlations are accounted for, both at LO and at NLO. Relying on a realistic fiducial volume, we highlight the most relevant effects coming from radiative corrections and from irreducible-background contamination on total and differential cross sections.
Scattering amplitudes are the fundamental building blocks of collider observables. Comparing high precision measurements with theory predictions requires computing them to high perturbative order. The growth in the number of loops significantly increases the complexity of the problem. Using novel methods allowed us to compute QCD corrections to four-point massless processes at the state-of-the-art three-loop order. In this talk, I will argue that employing a recently proposed projector method reduces the amount of independent Lorentz tensor structures. I will also discuss the derivation of a complete set of Master Integrals in all the relevant physical regions. It is based on regularity properties of the underlying Feynman integrals, which were observed before. I will present our results for the diphoton production in gluon fusion channel. Finally, I will show an application of this amplitude to LHC phenomenology. This particular process is a leading background for Higgs production in the discovery channel. Because of the interference with the signal, it can put new bounds on the Higgs width.
I discuss a new observable for the determination of the W mass at hadron colliders
The method of regions (MoR), a systematic way to compute Feynman integrals involving multiple kinematic scales, states that a Feynman integral can be approximated, and even reproduced, by summing over integrals that are expanded in certain regions. A modern perspective of the MoR is to consider any given Feynman integral as a certain Newton polytope, which is defined as the convex hull of the points associated to the terms of the Symanzik polynomials. The regions then, has a one-to-one correspondence to the "lower facets" of this polytope. Since the Symanzik polynomials are further related to the spanning trees and spanning 2-trees of the Feynman graph, a graph-theoretical study of these polynomials may allow us to unveil all the possible regions that are needed in the MoR. In this talk we mainly focus on three specific expansions of the wide-angle scattering process: the on-shell expansion, threshold expansion and mass expansion. After introducing the background knowledge, we will describe the basic strategy of the grah-theoretical approach, and formulate the generic form of the regions appearing in each of the three expansions above. The results, which hold for graphs at all orders, can be further applied to construct graph-finding algorithms for the MoR, and investigate the properties of the Soft-Collinear Effective Theory (SCET).
In this talk, I will present a calculation of the NNLO mixed QCD-EW corrections to the neutral-current Drell-Yan production of a pair of massless leptons in the high invariant-mass region. Our computation is fully differential with respect to the final state particles.
We find that the mixed corrections corrections are larger than what one would expect based on the magnitude of the coupling constants, and they can exceed the pure NNLO QCD contribution in a large portion of the phase space. At relatively low values of the dilepton invariant mass, mll \sim 200 GeV, we find unexpectedly large mixed QCD-electroweak corrections at the level of -1%. In the TeV region, we observe that these corrections can be well approximated by the product of QCD and electroweak corrections, as expected from Sudakov factorisation.
As one of the primary sources of QCD background to $pp \to t\bar{t}H(H\to b\bar{b})$ at the LHC, the $t\bar{t}b\bar{b}$ production process demands precise theoretical predictions and estimates of the dominant uncertainties. On top of that, the capacity of properly disentangling the prompt b-jets and the b-jets from top-quark decays has important phenomenological consequences. In this talk we present state-of-the-art predictions for ttbb production with dilepton decays at the LHC as obtained from a full off-shell calculation at NLO QCD accuracy. We discuss the dominant theory uncertainties, assess the relevance of double-, single- and non-resonant contributions and investigate the impact of different b-jet definitions on the cross section. Finally we present a kinematics-based prescription to cope with the identification of the prompt b-jets.
We have calculated the $n_f^2$ and $n_f^3$ contributions to the flavour non-singlet structure functions $F_2$ and $F_L$ and most recently $F_3$ in inclusive deep-inelastic scattering at the fourth order in the strong coupling $\alpha_s$. The coefficient functions have been obtained by computing a very large number of Mellin-N moments using the method of differential equations, and then determining the analytic forms in N and Bjorken-x from these. Our new $n_f^2$ terms are numerically much larger than the n3f leading large-nf parts which were already known; they agree with predictions of the threshold and high-energy resummations. Furthermore, our calculation confirms the earlier determination of the four-loop $n_f^2$ part of the corresponding anomalous dimension.
