Higgs production at the lHC

Abdelhak Djouadi; Julien Baglio

REVIEW

Higgs production at the lHC

Julien Baglio, Abdelhak Djouadi

High Energy Physics - Phenomenology · Submitted 2 Dec 2010 · 79 references

Pith's verdict: A solid, transparent uncertainty budget for Higgs production at 7 TeV; the headline percentages are prescription-dependent at the ten-point level, which the paper mostly admits.

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arXiv ID1012.0530 (version 5)

Pith IDITFYQXQR, Pith's permanent record of this paper and its review

CitationAbdelhak Djouadi, Julien Baglio. "Higgs production at the lHC." arXiv:1012.0530 (2010). https://pith.science/paper/ITFYQXQR

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Editor's note

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This is the reference paper you want on your shelf if you are quoting a theoretical error bar on gg → H at 7 TeV. Baglio and Djouadi take their Tevatron analysis, redo it at 7 TeV with MSTW2008 and the full NNLO/EW machinery, and — the part that actually mattered — add the decay-branching-ratio uncertainties that the Tevatron and early LHC experimental combinations had simply left out. The tables (2, 4, 8, 9, 11) are the useful artifact: individual sources broken out, so you can recombine them your own way if you disagree with the authors' prescription. The MSSM section extends the same treatment to gg, b bbar → Φ → ττ, bb, and the observation that the b-mass error largely cancels between production and the ττ branching ratio is a nice, correct point. The paper is honest about its judgment calls throughout, which is more than most uncertainty papers manage. On the soft spots: the stress-test concern about κ = 2 at the LHC versus κ = 3 at the Tevatron (footnote 6) is real and lands. The two numbers do not measure the same thing, and Fig. 2 shows κ = 3 would give roughly ±17% scale uncertainty at low MH, not ±10%. The qualitative claim that the LHC uncertainty is smaller survives, but the quantitative gap to the Tevatron shrinks from about ten points to about five. The paper discloses the choice and the criterion behind it, so this is a caveat on the headline, not a flaw in the work. Same for the A/B/C spread of roughly eleven points in the + direction at MH = 120 GeV — the paper shows all three and says which it prefers. One thing the stress test flags that I would check with the authors: the text quotes Δmb ≈ −4%, +14% for gg → Φ, but the Δmb column of Table 8 reads +26.7%/−17.6% at MΦ = 90 GeV. That looks like an internal inconsistency, or an unstated extra source folded into the column. Either way the 'of order 50%' MSSM conclusion holds. Who should read it: anyone quoting a 7 TeV gluon-fusion cross section with an error bar, and anyone building the same budget for a different channel — the bookkeeping is the model. It deserves a serious referee, and it got one in the working group. Cite it.

Referee report

Significance

The paper is a careful, transparent, and reproducible uncertainty budget built entirely on public codes (HIGLU, bbh@nnlo, HDECAY, V2HV) and public NNLO PDF sets, with every individual source tabulated (Tables 2, 4, 8, 9, 11) so that a reader can recombine them under a different prescription. Its most valuable and durable contributions are the explicit demonstration that the PDF-set spread is not captured by Hessian errors alone, the inclusion of branching-ratio parametric uncertainties that had been omitted from experimental analyses, and the quantitative statement that MSSM exclusion contours in tan β shift by ≈ √2 once theory errors are admitted. The results are falsifiable in the operative sense: they change the interpretation of exclusion limits, and the paper says so concretely. The judgment calls (central scale MH/2, κ = 2, linear addition, a hand-assigned 15% bottom-scheme error) are disclosed rather than hidden, which is the right practice for a paper of this kind.

Major objections (3)

[§2.2.1, footnote 6, Fig. 2, and Conclusions] The headline comparison with the Tevatron is drawn from two different scale-variation domains: κ = 2 at the LHC (§2.2.1) and κ = 3 at the Tevatron (footnote 6). The criterion used to pick κ — that the NLO band bracket the NNLO central value — is legitimate and is stated, but it means the two quoted numbers measure different things, and the paper's own Fig. 2 shows that κ = 3 at 7 TeV gives ≈ ±17% scale uncertainty at MH ≈ 120 GeV rather than ≈ ±10%. Combined linearly with the ≈ 9% PDF and ≈ 7% EFT errors, that moves the low-mass total from +27.5%/−24.5% to roughly ±33%, shrinking the quoted gap to the Tevatron's −35%/+40% from about ten points to about five. The qualitative conclusion survives, but the reader cannot extract the like-for-like number from the present text. I recommend adding one explicit sentence (or a row in Table 2) giving the 7 TeV total under κ = 3, so that the LHC-versus-Tevatron statement is made on a common footing.
[Table 8 versus §4.3] There is an apparent inconsistency between the text and the table for the bottom-mass uncertainty in gg → Φ. Section 4.3 states that the parametric input-mass error gives ∆mb ≈ −4%, +14% for gg → Φ and ≈ −3%, +10% for b̄b → Φ, and separately assigns a scheme uncertainty of about ±15% to gg → Φ only. The ∆mb column of Table 8, however, quotes +26.7%/−17.6% at MΦ = 90 GeV, which is close to the linear sum of the parametric and scheme errors rather than the parametric error alone. If the column indeed folds in the scheme dependence, the caption and the surrounding text should say so, because as it stands a reader comparing §4.3 with Table 8 will conclude the two are in conflict, and the column is load-bearing for the ∆tot entries. Please relabel the column or split it into separate parametric and scheme columns.
[Conclusions, versus Table 2 (procedure C)] The Conclusions state that all three combination procedures lead to approximately the same total uncertainty, '≈ −25%, +30% in the low mass range and ≈ ±20% at higher Higgs masses'. Table 2 does not support the second half of that statement: at MH = 500 GeV procedure C gives +8.9%/−35.2%, against +22.1%/−23.3% for A and +21.1%/−24.5% for B. The spread at high mass is therefore about 12 points on the negative side, not a convergence to ±20%. Since procedure C is precisely the one that captures the MSTW-versus-ABKM spread that the paper argues is physical (§2.2.3, Fig. 6), this is the case where the three prescriptions disagree most and where the disagreement matters. The Conclusions should either quote the range spanned by A, B and C at high MH or restrict the '±20%' statement to procedures A and B.

