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C. J. Maxwell

Publications and source records attributed to C. J. Maxwell.

At least 19 recordsLinked to original sources
arXiv2011

Using an Effective Charges Method to extract Lambda-MS-bar from event shape moments in e+e- annihilation

We use an Effective Charges (ECH) method to extract Lambda-MS-bar, and hence alpha_s(M_z), from event shape moments in e+e- annihilation. We compare these results with ones obtained using standard MS-bar perturbation theory. The ECH method at NLO is found to perform better than standard MS-bar perturbation theory when applied to means of event shape observables. For example, when we apply the NLO ECH method to <1-T> we get alpha_s(M_z)=0.1193\pm0.0003. However ECH at NNLO is found to work less well than ECH at NLO, and the ECH method also fails to describe data for higher moments of event shapes. We attempt to explain this by considering the ECH beta-function as an asymptotic series. We also examine the effect of adding two different models for non-perturbative power corrections to the perturbative approximation given by the ECH method and MS-bar perturbation theory. Whilst only small power corrections are required when using ECH at NLO, it is found that these models are insufficient to couteract the undesirable behaviour of ECH at NNLO.

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arXiv2007

Improved analysis of moments of F3 in neutrino-nucleon scattering using the Bernstein polynomial method

We use recently calculated next-to-next-to-leading order (NNLO) anaomalous dimension coefficients for the moments of the xF_3 structure function in neutrino- nucleon scattering, together with the corresponding three-loop Wilson coefficients, to obtain improved QCD predictions for both odd and even moments. To investigate the issue of renormalization scheme dependence the Complete Renormalization Group Improvement (CORGI) approach is used, in which all dependence on renormalization or factorization scales is avoided by a complete resummation of RG-predictable scale logarithms. We also consider predictions using the method of effective charges and compare with the standard ``physical scale'' choice. The Bernstein polynomial method is used to construct experimental moments from the xF_3 data of the CCFR collaboration insensitive to the data in the region of x which is inaccessible experimentally. Direct fits for Λ^(5)MSbar (α_s(M_Z)) are performed. The CORGI fits including target mass corrections give a value α_s(M_Z)=0.119+/-0.002, nicely consistent with the world average. The effective charge and physical scale fits give slightly smaller values which are still consistent within the errors.

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arXiv2006

On Effective Charges, Event shapes and the size of Power Corrections

We introduce and motivate the method of effective chsrges, and consider how to implement an all-orders resummation of large kinematical logarithms in this formalism. Fits for QCD Λand power corrections are performed for the e+e- event shape observables 1-thrust and heavy jet mass, and somewhat smaller power corrections are found than in the usual approach employing the ``physical scale'' choice.

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arXiv2006

Perturbative and non-perturbative QCD

In these lectures we give a concise introduction to the ideas of renormalon calculus in QED and QCD. We focus in particular on the example of the Adler D function of vacuum polarization, and on relations between perturbative renormalon ambiguities and corresponding non-perturbative Operator Product Expansion (OPE) ambiguities. Recent work on infrared freezing of Euclidean observables is also discussed.

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arXiv2006

Infrared freezing of Euclidean QCD observables in the one-chain approximation

We consider the one-chain term in a skeleton expansion for Euclidean QCD observables. Focusing on the particular example of the Adler D function, we show that although there is a Landau pole in the coupling at Q^2=Λ^2 which renders fixed-order perturbative results infinite, the Landau pole is absent in the all-orders one-chain result. In this approximation one has finiteness and continuity at Q^2=Λ^2, and a smooth freezing as Q^2 decreases to 0.

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arXiv2006

Infrared Freezing of Euclidean QCD observables

We consider the leading one-chain term in a skeleton expansion for QCD observables and show that for energies Q^2>Λ^2, where Q^2=Λ^2 is the Landau pole in the coupling, the skeleton expansion result is equivalent to the standard Borel integral representation, with ambiguities related to infrared (IR) renormalons. For Q^2<Λ^2 the skeleton expansion result is equivalent to a previously proposed modified Borel representation where the ambiguities are connected with ultraviolet (UV) renormalons. We investigate the Q^2-dependence of the perturbative corrections to the Adler D function, the GLS sum rule, and the polarized and unpolarized Bjorken sum rules. In all these cases the one-chain result changes sign in the vicinity of Q^2=Λ^2, and then exhibits freezing behaviour, vanishing at Q^2=0. Finiteness at Q^2=Λ^2 implies specific relations between the residues of IR and UV renormalons in the Borel plane. These relations, only one of which has previously been noted (though it remained unexplained) are shown to follow from the continuity of the characteristic function in the skeleton expansion. By considering the compensation of non-perturbative and perturbative ambiguities we are led to a result for the Q^2 dependence of these observables at all Q^2, in which there is a single undetermined non-perturbative parameter, and which involves the skeleton expansion characteristic function. The observables freeze to zero in the infrared. We briefly consider the freezing behaviour of the Minkowskian R_{e+e-} ratio.

