#### Limits on 1/$\mathit R$ = $\mathit M_{{{\mathit c}} }$

This section includes limits on 1/$\mathit R$ = $\mathit M_{{{\mathit c}} }$, the compactification scale in models with one TeV-sized extra dimension, due to exchange of Standard Model KK excitations. Bounds assume fermions are not in the bulk, unless stated otherwise. See the “Extra Dimensions” review for discussion of model dependence.

VALUE (TeV) CL% DOCUMENT ID TECN  COMMENT
$\bf{> 4.16}$ 95 1
 2012 CC
ATLS ${{\mathit p}}$ ${{\mathit p}}$ $\rightarrow$ ${{\mathit \ell}}{{\overline{\mathit \ell}}}$
$\bf{> 6.1}$ 2
 2004
RVUE Electroweak
• • We do not use the following data for averages, fits, limits, etc. • •
3
 2021
RVUE ${{\mathit p}}$ ${{\mathit p}}$ $\rightarrow$ multijet
4
 2018 AV
ATLS ${{\mathit p}}$ ${{\mathit p}}$ $\rightarrow$ ${{\mathit t}}{{\overline{\mathit t}}}{{\mathit t}}{{\overline{\mathit t}}}$
5
 2018 CE
ATLS ${{\mathit p}}$ ${{\mathit p}}$ $\rightarrow$ ${{\mathit t}}{{\overline{\mathit t}}}{{\mathit t}}{{\overline{\mathit t}}}$
$> 3.8$ 95 6
 2015
RVUE Electroweak
$> 3.40$ 95 7
 2015 T
CMS ${{\mathit p}}$ ${{\mathit p}}$ $\rightarrow$ ${{\mathit \ell}}{{\mathit X}}$
8
 2013 AQ
CMS ${{\mathit p}}$ ${{\mathit p}}$ $\rightarrow$ ${{\mathit \ell}}{{\mathit X}}$
$> 1.38$ 95 9
 2013 W
CMS ${{\mathit p}}$ ${{\mathit p}}$ $\rightarrow$ ${{\mathit \gamma}}{{\mathit \gamma}}$ , $\delta$=6, ${{\mathit M}_{{D}}}$ =5 TeV
$> 0.715$ 95 10
 2013
RVUE ${{\mathit p}}$ ${{\mathit p}}$ $\rightarrow$ ${{\mathit \ell}}{{\overline{\mathit \ell}}}{+}$ ${{\mathit X}}$
$> 1.40$ 95 11
 2012 CP
ATLS ${{\mathit p}}$ ${{\mathit p}}$ $\rightarrow$ ${{\mathit \gamma}}{{\mathit \gamma}}$ , $\delta$=6, ${{\mathit M}_{{D}}}$ =5 TeV
$> 1.23$ 95 12
 2012 X
ATLS ${{\mathit p}}$ ${{\mathit p}}$ $\rightarrow$ ${{\mathit \gamma}}{{\mathit \gamma}}$ , $\delta$=6, ${{\mathit M}_{{D}}}$ =5 TeV
$> 0.26$ 95 13
 2012 M
D0 ${{\mathit p}}$ ${{\overline{\mathit p}}}$ $\rightarrow$ ${{\mathit \mu}}{{\mathit \mu}}$
$> 0.75$ 95 14
 2012
RVUE Electroweak
15
 2012
RVUE Electroweak
$> 0.43$ 95 16
 2012
RVUE ${{\mathit H}}$ $\rightarrow$ ${{\mathit W}}{{\mathit W}}$ , ${{\mathit \gamma}}{{\mathit \gamma}}$
$> 0.729$ 95 17
 2011 F
ATLS ${{\mathit p}}$ ${{\mathit p}}$ $\rightarrow$ ${{\mathit \gamma}}{{\mathit \gamma}}$ , $\delta$=6, ${{\mathit M}_{{D}}}$ =5 TeV
$> 0.961$ 95 18
 2011 X
ATLS ${{\mathit p}}$ ${{\mathit p}}$ $\rightarrow$ ${{\mathit \gamma}}{{\mathit \gamma}}$ , $\delta$=6, ${{\mathit M}_{{D}}}$ =5 TeV
$> 0.477$ 95 19
 2010 P
D0 ${{\mathit p}}$ ${{\overline{\mathit p}}}$ $\rightarrow$ ${{\mathit \gamma}}{{\mathit \gamma}}$ , $\delta$=6, ${{\mathit M}_{{D}}}$ =5 TeV
$> 1.59$ 95 20
 2009 AE
D0 ${{\mathit p}}$ ${{\overline{\mathit p}}}$ $\rightarrow$ dijet, angular dist.
