On the neutral Higgs boson masses in the MSSM for arbitrary stop mixing

Fabio Zwirner; Giuseppe Degrassi; Pietro Slavich

REVIEW

On the neutral Higgs boson masses in the MSSM for arbitrary stop mixing

Giuseppe Degrassi, Pietro Slavich, Fabio Zwirner

High Energy Physics - Phenomenology · Submitted 10 May 2001 · 23 references

Pith's verdict: A genuinely useful repackaging of the O(αt αs) Higgs-mass corrections into compact analytical form, with one presentation gap and one unresolved disagreement with the literature.

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arXiv IDhep-ph/0105096 (version 2)

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CitationFabio Zwirner, Giuseppe Degrassi, Pietro Slavich. "On the neutral Higgs boson masses in the MSSM for arbitrary stop mixing." arXiv:hep-ph/0105096 (2001). https://pith.science/paper/7MIZVLW4

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Worth your time if you work on the MSSM Higgs sector; skip it otherwise. The O(αt αs) two-loop correction to the CP-even neutral Higgs mass matrix was already known from the Heinemeyer–Hollik–Weiglein diagrammatic code, but only as a program. Degrassi, Slavich and Zwirner turn it into three functions F1, F2, F3 (eqs. 25–27, 32–34, plus Appendix A) that you can evaluate by hand for any stop mixing and any mA. That is a real service, and it is the kind of thing that gets used rather than admired. The genuinely new technical content is the treatment of the field-dependent phases of the top and stop mass matrices (eqs. 15–21). Earlier effective-potential work dropped the dependence of the stop parameters on the CP-odd fields, which is harmless for mh in the decoupling limit but not for the CP-odd sector, hence not for mH. The c_φφ̃ derivatives in eqs. (28)–(30) fix that, and the scale-independence of the final answer is a decent check that they got it right. Appendix C, the two-loop relation between mA and m3², is a useful bonus for anyone imposing soft-mass boundary conditions. Soft spots, in order of weight. First, the agreement with the HHW code [18] is asserted, not shown: Section 4 says perfect agreement for arbitrary input values, and there is no table, plot, or scan. For a paper whose selling point is that its compact formulae reproduce the lengthy diagrammatic result, that is the one figure I would want. Minor to moderate, easy to fix. Second, the footnote disagreement with Carena et al. [16] over the four-squark vertex contribution to the stop self-energies is stated and dropped. If they are right, [16]'s numbers shift; if they are wrong, theirs do. That deserves a paragraph, not a footnote. On the stress-test worry about p²=0 and mH: I do not think it lands as a flaw. The paper is explicit throughout that this is the zero-momentum limit and that momentum-dependent pieces are future work (Section 1, Section 4). The 'arbitrary mA' in the abstract refers to the parameter range of the formulae, not to pole-mass accuracy for H. That said, a practitioner reading only the abstract could be misled, and one sentence quantifying the residual tanβ scale dependence would cost nothing. Who it is for: anyone computing MSSM Higgs masses, and the people maintaining the public codes. Send it out.

Referee report

Significance

If correct, this is a genuinely useful paper: it reduces a lengthy diagrammatic two-loop calculation to a few lines of formulae that can be implemented by hand or in a short code, for arbitrary stop mixing and arbitrary m_A, and it supplies the OS-scheme conversion needed to use it with physical input parameters. The observation that the field-dependent phase difference φ−φ̃ enters the effective potential and that its derivative ∂V/∂c_{φφ̃} is required for the scale independence of the corrections to the heavy CP-even state is a real technical contribution, not a cosmetic one. The paper is likely to become a standard reference for the O(α_t α_s) MSSM Higgs mass corrections, and the explicit formulae are the kind of result that is checked and reused by the community.

Major objections (3)

