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Journal Article•DOI•

Anomalous couplings in Higgs-boson pair production at approximate NNLO QCD

Daniel de Florian, Ignacio Fabre, Gudrun Heinrich1, Javier Mazzitelli2, Ludovic Michel Scyboz3 •
Karlsruhe Institute of Technology1, Max Planck Society2, University of Oxford3
23 Sep 2021-Journal of High Energy Physics (Springer Berlin Heidelberg)-Vol. 2021, Iss: 9, pp 161
TL;DR: In this paper, the authors combine NLO predictions with full top-quark mass dependence with approximate NNLO predictions for Higgs-boson pair production in gluon fusion, including the possibility to vary coupling parameters within a nonlinear Effective Field Theory framework containing five anomalous couplings for this process.
Abstract: We combine NLO predictions with full top-quark mass dependence with approximate NNLO predictions for Higgs-boson pair production in gluon fusion, including the possibility to vary coupling parameters within a non-linear Effective Field Theory framework containing five anomalous couplings for this process. We study the impact of the anomalous couplings on various observables, and present Higgs-pair invariant-mass distributions at seven benchmark points characterising different mhh shape types. We also provide numerical coefficients for the approximate NNLO cross section as a function of the anomalous couplings at $$ \sqrt{s} $$ = 14 TeV.

Summary (3 min read)

Jump to: [1 Introduction] – [2 Higgs-boson pair production within an EFT framework] – [3 Phenomenological results and coupling coefficients] – [3.1 Total cross section] – [3.2 Differential results and heat maps] – [3.3 Fitting procedure and results for the coupling coefficients] and [4 Conclusions]

1 Introduction

  • The precision of the measurements of Higgs boson couplings to other particles and itself will increase substantially in the high-luminosity phase of the LHC [14, 15].
  • The scale uncertainties at NLO are still at the 10% level, while they are decreased to about 5% when including the NNLO corrections and to about 3% at N3LO in the “NLO-improved” variant.
  • Thus NNLO′ contains NNLO results in the heavy top limit, where exact Born expressions have been used whenever the higher-order corrections in the HTL factorise, as well as NLO corrections with full topquark mass dependence.
  • Section 3 contains the phenomenological results, including total cross sections and differential distributions for the benchmark points, and the description of the fitting procedure for the coefficients of the anomalous couplings, together with the corresponding results.

2 Higgs-boson pair production within an EFT framework

  • The calculation builds on the ones presented in refs. [28, 38, 41] and therefore the methods will be described only briefly here, focusing on the new aspects.
  • It relies on counting the chiral dimension of the terms contributing to the Lagrangian [45], rather than counting the canonical dimension as in the Standard Model Effective Field Theory .
  • In the EWChL framework there are a priori no relations between the couplings.
  • In turn, approximate NNLO QCD corrections in a similar EFT framework have been computed in ref. [38], working in the heavy top limit improved by inserting LO form factors with full top mass dependence.
  • It is worth stressing that the functional dependence described in eq. (2.2), which holds for the exact NNLO cross section, is also valid for the approximate results presented in this work.

3 Phenomenological results and coupling coefficients

  • The given uncertainties are scale uncertainties based on 3-point scale variations, see text for details.
  • KNLO and KNNLO′ denote the corresponding ratio to the LO cross section.
  • The authors use NLO parton densities and strong coupling evolution for the LO and NLO predictions, and NNLO PDFs and strong coupling evolution for the NNLO′ calculation.
  • The masses of the Higgs boson and the top quark have been fixed to mh = 125GeV, mt = 173GeV and their widths have been set to zero.
  • The top-quark mass is renormalised in the on-shell scheme.

3.1 Total cross section

  • In ref. [42], shapes of the Higgs-boson pair invariant-mass distribution mhh were analysed in the 5-dimensional coupling parameter space, using machine learning techniques to classifymhh-shapes from NLO predictions.
  • This procedure led to seven shape characteristic benchmark points, for which the authors also show NNLO′ results.
  • The authors note that all other results in this paper , including the parametrisation presented in the following section, are insensitive to this additional factor, which cancels out in the ratio σ/σSM.
  • From the results in table 2 the authors can observe that the size of the QCD corrections, described by the NNLO′ K-factor, have a sizeable dependence on the EFT parameters.
  • In 1In this way the authors account for the effect of the top-quark mass in the double-real and real-virtual amplitudes in the SM case, as included in NNLOFTapprox.

