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Constraints on B and Higgs Physics in Minimal Low Energy Supersymmetric Models

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M. Carena, A. Menon, R. Noriega-Papaqui, A. Szynkman, C.E.M. Wagner

High Energy Physics - Phenomenology · Submitted 14 Mar 2006 · 65 references

Pith's verdict: A careful, technically substantive SUSY flavor paper; the corrected Kaon-sector double-penguin couplings are the real new result and the B_s->mu+mu- versus Delta M_s correlation holds up, with the split-squark caveat flagged by the authors themselves.

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arXiv IDhep-ph/0603106 (version 3)
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CitationA. Menon, A. Szynkman, C.E.M. Wagner, M. Carena, R. Noriega-Papaqui. "Constraints on B and Higgs Physics in Minimal Low Energy Supersymmetric Models." arXiv:hep-ph/0603106 (2006). https://pith.science/paper/SPT5S4ZX
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The paper

The paper claims

The Tevatron's upper bound on the rare decay B_s -> mu+ mu- forces supersymmetric double-penguin corrections to the B_s mass difference to be small and negative, no more than about 6 ps^-1, for CP-odd Higgs masses below 1 TeV in minimal…

The reading

This paper establishes that the Tevatron's upper bound on the rare decay B_s -> mu+ mu- tightly constrains supersymmetric corrections to the B_s mass difference in minimal flavor violating models. Because the same double-penguin loop diagrams generate both the decay and the shift in B_s mixing, the bound BR(B_s -> mu+ mu-) <= 1e-7 forces the correction to be negative and, for CP-odd Higgs masses below 1 TeV, no larger than about 6 $ps^{-1}$. The paper also corrects the earlier Kaon-sector double-penguin formulas, which were missing terms that matter for the (2,1) and (1,2) flavor-changing couplings, and uses the B_s -> mu+ mu- plus b -> s gamma constraints to map where light non-standard Higgs bosons could still appear at hadron colliders. If correct, the result sharpens the search program: a heavy Higgs signal in these models points to small stop mixing, while large positive B_s mixing effects would come from chargino-stop or gluino boxes rather than double penguins.

What carries the argument

The load-bearing object is the resummed effective Lagrangian of Eqs. (1)-(2), in which all large-tan-$\beta$ supersymmetric threshold corrections are encoded in momentum-independent loop factors epsilon_0 and epsilon_Y, with flavor structure dictated by inverse squark mass matrices and CKM elements. The argument runs through double-penguin diagrams, where a neutral Higgs boson is exchanged twice; the flavor-changing couplings (X^S_RL)_JI, especially (X^A_RL)_32 and (X^A_LR)_32, connect B_s -> mu+ mu- to $\Delta$ M_s. The dominance of the LR Wilson coefficient $C_2^{{LR}}$ over $C_1^{{SLL}}$ at large tan $\beta$ makes the same product of couplings control both observables, and the corrected $Gamma^{21}$ and $Gamma^{12}$ factors in Eqs. (12)-(13) carry the Kaon-sector prediction.

Extended reading notes

Core claim

The paper's central claim is that in low-energy supersymmetry with minimal flavor violation and large tan $\beta$, the current Tevatron bound BR(B_s -> mu+ mu-) <= 1e-7 effectively closes the door on large double-penguin corrections to the B_s mass difference. The ratio of the double-penguin contribution to $\Delta$ M_s to the branching ratio is fixed once the CP-odd Higgs mass and tan $\beta$ are chosen, and the measured bound then gives |$\Delta$ M_s|^SUSY <~ 4e-12 GeV, equivalently about 6 $ps^{-1}$, for MA < 1 TeV, with the correction necessarily negative and destructive with the standard model contribution. The paper further claims that previous Kaon-sector double-penguin formulas are incomplete; its corrected expressions, Eqs. (12)-(13), obtained by diagonalizing the one-loop quark mass matrix to second order in CKM elements, reproduce the exact uniform-squark limit and correctly describe the (2,1) and (1,2) flavor-changing couplings. In the CKM-governed non-minimal flavor-violating scenario the constraints are similar, and in light-stop electroweak baryogenesis scenarios positive chargino-stop box contributions to $\Delta$ M_s can reach about 25 percent of the standard model value without significantly enhancing B_s -> mu+ mu-.

