This section includes limits on on-shell production of gravitons in collider and astrophysical processes. Bounds quoted are on $\mathit R$, the assumed common radius of the flat extra dimensions, for $\delta $ = 2 extra dimensions. Studies often quote bounds in terms of derived parameter; experiments are actually sensitive to the masses of the KK gravitons: $\mathit m_{\vec n}$ = $\vert \vec n\vert /\mathit R$. See the Review on “Extra Dimensions” for details. Bounds are given in $\mu $m for $\delta $ = 2.

VALUE ($\mu {\mathrm {m}}$) CL% DOCUMENT ID TECN  COMMENT $\bf{<3.8}$ 95 1 AAD 2021 F ATLS ${{\mathit p}}$ ${{\mathit p}}$ $\rightarrow$ ${{\mathit j}}{{\mathit G}}$ $\bf{<0.00016}$ 95 2 HANNESTAD 2003 Neutron star heating • • We do not use the following data for averages, fits, limits, etc. • • $<56$ 95 3 SIRUNYAN 2021 A CMS ${{\mathit p}}$ ${{\mathit p}}$ $\rightarrow$ ${{\mathit Z}}{{\mathit G}}$ $<4.1$ 95 4 TUMASYAN 2021 D CMS ${{\mathit p}}$ ${{\mathit p}}$ $\rightarrow$ ${{\mathit j}}{{\mathit G}}$ 5 SIRUNYAN 2017 AQ CMS ${{\mathit p}}$ ${{\mathit p}}$ $\rightarrow$ ${{\mathit \gamma}}{{\mathit G}}$ $<90$ 95 6 AABOUD 2016 F ATLS ${{\mathit p}}$ ${{\mathit p}}$ $\rightarrow$ ${{\mathit \gamma}}{{\mathit G}}$ 7 KHACHATRYAN 2016 N CMS ${{\mathit p}}$ ${{\mathit p}}$ $\rightarrow$ ${{\mathit \gamma}}{{\mathit G}}$ 8 AAD 2015 CS ATLS ${{\mathit p}}$ ${{\mathit p}}$ $\rightarrow$ ${{\mathit \gamma}}{{\mathit G}}$ $<127$ 95 9 AAD 2013 C ATLS ${{\mathit p}}$ ${{\mathit p}}$ $\rightarrow$ ${{\mathit \gamma}}{{\mathit G}}$ $<34.4$ 95 10 AAD 2013 D ATLS ${{\mathit p}}$ ${{\mathit p}}$ $\rightarrow$ ${{\mathit j}}{{\mathit j}}$ $<0.0087$ 95 11 AJELLO 2012 FLAT Neutron star ${{\mathit \gamma}}$ sources $<245$ 95 12 AALTONEN 2008 AC CDF ${{\mathit p}}$ ${{\overline{\mathit p}}}$ $\rightarrow$ ${{\mathit \gamma}}{{\mathit G}}$ , ${{\mathit j}}{{\mathit G}}$ $<615$ 95 13 ABAZOV 2008 S D0 ${{\mathit p}}$ ${{\overline{\mathit p}}}$ $\rightarrow$ ${{\mathit \gamma}}{{\mathit G}}$ $<0.916$ 95 14 DAS 2008 Supernova cooling $<350$ 95 15 ABULENCIA,A 2006 CDF ${{\mathit p}}$ ${{\overline{\mathit p}}}$ $\rightarrow$ ${{\mathit j}}{{\mathit G}}$ $<270$ 95 16 ABDALLAH 2005 B DLPH ${{\mathit e}^{+}}$ ${{\mathit e}^{-}}$ $\rightarrow$ ${{\mathit \gamma}}{{\mathit G}}$ $<210$ 95 17 ACHARD 2004 E L3 ${{\mathit e}^{+}}$ ${{\mathit e}^{-}}$ $\rightarrow$ ${{\mathit \gamma}}{{\mathit G}}$ $<480$ 95 18 ACOSTA 2004 C CDF ${{\overline{\mathit p}}}$ ${{\mathit p}}$ $\rightarrow$ ${{\mathit j}}{{\mathit G}}$ $<0.00038$ 95 19 CASSE 2004 Neutron star ${{\mathit \gamma}}$ sources $<610$ 95 20 ABAZOV 2003 D0 ${{\overline{\mathit p}}}$ ${{\mathit p}}$ $\rightarrow$ ${{\mathit j}}{{\mathit G}}$ $<0.96$ 95 21 HANNESTAD 2003 Supernova cooling $<0.096$ 95 22 HANNESTAD 2003 Diffuse ${{\mathit \gamma}}$ background $<0.051$ 95 23 HANNESTAD 2003 Neutron star ${{\mathit \gamma}}$ sources $<300$ 95 24 HEISTER 2003 C ALEP ${{\mathit e}^{+}}$ ${{\mathit e}^{-}}$ $\rightarrow$ ${{\mathit \gamma}}{{\mathit G}}$ 25 FAIRBAIRN 2001 Cosmology $<0.66$ 95 26 HANHART 2001 Supernova cooling 27 CASSISI 2000 Red giants $<1300$ 95 28 ACCIARRI 1999 S L3 ${{\mathit e}^{+}}$ ${{\mathit e}^{-}}$ $\rightarrow$ ${{\mathit Z}}{{\mathit G}}$ 1  AAD 2021F search for ${{\mathit p}}$ ${{\mathit p}}$ $\rightarrow$ ${{\mathit j}}{{\mathit G}}$ , using 139 fb${}^{-1}$ of data at $\sqrt {s }$ = 13 TeV to place lower limits on ${{\mathit M}_{{D}}}$ for two to six extra dimensions (see their Table X), from which this bound on ${{\mathit R}}$ is derived. This limit supersedes that in AABOUD 2018I. 2  HANNESTAD 2003 obtain a limit on $\mathit R$ from the heating of old neutron stars by the surrounding cloud of trapped KK gravitons. Limits for all $\delta {}\leq{}$7 are given in their Tables$~$V and VI. These limits supersede those in HANNESTAD 2002 . 3  SIRUNYAN 2021A search for ${{\mathit p}}$ ${{\mathit p}}$ $\rightarrow$ ${{\mathit Z}}{{\mathit G}}$ , using 137 fb${}^{-1}$ of data at $\sqrt {s }$ = 13 TeV to place lower limits on ${{\mathit M}_{{D}}}$ for two to seven extra dimensions (see their Figure 12), from which this bound on ${{\mathit R}}$ is derived. These limits supersede those obtained in SIRUNYAN 2018BV. 4  TUMASYAN 2021D search for ${{\mathit p}}$ ${{\mathit p}}$ $\rightarrow$ ${{\mathit j}}{{\mathit G}}$ , using 137 fb${}^{-1}$ of data at $\sqrt {s }$ = 13 TeV to place lower limits on ${{\mathit M}_{{D}}}$ for two to seven extra dimensions (see their Table 3), from which this bound on ${{\mathit R}}$ is derived. This limit supersedes that in SIRUNYAN 2018S. 5  SIRUNYAN 2017AQ search for ${{\mathit p}}$ ${{\mathit p}}$ $\rightarrow$ ${{\mathit \gamma}}{{\mathit G}}$ , using 12.9 fb${}^{-1}$ of data at $\sqrt {s }$ = 13 TeV to place limits on ${{\mathit M}_{{D}}}$ for three to six extra dimensions (see their Table 3). 6  AABOUD 2016F search for ${{\mathit p}}$ ${{\mathit p}}$ $\rightarrow$ ${{\mathit \gamma}}{{\mathit G}}$ , using 3.2 fb${}^{-1}$ of data at $\sqrt {s }$ = 13 TeV to place limits on ${{\mathit M}_{{D}}}$ for two to six extra dimensions (see their Figure 9), from which this bound on ${{\mathit R}}$ is derived. 7  KHACHATRYAN 2016N search for ${{\mathit p}}$ ${{\mathit p}}$ $\rightarrow$ ${{\mathit \gamma}}{{\mathit G}}$ , using 19.6 fb${}^{-1}$ of data at $\sqrt {s }$ = 8 TeV to place limits on ${{\mathit M}_{{D}}}$ for three to six extra dimensions (see their Table 5). 8  AAD 2015CS search for ${{\mathit p}}$ ${{\mathit p}}$ $\rightarrow$ ${{\mathit \gamma}}{{\mathit G}}$ , using 20.3 fb${}^{-1}$ of data at $\sqrt {s }$ = 8 TeV to place lower limits on ${{\mathit M}_{{D}}}$ for two to six extra dimensions (see their Fig. 18). 