The decay of B mesons can be described in the Heavy Quark Expansion as the decay of a free bottom quark plus corrections which are suppressed by powers of 1/m_b. The focus of the talk will be on the calculation of the NNLO corrections to semileptonic and nonleptonic decays of a free bottom quark including a non-vanishing charm quark mass. For the semileptonic decays we obtain an analytic result by solving differential equations and fixing boundary conditions in the limit of a heavy charm quark. Our analytic expression can be compared to previous known results obtained via expansions in the mass ratio m_c/m_b. In a second approach we calculate precise numerical expansions of all master integrals with the help of differential equations which can describe the whole parameter space from m_c/m_b=1 to m_c/m_b=0. I will also give an outlook on the ongoing nonleptonic calculation, where the same techniques as in the semileptonic case are used.
Following up on some distant and little-known papers by Tullio Regge and collaborators, I will present an approach to integration-by-parts identities and differential equations for Feynman integrals, based on the Feynman parameter representation, and relying upon the projective nature of parameter integrands. A very general identity connecting projective forms allows to move across families of Feynman integrals, unifying IBP identities and dimensional shifts, and feeding into systems of differential equations, similar but not identical to the conventional ones. I will illustrate the results with simple examples at one and two loops.
Landau analysis aims to predict the singularity structure of Feynman integrals without their explicit evaluation. We point out a number of errors in its textbook formulation that prevented applications to the Standard Model processes in the past. After resolving these issues, we use a combination of tropical analysis and numerical algebraic geometry to implement an algorithm that classifies and consistently finds all possible singularities of multi-loop Feynman integrals.
Dynamics of high energy scattering in QCD are primarily probed through detector energy flow correlations. One important IRC safe energy-flow observable is the Energy-Energy Correlator (EEC). At leading power approximation in the back-to-back limit, EEC enjoys a factorization formula similar to the Drell-Yan production at small transverse momentum. Therefor studying the power corrections to EEC provides valuable insight to power corrections to Drell-Yan production. In this talk I will introduce a novel method to calculate power corrections to EEC by exploiting the power of conformal symmetry. I will show that there is a close correspondence between power corrections on one side, and twist and large spin perturbation in the operator product expansion of local correlator on the other side. I will demonstrate the method by computing the first NLP resummation for EEC.
We subtract the gluon-condensate renormalon singularity in the Adler function, which causes the discrepancy between fixed-order (FOPT) and contour-improved perturbation theory (CIPT), employing the gradient flow action density. The scheme leads to automatic subtraction, does not require knowledge of the Stokes constant (renormalon residue), and relates to a non-perturbatively defined cut-off gluon condensate. Unlike unsubtracted perturbation theory, FOPT and CIPT give consistent results for the inclusive hadronic tau decay width, removing a major uncertainty in the determination of the strong coupling from tau decay.
In my talk, I will present the calculation of the two-loop soft and beam functions for the transverse-momentum distribution of the leading jet in the production of a colour-singlet system such as a Higgs or Z boson. This calculation constitutes a vital component for the resummation of the transverse-momentum distribution and the jet-vetoed cross-section at next-to-next-to-next-to-leading logarithmic order (N3LL).
I will present recently published as well as yet unpublished results on multi-photon and multi-jet cross sections obtained with next-to-next-to-leading and possibly higher order in perturbative QCD.
In a recent work by Hoang, Plätzer and Samitz is has been shown at the parton level that the relation top quark mass in MC event generators to a well-defined renormalization scheme depends on the parton shower cutoff. Still, it has not been known to which extent the hadronization model may affect this relation and how much this relation depends on the MC event generator and the NLO matching scheme. Given the current uncertainties from direct measurements of well below 400 MeV this issue becomes increasingly important. In the presentation the discussion is extended to the hadron level , also showing new results based on a novel cluster hadronziation model in the Herwig event generator. The results represent an important additional step towards assigning a definite scheme to the MC top mass parameter.
We present an extension of HELAC for two-loop amplitudes. All basic two-loop topologies (Theta, Infinity, Dumbbell) are included in the skeleton construction. For colored particles, the color-connection representation is extended to two loops offering a unified framework for tree-order, one- and two-loop amplitudes. HELAC-2LOOP provides, at the moment, an automated algorithm capable to compute two-loop amplitudes at the integrand level. Several tests have been performed regarding 2-to-2 and 2-to-3 processes against publically available packages such as QGRAF, FeynArts, FeynCalc, and FORM. The reduction to a master integral basis is currently under study.