$> 0.6$ 95 21
 2007
RVUE ${{\overline{\mathit B}}}$ $\rightarrow$ ${{\mathit X}_{{s}}}{{\mathit \gamma}}$
$> 0.6$ 90 22
 2006
RVUE Electroweak
$>3.3$ 95 23
 2000
RVUE Electroweak
$\text{>3.3 - 3.8}$ 95 24
 2000
RVUE Electroweak
 1 AAD 2012CC 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 a lower bound on the mass of the lightest KK ${{\mathit Z}}$ /${{\mathit \gamma}}$ boson (equivalent to 1/${{\mathit R}}$ = ${{\mathit M}_{{c}}}$ ). The limit quoted here assumes a flat prior corresponding to when the pure ${{\mathit Z}}$ /${{\mathit \gamma}}$ KK cross section term dominates. See their Section 15 for more details.
 2 BARBIERI 2004 use electroweak precision observables to place a lower bound on the compactification scale 1/$\mathit R$. Both the gauge bosons and the Higgs boson are assumed to propagate in the bulk.
 3 AVNISH 2021 perform a study on the ATLAS collaboration search for multiple jets plus missing transverse energy from ${{\mathit p}}{{\mathit p}}$ collisions at $\sqrt {s }$ = 13 TeV and integrated luminosity of 139 fb${}^{-1}$, to place constraints on the compactification scale and cutoff scale ${{\mathit \Lambda}}$ in universal extra dimension models with Standard Model fields propagating in the bulk.
 4 AABOUD 2018AV use 36.1 fb${}^{-1}$ of data from ${{\mathit p}}{{\mathit p}}$ collisions at $\sqrt {s }$ = 13 TeV in final states with multiple b-jets, to place a lower bound on the compactification scale in a model with two universal extra dimensions. Assuming the radii of the two extra dimensions are equal, a lower limit of 1.8 TeV for the Kaluza-Klein mass is obtained.
 5 AABOUD 2018CE use 36.1 fb${}^{-1}$ of data from ${{\mathit p}}{{\mathit p}}$ collisions at $\sqrt {s }$ = 13 TeV in final states with same-charge leptons and b-jets, to place a lower bound on the compactification scale in a model with two universal extra dimensions. Assuming the radii of the two extra dimensions are equal, a lower limit of 1.45 TeV for the Kaluza-Klein mass is obtained.
 6 ACCOMANDO 2015 use electroweak precision observables to place a lower bound on the compactification scale 1/$\mathit R$. See their Fig. 2 for the bound as a function of sin$\beta$, which parametrizes the VEV contribution from brane and bulk Higgs fields. The quoted value is for the minimum bound which occurs at sin$\beta$ = 0.45.
 7 KHACHATRYAN 2015T use 19.7 fb${}^{-1}$ of data from ${{\mathit p}}{{\mathit p}}$ collisions at $\sqrt {s }$ = 8 TeV to place a lower bound on the compactification scale 1/$\mathit R$.
 8 CHATRCHYAN 2013AQ use 5.0 fb${}^{-1}$ of data from ${{\mathit p}}{{\mathit p}}$ collisions at $\sqrt {s }$ = 7 TeV and a further 3.7 fb${}^{-1}$ of data at $\sqrt {s }$ = 8 TeV to place a lower bound on the compactification scale 1/$\mathit R$, in models with universal extra dimensions and Standard Model fields propagating in the bulk. See their Fig. 5 for the bound as a function of the universal bulk fermion mass parameter ${{\mathit \mu}}$ .
