Bounds on Large Extra Dimensions from the Simulation of Black Hole Events at the LHC

Home , Large extra dimensions

Missouri University of Science and Technology Scholars' Mine

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01 Nov 2015

Shaoqi Hou

Benjamin Harms

Marco Cavaglia Missouri University of Science and Technology, [email protected]

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Recommended Citation S. Hou et al., "Bounds on Large Extra Dimensions from the Simulation of Black Hole Events at the LHC," Journal of High Energy Physics, vol. 2015, no. 11, pp. 1-16, Springer Verlag, Nov 2015. The definitive version is available at https://doi.org/10.1007/JHEP11(2015)185

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This Article - Journal is brought to you for free and open access by Scholars' Mine. It has been accepted for inclusion in Physics Faculty Research & Creative Works by an authorized administrator of Scholars' Mine. This work is protected by U. S. Copyright Law. Unauthorized use including reproduction for redistribution requires the permission of the copyright holder. For more information, please contact [email protected]. JHEP11(2015)185 Springer July 16, 2015 : October 17, 2015 : November 26, 2015 September 21, 2015 : : Received 10.1007/JHEP11(2015)185 Accepted Revised Published doi: b 6) of extra dimensions. Our analysis Published for SISSA by [email protected] − , [email protected] and Marco Cavagli`a , a . 3 1507.01632 The Authors. Benjamin Harms c Phenomenology of Large extra dimensions, Monte Carlo Simulations