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arXiv2006

Effective Charges, Event Shapes and Power Corrections

We introduce and motivate the method of effective charges, and consider how to implement an all-orders resummation of large kinematical logarithms in this formalism. Fits for QCD Λand power corrections are performed for the e+e- event shape observables 1-thrust and heavy-jet mass, and somewhat smaller power corrections found than in the usual approach employing the ``physical scale'' choice.

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arXiv2005

Resummation of Large Logarithms within the Method of Effective Charges

We show how the resummation of large logarithms can be incorporated into the method of effective charges. As an example, we apply this approach to the event shape variables thrust and heavy jet mass in e+e- annihilation. We find that, although the resummation creates problems with the behaviour of the efective charge in the 2-jet limit, smaller power corrections are required to fit the data compared to the standard approach. In addition, increasing the logarithmic accuracy reduces the size of the power corrections further. We also consider ``predicting'' the sub-leading logarithms in the MSbar scheme, obtaining surprisingly good results for the first few NLL terms.

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arXiv2004

New Application of the large-Nc expansion : comparison of the Gottfried and Adler sum rules

The Adler sum rule for deep inelastic neutrino scattering measures the isospin of the nucleus, and is hence exact. In contrast the Gottfried sum rule for charged lepton scattering does receive perturbative and non-perturbative corrections. We show that at two-loop level the Gottfried sum rule is suppressed by a factor 1/Nc^2 relative to higher moments, and we conjecture that this suppression holds to all-orders, and also for higher-twist effects. It is further noted that differences between radiative corrections for higher moments of neutrino and charged lepton deep inelastic scattering, are 1/Nc^2 suppressed at two-loops, and this is also conjectured to hold to all-orders. The 1/Nc^2 suppression of corrections to the Gottfried sum rule makes it plausible that the deviations from the parton model value are dominated by a light quark flavour asymmetry in the nucleon sea. This asymmetry indeed persists as Nc-->infinity as predicted in a chiral soliton model.

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arXiv2004

Lambda-based QCD perturbation theory-: sidestepping the scheme-dependence problem

We advocate the replacement of standard alphas(mu)-based QCD perturbation theory, in which the coupling and truncated perturbative predictions are dependent on the chosen renormalisation scheme, by a Lambda-based approach in which QCD observables are directly related to the dimensional transmutation parameter, Lambda, of the theory. The shortcomings of the standard approach are emphasised by formulating it in the Lambda-based language. We show how the Lambda-based approach can be extended to include massive quarks. We also consider the use of Lambda-based perturbation theory in the case when a resummation of large infrared logarithms is required, performing a phenomenological analysis for the e+e- event shape observables thrust and heavy jet mass. We show by fitting to data that smaller power corrections are required than in the standard approach.

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arXiv2004

All-orders infrared freezing of observables in perturbative QCD

We consider a Borel sum definition of all-orders perturbation theory for Minkowskian QCD observables such as the R(e+e-) ratio, and show that both this perturbative component and the additional non-perturbative Operator Product Expansion (OPE) component can remain separately well-defined for all values of energy sqrt(s), with the perturbative component dominating as s-->infinity, and with both components contributing as s-->0. In the infrared s-->0 limit the perturbative correction to the parton model result for R(e+e-) has an all-orders perturbation theory component which smoothly freezes to the value R(0)=2/b, where b=(33-2Nf)/6 is the first QCD beta-function coefficient with Nf flavours of massless quarks. For freezing one requires Nf<9. The freezing behaviour is manifested by the ``contour-improved'' or ``Analytic Perturbation Theory'' (APT), in which an infinite subset of analytical continuation terms are resummed to all-orders. We show that for the Euclidean Adler-D function, D(Q^2), the perturbative component remains defined into the infrared provided that ALL the renormalon singularities care taken into account, but no analogue of the APT reorganisation of perturbation theory is possible. We perform phenomenological comparisons of suitably smeared low-energy data for the R(e+e-) ratio, with the perturbative freezing perdictions, and find good agreement.

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arXiv2004

Comparison of the Gottfried and Adler sum rules within the large-Nc expansion

The Adler sum rule for deep inelastic neutrino scattering measures the isospin of the nucleon and is hence exact. By contrast, the corresponding Gottfried sum rule for charged lepton scattering was based merely on a valence picture and is modified both by perturbative and non-perturbative effects. Noting that the known perturbative corrections to two-loop order are suppressed by a factor 1/N_c^2, relative to those for higher moments, we propose that this suppression persists at higher orders and also applies to higher-twist effects. Moreover, we propose that the differences between the corresponding radiative corrections to higher non-singlet moments in charged-lepton and neutrino deep inelastic scattering are suppressed by 1/N_c^2, in all orders of perturbation theory. For the first moment, in the Gottfried sum rule, the substantial discrepancy between the measured value and the valence-model expectation may be attributed to an intrinsic isospin asymmetry in the nucleon sea, as is indeed the case in a chiral-soliton model, where the discrepancy persists in the limit N_c-->infinity.

