models of tev scale gravity at the lhc savina maria , jinr
DESCRIPTION
Models of TeV scale gravity at the LHC Savina Maria , JINR March 5, 2014 EU-Russia-JINR@Dubna Round Table. TeV scale gravity signals . Two types of signals KK-modes of graviton Microscopic black holes. - PowerPoint PPT PresentationTRANSCRIPT
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Models of TeV scale gravity at the LHC
Savina Maria, JINR
March 5, 2014EU-Russia-JINR@Dubna Round Table
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Very specific signature:Production without suppression from small coupling constant, Hawking evaporation, corrected black body decay spectrum, large multiplicity in FS, ellipsoid shape. Huge number of variables in analyses.
Experimental observables:Scalar sum of the transverse energies of jets (ST), an asymmetry in dijet production (like CI)
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TeV scale gravity signals
Heavy graviton resonances (RS1 model), one warped extra dimension nED=1
Non-resonant models like ADD and contact interactions, number of ED nED = 2 ÷ 7, scale MS(D)
Experimental observables:Dilepton (dijet, diphoton) spectra, Jet + missing ET, effective description like CI (non-resonant signs).
Two types of signals
KK-modes of graviton Microscopic black holes
curvature k (~MD), compactification radius r, coupling constant: c = k/MPl, gravity scale : MD
Number of ED nED = 2 ÷ 7Entangled MD, Mmin
BH
Observation of BH-type signals doesn’t allow to get a fundamental multidimensional scale directly from an experiment!
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Multidimensional gravity action with multidimensional constant G(D)
effective
4D-action
Planck mass becomes effective derived from the “true” multidimensional mass scale:
where
A size of extra dimensions depends on a number of ED and a multidimensional scale
The hierarchy problem solution!
22
11
161
dDD
DDD
D
MMG
RgXdG
S
444
16RgXd
GVS
D
deff
22 d
dPl MVM d
d RV
sm 1010~~ 17322
1
d
dPl
MMMR
dNd
N GV
G 441
241
PlN M
G
4Dd
N.Arkani-Hamed, S.Dimopoulos, G.Dvali ’98
(for М about a few ТэВ )
ADD: flat large extra dimensions
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Size of ED in ADD
4
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DY process in ADD
5
LO xsec
HLZ – (MS(ŝ) ,n) GRW – ΛT (n>2)Tao Han, Joseph D. Lykken, Gian F. Giudice, Riccardo Rattazzi, Ren-Jie Zhang James D. Wells
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Exclusion limits for ADD, 8 TeV, 2012
6
Dimuons, 20.6 fb-1
CMS PAS EXO-12-031 Dielectrons, 19,6 fb-1
ADD modelVirtual G exchange “Direct” measurement ΛT through Mmax
Ms is excluded up to 4940 GeV at 95% C.L. depending on nED
CMS PAS EXO-12-027
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Exclusion limits for ADD, 8 TeV, 2012
CMS PAS EXO-12-048
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A 5D action is a subject for fine-tuning:
4D asymptotically flat metric
can be obtained only putting
The hierarchy is solved to be exponential!
