This section includes limits on the cut-off mass scale, $\mathit M_{\mathit TT}$, of dimension-8 operators from KK graviton exchange in models of large extra dimensions. Ambiguities in the UV-divergent summation are absorbed into the parameter $\lambda $, which is taken to be $\lambda $ = $\pm{}$1 in the following analyses. Bounds for $\lambda $ = $-1$ are shown in parenthesis after the bound for $\lambda $ = $+1$, if appropriate. Different papers use slightly different definitions of the mass scale. The definition used here is related to another popular convention by $\mathit M{}^{4}_{TT}$ = (2/${{\mathit \pi}}$) $\Lambda {}^{4}_{T}$, as discussed in the above Review on “Extra Dimensions.”

VALUE (TeV) CL% DOCUMENT ID TECN  COMMENT $\bf{> 9.02}$ 95 1 SIRUNYAN 2018 DD CMS ${{\mathit p}}$ ${{\mathit p}}$ $\rightarrow$ dijet, ang. distrib. $ \bf{>20.6} $ $\bf{(>15.7)}$ 95 2 GIUDICE 2003 RVUE Dim-6 operators • • We do not use the following data for averages, fits, limits, etc. • • $> 6.7$ 95 3 SIRUNYAN 2021 N CMS ${{\mathit p}}$ ${{\mathit p}}$ $\rightarrow$ ${{\mathit e}^{+}}{{\mathit e}^{-}}$ , ${{\mathit \mu}^{+}}{{\mathit \mu}^{-}}$ $> 6.9$ 95 4 SIRUNYAN 2019 AC CMS ${{\mathit p}}$ ${{\mathit p}}$ $\rightarrow$ ${{\mathit e}^{+}}{{\mathit e}^{-}}$ , ${{\mathit \mu}^{+}}{{\mathit \mu}^{-}}$ , ${{\mathit \gamma}}{{\mathit \gamma}}$ $ > 7.0 $ ($>$5.6) 95 5 SIRUNYAN 2018 DU CMS ${{\mathit p}}$ ${{\mathit p}}$ $\rightarrow$ ${{\mathit \gamma}}{{\mathit \gamma}}$ $> 6.5$ 95 6 AABOUD 2017 AP ATLS ${{\mathit p}}$ ${{\mathit p}}$ $\rightarrow$ ${{\mathit \gamma}}{{\mathit \gamma}}$ $> 3.8$ 95 7 AAD 2014 BE ATLS ${{\mathit p}}$ ${{\mathit p}}$ $\rightarrow$ ${{\mathit e}^{+}}{{\mathit e}^{-}}$ , ${{\mathit \mu}^{+}}{{\mathit \mu}^{-}}$ $> 3.2$ 95 8 AAD 2013 E ATLS ${{\mathit p}}$ ${{\mathit p}}$ $\rightarrow$ ${{\mathit e}^{+}}{{\mathit e}^{-}}$ , ${{\mathit \mu}^{+}}{{\mathit \mu}^{-}}$ , ${{\mathit \gamma}}{{\mathit \gamma}}$ 9 BAAK 2012 RVUE Electroweak $ > 0.90 $ ($>$0.92) 95 10 AARON 2011 C H1 ${{\mathit e}^{\pm}}$ ${{\mathit p}}$ $\rightarrow$ ${{\mathit e}^{\pm}}{{\mathit X}}$ $> 1.48$ 95 11 ABAZOV 2009 AE D0 ${{\mathit p}}$ ${{\overline{\mathit p}}}$ $\rightarrow$ dijet, ang. distrib. $> 1.45$ 95 12 ABAZOV 2009 D D0 ${{\mathit p}}$ ${{\overline{\mathit p}}}$ $\rightarrow$ ${{\mathit e}^{+}}{{\mathit e}^{-}}$ , ${{\mathit \gamma}}{{\mathit \gamma}}$ $ > 1.1 $ ($>$ 1.0) 95 13 SCHAEL 2007 A ALEP ${{\mathit e}^{+}}$ ${{\mathit e}^{-}}$ $\rightarrow$ ${{\mathit e}^{+}}{{\mathit e}^{-}}$ $ > 0.898 $ ($>$ 0.998) 95 14 ABDALLAH 2006 C DLPH ${{\mathit e}^{+}}$ ${{\mathit e}^{-}}$ $\rightarrow$ ${{\mathit \ell}^{+}}{{\mathit \ell}^{-}}$ $ > 0.853 $ ($>$ 0.939) 95 15 GERDES 2006 ${{\mathit p}}$ ${{\overline{\mathit