3.2 Differential results and heat maps

  • In figure 2 the authors present the di-Higgs invariant-mass distribution for the SM and for the seven shape benchmarks listed in table 2, both at NLO and NNLO′.
  • In both cases the authors set ct = 1 and the remaining couplings to zero, except in the chhh–cggh case where they additionally set cgghh = cggh/2 in order to mimic the SMEFT situation, where the latter couplings are not independent of each other.
  • Comparing figures 3 and 4 (left), the authors observe that the cross section is more sensitive to variations of both chhh and ctt than variations of cggh (within the range suggested by current constraints).
  • The panel on the right shows the ratio to the NLO curves, that is (σ/σSM)NNLO′/(σ/σSM)NLO.
  • From this comparison the authors conclude that, with the only exception of cggh, all of the anomalous couplings can, within the limits given in eq. (3.1), generate variations in the di-Higgs cross section which are larger than the current experimental limit.

3.3 Fitting procedure and results for the coupling coefficients

  • The fit is carried out with the software Mathematica, and is based on the values of the NNLO′ cross section computed for 43 different points in the EFT parameter space.
  • This uncertainty is dominated by the statistical uncertainty associated with the determination of the top-mass-dependent two-loop virtual corrections, which are calculated numerically from a finite number of 6715 phase-space points, while the numerical uncertainties from the Monte Carlo integration are considerably smaller.
  • In order to check the robustness of their fit and to estimate the uncertainties associated to it, the authors produce 1000 replicas of the 43 cross section values entering the fit, by randomly generating Gaussian variations around their central value, and using the corresponding uncertainty as the standard deviation.
  • Finally, the authors perform a scan in the EFT parameter space, randomly generating 10000 points in the range indicated in eq. (3.1).
  • The authors note that this standard deviation can be regarded as an estimate of the final uncertainty in the cross section, encompassing both the uncertainties in the 43 original values of the cross section as well as the uncertainties coming from the fitting procedure.

4 Conclusions

  • The authors have presented a combination of NLO predictions with full top-quark mass dependence with approximate NNLO corrections for Higgs-boson pair production in gluon fusion.
  • Anomalous couplings are included in the framework of an Effective Field Theory where the dominant operators contributing to this process are parametrised by five anomalous couplings, chhh, ct, ctt, cggh and cgghh.
  • Based on the above parametrisation of the cross section in terms of coupling combinations, the authors have produced heat maps for slices of the coupling-parameter space, for both the cross section and the K-factor (normalised to their SM values), where they varied the anomalous couplings in a range motivated by current constraints.
  • The feature that the cross section is much more sensitive to variations of chhh and ctt than of cggh, found already at NLO, also can be seen at NNLO′.
  • The authors also provided the values for the ai coefficients at three different scale choices, thereby allowing fast and flexible studies of anomalous coupling variations at NNLO′ level.