a If large extra dimensions exist, the Planck scale may be as low as a TeV , [email protected] Tuscaloosa, Alabama 35487/0324, U.S.A. Department of Physics &University, Astronomy, Mississsippi The 38677/1848, University U.S.A. of Mississippi, E-mail: Department of Physics & Astronomy, The University of Alabama, b a Open Access Article funded by SCOAP ArXiv ePrint: and 2.2 TeV to 3.4 TeVwith (remnant) and is excluded difference at from 95% the C.L. CMS Our results. analysis showsKeywords: consistency data allows us tomicroscopic set black lower bounds hole on formationsets the for Planck lower a scale bounds number and (3 onblack various the holes parameters fully fundamental related decaying Planck to intoholes scale Standard settling ranging Model down from particles to 0.6 andformation. a TeV 0.3 remnant, to TeV Formation depending to 4.8 of TeV on 2.8 TeV black for the for holes minimum black with allowed black mass hole less mass than at 5.2 TeV to 6.5 TeV (SM decay) Abstract: and microscopic blackenergy holes scale. may We be simulateand microscopic produced compare black in hole the formation simulation high-energy results atSolenoid particle with the collaboration. collisions recent Large experimental Hadron at The data Collider this by absence the of Compact observed Muon black hole events in the experimental Shaoqi Hou, Bounds on large extraof dimensions black from hole the events simulation at the LHC JHEP11(2015)185 ∗ 5 M may , the ∗ R M , i.e., the ]. The Large 8 , 7 Planck mass observed Planck scale . SM particles are confined hierarchy problem fundamental bulk 10 limits 3 1 TeV) and the ∼ min EW M M – 1 – ]). These null results set upper bounds on the ( ] provides a way to solve the hierarchy problem 4 and – 47 , 2 ∗ 46 M , ] rule out ADD models with two LEDs. Constraints on 37 ]. is sufficiently large, the fundamental Planck mass , 15 + 4)-dimensional space-time 12 of large, compactified spatial dimensions (LEDs). Gravitons 17 R 4 is related to the 4-dimensional – – n . Assuming compactification on a torus with equal radii n 9 Pl , . If 15 1 electroweak scale (= , 2 M ] and even microscopic black hole (BH) formation [ D − brane 13 6 , D ∗ 5 1 M ]. However, the SM fails to explain the 9 n 1 ) km and is macroscopically ruled out because no deviations from Newtonian TeV). The ADD model [ πR 9 16 10 = (2 ∼ 2 Pl To date, experimental results have not confirmed the existence of large extra dimen- If the ADD model is realized in nature, strong gravitational effects should manifest M Pl M size of the largePlanck extra scale. dimensions, or Theorder equivalently, ADD lower of model bounds 10 with on onegravity the have LED the been requires fundamental observed at theFermi the size Large solar of system Area scale. the Telescope LED Observations [ of to neutron be stars by of the the particle scattering [ Hadron Collider (LHC), operating atto a probe center the of appearance mass oflarge energy these extra of new dimensions several physical [ TeVs, processes can and be shed used light on thesions existence (see, of eg. ref.s [ by be as low as a few TeVs. themselves in physical processesscale at could the include, TeV scale. for Gravitational example, phenomena graviton at and the Kaluza-Klein TeV (KK) mode production in ( by introducing a number can propagate in the to the 4-dimensional observed Planck mass 1 Introduction The Standard Model ofses Elementary Particles in (SM) is physics onehuge [ of gap the between most successful the hypothe- A Procedure for determining 3 BH event simulations 4 Results 5 Conclusions Contents 1 Introduction 2 Black hole formation in particle collisions JHEP11(2015)185 ]– 25 (1.2) (1.1) ] ]. The , which ]. Non- 36 T 45 17 – 38 ][ below 4.8 to of 2.4 TeV for 35 = 3 [ [ D min n M M † ] ], 9 34 [ by [ † ] ∗ directly. The search for the or the string scale Λ 33 M D . D M D ][ M M . 32 ∗ +2) derived from constraints on the string M n ( ][ D 1 +2 / from collider experiments in TeV. 1 n ]. 31 is related to M [ D n 37 D ) M 2 n π π † M 8 ] to be larger than 76 TeV for – 2 – References (2 Γ 30 D [ π M = ], setting limits on the production cross section and † √ ] ], all at 95% C.L.. The recent 13 TeV analysis done D 47 , 29 47 M [ = 2 T 46 , † Λ ] 13 , i.e., the minimum mass at which a BH can form. Depending 28 , min ] 27 indicate lower bounds on M (in units of TeV) from these experiments are shown in table 1, where ]. We then derive experimental bounds on the fundamental Planck † 18 D 14 ][ M by [ 26 . The observed lower limits on D M ][ ] and 4.6 to 6.2 TeV [ 25 [ ]. ], where the reduced Planck mass 46 Table 1 , and the remaining ones indicate lower bounds on 48 16 T below 4.3 to 6.2 TeV, while the ATLAS collaboration excludes 6 2.58 3.12 1.07 1.84 1.07 3.53 2.96 1.03 0.72 2.00 2.17 5 2.65 3.31 1.12 1.92 1.12 3.73 3.24 1.08 0.76 2.04 2.14 4 2.84 3.71 1.17 2.00 1.17 3.97 3.56 1.13 0.79 2.20 2.13 3 3.16 4.29 1.20 2.05 1.20 4.77 4.11 1.16 0.81 2.30 2.12 n The purpose of this paper is to revisit and extend the above results from CMS. We sim- Lower bounds on the Planck scale can also be derived by non-observation of production ] provide less stringent, albeit more accurate limits on min = 6 [ = 3 [ 36 by the ATLAS collaborationn has excluded the production of aulate rotating production and black decay hole of microscopicCATFISH with BHs (v2.10) at [ the LHC with the Monte Carlo generator CMS and ATLAS (A Toroidal LHCBH ApparatuS) collaborations