Aspects of phenomenology in the LHC era

I. Antoniadis

Pre-SUSY 2014, Manchester, 15-18 July 2014

I. Antoniadis (CERN) 1 / 91 Outline

1 LHC: where do we stand? where do we go?

2 : is it alive? 3 String phenomenology: what for? main issues

4 High string scale - heterotic string

5 High string scale - type IIA/B and intersecting/magnetized

6 Low string scale and large extra dimensions

7 Experimental predictions

8 Warped spaces and holography

I. Antoniadis (CERN) 2 / 91 Bibliography

Topics on String Phenomenology I. Antoniadis e-Print: arXiv:0710.4267 [hep-th] An Introduction to perturbative and nonperturbative Ignatios Antoniadis, Guillaume Ovarlez e-Print: hep-th/9906108 String theory and particle : An introduction to string phenomenology Luis E. Ibanez, Angel M. Uranga Published in Cambridge, UK: Univ. Pr. (2012) 673 p

I. Antoniadis (CERN) 3 / 91 Entrance of a Higgs Boson in the Particle Data Group 2013

particle listing

I. Antoniadis (CERN) 4 / 91 Combined mass measurement

37 [CMS-PAS-HIG-14-009]

! Float 3 signal strengths to not depend on yields.

! %%% and HZZ 4 results compatible at 1.6 / level.

[email protected] @CMSexperiment @ICHEP2014

I. Antoniadis (CERN) 5 / 91 +=9QXP=K=LR'M>'RF='&GEEQ':MQML'K9QQ' l9L<'QGEL9J'QRP=LERFQm'

) 4 ATLAS Combined γγ +ZZ* s = 7 TeV Ldt = 4.5 fb -1 H → γγ 3.5 ∫ H → ZZ* → 4 l s = 8 TeV ∫Ldt = 20.3 fb -1 Best fit

=125.36 GeV) =125.36 3 H 68% CL ,MR='K=9QXP=';F9LL=JQ'

(m 95% CL 2.5 SM QGEL9J'QRP=LERF' σ / σ 2 µγγ =1.29 ± 0.30 1.5 (mH =125.98GeV ) ZZ +0.45 1 µ =1.66 (m =124.51 ) −0.38 Signal yield ( yield Signal H GeV 0.5

0 123 123.5 124 124.5 125 125.5 126 126.5 127 127.5 88'9L<' γγ ';MKN9S:GR\' m [GeV] -J<'P=QXJRc' H +0.5 ∆ = 2.3± 0.9 -J<' m 125.5 ± 0.2 (stat) −0.6 (syst) GeV ,=Zc' '!MKN9S:GJGR\''vdx σ'' 125.36 ± 0.37 (stat) ± 0.18 (syst) GeV ∆m =1.47± 0.72 !MKN9S:GJGR\''ud}{ σ'' tdwÅ'.P=;GQGML'K=9QXP=K=LR'lQR9SQS;9J'XL;=PR9GLR\'

I. Antoniadis (CERN) 6 / 91 +9GL'"=;9\'9L<'.PM

ATLAS σ(stat.) Prelim. sys inc. Total uncertainty σ( ) m = 125.5 GeV theory H σ(theory) ± 1 σ on µ + 0.23 H → γγ - 0.22 + 0.24 +0.33 - 0.18 µ = 1.57 + 0.17 -0.28 - 0.12 + 0.35 - 0.32 H → ZZ* → 4l + 0.20 +0.40 - 0.13 µ = 1.44 + 0.17 -0.35 - 0.10 + 0.21 - 0.21 H → WW* → l νlν + 0.24 +0.32 - 0.19 µ = 1.00 + 0.16 -0.29 - 0.08 + 0.14 Combined - 0.14 H γγ→ , ZZ*, WW* + 0.16 +0.21 - 0.14 µ = 1.35 + 0.13 -0.20 - 0.11

W,Z H → b b ±0.5 ±0.4 µ = 0.2 +0.7 -0.6 <0.1 + 0.3 H → ττ (8 TeV data only) - 0.3 + 0.4 +0.5 - 0.3 µ = 1.4 + 0.2 -0.4 - 0.1 + 0.24 Combined - 0.24 + 0.27 H→bb, ττ +0.36 - 0.21 µ = 1.09 + 0.08 -0.32 - 0.04