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JHEP09(2021)161
Published for SISSA by Springer
Received: July 5, 2021
Accepted: September 5, 2021
Published: September 23, 2021
Anomalous couplings in Higgs-boson pair production
at approximate NNLO QCD
Daniel de Florian,
a
Ignacio Fabre,
a
Gudrun Heinrich,
b
Javier Mazzitelli
c
and
Ludovic Scyboz
d
a
International Center for Advanced Studies (ICAS) and ICIFI, ECyT-UNSAM,
Campus Miguelete, 25 de Mayo y Francia, 1650 Buenos Aires, Argentina
b
Institute for Theoretical Physics, Karlsruhe Institute of Technology (KIT),
Wolfgang-Gaede-Str. 1, 76131 Karlsruhe, Germany
c
Max Planck Institute for Physics,
Föhringer Ring 6, 80805 München, Germany
d
Rudolf Peierls Centre for Theoretical Physics, University of Oxford,
Parks Road, Oxford OX1 3PU, U.K.
E-mail: deflo@unsam.edu.ar, ifabre@unsam.edu.ar,
gudrun.heinrich@kit.edu, jmazzi@mpp.mpg.de,
ludovic.scyboz@physics.ox.ac.uk
Abstract: We combine NLO predictions with full top-quark mass dependence with ap-
proximate NNLO predictions for Higgs-boson pair production in gluon fusion, including the
possibility to vary coupling parameters within a non-linear Effective Field Theory frame-
work containing five anomalous couplings for this process. We study the impact of the
anomalous couplings on various observables, and present Higgs-pair invariant-mass dis-
tributions at seven benchmark points characterising different m
hh
shape types. We also
provide numerical coefficients for the approximate NNLO cross section as a function of the
anomalous couplings at
√
s = 14 TeV.
Keywords: NLO Computations, QCD Phenomenology
ArXiv ePrint: 2106.14050
Open Access,
c
The Authors.
Article funded by SCOAP
3
.
https://doi.org/10.1007/JHEP09(2021)161
JHEP09(2021)161
Contents
1 Introduction 1
2 Higgs-boson pair production within an EFT framework 3
3 Phenomenological results and coupling coefficients 4
3.1 Total cross section 5
3.2 Differential results and heat maps 6
3.3 Fitting procedure and results for the coupling coefficients 9
4 Conclusions 11
A EFT parameter points used for the fit 12
1 Introduction
The Higgs sector is being explored at the LHC with impressive success, having established
the coupling of the Higgs boson to all the electroweak gauge bosons [1], the top [2, 3]
and bottom quarks [4, 5], the tau lepton [6, 7] and recently moving towards indication for
Higgs couplings to muons [8, 9]. In addition to these important results, it is also crucial to
study Higgs boson self-couplings, which provide a way to explore the potential that drives
the electroweak symmetry breaking mechanism. The trilinear Higgs boson self-coupling is
still rather weakly constrained, even though the limits have improved considerably in Run
II [10–13]. The precision of the measurements of Higgs boson couplings to other particles
and itself will increase substantially in the high-luminosity phase of the LHC [14, 15].
Therefore, simulations of the effects of anomalous couplings in the Higgs sector also need
to achieve rather small uncertainties.
Higgs-boson pair production in gluon fusion is a process with direct access to the
trilinear Higgs boson self-coupling c
hhh
. An established deviation from its Standard Model
(SM) value would be a clear sign of new physics. However, if c
hhh
is different from the value
predicted by the SM, it is very likely that other Higgs couplings are also modified, such that
several anomalous couplings, entering the process gg → HH dominantly within an Effective
Field Theory (EFT) framework, should be studied simultaneously. Furthermore, in order
to get reliable predictions, higher-order QCD corrections need to be taken into account,
not only for the SM cross section but also in the case anomalous couplings are included.
The loop-induced process gg →HH at leading order has been calculated in refs. [16–18].
Before the full next-to-leading order (NLO) QCD corrections became available, the
m
t
→∞ limit (“Heavy Top Limit, HTL”), sometimes also called “Higgs Effective Field
– 1 –
JHEP09(2021)161
Theory (heft)” approximation, has been used. In this limit, the NLO corrections were
first calculated in ref. [19] using the so-called “Born-improved HTL”, which involves rescal-
ing the NLO results in the m
t
→ ∞ limit by the LO result in the full theory. In ref. [20] an
approximation called “FT
approx
” was introduced, which contains the real radiation matrix
elements with full top-quark mass dependence, while the virtual part is calculated in the
Born-improved HTL approximation. The NLO QCD corrections with full top-quark mass
dependence became available more recently [21–24]. The NLO results of refs. [21, 22] have
been combined with parton shower Monte Carlo programs in refs. [25–28], where ref. [28]
introduced the possibility of varying five Higgs couplings.
In the m
