Lecture III: Extra-Dimensional and Technicolor/Composite Higgs models
Alexander Belyaev Beyond The Standard Model 168 eXtra Dimensions (XD)
Alexander Belyaev Beyond The Standard Model 169 Motivations for XD String theory, the best candidate to unify gravity & gauge interactions, is only consistent in 10 D space-time
Extending symmetries: Internal symmetries - GUTs, technicolour...; Fermionic spacetime- SUSY Bosonic spacetime - Extra dimensions
The presence of XD could have an impact on
scales << Mplanck (started with ADD) The question is what is the size and the shape of XD ?!
Alexander Belyaev “Beyond the Standard Model” 170 New perspectives of XD
The nature of electroweak symmetry breaking The origin of fermion mass hierarchies The supersymmetry breaking mechanism The description of strongly interacting sectors (provide a way to model them) ......
Alexander Belyaev “Beyond the Standard Model” 171 Brief History 1914: Nordstrom tried to unify gravity and electromagnetism in 5D
(A AM, where M = 0,1,2,3,4)
1920's: Kaluza and Klein tried using Einstein's MN equations in 5D (g g ~ g g g )
1970's: Development of superstring theory and supergravity required extra dimensions
1998: Arkani-Hamed, Dimopoulos, and Dvali propose
Large Extra Dimensions (ADD) as a solution to the Hierarchy /Fine tuning problem of the Standard Model
Alexander Belyaev “Beyond the Standard Model” 172 The idea of ADD The Standard Model has been tested to r ~ 10-16 mm, Gravity has been tested to r ~ 1 mm only
Alexander Belyaev “Beyond the Standard Model” 173 The idea of ADD The Standard Model has been tested to r ~ 10-16 mm, Gravity has been tested to r ~ 1 mm only 4D (4 + n)D The effective D = 4 action is
In case of toroidal compactification of equal radii, R
Alexander Belyaev “Beyond the Standard Model” 174 The idea of ADD The Standard Model has been tested to r ~ 10-16 mm, Gravity has been tested to r ~ 1 mm only 4D (4 + n)D The effective D = 4 action is
In case of toroidal compactification of equal radii, R
r>>R ⇒ the torus effectively disappear
Alexander Belyaev “Beyond the Standard Model” 175 The idea of ADD The Standard Model has been tested to r ~ 10-16 mm, Gravity has been tested to r ~ 1 mm only 4D (4 + n)D The effective D = 4 action is
In case of toroidal compactification of equal radii, R
r>>R ⇒ the torus effectively disappear r< Alexander Belyaev “Beyond the Standard Model” 176 The idea of ADD The Standard Model has been tested to r ~ 10-16 mm, Gravity has been tested to r ~ 1 mm only 4D (4 + n)D The effective D = 4 action is In case of toroidal compactification of equal radii, R r>>R ⇒ the torus effectively disappear r< How big are these dimensions are? Let us assume Mf ~ 1 TeV, then Already ruled out Collider signature: Alexander Belyaev “Beyond the Standard Model” 178 KK-towers from XD Periodicity in Z Alexander Belyaev “Beyond the Standard Model” 179 KK-towers from XD Periodicity in Z Fourier series Alexander Belyaev “Beyond the Standard Model” 180 KK-towers from XD Periodicity in Z Fourier series The non-zero modes in the KK decomposition Alexander Belyaev “Beyond the Standard Model” 181 From Brane – to Bulk: Universal Extra Dimensions (UED) [Appelquist, Cheng, Dobrescu '01] all fields propagate in the extra dimensions, so 1/R > 1 TeV to obey experimental data for D=5 (minimal UED = MUED) we immediately 15 find that Mf=10 GeV for 1/R = 1TeV hierarchy problem is not addressed but MUED has interesting features ... Alexander Belyaev “Beyond the Standard Model” 182 Minimal Universal Extra Dimensions compactifying on the circle all fields propagate in the bulk – 5D momentum conservation Alexander Belyaev “Beyond the Standard Model” 183 Minimal Universal Extra Dimensions compactifying on the circle all fields propagate in the bulk – 5D momentum conservation This leads to the KK-number conservation at this point: Alexander Belyaev “Beyond the Standard Model” 184 Universal Extra Dimensions (UED) compactifying on the orbifold Choose action of Z2 symmetry on Dirac Fermions to project out ½ of them and arranges chirality: Alexander Belyaev “Beyond the Standard Model” 185 Universal Extra Dimensions (UED) compactifying on the orbifold Choose action of Z2 symmetry on Dirac Fermions to project out ½ of them and arranges chirality: Translational invariance along the 5th D is broken, but KK parity is preserved! KK number n broken down to the KK parity, (-1)n: KK