Load-bearing premise

The calculation assumes that the supersymmetric corrections can be captured by two momentum-independent loop factors, epsilon_0 and epsilon_Y, in the low-energy Lagrangian; if these factors vary significantly with the momentum flowing through the double-penguin diagrams, the tight connection between the B_s decay rate and the B_s mixing shift, and the resulting 6 $ps^{-1}$ cap, could change.

Editorial extensions

If this is right

  • For MA below 1 TeV in minimal flavor violating models, the double-penguin contribution to Delta M_s is negative and bounded by about 6 ps^-1; a future measurement of BR(B_s -> mu+ mu-) near 3e-8 would tighten that cap further.
  • Light stops and charginos consistent with electroweak baryogenesis can generate positive corrections to Delta M_s up to about 25 percent of the standard model value, almost independent of tan beta, while leaving BR(B_s -> mu+ mu-) essentially unchanged.
  • In the CKM-governed non-minimal flavor-violating scenario, gluino-box contributions rival double penguins only for gluino and left-handed sbottom masses near 100-200 GeV, and the epsilon_K constraint keeps those contributions small.
  • The combination of B_s -> mu+ mu- and b -> s gamma bounds restricts the MA-tan beta plane for Tevatron Higgs searches: a non-standard Higgs signal in these models requires stop mixing at or below the squark mass scale with modest |mu|, or very small stop mixing with large |mu|.
  • If the LHC does not observe B_s -> mu+ mu- with 10 fb^-1 of data, non-standard Higgs observation would remain allowed only for |mu| around 100 GeV with 350 <~ MA <~ 500 GeV in the maximal-mixing case, or for Xt <~ 1 TeV with |mu| <~ 300 GeV.

Reading between the lines

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

  • If the LHC later excludes B_s -> mu+ mu- at the few times 10^-9 level, the same correlation would effectively eliminate double-penguin contributions for MA below 1 TeV, making any observed shift in B_s mixing a clean signal of box-diagram sources such as chargino-stop or gluino loops.
  • The corrected Gamma^21 and Gamma^12 formulas suggest that earlier large-tan-beta constraints on Kaon mixing derived with the old double-penguin expressions should be re-evaluated in any model sharing this epsilon structure, since the old formulas missed terms that change the (2,1) and (1,2) couplings.
  • A precision program combining BR(B_s -> mu+ mu-) with Delta M_s could test the predicted scaling of the double-penguin contribution with MA/tan beta; if a measured deviation in B_s mixing fails to track the decay rate, the double-penguin interpretation would be excluded in favor of other supersymmetric contributions.
Original abstract

We study the implications of minimal flavor violating low energy supersymmetry scenarios for the search of new physics in the B and Higgs sectors at the Tevatron collider and the LHC. We show that the already stringent Tevatron bound on the decay rate B_s -> mu+ mu- sets strong constraints on the possibility of generating large corrections to the mass difference Delta M_s of the B_s eigenstates. We also show that the B_s -> mu+ mu- bound together with the constraint on the branching ratio of the rare decay b -> s gamma has strong implications for the search of light, non-standard Higgs bosons at hadron colliders. In doing this, we demonstrate that the former expressions derived for the analysis of the double penguin contributions in the Kaon sector need to be corrected by additional terms for a realistic analysis of these effects. We also study a specific non-minimal flavor violating scenario, where there are flavor changing gluino-squark-quark interactions, governed by the CKM matrix elements, and show that the B and Higgs physics constraints are similar to the ones in the minimal flavor violating case. Finally we show that, in scenarios like electroweak baryogenesis which have light stops and charginos, there may be enhanced effects on the B and K mixing parameters, without any significant effect on the rate of B_s -> mu+ mu-.