t
→ ∞ limit, the next-to-next-to-leading order (NNLO) QCD corrections
have been computed in refs. [29–33]. The calculation of ref. [33] has been combined with
results including the top-quark mass dependence as far as available in ref. [34], defining an
NNLO
FTapprox
result which contains the full top-quark mass dependence at NLO as well as
in the double real radiation part. Soft gluon resummation combined with these results has
been presented in ref. [35]. N
3
LO corrections are also available [36, 37], where in ref. [37]
the N
3
LO results in the HTL have been “NLO-improved” using the results of refs. [25, 27].
In ref. [38], NNLO results in the Born-improved heavy top limit including the effect of
anomalous couplings were presented, see also ref. [39] for the NLO case.
The scale uncertainties at NLO are still at the 10% level, while they are decreased
to about 5% when including the NNLO corrections and to about 3% at N
3
LO in the
“NLO-improved” variant. The uncertainties due to the chosen top mass scheme have been
assessed in refs. [23, 24, 40].
In this work we present a study of the anomalous couplings relevant to the process
gg → HH within a non-linear EFT operator expansion, at approximate NNLO in QCD
(which we will denote by NNLO
0
). It builds on the results presented in ref. [38], and extends
them to include the full NLO QCD corrections from ref. [41]. Thus NNLO
0
contains NNLO
results in the heavy top limit, where exact Born expressions have been used whenever the
higher-order corrections in the HTL factorise, as well as NLO corrections with full top-
quark mass dependence.
In particular, we provide coefficients for all the possible combinations of anomalous
couplings that can occur at NNLO for the total cross section, analogous to what has been
provided at NLO in ref. [41]. These coefficients can then be used to reconstruct the cross
section for any combination of coupling values. Furthermore, we show results for seven
benchmark points characteristic of certain shape types of the Higgs-boson pair invariant-
mass distribution m
hh
, which have been identified by an NLO shape analysis presented
in ref. [42].
This paper is organised as follows. In section 2 we describe the theoretical framework
and the definition of the anomalous couplings. Section 3 contains the phenomenological re-
sults, including total cross sections and differential distributions for the benchmark points,
and the description of the fitting procedure for the coefficients of the anomalous couplings,
together with the corresponding results. Finally, we conclude in section 4.
– 2 –
JHEP09(2021)161
Figure 1. Higgs-boson pair production in gluon fusion at leading order in QCD and at chiral
dimension d
χ
= 4. The black dots indicate vertices from anomalous couplings present already at
leading order in the chiral Lagrangian (d
χ
= 2), the black squares denote local operators contribut-
ing at (d
χ
= 4).
2 Higgs-boson pair production within an EFT framework
The calculation builds on the ones presented in refs. [28, 38, 41] and therefore the methods
will be described only briefly here, focusing on the new aspects.
We work in a non-linear EFT framework, sometimes also called Electroweak Chiral
Lagrangian (EWChL) including a light Higgs boson [43, 44] or HEFT (Higgs Effective Field
Theory), not to be confused with the heavy top limit, which is sometimes also called heft.
It relies on counting the chiral dimension of the terms contributing to the Lagrangian [45],
rather than counting the canonical dimension as in the Standard Model Effective Field
Theory (SMEFT). As a consequence, the EWChL is also suitable to describe strong
dynamics in the Higgs sector. Applying this framework to Higgs-boson pair production in
gluon fusion, keeping terms up to, and including, chiral dimension d
χ
= 4, we obtain the
effective Lagrangian relevant to this process as
L ⊃ −m
t
c
t
h
v
+ c
tt
h
2
v
2
!
¯
t t −c
hhh
m
2
h
2v
h
3
+
α
s
8π
c
ggh
h
v
+ c
gghh
h
2
v
2
!
G
a
µν
G
a,µν
. (2.1)
In the EWChL framework there are a priori no relations between the couplings. In general,
all couplings may have arbitrary values of O(1). The conventions are such that in the SM
c
t
= c
hhh
= 1 and c
tt
= c
ggh
= c
gghh
= 0. The EWChL coefficients can be related [39]
to those in the SMEFT at Lagrangian level, however how to treat double insertions of
operators and squared dimension-6 terms at cross section level is less straightforward when
attempting to relate the two EFT frameworks. The diagrams at leading order in QCD and
chiral dimension four are shown in figure 1.
There are different normalisation conventions for the anomalous couplings in the liter-
ature. In table 1 we summarise some conventions commonly used. For the relation to the
corresponding parameters in the SMEFT we refer to ref. [28].
– 3 –