signatures have at conducted the searches for the LHC minimal [ BH mass on model assumptionsM and using different6.2 final TeV [ states, the CMS collaboration excludes extinction of QCD jetprovides production an by additional the lower(equivalent Compact to limit Muon the of Solenoid fundamental 3.3 Planck (CMS) TeV scale) Collaboration at [ 95% C.L.and on decay the of TeV extinction BHs mass in scale collider experiments and cosmic ray observations [ Current limits on references labeled by scale Λ Neutron star-derived limits constrain observation of perturbative processes predicted by LED[ models in collider experiments [ is related to errors. The observationn of Supernova SN1987A sets a lower limit on space-times with three largeiments extra dimensions are from generally astrophysical very and stringent, cosmological although exper- they typically suffer from large systematic JHEP11(2015)185 ), − s √ bald- (2.2) (2.1) [(1 ( s ]. The S { / R 13 2 , ) min is the impact and accounts M z y = 1 (Black Disk = xs, n, y F m √ ). Therefore, if two ( x , and ], eventually settling σ is confined to a region M Q ) is ( ] S 54 x , M , ,Q R 51 0 10 1 +1 ]. During the balding stage, n x/x 1 is related to , the BH enters the quantum ( ], 53 ∗ j [ ∗ ≤ f 52 ) M M M – F ,Q ∼ 50 0 x 1 +1 ( i n min f # 0 Q 0 x and impact parameter smaller than x d 2 s +3 1 n x + 2 √ – 3 – quantum decay Z n x 8Γ d ], a BH forms when a mass " and 1 m ∗ x 49 [ Z 1 z πM d , where the form factor √ z 2 S 2 is the fraction of energy which escapes into the bulk as gravi- 1 = , as expected in the ADD scenario, the newly formed BH lives y 0 S R Z πF R R ]. ij X , and is the minimum-allowed mass of the BH. The total cross section in ) = S 14 s R √ ) = ) min Hoop Conjecture y thermal evaporation s, n, y M ]. The Schwarzschild BH then decays into elementary particles through the , ( − ) are the PDFs with four-momentum transfer squared σ -dimensional Kerr geometry. Angular momentum is radiated during the spin- 54 s, n, y ( D = (1 x, Q BH ( i → , where f M -dimensional space-time with negligible curvature at the BH scale. In this case, the } pp 2 spin-down D If the initial BH mass is much larger than the Planck mass, a semiclassical treatment σ )] , z ( Hawking mechanism (thermal evaporation stage).in Most of this the stage, energy of withevaporating the SM BH BH is particles approaches radiated dominating thephase, the Planck where decay scale, the products. decaygravitational effects. When ceases the to mass be of semiclassical the and becomes dominated by quantum suggests that the newly-formeding BH decays throughthe four, BH possibly radiates distinct multipoledown to stages: momenta a and quantumdown numbers stage [ [ where parameter normalized to its maximumy value. The cutoff at small the absence of graviton energy(BD) loss cross at section) formation [ is recovered by setting at the parton level, the totalover cross the section Parton for Distribution a Functions hadronic (PDFs) collision of is obtained the by hadrons integrating [ where tons, depending on the impactcross parameter. section The Hoop Conjecturefor implies the a energy BH of production called the “graviton colliding energy loss particles at which formation.” is Since not BH trapped production in in hadron the colliders event occurs horizon, the so in a Schwarzschild radius of the BH can be expressed as [ 2 Black hole formationAccording in to particle the collisions of typical size equalparticles to collide the with center Schwarzschild of radius massa for energy BH that may mass, form. If independent experimental limits on BHabsence production of from observed black the hole CMS eventson Collaboration in the various [ CMS physical experimental parameters data of allowsTeV-scale us the black to holes ADD set bounds which model may and form to in constrain hadronic the scattering minimum processes. mass of mass and the number of extra dimensions by comparing simulation results with model- JHEP11(2015)185 ]. . , or 63 p XMIN /n ≤ min ]), 1 (YR 1. =0, the BH Q 62 ≥ NP QMIN ] using the Les , ∗ ]. CATFISH is a 64 XMIN ] (used by CMS), , 14 ∗ /M 59 , = 3, 4, 5, 6. )[ . When /M p min 58 n Q min = = 0 (BD model), 1 (YR or = M ]. Our analysis is based on NP = 61 QMIN NEXTRADIM , = 0 (YN TS model [ XMIN n ], BlackMax [ = . . 57 ∗ , min GRAVITONLOSS M 56 Q of hard quanta, each with energy = p – 4 – n NEXTRADIM MSTAR GRAVITONMODEL ]). ], and Yoshino-Rychkov (YR) improved TS model [ 63 62 ], CHARYBDIS2 [ 55 ]. In our analysis, we run CATFISH (v2.10) with the CTEQ6PDF 65 Collider grAviTational FIeld Simulator for black Holes improved TS model [ forms a stable remnant with mass YN TS models, see below). Minimum initial BH mass in Planck units: Minimum quantum BH mass in PlanckNumber units: of quanta emitted in the Planck phase: Fundamental Planck mass: Number of extra dimensions: Graviton energy loss at formation: Gravitational loss model: ] and an unnamed generator by Tanaka et al. [ 1. 2. 2. 3. 1. 2. 1. 