[Abstract (abstract:s2) and Section 4] The abstract states that the authors 'find full agreement with the numerical output of the existing diagrammatic calculation', and Section 4 repeats that they 'find perfect agreement with the numerical results of [18], for arbitrary values of all the input parameters'. No numbers, table, or figure supporting this comparison appear anywhere in the manuscript. Since this is the paper's only external validation of the algebra, and since it is advertised in the abstract, at least one small table of benchmark points (m_A, tan β, m_t̃1, m_t̃2, s2θ, m_g̃, and the resulting entries of ΔM²_S from this work versus the code of [18]) should be included. It should also be stated explicitly that the comparison validates the algebra only, since [13,18] are themselves zero-momentum calculations and therefore do not test the p²=0 approximation.
[Eqs. (29)–(30), (33)–(34), and Section 4 / eq. (42)] The functions F2 and F3 contain explicit factors of 1/(m²_t̃1 − m²_t̃2) and 1/(m²_t̃1 − m²_t̃2)², and F3 also contains (s2θ)^{-4} multiplying ∂V/∂c_{φφ̃}. These are formally singular in the degenerate-mass and vanishing-mixing limits, which are precisely the limits used for eq. (42) and for fig. 2a. The manuscript does not state how these limits are taken, nor whether the apparent singularities cancel. Because the stated selling point of the paper is that the formulae are simple enough to be implemented directly, a reader coding eqs. (33)–(34) will encounter 0/0 at m²_t̃1 = m²_t̃2. Please add either the limiting expressions or an explicit statement (with the relevant cancellations identified) that the limit is smooth and how it is to be evaluated numerically.
[Appendix B, footnote 1] The footnote states that the authors 'disagree with [16] on the contributions to the stop self-energies coming from the diagrams that involve the O(α_s) four-squark vertex', but the offending term is not exhibited and no argument is given. Since the DR→OS shifts of Appendix B feed directly into the numerical results of fig. 2, and since this is a public disagreement with a published calculation, the specific diagram and the differing term (or at least the size of the numerical effect on δm²_t̃) should be shown. Otherwise the reader has no way to adjudicate between the two results.

Minor objections (5)

[Section 1 and Section 2] Two typographical errors: 'lenghty' in Section 1 (should be 'lengthy') and 'minumum' in Section 2 (should be 'minimum').
[Eqs. (25)–(27)] The notation s2θ is used for sin 2θ̃_t while s²_2θ and c²_2θ denote sin²2θ̃_t and cos²2θ̃_t. Because the entries of eqs. (25)–(27) multiply F3 by s²_2θ and F2 by s2θ, it would help to write sin 2θ̃_t and sin²2θ̃_t explicitly at least once in these equations to avoid a factor-of-two misreading by an implementer.
[Appendix A, eqs. (A4)–(A6)] The definition of Φ in eq. (A4) is stated to be valid for x/z < 1 and y/z < 1, but the physical applications include the heavy-gluino regime m_g̃ > m_t̃1 of fig. 2b, which requires another branch obtained via eq. (A6). Please state which branch is used in the numerical results of fig. 2, so that a reader reproducing the figure knows which continuation to apply.
[Section 4, discussion of eq. (23)] The authors correctly acknowledge that (M²_S)⁰ retains a residual scale dependence through tan β in eq. (23), removable only by including the momentum-dependent parts of the two-loop self-energies. This is an honest statement of scope and is not an error, but a quantitative estimate of the size of the momentum-dependent correction to m_H at large m_A (even a rough one) would substantiate the 'arbitrary m_A' wording of the abstract for the heavy state, rather than only for h.
[Fig. 2 and eq. (42)] The figure caption and the text around eq. (42) do not state the renormalization scale Q at which the logarithms in eq. (42) are evaluated, nor whether the one-loop O(α_t) piece used in producing fig. 2 is expressed in terms of the same OS parameters as the two-loop piece. Please specify both.

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The paper

The paper claims

The paper derives compact analytical two-loop corrections to the neutral Higgs boson masses of the Minimal Supersymmetric Standard Model, valid for any value of the CP-odd Higgs mass and any amount of stop mixing.

The reading

In the Minimal Supersymmetric Standard Model the mass of the lightest CP-even Higgs boson is not fixed at tree level: it receives large corrections from top quarks and their scalar partners, the stops. The known two-loop corrections of order $O(alpha_t alpha_s)$ existed only as a long diagrammatic computer code, or as short formulae restricted to small stop mixing and equal soft stop masses. This paper re-derives those corrections from the effective potential and reduces them to a handful of explicit functions, so that the whole two-loop mass matrix can be written on a page and evaluated for arbitrary stop masses, arbitrary mixing, and arbitrary $m_A$. The authors also resolve a subtlety that earlier effective-potential treatments missed: the Higgs background rotates the top and stop mass matrices, and the resulting field-dependent phase must be differentiated too, otherwise the correction to the heavier CP-even state is not renormalization-scale independent. They check the result against the existing diagrammatic code and find agreement, then work out what happens when the gluino is much heavier than the stops.