JHEP09(2021)161
Eq. (2.1), i.e. L of ref. [41] Ref. [46] Ref. [39]
c
hhh
κ
λ
c
3
c
t
κ
t
c
t
c
tt
c
2
c
tt
/2
c
ggh
2
3
c
g
8c
g
c
gghh
−
1
3
c
2g
4c
gg
Table 1. Translation between different conventions for the definition of the anomalous couplings.
In ref. [41] the NLO QCD corrections were calculated within this framework. These
corrections have been implemented into the code ggHH [27, 28], which is a public code avail-
able at [47], where the real radiation matrix elements were implemented using the interface
between GoSam [48, 49] and the POWHEG-BOX [50–52] and the virtual two-loop corrections
use the results of the calculations presented in refs. [21, 22]. In turn, approximate NNLO
QCD corrections in a similar EFT framework have been computed in ref. [38], working in
the heavy top limit improved by inserting LO form factors with full top mass dependence.
The results described in this paper are obtained by performing an additive combination of
the ones presented in refs. [38, 41], i.e. keeping the full top mass dependence up to NLO and
adding the approximate results for the genuine NNLO piece. We will denote our results
by NNLO
0
.
We can describe the dependence of the NNLO cross section on the five anomalous
couplings in terms of 25 coefficients a
i
, following refs. [41, 46, 53]:
σ
BSM
/σ
SM
= a
1
c
4
t
+ a
2
c
2
tt
+ a
3
c
2
t
c
2
hhh
+ a
4
c
2
ggh
c
2
hhh
+ a
5
c
2
gghh
+ a
6
c
tt
c
2
t
+ a
7
c
3
t
c
hhh
+ a
8
c
tt
c
t
c
hhh
+ a
9
c
tt
c
ggh
c
hhh
+ a
10
c
tt
c
gghh
+ a
11
c
2
t
c
ggh
c
hhh
+ a
12
c
2
t
c
gghh
+ a
13
c
t
c
2
hhh
c
ggh
+ a
14
c
t
c
hhh
c
gghh
+ a
15
c
ggh
c
hhh
c
gghh
+ a
16
c
3
t
c
ggh
+ a
17
c
t
c
tt
c
ggh
+ a
18
c
t
c
2
ggh
c
hhh
+ a
19
c
t
c
ggh
c
gghh
+ a
20
c
2
t
c
2
ggh
+ a
21
c
tt
c
2
ggh
+ a
22
c
3
ggh
c
hhh
+ a
23
c
2
ggh
c
gghh
+ a
24
c
4
ggh
+ a
25
c
3
ggh
c
t
. (2.2)
While at LO only the first 15 coefficients contribute, at NLO 23 coupling combinations
occur and at NNLO 25 combinations are possible.
It is worth stressing that the functional dependence described in eq. (2.2), which holds
for the exact NNLO cross section, is also valid for the approximate results presented in this
work. To this end, the fact that the combination of the full NLO and approximate NNLO
is done through an additive approach becomes crucial, since e.g. a simple multiplicative
rescaling would not respect the functional form of eq. (2.2) (and, in particular, due to
the new combinations appearing at NNLO it would be ill-defined for certain values of the
anomalous couplings).
3 Phenomenological results and coupling coefficients
Our results are calculated at a centre-of-mass energy of
√
s = 14 TeV. The parton distri-
bution functions PDF4LHC15 [54–57] have been used, interfaced via LHAPDF [58], along
– 4 –
Citations
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TL;DR: In this paper , a comprehensive study on Higgs pair production in various archetypical extended Higgs sectors such as the real and the complex 2-Higgs-Doublet Model, the 2-higgs-doublet Model augmented by a real singlet field and the Next-to-Minimal Supersymmetric extension of the Standard Model is presented.
Abstract: We present a comprehensive study on Higgs pair production in various archetypical extended Higgs sectors such as the real and the complex 2-Higgs-Doublet Model, the 2-Higgs-Doublet Model augmented by a real singlet field and the Next-to-Minimal Supersymmetric extension of the Standard Model. We take into account all relevant theoretical and experimental constraints, in particular the experimental limits on non-resonant and resonant Higgs pair production. We present the allowed cross sections for Standard Model (SM)-like Higgs pair production and the ranges of the SM-like Yukawa and trilinear Higgs self-coupling that are still compatible with the applied constraints. Furthermore, we give results for the pair production of a SM-like with a non-SM-like Higgs boson and for the production of a pair of non-SM-like Higgs bosons. We find that di-Higgs production in the models under investigation can exceed the SM rate substantially, not only in the non-resonance region but also due to resonant enhancement. We give several benchmarks with interesting features such as large cross sections, the possibility to test CP violation, Higgs-to-Higgs cascade decays or di-Higgs production beating single Higgs production. In all of our benchmark points, the next-to-leading order QCD corrections are included in the large top-mass limit. For these points, we found that, depending on the model and the Higgs pair final state, the corrections increase the leading order cross section by a factor of 1.79 to 2.24. We also discuss the relation between the description of Higgs pair production in an effective field theory approach and in the specific models investigated here.

