^{1}

^{3}.

The standard model of elementary particles (SM) suffers from various problems, such as power-law ultraviolet (UV) sensitivity, exclusion of general relativity (GR), and absence of a dark matter candidate. The LHC experiments, according to which the TeV domain appears to be empty of new particles, started sidelining TeV-scale SUSY and other known cures of the UV sensitivity. In search for a remedy, in this work, it is revealed that affine curvature can emerge in a way restoring gauge symmetries explicitly broken by the UV cutoff. This emergent curvature cures the UV sensitivity and incorporates GR as symmetry-restoring emergent gravity (

The SM, a spontaneously broken renormalizable quantum field theory (QFT) of the strong and electroweak interactions, has shown good agreement with all the experiments performed so far [

Quantum correction to the Higgs boson mass, quadratically sensitive to UV boundary [

The GR must be incorporated into the SM [

curvature arises as a manifestation of the elastication of the flat spacetime,

GR emerges along with the restoration of gauge invariance,

gravitational constant necessitates an NP sector,

SM + NP possesses exact Fermi-Bose balance and the induced gravitational constant is suggestive of a trans-Planckian SUSY breaking [

the UV boundary can be fixed, in principle, by suppression of the cosmological constant (with no immediate solution for the cosmological constant problem [

so that there arise a number of descriptive signatures with which symmergence can be probed via decisive experiments (Section

higher-curvature terms are predicted to be absent. This excludes, for instance,

NP scalars with trans-GZK [

symmergence does not necessitate any SM-NP coupling for it to work. This property, not found in the known SM completions (SUSY, extra dimensions, compositeness and others [

it is predicted that the heavier the NP the larger the luminosity needed to discover it. This distinctive feature can be probed at present [

It is also predicted that the right-handed neutrinos [

it turns out that the SM couplings (gauge and nongauge) must run as if NP is absent if the NP lies sufficiently above the electroweak scale. This feature, which rests on the fact that symmergence leaves behind only logarithmic sensitivity to the UV boundary [

symmergence accommodates both ebony (having only gravitational interactions with the SM) [

it is predicted that, in the SM, nonminimal Higgs-curvature coupling equals

The work is concluded in Section

The NP needed to complete the SM, roughly sketched in (

The Higgs mass-squared

In accordance with (

The power-law quantum corrections in (

Quantum corrections and problems they give cause to. The coefficients

| | | | Problem | |
---|---|---|---|---|---|

| | 0 | 0 | | |

| |||||

| | | 0 | 0 | BHP |

| |||||

| | 0 | | 0 | BHP |

| |||||

| | 0 | | 0 | BHP |

| |||||

| 0 | 0 | | 0 | CCB |

| |||||

| 0 | 0 | | 0 | CCB |

The SM is a renormalizable QFT. If so, why is it not possible to include

It is now time to ascertain how curvature can be incorporated into the flat spacetime effective SM in (

Gravity is incorporated into classical field theories in flat spacetime by first mapping the flat metric

The gauge part

It proves useful to start with the obvious identity [

Is there a simple way of killing

The contradiction can be avoided by introducing, for instance, a more general map [

The CCB attains a solution only if

Under the solution (

The flat spacetime is rigid. It remains flat independent of how big the energy it contains is. The quartic quantum correction

In search for a proper mechanism, it proves useful to start with the observation that, in general, the integral

The meaning of relation (

The emergence of the affine curvature. The metrical action

The emergence mechanism here is similar, at least in philosophy, to that of Sakharov [

The results of Sections

Having set up the symmergence principle, it is now time to determine under what conditions GR arises correctly. It will be found below that it cannot arise without a nontrivial NP sector.

Affine gravity, as in

MAG may or may not lead to GR. It depends on couplings of the affine connection. Indeed, solving the equation of motion for affine connection to integrate it out leads to the Levi-Civita connection of the metric plus possible contributions from other fields, including the affine curvature [

Under (

The problem is to determine how MAG can reduce to GR. This reduction is decided by the dynamics of the affine connection. And part of the total SM + NP action that governs the dynamics

The equation of motion for

The GR gets properly incorporated if Planck scale is generated correctly. In view of (

The NP sector, needed for induction of the gravitational scale as in (

This section collects various predictions and experimentally testable features from both the gravity and NP sectors. They can play a crucial role in revealing and testing the physics of symmergence.

Nullification of the gauge part in (

The total vacuum energy at one loop

Symmergent gravity and the NP it necessitates agree with all the existing bounds thanks to their prediction that gravity is Einstein (as in [

Symmergence leads uniquely to Einstein gravity. It excludes all higher-curvature terms. This is an important result since extinction of higher-curvature terms is impossible to guarantee in a theory in which general covariance is the only symmetry. To this end, the question of why it is not

The nonminimal Higgs-curvature coupling [

Obviously,

The nonminimal

Symmergence leaves behind only logarithmic sensitivity to the UV boundary. This remnant sensitivity, with all gauge symmetries restored, can naturally be interpreted in the language of dimensional regularization. Indeed, the formal correspondence [

Emergence of the gravitational scale does not necessitate any SM-NP coupling. The SM and NP do not have to interact. The NP sector can therefore come in three different kinds:

in which the couplings

The NP sector, whose subsectors are depicted in Figure

The three kinds of the NP sectors.

The Higgs part of (

The allowed and disallowed regions according to the electroweak stability bound in (

The Planck-suppressed

The NP scalar

One immediate implication of the bound (

One way to see if the underlying model is symmergent or not is to measure scalar and vector masses and then determine if their production cross sections comply with the seesawic couplings in (

Basic search channels for NP scalars ((a) and (b)) and NP vectors ((c) and (d)).

Symmergence has testable implications also for right-handed neutrinos. Indeed, if the bound (

Symmergence has candidates for missing matter in both the ebony and dark NP sectors. The question of which one is preferred by nature can be answered only by observations (on, for instance, less-baryonic galaxies like cosmic seagull [

The dark NP can be probed directly [

Needless to repeat, symmergence propounds a novel framework in which notorious problems of the SM can be consistently addressed. It incorporates GR into the SM with a seesawic NP sector and can be probed conclusively via various experimental tests ranging from collider searches to dark matter. Highlighted in Figure

Fundamental aspects of the symmergent GR plus seesawic NP setup.

The mechanism can be furthered in various aspects. First, the trans-Planckian SUSY, its breaking mechanism, and its possible role in solving the CCP need be explored properly. Second, the MAG with quadratic curvature terms (

No data were used to support this study.

The author declares that they have no conflicts of interest.

This work is supported in part by TÜBİTAK grants 115F212 and 118F387. The author is grateful to Hemza Azri, Dieter van den Bleeken, and Tekin Dereli for fruitful discussions on especially the emergent MAG. He thanks S. Vagnozzi and H. Terazawa for useful e-mail and mail exchanges.