Advances in High Energy Physics

Volume 2019, Article ID 4652048, 15 pages

https://doi.org/10.1155/2019/4652048

## Symmergent Gravity, Seesawic New Physics, and Their Experimental Signatures

Department of Physics, İzmir Institute of Technology, TR35430 İzmir, Turkey

Correspondence should be addressed to Durmuş Demir; rt.ude.hcetzi.scisyhp@rimed

Received 5 May 2019; Revised 13 July 2019; Accepted 24 July 2019; Published 22 August 2019

Academic Editor: Michele Arzano

Copyright © 2019 Durmuş Demir. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. The publication of this article was funded by SCOAP^{3}.

#### Abstract

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 (*symmergent gravity*, in brief) if a new physics sector (NP) exists to generate the Planck scale and if SM+NP is Fermi-Bose balanced. This setup, carrying fingerprints of trans-Planckian SUSY, predicts that gravity is Einstein (no higher-curvature terms), cosmic/gamma rays can originate from heavy NP scalars, and the UV cutoff might take right value to suppress the cosmological constant (alleviating fine-tuning with SUSY). The NP does not have to couple to the SM. In fact, NP-SM coupling can take any value from zero to if the SM is not to jump from to the NP scale . The zero coupling, certifying an undetectable NP, agrees with all the collider and dark matter bounds at present. The* seesawic* bound , directly verifiable at colliders, implies that (i) dark matter must have a mass , (ii) Higgs-curvature coupling must be , (iii) the SM RGEs must remain nearly as in the SM, and (iv) right-handed neutrinos must have a mass . These signatures serve as a concise testbed for symmergence.

#### 1. Introduction

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 [1, 2]. Its parameters have all been fixed experimentally. This does, however, not mean that it is a complete theory. Indeed, it is plagued by enigmatic problems like destabilizing UV sensitivities [3–7], exclusion of gravity [8], and absence of a dark matter candidate [9], which are impossible to address without new physics beyond the SM (BSM). Schematically, in which the general relativity (GR) structure of gravity is revealed by various experiments [10] and observations [11]. The NP is under way at colliders [2] and dark matter searches [12, 13].

Quantum correction to the Higgs boson mass, quadratically sensitive to UV boundary [3–7], exceeds the Higgs boson mass just above the electroweak scale. This means that the SM must stop working below the TeV scale. It does not stop, however. Indeed, the LHC has confirmed the SM [2] is up to multi-TeV energies. This contradiction between the SM loops and the LHC can be eliminated only if the NP in (1) improves the SM in a way without introducing any new interacting particles. The present work approaches this puzzling requirement via proof-by-contradiction; that is, it begins by assuming that the NP is absent (Sections 2 and 3) and, at a later stage, it ends up with NP through the consistency of the induced gravitational constant (Section 4).

The GR must be incorporated into the SM [10, 11]. This has been attempted with classical GR [14–16] (despite [17]), quantized GR [18, 19] (despite [20–23]), and emergent GR [24, 25] (see also [26–33]). The present work incorporates curvature into the SM effective action in flat spacetime (Section 2) by building on the nascent ideas proposed in [34–36] and subsequent developments voiced in [37–40]. It incorporates gravity in a way restoring the gauge symmetries broken by the UV cutoff [41, 42] (Section 3.2), in a way elasticating the rigid flat spacetime (Section 3.3), and in a way involving a nontrivial NP sector to induce the gravitational constant (Section 4). This gauge symmetry-restoring emergent gravity,* symmergent gravity* [38–40] in brief, sets up a framework (Section 4) in which(1)curvature arises as a manifestation of the elastication of the flat spacetime,(2)GR emerges along with the restoration of gauge invariance,(3)gravitational constant necessitates an NP sector,(4)SM + NP possesses exact Fermi-Bose balance and the induced gravitational constant is suggestive of a trans-Planckian SUSY breaking [43–45], and(5)the UV boundary can be fixed, in principle, by suppression of the cosmological constant (with no immediate solution for the cosmological constant problem [46, 47] though)