What carries the argument

The machinery is the effective potential differentiated at its minimum. Because the Higgs background enters the top and stop mass matrices, the second derivatives of the potential with respect to the CP-even and CP-odd fluctuations can be traded for derivatives with respect to five field-dependent quantities: the top mass $m_t^2$, the two stop mass eigenvalues $m_{tilde t_1}^2$ and $m_{tilde t_2}^2$, the combination $c_{2bar theta}^2 = 1 - sin^2 2bar theta_{tilde t}$ built from the field-dependent mixing angle, and the phase-difference cosine $c_{phi tilde phi}$ that tracks the relative rotation of the top and stop mass matrices. Applying the chain rule to these variables, and using the fact that the derivative of a bubble diagram with respect to an internal mass is another diagram of the same type, produces the three functions $F_1, F_2, F_3$ without ever writing the potential down in full. The $c_{phi tilde phi}$ derivatives contribute only through second derivatives with respect to the CP-odd fields, which is exactly the piece that earlier treatments dropped and that is needed for scale independence of the heavier state.

Extended reading notes

Core claim

The central claim is that the $O(alpha_t alpha_s)$ two-loop corrections to the $2 times 2$ CP-even Higgs mass matrix can be written in closed form for arbitrary parameters. Concretely, the corrections to the three independent entries are given in eqs. (25)-(27) as combinations of three functions $F_1, F_2, F_3$ multiplied by powers of $mu$ and $A_t$; the two-loop pieces of those functions are given explicitly in eqs. (32)-(34), with the gluino-mediated parts collected in Appendix A and the terms induced by the renormalization of $A_t$ in eqs. (35)-(36). The result is presented so that the top and stop inputs may be given either in the DR scheme or in an on-shell scheme, with the conversion shifts listed in Appendix B, and the companion two-loop shift of the CP-odd mass relation is given in Appendix C. The authors report full agreement with the numerical output of the existing diagrammatic calculation, and they isolate one ingredient that earlier effective-potential work did not include: the dependence of the stop masses and mixing angle on the CP-odd components of the Higgs fields, which is what makes the correction to the heavier CP-even state scale independent.

Load-bearing premise

The whole result is taken in the zero-external-momentum limit, where the masses are read off from second derivatives of the effective potential at its minimum and every momentum-dependent part of the two-loop self-energies is dropped.

Editorial extensions

If this is right

A user can evaluate the two-loop $O(alpha_t alpha_s)$ Higgs mass matrix by hand or in a few lines of code for any stop mixing, instead of running a lengthy diagrammatic program.
The result covers the whole $(m_A, tan beta)$ plane, not just the decoupling limit $m_A gg m_Z$ where the lightest mass becomes independent of $m_A$.
The heavy-gluino limit is worked out: the gluino does not decouple, and the lightest Higgs mass rises logarithmically with the gluino mass once the gluino is a few times heavier than the stops, with a maximum at low gluino mass in between.
In mass-independent schemes such as DR, terms proportional to $m_{tilde g}$ and $m_{tilde g}^2$ survive and can make the two-loop corrections very large; the paper shows these are cancelled in on-shell schemes by finite shifts, so the choice of input scheme matters for how the heavy-gluino limit should be read.
An approximate formula for the degenerate, unmixed case is given in eq. (42), including next-to-leading terms in $1/m_{tilde g}$, and is shown to track the complete result well once the gluino exceeds roughly twice the stop mass.

Reading between the lines

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

Because the residual scale dependence of the tree-level mass matrix enters through $tan beta$, the natural next step is to add the momentum-dependent parts of the two-loop self-energies; until that is done, the quoted two-loop correction and the residual scheme ambiguity are of comparable size for the heavier CP-even state.
The same chain-rule bookkeeping should carry over to the $O(alpha_t^2)$ corrections and to the resummation of large logarithms of the stop mass ratio, which the authors flag as the remaining steps of their programme.
The observed non-decoupling of the gluino gives a concrete target for future collider interpretation: a heavy gluino cannot be integrated out of the Higgs mass prediction, so fits that assume decoupling will bias the inferred stop parameters.
The compact form of the corrections makes it practical to scan parameter spaces where the two stop eigenstates are widely split, which is precisely where the low-energy effective description ceases to be a simple two-Higgs-doublet model.

