Can the renormalization group improved effective potential be used to estimate the Higgs mass in the conformal limit of the standard model?
Bibliographic record
Abstract
We consider the effective potential $V$ in the standard model with a single Higgs doublet in the limit that the only mass scale $\ensuremath{\mu}$ present is radiatively generated. Using a technique that has been shown to determine $V$ completely in terms of the renormalization group (RG) functions when using the Coleman-Weinberg renormalization scheme, we first sum leading-log (LL) contributions to $V$ using the one loop RG functions, associated with five couplings (the top quark Yukawa coupling $x$, the quartic coupling of the Higgs field $y$, the $SU(3)$ gauge coupling $z$, and the $SU(2)\ifmmode\times\else\texttimes\fi{}U(1)$ couplings $r$ and $s$). We then employ the two loop RG functions with the three couplings $x$, $y$, $z$ to sum the next-to-leading-log (NLL) contributions to $V$ and then the three to five loop RG functions with one coupling $y$ to sum all the ${N}^{2}LL\dots{}{N}^{4}LL$ contributions to $V$. In order to compute these sums, it is necessary to convert those RG functions that have been originally computed explicitly in the minimal subtraction scheme to their form in the Coleman-Weinberg scheme. The Higgs mass can then be determined from the effective potential: the $LL$ result is ${m}_{H}=219\text{ }\text{ }\mathrm{GeV}/{c}^{2}$ and decreases to ${m}_{H}=188\text{ }\text{ }\mathrm{GeV}/{c}^{2}$ at ${N}^{2}LL$ order and ${m}_{H}=163\text{ }\text{ }\mathrm{GeV}/{c}^{2}$ at ${N}^{4}LL$ order. No reasonable estimate of ${m}_{H}$ can be made at orders ${V}_{NLL}$ or ${V}_{{N}^{3}LL}$ since the method employed gives either negative or imaginary values for the quartic scalar coupling. The fact that we get reasonable values for ${m}_{H}$ from the $LL$, ${N}^{2}LL$, and ${N}^{4}LL$ approximations is taken to be an indication that this mechanism for spontaneous symmetry breaking is in fact viable, though one in which there is slow convergence towards the actual value of ${m}_{H}$. The mass $163\text{ }\text{ }\mathrm{GeV}/{c}^{2}$ is argued to be an upper bound on ${m}_{H}$.
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How this classification was reachedexpand
Full frame machine prediction
Teacher imitationNot calibrated prevalence, not ground truth. Human validation pending. The Gemma side is a direct model label for every work in the frame, read from the title-only record. The Codex side is a classifier learned from the 10,348 direct Codex labels and calibrated to design-weighted sample rates; fields without enough sample support carry no Codex call. Candidate is the union of the two sides; consensus is their intersection. These outputs are machine_predicted_unvalidated and are not human labels.
Distilled classifier scores by category (both heads)
| Category | Codex | Gemma |
|---|---|---|
| Metaresearch | 0.001 | 0.005 |
| Meta-epidemiology (narrow) | 0.001 | 0.000 |
| Meta-epidemiology (broad) | 0.001 | 0.001 |
| Bibliometrics | 0.001 | 0.000 |
| Science and technology studies | 0.000 | 0.001 |
| Scholarly communication | 0.001 | 0.003 |
| Open science | 0.002 | 0.001 |
| Research integrity | 0.001 | 0.001 |
| Insufficient payload (model declined to judge) | 0.001 | 0.000 |
Machine scores (provisional)
The two teacher heads of the student model, read on this work. A score orders the frame for review; it never asserts a category, and the validation status ships verbatim with every row.
Baseline scores from an immature model (maturity gate not passed, 7 training rounds). Scores rank; they never assert a category.
score_only:v0-immature-baseline · verbatim from the scoring run: score_only means the number may rank works, and no category label ships from itClassification
machine, unvalidatedMachine predicted; a candidate call from one source (direct Gemma or distilled Codex), not a consensus.
How this classification was reached, model by model and score by score, is at the end of the page under "How this classification was reached".