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arXiv2002

Direct extraction of QCD LambdaMSbar from moments of structure functions in neutrino-nucleon scattering, using the CORGI approach

We use recently calculated next-to-next-to-leading (NNLO) anomalous dimension coefficients for the n=1,3,5,...,13 moments of the xF3 structure function in nuN scattering, together with the corresponding three-loop Wilson coefficients, to obtain improved QCD predictions for the moments. The Complete Renormalization Group Improvement (CORGI) approach is used, in which all dependence on renormalization or factorization scales is avoided by a complete resummation of ultraviolet logarithms. The Bernstein Polynomial method is used to compare these QCD predictions to the xF3 data of the CCFR collaboration. Direct fits for LambdaMSbar(5), with Nf=5 effective quark flavours, over the range 20<Q^2<125.9 GeV^2 were performed. We obtain LambdaMSbar(5)=202+54/-45 MeV, corresponding to the three-loop running coupling alphas(MZ)=0.1174+0.0043-0.0043. Including target mass corrections as well we obtain LambdaMSbar(5)=228+35/-36 MeV, corresponding to alphas(MZ)=0.1196+0.0027-0.0031.

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arXiv2002

All-orders infra-red freezing of R(e+e-) in perturbative QCD

We consider the behaviour of the perturbative QCD corrections to the R(e+e-) ratio in the limit that the c.m. energy sqrt(s) vanishes. We find that for N(f)<9 flavours of massless quarks, the perturbative correction to the parton model result freezes to the infra-red limit 2/b as s-->0. Here b=(33-2N(f))/6 is the first QCD beta-function coefficient. The freezing holds to all-orders in perturbation theory. The s-dependence can be written analytically in closed form in terms of the Lambert W function.

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arXiv2001

Renormalon-inspired resummations for vector and scalar correlators- estimating the uncertainty in {alpha}_{s}({m}_τ^{2}) and and α({M}_{Z}^{2})

We perform an all-orders resummation of the QCD Adler D-function for the vector correlator, in which the portion of perturbative coefficients involving the leading power of b, the first beta-function coefficient, is resummed. To avoid a renormalization scale dependence when we match the resummation to the exactly known NLO and NNLO results, we employ the Complete Renormalization Group Improvement (CORGI) approach. These fixed-order and resummed CORGI results are analytically continued by numerically performing a contour integral to obtain corresponding fixed and all-orders ``contour-improved'' results for the e+e- R-ratio ands its tau decay analogue R_τ. The difference between these fixed-order and all-order results is used to estimate the uncertainty in the extraction of {alpha}_{s}({M}_{Z}^{2}} from R_τ measurements, and that in the QED coupling α({M}_{Z}^{2}) due to hadronic corrections related to R. Analogous resummations for the scalar correlator are performed, and used to assess the uncertainty in the Higgs decay width to a heavy quark pair. We point out that CORGI fixed-order contour-improved results for R and the Higgs decay width, can be given explicitly in terms of the Lambert-W function and hypergeometric functions, avoiding the need for numerical integration.

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arXiv2000

Direct Extraction of QCD Lambda MS-bar from e+e- Jet Observables

We directly fit the QCD dimensional transmutation parameter, Lambda MS-bar, to experimental data on e+e- jet observables, making use of next-to-leading order (NLO) perturbative calculations. In this procedure there is no need to mention, let alone to arbitrarily vary, the unphysical renormalisation scale mu, and one avoids the spurious and meaningless ``theoretical error'' associated with standard alpha_s determinations. PETRA, SLD, and LEP data are considered in the analysis. An attempt is made to estimate the importance of uncalculated next-NLO and higher order perturbative corrections, and power corrections, by studying the scatter in the values of Lambda MS-bar obtained for different observables.

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arXiv2000

Renormalons and multiloop estimates in scalar correlators, Higgs decay and quark-mass sum rules

The single renormalon-chain contribution to the correlator of scalar currents in QCD is calculated in the $\bar{MS}$-scheme in the limit of a large $N_f$. We find that in the factorial growth of the coefficients due to renormalons takes over almost immediatelly in the euclidean region. The essential differences between the large-order growth of coefficients in the scalar case, and in the vector case are analysed. In the timelike region a stabilization of the perturbative series for the imaginary part, with $n$-loop behaviour $S_n/[\log(s/Λ^2)]^{n-1}$, where $S_n$ is essential constant for $n\le{6}$, is observed. Only for $n\ge{7}$ does one discern the factorial growth and alternations of sign. Out all-order results are used to scrutinize the performance of multiloop estimates, within the ``naive nonabelianization'' procedure, and the effective charges approach. The asymtotic behaviour of perturbative coefficients, in both large $N_f$ and large $N_c$ limits, is analysed. A contour-improved resummation technique in the time-like region is developed. Some subtleties of scheme-dependence are illustrated using results in the $\bar{MS}$ and $V$-schemes. The all-order series under investigation are summed up with the help of the Borel resummation method. The results obtained are relevant to the analysis of the theoretical uncertainties in the 4-loop extractions of the running and invariant $s$-quark masses from QCD sum rules, and in calculations of the Higgs boson decay width into a quark-antiquark pair.

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