Original abstract

We compute the O(alpha_t alpha_s) two-loop corrections to the neutral Higgs boson masses in the Minimal Supersymmetric extension of the Standard Model. An appropriate use of the effective potential allows us to obtain simple analytical formulae, valid for arbitrary values of mA and of the mass parameters in the stop sector. We elucidate some subtleties of the effective potential calculation, and find full agreement with the numerical output of the existing diagrammatic calculation. We discuss in detail the limit of heavy gluino.

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What the abstract itself states, as probabilities: claims first 0.04 · states limitation 0.19 · human participants 0.01 · controlled comparison 0.05 · randomized assignment 0.01 · states quantitative result 0.06 · compares with prior results 0.95 · mentions code or data availability 0.02.

The abstract, sentence by sentence

arXiv listing abstract v2. Results and the main claim are underlined; show every role.

We compute the O(alpha_t alpha_s) two-loop corrections to the neutral Higgs boson masses in the Minimal Supersymmetric extension of the Standard Model. An appropriate use of the effective potential allows us to obtain simple analytical formulae, valid for arbitrary values of mA and of the mass parameters in the stop sector. We elucidate some subtleties of the effective potential calculation, and find full agreement with the numerical output of the existing diagrammatic calculation. We discuss in detail the limit of heavy gluino.

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 compute the O(alpha_t alpha_s) two-loop corrections to the neutral Higgs boson masses in the Minimal Supersymmetric extension of the Standard Model.	contribution 0.99	0.96	0.17	asserted 1.00
s1	An appropriate use of the effective potential allows us to obtain simple analytical formulae, valid for arbitrary values of mA and of the mass parameters in the stop sector.	method 0.79	0.94	0.24	asserted 1.00
s2	We elucidate some subtleties of the effective potential calculation, and find full agreement with the numerical output of the existing diagrammatic calculation.	result 0.87	0.95	0.18	asserted 1.00
s3	We discuss in detail the limit of heavy gluino.	contribution 0.97	0.89	0.06	asserted 0.76

What kind of paper the classifier reports this is: theoretical result 1.00 · evidence from proof or derivation 0.91.

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sources read

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not examined

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levels run

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Figures

**Figure 1.** Diagrams that contribute to the two–loop effective p

**Figure 2.** The mass mh from our effective potential calculation, as a function of the gluino mass mg˜, for (a) no mixing (mt˜1 = mt˜2 = 1015 GeV, s2θ = 0) and (b) large mixing (mt˜1 = 1175 GeV, mt˜2 = 825 GeV, s2θ = 1) in the stop sector. The other MSSM parameters are: mA = 500 GeV, tan β = 10, µ = 0 and mt = 175 GeV. The dashed line in fig. 2a is the approximate result of eq. (42). parameters, we would find in ∆M2 S terms proportional to m2 g˜ . In fact, as can be seen from eq. (B3), the finite shift δm2 t˜ scales for large mg˜ as m2 g˜ (ln(m2 g˜ /Q2 ) − 1), and cancels in the OS sche

Figures reproduced from arXiv:hep-ph/0105096 by the authors.

References

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Precise prediction for the light MSSM Higgs boson mass combining effective field theory and fixed-order calculations
hep-ph 2016-08 conditional novelty 5.0 of 10

Combining effective-field-theory resummation with fixed-order calculations shifts the predicted lightest MSSM Higgs mass down by about 1 GeV, mainly from higher-order corrections to the MS top-quark mass.
Higgs Bosons in Heavy Supersymmetry with an Intermediate $m_A$
hep-ph 2015-08 conditional novelty 5.0 of 10

A three-scale effective field theory calculation shows that in the MSSM with a CP-odd Higgs mass near the weak scale, matching the observed 125 GeV Higgs requires tan beta above roughly 3.4 when the Higgsino mass equa...
SusyHD: Higgs mass Determination in Supersymmetry
hep-ph 2015-04 conditional novelty 5.0 of 10

An improved effective-field-theory calculation of the MSSM Higgs mass, with new threshold corrections and a public code, finds sub-GeV theoretical uncertainty across most of the parameter space and pushes the preferre...
Two-loop Higgs mass calculation from a diagrammatic approach
hep-ph 2015-03 accept novelty 5.0 of 10

Analytic zero-momentum two-loop tadpole and self-energy expressions, obtained by differentiating Martin's effective potential, are implemented in SARAH/SPheno and validated against independent MSSM codes to ten digits.
FlexibleSUSY -- A spectrum generator generator for supersymmetric models
hep-ph 2014-06 accept novelty 5.0 of 10