Minor objections (6)

[Title, abstract, and throughout] The 'lHC' versus 'LHC' typographic convention is explained in the Introduction but is easy to miss and appears in figure axis labels and table captions where the explanation is not at hand. Consider adding a parenthetical reminder in the caption of Fig. 1 and in the abstract, or dropping the convention in figure labels.
[Table 8 caption] The caption should state explicitly that the cross sections are given for a Standard-Model-like Φbb Yukawa coupling (tan β = 1, no ∆b resummation) and must be rescaled by the factor of Eq. (4.4) squared, and by two for CP-even plus CP-odd. This is stated in §4.2 but a reader consulting Table 8 directly will not know it.
[§2.2.3 and §2.3] The paper argues that the PDF4LHC recommendation is 'rather optimistic'. That is a defensible position, but for usability by the experimental community it would help to also quote, at least for one benchmark mass, the total uncertainty obtained under the PDF4LHC prescription, so that the two numbers can be placed side by side rather than inferred.
[§3.3 and Fig. 13] The combination of production and branching-ratio uncertainties is shown only graphically. A short table giving σ × BR(H → WW*) with and without the BR error at, say, MH = 120, 135 and 150 GeV would make the size of the BR contribution unambiguous, particularly since the αs correlation argument between σ and BR is made verbally.
[§4.3] The ±15% scheme uncertainty for gg → Φ is assigned by hand from the on-shell versus MS difference, while the text also mentions an alternative estimate of −20%/+40% from varying the mb scale. It would strengthen the section to state what the total in Table 8 would become under the larger estimate, since the choice materially affects the quoted +58.9%/−41.7%.
[References] Several author names appear to be misspelled and should be checked against the published versions: 'Strirling' in Refs. [38] and [48], 'rewiew' in Ref. [3], 'Baikalov' and 'Chetyrkhin' in Refs. [61] and [65], and the inconsistent 'Pietriello' [27] versus 'Petriello' [31].

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The paper

The paper claims

The gluon-fusion Higgs rate at 7 TeV comes with a theory error of roughly a quarter, and the authors argue the error budget should be quoted rather than assumed away.

The reading

This paper asks a narrow but consequential question: if the early 7 TeV proton run produces a Higgs boson through gluon fusion, how well do we actually know the predicted rate? The authors assemble the best available perturbative calculation — exact next-to-leading order in QCD with finite top and bottom masses, next-to-next-to-leading order in the infinite-top-mass limit, plus electroweak and mixed corrections — and then account, source by source, for everything that could shift the number: the choice of renormalization and factorization scale, the spread among parton distribution parametrizations, the error on the strong coupling, and the error introduced by treating the top quark as infinitely heavy at higher orders. They find a total of about $-25/+30$ percent at low Higgs mass and roughly $20$ percent at high mass, smaller than the corresponding Tevatron figure but still large enough to matter for exclusion limits. They then repeat the exercise for the supersymmetric neutral Higgs bosons produced in gluon and bottom-quark fusion, where the budget swells to about $50$ percent. The point is not the central numbers but the bookkeeping: an exclusion limit quoted without these errors is quoting a precision the theory does not have.

What carries the argument

The load-bearing device is a prescription for combining uncertainties that have no statistical meaning. The authors insist that scale variation, the effective-theory approximation, and the spread of parton parametrizations are all theoretical, with flat priors, so they cannot be added in quadrature the way an experimental collaboration would. They propose three procedures — apply the PDF-plus-$alpha_s$ band on top of the maximal and minimal scale-varied cross sections and add the scheme error linearly (procedure A); add everything linearly (B); or take the envelope over different next-to-next-to-leading-order parton sets (C) — and show that A and B agree to a few percent. Around this sits the calculational stack: the HIGLU code for exact next-to-leading-order gluon fusion with finite quark masses, the infinite-mass next-to-next-to-leading-order piece normalized to the exact leading order, and grids for the electroweak and mixed corrections. For the supersymmetric channels the same logic is applied to a next-to-leading-order gluon-fusion calculation with only the bottom loop retained and to the next-to-next-to-leading-order bottom-fusion code, with a wider scale window in the latter case to absorb the scheme ambiguity that cannot be varied directly.