+ 0.12 =QQXK=Q'1+':P9L;FGLE'>P9;SMLQ' - 0.12 Combined + 0.14 +0.18 - 0.11 µ = 1.30 + 0.10 9L<'NPM

= 7 TeV s = 7 TeV ∫Ldt = 4.6-4.8 fb -1 -0.5 0 0.5 1 1.5 2 !MKN9S:J='ZGRF'1+'l9R'uxÅm'' = 8 TeV s = 8 TeV ∫Ldt = 20.3 fb -1 Signal strength ( µ)

µ =1.30 ± 0.12 (stat) ± 0.10 (th) ± 0.09 (syst) =JJ';F9LL=JQ';MXNJGLEQ'XN<9R=<'QMML'

1R9\'RXL=<'`'' wv'

I. Antoniadis (CERN) 7 / 91 Signal strength

53 [CMS-PAS-HIG-14-009]

! Grouped by production tag and dominant decay: ! 12/dof = 10.5/16 ! p-value = 0.84 (asymptotic) Same sign dimuons ! ttH-tagged 2.0 / above SM. ! Driven by one channel.

[email protected] @CMSexperiment @ICHEP2014

I. Antoniadis (CERN) 8 / 91 Fran¸cois Englert Peter Higgs Nobel Prize of Physics 2013 ↓ ↓

I. Antoniadis (CERN) 9 / 91 The value of its mass 125 GeV ∼ consistent with expectation from precision tests of the SM

favors perturbative physics quartic coupling λ = m2 /v 2 1/8 H ≃ 1st elementary scalar in nature signaling perhaps more to come

triumph of QFT and renormalized perturbation theory! Standard Theory has been tested with radiative corrections

Window to new physics ? very important to measure precisely its properties and couplings

several new and old questions wait for answers , neutrino masses, baryon asymmetry, flavor physics, axions, electroweak scale hierarchy, early , . . .

I. Antoniadis (CERN) 10 / 91 6 incertitude théorique ∆α 5 ∆α(5) ± had = 0.02761 0.00036

4 2 3 ∆χ

2 95% CL

1 région exclue 0 20100 400 260 [ ] mH GeV

I. Antoniadis (CERN) 11 / 91 Beyond the Standard Theory of : driven by the mass hierarchy problem

Standard picture: low energy supersymmetry

Natural framework: Heterotic string (or high-scale M/F) theory

Advantages: natural elementary scalars gauge coupling unification LSP: natural dark matter candidate radiative EWSB Problems: too many parameters: soft breaking terms

MSSM : already a % - %0 fine-tuning ‘little’ hierarchy problem

I. Antoniadis (CERN) 12 / 91 I. Antoniadis (CERN) 13 / 91 I. Antoniadis (CERN) 14 / 91 What is next?

I. Antoniadis (CERN) 15 / 91 What is next?

Physics is an experimental science

Exploit the full potential of LHC • Go on and explore the multi TeV energy range •

I. Antoniadis (CERN) 16 / 91 The LHC timeline ! #$'%"$#&"$ HFFN% $8'68%4,%! *% LS1 Machine Consolidation

#;3%G?%LOM%%+&?%CHK% -G%038@%1;20% LS2 Machine upgrades for high Luminosity HFGIAGJ% "6+5'6+%! *%,46% • Collimation ! !$ • Cryogenics *+70.3% !%D%1;20% • Injector upgrade for high intensity (lower emittance) *411+)8%CIF%- G%5+6% • Phase I for ATLAS : Pixel upgrade, FTK, and new small wheel =+'6%'8%GIAGJ%%+&%%