FlexibleSUSY generates a modular, fast C++ spectrum generator from a SARAH model file, validated against Softsusy at sub-permille level for the MSSM and NMSSM and benchmarked as faster than SPheno, Softsusy, and SPhenoMSSM.
Constraining the Natural MSSM through tunneling to color-breaking vacua at zero and non-zero temperature
hep-ph 2014-05 conditional novelty 5.0 of 10

Thermal tunneling to color-breaking vacua excludes a large part of the Natural MSSM region with a 125 GeV Higgs, including points whose zero-temperature vacuum lifetime is acceptable.
Stability of the CMSSM against sfermion VEVs
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In the constrained MSSM, parameter regions with light staus or light stops are mostly metastable against tunneling to charge- and color-breaking vacua, and the widely used analytic stability conditions fail to detect this.
Precise determination of the neutral Higgs boson masses in the MSSM
hep-ph 2004-06 conditional novelty 5.0 of 10

Implementing the full one-loop plus leading two-loop Higgs-mass corrections in three spectrum generators yields a 3 to 5 GeV theoretical uncertainty and a conservative upper bound of about 152 GeV on the light MSSM Hi...
SOFTSUSY: a program for calculating supersymmetric spectra
hep-ph 2001-04 accept novelty 5.0 of 10

SOFTSUSY 3.3.3 is a documented, freely available C++ code that solves the MSSM renormalisation group equations iteratively and returns a full superparticle spectrum, with its approximations and failure flags stated ex...
Precision calculations in the MSSM Higgs-boson sector with FeynHiggs 2.14
hep-ph 2018-11 conditional novelty 4.0 of 10

Version 2.14 of FeynHiggs adds a DR-renormalized stop sector, non-degenerate matching thresholds, and a linear interpolation over complex phases, improving MSSM Higgs-mass predictions across low and high SUSY scales.
Towards High-Precision Predictions for the MSSM Higgs Sector
hep-ph 2002-12 conditional novelty 4.0 of 10

Including the full two-loop O(alpha_t^2) and O(alpha_b alpha_s) corrections raises the MSSM upper bound on the light CP-even Higgs mass, weakening tan beta exclusion limits and enlarging the region where the light Hig...
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hep-ph 2015-03 conditional novelty 3.0 of 10

SARAH derives, from a short model definition, the full Lagrangian-level data of a supersymmetric model and exports it as a working spectrum generator and as Monte Carlo model files, demonstrated end to end on the B-L-SSM.
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hep-ph 2020-12 accept novelty 2.0 of 10

A comprehensive review of Higgs-mass calculations in supersymmetric models, documenting fixed-order, effective-field-theory, and hybrid approaches and their theory uncertainties.
A Supersymmetry Primer
hep-ph 1997-09 accept novelty 1.0 of 10

A self-contained pedagogical introduction to supersymmetry and the MSSM, from Lagrangian construction through soft breaking to collider phenomenology.

How later papers used it

73 later papers cite it

Evidence: substantial. 62 of the citing papers share no author with it, and 20 of those carry a confident label from Pith's citation classifier.

Pith read 16 of the 126 citing sentences, choosing only those whose citation markers point at this paper alone, and wrote the paraphrases from them. The summary, the counts, the evidence level, the links and the quotes come from code; the summary counts the papers listed below. A later paper is listed under a label when Pith's citation classifier gives one of its sentences that label at probability 0.8 or more (0.95 for support), Pith's reading finds that the citing paper itself did it, and a second check confirms the paraphrase against the sentence. This section lists uses only. It does not list criticism or disagreement, so their absence here says nothing about how the paper has been received. Papers that share an author with this one are listed apart, under "By the same authors". A quote is the citing authors' own sentence, shown when their paper's licence is CC BY, CC BY-SA or CC0. JSON

1 later paper by other authors is listed below: 1 used its data or values and 1 compared its own results with it. It appears under more than one label. 2 more papers by the same authors are listed: 2 used its method or tool.

Uses its method or tool 2 of 20 papers with this label · 2 by the same authors

By the same authors

Relied on the effective-potential techniques developed in this paper to compute leading corrections to the neutral Higgs boson masses in the MDGSSM and MRSSM.

Leading two-loop corrections to the Higgs boson masses in SUSY models with Dirac gauginos (2016) (same authors) · 0.95 · paraphrased: the licence does not allow quoting
Extracted the top mass from the input value for the pole mass by means of an equation from this paper.

