arXiv subjects

Philip G. Ratcliffe

Publications and source records attributed to Philip G. Ratcliffe.

At least 19 recordsLinked to original sources

arXiv2026

Novel analysis for the energy-energy correlation in electron-positron annihilation in the perturbative domain

The energy-energy correlation (EEC) in electron-positron annihilation plays a crucial role in precision tests of quantum chromodynamics (QCD) and measurements of the QCD coupling constant. In this paper, we provide a novel analysis for the EEC by using the Principle of Maximum Conformality (PMC), a systematic method for eliminating renormalization scheme-and-scale ambiguities. The PMC scales are determined by resumming the non-conformal $β$-terms that govern the behavior of the QCD running coupling via the renormalization group equation, and reflect the virtuality of the propagating gluons in QCD. It is noteworthy that the resulting PMC scale varies dynamically with the EEC's angular distribution, reflecting the expected scale's physical behavior. Moreover, due to the reabsorption of all $β$-terms, including also those related to the divergent renormalon terms such as $n!β^n_0α^n_s$, in the pQCD series, the behavior of the QCD perturbative coefficient using PMC, differs entirely from that of the conventional coefficient. Consequently, the PMC predicted EEC distribution agrees well with the experimental data in the perturbative domain.

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arXiv2025

Scheme-independent determination of the QCD running coupling at all scales from jet observables using the principle of maximum conformality and infinite-order scale setting

We present a new approach to determining the strong coupling $α_s(Q)$, over the entire range of validity of perturbative QCD, for scales above $Λ_{\mathrm{QCD}}$ and up to the Planck scale $\sim1.22\cdot10^{19}$\,GeV, with the highest precision and using the data of a single experiment. In particular, we use the results obtained for the thrust ($T$) and $C$-parameter ($C$) distributions in $e^+e^-$ annihilation at a single annihilation energy $\sqrt{s}=M_Z$ (i.e.\ at the $Z^0$ peak). This new method is based on the \emph{intrinsic conformality} (iCF) and on the Infinite-Order Scale Setting, using the Principle of Maximum Conformality (i.e.\ the PMC$_\infty$), which allows a rigorous determination of the renormalization scales for the event-shape variable distributions satisfying all of the requirements of Renormalization Group Invariance, including renormalization-scheme independence and consistency with Abelian theory in the $N_C \to 0$ limit. This new method is based on the scale-invariance of the iCF, which allows determination of $α_s(μ_0)$ at any scale $μ_0$, and on the Maximum Likelihood statistical approach. We propose a novel approach to determining the best-fitting range by considering all possible intervals over the entire range of bins available in the perturbative region and selecting that which returns the most-likely-lowest $χ^2_{\rm min}$. This new method is designed to eliminate the errors that arise due to selection of the bin-interval and that have been neglected in previous analyses. In particular, using data for thrust and $C$-parameter at the $Z^0$ peak from ALEPH, OPAL, DELPHI and L3 experiments, we obtain the average value: $α_s(M_Z)= 0.1182^{+0.0007}_{-0.0007}$, for the strong coupling. This determination of $α_s(M_Z)$ is consistent with the world average...

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arXiv2025

The Principle of Maximum Conformality Correctly Resolves the Renormalization-Scheme-Dependence Problem

In this paper, we clarify a serious misinterpretation and consequent misuse of the Principle of Maximum Conformality (PMC), which also can be served as a mini review of PMC. We emphasize that the purpose of the PMC is to achieve precise fixed-order pQCD predictions, free from conventional renormalization scheme and scale ambiguities. We demonstrate that the PMC predictions satisfy all of the self-consistency conditions of the renormalization group and standard renormalization-group invariance; the PMC predictions are thus independent of any initial choice of renormalization scheme and scale. The scheme independence of the PMC is also ensured by commensurate scale relations which relate different observables to each other. Moreover, in the Abelian limit, the PMC dovetails into the well-known Gell-Mann--Low framework, a method universally revered for its precision in QED calculations. Due to the elimination of factorially-divergent renormalon terms, the PMC series not only attains a convergence behavior far superior to that of its conventional counterparts but also deftly curtails any residual scale dependence caused by the unknown higher-order terms. This refined convergence, coupled with its robust suppression of residual uncertainties, furnishes a sound and reliable foundation for estimating the contributions from unknown higher-order terms. Anchored in the bedrock of standard renormalization group invariance, the PMC simultaneously eradicates the factorial divergences and eliminates superfluous systematic errors, which inversely provides a good foundation for achieving high-precision pQCD predictions. Consequently, owing to its rigorous theoretical underpinnings, the PMC is eminently applicable to virtually all high-energy hadronic processes.