HFGM% "/'7+BG%;5.6'*+%% LS3 Machine upgrades for high Luminosity ;192'8+%1;20% ! "$ • Upgrade interaction region • Crab cavities? %<0)+%34203'1%1;20% '8%GJ%%+&?%% • Phase II: full replacement of tracker, new trigger scheme (add L0), readout CGFF%- G%5+6%=+'6% electronics. CHFHH% "/'7+BH%;5.6'*+% ! #$ 84% !B! *% Europe’s top priority should be the exploitation of the full potential of the LHC, including the CIFF%- G%5+6%=+'6?% high-luminosity upgrade of the machine and 6;3%;5%84%P%I%'( G% detectors with a view to collecting ten times )411+)8+*% more data than in the initial design, by around CHFIF% 2030. #####IM%####

I. Antoniadis (CERN) 17 / 91 We must fully explore the 10-100 TeV energy range

ILC project

The future of LHC

I. Antoniadis (CERN) 18 / 91 I. Antoniadis (CERN) 19 / 91 I. Antoniadis (CERN) 20 / 91 I. Antoniadis (CERN) 21 / 91 I. Antoniadis (CERN) 22 / 91 VHE-LHC: location and size

A circumference of 100 km is being considered for cost-benefit reasons 20T magnet in 80 km / 16T magnet in 100 km 100 TeV → I. Antoniadis (CERN) 23 / 91 I. Antoniadis (CERN) 24 / 91 I. Antoniadis (CERN) 25 / 91 126 GeV Higgs compatible with supersymmetry

Upper bound on the lightest scalar mass:

3 m4 m2 A2 A2 m2 < m2 cos2 2β + t ln ˜t + t 1 t < (130GeV )2 h Z 2 v 2 2 2 2 ∼ (4π) " mt m˜t − 12m˜t !# ∼

mh 126 GeV => m 3 TeV or At 3m 1.5 TeV ≃ ˜t ≃ ≃ ˜t ≃

=> % to a few %0 fine-tuning m1 m2 tan2 minimum of the potential: m2 = 2 1 − 2 β 2m2 + Z tan2 β 1 ∼− 2 · · · − 2 2 2 3λt 2 MGUT m m M m [31] RG evolution: 2 = 2( GUT) 2 ˜t ln + − 4π m˜t · · · 2 2 m (MGUT) (1)m + ∼ 2 − O ˜t · · ·

I. Antoniadis (CERN) 26 / 91 Reduce the fine-tuning

minimize radiative corrections

MGUT Λ : low messenger scale (gauge mediation) →

2 8αs 2 Λ δm˜t = M3 ln + 3π M3 · · · increase the tree-level upper bound => extend the MSSM

extra fields beyond LHC reach effective field theory approach → Low scale SUSY breaking => extend MSSM with the goldstino

Non linear MSSM →

· · ·

I. Antoniadis (CERN) 27 / 91 Can the SM be valid at high energies?

Degrassi-Di Vita-Elias Mir´o-Espinosa-Giudice-Isidori-Strumia ’12

Instability of the SM Higgs potential => metastability of the EW vacuum

I. Antoniadis (CERN) 28 / 91 If the weak scale is tuned => split supersymmetry is a possibility Arkani Hamed-Dimopoulos ’04, Giudice-Romaninio ’04

natural splitting: gauginos, higgsinos carry R-symmetry, scalars do not main good properties of SUSY are maintained gauge coupling unification and dark matter candidate also no dangerous FCNC, CP violation, . . . experimentally allowed Higgs mass => ‘mini’ split

mS few - thousands TeV ∼ gauginos: a loop factor lighter than scalars ( m ) ∼ 3/2 natural string framework: intersecting (or magnetized) branes IA-Dimopoulos ’04 D- stacks are supersymmetric with massless gauginos intersections have chiral fermions with broken SUSY & massive scalars

I. Antoniadis (CERN) 29 / 91 Giudice-Strumia ’11

I. Antoniadis (CERN) 30 / 91 Alternative answer: Low UV cutoff Λ TeV ∼ - low scale gravity => extra dimensions: large flat or warped

- low string scale => low scale gravity, ultra weak string coupling

n 32 n −13 Ms 1 TeV => volume R = 10 l (R⊥ .1 10 mm for n =2 6) ∼ ⊥ s ∼ − − - spectacular model independent predictions

- radical change of high energy physics at the TeV scale

Moreover no little hierarchy problem:

radiative electroweak symmetry breaking with no logs [26]

Λ a few TeV and m2 = a loop factor Λ2 ∼ H × But unification has to be probably dropped

New Dark Matter candidates e.g. in the extra dims

I. Antoniadis (CERN) 31 / 91 Connect string theory to the real world Is it a tool for strong coupling dynamics or a theory of fundamental forces? Can string theory describe both particle physics and cosmology? What can we hope to learn from LHC and cosmological observations on string phenomenology?