so that there arise a number of descriptive signatures with which symmergence can be probed via decisive experiments (Section 5):(1)higher-curvature terms are predicted to be absent. This excludes, for instance, gravity [48] and agrees well with the current cosmological data [11].(2)NP scalars with trans-GZK [49, 50] VEVs are predicted to give cause to cosmic rays [51] (digluon) as well as gamma rays [52] (diphoton) via certain Planck-suppressed higher-dimension operators.(3)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 [53, 54]) for which a sizable SM-NP coupling is essential, provides a rationale for stabilizing the electroweak scale against the SM-NP mixing. Indeed, if the SM-NP coupling goes like , then the Higgs boson mass remains within the allowed limits. This seesawic (seesaw-wise) structure leads to various testable features:(a)it is predicted that the heavier the NP the larger the luminosity needed to discover it. This distinctive feature can be probed at present [55, 56] and future colliders [57, 58].(b)It is also predicted that the right-handed neutrinos [59] must weigh below a 1000 TeV (see also [60, 61]). This bound can be tested at future colliders [62] if not at the near-future SHiP experiment [63, 64].(c)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 [65, 66], can be tested at present [55, 56] and future colliders [57, 58].(d)symmergence accommodates both ebony (having only gravitational interactions with the SM) [35, 36, 67, 68] and dark (having seesawic couplings to the SM) matters. They both agree with the current bounds. The latter, thermal dark matter, is predicted to weigh below the electroweak scale. This agrees with current limits and can be tested further in future searches [12, 13, 69].(e)it is predicted that, in the SM, nonminimal Higgs-curvature coupling equals at one loop and remains so unless the NP lies near the electroweak scale. This coupling, too small to drive the Higgs inflation [70], can serve as a testbed at collider experiments [71] if not in the astrophysical or cosmological environments.

The work is concluded in Section 6.

#### 2. UV Boundary, Effective SM, and the UV Sensitivity Problems

The NP needed to complete the SM, roughly sketched in (1), can be elucidated only after a complete picture of the SM in regard to its UV boundary and UV sensitivity.

##### 2.1. UV Boundary

The Higgs mass-squared , measured to be at the LHC [72], is overwhelmed by the quantum correction [3–7] in which is the UV boundary of the SM, and is the loop factor. The correction (2), a one-loop SM effect, grows quadratically with and exceeds already at , where lies just above the electroweak scale . This low-lying , which can be changed slightly by incorporating subleading corrections to (2), is a characteristic feature of the SM spectrum and the experimental result . It implies that the SM must stop working at . It does not stop, however. Indeed, the LHC experiments show that the SM continues to hold good up to multi-TeV energies without any new field. This contradictory UV overextension is the problem. There is no clear solution. There is even no clear way to search for a solution. There is, however, a possibility that a mechanism, not necessarily unique, might be constructed via proof-by-contradiction [35, 36, 38], that is, by first and then The first step sets up a UV boundary and reveals SM’s UV sensitivity. The second, on the other hand, uncovers NP via induction of gravity and fixes in terms of the NP scale.

##### 2.2. SM Effective Action

In accordance with (5), integration of the fast modes (fields with energies ) out of the SM spectrum gives an effective action for slow modes (fields with energies ) [73, 74] in which is the flat metric, is the slow Higgs field, are the slow gauge fields (photon, gluon, and ), and finally is the UV-EW gap. The tree-level SM action and the logarithmic corrections both lie below . But, the other three pull the SM off the electroweak scale depending on how large is. They tend to destabilize the SM and it is this destabilization that necessitates a neutralization mechanism. Their Wilson coefficients involve only the ratio [3–7] as the measure of the EW-UV hierarchy.

##### 2.3. UV Sensitivity Problems

The power-law quantum corrections in (9), (10), and (11) give cause to serious destabilization problems. They are tabulated in Table 1. The cosmological constant problem (CCP) [46, 47], caused by , exists only when gravity is present. The big hierarchy problem (BHP) [3–7] (gauge hierarchy problem) refers to quadratic UV sensitivities of the Higgs (from ) and (from ) masses. The electric charge or color breaking (CCB) [41, 42], on the other hand, arises from the photon and the gluon mass terms in (purely quadratic in ). The SM is impossible to make sense in the UV before these problems are satisfactorily resolved.