60 BH evaporation parameters BH formation parameters ADD parameters The simulation of a BH event in CATFISH follows these steps. First, CATFISH • • • by the BH areinitial- instantaneously and hadronized final-state or radiation decayeddecay, particles. by CATFISH uses PYTHIA, To several determine which external the also parameters physics simulates and of switches: BH formation and computes the total andmass differential is cross sampled sections fromHawking for the mechanism differential the cross until BH section. the formation.thermal hard BH The event The BH is mass initial is generated reaches or BH then the a decayed BH through quantum remnant the is limit, created. where The a unstable quanta final emitted non- forming a BH remnant.inelasticity, CATFISH also exact incorporates field several emissivities othergenerator and physical interfaces corrections effects, to to such as the semiclassicalHouches PYTHIA BH interface evaporation. Monte [ Carlo The PDF fragmentation set code and [ PYTHIA (v6.425) Tune Z1. LHC. It incorporates three models for(YN) BH formation Trapped and cross Surface section: (TS) BD,The Yoshino-Nambu [ lack of afinal quantum stage. theory CATFISH ofthermally offers decaying gravity the the requires BH choice into a of a simulating phenomenological number the treatment quantum of phase the by either non- Several Monte Carlo generatorsthe for years: BH production TRUENOIR at [ QBH colliders [ have been developedCATFISH ( over Fortran 77 Monte Carlo generator designed specifically for simulating BH events at CERN’s 3 BH event simulations JHEP11(2015)185 - ) ) ], > BH D 66 T 4.2 → (4.1) (4.2) S using XMIN ( pp 5 TeV, ; 3) In ]. The . . Thus, σ σ ∗ NP ∗ 13 M M = 1 NEXTRADIM in eq. ( is inversely (i.e., is expected = 0, 4. The ∗ , and k A =0 (BD cross BD M min NP σ × M ) for XMIN MSTAR , = 5, min T and is at a fixed is obtained by running ∗ XMIN . The results are shown > S ∗ ). The ratio M QMIN NP ∗ BH T , . M for fixed = S → GRAVITONLOSS M ( ( is an increasing function of the pp NEXTRADIM is σ min T σ , k QMIN k XMIN XMIN of an event is defined as the scalar BH > S = XMIN → T T S pp S and = 3, is defined as the number of final-state σ = 1 will be presented in a future report. XMIN · ) as a function of of events , N as a function of k min . min appears as a lower limit of integration in the T M , the smaller BH ) = ) as a function of . Taking into account all these factors, → – 5 – flattens. Following the CMS collaboration [ Q > S pp min min T T XMIN XMIN T NEXTRADIM σ S min T . BH events are expected to have high multiplicities. ( of events with > S S T > S Total Num . σ ) increases at fixed GRAVITONLOSS for and whose multiplicities are greater than some chosen S T T GRAVITONLOSS 1 increases. S vs. S , ( are derived by evaluating the partial cross section ( min T Num σ XMIN k σ ; 2) Since ( ∗ = min ∗ XMIN display > S ). There are 3 factors: 1) The BD cross section ]. The transverse energy M , the greater k M M 1 T or 13 2.2 BH S ∗ . The event multiplicity → and and final decay into 2, 4, or 6 quanta or formation of a stable BH NEXTRADIM T M ), ( pp ∗ S σ 2.1 M QMIN = =0). The stable BH remnant is invisible to the detector and thus contributes is the minimal transverse energy chosen, and and then averaging over all final state particles. ]. We also derive lower limits on NP XMIN min T 13 min T increases, the graph of . For simplicity, we consider only BH formation with S ∗ ) for events whose NP The partial cross section The CMS search for BH events looks at excess transverse energy with respect to SM The primary goal of this investigation is to determine lower bounds on the > S M min T T to decrease as either CATFISH with fixed by the upper two graphslower in two graphs figure in figure is expected to decrease as can be estimated by integrating over theS spectra of visible final stateHawking particles temperature, over the which, range in turn,as is a monotonically increasingwe function of choose the signal acceptance to be 100%. In summary, The behavior of thefollows total from cross eqs. section ( proportional to a power of total cross section addition, the PDFs fall off rapidly at high where 4 Results Lower bounds on S value, given by, missing transverse energy is definedmomenta of as all the the magnitude final-stateenergy of objects. the is vector If added sum it to objects of is which the greater are transverse than used 50 to GeV, calculate the missing transverse remnant ( to missing energy. The results with background predictions [ sum of the transversemuons, energies electrons of and all photons the satisfying final-state the objects selection in criteria excess of discussed 50 in GeV, ref. i.e., [ jets, dimensional fundamental Planck scale for differentthe values of model-independent 95%search C.L. [ upper limitsand on the BHsection), cross section from the CMS JHEP11(2015)185 ● ■ ● ▲ ◆ ● ■ ● ▲ ◆ ● ■ ● ▲ ◆ 5000 0.8 1 1.2 1.4 ● ■ ● 5000 ▲ ◆ 3. 3.5 3.7 3.9 4.1 ● ■ ● ▲ ◆ ● ■ ● ▲ ◆ CMS ● ■ ▲ ◆ ● ■ CMS ▲ ◆ ● ■ ≥ ● ■ ▲ ▲ ◆ ◆ ● ■ ● ● ● ▲ ◆ ● ● ■ ● ● ▲ ◆ 5.85 TeV. ● ■ ● ▲ ◆ ● ■ ● ▲ ◆ N ’s chosen in ● ■ ● ▲ ◆ − 4500 ∗ ● ■ ● 4500 ▲ ◆ ● ■ ● ▲ ◆ 1.2 TeV, and ● ■ ● ▲ ◆ ) and require M ● ■ ● ▲ ◆ ● ■ ● ▲ ◆ 3.9. Multiply- − ● ■ ● ▲ ◆ ● ■ ● ▲ ◆ A ● ■ ● ▲ − ◆ ● ■ ● ▲ ◆ ● ■ ● ▲ ◆ 4000 ● ■ ● 4000 ▲ ◆ 55 TeV ● ■ ● ▲ ◆ ● ■ ● ▲ ◆ . ● ■ ● ▲ ◆ ● ■ ● ▲ ◆ ● ■ ● ▲ ◆ (GeV) ● ■ ● ▲ ◆ (GeV) ● ■ ● ▲ ◆ ● ■ ● ▲ ◆ = 5 ● ■ ▲ ◆ 3500 ● ■ ● 3500 ◆ min T min T ● ■ ▲ ◆ ● ■ ● S ▲ ▲ ◆ S ● ■ ▲ ◆ ● ■ ● ▲ ◆ min ● ■ ▲ ◆ ● ■ ● ▲ ◆ ● ■ ▲ ◆ by comparing the simulated ● ■ ● ▲ ◆ M ● ■ does not strongly depend on ▲ ◆ 3000 ● ■ ● 3000 ◆ ● ■ . As expected, the lower limit ▲ ◆ ● ■ ● ▲ ▲ ◆ ∗ ● ■ ▲ ◆ ● ■ ● ◆ ● ■ ▲ ◆ exp ● ● ■ ◆ XMIN M , ● ■ ▲ ◆ ● ● ■ ▲ ▲ ▲ ◆ ∗ ● ■ ▲ ◆ 2500 lies in the range 3.7 ● ● ■ 2500 ◆ ● ■ ▲ ◆ ● ● ■ M ◆ ● ■ ▲ ◆ and ● ● ■ ▲ ▲ ▲ ◆ lies in the range 1.0 TeV shows that the cross section decreases -3 -4 -4 -5 ∗ -5 -7 ∗ 1 XMIN 10