I. Antoniadis (CERN) 32 / 91 At what energies strings may be observed?

Very different answers depending mainly on the value of the string scale Ms

18 −32 Before 1994: Ms MPlanck 10 GeV ls 10 cm After 1994: ≃ ∼ ≃

- arbitrary parameter : Planck mass MP TeV −→ - physical motivations => favored energy regions:

∗ 18 MP 10 GeV Heterotic scale High : ≃ 16 ( MGUT 10 GeV Unification scale ≃ 11 2 Intermediate : around 10 GeV (M /MP TeV) s ∼ SUSY breaking, strong CP axion, see-saw scale

Low : TeV (hierarchy problem)

I. Antoniadis (CERN) 33 / 91 High string scale

perturbative heterotic string : the most natural for SUSY and unification

gravity and gauge interactions have same origin massless excitations of the closed string

But mismatch between string and GUT scales:

2 Ms = gH MP 50 M GUT g α GUT 1/25 [51] ≃ H ≃ ≃ 2 in GUTs only one prediction from 3 gauge couplings unification: sin θW

introduce large threshold corrections or strong coupling Ms M GUT → ≃ but loose predictivity

I. Antoniadis (CERN) 34 / 91 Heterotic string

gravity + gauge kinetic terms [52]

1 1 [d 10x] M8 (10) + [d 10x] M6 2 simplified units: 2 = π =1 g 2 H R g 2 H FMN Z H Z H

Compactification in 4 dims on a 6-dim manifold of volume V6 =>

V V [d 4x] 6 M8 (4) + [d 4x] 6 M6 2 g 2 H R g 2 H Fµν Z H Z H ||2 || 2 MP 1/g => 1 1 1 M2 M2 V M6 M gM g g√V M3 P = 2 H 2 = 2 6 H => H = P H = 6 H g g gH

gH < 1=> V6 string size ∼ ∼

I. Antoniadis (CERN) 35 / 91 Heterotic string: Spectrum

Gauge group G affine current algebra in the R-movers (bosonic) CFT ↔ a b abc c ab Jn , Jm = f Jn+m + kG δ δn+m kG : integer level of central extension

h 2 i 2 gG = gH /kG · => kG = 1 : dims of allowed matter reps constrained by kG ) · simplest constructions (CY’s, orbifolds, lattices, free fermions) maximum rank: 22

guarantee gauge coupling unification at MH allowed reps: fundamentals & 2-index antisym of unitary groups, spinors of orthogonal groups However: - no adjoints to break GUT groups 2 - in SM sin θW = 3/8=> fractional electric charges Schellekens ’90

I. Antoniadis (CERN) 36 / 91 (Hyper)charge quantization

All color singlet states have integer charges

fractional electric charged states: nice prediction or problematic? lightest is stable => problematic? ways out: - superheavy + inflate away - be confined to integrally charged by extra gauge group

live without adjoints => non conventional ‘semi’-GUTs e.g. break fictitious SO(10) by discrete Wilson lines or projection to

flipped SU(5) U(1), Pati-Salam type SU(4) SU(2)L SU(2)R , or direct SM × × × Heterotic models revived: Orbifold GUTs groups in Munich, Bonn, Hamburg, Ohio, U Penn

