# Publications by Luca Rottoli

## Maximal Entanglement in High Energy Physics

SciPost Physics Stichting SciPost **3** (0) 036

<jats:p>We analyze how maximal entanglement is generated at the fundamental level in QED by studying correlations between helicity states in tree-level scattering processes at high energy. We demonstrate that two mechanisms for the generation of maximal entanglement are at work: <jats:italic>i)</jats:italic><jats:inline-formula><jats:alternatives><jats:tex-math>s</jats:tex-math><mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mi>s</mml:mi></mml:math></jats:alternatives></jats:inline-formula>-channel processes where the virtual photon carries equal overlaps of the helicities of the final state particles, and <jats:italic>ii)</jats:italic> the indistinguishable superposition between <jats:inline-formula><jats:alternatives><jats:tex-math>t</jats:tex-math><mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mi>t</mml:mi></mml:math></jats:alternatives></jats:inline-formula>- and <jats:inline-formula><jats:alternatives><jats:tex-math>u</jats:tex-math><mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mi>u</mml:mi></mml:math></jats:alternatives></jats:inline-formula>-channels. We then study whether <jats:italic>requiring</jats:italic> maximal entanglement constrains the coupling structure of QED and the weak interactions. In the case of photon-electron interactions unconstrained by gauge symmetry, we show how this requirement allows to reproduce QED. For <jats:inline-formula><jats:alternatives><jats:tex-math>Z</jats:tex-math><mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mi>Z</mml:mi></mml:math></jats:alternatives></jats:inline-formula>-mediated weak scattering, the maximal entanglement principle leads to non-trivial predictions for the value of the weak mixing angle <jats:inline-formula><jats:alternatives><jats:tex-math>\theta_W</jats:tex-math><mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:msub><mml:mi>θ</mml:mi><mml:mi>W</mml:mi></mml:msub></mml:math></jats:alternatives></jats:inline-formula>. Our results are a first step towards understanding the connections between maximal entanglement and the fundamental symmetries of high-energy physics.</jats:p>

## Three loop soft function for N3LL′ gluon fusion Higgs boson production in soft-collinear effective theory

Physical Review D American Physical Society **91** (2015) 1-6

We derive the three loop soft function for inclusive Higgs production in gluon fusion, and use it to perform the resummation of the Higgs cross section at N3LL′ in soft-collinear effective theory. We improve the accuracy of the resummation by including contributions of collinear origin. We include finite top, bottom and charm mass effect where available. These results are available through the public code ResHiggs.

## Resummation prescriptions and ambiguities in SCET vs. direct QCD: Higgs production as a case study

Journal of High Energy Physics Springer **46** (2015) 1-23

We perform a comparison of soft-gluon resummation in SCET vs. direct QCD (dQCD), using Higgs boson production in gluon fusion as a case study, with the goal of tracing the quantitative impact of each source of difference between the two approaches. We show that saddle-point methods enable a direct quantitative comparison despite the fact that the scale which is resummed in the two approaches is not the same. As a byproduct, we put in one-to-one analytic correspondence various features of either approach: specifically, we show how the SCET method for treating the Landau pole can be implemented in dQCD, and how the resummation of the optimal partonic scale of dQCD can be implemented in SCET. We conclude that the main quantitative difference comes from power-suppressed subleading contributions, which could in fact be freely tuned in either approach, and not really characteristic of either. This conclusion holds for Higgs production in gluon fusion, but it is in fact generic for processes with similar kinematics. For Higgs production, everything else being equal, SCET resummation at NNLL in the Becher-Neubert implementation leads to essentially no enhancement of the NNLO cross-section, unlike dQCD in the standard implementation of Catani et al.

## Charm in Deep-Inelastic Scattering

(2015)

We show how to extend systematically the FONLL scheme for inclusion of heavy quark mass effects in DIS to account for the possible effects of an intrinsic charm component in the nucleon. We show that when there is no intrinsic charm, FONLL is equivalent to S-ACOT to any order in perturbation theory, while when an intrinsic charm component is included FONLL is identical to ACOT, again to all orders in perturbation theory. We discuss in detail the inclusion of top and bottom quarks to construct a variable flavour number scheme, and give explicit expressions for the construction of the structure functions $F^c_2$, $F^c_L$ and $F^c_3$ to NNLO.

## Charm production in the forward region: constraints on the small-x gluon and backgrounds for neutrino astronomy

Journal of High Energy Physics Springer Verlag **2015** (2015) 1-46

The recent observation by the IceCube experiment of cosmic neutrinos at energies up to a few PeV heralds the beginning of neutrino astronomy. At such high energies, the conventional neutrino flux is suppressed and the prompt component from charm meson decays is expected to become the dominant background to astrophysical neutrinos. Charm production at high energies is however theoretically uncertain, both since the charm mass is at the boundary of applicability of perturbative QCD, and also because the calculations are sensitive to the poorly-known gluon PDF at small-x. In this work we provide detailed perturbative QCD predictions for charm and bottom production in the forward region, and validate them by comparing with recent data from the LHCb experiment at 7 TeV. Finding good agreement between data and theory, we use the LHCb measurements to constrain the small-x gluon PDF, achieving a substantial reduction in its uncertainties. Using these improved PDFs, we provide predictions for charm and bottom production at LHCb at 13 TeV, as well as for the ratio of cross-sections between 13 and 7 TeV. The same calculations are used to compute the energy distribution of neutrinos from charm decays in pA collisions, a key ingredient towards achieving a theoretically robust estimate of charm-induced backgrounds at neutrino telescopes.