4454554
5
16
1 gxdgdzxdRgdzxdG
Sg
222 dzdxdxzads
2
534 G
11
254
ckzekGG
EWkz
Pl MeM ~
F.R.: H. Davoudiasl, J.L. Hewett, and T.G. Rizzo, hep-ph/0006041
Gravity in a curved bulk space: RS1
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RS1 graviton in dilepton spectra
CMS EXO-12-061
Full statistics on resonances in dileptons,
2012the latest result
A paper for RS1 graviton:Phys. Lett. B720 (2013) 63C=0.10 is excluded below 2390 GeV
C=0.05 is excluded below 2030 GeV
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II-III. Hawking radiation phases (short spin down + more longer Schwarzschild) Quantum-mechanical decay trough tunneling, transition from Kerr spinning BH to stationary Schwarzschild one. angular momentum shedding. After this – thermal decay to all SM particles with blackbody energy spectra. Accelerating decay with a varying growing temperature. No flavor dependence, only numberof D.o.f.– “democratic” decay Correction with Gray Body Factors
IV. Planck phase: final explosion (subj for QGr)BH remnant (non-detectable energy losses), N-body decay, Q, B, color are conserved or not conserved
I. Balding phaseAsymmetric production, but “No hair” theorem: BH sheds its high multipole moments for fields (graviton and GB emitting classically), as electric charge and color.Characteristic time is about t ~ RSResult: BH are classically stable objects
Evolution Stages for BH
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SBH solutions: 4D vs (4+n)D
11
2221
22 2121
drdrrMdt
rMds
221
2 2121 dtdtdr
rM
rMds
ddt
rM
ddtgE
2100
22 ,0 ddsd
MrE
Mr S 2 ,1
220
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1
21
22122
22
381
1)(
,)(
n
D
BH
DS
nS
n
n
n
MM
Mr
rrrf
drdrrfdtrfds
Schwarzschild raduis of a multidimensional BH(R.C. Myers and M.J. Perry, Ann. Phys. 172, 304, 1986)
4D flat (4+n)D flat
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BH production cross section(S. Dimopoulos, G. Landsberg, Phys.Rev.Lett.87:161602, 2001hep-ph/0106295v1)
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BH
22
3(81
n
S n
n
MM
MR
PDF’s
ba ab
sMaa
a
a
sxMfxf
xdx
sM
dMdL
,
2BH
1BH
BH 2BH
)(2
2BHˆ
BHBH
BH )BH(ˆMs
abdM
dLdMd
2SR
BH Production in pp collisions: well-known formulas
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Increasing cross section, no suppression from small couplings
Production of KK modes in TeV scale gravity:
ADD, Md=3 TeV,
RS, c = k/MPl = 0.01-0.1Md=1.5 TeV,
GeVpb 1010 35
dMd
GeVpb 1010 24
dMd
BH Production in pp collisions at the LHC
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What part of initial collision energy actually was trapped in BH formation process?
inelasticity (pp BH + X) – function of n,b
jiji
u ssy
xpp
QvufQvf
MnusrnFvdvduzdzMnxs M
,
1 21(
1
0min
),(),(
),,()(2,,,2
2)min
MMx BHmin
min sMy BH ˆ maxbbz ; ;
H. Yoshino and Y. Nambu, Phys. Rev. D 67, 024009(2003), gr-qc/0209003;H. Yoshino and V. S. Rychkov, Phys. Rev. D 71, 104028 (2005), arXiv:hep-th/0503171L. A. Anchordoqui, J.L. Feng, H. Goldberg, and A.D. Shapere, hep-ph/0311365
TSM and an inelasticity in BH production
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TSM: xsec enhancement
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22max )( SBH rnFb
H. Yoshino and V. S. Rychkov, Phys. Rev. D 71, 104028 (2005), arXiv:hep-th/0503171
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TSM: inelasticity and “production efficiency curves”
H. Yoshino and Y. Nambu, Phys. Rev. D 67, 024009 (2003), gr-qc/0209003
P. Meade and L. Randall, JHEP 05, 003 (2008), arXiv:0708.3017
Total BH prod.xsecs, fbwith (solid) andwithout (dashed)an inelasticity
n=6, ADD n=1, RS
Apparent horizon, MAH
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Hawking temperature(R.C. Myers and M.J. Perry, Ann. Phys. 172, 304, 1986)
S
n
BHH R
nnn
nMMMT
41
41
238
21
1
chS Rr )(
Hawking Evaporation of BH
11
23
12
BHBH 2
232
24
nnn
nn
n
n
MM
nS
BH
BH
TM
nnS
21
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4D vs (4+n)D: relations for TH, rS, τ
(4+n)D BH is larger, colder and has a larger lifetime in comparison to 4D BH with the same mass М
