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Resilience of the Spectral Standard Model
Ali H. Chamseddine, Alain Connes
TL;DR
The spectral model’s earlier Higgs-mass prediction conflicts with the measured low mass and the resulting high-energy instability. The paper reexamines the spectral action with its real singlet included in the Higgs-sector RG analysis. It finds parameter choices compatible with a Higgs mass around 125.5 GeV while the quartic couplings remain positive during running.
Problem
The spectral model’s earlier Higgs-mass prediction conflicts with the experimental value around 125 GeV, while the low mass also challenges high-energy Higgs-potential stability.
Source: §I · p. 2Method
The authors include the real singlet already present in the spectral action and numerically study one-loop RG running across the parameter space (n, u).
Source: §I · p. 2, §III · p. 8Results
Around 125.5 GeV is reached along an almost straight curve in (n, u), with suitable n values for unification scales u ∈ (25, 35) and positive quartic couplings during running.
Source: §III · p. 8Takeaways & Limitations
The authors report that Higgs-singlet quartic mixing shifts the mostly Higgs state down and the mostly σ state up, allowing initial conditions consistent with a Higgs mass around 125 GeV and a top mass of 170 GeV.
Source: §IV · p. 11The three gauge couplings do not meet exactly, differing by a few percent; the authors suggest the cutoff-function use in the spectral action’s asymptotic heat-kernel expansion may be related.
Source: §III · p. 5
Abstract
from arXiv · showhide
We show that the inconsistency between the spectral Standard Model and the experimental value of the Higgs mass is resolved by the presence of a real scalar field strongly coupled to the Higgs field. This scalar field was already present in the spectral model and we wrongly neglected it in our previous computations. It was shown recently by several authors, independently of the spectral approach, that such a strongly coupled scalar field stabilizes the Standard Model up to unification scale in spite of the low value of the Higgs mass. In this letter we show that the noncommutative neutral singlet modifies substantially the RG analysis, invalidates our previous prediction of Higgs mass in the range 160--180 Gev, and restores the consistency of the noncommutative geometric model with the low Higgs mass.
I. INTRODUCTION
The low experimental Higgs mass conflicts with the spectral model’s earlier prediction and challenges the high-energy positivity required by the model. The paper argues that the previously neglected real singlet, whose couplings match those supplied by the spectral action, restores compatibility.
I. INTRODUCTION
- The low Higgs mass of about 125 GeV challenges the spectral model’s earlier 160–180 GeV prediction and the high-energy positivity required by the model.The low mass is also associated with instability of the Higgs potential, challenging the big-desert hypothesis.Source: §I · p. 2
- The full spectral action already contains a real singlet responsible for neutrino Majorana masses, whose role in the Higgs prediction was incorrectly neglected.The authors say they had assumed the singlet would not significantly affect the prediction.Source: §I · p. 2
- The singlet’s couplings match those proposed to stabilize the Standard Model at high energies, and the authors say these couplings were already delivered by the spectral action.The cited work markers for the independent proposals are, [4],, [6], and [7].Source: §I · pp. 2–3
II. HIGGS-SINGLET SCALAR POTENTIAL
The Higgs-singlet scalar potential is derived from the spectral action, with the singlet identified with the right-handed-neutrino Majorana mass sector. In the stated approximation, the resulting quartic couplings depend on a dimensionless parameter n, and the singlet coupling is strong.
II. HIGGS-SINGLET SCALAR POTENTIAL
- The spectral action, computed from the noncommutative-space Dirac operator using heat-kernel methods, supplies the Higgs-singlet scalar potential.The potential’s fields are the Higgs doublet H and real singlet σ, associated with the right-handed-neutrino Majorana mass.Source: §II · p. 3
- The analysis uses a rough approximation in which the top-quark and neutrino Yukawa couplings are dominant, and introduces a dimensionless parameter n.The treatment retains flexibility in the Majorana matrix for the general three-family case and works in unitary gauge.Source: §II · p. 3
- The singlet quartic coupling is λσ = 8g², while λhσ rises from zero at n = 0 to 8g² as n approaches infinity.The Higgs quartic λh decreases from 4 to 1 and then increases toward 4g² as n approaches infinity.Source: §II · p. 4
III. RUNNING THE INITIAL CONDITIONS FOR THE MODEL WITH CUTOFF FUNCTION
One-loop RG running across the scanned parameter space yields a family of theories matching the 125.5 GeV Higgs mass, with positive scalar couplings and a low-scale stability condition. The analysis also identifies limits in top-mass agreement, fine-tuning, and gauge-coupling unification.
- Gauge-coupling unification is not exact, with a few-percent mismatch indicating a possible missing ingredient related to the cutoff function.The authors leave this issue aside and assume uncertainty in the unification scale.Source: §III · p. 5
- The low-scale mass terms require fine-tuning, which the authors do not address; they note a dilaton could technically solve the quadratic-divergence problem.The Higgs-scale parameter is of order 10^2 GeV while the singlet-scale parameter is of order 10^11 GeV.Source: §III · p. 7
- The singlet reduces the Higgs mass by a factor of 0.78 at low scale.The physical states are mixtures of the Higgs and singlet fields, with very small mixing.Source: §III · p. 8
- The scalar mass matrix has positive determinant at low scale, the stated condition for a stable Higgs mass near 125 GeV.The authors check the condition numerically.Source: §III · p. 8
- The numerical study places the predicted top-quark mass a few percent below the experimental value.The authors expect two-loop RG equations with a singlet to improve agreement for both top and Higgs masses.Source: §III · p. 8
- A 125.5 GeV Higgs mass is reached along an almost straight curve in (n, u), yielding consistent theories across u ∈ (25, 35).For this family, all three quartic couplings remain positive during running and the low-scale stability inequality holds.Source: §III · p. 8, Figure 2 · p. 9
IV. CONCLUSIONS
The spectral model gives the Higgs a geometric origin, but its earlier mass prediction relied on an oversimplified treatment of the neutral singlet. Including Higgs–singlet mixing permits a low Higgs mass, while important questions about unification and the model’s geometric structure remain open.
IV. CONCLUSIONS
- The spectral model is presented as a conceptual explanation of the Standard Model coupled to gravity, using an extension of the geometric paradigm and the spectral action principle.The principle asserts that the action functional is a spectral function of the line element.Source: §IV · p. 9
- The model derives the Higgs doublet’s geometric origin from the discrete dimension and includes a neutral singlet whose vev gives Majorana mass to the right-handed neutrino.The finite-space classification also singled out, almost uniquely, the symmetries of the Standard Model.Source: §IV · p. 10
- The Higgs–singlet potential mixes the fields and shifts the mostly Higgs state down and the mostly sigma state up, allowing initial conditions consistent with a Higgs mass around 125 GeV and a top mass of 170 GeV.The earlier 160–180 GeV prediction followed from integrating out the singlet and replacing it by its vev, an assumption described as simplistic.Source: §IV · p. 11
- The paper identifies resolving how the three gauge couplings meet at a unification scale as an outstanding issue.It also names a geometric framework for all fermion Yukawa couplings and an explanation for the number of families as open questions.Source: §IV · pp. 11–12