excitations must be produced in pairs These vertices are allowed and LKP is stable DM candidate! can be generated at loop-level Alexander Belyaev “Beyond the Standard Model” 186 Minimal Universal Extra Dimensions brane localised terms are zero at the cutoff scale Alexander Belyaev “Beyond the Standard Model” 187 The role of radiative corrections e.g. the 1st KK excitation of the electron is stable at tree-level! Dark Matter would be charged – which is not acceptable Alexander Belyaev “Beyond the Standard Model” 188 The role of radiative corrections Alexander Belyaev Beyond The Standard Model 189 MUED spectrum at 1loop vs tree-level Alexander Belyaev “Beyond the Standard Model” 190 Model implementation MUED is implemented in Feynman and unitary gauges in LanHEP (generates the Feynman rules out of a Lagrangian) [AB,Brown,Moreno,Papineau arXiv:1212.4858] (BBMP) Alexander Belyaev Beyond The Standard Model 191 Model implementation MUED is implemented in Feynman and unitary gauges in LanHEP (generates the Feynman rules out of a Lagrangian) [AB,Brown,Moreno,Papineau arXiv:1212.4858] (BBMP) Publicly available at High Energy Physcs Model Database (HEPMDB) http://hepmdb.soton.ac.uk/hepmdb:1212.0121 Alexander Belyaev Beyond The Standard Model 192 Model implementation MUED is implemented in Feynman and unitary gauges in LanHEP (generates the Feynman rules out of a Lagrangian) [AB,Brown,Moreno,Papineau arXiv:1212.4858] (BBMP) Publicly available at High Energy Physcs Model Database (HEPMDB) http://hepmdb.soton.ac.uk/hepmdb:1212.0121 Compared and Validated against existing implementation by Datta,Kong,Matchev, arXiv:1002.4624 (DKM) and private implementation form Belanger, Semenov, Pukhov,Kakizaki. If the sum of KK numbers of the external particles is 5 or less [<2*(n+1) in general] gauge invariance is ensured Proper implementation of the Higgs sector lead to the correct High Energy asymptotic which respects Unitarity Alexander Belyaev Beyond The Standard Model 193 EW precision constraints MH Alexander Belyaev “Beyond the Standard Model” 194 FCNC and DM constraints Matsumoto, Senami '05; Kong, Matchev '05 Brunel, Kribs '05; Belanger, Kakizaki, Pukhov '10 ...... Plank/WMAP set Alexander Belyaev “Beyond the Standard Model” 195 The role of the 2nd level of KK excitation Alexander Belyaev “Beyond the Standard Model” 196 The role of the 2nd level of KK excitation [Belanger et. al. 2010] Alexander Belyaev “Beyond the Standard Model” 197 The role of the 2nd level of KK excitation an upper limit on the MUED scale! [Belanger et. al. 2010] Alexander Belyaev “Beyond the Standard Model” 198 Constraints from the Higgs data Production is enchanced AB, Belanger, Brown, Kakizaki, Pukhov '12 Decay is slightly suppressed Overall, the GG->H-> is enhanced Alexander Belyaev “Beyond the Standard Model” 199 Data Fit with MUED vs SM SM MUED Alexander Belyaev “Beyond the Standard Model” 200 Data Fit with MUED vs SM There is no hint on MUED from the Higgs data ... The fit of the SM if perfect :-( SM MUED Alexander Belyaev “Beyond the Standard Model” 201 Data Fit with MUED vs SM There is no hint on MUED from the Higgs data ... The fit of the SM if perfect :-( But SM does not predict DM! SM MUED Alexander Belyaev “Beyond the Standard Model” 202 Data Fit with MUED vs SM There is no hint on MUED from the Higgs data ... The fit of the SM if perfect :-( But SM does not predict DM! The fit of MUED is good as well SM MUED Alexander Belyaev “Beyond the Standard Model” 203 mUED: the mass spectrum defines dominant decay pattern to leptons!!! Alexander Belyaev “Beyond the Standard Model” 204 mUED: the mass spectrum defines dominant decay pattern to leptons!!! Can SUSY have this pattern?! Alexander Belyaev “Beyond the Standard Model” 205 mUED collider phenomenology with leptons AB, Brown, Moreno, Papineau'12 Q1 Q1 production rate is the highest Alexander Belyaev “Beyond the Standard Model” 206 mUED collider phenomenology with leptons Lepton multiplicity: AB, Brown, Moreno, Papineau'12 Signal vs BG before (left) and after(right) selection cuts Selection/Analysis cuts Alexander Belyaev “Beyond the Standard Model” 207 mUED collider phenomenology with leptons AB, Brown, Moreno, Papineau'12 preliminary Small mass gap (as compared to MSSM) – much lower missing PT Quite a few PHENO papers, but there is only one (ATLAS) dedicated study the projected limit from this study: R-1 > 1.2—1.3 TeV 3-lepton