Natural Tuning: Towards A Proof of Concept

TL;DR

The paper proposes natural tuning as a non-Wilsonian alternative to traditional naturalness, focusing on asymptotic fragility rather than UV fixed points. It introduces gravitational dressing, where any UV-complete QFT S-matrix $S(p_i)$ is mapped to $oxed{\hat{S}(p_i)=oxed{ ext{D}}(p_i)S(p_i)}$ with $oxed{ ext{D}}(p_i)=e^{irac{ extell^2}{4}\sum_{i<j}p_i*p_j}$, and shows that this dressing preserves crossing while ensuring unitarity through a factorized form $oxed{ ext{D}}(p_i)=e^{irac{ extell^2}{4}\sum_{a<a'}k_a*k_{a'}}e^{irac{ extell^2}{4}\sum_{b<b'}q_b*q_b'}$, effectively yielding $oxed{ ext{S}}=USU$ for some unitary $U$. The framework is grounded in two-dimensional gravitating systems with asymptotic fragility (no UV fixed point) and is shown to reproduce perturbative amplitudes in EFTs at low energies and to remain consistent at one loop, even for non-integrable interactions. The results suggest a concrete realization of natural tuning, with testable LHC signatures such as additional unprotected scalars, and prompt further exploration of UV completions, cosmological constant implications, and possible extensions to higher dimensions. Overall, the work provides a self-consistent S-matrix-based demonstration that natural tuning can be realized without fine-tuning in a Wilsonian sense, by embracing a non-Wilsonian UV completion governed by gravitational dressing.

Abstract

The cosmological constant problem and the absence of new natural physics at the electroweak scale, if confirmed by the LHC, may either indicate that the nature is fine-tuned or that a refined notion of naturalness is required. We construct a family of toy UV complete quantum theories providing a proof of concept for the second possibility. Low energy physics is described by a tuned effective field theory, which exhibits relevant interactions not protected by any symmetries and separated by an arbitrary large mass gap from the new "gravitational" physics, represented by a set of irrelevant operators. Nevertheless, the only available language to describe dynamics at all energy scales does not require any fine-tuning. The interesting novel feature of this construction is that UV physics is not described by a fixed point, but rather exhibits asymptotic fragility. Observation of additional unprotected scalars at the LHC would be a smoking gun for this scenario. Natural tuning also favors TeV scale unification.

Figures (6)

• Figure 1: Fine-tuning in the Standard Model embedded in a non-supersymmetric $SU(5)$ GUT.
• Figure 2: (a) Null in and out momenta at the holographic boundary of $M_2$ for integrable relativistic shock waves. (b) Generalization to time-like momenta and non-integrable case.
• Figure 3: Minkowskian momenta are naturally cyclically ordered in $2d$. The dressing factor (\ref{['Ddress']}) factorizes for an arbitrary decomposition of the external momenta into two clusters.
• Figure 4: The physical sheet is defined using the physical two-particle thresholds for all pairs $p_i,p_j$.
• Figure 5: The discontinuity of the tree-level $3\to 3$ diagram is dictated by the amplitude of the disconnected diagrams and is proportional to $\mathbf{1}$ in the momentum space.