REVIEW
The anthropic principle and the mass scale of the Standard Model
High Energy Physics - Phenomenology · Submitted 17 Jul 1997 · 24 references
Pith's verdict: An early, honest anthropic sweep of the Higgs mass parameter — the nuclear physics is solid, the QCD–weak coincidence observation is the part worth citing, and the '5' in the abstract is looser than the explanatory claim needs.
T0 · AI review
Why Pith says this
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Referee report
The paper
The paper claims
The paper argues that the Higgs mass parameter is small because larger or positive values would leave a universe with no stable nuclei, no chemistry, or no baryons surviving long enough for chemistry to begin.
The reading
What carries the argument
The machinery is a one-parameter scan: hold every dimensionless coupling of the Standard Model fixed, vary only $mu^2$ between $-M_P^2$ and $+M_P^2$, and follow the consequences down a chain that runs from the Higgs potential $V(phi) = lambda (phi^dagger phi)^2 + mu^2 phi^dagger phi + (sum_i lambda_i langle q_i q_i rangle phi + h.c.)$ to the expectation value $v$, then to lepton and quark masses, then to the pion mass via $m_pi^2 propto (m_u+m_d)langle bar{q}q rangle / f_pi^2$, then to the deuteron binding energy and the depth of the nuclear potential, and finally to which nuclei are stable and whether they can be assembled in primordial or stellar nucleosynthesis. The selection criterion is deliberately minimal: life requires complex chemistry, chemistry requires a variety of stable nuclei dressed with electrons, and that single requirement does the excluding. The deuteron is the load-bearing link, because all nucleosynthesis starts there, and the authors model its binding with both a square well whose range shrinks as $m_pi^{-1}$ and a six-boson one-boson-exchange potential fitted to scattering data.
Extended reading notes
Core claim
The central claim is that the anthropically allowed range of the Higgs mass parameter is narrow enough that the observed value is a typical member of it, and that the same requirement explains the proximity of the weak scale to the QCD scale. For $mu^2<0$, increasing $|mu^2|$ raises $v$ and with it the quark masses; the neutron-proton mass difference grows as $m_d-m_u$ while the pion mass grows and the nuclear potential shortens in range, so nuclei become unstable and the deuteron unbinds. The authors estimate that beyond $v/v_0$ of about 5 no stable nuclei remain and only protons survive, while above $v/v_0$ of roughly $10^3$ the only stable baryon is the $Delta^{++}$, giving a chemically inert helium-like universe. For $mu^2>0$ the vacuum is driven by the quark condensate, so $v sim f_pi^3/mu^2$ and all quark and lepton masses become tiny; chemistry then cannot begin until the cosmic background has cooled below a biochemical energy of order $epsilon alpha^2 m_e$, which pushes the onset of chemistry to times scaling as $(mu^2/mu_0^2)^{3/2}$, so the requirement that baryons have not yet decayed bounds $mu^2$ many orders of magnitude below $M_P^2$.
Load-bearing premise
The exclusion of large $v$ depends on the modeled falloff of the deuteron binding energy as the pion mass rises, and the two models the authors use already disagree about where the deuteron dies, at $v/v_0$ of 1.2 to 1.4 for weak decay and 1.4 to 2.7 for strong decay.
Editorial extensions
If this is right
- Values of $v$ more than about five times the observed value are excluded, because the neutron-proton mass difference would exceed the nuclear binding energy and leave a universe of bare protons.
- Values of $v$ above roughly $10^3 v_0$ are excluded more sharply, because the only stable baryon becomes the $Delta^{++}$, which cannot bind to itself and is chemically equivalent to helium.
- For positive $mu^2$, the requirement that baryons survive until the universe cools to a biochemical temperature gives $mu^2 lesssim epsilon (4 times 10^5$ GeV$)^2 (M/10^{16}$ GeV$)^2$, a bound some 27 orders of magnitude below the Planck scale.
- If the weak scale is what it is for anthropic reasons, there is no need for supersymmetry, technicolor, or other new structure at the TeV scale to make the fine-tuning natural.