p}}}$ $\rightarrow$ ${{\mathit e}^{+}}{{\mathit e}^{-}}$ , ${{\mathit \gamma}}{{\mathit \gamma}}$ $ > 0.96 $ ($>0.93$) 95 16 ABAZOV 2005 V D0 ${{\mathit p}}$ ${{\overline{\mathit p}}}$ $\rightarrow$ ${{\mathit \mu}^{+}}{{\mathit \mu}^{-}}$ $ >0.78 $ ($>0.79$) 95 17 CHEKANOV 2004 B ZEUS ${{\mathit e}^{\pm}}$ ${{\mathit p}}$ $\rightarrow$ ${{\mathit e}^{\pm}}{{\mathit X}}$ $ >0.805 $ ($>0.956$) 95 18 ABBIENDI 2003 D OPAL ${{\mathit e}^{+}}$ ${{\mathit e}^{-}}$ $\rightarrow$ ${{\mathit \gamma}}{{\mathit \gamma}}$ $ >0.7 $ ($>0.7$) 95 19 ACHARD 2003 D L3 ${{\mathit e}^{+}}$ ${{\mathit e}^{-}}$ $\rightarrow$ ${{\mathit Z}}{{\mathit Z}}$ $ >0.82 $ ($>0.78$) 95 20 ADLOFF 2003 H1 ${{\mathit e}^{\pm}}$ ${{\mathit p}}$ $\rightarrow$ ${{\mathit e}^{\pm}}{{\mathit X}}$ $ >1.28 $ ($>1.25$) 95 21 GIUDICE 2003 RVUE $ >0.80 $ ($>0.85$) 95 22 HEISTER 2003 C ALEP ${{\mathit e}^{+}}$ ${{\mathit e}^{-}}$ $\rightarrow$ ${{\mathit \gamma}}{{\mathit \gamma}}$ $ >0.84 $ ($>0.99$) 95 23 ACHARD 2002 D L3 ${{\mathit e}^{+}}$ ${{\mathit e}^{-}}$ $\rightarrow$ ${{\mathit \gamma}}{{\mathit \gamma}}$ $ >1.2 $ ($>1.1$) 95 24 ABBOTT 2001 D0 ${{\mathit p}}$ ${{\overline{\mathit p}}}$ $\rightarrow$ ${{\mathit e}^{+}}{{\mathit e}^{-}}$ , ${{\mathit \gamma}}{{\mathit \gamma}}$ $ >0.60 $ ($>0.63$) 95 25 ABBIENDI 2000 R OPAL ${{\mathit e}^{+}}$ ${{\mathit e}^{-}}$ $\rightarrow$ ${{\mathit \mu}^{+}}{{\mathit \mu}^{-}}$ $ >0.63 $ ($>0.50$) 95 25 ABBIENDI 2000 R OPAL ${{\mathit e}^{+}}$ ${{\mathit e}^{-}}$ $\rightarrow$ ${{\mathit \tau}^{+}}{{\mathit \tau}^{-}}$ $ >0.68 $ ($>0.61$) 95 25 ABBIENDI 2000 R OPAL ${{\mathit e}^{+}}$ ${{\mathit e}^{-}}$ $\rightarrow$ ${{\mathit \mu}^{+}}{{\mathit \mu}^{-}}$ , ${{\mathit \tau}^{+}}{{\mathit \tau}^{-}}$ 26 ABREU 2000 A DLPH ${{\mathit e}^{+}}$ ${{\mathit e}^{-}}$ $\rightarrow$ ${{\mathit \gamma}}{{\mathit \gamma}}$ $ >0.680 $ ($>0.542$) 95 27 ABREU 2000 S DLPH ${{\mathit e}^{+}}$ ${{\mathit e}^{-}}$ $\rightarrow$ ${{\mathit \mu}^{+}}{{\mathit \mu}^{-}}$ , ${{\mathit \tau}^{+}}{{\mathit \tau}^{-}}$ $\text{>15 - 28}$ 99.7 28 CHANG 2000 B RVUE Electroweak $>0.98$ 95 29 CHEUNG 2000 RVUE ${{\mathit e}^{+}}$ ${{\mathit e}^{-}}$ $\rightarrow$ ${{\mathit \gamma}}{{\mathit \gamma}}$ $\text{>0.29 - 0.38}$ 95 30 GRAESSER 2000 RVUE ($\mathit g–2)_{\mu }$ $\text{>0.50 - 1.1}$ 95 31 HAN 2000 RVUE Electroweak $ >2.0 $ ($>2.0$) 95 32 MATHEWS 2000 RVUE ${{\overline{\mathit p}}}$ ${{\mathit p}}$ $\rightarrow$ ${{\mathit j}}{{\mathit j}}$ $ >1.0 $ ($>1.1$) 95 33 MELE 2000 RVUE ${{\mathit e}^{+}}$ ${{\mathit e}^{-}}$ $\rightarrow$ ${{\mathit V}}{{\mathit V}}$ 34 ABBIENDI 1999 P OPAL 35 ACCIARRI 1999 M L3 36 ACCIARRI 1999 S L3 $ >1.412 $ ($>1.077$) 95 37 BOURILKOV 1999 ${{\mathit e}^{+}}$ ${{\mathit e}^{-}}$ $\rightarrow$ ${{\mathit e}^{+}}{{\mathit e}^{-}}$ 1  SIRUNYAN 2018DD use dijet angular distributions in 35.9 fb${}^{-1}$ of data from ${{\mathit p}}{{\mathit p}}$ collisions at $\sqrt {s }$ = 13 TeV to place a lower bound on ${{\mathit \Lambda}_{{T}}}$, here converted to ${{\mathit M}_{{TT}}}$. This updates the results of SIRUNYAN 2017F. 2  GIUDICE 2003 place bounds on $\Lambda _{6}$, the coefficient of the gravitationally-induced dimension-6 operator (2$\pi \lambda /\Lambda {}^{2}_{6})(\sum{{\overline{\mathit f}}}\gamma _{\mu }\gamma {}^{5}\mathit f)(\sum{{\overline{\mathit f}}}\gamma {}^{\mu }\gamma {}^{5}\mathit f$), using data from a variety of experiments. Results are quoted for $\lambda =\pm1$ and are independent of $\delta $. 3  SIRUNYAN 2021N use 137 (140) fb${}^{-1}$ of data from ${{\mathit p}}{{\mathit p}}$ collisions at $\sqrt {s }$ = 13 TeV in the dielectron (dimuon) channels to place a lower limit on ${{\mathit \Lambda}_{{T}}}$, here converted to ${{\mathit M}_{{TT}}}$. Bounds on individual channels can be found in their Table 7. 4  SIRUNYAN 2019AC use 35.9 (36.3) fb${}^{-1}$ of data from ${{\mathit p}}{{\mathit p}}$ collisions at $\sqrt {s }$ = 13 TeV in the dielectron (dimuon) channels to place a lower limit on ${{\mathit \Lambda}_{{T}}}$, here converted to ${{\mathit M}_{{TT}}}$. The dielectron and dimuon channels are combined with previous results in the diphoton channel to set the best limit. Bounds on individual channels and different priors can be found in their Table 2. This updates the results in KHACHATRYAN 2015AE. 5  SIRUNYAN 2018DU use 35.9 fb${}^{-1}$ of data from ${{\mathit p}}{{\mathit p}}$ collisions at $\sqrt {s }$ = 13 TeV to place lower limits on ${{\mathit M}_{{TT}}}$ (equivalent to their ${{\mathit M}_{{S}}}$). This updates the results of CHATRCHYAN 2012R. 6  AABOUD 2017AP use 36.7 fb${}^{-1}$ of data from ${{\mathit p}}{{\mathit p}}$ collisions at $\sqrt {s }$ = 13 TeV to place lower limits on ${{\mathit M}_{{TT}}}$ (equivalent to their ${{\mathit M}_{{S}}}$). This updates the results of AAD 2013AS. 7  AAD 2014BE use 20 fb${}^{-1}$ of data from ${{\mathit p}}{{\mathit p}}$ collisions at $\sqrt {s }$ = 8 TeV in the dilepton channel to place lower limits on ${{\mathit M}_{{TT}}}$ (equivalent to their ${{\mathit M}_{{S}}}$). 8  AAD 2013E use 4.9 and 5.0 fb${}^{-1}$ of data from ${{\mathit p}}{{\mathit p}}$ collisions at $\sqrt {s }$ = 7 TeV in the dielectron and dimuon channels, respectively, to place lower limits on ${{\mathit M}_{{TT}}}$ (equivalent to their ${{\mathit M}_{{S}}}$). The dielectron and dimuon channels are combined with previous results in the diphoton channel to set the best limit. Bounds on individual channels and different priors can be found in their Table VIII. 9  BAAK 