BH radiates predominantly on the brane
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Entropy, BH decay and Mmin(BH)
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Democratic decay blinded to flavor: probabilities are the same for all species (violation of some conservation laws)
SBH must be large enough to reproduce thermal BH decay
11
23
12
BHBH 2
232
24
nnn
nn
n
n
MM
nS
(S.B. Giddings, hep-ph/0110127v3,K. Cheung, Phys. Rev. Lett. 88, 221602, 2002)
25 11 BHBH
SS
MM 5minBH
BH Entropy
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Quantum Black HolesProduction near the threshold, small entropy, Mmin ~ MD
Patrick Meade and Lisa Randall, arXiv:0708.3017Douglas M. Gingrich, arXiv:0912.0826
Sc R significant back-reaction,strongly coupled resonances or gravity bound state
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Quantum Black Holes
Douglas M. Gingrich, arXiv:0912.0826
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22P. Meade and L. Randall, JHEP 05, 003 (2008), arXiv:0708.3017
Quantum BH – two body final states
15.0
5.00
events
events
NN
R
QBH production xsec
FS asymmetry
n=6, ADDM=1,2,3,4
n=1, RSM=1,2,3,4
x_min=1 x_min=1
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P. Meade and L. Randall, JHEP 05, 003 (2008), arXiv:0708.3017
More about strategy of compositeness tests, an asymmetry for TBFS etc. in CMS:CMS Collaboration, PRL 105, 211801 (2010); PRL 105, 262001 (2010);
PRL 106, 201804 (2010).
See also ATLAS Collaboration, New J. Phys. 13, 053044 (2011).
Quantum BH – two body final states (TBFS)
String xsecs and
an asymmetry
for different γ
M_s=1 TeV M_s=3 TeV
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Quantum black holes, more ideas BH is a cross-point, in a some sense, between a quantum and semiclassical
approaches
New (fundamental) quantization rules for the compact ED volume and BH area in Planck units
QBH gives a number of sharp resonance states (trajectory) with a Planck spacing G. Dvali, C. Gomez, S. Mukhanov, JHEP 11, 012 (2011), arXiv:1006.2466;
arXiv: 1106. 5894.
...or, maybe, so:
QBH in non-commutative geometry approach
Strictly suppressed bulk emission, emission into a brane dominates
Softer spectra P. Nicolini and E. Winstanley, JHEP 11, 075 (2011), arXiv:1108.4419
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MBH >> MD : semiclassical well-known description for BH’s.
What happens when MBH approach MD?BH becomes “stringy”, their properties become complex.
2
22
s
nsn
D gMM
4,0sg
GeV 1600GeV 1300
D
s
MM
Black Hole or String Ball?
QBH, KK-modes of G
…..
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s
sSBs
s
SBs
s
sSB
s
s
s
dss
BHs
sd
BH
gMMMdf
MMg
gMM
gMdf
Mdf
MgM
M
MgMdf
MM
M
BHSB
;)(
;)()(
;)(
24
22
22
22
12
2
2
221
2
2
11
23
22
32)(
ddd
d
d
nf
2minssBH gMM 22 )()(
ssBHssSB gMMgMMBHSB
S. Dimopoulos and R. Emparan, Phys. Lett. B526, 393 (2002), hep-ph/0108060
Matching:
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Final state of the SM process vs typical BH decay spectra
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Multi-jet and hard leptons events High spherical High energy and pT
SM ProcessBH decay
Experimental observables which are sensitive to these features
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CMS real event visualisation, BH candidates
CMS 3D real event visualisation, N = 9 BH candidate
ST = 2.5 TeV (Run 165567, Event 347495624)
CMS Data, 2011
CMS: the transverse view, N = 10 BH candidate
ST = 1.1 TeV (Run 163332,
Event 196371106) CMS Data, 2011
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ST for events with N objects in the FS
The CMS analysis 2012-2013, 12.1 fb-1:
JHEP 07 (2013) 178arXiv:1303.5338 [hep-ex]
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ST for events with N objects in the FS
The CMS analysis 2012-2013, 12.1 fb-1:
JHEP 07 (2013) 178arXiv:1303.5338 [hep-ex]
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JHE
P 07
(201
3) 1
78ar
Xiv
:130
3.53
38 [h
ep-e
x] (2
1 M
ar 2
013)
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Mmin is excluded from 4.7 to 6.2 TeV
forMD up to 5 TeV
at 95 % CL.