In this talk I investigate the interplay of NLO matching and next-to-leading-logarithmic (NLL) parton showers in the context of two-body decays. Three matching schemes have been implemented in the NLL-accurate PanScales showers: a multiplicative scheme, MC@NLO and POWHEG. By means of both analytic and numerical arguments, I show how these retain the shower’s NLL accuracy, and (under certain provisions in the case of POWHEG) can augment it so that it achieves NNDL accuracy for global event shapes. The talk will also briefly explore some phenomenological considerations.
In this talk I will present an automated framework calculating NLO corrections in the full SM for arbitrary processes at hadron and lepton colliders. This framework is an element of the Monte-Carlo program WHIZARD simulating cross sections and differential distributions. The generalization of the implemented FKS scheme to systematically subtract QED and QCD infrared divergences in mixed coupling expansions will be discussed. Also, recent progress of the POWHEG-matched event generation and the inclusion of electroweak corrections in future lepton collider processes are subjects of this talk. In particular, results of our recent study will be shown applying EW corrections to multi-boson processes at a future multi-TeV muon collider.
In this talk, I will discuss a framework that resums soft (logarithms ln^k(N) in Mellin space) and next-to-soft (power-suppressed terms ln^k(N)/N in Mellin space) logarithms to all orders in perturbative QCD. We use the concepts of collinear factorisation and renormalisation group invariance to achieve this. The former allows one to define a soft-collinear (SC) function that encapsulates soft and collinear dynamics of the perturbative results to all orders in the strong coupling constant. The logarithmic structure of these results is governed by universal infrared anomalous dimensions and process-dependent functions of the Sudakov differential equation that the SC satisfies. The solution to the differential equation is obtained by proposing an all-order ansatz in dimensional regularization, owing to several state-of-the-art perturbative results available to third order. Using this framework we study the numerical impact of resumming the NSV logarithms in the context of Drell-Yan and Higgs boson production processes at the LHC to next-to-next-to leading logarithmic (NNLL) accuracy. The talk is based on the works : Eur.Phys.J.C 82 (2022) 3, 234, Eur.Phys.J.C 82 (2022) 9, 774 , Phys.Rev.D 106 (2022) 3, 034005, hep-ph/2205.11560.
I will describe recent progress on sector showers that consistently incorporate second-order "direct" 2->4 branchings. These showers are able to reproduce the full singularity structure of QCD through NNLO and can be matched in a very natural and fully differential way to calculations at this accuracy, provided that consistent "Born-local" K-factors can be defined. The method appears straightforward to extend to N3LO should that be desired in the future.
Double parton scattering (DPS) is the process in which one has two hard scatterings in an individual proton-proton collision. It can compete in rate with single scattering in certain kinematic regions and/or for certain processes, and reveals information on nucleon structure not accessible in single parton scattering: spatial, spin, and colour correlations between the partons inside the nucleon. The parton densities relevant to DPS are the double parton distributions (DPDs); at small distance between the two probed partons the DPDs can be computed in perturbation theory. I discuss this perturbative calculation at next-to-leading order – this is the key missing piece required for computations of DPS at NLO. The calculation for both the colour-singlet and colour-correlated DPDs will be covered – in the latter case, one encounters rapidity divergences, the treatment of which I will discuss in detail. We used two different regulator schemes, the δ regulator and Collins' regulator using space-like Wilson lines, and obtained identical results in both, providing a strong cross-check. To our knowledge this is the first application of the Collins regulator in a two-loop calculation.
In view of the increasing level of precision of current and future experimental measurements, matching NNLO QCD and NLO EW corrections represents a crucial step for LHC phenomenology. Furthermore, complementing fixed-order perturbative computations with parton-shower effects is indispensable for a realistic description of LHC processes. In this talk we present the computation of WZ production at NNLO QCD and NLO EW consistently matched to parton showers using the MiNNLOPS method. We investigate different combination schemes based on an a-posteriori recombination of QCD and EW contributions, showing that the inclusion of EW effects gives sizable effects. We also comment on the possibility of extending the MiNNLOPS method towards the inclusion of NLO EW corrections avoiding an a-posteriori reweighting of simulated events.
The advancement of computation techniques enables a number of N3LO calculations in perturbative QCD, which are crucial to reaching percent level accuracy in the LHC (and the upcoming HL-LHC) phenomenology. An important part of this effort involves properly extracting IR singularities at N3LO. The N-jettiness slicing scheme is one of the techniques to deal with this problem, but is only available up to N2LO due to the complexity introduced by the Heaviside functions in the soft function. In this talk, we will discuss how we handle the Heaviside functions in the computation and report the recent progress of the zero-jettiness soft function calculation at N3LO QCD.
