We present the new MSHT20 set of parton distribution functions (PDFs) of the proton, determined from global analyses of the available hard scattering data. The PDFs are made available at NNLO, NLO, ...and LO, and supersede the MMHT14 sets. They are obtained using the same basic framework, but the parameterisation is now adapted and extended, and there are 32 pairs of eigenvector PDFs. We also include a large number of new data sets: from the final HERA combined data on total and heavy flavour structure functions, to final Tevatron data, and in particular a significant number of new LHC 7 and 8 TeV data sets on vector boson production, inclusive jets and top quark distributions. We include up to NNLO QCD corrections for all data sets that play a major role in the fit, and NLO EW corrections where relevant. We find that these updates have an important impact on the PDFs, and for the first time the NNLO fit is strongly favoured over the NLO, reflecting the wider range and in particular increased precision of data included in the fit. There are some changes to central values and a significant reduction in the uncertainties of the PDFs in many, though not all, cases. Nonetheless, the PDFs and the resulting predictions are generally within one standard deviation of the MMHT14 results. The major changes are the
u
-
d
valence quark difference at small
x
, due to the improved parameterisation and new precise data, the
d
¯
,
u
¯
difference at small
x
, due to a much improved parameterisation, and the strange quark PDF due to the effect of LHC
W
,
Z
data and inclusion of new NNLO corrections for dimuon production in neutrino DIS. We discuss the phenomenological impact of our results, and in general find reduced uncertainties in predictions for processes such as Higgs, top quark pair and
W
,
Z
production at post LHC Run-II energies.
Parton distributions in the LHC era: MMHT 2014 PDFs Harland-Lang, L. A.; Martin, A. D.; Motylinski, P. ...
The European physical journal. C, Particles and fields,
05/2015, Letnik:
75, Številka:
5
Journal Article
Recenzirano
Odprti dostop
We present LO, NLO and NNLO sets of parton distribution functions (PDFs) of the proton determined from global analyses of the available hard scattering data. These MMHT2014 PDFs supersede the ...‘MSTW2008’ parton sets, but they are obtained within the same basic framework. We include a variety of new data sets, from the LHC, updated Tevatron data and the HERA combined H1 and ZEUS data on the total and charm structure functions. We also improve the theoretical framework of the previous analysis. These new PDFs are compared to the ‘MSTW2008’ parton sets. In most cases the PDFs, and the predictions, are within one standard deviation of those of MSTW2008. The major changes are the
u
-
d
valence quark difference at small
x
due to an improved parameterisation and, to a lesser extent, the strange quark PDF due to the effect of certain LHC data and a better treatment of the
D
→
μ
branching ratio. We compare our MMHT PDF sets with those of other collaborations; in particular with the NNPDF3.0 sets, which are contemporary with the present analysis.
We present the MMHT2015qed PDF set, resulting from the inclusion of QED corrections to the existing set of MMHT Parton Distribution Functions (PDFs), and which contain the photon PDF of the proton. ...Adopting an input distribution from the LUXqed formulation, we discuss our methods of including QED effects for the full, coupled DGLAP evolution of all partons with QED at
O
(
α
)
,
O
(
α
α
S
)
,
O
(
α
2
)
. While we find consistency for the photon PDF of the proton with other recent sets, building on this we also present a set of QED corrected neutron PDFs and provide the photon PDF separated into its elastic and inelastic contributions. The effect of QED corrections on the other partons and the fit quality is investigated, and the sources of uncertainty for the photon are outlined. Finally we explore the phenomenological implications of this set, giving the partonic luminosities for both the elastic and inelastic contributions to the photon and the effect of our photon PDF on fits to high mass Drell–Yan production, including the photon-initiated channel.
We investigate the impact of the high precision ATLAS and CMS 7 TeV measurements of inclusive jet production on the MMHT global PDF analysis at next-to-next-to-leading order (NNLO). This is made ...possible by the recent completion of the long-term project to calculate the NNLO corrections to the hard cross section. We find that a good description of the ATLAS data is not possible with the default treatment of experimental systematic errors, and propose a simplified solution that retains the dominant physical information of the data. We then investigate the fit quality and the impact on the gluon PDF central value and uncertainty when the ATLAS and CMS data are included in a MMHT fit. We consider both common choices for the factorization and renormalization scale, namely the inclusive jet transverse momentum,
p
⊥
, and the leading jet
p
⊥
, as well as the different jet radii for which the ATLAS and CMS data are made available. We find that the impact of these data on the gluon is relatively insensitive to these inputs, in particular the scale choice, while the inclusion of NNLO corrections tends to improve the data description somewhat and has a qualitatively similar though not identical impact on the gluon in comparison to NLO.
We present an investigation of the theoretical uncertainties in parton distribution functions (PDFs) due to missing higher-order corrections in the perturbative predictions used in the fit, and their ...relationship to the uncertainties in subsequent predictions made using the PDFs. We consider in particular the standard approach of factorization and renormalization scale variation, and derive general results for the consistent application of these at the PDF fit stage. To do this, we use the fact that a PDF fit may be recast in a physical basis, where the PDFs themselves are bypassed entirely, and one instead relates measured observables to predicted ones. In the case of factorization scale variation we find that in various situations there is a high degree of effective correlation between the variation in the fit and in predicted observables. In particular, including such a variation in both cases can lead to an exaggerated theoretical uncertainty. More generally, a careful treatment of this correlation appears mandatory, at least within the standard scale variation paradigm. For the renormalization scale, the situation is less straightforward, but again we highlight the potential for correlations between related processes in the fit and predictions to enter at the same level as between processes in the fit or prediction alone.