9  AAD 2013C search for ${{\mathit p}}$ ${{\mathit p}}$ $\rightarrow$ ${{\mathit \gamma}}{{\mathit G}}$ , using 4.6 fb${}^{-1}$ of data at $\sqrt {s }$ = 7 TeV to place bounds on ${{\mathit M}_{{D}}}$ for two to six extra dimensions, from which this bound on ${{\mathit R}}$ is derived. 10  AAD 2013D search for the dijet decay of quantum black holes in 4.8 fb${}^{-1}$ of data produced in ${{\mathit p}}{{\mathit p}}$ collisions at $\sqrt {s }$ = 7 TeV to place bounds on ${{\mathit M}_{{D}}}$ for two to seven extra dimensions, from which these bounds on ${{\mathit R}}$ are derived. Limits on ${{\mathit M}_{{D}}}$ for all $\delta $ ${}\leq{}$ 7 are given in their Table 3. 11  AJELLO 2012 obtain a limit on ${{\mathit R}}$ from the gamma-ray emission of point ${{\mathit \gamma}}$ sources that arise from the photon decay of KK gravitons which are gravitationally bound around neutron stars. Limits for all ${{\mathit \delta}}$ ${}\leq{}$ 7 are given in their Table 7. 12  AALTONEN 2008AC search for ${{\mathit p}}$ ${{\overline{\mathit p}}}$ $\rightarrow$ ${{\mathit \gamma}}{{\mathit G}}$ and ${{\mathit p}}$ ${{\overline{\mathit p}}}$ $\rightarrow$ ${{\mathit j}}{{\mathit G}}$ at $\sqrt {s }$ = 1.96 TeV with 2.0 fb${}^{-1}$ and 1.1 fb${}^{-1}$ respectively, in order to place bounds on the fundamental scale and size of the extra dimensions. See their Table III for limits on all $\delta {}\leq{}$ 6. 13  ABAZOV 2008S search for ${{\mathit p}}$ ${{\overline{\mathit p}}}$ $\rightarrow$ ${{\mathit \gamma}}{{\mathit G}}$ , using 1 fb${}^{-1}$ of data at $\sqrt {s }$ = 1.96 TeV to place bounds on ${{\mathit M}_{{D}}}$ for two to eight extra dimensions, from which these bounds on $\mathit R$ are derived. See their paper for intermediate values of $\delta $. 14  DAS 2008 obtain a limit on $\mathit R$ from Kaluza-Klein graviton cooling of SN1987A due to plasmon-plasmon annihilation. 15  ABULENCIA,A 2006 search for ${{\mathit p}}$ ${{\overline{\mathit p}}}$ $\rightarrow$ ${{\mathit j}}{{\mathit G}}$ using 368 pb${}^{-1}$ of data at $\sqrt {s }$ = 1.96 TeV. See their Table II for bounds for all $\delta $ ${}\leq{}$ 6. 16  ABDALLAH 2005B search for ${{\mathit e}^{+}}$ ${{\mathit e}^{-}}$ $\rightarrow$ ${{\mathit \gamma}}{{\mathit G}}$ at $\sqrt {s }$ = $180 - 209$~GeV to place bounds on the size of extra dimensions and the fundamental scale. Limits for all $\delta $ ${}\leq{}$ 6 are given in their Table~6. These limits supersede those in ABREU 2000Z. 17  ACHARD 2004E search for ${{\mathit e}^{+}}$ ${{\mathit e}^{-}}$ $\rightarrow$ ${{\mathit \gamma}}{{\mathit G}}$ at $\sqrt {s }$ = $189 - 209$~GeV to place bounds on the size of extra dimensions and the fundamental scale. See their Table~8 for limits with $\delta $ ${}\leq{}$ 8. These limits supersede those in ACCIARRI 1999R. 18  ACOSTA 2004C search for ${{\overline{\mathit p}}}$ ${{\mathit p}}$ $\rightarrow$ ${{\mathit j}}{{\mathit G}}$ at $\sqrt {s }$ = 1.8~TeV to place bounds on the size of extra dimensions and the fundamental scale. See their paper for bounds on $\delta $~=~4,~6. 