I. Antoniadis (CERN) 37 / 91 Higgs from untwisted sector => gauge-Higgs unification

λtop = gGUT => mtop IR fixed point 170 GeV ∼ ≃ Yukawa couplings: hierarchies `ale Froggatt-Nielsen discrete symmetries => couplings allowed with powers of a singlet field n λn Φ Φ 0.1 Ms hierarchies ∼ h i∼ → A single anomalous U(1) => Φ = 0 to cancel the FI D-term h i 6 TrQ 2 D-term is shifted to D + 192π2 gH [74] R-neutrinos: natural framework for see-saw mechanism 2 h νLνR + MνR νR h = v << M => mR M ; mL v /M h i h i ∼ ∼ proton decay: problematic dim-5 operators

in general need suppression higher than Ms or small couplings SUSY/ in a hidden sector from the other E gravity mediation 8 →

I. Antoniadis (CERN) 38 / 91 Open strings and D-branes string propagation in space-time => 2-dim world-sheet (τ,σ) X µ(τ,σ) τ: time, σ [0,π]: spatial extension of the string ∈ closed strings =>σ: periodic X µ(τ, 0) = X µ(τ,π) open string => endpoints: σ = 0,π world-sheet boundaries they also carry gauge charges D-branes = hypersurfaces where open strings can end Dp-brane: parallel dimensions: X 1,..., X p (also time X 0) µ ∂σX =0 at σ = 0 normal derivative vanishes Newmann boundary conditions => free propagation along the boundary transverse dimensions: X p+1,..., X 9 µ µ µ X = X0 at σ = 0 (∂τ X =0 at σ = 0) Dirichlet conditions: endpoint fixed at the boundary

I. Antoniadis (CERN) 39 / 91 D-brane spectrum

Generic spectrum: N coincident branes => U(N) a-stack endpoint transformation: Na or N¯ a U(1)a charge: +1 or 1 − ւ => “baryon” number

open strings from the same stack => adjoint gauge multiplets of U(Na) • stretched between two stacks => bifundamentals of U(Na) U(Nb) • ×

a-stack

b-stack non-oriented strings => also:

- orthogonal and symplectic groups SO(N), Sp(N)

- matter in antisymmetric + symmetric reps

I. Antoniadis (CERN) 40 / 91 Non oriented strings => orientifold planes

where closed strings change orientation

=> mirror branes identified with branes under orientifold action

strings stretched between two mirror stacks • X T

a antisymmetric or => θ Orientifold O symmetric of U(Na) → X// X⊥ X⊥ →− a*

I. Antoniadis (CERN) 41 / 91 Minimal embedding

General analysis using 3 brane stacks [56]

=> U(3) U(2) U(1) × × antiquarks uc , d c (3¯, 1) :

antisymmetric of U(3) or bifundamental U(3) U(1) ↔ => 3 models: antisymmetric is uc , d c or none

I. Antoniadis (CERN) 42 / 91 Ni stack of D-branes: U(Ni )= SU(Ni ) U(1)i × g 2 Ni gauge couplings: α = and αi Ni 4π

a b 1 ab αNi normalization: TrT T = δ => αi = 2 2Ni

2 2 2 1 2c1 4c2 6c3 Y = c1Q1 + c2Q2 + c3Q3 => 2 = 2 + 2 + 2 gY g1 g2 g3

2 2 gY 1 1 sin θW = 2 2 = 2 2 = 2 2 2 2 2 2 2 g2 + gY g2 /gY + 1 1 + 4c2 + 2c1 g2 /g1 + 6c3 g2 /g3

I. Antoniadis (CERN) 43 / 91 U(3) U(2) U(3) U(2) U(3) U(2) Q Q Q

c c c c νc u U(1) l d U(1) ν U(1)

c d L uc L uc L c d c c νc l l

Model A Model B Model C

Q (3, 2;1, 1, 0)1/6 (3, 2;1,εQ, 0)1/6 (3, 2;1,εQ, 0)1/6 uc (3¯, 1;2, 0, 0) (3¯, 1; 1, 0, 1) (3¯, 1; 1, 0, 1) −2/3 − −2/3 − −2/3 c d (3¯, 1; 1, 0,εd) (3¯, 1;2, 0, 0) (3¯, 1; 1, 0, 1) − 1/3 1/3 − − 1/3 L (1, 2;0, 1,εL)−1/2 (1, 2;0,εL, 1)−1/2 (1, 2;0,εL, 1)−1/2 c − l (1, 1;0, 2, 0)1 (1, 1;0, 0, 2)1 (1, 1;0, 0, 2)1 c − − ν (1, 1;0, 0, 2εν)0 (1, 1;0, 2εν, 0)0 (1, 1;0, 2εν, 0)0