Extended reading notes

Core claim

The paper's central claim is that the Standard Model Higgs production cross section in gluon fusion at $7$ TeV carries a total theoretical uncertainty of approximately $-25/+30$ percent for $M_H < 200$ GeV and about $20$ percent at higher masses, and that this uncertainty is dominated by three comparably sized, non-statistical sources that should be combined linearly rather than in quadrature. The individual pieces are: a scale variation of about $10$ percent obtained by varying $mu_R$ and $mu_F$ between $M_H/4$ and $M_H$ around a central scale $mu_0 = M_H/2$; a parton-distribution plus strong-coupling uncertainty of $11$ to $15$ percent, built from the MSTW Hessian eigenvectors, the experimental error on $alpha_s$, and an added theoretical error on $alpha_s$; and an effective-field-theory uncertainty of $3$ to $7$ percent from the infinite-top-mass approximation used beyond next-to-leading order, together with the scheme dependence of the bottom-quark mass. The authors stress that the resulting band is noticeably tighter than the roughly $-35/+40$ percent they previously found at the Tevatron, because the QCD K-factors are smaller at $7$ TeV and the relevant gluon momentum fractions are less extreme. For the supersymmetric case, adding the bottom-mass scheme ambiguity, the parametric bottom-mass error, and the bottom density in the proton pushes the total to about $50$ percent in both $gg to Phi$ and $b bar b to Phi$, which translates into a factor of about $sqrt{2}$ on the $tan beta$ values that can be excluded.

Load-bearing premise

The headline percentages depend on judgement calls rather than derived results: the central scale is set to half the Higgs mass and the variation window to a factor of two precisely because that choice makes the lower-order band bracket the higher-order central value, and the supersymmetric bottom-mass scheme error is assigned by hand at 15 percent.

Editorial extensions

If this is right

Exclusion limits on the Standard Model Higgs mass derived from the $7$ TeV gluon-fusion channel should be quoted with a rate uncertainty near $25$ percent at low mass, not the smaller numbers used in early experimental combinations.
Because the branching ratios to $WW$, $ZZ$, and $gamma gamma$ inherit $3$ to $10$ percent parametric uncertainties in the intermediate mass region where $b bar b$ and $WW$ compete, the uncertainty on cross section times branching ratio is larger than the cross section uncertainty alone in that window.
The same uncertainty budget carries over almost unchanged to $8$, $9$, and $10$ TeV running, so cross sections measured at those energies inherit the $7$ TeV error band even though the central rates rise by $20$ to $100$ percent.
In the supersymmetric case, a $50$ percent rate uncertainty means the $tan beta$ reach of the early run is weaker by about a factor of $sqrt{2}$ than a central-value estimate would suggest.
Any future global fit that treats the gluon-fusion rate as a precision observable must inflate its error bar to match this budget or it will draw unjustified conclusions about Higgs couplings.

Reading between the lines

Editorial extensions of the paper, not claims the author makes directly.

The paper's insistence on linear combination is really a statement about how to report a prediction that has a flat-prior uncertainty: if the community adopted it uniformly, many quoted Higgs signal strengths would acquire visibly asymmetric error bars, which would in turn change how much room is left for new physics in coupling fits.
The fact that the effective-theory error is estimated by rescaling an exact-versus-approximate difference with a ratio of K-factors suggests a concrete improvement path: a fully finite-mass next-to-next-to-leading-order calculation would replace an estimate with a number, and the size of the shift would test whether the estimate was conservative.
The observation that the $7$ TeV uncertainty is smaller than the Tevatron one because the relevant gluon momentum fractions are less extreme implies that the error budget is a function of energy in a way that could be mapped and used to choose an optimal running energy for a precision Higgs measurement, a question the paper raises but does not pursue quantitatively.
The authors note in passing that the decay $H to gg$ carries a residual scale dependence of about $10$ percent at next-to-next-to-leading order, which they discard because the branching ratio is small; if that channel ever becomes a discovery mode, that neglected error would need to be reinstated and could dominate the budget.