10 10

0.100 0.001 M

) pb ( A × σ

5.× 10 1.× 10 5.× 10 ) pb ( A × σ (Upper two graphs, numbers being ∗ ■ ● – 6 – 0.3 0.4 0.5 0.6 0.7 ● 3400 M ● ● ● ● ▼ 1.6 1.8 2 2.2 2.4 ● ■ ▲ ▼ ◆ CMS . The value of ● ■ ■ ■ CMS ● ● ■ ▲ ▼ ◆ ● ● ▲ ▼ ◆ ◆ ● ● ● ■ ● 3200 ● ● XMIN ● ● ■ ■ ■ ◆ 4000 ● ● ■ ■ ● ● ■ ● ■ ● ▲ ▲ ◆ ● ● ■ ◆ 3000 ● ● ■ ◆ ● ■ ● ▲ ▼ ▼ ▼ ◆ ) to be less than the experimental limits for all muliplicities ● ● ■ ▼ ▼ ▲ ◆ as a function of 3500 ● ● ■ ▲ ◆ ● ■ ● ▲ ▼ ◆ shows the exclusion region for (GeV) 5 TeV, we obtain the lower limits on min ● ● ■ T 2800 ▲ ▼ ▼ ◆ . A (GeV) 2 = 0, 4. As expected, ﬁgure ● ● ■ ▲ ▼ ● ■ ● ◆ ▲ ▼ min ◆ T × S min T ● ● ■ ▲ ▼ ) ◆ = 1 S > S NP ● ■ ● ▲ ▼ ◆ ● ● ■ ▲ ▼ ◆ ∗ 2600 3000 min ● ● ■ ▲ ▼ T ◆ T ● ■ ● ▲ ▼ ◆ ● ● ■ ▲ ▼ M ◆ S increase. ( ● ● ■ ▲ ▼ ◆ > S ● ■ ● ▲ ▼ ◆ σ ● ● ■ ▲ ▼ ◆ 2400 10. Figure T ● ● ■ ▲ ▼ ◆ ) with the experimental limits (the solid curves in the graphs). For example, can be used to determine bounds on ● ■ ● ▲ ▼ ◆ S 2500 = 5, and ● ● ■ ( ▲ ▼ ◆ XMIN 1 σ ● ● ■ ▲ ▼ ◆ min ● ■ ● T ▲ ▼ ◆ . ,..., 2200 ● ● ■ ▲ ▼ ◆ 1 -4 10 is a decreasing function of 4