2012 use electroweak precision observables to place bounds on the ratio ${{\mathit \Lambda}_{{T}}}/{{\mathit M}_{{D}}}$ as a function of ${{\mathit M}_{{D}}}$. See their Fig. 22 for constraints with a Higgs mass of 120 GeV. 10  AARON 2011C search for deviations in the differential cross section of ${{\mathit e}^{\pm}}$ ${{\mathit p}}$ $\rightarrow$ ${{\mathit e}^{\pm}}{{\mathit X}}$ in 446 pb${}^{-1}$ of data taken at $\sqrt {s }$ = 301 and 319 GeV to place a bound on ${{\mathit M}_{{TT}}}$. 11  ABAZOV 2009AE use dijet angular distributions in 0.7 fb${}^{-1}$ of data from ${{\mathit p}}{{\overline{\mathit p}}}$ collisions at $\sqrt {s }$ = 1.96 TeV to place lower bounds on $\Lambda _{T}$ (equivalent to their $\mathit M_{S}$), here converted to $\mathit M_{TT}$. 12  ABAZOV 2009D use 1.05 fb${}^{-1}$ of data from ${{\mathit p}}{{\overline{\mathit p}}}$ collisions at $\sqrt {s }$ = 1.96 TeV to place lower bounds on ${{\mathit \Lambda}_{{T}}}$ (equivalent to their ${{\mathit M}_{{s}}}$), here converted to ${{\mathit M}_{{TT}}}$. 13  SCHAEL 2007A use ${{\mathit e}^{+}}{{\mathit e}^{-}}$ collisions at $\sqrt {s }$ = $189 - 209$ GeV to place lower limits on ${{\mathit \Lambda}_{{T}}}$, here converted to limits on ${{\mathit M}_{{TT}}}$. 14  ABDALLAH 2006C use ${{\mathit e}^{+}}{{\mathit e}^{-}}$ collisions at $\sqrt {s }\sim{}130 - 207$ GeV to place lower limits on ${{\mathit M}_{{TT}}}$, which is equivalent to their definition of ${{\mathit M}_{{s}}}$. Bound shown includes all possible final state leptons, ${{\mathit \ell}}$ = ${{\mathit e}}$, ${{\mathit \mu}}$, ${{\mathit \tau}}$. Bounds on individual leptonic final states can be found in their Table 31. 15  GERDES 2006 use 100 to 110 pb${}^{-1}$ of data from ${{\mathit p}}{{\overline{\mathit p}}}$ collisions at $\sqrt {s }$ = 1.8 TeV, as recorded by the CDF Collaboration during Run I of the Tevatron. Bound shown includes a ${{\mathit K}}$-factor of 1.3. Bounds on individual ${{\mathit e}^{+}}{{\mathit e}^{-}}$ and ${{\mathit \gamma}}{{\mathit \gamma}}$ final states are found in their Table I. 16  ABAZOV 2005V use 246 pb${}^{-1}$ of data from ${{\mathit p}}{{\overline{\mathit p}}}$ collisions at $\sqrt {s }$ = 1.96 TeV to search for deviations in the differential cross section to ${{\mathit \mu}^{+}}{{\mathit \mu}^{-}}$ from graviton exchange. 17  CHEKANOV 2004B search for deviations in the differential cross section of ${{\mathit e}^{\pm}}$ ${{\mathit p}}$ $\rightarrow$ ${{\mathit e}^{\pm}}{{\mathit X}}$ with 130~$\mathit pb{}^{-1}$ of combined data and ${{\mathit Q}^{2}}$ values up to 40,000~GeV${}^{2}$ to place a bound on ${{\mathit M}}_{TT}$. 