Original abstract

We analyze the production of Higgs particles at the early stage of the CERN large Hadron Collider with a 7 TeV center of mass energy (lHC). We first consider the case of the Standard Model Higgs boson that is mainly produced in the gluon-gluon fusion channel and to be detected in its decays into electroweak gauge bosons, $gg\to H \to WW,ZZ,\gamma\gamma$. The production cross sections at $\sqrt s=7$ TeV and the decay branching ratios, including all relevant higher order QCD and electroweak corrections, are evaluated. An emphasis is put on the various theoretical uncertainties that affect the production rates: the significant uncertainties from scale variation and from the parametrization of the parton distribution functions as well as the uncertainties which arise due to the use of an effective field theory in the calculation of the next-to-next-to-leading order corrections. The parametric uncertainties stemming from the values of the strong coupling constant and the heavy quark masses in the Higgs decay branching ratios, which turn out to be non-negligible, are also discussed. The implications for different center of mass energies of the proton collider, $\sqrt s=8$-10 TeV as well as for the design energy $\sqrt s= 14$ TeV, are briefly summarized. We then discuss the production of the neutral Higgs particles of the Minimal Supersymmetric extension of the Standard Model in the two main channels: gluon-gluon and bottom quark fusion leading to Higgs bosons which subsequently decay into tau lepton or $b$-quark pairs, $gg, b\bar b \to {\rm Higgs} \to \tau^+\tau^-,b\bar b$. The Higgs production cross sections at the $\lhc$ and the decay branching ratios are analyzed. The associated theoretical uncertainties are found to be rather large and will have a significant impact on the parameter space of the model that can be probed.

The compiled record

The paper's own sentences, arranged, kept beside the review and separate from it. Each label is drawn from a closed vocabulary; the number beside it is the probability the classifier gave that label. Numbers in the tables are the authors', checked by code. No sentence in this record was written by a model.

Compiled by classifier-1.13-20260917 via OpenRouter, question bank abstract-p1-20260923, 2026-09-23: 1 request, 7,288 input tokens, $0.0003 reported.

What the abstract itself states, as probabilities: claims first 0.03 · states limitation 0.88 · human participants 0.01 · controlled comparison 0.03 · randomized assignment 0.01 · states quantitative result 0.17 · compares with prior results 0.09 · mentions code or data availability 0.02.

The abstract, sentence by sentence

arXiv listing abstract v5. Results and the main claim are underlined; show every role.

We analyze the production of Higgs particles at the early stage of the CERN large Hadron Collider with a 7 TeV center of mass energy (lHC). We first consider the case of the Standard Model Higgs boson that is mainly produced in the gluon-gluon fusion channel and to be detected in its decays into electroweak gauge bosons, $gg\to H \to WW,ZZ,\gamma\gamma$. The production cross sections at $\sqrt s=7$ TeV and the decay branching ratios, including all relevant higher order QCD and electroweak corrections, are evaluated. An emphasis is put on the various theoretical uncertainties that affect the production rates: the significant uncertainties from scale variation and from the parametrization of the parton distribution functions as well as the uncertainties which arise due to the use of an effective field theory in the calculation of the next-to-next-to-leading order corrections. The parametric uncertainties stemming from the values of the strong coupling constant and the heavy quark masses in the Higgs decay branching ratios, which turn out to be non-negligible, are also discussed. The implications for different center of mass energies of the proton collider, $\sqrt s=8$-10 TeV as well as for the design energy $\sqrt s= 14$ TeV, are briefly summarized. We then discuss the production of the neutral Higgs particles of the Minimal Supersymmetric extension of the Standard Model in the two main channels: gluon-gluon and bottom quark fusion leading to Higgs bosons which subsequently decay into tau lepton or $b$-quark pairs, $gg, b\bar b \to {\rm Higgs} \to \tau^+\tau^-,b\bar b$. The Higgs production cross sections at the $\lhc$ and the decay branching ratios are analyzed. The associated theoretical uncertainties are found to be rather large and will have a significant impact on the parameter space of the model that can be probed.

background contribution method result interpretation main claim

What the classifier reports for each sentence. The number is the probability it gave the label.
#	sentence	role	the authors' own work	states the main conclusion	strength
s0	We analyze the production of Higgs particles at the early stage of the CERN large Hadron Collider with a 7 TeV center of mass energy (lHC).	contribution 0.94	0.85	0.03	asserted 0.94
s1	We first consider the case of the Standard Model Higgs boson that is mainly produced in the gluon-gluon fusion channel and to be detected in its decays into electroweak gauge bosons, $gg\to H \to WW,ZZ,\gamma\gamma$.	contribution 0.81	0.20	0.04	asserted 0.99
s2	The production cross sections at $\sqrt s=7$ TeV and the decay branching ratios, including all relevant higher order QCD and electroweak corrections, are evaluated.	method 0.46	0.92	0.05	asserted 1.00
s3	An emphasis is put on the various theoretical uncertainties that affect the production rates: the significant uncertainties from scale variation and from the parametrization of the parton distribution functions as well as the uncertainties which arise due to the use of an effective field theory in the calculation of the next-to-next-to-leading order corrections.	contribution 0.40	0.71	0.09	asserted 0.99
s4	The parametric uncertainties stemming from the values of the strong coupling constant and the heavy quark masses in the Higgs decay branching ratios, which turn out to be non-negligible, are also discussed.	result 0.65	0.84	0.05	asserted 1.00
s5	The implications for different center of mass energies of the proton collider, $\sqrt s=8$-10 TeV as well as for the design energy $\sqrt s= 14$ TeV, are briefly summarized.	interpretation 0.42	0.74	0.04	asserted 0.78
s6	We then discuss the production of the neutral Higgs particles of the Minimal Supersymmetric extension of the Standard Model in the two main channels: gluon-gluon and bottom quark fusion leading to Higgs bosons which subsequently decay into tau lepton or $b$-quark pairs, $gg, b\bar b \to {\rm Higgs} \to \tau^+\tau^-,b\bar b$.	contribution 0.98	0.77	0.04	asserted 0.95
s7	The Higgs production cross sections at the $\lhc$ and the decay branching ratios are analyzed.	contribution 0.92	0.87	0.05	asserted 0.94
s8	The associated theoretical uncertainties are found to be rather large and will have a significant impact on the parameter space of the model that can be probed.	interpretation 0.66	0.91	0.26	asserted 0.97

What kind of paper the classifier reports this is: theoretical result 0.61 · evidence from simulation or computation 0.98.