signature – is very promising: LHC@13/14 will eventually discover or close MUED! Alexander Belyaev “Beyond the Standard Model” 208 First Results from Atlas! Di-muon channel Herwig++ for signal Limits are stronger than from loop-induced processes: 800-900 GeV vs 600 GeV based on dilepton signature But from trilepton signature we expect the limit to be ~1.2 TeV Because the reducible and irreducible BGs are much higher for 2-lepton signature, while signal difference is small Alexander Belyaev “Beyond the Standard Model” 209 UED summary UED are limited from above by DM relic abundance and from below by the LHC searches LHC and DM search experiments provide an important test: LHC@13 TeV will discover or exclude the complete parameter space for 5 & 6D UED There is only one (ATLAS) limit on MUED from di-muon signature only! 3-lepton signal is very promising for MUED at the LHC. Consistent MUED with EWSB and loop-corrections is implemented into LanHEP and publicly available at HEPMDB [CalcHEP and UFO(Madgraph5) formats are available]. It is ready to be used by experimentalists and theorists! Alexander Belyaev “Beyond the Standard Model” 210 Rundal Sundrum (“warp scenario”)[1999] a warped geometry is described by a metric of the form where is the 4D Minkowski line element n y parameterise the XD of space-time, with metric gmn The function eA is the warp factor, defining 4D massscales gravity propagates in the compact & non-compact directions The 4D Newton's constant is related to the the D dimensional one by 4D Planck scale M exponentially D suppressed by the warp factor Planck (UV) TeV(IR) where k,R are related to A(y) Alexander Belyaev “Beyond the Standard Model” 211 Technicolor Alexander Belyaev Beyond The Standard Model 212 (Farhi(Farhi && SusskindSusskind 81)81) Left-handed technifermions in At the weak scale, the technifermions weak doublets, condense and break the weak symmetries right-handed in weak singlets correctly to EM: Alexander Belyaev “Beyond the Standard Model” 213 Alexander Belyaev “Beyond the Standard Model” 214 Alexander Belyaev “Beyond the Standard Model” 215 Alexander Belyaev “Beyond the Standard Model” 216 (SD=Strong Dynamics/Technicolor) Minimal fermion content: 2 Dirac techni-fermions in a weak doublet, TC charge but no QCD charges: Alexander Belyaev “Beyond the Standard Model” 217 Higgs boson mass Alexander Belyaev “Beyond the Standard Model” 218 Higgs boson mass Alexander Belyaev “Beyond the Standard Model” 219 Higgs boson mass Alexander Belyaev “Beyond the Standard Model” 220 Extended Technicolor SU(NTC) break the chiral symmetry of techniquarks their condensate breaks EW Symmetry Important componet of the theory- Extended Technicolor Sector – describes how SM fermions interact with the technifermion condensate to acquire mass Alexander Belyaev “Beyond the Standard Model” 221 Extended Technicolor For QCD – like running TC m is small over this range, so: Alexander Belyaev “Beyond the Standard Model” 222 Extended Technicolor For QCD – like running TC m is small over this range, so: To avoid FCNC, one should have: which implies Difficult to get masses even for s- and c-quarks: TC dynamics should be NOT like QCD. Theory should “walk” and in this case we have: Holdom 81; Appelquist, Wijewardhana 86 Enhanced SM fermion masses and suppressed FCNC Alexander Belyaev “Beyond the Standard Model” 223 “Near conformal” regions for SU(N) Alexander Belyaev “Beyond the Standard Model” 224 SM Higgs vs Technicolor simple and economical complicated at the eff theory level GIM mechanism, no FCNC FCNC constraints requires walking, problems, EW precision data are potential tension with EW precision OK for preferably light Higgs data SM is established, perfectly no viable ETC model suggested describes data yet, work in progress fine-tuning and naturalness no fine-tuning, the scale is problem; triviality problem dynamically generated there is no example of Superconductivity and QCD are fundamental scalar examples of dynamical symmetry breaking Scalar potential parameters and parameters of low-energy effective yukawa couplings are inputs theory are derived once underlying ETC is constructed Alexander Belyaev “Beyond the Standard Model” 225 Walking TC @the LHC Model implementation: AB,Foadi, Frandsen,Jarvinen,Sannino,Pukhov 2009 http://hepmdb.soton.ac.uk/hepmdb:1012.0102 Alexander Belyaev “Beyond the Standard Model” 226 Walking TC @the LHC