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04 Aug 2022-Journal of High Energy Physics
TL;DR: In this article , the effects of truncation options of the EFT expansion in 1 / Λ and of double operator insertions, both at total cross-section level as well as for the distribution of the invariant mass of the Higgs-boson pair, were investigated.
Abstract: A bstract We present a calculation of the NLO QCD corrections for Higgs-boson pair production in gluon fusion including effects of anomalous couplings within Standard Model Effective Field Theory (SMEFT). We study effects of different truncation options of the EFT expansion in 1 / Λ and of double operator insertions, both at total cross-section level as well as for the distribution of the invariant mass of the Higgs-boson pair, at $$ \sqrt{s} $$ s = 13 TeV. The NLO corrections are implemented in the generator ggHH_SMEFT in the Powheg-Box-V2 framework.

4 citations

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University of Glasgow1, University of Edinburgh2, University of Granada3, University of Zurich4, Durham University5
20 Mar 2015-European Physical Journal C
TL;DR: In this paper, the authors present the LHAPDF-6 library, a ground-up re-engineering of the PDFLIB/LHAPDF paradigm for PDF access which removes all limits on use of concurrent PDF sets, massively reduces static memory requirements, offers improved CPU performance, and fixes fundamental bugs in multi-set access to PDF metadata.
Abstract: The Fortran LHAPDF library has been a long-term workhorse in particle physics, providing standardised access to parton density functions for experimental and phenomenological purposes alike, following on from the venerable PDFLIB package During Run 1 of the LHC, however, several fundamental limitations in LHAPDF’s design have became deeply problematic, restricting the usability of the library for important physics-study procedures and providing dangerous avenues by which to silently obtain incorrect results In this paper we present the LHAPDF 6 library, a ground-up re-engineering of the PDFLIB/LHAPDF paradigm for PDF access which removes all limits on use of concurrent PDF sets, massively reduces static memory requirements, offers improved CPU performance, and fixes fundamental bugs in multi-set access to PDF metadata The new design, restricted for now to interpolated PDFs, uses centralised numerical routines and a powerful cascading metadata system to decouple software releases from provision of new PDF data and allow completely general parton content More than 200 PDF sets have been migrated from LHAPDF 5 to the new universal data format, via a stringent quality control procedure LHAPDF 6 is supported by many Monte Carlo generators and other physics programs, in some cases via a full set of compatibility routines, and is recommended for the demanding PDF access needs of LHC Run 2 and beyond

1,563 citations

Journal Article•DOI•
New parton distribution functions from a global analysis of quantum chromodynamics

[...]

Sayipjamal Dulat1, Sayipjamal Dulat2, Tie-Jiun Hou3, Jun Gao4, Marco Guzzi5, Joey Huston1, Pavel Nadolsky3, Jon Pumplin1, Carl Schmidt1, Daniel R. Stump1, C.-P. Yuan1 •
Michigan State University1, Xinjiang University2, Southern Methodist University3, Argonne National Laboratory4, University of Manchester5
16 Feb 2016-Physical Review D
TL;DR: Parton distribution functions (PDFs) are crucial ingredients for the calculation of the relevant cross sections for various scattering processes at the Large Hadron Collider (LHC). as mentioned in this paper found new PDFs, which will be important for the data analysis at the LHC Run-2.
Abstract: Parton distribution functions (PDFs) are crucial ingredients for the calculation of the relevant cross sections for various scattering processes at the Large Hadron Collider (LHC). Including data from several previous experiments, the authors find new PDFs, which will be important for the data analysis at the LHC Run-2.

1,521 citations

Journal Article•DOI•
Parton distributions in the LHC era: MMHT 2014 PDFs

[...]

Lucian Harland-Lang1, Alan D. Martin2, P. Motylinski1, Robert S. Thorne1•
University College London1, Durham University2
09 May 2015-European Physical Journal C
TL;DR: In this paper, the authors presented LO, NLO and NNLO sets of parton distribution functions (PDFs) of the proton determined from global analyses of the available hard scattering data.
Abstract: 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 [Formula: see text] valence quark difference at small [Formula: see text] 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 [Formula: see text] 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.

1,238 citations

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Frequently Asked Questions (1)
Q1. What have the authors contributed in "Anomalous couplings in higgs-boson pair production at approximate nnlo qcd" ?

The authors study the impact of the anomalous couplings on various observables, and present Higgs-pair invariant-mass distributions at seven benchmark points characterising different mhh shape types. The authors also provide numerical coefficients for the approximate NNLO cross section as a function of the anomalous couplings at √ s = 14TeV.