 9 CHATRCHYAN 2013W use diphoton events with large missing transverse momentum in 4.93 fb${}^{-1}$ of data produced from ${{\mathit p}}{{\mathit p}}$ collisions at $\sqrt {s }$ = 7 TeV to place a lower bound on the compactification scale in a universal extra dimension model with gravitational decays. The bound assumes that the cutoff scale ${{\mathit \Lambda}}$ , for the radiative corrections to the Kaluza-Klein masses, satisfies $\Lambda /{{\mathit M}_{{c}}}$ = 20. The model parameters are chosen such that the decay ${{\mathit \gamma}^{*}}$ $\rightarrow$ ${{\mathit G}}{{\mathit \gamma}}$ occurs with an appreciable branching fraction.
 10 EDELHAUSER 2013 use 19.6 and 20.6 fb${}^{-1}$ of data from ${{\mathit p}}{{\mathit p}}$ collisions at $\sqrt {s }$ = 8 TeV analyzed by the CMS Collaboration in the dielectron and dimuon channels, respectively, to place a lower bound on the mass of the second lightest Kaluza-Klein ${{\mathit Z}}$ /${{\mathit \gamma}}$ boson (converted to a limit on 1/${{\mathit R}}$ = ${{\mathit M}_{{c}}}$ ). The bound assumes Standard Model fields propagating in the bulk and that the cutoff scale ${{\mathit \Lambda}}$ , for the radiative corrections to the Kaluza-Klein masses, satisfies $\Lambda /{{\mathit M}_{{c}}}$ = 20.
 11 AAD 2012CP use diphoton events with large missing transverse momentum in 4.8 fb${}^{-1}$ of data produced from ${{\mathit p}}{{\mathit p}}$ collisions at $\sqrt {s }$ = 7 TeV to place a lower bound on the compactification scale in a universal extra dimension model with gravitational decays. The bound assumes that the cutoff scale ${{\mathit \Lambda}}$ , for the radiative corrections to the Kaluza-Klein masses, satisfies $\Lambda /{{\mathit M}_{{c}}}$ = 20. The model parameters are chosen such that the decay ${{\mathit \gamma}^{*}}$ $\rightarrow$ ${{\mathit G}}{{\mathit \gamma}}$ occurs with an appreciable branching fraction.
 12 AAD 2012X use diphoton events with large missing transverse momentum in 1.07 fb${}^{-1}$ of data produced from ${{\mathit p}}{{\mathit p}}$ collisions at $\sqrt {s }$ = 7 TeV to place a lower bound on the compactification scale in a universal extra dimension model with gravitational decays. The bound assumes that the cutoff scale ${{\mathit \Lambda}}$ , for the radiative corrections to the Kaluza-Klein masses, satisfies ${{\mathit \Lambda}}$ /${{\mathit M}_{{c}}}$ = 20. The model parameters are chosen such that the decay ${{\mathit \gamma}^{*}}$ $\rightarrow$ ${{\mathit G}}{{\mathit \gamma}}$ occurs with an appreciable branching fraction.
 13 ABAZOV 2012M use same-sign dimuon events in 7.3 fb${}^{-1}$ of data from ${{\mathit p}}{{\overline{\mathit p}}}$ collisions at $\sqrt {s }$ = 1.96 TeV to place a lower bound on the compactification scale 1/$\mathit R$, in models with universal extra dimensions where all Standard Model fields propagate in the bulk.
 14 BAAK 2012 use electroweak precision observables to place a lower bound on the compactification scale 1/$\mathit R$, in models with universal extra dimensions and Standard Model fields propagating in the bulk. Bound assumes a 125 GeV Higgs mass. See their Fig. 25 for the bound as a function of the Higgs mass.