18  ABBIENDI 2003D use ${{\mathit e}^{+}}{{\mathit e}^{-}}$ collisions at $\sqrt {\mathit s }=181 - 209$ GeV to place bounds on the ultraviolet scale $\mathit M_{\mathit TT}$, which is equivalent to their definition of $\mathit M_{\mathit s}$. 19  ACHARD 2003D look for deviations in the cross section for ${{\mathit e}^{+}}$ ${{\mathit e}^{-}}$ $\rightarrow$ ${{\mathit Z}}{{\mathit Z}}$ from $\sqrt {\mathit s }$ = $200 - 209$ GeV to place a bound on $\mathit M_{\mathit TT}$. 20  ADLOFF 2003 search for deviations in the differential cross section of ${{\mathit e}^{\pm}}$ ${{\mathit p}}$ $\rightarrow$ ${{\mathit e}^{\pm}}{{\mathit X}}$ at $\sqrt {\mathit s }$=301 and 319 GeV to place bounds on $\mathit M_{\mathit TT}$. 21  GIUDICE 2003 review existing experimental bounds on $\mathit M_{\mathit TT}$ and derive a combined limit. 22  HEISTER 2003C use ${{\mathit e}^{+}}{{\mathit e}^{-}}$ collisions at $\sqrt {\mathit s }$= $189 - 209$ GeV to place bounds on the scale of dim-8 gravitational interactions. Their $\mathit M{}^{\pm{}}_{\mathit s}$ is equivalent to our $\mathit M_{\mathit TT}$ with $\lambda =\pm1$. 23  ACHARD 2002 search for $\mathit s$-channel graviton exchange effects in ${{\mathit e}^{+}}$ ${{\mathit e}^{-}}$ $\rightarrow$ ${{\mathit \gamma}}{{\mathit \gamma}}$ at $\mathit E_{{\mathrm {cm}}}$ = $192 - 209$ GeV. 24  ABBOTT 2001 search for variations in differential cross sections to ${{\mathit e}^{+}}{{\mathit e}^{-}}$ and ${{\mathit \gamma}}{{\mathit \gamma}}$ final states at the Tevatron. 25  ABBIENDI 2000R uses ${{\mathit e}^{+}}{{\mathit e}^{-}}$ collisions at $\sqrt {\mathit s }$= 189 GeV. 26  ABREU 2000A search for $\mathit s$-channel graviton exchange effects in ${{\mathit e}^{+}}$ ${{\mathit e}^{-}}$ $\rightarrow$ ${{\mathit \gamma}}{{\mathit \gamma}}$ at $\mathit E_{{\mathrm {cm}}}$= $189 - 202$ GeV. 27  ABREU 2000S uses ${{\mathit e}^{+}}{{\mathit e}^{-}}$ collisions at $\sqrt {\mathit s }$=183 and 189 GeV. Bounds on ${{\mathit \mu}}$ and ${{\mathit \tau}}$ individual final states given in paper. 28  CHANG 2000B derive 3$\sigma $ limit on $\mathit M_{\mathit TT}$ of (28,19,15) TeV for $\delta $=(2,4,6) respectively assuming the presence of a torsional coupling in the gravitational action. Highly model dependent. 29  CHEUNG 2000 obtains limits from anomalous diphoton production at OPAL due to graviton exchange. Original limit for $\delta $=4. However, unknown $\mathit UV$ theory renders $\delta ~$dependence unreliable. Original paper works in HLZ convention. 30  GRAESSER 2000 obtains a bound from graviton contributions to $\mathit g–$2 of the muon through loops of 0.29 TeV for $\delta $=2 and 0.38 TeV for $\delta $=4,6. Limits scale as $\lambda {}^{1/2}$. However calculational scheme not well-defined without specification of high-scale theory. See the ``Extra Dimensions Review.'' 