## Parton distributions with threshold resummation

Journal of High Energy Physics Springer **2015** (2015) 1-45

We construct a set of parton distribution functions (PDFs) in which fixed-order NLO and NNLO calculations are supplemented with soft-gluon (threshold) resummation up to NLL and NNLL accuracy respectively, suitable for use in conjunction with any QCD calculation in which threshold resummation is included at the level of partonic cross sections. These resummed PDF sets, based on the NNPDF3.0 analysis, are extracted from deep-inelastic scattering, Drell-Yan, and top quark pair production data, for which resummed calculations can be consistently used. We find that, close to threshold, the inclusion of resummed PDFs can partially compensate the enhancement in resummed matrix elements, leading to resummed hadronic cross-sections closer to the fixed-order calculations. On the other hand, far from threshold, resummed PDFs reduce to their fixed-order counterparts. Our results demonstrate the need for a consistent use of resummed PDFs in resummed calculations.

## Les Houches 2017: Physics at TeV Colliders Standard Model Working Group Report

ArXiv (0)

This Report summarizes the proceedings of the 2017 Les Houches workshop on Physics at TeV Colliders. Session 1 dealt with (I) new developments relevant for high precision Standard Model calculations, (II) theoretical uncertainties and dataset dependence of parton distribution functions, (III) new developments in jet substructure techniques, (IV) issues in the theoretical description of the production of Standard Model Higgs bosons and how to relate experimental measurements, (V) phenomenological studies essential for comparing LHC data from Run II with theoretical predictions and projections for future measurements, and (VI) new developments in Monte Carlo event generators.

## Accurate single- and double-differential resummation of colour-singlet processes with MATRIX+RadISH: $W^+W^-$ production at the LHC

ArXiv (0)

We present the combination of fully differential cross sections for colour-singlet production processes at next-to-next-to-leading order (NNLO) QCD obtained with MATRIX and all-order resummation through RadISH. This interface allows us to achieve unprecedented accuracy for various transverse observables in $2 \rightarrow 2$ production processes. As an important application we consider $W^+ W^-$ production at the LHC, more precisely the full leptonic process $pp\to \ell^+\ell^{\prime\, -}\nu_{\ell}{\bar\nu}_{\ell^\prime}+X$ with $\ell'\neq\ell$, and we present resummed predictions for differential distributions in presence of fiducial selection cuts. In particular, we resum the transverse-momentum spectrum of the $W^+ W^-$ pair at next-to-next-to-next-to-leading logarithmic (N$^3$LL) accuracy and match it to the integrated NNLO cross section. The transverse-momentum spectrum of the leading jet in $W^+ W^-$ production is calculated at NNLO+NNLL accuracy. Finally, the joint resummation for the transverse-momentum spectrum of the $W^+ W^-$ pair in the presence of a jet veto is performed at NNLO+NNLL. Our phenomenological study highlights the importance of higher-order perturbative and logarithmic corrections for precision phenomenology at the LHC.

## Precision QCD at the LHC: from the structure of the proton to all-order resummations

ArXiv (0)

Experiments at the LHC are collecting a wealth of data with an unprecedented level of precision. As a consequence, the theoretical error is now starting to lag behind the experimental one, and a ceaseless effort is required to reduce the theory uncertainty to match the precision of the data. At hadron colliders, QCD predictions are obtained by convoluting perturbative parton-level results with non-perturbative PDFs, whose precise determination is crucial to reach percent-accurate theoretical predictions. At the parton level, cross sections are obtained through a perturbative expansion in the strong coupling. In some cases, large terms appear at all orders and spoil the convergence of the series. The perturbative description is rescued by resumming the series to all orders, thereby making theory calculations accurate in regions where a fixed-order treatment is not sufficient. In this thesis I first present two global PDF sets where fixed-order calculations are supplemented by threshold and high-energy resummation, respectively. In the first case, it is found that including resummation into PDFs can compensate for the enhancement in the partonic cross sections, with implications for high-mass resonance searches. In the second case, resummation quantitatively improves the description of the HERA structure functions, thus providing evidence of the onset of a new dynamical regime of QCD in the HERA data. I then focus on Higgs production in gluon fusion. The effect of threshold resummation on the total cross section is found to significantly improve the convergence of the perturbative series and to provide a robust method for estimating missing higher order uncertainty. Finally, I present predictions for the Higgs transverse-momentum spectrum both in the inclusive case and within fiducial cuts, exploiting a novel approach where transverse-momentum resummation is performed in direct space.

## Threshold resummation in SCET vs. direct QCD: a systematic comparison

(0)

We perform a systematic comparison of soft-gluon resummation in SCET and in a standard "direct" QCD (dQCD) approach, both from an analytical and a phenomenological point of view. In particular, we concentrate on Higgs boson production in gluon-gluon fusion at a hadron collider. Using specifically a saddle point argument, we arrive at a detailed understanding of the quantitative differences between these two approaches.