and -4 -5

0.010 0.001 0.100 > S

) pb ( A ×

σ 3 10 10

∗

0.010 0.001 0.100

We run CATFISH over a large range of parameter space (see appendix Figure ) pb ( A × σ exp T , M ≥ S ∗ ( ing this range by the simulated N M as σ the upper right plot shows thatthe the bottom lower limit right on plot shows that the lower limit on units of TeV) or XMINand (Lower two NP graphs, = numbers being 4counting XMIN’s) experiments (Left at from two NP the = graphs). CMS 0 Collaboration (Right The are two graphs) also model-independent shown. 95% The CL multiplicity is experimentalNEXTRADIM upper limits for Figure 1 JHEP11(2015)185 is NP NP ] have 10 10 2.5. XMIN 26 . NP=0 NP=2 NP=4 NP=6 NP=0 NP=2 NP=4 NP=6 shows that 8 8 2 XMIN = 8 TeV [ s 6 6 √ 6= 0. The lower limits ). As experimental data XMIN XMIN NP = 0) are excluded, and the 4 4 XMIN ( 2 for NP min ∼ becomes much smaller. This is due 2 2 M = 0 set an upper limit exp ,

∗

5 4 3 2 1 0

2 1 0 5 4 3 NP . As expected, the lower limit of

* ) TeV ( of limit Lower * oe ii of limit Lower ) TeV ( M M 6. More experimental limits are shown in M . XMIN – 7 – 10 10 = 3. The upper left panel in ﬁgure XMIN also shows that these limits do not depend on n is restricted to 1 vs. XMIN as a function of NP and NEXTRADIM = 3 NP=0 NP=2 NP=4 NP=6 NP=0 NP=2 NP=4 NP=6 3 ∗ M 8 8 XMIN ], our results for set upper bounds on ∗ 14 M . Figure = 0, the bound on 71 TeV for ∗ 6 6 . 2 M NP 1 TeV [ XMIN XMIN ∼ ∗ . 4 4 ∗ M 6 do not exclude events with remnants as BH ﬁnal products, but never , 6= 0. If M 5 , NP shows the exclusion region for 2 2 = 4 3 n . Simulated lower limit on

1 0 3 2 5 4

0 2 1 5 4 3

* * , leading to more stringent constraints. For instance, the CMS searches for events oe ii of limit Lower ) TeV ( ) TeV ( oe ii of limit Lower for M M 1 ∗ Figure M , as long as a decreasing function of the events with microscopicexperimentally BHs allowed range decaying of toof remnants ( the less, set strong constraints on the ranges where the semi-classical treatment is valid. exclude values of 6= 0 results givetable the milder constraint, with an energetic jetset and an the imbalance lower in limit transverse momentum at (top left), 4 (top right), 5 (bottom left), and 6 (bottom right). NP to the high transverseenergy. momentum The of lower the limits BH on remnant, which contributes to the missing Figure 2 JHEP11(2015)185 2.5 1.8 1.6 2.0 , the ranges of 1.4 3 = 2) in the upper 5 TeV. This shows . 1 1.2 NP (TeV) (TeV) 1.5 & ]. It shows that as long * * ∗ M M 1.0 13 M . In ﬁgure 0.8 1.0 XMIN = 4, = 0. This ﬁgure can be combined 0.6 NP=0 NP=2 NP=4 NP=6 NP=0 NP=2 NP=4 NP=6 NP XMIN 0.4 0.5

5 0 8 6 4 2 0

15 10 12 10

predicted by CATFISH with those from oe ii fXMIN of limit Lower oe ii fXMIN of limit Lower as a function of NP and NEXTRADIM = 3 ∗ min M M – 8 – 5 TeV. At the same time, the dashed curve in the . 3.0 1 2.0 ∼ ∗ indicates that if ]. M 2 2.5 46 further. For example, if there are 3 extra dimensions, and a , are consistent with those of 1.5 ∗ 4 at 13 ∗ M 2.0 & M (TeV) (TeV) * * M M XMIN 1.5 1.0 = 3) of ﬁgure 6= 0, but become much smaller at n NP compares the lower limits of 1.0 to constrain NP=0 NP=2 NP=4 NP=6 NP=0 NP=2 NP=4 NP=6 2 4 0.5 . Simulated lower limit on XMIN vs.