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, 5,234 input tokens, $0.0002 reported.

What the abstract itself states, as probabilities: claims first 0.03 · states limitation 0.43 · human participants 0.01 · controlled comparison 0.08 · randomized assignment 0.01 · states quantitative result 0.13 · compares with prior results 0.65 · mentions code or data availability 0.01.

The abstract, sentence by sentence

arXiv listing abstract v3. Results and the main claim are underlined; .

We study the implications of minimal flavor violating low energy supersymmetry scenarios for the search of new physics in the B and Higgs sectors at the Tevatron collider and the LHC. We show that the already stringent Tevatron bound on the decay rate B_s -> mu+ mu- sets strong constraints on the possibility of generating large corrections to the mass difference Delta M_s of the B_s eigenstates. We also show that the B_s -> mu+ mu- bound together with the constraint on the branching ratio of the rare decay b -> s gamma has strong implications for the search of light, non-standard Higgs bosons at hadron colliders. In doing this, we demonstrate that the former expressions derived for the analysis of the double penguin contributions in the Kaon sector need to be corrected by additional terms for a realistic analysis of these effects. We also study a specific non-minimal flavor violating scenario, where there are flavor changing gluino-squark-quark interactions, governed by the CKM matrix elements, and show that the B and Higgs physics constraints are similar to the ones in the minimal flavor violating case. Finally we show that, in scenarios like electroweak baryogenesis which have light stops and charginos, there may be enhanced effects on the B and K mixing parameters, without any significant effect on the rate of B_s -> mu+ mu-.

background contribution method result interpretation main claim

What the classifier reports for each sentence. The number is the probability it gave the label.
#sentencerolethe authors' own workstates the main conclusionstrength
s0 We study the implications of minimal flavor violating low energy supersymmetry scenarios for the search of new physics in the B and Higgs sectors at the Tevatron collider and the LHC. contribution 0.98 0.79 0.07 asserted 0.59
s1 We show that the already stringent Tevatron bound on the decay rate B_s -> mu+ mu- sets strong constraints on the possibility of generating large corrections to the mass difference Delta M_s of the B_s eigenstates. result 0.98 0.83 0.22 asserted 1.00
s2 We also show that the B_s -> mu+ mu- bound together with the constraint on the branching ratio of the rare decay b -> s gamma has strong implications for the search of light, non-standard Higgs bosons at hadron colliders. result 0.80 0.85 0.30 asserted 1.00
s3 In doing this, we demonstrate that the former expressions derived for the analysis of the double penguin contributions in the Kaon sector need to be corrected by additional terms for a realistic analysis of these effects. contribution 0.49 0.83 0.06 asserted 1.00
s4 We also study a specific non-minimal flavor violating scenario, where there are flavor changing gluino-squark-quark interactions, governed by the CKM matrix elements, and show that the B and Higgs physics constraints are similar to the ones in the minimal flavor violating case. result 0.59 0.94 0.10 asserted 1.00
s5 Finally we show that, in scenarios like electroweak baryogenesis which have light stops and charginos, there may be enhanced effects on the B and K mixing parameters, without any significant effect on the rate of B_s -> mu+ mu-. result 0.98 0.88 0.13 hedged possibility 0.98

What kind of paper the classifier reports this is: theoretical result 0.99 · evidence from proof or derivation 0.52.