19  CASSE 2004 obtain a limit on $\mathit R$ from the gamma-ray emission of point ${{\mathit \gamma}}$ sources that arises from the photon decay of gravitons around newly born neutron stars, applying the technique of HANNESTAD 2003 to neutron stars in the galactic bulge. Limits for all $\delta {}\leq{}$7 are given in their Table~I. 20  ABAZOV 2003 search for ${{\mathit p}}$ ${{\overline{\mathit p}}}$ $\rightarrow$ ${{\mathit j}}{{\mathit G}}$ at $\sqrt {\mathit s }$=1.8 TeV to place bounds on $\mathit M_{\mathit D}$ for 2 to 7 extra dimensions, from which these bounds on $\mathit R$ are derived. See their paper for bounds on intermediate values of $\delta $. We quote results without the approximate NLO scaling introduced in the paper. 21  HANNESTAD 2003 obtain a limit on $\mathit R$ from graviton cooling of supernova SN1987a. Limits for all $\delta {}\leq{}$7 are given in their Tables$~$V and VI. 22  HANNESTAD 2003 obtain a limit on $\mathit R$ from gravitons emitted in supernovae and which subsequently decay, contaminating the diffuse cosmic$~{{\mathit \gamma}}$ background. Limits for all $\delta {}\leq{}$7 are given in their Tables$~$V and VI. These limits supersede those in HANNESTAD 2002 . 23  HANNESTAD 2003 obtain a limit on $\mathit R$ from gravitons emitted in two recent supernovae and which subsequently decay, creating point$~{{\mathit \gamma}}$ sources. Limits for all $\delta {}\leq{}$7 are given in their Tables$~$V and VI. These limits are corrected in the published erratum. 24  HEISTER 2003C use the process ${{\mathit e}^{+}}$ ${{\mathit e}^{-}}$ $\rightarrow$ ${{\mathit \gamma}}{{\mathit G}}$ at $\sqrt {\mathit s }$ = $189 - 209$ GeV to place bounds on the size of extra dimensions and the scale of gravity. See their Table$~$4 for limits with $\delta {}\leq{}$6 for derived limits on $\mathit M_{\mathit D}$. 25  FAIRBAIRN 2001 obtains bounds on $\mathit R$ from over production of KK gravitons in the early universe. Bounds are quoted in paper in terms of fundamental scale of gravity. Bounds depend strongly on temperature of QCD phase transition and range from $\mathit R<0.13~\mu $m to $0.001~\mu $m for $\delta $=2; bounds for $\delta $=3,4 can be derived from Table$~$1 in the paper. 26  HANHART 2001 obtain bounds on $\mathit R$ from limits on graviton cooling of supernova SN$~$1987a using numerical simulations of proto-neutron star neutrino emission. 27  CASSISI 2000 obtain rough bounds on $\mathit M_{\mathit D}$ (and thus $\mathit R$) from red giant cooling for $\delta $=2,3. See their paper for details. 28  ACCIARRI 1999S search for ${{\mathit e}^{+}}$ ${{\mathit e}^{-}}$ $\rightarrow$ ${{\mathit Z}}{{\mathit G}}$ at $\sqrt {\mathit s }$=189 GeV. Limits on the gravity scale are found in their Table$~$2, for $\delta {}\leq{}$4.