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The CMS analysis 2012-2013, 12.1 fb-1:
JHEP 07 (2013) 178arXiv:1303.5338 [hep-ex]
QBH Signatures
Randall-Sundrum type
ADD
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String ball limits from the counting experiments for a set of model parameters (string coupling gs=0.4, fundamental scale Md and string scale Ms)
Mmin is excluded from 5.5 to 5.7 TeV at 95 % CL.
String Ball Exclusion Plot
The CMS analysis 2012-2013, 12.1 fb-1:
JHEP 07 (2013) 178arXiv:1303.5338 [hep-ex]
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JHE
P 07
(201
3) 1
78ar
Xiv
:130
3.53
38 [h
ep-e
x] (2
1 M
ar 2
013)
Model independent cross section upper limits
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CMS Exotica Summary (95% C.L.)
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Backup Slides
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][16
)5(5
55 MND
NDEinstein GR
GGXdS
esKKhRG
gXdS D
ND mod][
16)0()4(
44
4
5D гравитация – одно дополнительное измерение
55'
5 )()( MXhXh
)()0( xhMN
)()( xh nMN
)()0(5 xh
5D действие - только производные от полей
нулевая мода – безмассовое 4D поле, без потенциала (в приближении малости флуктуаций)
массивные КК-поля
безмассовое калибровочное поле, защищенное остаточной калибровочной симметрией: оригинальная идея
Калуцы-Клейна пообъединению гравитациии электромагнетизма
Эффективное 4D действиеостаточные симметрии :
4D калибровочная 4D общекоординатная
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Результат КК-декомпозиции для 5D метрикиhAB , А,В=1,…5 – многомерное поле. После декомпозиции получаем набор полей в эффективном 4D действии:
4D тензоры (массивные КК-моды)
4D вектор(калибр. бозон)гравискаляр
(модуль)
)0(55h
h
)0(5h стандартный
4D гравитон
R1
)0(55h
Скаляр вводится как поле без потенциала и не зависит от доп. координат (по выборукалибровки) Ненулевое произвольное ваккумное среднее 22
552 )1()1(
dRdxdxdxdxdxdxds
0)0( h
0)0(5 h
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RS1 graviton vs Z’. Extended gauge sector
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The Left-Right model (LR),
SU(2)L
× SU(2)R
× U(1)B−L,
g
L = g
R = 0.64 (like the SM). # EFG = 3.
Z′χ-, Z′η-, and Z′ψ-models,
GUT E6 → SO(10) × U(1)ψ →
SU(5) × U(1)χ × U(1)ψ → SM×U(1)_θ6 .
Z′ = Z′χ cos(θE6 ) + Z′ψ sin(θE6 )
«Sequential» standard model (SSM) Z′, W′ coupled only to left fermions with couplings and total widths as W, Z in SM.
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40Sergei Shmatov, Search for Extra Dimensions.., ICHEP2006, Moscow, 29 July 2006
Spin-1 States: Z from extended gauge models, ZKK
Spin-2 States: RS1-graviton Method: unbinned likelihood ratio statistics incorporating the angles in of the decay products the Collins-Soper frame (R.Cousins et al. JHEP11 (2005) 046). The statististical technique has been applied to fully simu/reco events.
Spin-1/Spin-2 Discrimination
Angular distributions
B.C. Allanach et al, JHEP 09 (2000) 019; ATL-PHYS-2000-029
I. Belotelov et al. CMS NOTE 2006/104CMS PTDR 2006
Z’ vs RS1-graviton