arXiv subjects

Giovanni Ridolfi

Publications and source records attributed to Giovanni Ridolfi.

At least 19 recordsLinked to original sources

arXiv2026

Threshold resummation of Semi-Inclusive Deep-Inelastic Scattering

We derive threshold resummation of semi-inclusive deep-inelastic scattering (SIDIS), by building upon previous results by some of us for the resummation of the Drell-Yan process at fixed rapidity, which is related to SIDIS by crossing. We consider both a double-soft limit, in which both the Bjorken and the fragmentation scaling variables tend to their threshold value, and single soft limits in which either of them does. We show that in the former limit only soft radiation contributes, and in the latter limit only collinear radiation, and we derive resummed expressions for the coefficient functions in all cases. We determine explictly resummation coefficients in the nonsinglet channel up to next-to-next-to-leading log by comparing to recent fixed next-to-next-to-leading order results. Expanding out the single-soft resummation we reproduce recent next-to-leading power results.

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arXiv2026

Threshold resummation of rapidity distributions at fixed partonic rapidity

We derive a general expression for the resummation of rapidity distributions for processes with a colorless final state, such as Drell-Yan or Higgs production, in the limit in which the center-of-mass energy goes on threshold, but with fixed rapidity of the Higgs or gauge boson in the partonic center-of-mass frame. The result is obtained by suitably generalizing the renormalization-group based approach to threshold resummation previously pursued by us. The ensuing expression is valid to all logarithmic orders but the resummation coefficients must be determined by comparing to fixed order results. We perform this comparison for the Drell-Yan process using the fixed-order next-to-next-to-leading (NNLO) result, thereby determining resummation coefficients up to next-to-next-to-leading logarithmic (NNLL) accuracy, for the quark-antiquark coefficient function in the quark nonsinglet channel. We provide a translation to direct QCD of a result for this resummation previously obtained using SCET methods, and we show that it agrees with our own.

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arXiv2025

A simple introduction to soft resummation

We provide an elementary pedagogical introduction to some basic concepts and techniques of soft (or Sudakov) resummation, specifically in QCD, paying particular attention to simple but useful tricks of the trade. We briefly review collinear (Altarelli-Parisi) and infrared (eikonal)factorization, cancellation of infrared singularities and factorization of mass singularities. We recall basic concepts on renormalization group invariance and the solution of renormalization group equations. We then show how threshold resummation can be derived from a renormalization group argument following from the cancellation of infrared singularities. We discuss various equivalent forms of the resummed result, and we briefly present transverse momentum resummation.

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arXiv2024

An improved description of charm fragmentation data

We consider the fragmentation of heavy quarks into heavy-flavoured hadrons, specifically the production of charmed mesons in $e^+e^-$ collisions, at different centre-of-mass energies. We focus our attention on the ratio of moments of the $D^{*+}$ energy spectrum measured by ALEPH and CLEO. This ratio is believed to provide us with a direct test of perturbative QCD evolution because hadronisation effects should cancel between the numerator and denominator. However, state-of-the-art calculations based on standard (final-state) collinear factorisation fail to describe the experimental data. We show that this discrepancy is considerably reduced if heavy-quark threshold effects are accounted for not only in DGLAP evolution, as it is usually done, but also in the resummed coefficient functions.

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arXiv2023

On positivity of parton distributions

We discuss the bounds on polarized parton distributions which follow from their definition in terms of cross section asymmetries. We spell out how the bounds obtained in the naive parton model can be derived within perturbative QCD at leading order when all quark and gluon distributions are defined in terms of suitable physical processes. We specify a convenient physical definition for the polarized and unpolarized gluon distributions in terms of Higgs production from gluon fusion. We show that these bounds are modified by subleading corrections, and we determine them up to NLO. We examine the ensuing phenomenological implications, in particular in view of the determination of the polarized gluon distribution.

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arXiv2023

A consistent resummation of mass and soft logarithms in processes with heavy flavours

Perturbative calculations for processes that involve heavy flavours can be performed in two approaches: the massive scheme and the massless one. The former enables one to fully account for the heavy-quark kinematics, while the latter allows one to resum potentially-large mass logarithms. Furthermore, the two schemes can be combined to take advantage of the virtues of each of them. Both massive and massless calculations can be supplemented by soft-gluon resummation. However matching between massive and massless resummed calculations is difficult, essentially because of the non-commutativity of the soft and massless limits. In this paper, we develop a formalism to combine resummed massless and massive calculations. We obtain an all-order expression that consistently resums both mass and soft logarithms to next-to-leading logarithmic accuracy. We perform detailed calculations for the decay of the Higgs into a heavy-quark pair and discuss the applications of this formalism to different processes.

