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The effect on PDFs and $\alpha_S(M_Z^2)$ due to changes in flavour scheme and higher twist contributions
High Energy Physics - Phenomenology · Submitted 14 Feb 2014
abstract compiled · 2026-09-23 · no language-model review
The authors' main claim I conclude that some of the most significant differences in PDF sets are largely due to the choice of flavour scheme used.
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The abstract, sentence by sentence
I consider the effect on MSTW partons distribution functions (PDFs) due to changes in the choices of theoretical procedure used in the fit. I first consider using the 3-flavour fixed flavour number scheme instead of the standard general mass variable flavour number scheme used in the MSTW analysis. This results in the light quarks increasing at all relatively small $x$ values, the gluon distribution becoming smaller at high values of $x$ and larger at small $x$, the preferred value of the coupling constant $\alpha_S(M_Z^2)$ falling, particularly at NNLO, and the fit quality deteriorates. I also consider lowering the kinematic cut on $W^2$ for DIS data and simultaneously introducing higher twist terms which are fit to data. This results in much smaller effects on both PDFs and $\alpha_S(M_Z^2)$ than the scheme change, except for quarks at very high $x$. I show that the structure function one obtains from a fixed input set of PDFs using the fixed flavour scheme and variable flavour scheme differ significantly for $x \sim 0.01$ at high $Q^2$, and that this is due to the fact that in the fixed flavour scheme there is a slow convergence of large logarithmic terms of the form $(\alpha_S\ln(Q^2/m_c^2))^n$ relevant for this regime. I conclude that some of the most significant differences in PDF sets are largely due to the choice of flavour scheme used.
background contribution method result interpretation main claim
| # | sentence | role | the authors' own work | states the main conclusion | strength |
|---|---|---|---|---|---|
| s0 | I consider the effect on MSTW partons distribution functions (PDFs) due to changes in the choices of theoretical procedure used in the fit. | contribution 0.97 | 0.87 | 0.03 | unclear 0.62 |
| s1 | I first consider using the 3-flavour fixed flavour number scheme instead of the standard general mass variable flavour number scheme used in the MSTW analysis. | method 0.70 | 0.79 | 0.02 | asserted 0.62 |
| s2 | This results in the light quarks increasing at all relatively small $x$ values, the gluon distribution becoming smaller at high values of $x$ and larger at small $x$, the preferred value of the coupling constant $\alpha_S(M_Z^2)$ falling, particularly at NNLO, and the fit quality deteriorates. | result 1.00 | 0.93 | 0.08 | asserted 1.00 |
| s3 | I also consider lowering the kinematic cut on $W^2$ for DIS data and simultaneously introducing higher twist terms which are fit to data. | method 0.79 | 0.88 | 0.02 | unclear 0.51 |
| s4 | This results in much smaller effects on both PDFs and $\alpha_S(M_Z^2)$ than the scheme change, except for quarks at very high $x$. | result 1.00 | 0.93 | 0.07 | asserted 1.00 |
| s5 | I show that the structure function one obtains from a fixed input set of PDFs using the fixed flavour scheme and variable flavour scheme differ significantly for $x \sim 0.01$ at high $Q^2$, and that this is due to the fact that in the fixed flavour scheme there is a slow convergence of large logarithmic terms of the form $(\alpha_S\ln(Q^2/m_c^2))^n$ relevant for this regime. | result 0.60 | 0.90 | 0.05 | asserted 1.00 |
| s6 | I conclude that some of the most significant differences in PDF sets are largely due to the choice of flavour scheme used. | interpretation 0.99 | 0.73 | 0.95 | asserted 0.71 |
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The paper
Original abstract
I consider the effect on MSTW partons distribution functions (PDFs) due to changes in the choices of theoretical procedure used in the fit. I first consider using the 3-flavour fixed flavour number scheme instead of the standard general mass variable flavour number scheme used in the MSTW analysis. This results in the light quarks increasing at all relatively small $x$ values, the gluon distribution becoming smaller at high values of $x$ and larger at small $x$, the preferred value of the coupling constant $\alpha_S(M_Z^2)$ falling, particularly at NNLO, and the fit quality deteriorates. I also consider lowering the kinematic cut on $W^2$ for DIS data and simultaneously introducing higher twist terms which are fit to data. This results in much smaller effects on both PDFs and $\alpha_S(M_Z^2)$ than the scheme change, except for quarks at very high $x$. I show that the structure function one obtains from a fixed input set of PDFs using the fixed flavour scheme and variable flavour scheme differ significantly for $x \sim 0.01$ at high $Q^2$, and that this is due to the fact that in the fixed flavour scheme there is a slow convergence of large logarithmic terms of the form $(\alpha_S\ln(Q^2/m_c^2))^n$ relevant for this regime. I conclude that some of the most significant differences in PDF sets are largely due to the choice of flavour scheme used.
