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A compression algorithm for the combination of PDF sets.

Carrazza S, Latorre JI, Rojo J, Watt G - Eur Phys J C Part Fields (2015)

Bottom Line: We illustrate our strategy with the combination and compression of the recent NNPDF3.0, CT14 and MMHT14 NNLO PDF sets.The resulting compressed Monte Carlo PDF sets are validated at the level of parton luminosities and LHC inclusive cross sections and differential distributions.We determine that around 100 replicas provide an adequate representation of the probability distribution for the original combined PDF set, suitable for general applications to LHC phenomenology.

View Article: PubMed Central - PubMed

Affiliation: Dipartimento di Fisica, Università di Milano and INFN, Sezione di Milano, Via Celoria 16, 20133 Milan, Italy.

ABSTRACT

The current PDF4LHC recommendation to estimate uncertainties due to parton distribution functions (PDFs) in theoretical predictions for LHC processes involves the combination of separate predictions computed using PDF sets from different groups, each of which comprises a relatively large number of either Hessian eigenvectors or Monte Carlo (MC) replicas. While many fixed-order and parton shower programs allow the evaluation of PDF uncertainties for a single PDF set at no additional CPU cost, this feature is not universal, and, moreover, the a posteriori combination of the predictions using at least three different PDF sets is still required. In this work, we present a strategy for the statistical combination of individual PDF sets, based on the MC representation of Hessian sets, followed by a compression algorithm for the reduction of the number of MC replicas. We illustrate our strategy with the combination and compression of the recent NNPDF3.0, CT14 and MMHT14 NNLO PDF sets. The resulting compressed Monte Carlo PDF sets are validated at the level of parton luminosities and LHC inclusive cross sections and differential distributions. We determine that around 100 replicas provide an adequate representation of the probability distribution for the original combined PDF set, suitable for general applications to LHC phenomenology.

No MeSH data available.


Comparison between the PDF correlations among different PDF flavors, as a function of Bjorken-x, for  GeV, for the original NNPDF3.0 set with  replicas and the compressed sets for various values of . From top to bottom and from left to right, we show the correlations between up and down quarks, between up and strange antiquarks, between down quarks and down antiquarks, and between up quarks and down antiquarks
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Fig11: Comparison between the PDF correlations among different PDF flavors, as a function of Bjorken-x, for  GeV, for the original NNPDF3.0 set with replicas and the compressed sets for various values of . From top to bottom and from left to right, we show the correlations between up and down quarks, between up and strange antiquarks, between down quarks and down antiquarks, and between up quarks and down antiquarks

Mentions: It is also important to verify that not only central values and variances are reproduced, but also that higher moments and correlations are well reproduced by the compression. Indeed, one of the main advantages of the replica sets of NNPDF as compared to the sets is that correlations should be reproduced more accurately in the former case. In Fig. 11 we show the results for the correlation coefficient between different PDFs, as a function of Bjorken-x, for  GeV. We compare the results of the original replica set, together with the results of the compressed sets for a number of values. From top to bottom and from left to right we show the correlations between up and down quarks, between up and strange antiquarks, between down quarks and down antiquarks, and between up quarks and down antiquarks. The correlations between PDF flavors have been computed using the suitable expression for Monte Carlo sets [31]. As we can see, correlations are reasonably well reproduced, already with the results of the compressed set and of the prior are very close to each other.Fig. 9


A compression algorithm for the combination of PDF sets.

Carrazza S, Latorre JI, Rojo J, Watt G - Eur Phys J C Part Fields (2015)

Comparison between the PDF correlations among different PDF flavors, as a function of Bjorken-x, for  GeV, for the original NNPDF3.0 set with  replicas and the compressed sets for various values of . From top to bottom and from left to right, we show the correlations between up and down quarks, between up and strange antiquarks, between down quarks and down antiquarks, and between up quarks and down antiquarks
© Copyright Policy - OpenAccess
Related In: Results  -  Collection

License
Show All Figures
getmorefigures.php?uid=PMC4594162&req=5

Fig11: Comparison between the PDF correlations among different PDF flavors, as a function of Bjorken-x, for  GeV, for the original NNPDF3.0 set with replicas and the compressed sets for various values of . From top to bottom and from left to right, we show the correlations between up and down quarks, between up and strange antiquarks, between down quarks and down antiquarks, and between up quarks and down antiquarks
Mentions: It is also important to verify that not only central values and variances are reproduced, but also that higher moments and correlations are well reproduced by the compression. Indeed, one of the main advantages of the replica sets of NNPDF as compared to the sets is that correlations should be reproduced more accurately in the former case. In Fig. 11 we show the results for the correlation coefficient between different PDFs, as a function of Bjorken-x, for  GeV. We compare the results of the original replica set, together with the results of the compressed sets for a number of values. From top to bottom and from left to right we show the correlations between up and down quarks, between up and strange antiquarks, between down quarks and down antiquarks, and between up quarks and down antiquarks. The correlations between PDF flavors have been computed using the suitable expression for Monte Carlo sets [31]. As we can see, correlations are reasonably well reproduced, already with the results of the compressed set and of the prior are very close to each other.Fig. 9

Bottom Line: We illustrate our strategy with the combination and compression of the recent NNPDF3.0, CT14 and MMHT14 NNLO PDF sets.The resulting compressed Monte Carlo PDF sets are validated at the level of parton luminosities and LHC inclusive cross sections and differential distributions.We determine that around 100 replicas provide an adequate representation of the probability distribution for the original combined PDF set, suitable for general applications to LHC phenomenology.

View Article: PubMed Central - PubMed

Affiliation: Dipartimento di Fisica, Università di Milano and INFN, Sezione di Milano, Via Celoria 16, 20133 Milan, Italy.

ABSTRACT

The current PDF4LHC recommendation to estimate uncertainties due to parton distribution functions (PDFs) in theoretical predictions for LHC processes involves the combination of separate predictions computed using PDF sets from different groups, each of which comprises a relatively large number of either Hessian eigenvectors or Monte Carlo (MC) replicas. While many fixed-order and parton shower programs allow the evaluation of PDF uncertainties for a single PDF set at no additional CPU cost, this feature is not universal, and, moreover, the a posteriori combination of the predictions using at least three different PDF sets is still required. In this work, we present a strategy for the statistical combination of individual PDF sets, based on the MC representation of Hessian sets, followed by a compression algorithm for the reduction of the number of MC replicas. We illustrate our strategy with the combination and compression of the recent NNPDF3.0, CT14 and MMHT14 NNLO PDF sets. The resulting compressed Monte Carlo PDF sets are validated at the level of parton luminosities and LHC inclusive cross sections and differential distributions. We determine that around 100 replicas provide an adequate representation of the probability distribution for the original combined PDF set, suitable for general applications to LHC phenomenology.

No MeSH data available.