I. Antoniadis (CERN) 44 / 91 U(3) U(2) U(3) U(2) U(3) U(2) Q Q Q

c c c c νc u U(1) l d U(1) ν U(1)

c d L uc L uc L c d c c νc l l

Model A Model B Model C

1 1 1 1 YA = Q + Q YB C = Q Q −3 3 2 2 , 6 3 − 2 1

2 1 3 1 6 sin θW = = = 2+2α2/3α3 α =α 8 1+ α2/2α1 + α2/6α3 α =α 7+3α2/α1 2 3 2 3

I. Antoniadis (CERN) 45 / 91 SU(5) GUT

U(3) U(2) Q U(5) Q, uc ,l c c u U(1) c 10 l U(1) c L c d −→ 5 c d ,L

νc νc

I. Antoniadis (CERN) 46 / 91 String moduli

String compactifications from 10/11 to 4 dims scalar moduli → arbitrary VEVs: parametrize the compactification manifold

size of cycles, shapes, ..., string coupling

N =1 SUSY => complexification: scalar + i pseudoscalar φi ≡ Low energy couplings: functions of moduli

I. Antoniadis (CERN) 47 / 91 1 F 2 a e.g. gauge couplings: 2 a : gauge group ga 1 N Re f =1 SUSY => holomorphicity: 2 = a(φi ) ga SUSY transformation => moduli-dependent θ-angles:

θaFaF˜a with θa = Im fa(φi )

2 2 In superspace: d θ f (φi ) W gauge field-strength chiral superfield a ← Z

I. Antoniadis (CERN) 48 / 91 Moduli stabilization

If moduli massless inconsistent → long range forces, cosmological production, accelerators

Outstanding problem: moduli stabilization

avoid experimental conflict fix their VEVs => compute low energy couplings - preserving SUSY Generate moduli potential: via - after SUSY breaking

non-perturbative effects or by • turn-on fluxes: constant field-strengths of generalized gauge potentials • gauge fields: internal magnetic fields generalization: higher rank antisymmetric tensors

I. Antoniadis (CERN) 49 / 91 Intersecting branes: ‘perfect’ for SM embedding

product of unitary gauge groups (brane stacks) and bi-fundamental reps

but no unification: no prediction for Ms , independent gauge couplings however GUTs: problematic: no perturbative SO(10) spinors

no top-quark Yukawa coupling in SU(5): 10 10 5H

SU(5) is part of U(5) => U(1) charges : 10 charge 2 ; 5H charge 1 ± => cannot balance charges with SU(5) singlets can be generated by D-brane instantons but . . . Non-perturbative M/F-theory models: → combine good properties of heterotic and intersecting branes but lack exact description for systematic studies

I. Antoniadis (CERN) 50 / 91 => D-brane world I.A.-Arkani-Hamed-Dimopoulos-Dvali ’98

gravity: closed strings propagating in 10 dims • gauge interactions: open strings with their ends attached on D-branes • Dimensions of finite size: n transverse 6 n parallel [54] − calculability => R lstring ; R arbitrary k ≃ ⊥ 2 1 2+n n Mp 2 Ms R⊥ gs = α : weak string coupling [34] ≃ gs տ 2+n Planck mass in 4+ n dims: M∗

small Ms /MP : extra-large R⊥ n 32 n Ms 1 TeV => R = 10 l [83] ∼ ⊥ s R .1 10−13 mm for n = 2 6 ⊥ ∼ − − distances < R : gravity (4+n)-dim strong at 10−16 cm ⊥ → I. Antoniadis (CERN) 51 / 91 Type I/II strings: gravity and gauge interactions have different origin gravity + gauge kinetic terms

10 1 8 (10) p+1 1 p−3 2 [d x] M + [d x] M [35] g 2 s R g s FMN Z s Z s Compactification in 4 dims =>

