# A determination of the fragmentation functions of pions, kaons, and protons with faithful uncertainties

Valerio Bertone, Stefano Carrazza, Nathan P. Hartland, Emanuele R. Nocera, Juan Rojo

### Abstract

We present NNFF1.0, a new determination of the fragmentation functions (FFs) of charged pions, charged kaons, and protons/antiprotons from an analysis of single-inclusive hadron production data in electron-positron annihilation. This determination, performed at leading, next-to-leading, and next-to-next-to-leading order in perturbative QCD, is based on the NNPDF methodology, a fitting framework designed to provide a statistically sound representation of FF uncertainties and to minimise any procedural bias. We discuss novel aspects of the methodology used in this analysis, namely an optimised parametrisation of FFs and a more efficient $\chi^2$ minimisation strategy, and validate the FF fitting procedure by means of closure tests. We then present the NNFF1.0 sets, and discuss their fit quality, their perturbative convergence, and their stability upon variations of the kinematic cuts and the fitted dataset. We find that the systematic inclusion of higher-order QCD corrections significantly improves the description of the data, especially in the small-$z$ region. We compare the NNFF1.0 sets to other recent sets of FFs, finding in general a reasonable agreement, but also important differences. Together with existing sets of unpolarised and polarised parton distribution functions (PDFs), FFs and PDFs are now available from a common fitting framework for the first time.
Original language English 516 European Journal of Physics C 77 https://doi.org/10.1140/epjc/s10052-017-5088-y Published - 3 Aug 2017

### Fingerprint

kaons
Protons
fragmentation
pions
protons
partons
Distribution functions
quantum chromodynamics
distribution functions
methodology
Positron annihilation
antiprotons
positron annihilation
closures
Uncertainty
Kinematics
kinematics
Acoustic waves
inclusions
optimization

### Bibliographical note

50 pages, 22 figures, 5 tables

• hep-ph
• hep-ex
• nucl-ex
• nucl-th

### Cite this

Bertone, Valerio ; Carrazza, Stefano ; Hartland, Nathan P. ; Nocera, Emanuele R. ; Rojo, Juan. / A determination of the fragmentation functions of pions, kaons, and protons with faithful uncertainties. In: European Journal of Physics C. 2017 ; Vol. 77.
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abstract = "We present NNFF1.0, a new determination of the fragmentation functions (FFs) of charged pions, charged kaons, and protons/antiprotons from an analysis of single-inclusive hadron production data in electron-positron annihilation. This determination, performed at leading, next-to-leading, and next-to-next-to-leading order in perturbative QCD, is based on the NNPDF methodology, a fitting framework designed to provide a statistically sound representation of FF uncertainties and to minimise any procedural bias. We discuss novel aspects of the methodology used in this analysis, namely an optimised parametrisation of FFs and a more efficient $\chi^2$ minimisation strategy, and validate the FF fitting procedure by means of closure tests. We then present the NNFF1.0 sets, and discuss their fit quality, their perturbative convergence, and their stability upon variations of the kinematic cuts and the fitted dataset. We find that the systematic inclusion of higher-order QCD corrections significantly improves the description of the data, especially in the small-$z$ region. We compare the NNFF1.0 sets to other recent sets of FFs, finding in general a reasonable agreement, but also important differences. Together with existing sets of unpolarised and polarised parton distribution functions (PDFs), FFs and PDFs are now available from a common fitting framework for the first time.",
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author = "Valerio Bertone and Stefano Carrazza and Hartland, {Nathan P.} and Nocera, {Emanuele R.} and Juan Rojo",
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A determination of the fragmentation functions of pions, kaons, and protons with faithful uncertainties. / Bertone, Valerio; Carrazza, Stefano; Hartland, Nathan P.; Nocera, Emanuele R.; Rojo, Juan.

In: European Journal of Physics C, Vol. 77, 516, 03.08.2017.

TY - JOUR

T1 - A determination of the fragmentation functions of pions, kaons, and protons with faithful uncertainties

AU - Bertone, Valerio

AU - Carrazza, Stefano

AU - Hartland, Nathan P.

AU - Nocera, Emanuele R.

AU - Rojo, Juan

N1 - 50 pages, 22 figures, 5 tables

PY - 2017/8/3

Y1 - 2017/8/3

N2 - We present NNFF1.0, a new determination of the fragmentation functions (FFs) of charged pions, charged kaons, and protons/antiprotons from an analysis of single-inclusive hadron production data in electron-positron annihilation. This determination, performed at leading, next-to-leading, and next-to-next-to-leading order in perturbative QCD, is based on the NNPDF methodology, a fitting framework designed to provide a statistically sound representation of FF uncertainties and to minimise any procedural bias. We discuss novel aspects of the methodology used in this analysis, namely an optimised parametrisation of FFs and a more efficient $\chi^2$ minimisation strategy, and validate the FF fitting procedure by means of closure tests. We then present the NNFF1.0 sets, and discuss their fit quality, their perturbative convergence, and their stability upon variations of the kinematic cuts and the fitted dataset. We find that the systematic inclusion of higher-order QCD corrections significantly improves the description of the data, especially in the small-$z$ region. We compare the NNFF1.0 sets to other recent sets of FFs, finding in general a reasonable agreement, but also important differences. Together with existing sets of unpolarised and polarised parton distribution functions (PDFs), FFs and PDFs are now available from a common fitting framework for the first time.

AB - We present NNFF1.0, a new determination of the fragmentation functions (FFs) of charged pions, charged kaons, and protons/antiprotons from an analysis of single-inclusive hadron production data in electron-positron annihilation. This determination, performed at leading, next-to-leading, and next-to-next-to-leading order in perturbative QCD, is based on the NNPDF methodology, a fitting framework designed to provide a statistically sound representation of FF uncertainties and to minimise any procedural bias. We discuss novel aspects of the methodology used in this analysis, namely an optimised parametrisation of FFs and a more efficient $\chi^2$ minimisation strategy, and validate the FF fitting procedure by means of closure tests. We then present the NNFF1.0 sets, and discuss their fit quality, their perturbative convergence, and their stability upon variations of the kinematic cuts and the fitted dataset. We find that the systematic inclusion of higher-order QCD corrections significantly improves the description of the data, especially in the small-$z$ region. We compare the NNFF1.0 sets to other recent sets of FFs, finding in general a reasonable agreement, but also important differences. Together with existing sets of unpolarised and polarised parton distribution functions (PDFs), FFs and PDFs are now available from a common fitting framework for the first time.

KW - hep-ph

KW - hep-ex

KW - nucl-ex

KW - nucl-th

U2 - 10.1140/epjc/s10052-017-5088-y

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