What was examined, and what was not

sources read
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  • 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. SUSY radiative corrections to the self-energies of the d-
Figure 2. Correlation between BR(Bs → µ +µ −) and ∆Ms. The squark masses are all uniform and have been set to 2 TeV. The rest of the SUSY parameters have been chosen so that |ǫ0| and |ǫY | have their maximal values. The black lines have fixed values of MA/ tan β, but varying gluino phase. The contours represent ∆Ms for different ranges of MA (MA ≥ 500, 1000, 2000 GeV) for gluino mass and At phases equal to π, and varying tan β values. The red (grey) vertical line is the experimental bound on BR(Bs → µ +µ −). The horizontal black line is the 2σ upper bound on the double penguin contributions t
Figure 3. Same as Fig. 2, but for third generation soft supersymme
Figure 4. Correlation between BR(Bs → µ +µ −) and ∆MK. The squark masses are all uniform and have been set to 2 TeV. The rest of the SUSY parameters have been chosen so that |ǫ0| and |ǫY | have their maximal values. The black lines have fixed values of MA/ tan β. The contours are the double penguin contributions to ∆MK for gluino mass and At phases equal to π, but varying tan β. The left red (grey) vertical line is the present experimental bound on BR(Bs → µ +µ −) while the right blue (black) verticle line is the previous limit. BR(B ) x 10 s µ µ+ − 6 AM /Tan( )= 50 GeV β AM /Tan( )= 40 GeV β…
Figure 5. Same as Fig. 4, but for
Figure 6. Variation of SUSY contributions to ∆Ms with input parameters MA = 200 GeV, M3 = 1000 GeV, MD3 = MSUSY = 2000 GeV, 2M1 = M2 = µ, M2 U3 = −902 GeV2 , At = −1000 GeV and tan β = 10 ∆ K SUSY ∆ K ( Μ ) /( Μ )Exp | | (GeV) µ Arg( ) − Arg(M ) = 0 µ Arg( ) − Arg(M ) = /2 µ Arg( ) − Arg(M ) = µ 2 π 2 2 π 0.0002 0.0004 0.0006 0.0008 0.001 0.0012 0.0014 0.0016 0.0018 0.002 100 150 200 250 300 350 400 450 500
Figure 7. Variation of SUSY contributions to ∆MK with input parameters MA = 200 GeV, M3 = 1000 GeV, MD3 = MSUSY = 2000 GeV, 2M1 = M2 = µ, M2 U3 = −902 GeV2 , At = −1000 GeV and tan β = 10 20
Figure 8. Variation of SUSY contributions to ǫK with input parameters MA = 200 GeV, M3 = 1000 GeV, MD3 = MSUSY = 2000 GeV, 2M1 = M2 = µ, M2 U3 = −902 GeV2 At = −1000 GeV and tan β = 10 possible for scenarios in which the stops and charginos are light, so that the chargino-stop box diagrams become larger. Furthermore, the bound on BR(Bs → µ +µ −) can be satisfied by going to regions of large MA or low tan β as chargino-stop box contributions are not very sensitive to tan β. This scenario is similar to that discussed in Ref. [29] where low values of tan β satisfy both the dark matter and…
Figure 9. The dashed(dotted) line is the BR(Bs → µ +µ −) experimental bound in the MA −tan β plane for µ = −200(−100) GeV and the yellow (light grey) and blue (dark grey) bands are the b → sγ allowed regions for µ = −200 GeV and −100 GeV, respectively, in the uniform squark limit with MSUSY = 1 TeV, |M3| = 0.8 TeV, and 2M1 = M2 = 110 GeV. The red (grey) line is the projected CDF limit on H → τ τ for 1fb−1 luminosity. Larger luminosities would probe larger MA and smaller tan β. Also changing µ from −200 GeV to −100 GeV does not affect the CDF limit significantly. Figures (a),(c) and (e) have di
Figure 10. (a)–(c) Corresponds to µ = 500 − −1500 GeV with the blue (dark grey) band showing b → sγ allowed regions for these values of µ in the uniform squark mass limit with a common value of the squark masses MSUSY = 1 TeV, M3 = 0.8 TeV, 2M1 = M2 = 110 GeV. The red (grey) line is the projected CDF limit on H → τ τ for 1fb−1 luminosity. The dashed part of the projected Tevatron reach is an extrapolation of the curve. (d) Shows the effect of including the squark loop correction to P H+ RL vertex, proportional to ǫ 3 ′ 0 , on b → sγ rate for µ = 1 TeV. The dashed line corresponds to the case…
Figure 11. Comparison of the projected reach for non-standard
Figure 12. Gluino box diagrams that make contributions to ∆
Figure 13. Variation of SUSY contributions to ∆Ms with input parameters MA = 250 GeV, MSUSY = 1000 GeV, M1 = 110 GeV M2 = 1000 GeV, µ = 1100 GeV, M(U˜L,D˜L)12 = MU˜R,D˜R = 1000 GeV, M(U˜L,D˜L)3 = 100 GeV, At = 1110 GeV, tan β = 10 and all relevant SUSY phases are zero.(a) Shows the variation of ∆Ms over small values of gluino mass, while (b) shows that in limit of large gluino mass we recover the SM value. the right handed stop mass parameter MU˜R and Xt ≃ MU˜R , the lightest stop mass becomes mainly left-handed and its mass is given by m2 t˜1 ≃ M2 U˜L + m2 t
Figure 14. Variation of the gluino contributions to

