Graviton paper submission

This page is specifically created for addressing the comments provided by reviewers for the paper "Collider constraints on massive gravitons coupling to photons" https://arxiv.org/abs/2306.15558

PLB comments

1. Include explicitly the denomination "hidden gravitons", "dark gravitons" and "slim spin-2 particles" in the introduction, since these are different names received by these particles in present literature. For instance, the authors can read the article "LHC constraints on hidden gravitons" JHEP 01 (2022) 129, e-Print: 2108.00930 [hep-ph] to have an overall perspective.

We have reorganized a bit the introduction contents, as well as added a few more references, to address this point. The following text has been moved from the Discussion Section:

Massive spin-2 particles are typically predicted by BSM models proposed to explain the very large gap between the electroweak (10^2 GeV) and Planck (10^19 GeV) scales (“hierarchy problem”) based on the existence on new compact spatial dimensions. Graviton-like particles appear as Kaluza–Klein (KK) excitations of these extra dimensions in the Randall–Sundrum (RS) [73], and Arkani-Hamed–Dimopoulos–Dvali (ADD) [74] approaches (with model differences arising mostly from the number of extra dimensions considered, and their compactification).

and has been integrated as a new paragraph in the Introduction, after "of the underlying quantum theory of GR by employing an EFT approach [45]." (page 3):

New massive spin-2 degrees of freedom have been also shown to arise in different modifications of gravity. Extradimensional theories of gravity, like the Arkani-Hamed–Dimopoulos–Dvali (ADD) [X] and Randall-Sundrum (RS) [X] BSM models, proposed to explain the very large gap between the electroweak (10^2 GeV) and Planck (10^19 GeV) scales (“hierarchy problem”), generically predict massive tensor particles appearing as Kaluza–Klein (KK) excitations of these extra dimensions, either with a continuum mass spectrum, or as a number of widely separated resonances. Models with an extra dimension at the micron scale, predict also KK modes called "dark gravitons", that are a natural dark matter candidate [https://inspirehep.net/literature/2154234]. In addition, graviton-like particles, sometimes dubbed "hidden gravitons" [https://inspirehep.net/literature/1897474], naturally appear in the context of bimetric theories of gravity [https://inspirehep.net/literature/894626].

2. Rewriting the introduction: It should be emphasized in the introduction that the authors are studying additional and hypothetical spin-2 particles.

We have extended the introduction as explained above, to address this point.

3. Add graphical representations of the exclusion limits in terms of the "dark Planck scale", i.e. the effective scale that suppresses the interactions of the new spin-2 particle and plays the analogous role of the Planck scale for the standard graviton. It would be very nice if the authors can plot their constraints with previous ones (provided in the aformentioned reference).

We thank the referee for the suggestion.In page 3, we have changed "M_Pl being the Planck mass" to be "M_Pl being the (dark/hidden) Planck mass". However, we prefer to just keep our current upper limits plots on the photon-graviton coupling, as they are now in terms of generic (universal coupling) and "photophilic" graviton scenarios, whose "inverse" can be just interpreted as providing the Lambda scale limits.

4. Further Discussion on experimental constraints and sensitivity : A discussion of the present constraints of other LHC analyses or non-collider analises for detecting hidden gravitons, particularly in different mass regions, would provide more context for the readers.

The focus of the paper, as stressed in its title itself, is on massive gravitons produced via two-photon fusion at accelerators. To extend a bit more the scope towards the lower mass range, we have added more information in the introduction, as follows:

spin-2 states at colliders is still at an early stage, notwithstanding some exploratory works [23, 26, 32, 33, 35].

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spin-2 states at accelerators is still at an early stage, notwithstanding some exploratory works at collider [23, 26, 32, 33, 35], and fixed-target via the Primakoff process [https://inspirehep.net/literature/2159454, https://inspirehep.net/literature/2658416], facilities.

5. Add information in the appendix : For instance, I think particularly illuminating the branching ratios provided at Figure 2 and Table 1. It may be useful for interesting readers if the authors can complete this information by providing the complete decay formulas, for example, in an appendix

Details on the partial decays widths formulas can be found in the reference provided for the universal-coupling scenario [http://arxiv.org/abs/1605.09359, coauthored by one of the authors of this paper], and we prefer not to repeat the information here.