 15 FLACKE 2012 use electroweak precision observables to place a lower bound on the compactification scale 1/$\mathit R$, in models with universal extra dimensions and Standard Model fields propagating in the bulk. See their Fig. 1 for the bound as a function of the universal bulk fermion mass parameter ${{\mathit \mu}}$ .
 16 NISHIWAKI 2012 use up to 2 fb${}^{-1}$ of data from the ATLAS and CMS experiments that constrains the production cross section of a Higgs-like particle to place a lower bound on the compactification scale 1/$\mathit R$ in universal extra dimension models. The quoted bound assumes Standard Model fields propagating in the bulk and a 125 GeV Higgs mass. See their Fig. 1 for the bound as a function of the Higgs mass.
 17 AAD 2011F use diphoton events with large missing transverse energy in 3.1 pb${}^{-1}$ of data produced from ${{\mathit p}}{{\mathit p}}$ collisions at $\sqrt {s }$ = 7 TeV to place a lower bound on the compactification scale in a universal extra dimension model with gravitational decays. The bound assumes that the cutoff scale ${{\mathit \Lambda}}$ , for the radiative corrections to the Kaluza-Klein masses, satisfies ${{\mathit \Lambda}}$ /M$_{c}$ = 20. The model parameters are chosen such that the decay ${{\mathit \gamma}^{*}}$ $\rightarrow$ ${{\mathit G}}{{\mathit \gamma}}$ occurs with an appreciable branching fraction.
 18 AAD 2011X use diphoton events with large missing transverse energy in 36 pb${}^{-1}$ of data produced from ${{\mathit p}}{{\mathit p}}$ collisions at $\sqrt {s }$ = 7 TeV to place a lower bound on the compactification scale in a universal extra dimension model with gravitational decays. The bound assumes that the cutoff scale ${{\mathit \Lambda}}$ , for the radiative corrections to the Kaluza-Klein masses, satisfies ${{\mathit \Lambda}}$ /${{\mathit M}_{{c}}}$ = 20. The model parameters are chosen such that the decay ${{\mathit \gamma}^{*}}$ $\rightarrow$ ${{\mathit G}}{{\mathit \gamma}}$ occurs with an appreciable branching fraction.
 19 ABAZOV 2010P use diphoton events with large missing transverse energy in 6.3 fb${}^{-1}$ of data produced from ${{\mathit p}}{{\overline{\mathit p}}}$ collisions at $\sqrt {s }$ = 1.96 TeV to place a lower bound on the compactification scale in a universal extra dimension model with gravitational decays. The bound assumes that the cutoff scale $\Lambda$, for the radiative corrections to the Kaluza-Klein masses, satisfies $\Lambda /M_{c}$=20. The model parameters are chosen such that the decay ${{\mathit \gamma}^{*}}$ $\rightarrow$ ${{\mathit G}}{{\mathit \gamma}}$ occurs with an appreciable branching fraction.
 20 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 a lower bound on the compactification scale.
 21 HAISCH 2007 use inclusive ${{\overline{\mathit B}}}$ -meson decays to place a Higgs mass independent bound on the compactification scale 1/$\mathit R$ in the minimal universal extra dimension model.
 22 GOGOLADZE 2006 use electroweak precision observables to place a lower bound on the compactification scale in models with universal extra dimensions. Bound assumes a 115 GeV Higgs mass. See their Fig. 3 for the bound as a function of the Higgs mass.
 23 CORNET 2000 translates a bound on the coefficient of the 4-fermion operator ( ${{\overline{\mathit \ell}}}{{\mathit \gamma}_{{\mu}}}{{\mathit \tau}^{a}}{{\mathit \ell}}$ )( ${{\overline{\mathit \ell}}}{{\mathit \gamma}}{}^{{{\mathit \mu}} }$ ${{\mathit \tau}^{a}}{{\mathit \ell}}$ ) derived by Hagiwara and Matsumoto into a limit on the mass scale of KK ${{\mathit W}}$ $~$bosons.