0 5 2 0 6 4 8

15 10 10

oe ii fXMIN of limit Lower oe ii fXMIN of limit Lower = 0, CATFISH’s limits are much smaller than those of BlackMax and CHARYBDIS2. Figure were chosen in order to compare the CATFISH results with those of BlackMax and NP ∗ BlackMax and CHARYBDIS2 done byas the CMS Collaboration [ The difference in predictions between CATFISHmodel and CHARYBDIS2 when is a produced stable remnant is due to the different treatments of the quantum phase by the two left plot shows that upper left plot ( that the lower limitsM of CHARYBDIS2 from ref.’s [ (top left), 4 (top right), 5 (bottom left), and 6 (bottom right). strongly when with figure BH decays into 2 quanta in the quantum phase, the dashed curve ( Figure 3 JHEP11(2015)185 ]. min 46 M ■ ◆ 1.8 = 0 (BH ■ ▲ shows the ◆ 5 NP 1.6 ■ ▲ ◆ ● for 1.4 6= 0, the situation ∗ ■ ▲ ◆ ● M NP 6. Figure ]. Various models im- 1.2 , ■ ▲ ◆ ● (TeV) 13 * vs. 6= 0, but predicts much M = 4 1.0 ■ ▲ ◆ ● n and minimal BH mass NP min from CATFISH with those from = 6. CATFISH gives limits ∗ 0.8 M ■ ▲ ◆ ● M n min BH 0.6 M ■ ▲ ◆ ● NP=0 NP=2 NP=4 NP=6 Charybdis StableYR remnant( loss ) BlackMax Nonrotating Charybdis Nonrotating Charybdis Boiling(YR remnant loss ) ■ ▲ ● ◆ 0.4

0 6 5 4 3 2 1 min ) TeV ( of limit Lower M 13 . The dedicated CMS limits use the optimum D – 9 – M ● 2.5 6= 0 are due to the fact that the three generators ■ ● ◆ NP ■ ▲ ● ◆ for 2.0 ∗ ■ ▲ ● ◆ M vs ■ ▲ ● ◆ = 0. The similarities among the three generators as shown in (TeV) 1.5 * M min ]. Moreover, CATFISH’s stable remnant is invisible to the detector NP ■ ▲ ● ◆ M 68 , ■ ▲ ● ◆ 1.0 67 , ■ ▲ ● ◆ 13 NP=0 NP=2 NP=4 NP=6 Charybdis StableYR remnant( loss ) BlackMax Nonrotating Charybdis Nonrotating Charybdis Boiling(YR remnant loss ) ▲ ■ ● ◆ = 4, but gives higher limits than BlackMax if . Comparison of the predictions on lower limits of

0.5

2 1 0 6 5 4 3 min oe ii of limit Lower ) TeV ( M n plemented in CATFISH have been exploredresults and different for limits models have without been determined. aCMS BH collaboration Our stable and remnant the generallyDIS ATLAS agree generators, collaboration with where based earlier some on results ofmethods the the by used observed the BlackMax by discrepancies and the can analyses CHARYB- be to constrain explained by the different 5 Conclusions In this work, lower limits onat the formation fundamental Planck have scale limits been on obtained the partial in production a cross vast section of parameter microscopic space, BHs [ using experimental upper incorporate the same basicthree physics generators of differ microscopic from BH onein formation another and the in decay. inclusion the However, or implementation the the exclusion of BHs. the of quantum the For phase effect example,remnant) and by of the CATFISH gravitational predictions differ energy of from loss those the at of behavior BlackMax the of and formation CHARYBDIS2. of similiar to those of CHARYBDIS2 (nonrotatingcomparison BH between model) CATFISH for predictions with thoseCATFISH from agrees the ATLAS with Collaboration [ BlackMaxsmaller and limits CHARYBDIS2 when when the two figures for generators [ and contributes tofundamental missing particle with energy, conventional while interactions inis CHARYBDIS2’s the detector. more remnant complicated. If behaves CATFISH aswhen agrees a with BlackMax heavy (nonrotating BH model) very well Figure 4 BlackMax and CHARYBDIS2 at NEXTRADIMand = CHARBDIS 4 are (left) extracted and from 6 figure (right). 4 The in results ref. of [ BlackMax JHEP11(2015)185 ], 13 = 1). (= 0, 2, 1.8 NP 1.6 10. In general, ) and 1.4 )) used in ref. [ 1, so the lower limit ,..., GRAVITONLOSS 3 1.1 QMIN 1.2 ≥ (TeV) ≥ * (= M -dimensional fundamental 1.0 (eq. ( XMIN D D from CATFISH with those from XMIN 0.8 M ]. min BH limits 46 0.6 M NP=0 NP=2 NP=4 NP=6 BlackMax Nonrotating BlackMax Nonrotating with graviton emission Charybdis Nonrotating (= 0), min 0.4