What was examined, and what was not

sources read

arXiv listing abstract v5

not examined

full text
figures and tables
references and citing sentences
relations to other papers

levels run

P abstract

not run

S sections
T body sentences
C citations
R cross-paper relations

Every quoted sentence on this record is the authors'. Every label is from Pith's closed vocabulary, with the probability shown beside it. Every number in the measurements table is the authors', checked by code. Record as JSON

Figures

**Figure 1.** The total cross sections for Higgs production at the lHC with √ s = 7 TeV as a function of the Higgs mass. The MSTW set of PDFs has been used and the higher order corrections are included as discussed in the text. level of a few percent; there are also small mixed NNLO QCD–electroweak effects which have been calculated [27] in an effective approach valid for MH ≪ MW . Our calculation3 of the gg → H production cross section at the lHC, including these higher order corrections strictly follows the one performed in Ref. [18] for the Tevatron: the starting point is the Fortran code…

**Figure 2.** The scale uncertainty band of σ NNLO(gg → H) at the lHC as a function of MH for a scale variation in the domain MH/(2κ) ≤ µR, µF ≤ κ× 1 2MH for κ = 2 and 3; in the insert, shown are the relative deviations from the central value with a scale µR = µF = 1 2MH. 2.2.2 The use of an effective theory approach Another source of theoretical uncertainties is specific to the gluon–gluon fusion mechanism in which the cross section beyond the NLO approximation is evaluated in an effective theory (EFT) approach where the particles that are running in the loops are assumed to be much heavier than…

**Figure 3.** The estimated uncertainties (in %) due to the use of the EFT approach in the evaluation of σ(gg → H) at NNLO for the top quark loop contribution for Higgs masses beyond 2mt (left) and for the bottom–quark loop contributions (right). Furthermore, the EFT approach is certainly also not valid for the b–quark loop and, for instance, the omission of this contribution (at LO) leads to a ≈ 10% difference compared to the exact case. Furthermore, the NLO K–factor for the b–quark loop, KNNLO b−loop ≈ 1.2–1.4, is much smaller than that for the top–quark loop. In fact, the problem arises mainly…

**Figure 4.** The estimated total uncertainty (in %) at lHC energies and as a function of MH from the use of the EFT approach for the calculation of the gg → H amplitude at NNLO and from the scheme dependence of the b–quark mass. Adding the uncertainties from these three sources linearly, the resulting overall uncertainty is displayed in

**Figure 5.** The central values and the 90% CL PDF, PDF+∆expαs and PDF+∆expαs + ∆thαs uncertainty bands in σ NNLO(gg → H +X) at the lHC when evaluated within the MSTW scheme. In the inserts, shown are the same but with the cross sections normalized to the central cross section. The previous Hessian errors do not account for the theoretical assumptions that enter into the parametrization of the PDFs and which may come from many different sources. These assumptions lead to an uncertainty in the parametrization that is difficult to quantify in a given scheme, say the MSTW scheme. A way to access…

**Figure 6.** The central values of the NNLO cross section σ(gg → H + X) at the lHC as a function of MH when evaluated in the four schemes which provide NNLO PDFs. In the inserts, shown are the same but with the cross sections normalized to the MSTW central cross section. We thus conclude when comparing

**Figure 7.** The production cross section σ(gg → H) at NNLO at the lHC with √ s = 7 TeV, including the total theoretical uncertainty band when all the individual uncertainties are combined using the three procedures A, B and C described in the text. In the inserts, the relative deviations from the central cross section value are shown. Using the three procedures A, B, C described above, one obtains the overall theoretical uncertainties on σ NNLO(gg → H) at the 7 TeV lHC that are shown in

**Figure 8.** The production cross section σ(gg → H) at NNLO as a function of MH at the lHC with center of mass energies of √ s = 8, 9 and 10 TeV. In the inserts, the relative increase compared to the cross section at √ s = 7 TeV are shown. We see that in the low Higgs mass range, MH ≈ 120 GeV, the cross section σ(gg → H) is ≈ 20%, 40% and ≈ 100% higher at, respectively, √ s = 8, 9 and 10 TeV, compared to √ s = 7 TeV. At higher Higgs masses, MH >∼ 300 GeV, the increase of the cross section is slightly larger as a result of the reduction of the phase space at lower energies. As far as the theoret