In addition we have dropped (previous) ref. [42] which was not relevant in this context, and added a reference to https://inspirehep.net/literature/2639544 when discussing violation of unitary, above Eq. (14).

solve this perturbative unitarity problem [48].

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solve this perturbative unitarity problem [48,https://inspirehep.net/literature/2639544].

JHEP comments

1. Rewrting the introduction: The discussion about motivation on page 3 is a bit unclear or even misleading, as it seems to imply that the graviton could potentially be re- placed by a massive strongly coupled state. The parameter space probed in the present paper is completely ruled out, for instance see [42]. The motivation why people study massive "gravitons" nevertheless is rather because they appear as resonances in theories such as Randall-Sundrum or other extra-dimensional scenarios, as well as mesons in composite Higgs models (as mentioned in fact in the discussion, section 4), where they are present on top of the standard massless (or nearly massless) weakly coupled gravi- ton. I would recommend the authors rewrite this discussion to avoid any confusion.

To address the concern of the referee, we have reorganized a bit, as well as added a few more references, in the introduction contents. The following text has been moved from the Discussion Section:

Massive spin-2 particles are typically predicted by BSM models proposed to explain the very large gap between the electroweak (10^2 GeV) and Planck (10^19 GeV) scales (“hierarchy problem”) based on the existence on new compact spatial dimensions. Graviton-like particles appear as Kaluza–Klein (KK) excitations of these extra dimensions in the Randall–Sundrum (RS) [73], and Arkani-Hamed–Dimopoulos–Dvali (ADD) [74] approaches (with model differences arising mostly from the number of extra dimensions considered, and their compactification).

and has been integrated as a new paragraph in the Introduction, after "of the underlying quantum theory of GR by employing an EFT approach [45]." (page 3):

New massive spin-2 degrees of freedom have been also shown to arise in different modifications of gravity. Extradimensional theories of gravity, like the Arkani-Hamed–Dimopoulos–Dvali (ADD) [X] and Randall-Sundrum (RS) [X] BSM models, proposed to explain the very large gap between the electroweak (10^2 GeV) and Planck (10^19 GeV) scales (“hierarchy problem”), generically predict massive tensor particles appearing as Kaluza–Klein (KK) excitations of these extra dimensions, either with a continuum mass spectrum, or as a number of widely separated resonances. Models with an extra dimension at the micron scale, predict also KK modes called "dark gravitons", that are a natural dark matter candidate [https://inspirehep.net/literature/2154234]. In addition, graviton-like particles, sometimes dubbed "hidden gravitons" [https://inspirehep.net/literature/1897474], naturally appear in the context of bimetric theories of gravity [https://inspirehep.net/literature/894626].

In addition, we have added a couple of references in the introduction, to mention similar fixed-target searches at somewhat lower masses, as follows:

spin-2 states at colliders is still at an early stage, notwithstanding some exploratory works [23, 26, 32, 33, 35].

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spin-2 states at colliders is still at an early stage, notwithstanding some exploratory works at collider [23, 26, 32, 33, 35] and fixed-target [https://inspirehep.net/literature/2159454, https://inspirehep.net/literature/2658416] facilities.

2. Including the limits from inclusive production of massive gravitons in the plots, at least in the case of a universal coupling to SM fields, which is a common scenario studied, for instance, in the context of the Randall-Sundrum model

We thank the referee for the suggestion, but including the collider limits from the inclusive production of massive gravitons in the universal-coupling scenario (with 7--8 potential decay modes shown in Fig. 2) would require recasting all current (lack of excesses above the SM backgrounds in the) measurements of inclusive production of dileptons, diphotons, dijets, dibosons, top-pairs, MET (neutrinos),.. measured by the ATLAS and CMS collaborations in p-p collisions at 7, 8, 13 TeV, within the RS model. Such a plot would be certainly informative and interesting, but goes well beyond the scope of this paper, which focuses on the photon-graviton coupling case via exclusive production. Such an effort should be done in the context of ATLAS+CMS BSM limits combinations, properly taking into account the experimental correlations, and avoiding double-counting among exclusive and inclusive searches.