Precision physics in the Higgs sector has been one of the main challenges in recent years. The pure fixed-order calculations entering in the \textit{collinear factorization} framework, which have been pushed up to N3LO, are not able to describe the entire kinematic spectrum. In particular conditions, they must be necessarily supplemented by all-order \textit{resummations}; for instance, in the so called \textit{Regge} kinematical region, large energy-type logarithms spoil the perturbative behavior of the series and must be resummed to all orders. This resummation is necessary to describe the inclusive hadroproduction of a forward Higgs in the limit of small Bjorken $x$, as well to study inclusive forward emissions of a Higgs boson in association with a backward identified object. A complete resummation for these processes, at next-to-leading logarithmic accuracy (NLLA), can be achived through the Balitsky-Fadin-Kuraev-Lipatov (BFKL) approach, but it requires the knowledge of the next-to-leading order Higgs impact factor. We present the full NLO result for the impact factor of a forward Higgs boson, obtained in the infinite top-mass limit, both in the momentum representation and as superposition of the eigenfunctions of the LO BFKL kernel. We also discuss the application of the result to the inclusive hadroproduction of a Higgs boson in association with a jet.
We discuss new observables for probing physics beyond the SM within the framework of the Standard Model Effective Field Theory (SMEFT). We consider both existing measurements at the LHC, and potential future ones at upcoming colliders such as the Electron-Ion Collider (EIC).
Using diagrammatic resummation techniques, I discuss the double logarithmic series of B_c to eta_c form factors at large hadronic recoil. In the non-relativistic limit, mb >> mc >> LambdaQCD, this process provides one of the simplest setups to study the problem of endpoint singularities appearing in the SCET factorization of exclusive B decay amplitudes in a perturbative framework. The leading double logarithms arise from a peculiar interplay of energy-ordered ladder diagrams -- for which an RGE treatment using effective Theories is currently unknown -- as well as Standard Sudakov-type corrections.
Quantum computers offer major speed-ups for problems like prime factorisation, searching, and quantum simulation. Recent years have seen the emergence of quantum algorithms for simulating lattice QCD and parton showers, but the quantum simulation of generic perturbative QCD processes has largely remained unexplored. As a first non-trivial step, I will discuss the quantum simulation of colour in perturbative QCD. In particular, I will present quantum computing circuits that simulate the colour parts of QCD Feynman diagrams. As an example application, we use these circuits to calculate the colour algebra for various perturbative QCD processes and diagrams. (Based on arXiv:2302.xxxxx by H.A.Chawdhry and M.Pellen)
The renormalization scale setting in QCD is a fundamental problem for high precision tests of the Standard Model (SM). It is considered a conventional practice to set the renormalization scale to the typical scale of a process Q, namely to the momentum transfer and to determine theoretical errors by varying it in a range of two. According to the Conventional Scale Setting (C.S.S.), perturbative QCD ( pQCD) predictions are affected by the renormalization scheme and scale ambiguities. The Principle of Maximum Conformality (PMC) provides a systematic way to remove such ambiguities from perturbative calculations satisfying at once the renormalization group invariance and the self-consistency conditions deriving from the renormalization group. We present here the recent developments and applications of the PMC method also showing the comparison of the results with those obtained with other methods.
Scattering amplitudes greatly simplify in the Regge limit, and yet exhibit a very interesting structure, which is far richer in the full gauge theory than in the planar limit. Prior to the development of QCD, Regge and others showed that the asymptotic high-energy behaviour of amplitudes is governed by poles and cuts in the complex angular momentum plane. It was also shown (Mandelstam, 1963) that Regge cuts emerge from non-planar diagrams. Here we explore the separation between Regge poles and cuts in perturbative QCD using rapidity evolution equations. We study Regge-pole factorisation in 2 \to n gauge theory amplitudes in multi-Regge kinematics, whose parameters, the impact factors, the trajectory and the Lipatov vertex, can be fully determined from 2 \to 2 and 2 \to 3 amplitudes. The factorisation is broken at Next-to-Next-to-Leading-Logarithmic (NNLL) accuracy by the appearance of a Regge cut owing to multiple Reggeon exchange in the $t$ channel. We compute the multiple Reggeon exchange contributions through four loops and show how to define the NNLL Regge-pole parameters in the presence of a Regge cut, maintaining the non-planar nature of the cut as well as the universality of the Regge pole parameters. Remarkably, this separation between pole and cuts directly leads to the generalization of the Korchemsky-Korchemskaya relation between the singularities of the gluon Regge trajectory and the cusp anomalous dimension to three loops.