**Figure 9.** The uncertainty bands of σ NNLO gg→H from scale variation with κ = 2 (left) and the total EFT uncertainty (right) at √ s = 14 TeV as a function of MH. 100 500 1000 1.0 0.9 0.8 HERAPDF(αS =0.1176) HERAPDF(αS =0.1145) JR09 ABKM MSTW NNLO at µR = µF = 1 2MH √ s = 14 TeV σ(gg → H) [pb] MH [GeV] 100 250 500 750 1000 100 10 1 0.1 100 500 1000 1.2 1.1 1.0 0.9 0.8 PDF PDF+∆expαs PDF+∆exp+thαs NNLO at µR = µF = 1 2MH √ s = 14 TeV σ(gg → H) [pb] MH [GeV] 100 250 500 750 1000 100 10 1 0.1

**Figure 10.** The PDF uncertainties in σ NNLO(gg → H) at the LHC with √ s = 14 TeV as a function of MH. Left: the central values when using the four NNLO PDFs and right: the 90% CL PDF, PDF+∆expαs and PDF+∆expαs + ∆thαs uncertainties in the MSTW scheme. 100 500 1000 1.30 1.15 1.00 0.85 0.75 ∆tot NNLO at µR = µF = 1 2MH √ s = 14 TeV σ(gg → H) [pb] MH [GeV] 100 250 500 750 1000 100 10 1 0.1

**Figure 11.** The cross section σ NNLO(gg → H) at the LHC with the uncertainty band when all theoretical uncertainties are added using our procedure A described in the text. – 21 –

**Figure 12.** The Higgs decay branching ratios as a function of MH including the total uncertainty bands from the 1σ errors on the input quark masses and the coupling αs (the individual errors have been added in quadrature). ratio BR(H → WW) drops to a level below 1%. The uncertainty on BR(H → b ¯b) stays relatively large, ≈ −4%, +11%, but the branching ratio itself is too small to be relevant. For Higgs masses beyond MH >∼ 350 GeV, the decay channel H → tt¯ opens up and has a branching ratio of ≈ 20% at MH ≈ 500 GeV dropping to less than 10% for MH <∼ 400 GeV or MH >∼ 700 GeV. It will be…

**Figure 13.** The production cross section times branching ratio for the process gg → H → WW at the lHC with √ s = 7 TeV, including the total theoretical uncertainty band when the errors in the decay branching ratios are taken into account. In the inserts the relative deviations are shown. 18For instance, the branching ratio uncertainties have no effect in the Higgs mass range MH ≈ 150–180 GeV to which both the Tevatron and the lHC are most sensitive. However, at the Tevatron these errors should be taken into account for MH <∼ 150 GeV in both the H → b¯b and WW channels. – 28 –

**Figure 14.** The production cross sections in the processes gg → Φ (left) at a central scale µR = µF = µ0 = 1 2MΦ and b ¯b → Φ (right) at a central scale µR = µF = µ0 = 1 4MΦ as a function of MΦ for several center of mass energies relevant for the LHC. The MSTW sets of PDFs at the required perturbative order have been used. Only the cross section in the pseudoscalar A case but with a SM-like Yukawa coupling is included. – 33 –

**Figure 15.** The scale uncertainty bands of the NLO gg → Φ (left) and the NNLO b ¯b → Φ (right) cross sections at the lHC at 7 TeV as a function of MΦ; different values κ = 2, 3 are used and the results are shown when the additional constraint 1/κ ≤ µR/µF ≤ κ is imposed or not (marked as κb). In the inserts, the relative deviations (compared to the central cross section values) are shown. Let us now turn to the estimation of the uncertainties from the parton densities and αs. The 90% CL PDF+∆expαs uncertainty, with αs(M2 Z ) = 0.120 ± 0.002 at NLO for gg → Φ and αs(M2 Z ) = 0.1171 ± 0.0014 at…

**Figure 16.** The PDF 90% CL PDF, PDF+∆expαs and PDF+∆expαs +∆thαs uncertainties in the MSTW scheme in the gg → Φ (left) and b ¯b → Φ (right) cross sections at the lHC at 7 TeV as a function of MΦ. In the inserts, the relative deviations are shown. 100 300 500 1.1 1.0 0.9 GJR ABKM MSTW √ s = 7 TeV σ(gg → Φ) [fb] MΦ [GeV] 100 150 200 300 400 500 1000 500 200 50 10 1 0.01 100 300 500 1.2 1.1 1.0 0.9 0.8 0.7 JR ABKM MSTW √ s = 7 TeV σ(bb¯ → Φ) [fb] MΦ [GeV] 100 150 200 300 400 500 1000 500 200 50 10 1

**Figure 17.** The cross sections in the gg → Φ (left) and b ¯b → Φ (right) at the lHC at 7 TeV as a function of MΦ evaluated when using the ABKM and (G)JR PDF sets. In the inserts, the relative deviations from the value in the MSTW scheme are shown. The first one is of purely theoretical nature and is due to the choice of the renormalization scheme for the b–quark mass. In our analysis, we have adopted the MS renormalization scheme mainly because of the fact that the calculation of the b ¯b → Φ process is available only in this scheme and we to have chosen to treat the same way both the b ¯b →…