- The same window explains why the weak scale sits near the QCD scale: the up and down masses must be small compared with the QCD scale by roughly the amount seen in nature for the pion to be light enough to bind the deuteron.
Reading between the lines
- The deuteron slope is the one number the whole exclusion rests on, and it is now checkable: lattice QCD computations of deuteron binding at pion masses two to four times the physical value would either confirm the rapid unbinding the paper assumes or push the threshold to much larger $v$ and widen the window.
- Because the positive-$mu^2$ boundary scales with the assumed baryon lifetime, an improved proton-lifetime limit or a firmer grand-unification scale would move that edge without touching the negative-$mu^2$ edge, so the two sides of the argument can be tested independently.
- The paper's logic treats $mu^2$ and the cosmological constant as separate environmental parameters; if both are scanned together, the requirement that structure form before chemistry begins couples the two windows and could sharpen or loosen each.
- The argument's asymmetry is worth noting for readers: the negative-$mu^2$ side is bounded from above by nuclear physics, while the positive-$mu^2$ side is bounded from below by cosmology, so a universe with $mu^2$ slightly positive and tiny is not obviously excluded by anything the paper computes.
Original abstract
In theories in which different regions of the universe can have different values of the the physical parameters, we would naturally find ourselves in a region which has parameters favorable for life. We explore the range of anthropically allowed values of the mass parameter in the Higgs potential, $\mu^2$. For $\mu^2<0$, the requirement that complex elements be formed suggests that the Higgs vacuum expectation value $v$ must have a magnitude less than 5 times its observed value. For $\mu^2>0$, baryon stability requires that $|\mu|<<M_P$, the Planck Mass. Smaller values of $|\mu^2|$ may or may not be allowed depending on issues of element synthesis and stellar evolution. We conclude that the observed value of $\mu^2$ is reasonably typical of the anthropically allowed range, and that anthropic arguments provide a plausible explanation for the closeness of the QCD scale and the weak scale.
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.
The abstract, sentence by sentence
In theories in which different regions of the universe can have different values of the the physical parameters, we would naturally find ourselves in a region which has parameters favorable for life. We explore the range of anthropically allowed values of the mass parameter in the Higgs potential, $\mu^2$. For $\mu^2<0$, the requirement that complex elements be formed suggests that the Higgs vacuum expectation value $v$ must have a magnitude less than 5 times its observed value. For $\mu^2>0$, baryon stability requires that $|\mu|<<M_P$, the Planck Mass. Smaller values of $|\mu^2|$ may or may not be allowed depending on issues of element synthesis and stellar evolution. We conclude that the observed value of $\mu^2$ is reasonably typical of the anthropically allowed range, and that anthropic arguments provide a plausible explanation for the closeness of the QCD scale and the weak scale.
background contribution method result interpretation main claim
| # | sentence | role | the authors' own work | states the main conclusion | strength |
|---|---|---|---|---|---|
| s0 | In theories in which different regions of the universe can have different values of the the physical parameters, we would naturally find ourselves in a region which has parameters favorable for life. | background 1.00 | 0.06 | 0.03 | asserted 0.56 |
| s1 | We explore the range of anthropically allowed values of the mass parameter in the Higgs potential, $\mu^2$. | contribution 1.00 | 0.86 | 0.02 | asserted 0.67 |
| s2 | For $\mu^2<0$, the requirement that complex elements be formed suggests that the Higgs vacuum expectation value $v$ must have a magnitude less than 5 times its observed value. | result 1.00 | 0.77 | 0.04 | hedged possibility 0.98 |
| s3 | For $\mu^2>0$, baryon stability requires that $|\mu|<<M_P$, the Planck Mass. | result 1.00 | 0.67 | 0.03 | asserted 0.99 |
| s4 | Smaller values of $|\mu^2|$ may or may not be allowed depending on issues of element synthesis and stellar evolution. | limitation 0.69 | 0.37 | 0.02 | hedged possibility 1.00 |
| s5 | We conclude that the observed value of $\mu^2$ is reasonably typical of the anthropically allowed range, and that anthropic arguments provide a plausible explanation for the closeness of the QCD scale and the weak scale. | interpretation 0.85 | 0.87 | 0.97 | hedged possibility 0.58 |
What was examined, and what was not
- arXiv listing abstract v2
- full text
- figures and tables
- references and citing sentences
- relations to other papers
- P abstract
- S sections
- T body sentences
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- R cross-paper relations
Figures
Figures reproduced from arXiv:hep-ph/9707380 by the authors.