QED parton distribution functions in the MSHT20 fit Cridge, T.; Harland-Lang, L. A.; Martin, A. D. ...
The European physical journal. C, Particles and fields,
2022/1, Letnik:
82, Številka:
1
Journal Article
Recenzirano
Odprti dostop
We present the MSHT20qed set of parton distribution functions (PDFs). These are obtained from the MSHT20 global analysis via a refit including QED corrections to the DGLAP evolution at
O
(
α
)
,
O
(
...α
α
S
)
and
O
(
α
2
)
, and containing the photon PDF of the proton. As in the previous MMHT15qed study we use an input distribution for the photon that is derived from the LUXqed formulation, and find good consistency for the photon PDF with that of MMHT15qed, as well as with other recent sets. We also present a set of QED corrected neutron PDFs and accompanying photon distribution, and provide the photon PDF of the nucleons separated into elastic and inelastic contributions. We assess the general expectations for the impact of photon-initiated (PI) corrections to processes entering PDF fits, and review the effect of QED corrections on the other partons and on the fit quality, where electroweak corrections (including PI production) are appropriately added to the cross sections wherever possible. We explore the phenomenological implications of this set by comparing to a variety of benchmark cross sections, finding small but significant corrections due to the inclusion of QED effects in the PDFs.
We present the first global analysis of parton distribution functions (PDFs) at approximate N Formula omittedLO in the strong coupling constant Formula omitted, extending beyond the current highest ...NNLO achieved in PDF fits. To achieve this, we present a general formalism for the inclusion of theoretical uncertainties associated with the perturbative expansion in the strong coupling. We demonstrate how using the currently available knowledge surrounding the next highest order (N Formula omittedLO) in Formula omitted can provide consistent, justifiable and explainable approximate N Formula omittedLO (aN Formula omittedLO) PDFs. This includes estimates for uncertainties due the currently unknown N Formula omittedLO ingredients, but also implicitly some missing higher order uncertainties (MHOUs) beyond these. Specifically, we approximate the splitting functions, transition matrix elements, coefficient functions and K-factors for multiple processes to N Formula omittedLO. Crucially, these are constrained to be consistent with the wide range of already available information about N Formula omittedLO to match the complete result at this order as accurately as possible. Using this approach we perform a fully consistent approximate N Formula omittedLO global fit within the MSHT framework. This relies on an expansion of the Hessian procedure used in previous MSHT fits to allow for sources of theoretical uncertainties. These are included as nuisance parameters in a global fit, controlled by knowledge and intuition based prior distributions. We analyse the differences between our aN Formula omittedLO PDFs and the standard NNLO PDF set, and study the impact of using aN Formula omittedLO PDFs on the LHC production of a Higgs boson at this order. Finally, we provide guidelines on how these PDFs should be used in phenomenological investigations.
Blue‐Green Infrastructure (BGI) and Sustainable Drainage Systems (SuDS) are increasingly recognised as vital components of urban flood risk management. However, uncertainty regarding their hydrologic ...performance and lack of confidence concerning their public acceptability create concerns and challenges that limit their widespread adoption. This paper investigates barriers to implementation of BGI in Portland, Oregon, using the Relevant Dominant Uncertainty (RDU) approach. Two types of RDU are identified: scientific RDUs related to physical processes that affect infrastructure performance and service provision, and socio‐political RDUs that reflect a lack of confidence in socio‐political structures and public preferences for BGI. We find that socio‐political RDUs currently exert the strongest negative influences on BGI decision making in Portland. We conclude that identification and management of both biophysical and socio‐political uncertainties are essential to broadening the implementation of BGI and sustainable urban flood risk management solutions that are practical, scientifically sound, and supported by local stakeholders.
We investigate the effect of including the HERA run I + II combined cross section data on the MMHT2014 PDFs. We present the fit quality within the context of the global fit and when only the HERA ...data are included. We examine the changes in both the central values and the uncertainties in the PDFs. We find that the prediction for the data is good, and only relatively small improvements in
χ
2
and changes in the PDFs are obtained with a refit at both NLO and NNLO. PDF uncertainties are slightly reduced. There is a small dependence of the fit quality on the value of
Q
min
2
. This can be improved by phenomenologically motived corrections to
F
L
(
x
,
Q
2
)
which parametrically are largely in the form of higher-twist type contributions.
We investigate the variation in the MMHT2014 PDFs when we allow the heavy-quark masses
m
c
and
m
b
to vary away from their default values. We make PDF sets available in steps of
Δ
m
c
=
0.05
GeV
and
...Δ
m
b
=
0.25
GeV
, and present the variation in the PDFs and in the predictions. We examine the comparison to the HERA data on charm and beauty structure functions and note that in each case the heavy-quark data, and the inclusive data, have a slight preference for lower masses than our default values. We provide PDF sets with three and four active quark flavours, as well as the standard value of five flavours. We use the pole mass definition of the quark masses, as in the default MMHT2014 analysis, but briefly comment on the
MS
¯
definition.
PDF