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arXiv2023

High precision tests of QCD without scale or scheme ambiguities

A key issue in making precise predictions in QCD is the uncertainty in setting the renormalization scale $μ_R$ and thus determining the correct values of the QCD running coupling $α_s(μ_R^2)$ at each order in the perturbative expansion of a QCD observable. It has often been conventional to simply set the renormalization scale to the typical scale of the process $Q$ and vary it in the range $μ_R \in [Q/2,2Q]$ in order to estimate the theoretical error. This is the practice of Conventional Scale Setting (CSS). The resulting CSS prediction will however depend on the theorist's choice of renormalization scheme and the resulting pQCD series will diverge factorially. It will also disagree with renormalization scale setting used in QED and electroweak theory thus precluding grand unification. A solution to the renormalization scale-setting problem is offered by the Principle of Maximum Conformality (PMC), which provides a systematic way to eliminate the renormalization scale-and-scheme dependence in perturbative calculations. The PMC method has rigorous theoretical foundations, it satisfies Renormalization Group Invariance (RGI) and preserves all self-consistency conditions derived from the renormalization group. The PMC cancels the renormalon growth, reduces to the Gell-Mann--Low scheme in the $N_C\to 0$ Abelian limit and leads to scale- and scheme-invariant results. The PMC has now been successfully applied to many high-energy processes. In this article we summarize recent developments and results in solving the renormalization scale and scheme ambiguities in perturbative QCD. [full abstract is in the paper].

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arXiv2023

Elimination of QCD Renormalization Scale and Scheme Ambiguities

We present results for the thrust distribution in the electron positron annihilation to the three jet process at NNLO in the perturbative conformal window of QCD, as a function of the number of flavors $N_f$. Given the existence of an infrared interacting fixed point in this region, we can compare the Conventional Scale Setting (CSS) and the Principle of Maximum Conformality (PMC$_\infty$) methods along the entire renormalization group flow from the highest energies to zero energy. We then consider also the QED thrust, obtained as the limit $N_c \rightarrow 0$ of the number of colors and we show analogous comparison. QED in the low energy regime develops an infrared non-interacting fixed point. Using these quantum field theory limits as theoretical laboratories, we arrive at interesting results showing new features of the PMC$_\infty$.

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arXiv2014

On the Evolution of Sum Rules for T-Odd Distribution and Fragmentation Functions

We test stability against probabilistic evolution of sum rules for transverse-momentum-dependent distribution and fragmentation functions. We find that preservation of the Burkardt sum rule for Sivers distribution functions is similar to the conservation of longitudinal momentum related to spin-averaged parton distributions. At the same time, preservation of the Schaefer-Teryaev sum rule for Collins functions is similar to preservation of the Burkhardt-Cottingham sum rule for the spin-dependent g_2 structure function.

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arXiv2014

Single Transverse-Spin Asymmetries in Drell-Yan Processes

The asymmetry in the angular distribution of Drell--Yan dilepton pairs generated in collisions where just one nucleon is transversely polarised has been examined in the literature with a variety of results, mainly differing by factors of two. We re-evaluate the asymmetry via twist-3 contributions in collinear factorisation. In order to allow complete and in-depth comparison with existing calculations, we supply all calculational details.

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arXiv2009

Colour Modification of Factorisation in Single-Spin Asymmetries

We discuss the way in which factorisation is partially maintained but nevertheless modified by process-dependent colour factors in hadronic single-spin asymmetries. We also examine QCD evolution of the twist-three gluonic-pole strength defining an effective T-odd Sivers function in the large-x limit, where evolution of the T-even transverse-spin DIS structure function g2 is known to be multiplicative.

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arXiv2009

Non-Universality and Evolution of the Sivers Function

We examine the large-x QCD evolution of the twist-three gluonic-pole strength defining an effective T-odd Sivers function, where evolution of the T-even transverse-spin DIS structure function g2 is multiplicative. The result corresponds to a colour-factor modified spin-averaged twist-two evolution.