References
How the literature uses it
89 arXiv papers cite this in 120 sentences
Papers citing it · 94 sentences without a confident label
Uses its data or values 2 papers
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The parameter $a$ is uncertain, but it is estimated in Ref. [ref] to be $a ≃(1.3$ – $5.5) MeV$ using models of nucleon binding.
Evidence for the Multiverse in the Standard Model and Beyond · Stability boundaries for neutrons, deuterons and complex nuclei · 0.98
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In Ref. [ref] , it was noted that the QCD scale is also sensitive to the VEV of the Higgs field through quark threshold effects, and they estimated that the scale varies as $(v/v_0)^ζ$, where $ζ$ varies between $0.25$ and $0.3$–we will take it be $0.25$ here.
A Slant on Warped Extra Dimensions · Fermion and gauge fields on the brane · 0.95
Compares with it 3 papers
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Using a mass-independent renormalization scheme at one-loop, for $Q$ much larger than $2m_t$, one has [equation] Now, if one multiplies all of the quark masses by $1+δv/v$, one finds that [equation] and plugging this into the standard one-loop formula for , [equation] one finds that [equation] which is close to the results in [ref] .
Constraints on Variation of the Weak Scale from Big Bang Nucleosynthesis · The evolution of the strong coupling constant · 0.98
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An appealing feature of this work is that, unlike the case of anthropic selection [ref] , our selection mechanism is robust to the variation of almost all the parameters of our model (the only exception being the sign of the mass term in the $ϕ$-potential).
Cosmological selection of a small weak scale from large vacuum energy: a minimal approach · Conclusions · 0.96
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This approach is therefore distinct from the “atomic principle” argument for anthropic selection of the weak scale [ref] .
Mass Hierarchy and Vacuum Energy · Anthropic Arguments · 0.91
Cites it as support 3 papers
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This higher $m_1/2$ natural region is actually favored by rather general considerations of the string landcape, where a power-law draw [ref] to large soft terms is exected so long as the derived value of the weak scale lies within the ABDS window [ref] $m_Z^OU/2m_Z^PU(2-5)m_Z^OU$ (where $m_Z^PU$ is the pocket-universe value of $m_Z$ while $m_Z^OU$ is the $Z$ mass in our universe).
Implications of Higgs mass for hidden sector SUSY breaking · Singlet SUSY breaking fields · 0.97
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Without the anthropic constraint on the electroweak scale, the distribution is given by Eq.([ref]) with $s=1$.] as is argued in [ref] ,
New Inflation in the Landscape and Typicality of the Observed Cosmic Perturbation · Probability Distribution of the Observables · 0.97
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On the other hand, it is intriguing that if the weak scale were increased by a factor of $2$, the SM would not yield any complex stable nuclei [ref] , suggesting that the weak scale may also be selected environmentally.
Environmentally Selected WIMP Dark Matter with High-Scale Supersymmetry Breaking · Introduction and Framework · 0.97
Cites it as background 16 papers
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In the seminal papers by Agrawal, Barr, Donoghue and Seckel (ABDS) [ref] , the scenario of the Standard Model emerging from the multiverse via an anthropic solution to the hierarchy problem is investigated.
Fine-tuned vs. natural supersymmetry: what does the string landscape predict? · Introduction · 0.98
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For the hierarchy problem, the smallness of the weak scale can be explained by either dynamics, such as supersymmetry or compositeness, or by anthropics—the “atomic principle” that postulates the necessity of the existence of atoms [ref] .
A small weak scale from a small cosmological constant · Framework · 0.83
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Agrawal et al. [ref] (ABDS) explored the plausible range of the weak scale for pocket universes within the multiverse already in 1998.
Radiative natural supersymmetry emergent from the string landscape · The ABDS window · 0.98
Discussion
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