Human review
References
How the literature uses it
15 arXiv papers cite this in 19 sentences
Papers citing it · 16 sentences without a confident label
Contests it 1 paper
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In this regard we disagree with Refs. [ref] which claim higher twist effects to be negligible in the framework of MSTW [ref] and NNPDF2.3 [ref] .
A Critical Appraisal and Evaluation of Modern PDFs · Strong coupling constant · contest 0.87
Cites it as background 2 papers
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Examples of matched general-mass schemes in electro-, photo- and hadroproduction include FONLL [ref] , TR [ref] , ACOT [ref] , and a scheme generically referred to as GMVFNS [ref] .
A determination of mc(mc) from HERA data using a matched heavy-flavor scheme · Introduction · 0.95
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In the case of the parton shower, the splitting kernels are modified as explained in Section [ref], whereas the specifics of the treatment of mass thresholds depends on the PDF collaboration [ref] .
Matching the Nagy-Soper parton shower at next-to-leading order · Matching in the presence of singularities in the born approximation · 0.83
What it cites · 39 sentences without a confident label
Contests 1 paper
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It is similar in some sense to the results for the bottom quark of Eq. (3.5) in [ref] , but this neglected the evolution of the gluon and hence the $p^0_gg$ terms, which as shown here are actually the dominant effect at lowish orders.
b-Initiated processes at the LHC: a reappraisal · Perturbative Convergence of Heavy Flavour Evolution · contest 0.74
Builds on 1 paper
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In order to test the importance of this difference between FFNS and GM-VFNS in inclusive $F_2(x,Q^2)$ I have extended an investigation begun in [ref] and performed fits using the FFNS scheme in order to compare the fit quality and resulting PDFs and $α_S(M_Z^2)$ to those obtained from fits using the GM-VFNS.
Effect of changes of variable flavor number scheme on parton distribution functions and predicted cross sections · Flavour Number · 0.99
Uses the method or tool of 2 papers
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This is similar to the procedure in [ref] and more recent PDF fits by the same group.
The 3-, 4-, and 5-flavor NNLO Parton from Deep-Inelastic-Scattering Data and at Hadron Colliders · Higher Twist · 0.90
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At NNLO the fit to Tevatron jet data uses the NNLO threshold corrections that are available [ref] (though more complete calculations which take into account the dependence on the jet radius $R$ have just appeared in [ref] these are not available for use yet).
Approximate next-to-next-to-leading order corrections to hadronic jet production · Flavour Number · 0.93
Compares with 11 papers
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The predictions for $F_2^c(x,Q^2)$ using the TR' GM-VFNS [ref] and the MSTW2008 PDFs [ref] are compared to those using the FFNS and three-flavour PDFs generated using the MSTW2008 input distributions [ref] , and are shown in Fig. [ref].
A Variable-Flavour Number Scheme for NNLO · Flavour Number · 0.99
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The predictions for $F_2^c(x,Q^2)$ using the TR' GM-VFNS [ref] and the MSTW2008 PDFs [ref] are compared to those using the FFNS and three-flavour PDFs generated using the MSTW2008 input distributions [ref] , and are shown in Fig. [ref].
Heavy-quark mass dependence in global PDF analyses and 3- and 4-flavour parton distributions · Flavour Number · 0.99
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The predictions for $F_2^c(x,Q^2)$ using the TR' GM-VFNS [ref] and the MSTW2008 PDFs [ref] are compared to those using the FFNS and three-flavour PDFs generated using the MSTW2008 input distributions [ref] , and are shown in Fig. [ref].
Parton distributions for the LHC · Flavour Number · 0.99
Cites as support 5 papers
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However, the results of the previous section, plus those in [ref] demonstrate that differences are indeed significant, and the origin of this needs to be understood.
Effect of changes of variable flavor number scheme on parton distribution functions and predicted cross sections · Perturbative Convergence of Heavy Flavour Evolution · 0.97
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However, the results of the previous section, plus those in [ref] demonstrate that differences are indeed significant, and the origin of this needs to be understood.
Including heavy flavour production in PDF fits · Perturbative Convergence of Heavy Flavour Evolution · 0.97
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However, the results of the previous section, plus those in [ref] demonstrate that differences are indeed significant, and the origin of this needs to be understood.
Theoretical issues in PDF determination and associated uncertainties · Perturbative Convergence of Heavy Flavour Evolution · 0.97
Cites as background 14 papers
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Some of the variants are reviewed and compared in [ref] , and for specific examples see e.g. [ref]
Comparison between variable flavor number schemes for charm quark electroproduction · Flavour Number · 0.90
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Some of the variants are reviewed and compared in [ref] , and for specific examples see e.g. [ref]
The SM and NLO multileg working group: Summary report · Flavour Number · 0.90
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Some of the variants are reviewed and compared in [ref] , and for specific examples see e.g. [ref]
Heavy quarks in deep-inelastic scattering · Flavour Number · 0.90
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