I'd like to present the new developments and talk about the current status of numerical evaluation of multi-loop integrals and amplitudes using the new release of pySecDec (v1.6), particularly concentrating on significant integration performance improvements and automation related to expansion-by-regions.
This talk presents the construction of the NNLO subtraction formula for the cancellation of IR singularities obtained within the framework of Local Analytic Sector Subtraction. Such general program has been (so far) completed for the treatment of unresolved radiation in processes featuring any partonic final state in massless QCD. The outcome of the subtraction is a compact and analytic expression suitable for direct numerical implementation, thus enabling the production of relevant phenomenological results. Updated developments on the extension to ISR at NNLO and the numerical implementation of the scheme are discussed.
We present high energy next-to-leading logarithmic corrections, their inclusion within the framework of High Energy Jets, and their impact on the stabilisation of the perturbative prediction of R32 for large rapidity separations.
At high energies, fixed-order predictions for the production of a Higgs boson together with one or more jets suffer from large logarithms in invariant masses over transverse momenta. We resum these high-energy logarithms to all orders within the High Energy Jets (HEJ) framework, retaining the exact dependence on the top-quark mass. We compare our predictions to ATLAS and CMS measurements at 8 and 13 TeV.
In the past decade the antenna subtraction method has been successfully implemented to compute Next-to-Next-to-Leading Order (NNLO) corrections in QCD for a series of relevant processes. In this talk we discuss the first steps towards the extension of this method at Next-to-Next-to-Next-to-Leading Order (N3LO). In particular, the calculation of N3LO antenna functions for final state radiation is presented, where each configuration of hard radiators (quark-antiquark, gluon-gluon, quark-gluon) is suitably decomposed into partonic sub-processes. Unintegrated antenna functions are directly extracted from physical squared matrix elements, while their integrated counterparts are obtained relating inclusive phase space integrals to unitarity cuts of massless four-loop integrals. We conclude commenting how the newly computed antenna functions would fit in the context of a local N3LO subtraction scheme.
In this talk, I will present recent progress in the generalisation of the nested soft-collinear subtraction scheme to multi-parton final state processes. The scheme has already been successfully applied to scatterings involving a limited number of coloured partons, and it has shown remarkable flexibility and good numerical performances. I will discuss how to overcome the difficulties that arise from going beyond the previous implementations, considering as a case study the vector boson production in association with a jet at next-to-next-to-leading order in QCD.
Recent analyses on high-energy inclusive Higgs-boson rates in proton collisions via the gluon fusion channel, matched with the state of-the-art fixed-order N3LO accuracy, have shown that the impact of high-energy resummation corrections reaches 10% at the FCC nominal energies. This supports the statement that electroweak physics at 100 TeV is expected to receive relevant contributions from small-x physics. In this talk we will present novel predictions for transverse-momentum and rapidity distributions sensitive the inclusive emission of a Higgs boson in association with a light-flavored jet in proton collisions, calculated within the NLL accuracy of the energy-logarithmic resummation as implemented in the JETHAD code and matched with NLO fixed-order computations from POWHEG. According to our knowledge, this represent a first and novel implementation of a matching procedure in the context of the high-energy resummation for rapidity-separated two-particle final states. We come out with the message that the improvement of fixed-order calculations on Higgs-plus-jet QCD distributions is a core ingredient to reach the precision level of the description of observables relevant for the Higgs physics at current LHC energies as well as at nominal FCC ones.
In this talk I will present the method to merge the resummation of high energy logarithms implemented in High Energy Jets (HEJ) partonic Monte Carlo framework with the soft-collinear effects described by the Pythia parton shower. The method preserves the accuracy of the leading order cross sections and the logarithmic accuracy of both resummation schemes across all of phase space. I will show predictions obtained within this framework and compare to data from experimental studies.