31  HAN 2000 calculates corrections to gauge boson self-energies from KK graviton loops and constrain them using $\mathit S$ and $\mathit T$. Bounds on $\mathit M_{\mathit TT}$ range from 0.5 TeV ($\delta $=6) to 1.1 TeV ($\delta $=2); see text. Limits have strong dependence, $\lambda {}^{\delta +2}$, on unknown $\lambda $ coefficient. 32  MATHEWS 2000 search for evidence of graviton exchange in CDF and ${D0}$ dijet production data. See their Table$~$2 for slightly stronger $\delta $-dependent bounds. Limits expressed in terms of ${{\widetilde{\mathit M}}}{}^{4}_{\mathit S}$ = $\mathit M{}^{4}_{\mathit TT}$/8. 33  MELE 2000 obtains bound from KK graviton contributions to ${{\mathit e}^{+}}$ ${{\mathit e}^{-}}$ $\rightarrow$ ${{\mathit V}}{{\mathit V}}$ (${{\mathit V}}={{\mathit \gamma}},{{\mathit W}},{{\mathit Z}}$) at LEP. Authors use Hewett conventions. 34  ABBIENDI 1999P search for $\mathit s$-channel graviton exchange effects in ${{\mathit e}^{+}}$ ${{\mathit e}^{-}}$ $\rightarrow$ ${{\mathit \gamma}}{{\mathit \gamma}}$ at $\mathit E_{{\mathrm {cm}}}$=189 GeV. The limits $\mathit G_{+}>660$ GeV and $\mathit G_{−}>634$ GeV are obtained from combined $\mathit E_{{\mathrm {cm}}}$=183 and 189 GeV data, where $\mathit G_{\pm{}}$ is a scale related to the fundamental gravity scale. 35  ACCIARRI 1999M search for the reaction ${{\mathit e}^{+}}$ ${{\mathit e}^{-}}$ $\rightarrow$ ${{\mathit \gamma}}{{\mathit G}}$ and $\mathit s$-channel graviton exchange effects in ${{\mathit e}^{+}}$ ${{\mathit e}^{-}}$ $\rightarrow$ ${{\mathit \gamma}}{{\mathit \gamma}}$ , ${{\mathit W}^{+}}{{\mathit W}^{-}}$ , ${{\mathit Z}}{{\mathit Z}}$ , ${{\mathit e}^{+}}{{\mathit e}^{-}}$ , ${{\mathit \mu}^{+}}{{\mathit \mu}^{-}}$ , ${{\mathit \tau}^{+}}{{\mathit \tau}^{-}}$ , ${{\mathit q}}{{\overline{\mathit q}}}$ at $\mathit E_{{\mathrm {cm}}}$=183 GeV. Limits on the gravity scale are listed in their Tables$~$1 and 2. 36  search for the reaction ${{\mathit e}^{+}}$ ${{\mathit e}^{-}}$ $\rightarrow$ ${{\mathit Z}}{{\mathit G}}$ and $\mathit s$-channel graviton exchange effects in ${{\mathit e}^{+}}$ ${{\mathit e}^{-}}$ $\rightarrow$ ${{\mathit \gamma}}{{\mathit \gamma}}$ , ${{\mathit W}^{+}}{{\mathit W}^{-}}$ , ${{\mathit Z}}{{\mathit Z}}$ , ${{\mathit e}^{+}}{{\mathit e}^{-}}$ , ${{\mathit \mu}^{+}}{{\mathit \mu}^{-}}$ , ${{\mathit \tau}^{+}}{{\mathit \tau}^{-}}$ , ${{\mathit q}}{{\overline{\mathit q}}}$ at $\mathit E_{{\mathrm {cm}}}$=189 GeV. Limits on the gravity scale are listed in their Tables$~$1 and 2. 37  BOURILKOV 1999 performs global analysis of LEP data on ${{\mathit e}^{+}}{{\mathit e}^{-}}$ collisions at $\sqrt {\mathit s }$=183 and 189 GeV. Bound is on $\Lambda _{\mathit T}$.

References:

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