**Figure 18.** The scheme, parametric and PDF uncertainties due to the b-quark mass in the gg → Φ (left) and b ¯b → Φ (right) cross sections at the lHC at 7 TeV as a function of MΦ. In the inserts, the relative deviations are shown. 4.4 The Higgs decay branching fractions In the most general case, the decay pattern of the MSSM Higgs particles can be rather complicated, in particular for the heavy states. Indeed, besides the standard decays into pairs of fermions and gauge bosons, the latter can have mixed decays into gauge and Higgs bosons (and the H bosons can decay into hh states) and, if some…

**Figure 19.** The total uncertainties due to the scale, PDF and b-quark mass in the gg → Φ (left) and b ¯b → Φ (right) cross sections at the lHC with 7 TeV as a function of MΦ. The dotted lines show the uncertainties when those on the branching rations for Higgs decays into τ +τ − final states are added. In the inserts, the relative deviations are shown. 26This is also the case of the ∆b SUSY correction which enters both σ(gg, b¯b → Φ) and BR(Φ → τ +τ −) and which thus cancels in the product. This justifies, a posteriori, why we ignored this correction. – 41 –

**Figure 21.** Same as in Figs. 9, 10, 11 for √ s = 8 TeV. – 48 –

Showing 20 of the paper's 21 figures. See all figures in the PDF ↗ Figures reproduced from arXiv:1012.0530 by the authors.

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Implications of the ATLAS and CMS searches in the channel $pp \to Higgs \to \tau^+\tau^$ for the MSSM and SM Higgs bosons (2011) (same authors) · 0.80 · paraphrased: the licence does not allow quoting

Uses its data or values 6 of 25 papers with this label · 1 by the same authors

Used the K-factor from this paper, about 2.5 at 7 and 8 TeV and about 2 at 14 TeV, to calculate the NNLO cross section from the LO one.

Extending the Higgs sector: an extra singlet (2015) · 0.93 · paraphrased: the licence does not allow quoting
Took from this paper the 14 TeV LHC cross section for gg to h' at 1000 GeV and multiplied it by 0.9 to get the 13 TeV values.

Gauge Singlet Vector-like Fermion Dark Matter, LHC Diphoton Rate and Direct Detection (2017) · 1.00 · paraphrased: the licence does not allow quoting
Used the uncertainties on the branching fraction for H to W+W- from this paper.

Combined CDF and D0 Upper Limits on Standard Model Higgs Boson Production with up to 8.2 fb-1 of Data (2011) · 1.00 · paraphrased: the licence does not allow quoting
Used the uncertainties on the branching fraction for H to W+W- from this paper.

Updated Combination of Searches for the Standard Model Higgs Boson at the D0 Experiment in 9.7 fb-1 of Data (2012) · 1.00 · paraphrased: the licence does not allow quoting
Multiplied the production cross section by a K-factor of 1.3 from NNLO results of this paper.

Measuring the Invisible Higgs Width at the 7 and 8 TeV LHC (2011) · 0.95 · paraphrased: the licence does not allow quoting

By the same authors

Took the inclusive cross sections for ggF, VBF and VH from this paper, assuming SM proportions.

Direct detection of Higgs-portal dark matter at the LHC (2012) (same authors) · 1.00 · paraphrased: the licence does not allow quoting

How the literature uses it

67 arXiv papers cite this in 105 sentences

Each citing sentence is taken from the citing paper's LaTeX source and typed by Pith's classifier. A label appears at probability 0.8 or more (0.95 for support), a contest at 0.7 or more; the quoted words are the citing authors'. How each label was checked · JSON

Papers citing it · 57 sentences without a confident label

Contests it 1 paper

[ref] . * The claim [ref] that the HERAPDF1.0 NNLO set with $α_S(M_Z^2)=0.1145$ lowers the Higgs cross section compared to MSTW08 by $≈40%$ for $M_H≈160$ GeV at the Tevatron is due to a mistake in the calculation, and therefore the conclusions in the published version of ref.

PDF dependence of Higgs cross sections at the Tevatron and LHC: response to recent criticism · Conclusions · contest 0.92

Uses its method or tool 3 papers

Using those formulae we were able to express the production factors in terms of next-to-leading order cross sections for each of the mechanisms considered, calculated using HIGLU [ref] for the gluon-gluon cross section, bb@nnlo [ref] for the $b b̅$ process and reference [ref] (and references therein), for the remaining processes, all multiplied by the adequate factors pertaining to the mixing of scalar-pseudoscalar states.

Probing the scalar-pseudoscalar mixing in the 125 GeV Higgs particle with current data · A specific model for scalar-pseudoscalar mixing · 0.96
We have evaluated them with HATHOR [ref] and, in the production channel $σ(p p → tt̅)$ and for $m_t= 173.3 ± 1.1$GeV, we find $σ(p p →tt̅)= 163 ^+2.5%_-5.6% (factor 2 from central m_t scale) ^+10.4%_-10.1% (PDF+Δ^exp+thα_s@90%CL) ±3.3% ( Δm_t)$ pb, which leads using the procedure of Ref. [ref] to a total uncertainty of $Δσ/σ= ^+16%_-19%$, i.e three times larger than the one assumed in the CMS analysis.