Low-energy experiments allow for some of the most precise measurements in particle physics, such as g-2. To make the most of these experiments, theory needs to match the experimental precision. Over the last decade, this meant that even in QED next-to-next-to-leading order calculations (or even more in some cases) became necessary. I will discuss some of the challenges faced when dealing with QED corrections and discuss some possible solutions that we have implemented in McMule (Monte Carlo for MUons and other LEptons). McMule is a framework that we have developed to obtain NNLO predictions for a number of processes, such as $e\mu \to e\mu$, $ee \to ee$ and $\mu \to e\nu\bar\nu$.
A recently proposed experiment, MUonE, aims to extract the hadronic vacuum polarisation contribution to the muon g-2 from muon-electron scattering at low energy. The extrapolation requires that both experimental and theoretical uncertainties do not exceed 10 ppm. This corresponds, at least, to next-to-next-to leading order QED corrections to $e\mu \to e\mu$. I will discuss the implementation of a Monte Carlo generator for this process in the McMule framework, which provides infrared-safe differential results at said order in QED. An approximation of the MUonE setup provides some phenomenological results and sheds light on the need for higher-order corrections, which are currently under study within McMule.
This talk will present radiative corrections and their interpretation for the so-called D-term. This is related to the Electron-Ion Collider project, where Generalized Parton Distributions (GPD) will be measured. GPD give access to matrix elements of the energy-momentum tensor of a nucleon. The D-term is sometimes roughly interpreted as characterizing pressure distribution. Calculated it in simple bound states such as the hydrogen atom it exhibits an interesting new type of a log correction that resembles the Lamb shift but has a different physical interpretation.
The antenna subtraction method has been successfully applied to a wide range of processes relevant for the Large Hadron Collider at next-to-next-to-leading order in $\alpha_s$ (NNLO). We propose an algorithm for building antenna functions for any number of real emissions directly out of the unresolved limits we require. Antenna functions of this kind always identify two hard radiators. We then use the algorithm to explicitly build all single- and double-real QCD antenna functions and compare them to the previous antenna functions, which were extracted from matrix elements. These antenna functions should be more easily applicable to NNLO subtraction terms than previously. Finally, we match the integration of the antenna functions over the final-final unresolved phase space to the previous incarnation, serving as an independent check on our results.
The anomalous excess of soft photons radiated in inelastic hadronic collisions, has been challenging the physics community over four decades, but no solution was proposed so far. We argue that the problem is rooted in comparison with an incorrect model for radiative corrections, usually called bremsstrahlung model. It is based on an illegitimate extension of the Low theorem to radiative multi-particle production processes 2 → n + γ. We demonstrate that this breaks down unitarity of the S-matrix in contradiction with the optical theorem. We propose an alternative description of photon radiation within the light-front color-dipole phenomenology. The results of calculations are in a good accord with available data.
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.
The gravitation binary problem and the associated production of gravitational waves can be treated efficiently within the framework of quantum field theory. This allows to make use of a variety of tools ranging from double copy relations between gauge theory and gravity to methods from effective field theory and multi-loop integration. I will show recent progress in applying this approach to state-of-the art problems in classical perturbation theory and will highlight the fruitful interplay with other more traditional approaches to the binary problem.
We consider two-loop corrections to $2\to 2$ scattering processes with massive particles in the final state and massive particles in the loop. We discuss the combination of analytic expansions in the high-energy limit and for small Mandelstam variable~$t$. For the example of double Higgs boson production we show that the whole phase space can be covered and time-consuming numerical integrations can be avoided.
In this talk we present the analytic results for two-loop QCD as well as QED corrections to light-by-light scattering including contributions due to massive internal fermions.
One-loop integrands can be written in terms of a simple, process-independent basis. A similar basis exists for integrands of phase-space integrals for the real-emission contribution at next-to-leading order. The demonstration deploys techniques from computational algebraic geometry in order to partial-fraction integrands in a systematic way. This provides the first step towards a decomposition of phase-space integrals in a basis of master integrals.
Shower Monte Carlo generators simulate fully realistic collider events, and reproduce much of the data from the LHC and its predecessors. Their core is represented by Parton Shower~(PS) algorithms, which provide the inclusion of soft radiation and enable us to mimic a realistic high-multiplicity collider event. The flexibility of these tools comes at a cost of a lower accuracy, which can lead to large systematic uncertainties and compromise the physics potential of the LHC and future colliders. In this talk I will discuss the criteria introduced by the PanScales collaboration to assess the logarithmic accuracy of PS's. I will also show new results for the PanScales dipole showers, which represent the first family of dipole showers with demonstrated NLL accuracy for Drell-Yan and gluon-fusion production at hadron colliders.