On the NLO QCD corrections to the production of the heaviest neutral Higgs scalar in the MSSM (2012) (same authors) · 0.99 · paraphrased: the licence does not allow quoting

Uses its data or values 1 paper

Used the exact two-loop result from this paper for the O(alpha_t alpha_s) corrections.

Three-loop corrections to the mass of the light Higgs boson in the MSSM (2010) · 0.85 · paraphrased: the licence does not allow quoting

Compares with it 1 of 8 papers with this label

Systematically compared, at the two-loop level, with the exact result given in this paper in very compact form to estimate the error from expanding around hierarchies.

Three-loop corrections to the mass of the light Higgs boson in the MSSM (2010) · 0.97 · paraphrased: the licence does not allow quoting

How the literature uses it

71 arXiv papers cite this in 123 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 · 68 sentences without a confident label

Builds on it 1 paper

[ref] , whereas $δx_k^octet$ are novel contributions involving the octet scalar.

Leading two-loop corrections to the Higgs boson masses in SUSY models with Dirac gauginos · On-shell parameters in the top/stop sector · 0.89

Uses its method or tool 19 papers

We combine the results of the recent EFT calculation assuming a THDM as low-energy theory and allowing for non-vanishing phases of the complex parameters [ref] with the fixed-order calculation provided by [ref] .

Hybrid calculation of the MSSM Higgs boson masses using the complex THDM as EFT · Introduction · 0.87
While the versions used to define the -conserving scenarios of Carena:2013ytb and to produce the corresponding files relied on a fixed-order (namely, full one-loop [ref] and partial two-loop [ref] ) calculation of the masses, the latest version of the code includes also a full NLL and partial NNLL resummation of the corrections involving logarithms of the ratio between the SUSY scale and the EWSB scale [ref] .

MSSM Higgs Boson Searches at the LHC: Benchmark Scenarios for Run 2 and Beyond · Higgs-boson masses and branching ratios · 0.97
In this context, 3, like former , follows mainly Ref. [ref] , which provides most of the necessary radiative corrections at the one-loop level for the Higgs and sparticle masses, while the leading two–loop corrections to the masses of the (neutral) Higgs bosons [ref] are implemented following Ref. [ref] .

SuSpect3: A C++ Code for the Supersymmetric and Higgs Particle Spectrum of the MSSM · Spectrum calculation · 1.00

Uses its data or values 1 paper

In particular, we use the exact two-loop result from [ref] for the $𝒪(α_tα_s)$ corrections.

Three-loop corrections to the mass of the light Higgs boson in the MSSM · Results · 0.85

Compares with it 8 papers

This is done by comparing, at the two-loop level, the full result from Ref. [ref] with the expansions in all the mass hierarchies and choosing the one minimizing the error.

Light MSSM Higgs boson mass to three-loop accuracy · Description of · 0.86
To estimate the error introduced by expanding around these hierarchies, we systematically compare, at the two-loop level, with the exact result which is given in [ref] in very compact form.

Three-loop corrections to the mass of the light Higgs boson in the MSSM · Outline of the Calculation · 0.97
We have intensively used the output to validate our new two-loop functions, in particular: * We found a numerical agreement of more than $10$ digits between our code and using public routines for the MSSM based on Refs. [ref] for the self-energies.

Two-loop Higgs mass calculation from a diagrammatic approach · Validation · 0.97

Cites it as background 20 papers

The computation of the two-loop corrections has meanwhile reached a stage where all the presumably dominant contributions are available [ref] .

The Charged Higgs Boson Mass of the MSSM in the Feynman-Diagrammatic Approach · Introduction · 0.89
Significant efforts have also been devoted to the Higgs-mass calculation in the presence of CP-violating phases, as well as in non-minimal SUSY extensions of the SM.] is quite advanced: full one-loop corrections [ref] and two-loop corrections in the limit of vanishing external momentum [ref] are available, and the dominant momentum-dependent two-loop corrections [ref] as well as the dominant three-loop corrections [ref] have also been obtained.

Improved determination of the Higgs mass in the MSSM with heavy superpartners · Introduction · 0.97
A large amount of work has been invested into calculating higher-order corrections to the mass spectrum within the MSSM with real parameters [ref] as well as the MSSM with complex parameters [ref] .

Complete two-loop QCD contributions to the lightest Higgs-boson mass in the MSSM with complex parameters · Introduction · 0.93

Discussion

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