Just standard model and gravity, up to high energies? An update

[mitchell porter]

A recurring topic in particle physics, is the possibility of a "desert" above the electroweak scale: no new physics (new particles, new forces) until the grand unification scale or the Planck scale. It's important to remember that the Higgs boson mass was correctly predicted three years in advance, in 2009, by assuming such a desert.

Here we have a new perspective on the issue:

https://arxiv.org/abs/2104.09682
Is the Standard Model in the Swampland?
Katsuki Aoki, Tran Quang Loc, Toshifumi Noumi, Junsei Tokuda
[Submitted on 19 Apr 2021]

Obviously no, leading to a necessary condition for quantum gravity. We study compatibility of the Standard Model of particle physics and General Relativity by means of gravitational positivity bounds, which provide a necessary condition for a low-energy gravitational theory to be UV completable within the weakly coupled regime of gravity. In particular, we identify the cutoff scale of the Standard Model coupled to gravity by studying consistency of light-by-light scattering. While the precise value depends on details of the Pomeron effects in QCD, the cutoff scale reads 10¹⁶ GeV if the single-Pomeron exchange picture works well up to this scale. We also demonstrate that the cutoff scale is lowered to 10¹³ GeV if we consider the electroweak theory without the QCD sector.

This paper belongs to a recent genre which seeks theoretical (rather than empirical) bounds on the possible values of coefficients in quantum field theory, by making assumptions about the properties of an unknown deeper theory. In this case: "gravitational positivity bounds, which provide a necessary condition for a low-energy gravitational theory to be UV completable within the weakly coupled regime of gravity".

Their conclusion is that new physics must enter between 10¹⁵-10¹⁷ GeV. This is around the usual scale of grand unification theory, and not too far from the usual Planck scale (10¹⁹ GeV).

Some considerations bearing upon the possibility of a desert:

First, a reminder of why grand unification is attractive: a single generation of the standard model neatly fits into a single multiplet of SU(5) or SO(10); and the running gauge couplings converge on similar values, around these high scales (as if they were all descended from a single coupling).

However, grand unification has the potential to spoil that prediction of the Higgs boson mass, or anything else which would attribute significance to the criticality of the electroweak vacuum. (One may see here an attempt, by a coauthor of that Higgs prediction, to have grand unification without the extra particles that spoil everything.)

Another problem is the tuning of the Higgs coupling that seems to be necessary to keep its mass light. Even just adding gravity is supposed to cause a tuning problem (since virtual black holes should be adding superheavy corrections to the observed mass), though perhaps this can be avoided in the right kind of gravitational theory.

Perhaps the main question I have regarding this new paper, is whether these familiar high scales have an independent origin in their argument. If they do, then their argument may tell us something new about what kind of theory naturally has a desert, namely, a theory which "saturates" their bounds, i.e. comes as close as possible to violating the positivity bounds.

 

[Demystifier]

I have an issue with the first sentence of the Abstract. Why is it obvious that the Standard Model is not in the swampland? Does this claim assume that string theory is correct?

 

[stevendaryl]

I have an issue with the first sentence of the Abstract. Why is it obvious that the Standard Model is not in the swampland? Does this claim assume that string theory is correct?

As I understand it (which is based on 5 minutes' worth of Googling), the issue is not whether string theory is correct, but whether it is falsified by the standard model. Because there are so many possible configurations of the universe that are consistent with string theory, it's difficult to say that anything absolutely rules out string theory. Even if none of the predictions of string theory are observed, it's always possible that we just haven't probed things at a high enough energy level. So if it were absolutely true that everything is consistent with string theory, then that wouldn't make string theory correct, it would make it unfalsifiable.

 

[ohwilleke]

The paper's conclusion better articulates what it is trying to show and claims to show (emphasis and additional paragraph breaks mine) in a manner that somewhat contradicts the "objectionable" language of the abstract:

In this letter, we identified the cutoff scale of the Standard Model coupled to gravity as 10¹⁶GeV, applying gravitational positivity bounds to the light-by-light scattering (γγ → γγ). This means that quantum gravity requires a new physics below 10¹⁶GeV, otherwise the Standard Model falls into the Swampland.

As we mentioned, weakly coupled charged particles up to spin-1 do not help to push up the cutoff scale, suggesting that beyond SM physics (described within non-gravitational QFT) at E >> GeV would be irrelevant to our analysis. In fact, the crucial point is that GR is not UV complete: B ⁽²⁾ _GR(Λ) converges to a negative constant rather than zero as Λ → ∞, violating the bound (8) at UV.

A natural expectation would be thus that quantum gravity shows up around or below the obtained cutoff scale to reconcile the gravitational positivity. It is suggestive that this scale is close to the Grand Unification scale and the typical string scale.

Nevertheless, it is worth again emphasizing that our result ΛSM ∼ 10¹⁶GeV is obtained from the consistency of the scattering amplitude based on the well established physics, the Standard Model and General Relativity7 . Also, it is interesting that the Pomeron physics is crucial to understanding the cutoff scale of the Standard Model, even though our result is qualitatively insensitive to its details.

We also studied the electroweak theory without the QCD sector, whose cutoff scale is found to be 10¹³GeV. Although the electroweak sector alone is not a realistic theory in nature, this consideration may provide insights into the Swampland Program. The gravitational positivity bound (8) would conclude that arbitrary hierarchy of physics cannot be realized in quantum gravity. In this context, it is suggestive to rewrite our result as

M_W/M_Pl = sqrt(2880απ/11) m_e/ Λ_EW , (25)

which means that the W boson mass and therefore the electroweak scale in the Planck unit are correlated with the ratio of the electron mass me and the maximum cutoff Λ_EW. In particular, the electroweak scale has to be well below the Planck scale. This could offer a new solution to the hierarchy problem. It would be interesting to study this possibility further based on string theory construction. Such a study could also be useful for better understanding of the Higgs mechanism in string theory, especially the mechanism based on D-brane recombination.

7 Note that we have assumed a weakly coupled UV completion where the graviton is Reggeized below the Planck scale. Our precise statement is if the SM coupled to GR is UV completed at a scale below the Planck scale, the scale should be less than 10¹⁶GeV. It would be interesting to generalize our argument to strongly coupled UV completion of gravity. For this, one would need to first carefully reconsider the standard assumptions of positivity bounds such as locality and unitarity because superPlanckian physics such as black hole creation cannot be ignored.

Recall also, of course, that "swampland" refers to: "effective low-energy physical theories which are not compatible with string theory, in contrast to the so-called "string theory landscape" of compatible theories. In other words, the swampland is the set of consistent-looking theories with no consistent ultraviolet completion in string theory."

 

[Cyroos]

It was believed that every quantum gravity theory must not permit global symmetries (discrete and continuous). Even if from the standpoint of powerful theories of the lower dimension this would be very unexpected, string theory meets this restriction: The Noethers theorem allows a preserved current by a global symmetry of the world sheet, which results in the release of a massive string excitement. Therefore, we face a gauge symmetry in the goal space.