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arXiv2022

Resummation effects in the bottom-quark fragmentation function

We compute the perturbative component of the fragmentation function of the $b$ quark to the best of the present theoretical knowledge. The fixed-order calculation to order $α_s^2$ of the fragmentation function at the initial scale is matched with soft-emission logarithm resummation to next-to-next-to-leading logarithmic accuracy, so that order-$α_s^2$ corrections are accounted for exactly, and logarithmically enhanced contributions from loops of $b$ quarks are included. This requires the calculation of the Mellin transform of the order-$α_s^2$ result in the whole complex plane for the Mellin variable, which we provide for the first time for all the fragmenting partons. Evolution is performed to next-to-next- to-leading log accuracy, and mixing with the gluon fragmentation function is taken into account. The perturbative fragmentation functions are made available via LHAPDF grids.

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arXiv2022

Soft logarithms in processes with heavy quarks

Observables involving heavy quarks can be computed in perturbative QCD in two different approximation schemes: either the quark mass dependence is fully retained, or it is retained only where needed to regulate the collinear singularity. The two schemes have different advantages and drawbacks. In particular, it is known that the structure of large logarithms arising from soft emissions is different in the two approaches. We investigate the origin of this difference in some detail, focussing on a few specific processes. We show that it is related to the non-commutativity of the small-mass and soft-emission limits. Finally, we perform the resummation of soft-emission logarithms to next-to-leading accuracy in the case of Higgs decay into a $b\bar b$ pair, in the scheme in which the quark mass dependence is fully accounted for.

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arXiv2022

False vacuum decay: an introductory review

We review the description of tunnelling phenomena in the semi-classical approximation in ordinary quantum mechanics and in quantum field theory. In particular, we describe in detail the calculation, up to the first quantum corrections, of the decay probability per unit time of a metastable ground state. We apply the relevant formalism to the case of the standard model of electroweak interactions, whose ground state is metastable for sufficiently large values of the top quark mass. Finally, we discuss the impact of gravitational interactions on the calculation of the tunnelling rate.

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arXiv2021

Threshold resummation of transverse momentum distributions beyond next-to-leading log

We derive a general expression for the threshold resummation of transverse momentum distributions for processes with a colorless final state, by suitably generalizing the renormalization-group based approach to threshold resummation previously pursued by two of us. The ensuing expression holds to all logarithmic orders, and it can be used to extend available results in the literature, which only hold up to the next-to-leading log (NLL) level. We check agreement of our result with the existing NLL result, as well as against the known fixed next-to-leading order results for the Higgs transverse momentum distribution in gluon fusion, and we provide explicit expressions at the next-to-next-to-leading log level.

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arXiv2020

A fragmentation-based study of heavy quark production

Processes involving heavy quarks are a crucial component of the LHC physics program, both by themselves and as backgrounds for Higgs physics and new physics searches. In this work, we critically reconsider the validity of the widely-adopted approximation in which heavy quarks are generated at the matrix-element level, with special emphasis on the impact of the collinear logarithms associated with final-state heavy quark and gluon splittings. Our study, based on a perturbative fragmentation-function approach, explicitly shows that neglecting the resummation of collinear logarithms may yield inaccurate predictions, in particular when observables exclusive in the heavy quark degrees of freedom are considered. Our findings motivate the use of schemes which encompass the resummation of final-state collinear logarithms.

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arXiv2017

Combined threshold and transverse momentum resummation for inclusive observables

We present a combined resummation for the transverse momentum distribution of a colorless final state in perturbative QCD, expressed as a function of transverse momentum pt and the scaling variable x. Its expression satisfies three requirements: it reduces to standard transverse momentum resummation to any desired logarithmic order in the limit pt-> 0 for fixed x, up to power suppressed corrections in pt; it reduces to threshold resummation to any desired logarithmic order in the limit x-> 1 for fixed pt, up to power suppressed correction in 1-x; upon integration over transverse momentum it reproduces the resummation of the total cross cross at any given logarithmic order in the threshold x->1 limit. Its main ingredient, and our main new result, is a modified form of transverse momentum resummation, which leads to threshold resummation upon integration over pt, and for which we provide a simple closed-form analytic expression in Fourier-Mellin (b,N) space. We give explicit coefficients up to NNLL order for the specific case of Higgs production in gluon fusion in the effective field theory limit. Our result allows for a systematic improvement of the transverse momentum distribution through threshold resummation which holds for all pt, and elucidates the relation between transverse momentum resummation and threshold resummation at the inclusive level, specifically by providing within perturbative QCD a simple derivation of the main consequence of the so-called collinear anomaly of SCET.