V Vk [d 4x] 6 M8 (4) + [d 4x] Mp−3 2 V = V V g 2 s R g s Fµν 6 k ⊥ Z s Z s ||2 || 2 MP 1/g => 2 p−3 gs = g VkMs < 1=> Vk string size ∼ ∼ V M2 ⊥ M2+n g g 2 => P = 2 s s gs ≃

I. Antoniadis (CERN) 52 / 91 string propagation in space-time => 2-dim world-sheet string perturbation theory : world-sheet topological expansion

−χ .... gs χ: Euler number ∼ general characterization of 2-dim Riemann surfaces: χ = 2 2h b c − − − genus=nb of handlesր boundaries ↑ տ crosscaps

2 tree-level: h = b = c =0 => 1/gs

“tree-level” open strings: h = c = 0, b =1 => 1/gs

I. Antoniadis (CERN) 53 / 91 Braneworld

−16 2 types of compact extra dimensions: parallel (d ): < 10 cm (TeV) [51] • k transverse ( ):∼ < 0.1 mm (meV) • ⊥ p=3+d // -dimensional brane ∼ 3-dimensional brane open string

closed string Minkowski 3+1 dimensions

Extra dimension(s) perp. to the brane

d || extra dimensions

I. Antoniadis (CERN) 54 / 91 Standard Model on D-branes I.A.-Kiritsis-Rizos-Tomaras ’02

U(1)4 : hypercharge + B, L, PQ global • νR in the bulk : small neutrino masses •

I. Antoniadis (CERN) 55 / 91 fermion generation U(3) U(2) U(1) [42] × × Q (3, 2; 1, w, 0) w = 1 1/6 ± uc (3¯, 1; 1, 0, x) x = 1, 0 − −2/3 ± d c (3¯, 1; 1, 0, y) y = 1, 0 − 1/3 ± L (1, 2; 0, 1, z)−1/2 z = 1, 0 c ± l (1, 1; 0, 0, 1)1 hypercharge Y = c1Q1 + c2Q2 + c3Q3 => 2 possibilities:

c = 1/3 c = 1/2 x = 1 y =0 w = 1 z = 1/0 3 − 2 ± − ± − c =2/3 c = 1/2 x =0 y =1 w = 1 z = 1/0 3 2 ± ∓ −

I. Antoniadis (CERN) 56 / 91 R-neutrinos: in the bulk

Arkani Hamed-Dimopoulos-Dvali-March Russell ’98 Dienes-Dudas-Gherghetta ’98 Dvali-Smirnov ’98

R-neutrino: νR (x, y) y: bulk coordinates

4 Sint = gs d x H(x) L(x) νR (x, y = 0) Z gs v 0 H = v => mass-term: νLν 4d zero-mode h i n/2 R ← R⊥ g v M Dirac neutrino masses: m s v ∗ ν n/2 ≃ ≃ Mp R⊥ 10−3 10−2 eV for M 1 10 TeV ≃ − ∗ ≃ −

mν << 1/R⊥ => KK modes unaffected

I. Antoniadis (CERN) 57 / 91 Origin of EW symmetry breaking?

possible answer: radiative breaking

V = µ2H†H + λ(H†H)2

µ2 = 0 at tree but becomes < 0 at one loop non-susy vacuum

simplest case: one Higgs from the same brane

1 2 2 => tree-level V same as susy: λ = 8 (g2 + gY ) D-terms µ2 = g 2ε2M2 effective UV cutoff − s ← UV e−πl

3ց∞ 4 ր R θ 1 2 2 ε2(R) = dll 3/2 2 il + n2e−2πn R l 2π2 16l 4η12 2 0 n Z   X IRր ց 1

I. Antoniadis (CERN) 58 / 91 0.20

0.15

ε 0.10

0.05

0.00 0.25 1.00 1.75 2.50 3.25 4.00 4.75 R R 0 : ε(R) 0.14 large transverse dim R = l 2/R → ≃ ⊥ s → ∞

R : ε(R)Ms ε /R ε 0.008 UV cutoff: Ms 1/R → ∞ ∼ ∞ ∞ ≃ → Higgs scalar = component of a higher dimensional gauge field