References:

AAD 2021F PR D103 112006 Search for new phenomena in events with an energetic jet and missing transverse momentum in $pp$ collisions at $\sqrt {s}$ =13 TeV with the ATLAS detector SIRUNYAN 2021A EPJ C81 13 Search for dark matter produced in association with a leptonically decaying Z boson in proton-proton collisions at $\sqrt{s} =$ 13 TeV Also EPJ C81 333 (errat.) Search for dark matter produced in association with a leptonically decaying Z boson in proton-proton collisions at $\sqrt{s} =$ 13 TeV TUMASYAN 2021D JHEP 2111 153 SIRUNYAN 2017AQ JHEP 1710 073 Search for New Physics in the Monophoton Final State in Proton-Proton Collisions at $\sqrt {s }$ = 13 TeV AABOUD 2016F JHEP 1606 059 Search for New Phenomena in Events with a Photon and Missing Transverse Momentum in ${{\mathit p}}{{\mathit p}}$ Collisions at $\sqrt {s }$ = 13 TeV with the ATLAS Detector KHACHATRYAN 2016N PL B755 102 Search for New Phenomena in Monophoton Final States in Proton-Proton Collisions at $\sqrt {s }$ = 8 TeV AAD 2015CS PR D91 012008 Search for New Phenomena in Events with a Photon and Missing Transverse Momentum in ${{\mathit p}}{{\mathit p}}$ Collisions at $\sqrt {s }$ = 8 TeV with the ATLAS Detector Also PR D92 059903 (errat.) Erratum to AAD 2015CS: Search for New Phenomena in Events with a Photon and Missing Transverse Momentum in ${{\mathit p}}{{\mathit p}}$ Collisions at $\sqrt {s }$ = 8 TeV with the ATLAS Detector AAD 2013C PRL 110 011802 Search for Dark Matter Candidates and Large Extra Dimensions in Events with a Photon and Missing Transverse Momentum in ${{\mathit p}}{{\mathit p}}$ Collision Data at $\sqrt {s }$ = 7 TeV with the ATLAS Detector AAD 2013D JHEP 1301 029 ATLAS Search for New Phenomena in Dijet Mass and Angular Distributions using ${{\mathit p}}{{\mathit p}}$ Collisions at $\sqrt {s }$ = 7 TeV AJELLO 2012 JCAP 1202 012 Limits on Large Extra Dimensions Based on Observations of Neutron Stars with the Fermi-LAT AALTONEN 2008AC PRL 101 181602 Search for Large Extra Dimensions in Final States Containing one Photon or Jet and Large Missing Transverse Energy Produced in ${{\mathit p}}{{\overline{\mathit p}}}$ Collisions at $\sqrt {s }$ = 1.96$~$TeV ABAZOV 2008S PRL 101 011601 Search for Large Extra Dimensions via Single Photon Plus Missing Energy Final States at $\sqrt {s }$ = 1.96 TeV DAS 2008 PR D78 063011 Plasmon Annihilation into Kaluza-Klein Gravitons: New Astrophysical Constraints on Large Extra Dimensions? ABULENCIA,A 2006 PRL 97 171802 Search for Large Extra Dimensions in the Production of Jets and Missing Transverse Energy in ${{\mathit p}}{{\overline{\mathit p}}}$ Collisions at $\sqrt {s }$ = 1.96 TeV ABDALLAH 2005B EPJ C38 395 Photon Events with Missing Energy in ${{\mathit e}^{+}}{{\mathit e}^{-}}$ Collisions at $\sqrt {s }$ = 130 to 209 GeV ACHARD 2004E PL B587 16 Single Photon and Multiphoton Events with Missing Energy in ${{\mathit e}^{+}}{{\mathit e}^{-}}$ Collisions at LEP ACOSTA 2004C PRL 92 121802 Search for Kaluza-Klein Graviton Emission in ${{\mathit p}}{{\overline{\mathit p}}}$ Collisions at $\sqrt {s }$ = 1.8 TeV using the Missing Energy Signature CASSE 2004 PRL 92 111102 ${{\mathit \gamma}}$ -Rays from the Galactic Bugle and Large Extra Dimensions ABAZOV 2003 PRL 90 251802 Search for Large Extra Dimensions in the Monojet + $\not E_T$ Channel at ${D0}$ Detector HANNESTAD 2003 PR D67 125008 Supernova and Neutron Star Limits on Large Extra Dimensions Reexamined Also PR D69 029901(errat.) Erratum: HANNESTAD 2003 Supernova and Neutron-Star Limits on Large Extra Dimensions Reexamined HEISTER 2003C EPJ C28 1 Single Photon and Multiphoton Production in ${{\mathit e}^{+}}{{\mathit e}^{-}}$ Collisions at $\sqrt {s }$ up to 209 GeV FAIRBAIRN 2001 PL B508 335 Cosmological Constraints on Large Extra Dimensions HANHART 2001 PL B509 1 The Likelihood of GODs' Existence: Improving the SN1987a Constraint on the Size of Large Compact Dimensions CASSISI 2000 PL B481 323 Stellar Evolution and Large Extra Dimensions ACCIARRI 1999S PL B470 281 Search for Extra Dimensions in Boson and Fermion Pair Production in ${{\mathit e}^{+}}$ ${{\mathit e}^{-}}$ Interactions at LEP