0 6 5 4 3 2 1 M min ) TeV ( of limit Lower M and – 10 – ∗ 2.5 M GRAVITONLOSS 2.0 ]) were used. CATFISH accepts only (TeV) 1.5 (= 3, 4, 5, 6), * 13 M ] at the University of Alabama and the Alabama Supercomputer constrain the the size of LEDs in ADD models. Future investigations 73 ∗ M ]. The steps outlined above for the simulation of microscopic BH events , or equivalently, the reduced Planck scale 1.0 ∗ ] for providing the computing infrastructure essential to our analyses. 72 M , NEXTRADIM NP=0 NP=2 NP=4 NP=6 74 BlackMax Nonrotating BlackMax Nonrotating with graviton emission Charybdis Nonrotating 71 . Comparison of the predictions on lower limits of is 1 and its upper limit is determined by noticing that the mass of the BH must

0.5

2 1 0 6 5 4 3 min oe ii of limit Lower ) TeV ( M XMIN Planck scale for different 4, 6). The model-independent 95%(figures C.L. 6 upper and cross 7 section in limitsof ref. for counting [ experiments Authority [ A Procedure for determining This appendix describes how to determine the limits on the Acknowledgments We wish to thank C. Hendersonwish and to P. thank Rumerio G. for their Landsbergacknowledge constructive and RC2 discussions. the We [ CMS also Exotica conveners for their help. We gratefully the additional feature ofAnother graviton refinement energy of loss the duringprinciple models BH [ formation is ( tocan include also the be effects carried of out the for generalized string balls, uncertainty string resonances and other exotic particles. minimum multiplicity distribution for each casecross considered, section while to we be requireBH the less simulated remnant than models the CMS givelower bounds limits milder on for constraints all thanwill multiplicities focus non-remnant on models. performing a similar The analysis calculated to the one carried out in the present paper with Figure 5 BlackMax and CHARYBDIS2 at NEXTRADIMand = CHARBDIS 4 are (left) extracted and from 6 figure’s (right). 8 The and results 10 of in BlackMax ref. [ JHEP11(2015)185 , , . 1 . 4 M 10). (A.1) (A.2) = 10 ,..., 4 NEXTRADIM NEXTRADIM , run 3 , N is the result of ≥ i ]. We require that M ]. MSTAR 13 ) and the condition SPIRE A.1 must be smaller than IN 1 TeV. , where . ∗ 2 and the simulated partial ][ M / ) M )], = 0 ∆ 0 1 is the LHC integrated luminosity, − M < i M . 1 is determined at a given confidence | . 1 + − p 1 . − ,M 0 i − i i 2. Otherwise, CATFISH is run with , m , satisfies eq. ( M / M 8 TeV 100 M 0 ) 2 1 Collider signatures of new large space − run ./ 1 = ( ≤ M + = 12 fb i hep-ph/9811337 L , where M 2 N i . | 1 as a function of the parameters. Similarily, [ L Max( 1 M C | M , + M ≥ − , is determined for a given choice of ) i 0 − – 11 – 1 = exp L is then determined as = , MSTAR M − 1 · exp m ∗ i ∗ is determined by fixing all other parameters. The , . Different sets of these parameters are chosen and − ∗ × σ i exp M = ∗ M , NP ,M M = ( ∗ p MSTAR M i M | (1999) 2236 2 p M M XMIN times until ), which permits any use, distribution and reproduction in can be obtained for different choices of M 82 = i ) and = is the required precision, ∆ . exp , ) be less than CMS limits for all multiplicities ( XMIN ∗ 2. ) for BH production is too small, M QMIN NP ) is compared with CMS cross section limits [ / A ) M min MSTAR T or 0 min T (= is set to 0.5. We use a bisection method to find the limits on the CC-BY 4.0 M is ∆ > S min + > S is allowed by experimental data, i.e., the simulated cross section (times This article is distributed under the terms of the Creative Commons T M = 1 TeV and the upper limit, 1 1 exp T S XMIN Phys. Rev. Lett. , 0 ( S (= 0) and ∗ M , M σ ( m σ M = ( 2 is the number of events of each run. In our simulations we choose is the cross section of the production, M σ run = -th simulation and ∆ dimensions N Step 4. 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