 24 RIZZO 2000 obtains limits from global electroweak fits in models with a Higgs in the bulk (3.8 TeV) or on the standard brane (3.3 TeV).
References:
 AVNISH 2021
PR D103 115011 Minimal and non-minimal Universal Extra Dimension models in the light of LHC data at 13 TeV
 AABOUD 2018CE
JHEP 1812 039 Search for new phenomena in events with same-charge leptons and $b$-jets in $pp$ collisions at $\sqrt{s}= 13$ TeV with the ATLAS detector
 AABOUD 2018AV
JHEP 1807 089 Search for pair production of up-type vector-like quarks and for four-top-quark events in final states with multiple $b$-jets with the ATLAS detector
 ACCOMANDO 2015
MPL A30 1540010 Bounds on Kaluza$−$Klein States from EWPT and Direct Searches at the LHC
 KHACHATRYAN 2015T
PR D91 092005 Search for Physics Beyond the Standard Model in Final States with a Lepton and Missing Transverse Energy in Proton-Proton Collisions at $\sqrt {s }$ = 8 TeV
 CHATRCHYAN 2013W
JHEP 1303 111 Search for New Physics in Events with Photons, Jets, and Missing Transverse Energy in ${{\mathit p}}{{\mathit p}}$ Collisions at $\sqrt {s }$ = 7 TeV
 CHATRCHYAN 2013AQ
PR D87 072005 Search for New Physics in Final States with a Lepton and Missing Transverse Energy in ${{\mathit p}}{{\mathit p}}$ Collisions at the LHC
 EDELHAUSER 2013
JHEP 1308 091 Constraints on Models with Universal Extra Dimensions from Dilepton Searches at the LHC
PL B718 411 Search for Diphoton Events with Large Missing Transverse Momentum in 7 TeV Proton$−$Proton Collision Data with the ATLAS Detector
PL B710 519 Search for Diphoton Events with Large Missing Transverse Momentum in 1 ${\mathrm {fb}}{}^{-1}$ of 7 TeV Proton$−$Proton Collision Data with the ATLAS Detector
JHEP 1211 138 Search for High-Mass Resonances Decaying to Dilepton Final States in ${{\mathit p}}{{\mathit p}}$ Collisions at $\sqrt {s }$ = 7 TeV with the ATLAS Detector
 ABAZOV 2012M
PRL 108 131802 Search for Universal Extra Dimensions in ${{\mathit p}}{{\overline{\mathit p}}}$ Collisions
 BAAK 2012
EPJ C72 2003 Updated Status of the Global Electroweak Fit and Constraints on New Physics
 FLACKE 2012
PR D85 126007 Constraints on Split Universal Extra Dimensions from Electroweak Precision Tests
 NISHIWAKI 2012
PL B707 506 A Bound on Universal Extra Dimension Models from up to 2 ${\mathrm {fb}}{}^{-1}$ of LHC data at 7 TeV
PRL 106 121803 Search for Diphoton Events with Large Missing Transverse Energy in 7 TeV Proton$−$Proton Collisions with the ATLAS Detector
EPJ C71 1744 Search for Diphoton Events with Large Missing Transverse Energy with 36 pb${}^{-1}$ of 7 TeV Proton$−$Proton Collision Data with the ATLAS Detector
 ABAZOV 2010P
PRL 105 221802 Search for Diphoton Events with Large Missing Transverse Energy in 6.3 fb${}^{-1}$ of ${{\mathit p}}{{\overline{\mathit p}}}$ Collisions at $\sqrt {s }$ = 1.96 TeV
 ABAZOV 2009AE
PRL 103 191803 Measurement of Dijet Angular Distributions at $\sqrt {s }$=1.96 TeV and Searches for Quark Compositeness and Extra Spatial Dimensions
 HAISCH 2007
PR D76 034014 Bound on Minimal Universal Extra Dimensions from ${{\overline{\mathit B}}}$ $\rightarrow$ ${{\mathit X}_{{s}}}{{\mathit \gamma}}$