Alexander Belyaev “Beyond the Standard Model” 227 Walking TC @the LHC complementary di-boson signature Alexander Belyaev “Beyond the Standard Model” 228 Lets take a look at di-boson invariant mass in the current data around 2 TeV ... Sounds quite interesting ... Alexander Belyaev “Beyond the Standard Model” 229 It is also intriguing to look at the correlation in di-lepton channel ... Alexander Belyaev “Beyond the Standard Model” 230 Do we think that TC is really dead? Alexander Belyaev Beyond The Standard Model 231 Do we think that TC is really dead? If title contains question, then the answer is ... Alexander Belyaev Beyond The Standard Model 232 Do we think that TC is really dead? If title contains question, then the answer is ... NO! Alexander Belyaev Beyond The Standard Model 233 Composite Higgs Unified approach Alexander Belyaev Beyond The Standard Model 234 Alexander Belyaev “Beyond the Standard Model” 235 Alexander Belyaev “Beyond the Standard Model” 236 Alexander Belyaev “Beyond the Standard Model” 237 Alexander Belyaev “Beyond the Standard Model” 238 Higgs boson properties are consistent with all promising BSM models encouraging us to keep searching for underlying theory of Nature! UED SUSY ADD CHM Technicolour RS Alexander Belyaev “Beyond the Standard Model” 239 Theories and new particles SUSY partners New gauge bosons (USSM, E6SSM) Technicolour, Exotics – SUSY Composite diquarks, LQ (E6SSM) higgs models LSP is stable under Spin 0,1 bound states of techni-quarks: the R-parity LTB is stable under the Extra- TB number conservation KK – towers: dimensions KK-gravitons KK-fermions KK-gauge bosons LKP is stable under the KK-parity (UED) Alexander Belyaev “New Physics: models and searches” 24 0 Theories and new signatures 0,1,2,3,... leptons+ jets + Missing PT Di-lepton resonances Technicolour, SUSY Composite Same-sign leptons higgs models 0,1,2,3,... leptons+ jets + Missing PT Extra- Di-lepton resonances 0,1,2,3,... leptons+ dimensions Lepton-neutrino jets + resonances Missing PT Di-lepton resonances Same-sign leptons Signatures can be really similar! Alexander Belyaev “New Physics: models and searches” 24 1 The main problem is to decode an underlying theory from the complicated set of signatures: down->top Little SUSY UED ADD Technicolour CHM RS Higgs top->down Easy Tons of Signatures Alexander Belyaev “Beyond the Standard Model” 242 The main problem is to decode an underlying theory from the complicated set of signatures: down->top Little SUSY UED ADD Technicolour CHM RS Higgs top->down down->top Easy Very difficult Tons of Signatures Alexander Belyaev “Beyond the Standard Model” 243 The main problem is to decode an underlying theory from the complicated set of signatures: down->top Little SUSY UED ADD Technicolour CHM RS Higgs top->down down->top Easy Very difficult Tons of Signatures https://hepmdb.soton.ac.uk/ Alexander Belyaev “Beyond the Standard Model” 244 THANK YOU! Thanks to all organizers for fantastic School/Workshop/time in Dubna, boat trip and weather during the weekend! Thanks to all for inspiring talks, questions and discussions! Thanks to everybody! Alexander Belyaev Beyond The Standard Model 245 Additional Slides Alexander Belyaev Beyond The Standard Model 246 6D UED (Dark Matter in a twisted bottle) Arbey,Cacciapaglia,Deandrea,Kubik'12 Alexander Belyaev “Beyond the Standard Model” 247 6D UED DM bounds Arbey,Cacciapaglia,Deandrea,Kubik'12 DM relic abundance bounds DM direct detection bounds Alexander Belyaev “Beyond the Standard Model” 248 Cacciapaglia,Deandrea, 6D UED LHC bounds Ellis,Marrouche,Panizzi '13 ““compositioncomposition ““ ofof signalsignal signaturessignatures MHT-HT analysis plane Exclusion limit: M >600-700 GeV KK Almost all parameter space is excluded Alexander Belyaev “Beyond the Standard Model” 249 The lightest scalar in QCD QCD σ-photon model Lagrangian, aσγγ composite fudge-factor Compare with QCD data: (Belyaev, Brown, Foadi, MTF & Sannino ’13) Alexander Belyaev “Beyond the Standard Model” 250 The Techni-Higgs scalar in QCD Scaled up QCD-like Techni-Higgs would have (diboson) Higgs-like couplings Coefficient cπ~ 1 is independent of number of colors or size of representation Techni-Higgs photon model Lagrangian Alexander Belyaev “Beyond the Standard Model” 251 The Techni-Higgs scalar in QCD Example fit to LHC Data Fit to QCD data Fit to LHC data Alexander Belyaev “Beyond the Standard Model” 252