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arXiv2009

Transverse Polarisation of Quarks in Hadrons

We review the present state of knowledge regarding the transverse polarisation (or transversity) distributions of quarks. After some generalities on transverse polarisation, we formally define the transversity distributions within the framework of a classification of all leading-twist distribution functions. We describe the QCD evolution of transversity at leading and next-to-leading order. A comprehensive treatment of non-perturbative calculations of transversity distributions (within the framework of quark models, lattice QCD and QCD sum rules) is presented. The phenomenology of transversity (in particular, in Drell-Yan processes and semi-inclusive leptoproduction) is discussed in some detail. Finally, the prospects for future measurements are outlined.

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arXiv2008

Dominant Contribution in Pion Production Single-Spin Asymmetries

Working with a completely collinear twist-3 factorized cross-section formula, we identify two largely dominant partonic sub-processes, which contribute to the single-spin asymmetries in semi-inclusive pion production, in the region of large pT and medium-large xF.

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arXiv2007

Colour Modification of Effective T-odd Distributions

We show that soft-gluon twist-3 contributions to single-spin asymmetries (SSA) in hard processes may be expressed in the form of effective T-odd Sivers distributions, whose signs and scales are modified by process-dependent colour factors. We thus prove that the Sivers mechanism may also be applied at large transverse momenta. We stress that twist-3 SSA in semi-inclusive deeply inelastic scattering and Drell-Yan processes are suppressed by transverse momentum rather than a virtual-photon momentum transfer and thus naively correspond to twist two at the hadronic level. More rigorously, the transverse-momentum weighted averages of the Sivers function correspond to increasing twist (3, 5, 7, ...) while the full kT-dependent Sivers function (just as other transverse-momentum dependent distribution and fragmentation functions) corresponds to a resummed infinite tower of higher twists.

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arXiv2005

Transversity K Factors for Drell-Yan

The question of the K factor in transversely polarised Drell-Yan (DY) processes is examined. The transverse-spin case is peculiar for the absence of a reference point in deeply inelastic scattering (DIS). Therefore, in order to study more fully the possible effects of higher-order corrections on DY asymmetries, a DIS definition for transversity is devised using a hypothetical scalar (Higgs-like) vertex. The results show that some care may be required in interpreting experimentally extracted partonic transversity, in particular when comparing with model calculations or predictions.

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arXiv2004

Transversity and Drell-Yan $K$-Factors

The Drell-Yan $K$-factors for transversely polarised hadrons are examined. Since transverse spin is peculiar in having no DIS reference point, the effects of higher-order corrections on DY asymmetries are examined via a DIS definition for transversity devised using a hypothetical scalar vertex. The results suggest that some care may be required when interpreting experimentally extracted partonic transversity, particularly when comparing with model calculations or predictions.

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arXiv2004

Semi-Inclusive DIS and Transversity

A review is presented of some aspects of semi-inclusive deeply inelastic scattering and transversity. In particular, the role of $k_T$-dependent and higher-twist (or multi-parton) distributions in generating single-spin asymmetries is discussed.

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arXiv2004

Hyperon Beta Decay and the CKM Matrix

I shall present a pedagogical discussion of hyperon semileptonic decays, covering some of the historical background, the basics notions of hyperon semileptonic decays, deeply inelastic scattering and the CKM matrix, and the description of SU(2) and SU(3) breaking. I shall also present a prediction for a process under current experimental study.

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arXiv2003

QCD and Transverse-Spin Physics

A pedagogical presentation of single-spin asymmetries and transversity is offered. Detailed discussion is given of various aspects of single-spin asymmetries in lepton-nucleon and in hadron-hadron scattering and of the role of perturbative QCD and evolution in the context of transversity.

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arXiv2002

QCD Evolution of Transversity in Leading and Next-to-Leading Order

I shall present a rather pedagogical discussion of the transversity distributions in the quark-parton model and, in particular, the role of perturbative QCD corrections. Among the topics I shall discuss are: LO and NLO evolution, the Soffer bound and so-called K factors in the Drell-Yan process. The main conclusion will be that, compared to unpolarised or even longitudinally polarised hadron scattering, the case of transverse spin should actually provide a far clearer window onto the workings of QCD and the interplay with the quark-parton model.

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