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arXiv2016

Massive vectors and loop observables: the $g-2$ case

We discuss the use of massive vectors for the interpretation of some recent experimental anomalies, with special attention to the muon $g-2$. We restrict our discussion to the case where the massive vector is embedded into a spontaneously broken gauge symmetry, so that the predictions are not affected by the choice of an arbitrary energy cut-off. Extended gauge symmetries, however, typically impose strong constraints on the mass of the new vector boson and for the muon $g-2$ they basically rule out, barring the case of abelian gauge extensions, the explanation of the discrepancy in terms of a single vector extension of the standard model. We finally comment on the use of massive vectors for $B$-meson decay and di-photon anomalies.

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arXiv2016

Anatomy of double heavy-quark initiated processes

A number of phenomenologically relevant processes at hadron colliders, such as Higgs and Z boson production in association with b quarks, can be conveniently described as scattering of heavy quarks in the initial state. We present a detailed analysis of this class of processes, identifying the form of the leading initial-state collinear logarithms that allow the relation of calculations performed in different flavour schemes in a simple and reliable way. This procedure makes it possible to assess the size of the logarithmically enhanced terms and the effects of their resummation via heavy-quark parton distribution functions. As an application, we compare the production of (SM-like and heavy) scalar and vector bosons in association with b quarks at the LHC in the four- and five-flavour schemes as well as the production of a heavy Z' in association with top quarks at a future 100 TeV hadron collider in the five- and six-flavour schemes. We find that, in agreement with a previous analysis of single heavy-quark initiated processes, the size of the initial-state logarithms is mitigated by a kinematical suppression. The most important effects of the resummation are a shift of the central predictions typically of about 20% at a justified value of the scale of each considered process and a significant reduction of scale variation uncertainties.

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arXiv2015

Stability of the electroweak ground state in the Standard Model and its extensions

We review the formalism by which the tunnelling probability of an unstable ground state can be computed in quantum field theory, with special reference to the Standard Model of electroweak interactions. We describe in some detail the approximations implicitly adopted in such calculation. Particular attention is devoted to the role of scale invariance, and to the different implications of scale-invariance violations due to quantum effects and possible new degrees of freedom. We show that new interactions characterized by a new energy scale, close to the Planck mass, do not invalidate the main conclusions about the stability of the Standard Model ground state derived in absence of such terms.

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arXiv2015

Top Quark Pair Production beyond NNLO

We construct an approximate expression for the total cross section for the production of a heavy quark-antiquark pair in hadronic collisions at next-to-next-to-next-to-leading order (N$^3$LO) in $α_s$. We use a technique which exploits the analyticity of the Mellin space cross section, and the information on its singularity structure coming from large N (soft gluon, Sudakov) and small N (high energy, BFKL) all order resummations, previously introduced and used in the case of Higgs production. We validate our method by comparing to available exact results up to NNLO. We find that N$^3$LO corrections increase the predicted top pair cross section at the LHC by about 4% over the NNLO.

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arXiv2015

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

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..

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arXiv2014

A first unbiased global determination of polarized PDFs and their uncertainties

We present a first global determination of spin-dependent parton distribution functions (PDFs) and their uncertainties using the NNPDF methodology: NNPDFpol1.1. Longitudinally polarized deep-inelastic scattering data, already used for the previous NNPDFpol1.0 PDF set, are supplemented with the most recent polarized hadron collider data for inclusive jet and $W$ boson production from the STAR and PHENIX experiments at RHIC, and with open-charm production data from the COMPASS experiment, thereby allowing for a separate determination of the polarized quark and anti-quark PDFs, and an improved determination of the medium- and large-$x$ polarized gluon PDF. We study the phenomenological implications of the NNPDFpol1.1 set, and we provide predictions for the longitudinal double-spin asymmetry for semi-inclusive pion production at RHIC.

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