Implications of the ATLAS and CMS searches in the channel $pp \to Higgs \to \tau^+\tau^$ for the MSSM and SM Higgs bosons · 4. Implications in the MSSM for higher luminosities · 0.80
We generate our signal events $h$+jets using MadGraph's native MLM matching [ref] scheme and normalize to the inclusive production cross section of $h$+jets at NNLO from Ref. [ref] to account for the large $K$-factor from next-to-leading order (NLO) and next-to-next-to-leading order (NNLO) corrections.

Measuring the Invisible Higgs Width at the 7 and 8 TeV LHC · Monojet Searches · 0.90

Uses its data or values 25 papers

The uncertainties induced by the use of the EFT approach at NNLO are estimated, from the NLO case in which both the exact and EFT calculations are available, to be of $O(9%)$ for $M_H≈126$ GeV [ref] .

The apparent excess in the Higgs to di-photon rate at the LHC: New Physics or QCD uncertainties? · Introduction · 0.85
We display the predicted event yields $N_inv^gg$, $N_inv^V$ in, respectively, the ggF and VBF+VH channels for the four CMS $p_T^miss$ cuts.[ Note that we did not consider the theoretical uncertainties on the cross sections [ref] and the efficiencies of the $p_T$ cuts which, although significant, are currently smaller than the experimental ones.] For convenience, we also reproduce the expected $ΔN_95 %^i,exp$ and observed $ΔN_95 %^obs$ 95% CL limits on the number of extra non-SM events quoted by CMS in Ref. [ref] for each cut.

Direct detection of Higgs-portal dark matter at the LHC · Monojet constraints on the invisible width · 0.82
$σ(gg→ϕ)$ is obtained using Eq. ([ref]) and the $σ(gg→h)$ from Ref. [ref] as mentioned earlier.

Extra Neutral Scalars with Vector-like Fermions at the LHC · Model-independent Analysis · 0.96

Compares with it 1 paper

Our results published in Ref. [ref] agree with those given in Refs. [ref] and updated in Ref. [ref] within a few percent.

Phenomenology of the Higgs at the hadron colliders: from the Standard Model to Supersymmetry · The main channel at the lHC (or LHC at 7 TeV) · 1.00

Cites it as background 12 papers

For calculations of Higgs production cross sections in the SM see for example [ref] and [ref] in fourth generation models.

Higgs Search Constraints on Fourth Generation Scenarios with General Lepton Sectors · Higgs production and decay · 0.80
Below, I summarise the main features and refer the reader to [ref] and references therein for further details.

Higgs Physics at the Large Hadron Collider · Production of the Higgs at the LHC · 0.90
The accuracy of the $M_t→∞$ approximation at NNLO has been investigated in Refs. [ref] .[Scale, PDF, strong coupling and heavy-top-limit uncertainties have recently been reappraised in Ref. [ref] .]

Inadequacy of zero-width approximation for a light Higgs boson signal · Introduction · 0.92

What it cites · 12 sentences without a confident label

Uses data or values from 3 papers

Analyses performed by the CDF and D0 experiments, under some assumptions for the production cross sections and their associated uncertainties, have recently excluded the Higgs mass range $M_H=158$–175 GeV at the 95% confidence level (CL) [ref] .

Combined CDF and D0 Upper Limits on Standard Model Higgs-Boson Production with up to 6.7 fb-1 of Data · Introduction · 0.89
In the later case, two sets are provided: one with the value $α_s=0.1176$ that is close to the world average value [ref] and the MSTW best–fit $α_s=0.1171$ [ref] , and one with the value $α_s=0.1145$ used also in the ABKM set [ref] , that is close to the preferred values that one obtains using deep–inelastic scattering data alone.

The 3-, 4-, and 5-flavor NNLO Parton from Deep-Inelastic-Scattering Data and at Hadron Colliders · The PDFs and $α_s$ uncertainties · 0.90
The MSTW collaboration has recently released a set of PDFs with different bottom quark masses [ref] : it involves six different central PDFs with a range of on–shell $m_b$ values between $4.00$ GeV and $5.50$ GeV in $0.25$ GeV steps, in addition to the central best–fit with $m_b=4.75$ GeV.

Heavy-quark mass dependence in global PDF analyses and 3- and 4-flavour parton distributions · The theoretical uncertainties · 0.85

Compares with 1 paper

This overall uncertainty is much larger than the uncertainty assumed in the CDF and D0 combined analysis that excluded the SM Higgs boson at the 95% CL in the mass range $M_H=158$–175 GeV [ref] .

Combined CDF and D0 Upper Limits on Standard Model Higgs-Boson Production with up to 6.7 fb-1 of Data · Introduction · 0.96

Discussion

Disagree with the review, or know something it missed? Leave a comment, highlight any passage above to comment on it, or challenge this review formally.

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