Figures reproduced from arXiv:hep-ph/0603106 by the authors.

References
How the literature uses it

21 arXiv papers cite this in 31 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 · 18 sentences without a confident label

Uses its method or tool 2 papers
  • At large $tanβ$, we absorb this modification by redefining the bottom quark mass occuring in the Yukawa coupling, [ref] [equation] where [equation] and the auxiliary function is defined as, [equation] The contributions to the bottom Yukawa couplings which are enhanced at large $tanβ$ can be included to all orders by making the following replacements [ref] : [equation] We use these effective Yukawa couplings in our NLO computation.

    SUSY QCD Corrections to Higgs Pair Production from Bottom Quark Fusion · Next-To-Leading Order Corrections for $b b̅ →ϕϕ$ · 0.89

  • The contributions to the bottom Yukawa couplings which are enhanced at large $tanβ$ can be included to all orders by making the following replacements [ref]

    Higgs boson enhancement effects on squark-pair production at the LHC · Radiative corrections to the Yukawa couplings · 0.87

Uses its data or values 3 papers
  • Accordingly, together with the uncertainties from the hadronic parameter $f_B$, quite different SM predictions for $BR(B̅^+ →τ^+ ν_τ)$ can be obtained, ranging from $.BR(B̅^+→τ^+ν_τ)|_SM= (0.85 ±.13) ×10^-4$ [ref] to $.BR(B̅^+→τ^+ν_τ)|_SM= (1.59 ±.40) ×10^-4$ [ref] .

    Updated Constraints from B Physics on the MSSM and the NMSSM · Introduction · 0.92

  • Moreover we impose the following condition on the SUSY prediction: $|ΔM_B_s^SUSY - 17.77| < ((0.12 ×1.96)^2 + 3.3^2)^1/2 ps^-1 = 3.31 ps^-1$ (95% CL), where we have combined the experimental error of $0.12 ×1.96 ps^-1$ (95% CL) [ref] quadratically with the theoretical uncertainty of $3.3 ps^-1$ (95% CL) [ref] .

    Impact of squark generation mixing on the search for squarks decaying into fermions at LHC · Constraints · 0.95

  • Moreover we impose the following condition on the SUSY prediction: $|ΔM_B_s^SUSY - 17.77| < ((0.12 ×1.96)^2 + 3.3^2)^1/2 ps^-1 = 3.31 ps^-1$ (95% CL), where we have combined the experimental error of $0.12 ps^-1$ (at 68% CL) [ref] quadratically with the theoretical uncertainty of $3.3 ps^-1$ (at 95% CL) [ref] .

    Impact of squark generation mixing on the search for gluinos at LHC · Constraints · 0.98

Compares with it 1 paper
Cites it as background 6 papers

Discussion

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