=>ε∞ calculable in the effective field theory

2 λ = g /4 1/8 => MH v/2 = 125 GeV ∼ ≃ Ms or 1/R a few or several TeV ∼

I. Antoniadis (CERN) 59 / 91 Accelerator signatures: 4 different scales

Gravitational radiation in the bulk => missing energy [62]

present LHC bounds: M∗ > 3 5 TeV ∼ − Massive string vibrations => e.g. resonances in dijet distribution [64]

2 2 2 Mj = M0 + Ms j ; maximal spin : j + 1 higher spin excitations of quarks and gluons with strong interactions

present LHC limits: Ms > 5 TeV ∼ Large TeV dimensions => KK resonances of SM gauge bosons I.A. ’90 M2 = M2 + k2/R2 ; k = 1, 2,... k 0 ± ± −1 experimental limits: R > 0.5 4 TeV (UED - localized fermions) [68] ∼ − extra U(1)’s and anomaly induced terms

masses suppressed by a loop factor from Ms [73]

I. Antoniadis (CERN) 60 / 91 I. Antoniadis (CERN) 61 / 91 Gravitational radiation in the bulk => missing energy

P Angular distribution => spin of the graviton

P γ or jet

Collider bounds on R⊥ in mm n =2 n =4 n =6 LEP 2 4.8 10−1 1.9 10−8 6.8 10−11 present LHC bounds: × × × −1 −8 −11 M∗ > 3 5 TeV Tevatron 5.5 10 1.4 10 4.1 10 ∼ − × × × LHC 4.5 10−3 5.6 10−10 2.7 10−12 × × ×

I. Antoniadis (CERN) 62 / 91 Black hole production

2 String-size black hole energy threshold : M BH Ms /g ≃ s Horowitz-Polchinski ’96, Meade-Randall ’07

−1 string size black hole: rH ls = M ∼ s d−3 d−2 2 black hole mass: MBH r /GN GN l g ∼ H ∼ s s

weakly coupled theory => strong gravity effects occur much above Ms, M∗

gs 0.1 (gauge coupling) => M BH 100Ms ∼ ∼

Comparison with Regge excitations : Mn = Ms √n =>

4 4 production of n 1/g 10 string states before reach M BH [60] ∼ s ∼

I. Antoniadis (CERN) 63 / 91 Universal deviation from Standard Model in dijet distribution

Ms = 2 TeV Width = 15-150 GeV

Anchordoqui-Goldberg- L¨ust-Nawata-Taylor- Stieberger ’08

I. Antoniadis (CERN) 64 / 91 Tree level superstring amplitudes involving at most 2 fermions and gluons: model independent for any compactification, # of susy’s, even none no intermediate exchange of KK, windings or graviton emmission Universal sum over infinite exchange of string (Regge) excitations

Parton luminosities in pp above TeV are dominated by gq, gg

=> model independent gq gq, gg gg, gg qq¯ → → →

I. Antoniadis (CERN) 65 / 91 Cross sections

(gg gg) 2 , (gg qq¯) 2 |M → | |M → | model independent  for any compactification (qq¯ gg) 2 , (qg qg) 2  |M → | |M → |   (gg gg) 2 = g 4 1 + 1 + 1  |M → | YM s2 t2 u2  9 2 2 2 2 2 2 1 2 s V + t V + u V (sVs + tVt + uVu) × 4 s t u − 3 h  i 2 2 2 4 t + u 1 1 2 3 Ms = 1 (gg qq¯) = g (tVt + uVu) Vt Vu |M → | YM s2 6 tu − 8  

tu 2 2 Vs = B(t, u) = 1 π tu + . . . Vt : s t Vu : s u − s − 3 ↔ ↔ YM limits agree with e.g. book ”Collider Physics” by Barger, Phillips

I. Antoniadis (CERN) 66 / 91 String Resonances production at Hadron Colliders I.A.-Anchordoqui-Dai-Feng-Goldberg-Huang-L¨ust-Stojkovic-Taylor in prep

100 cteq6l1 CT10nlo NNPDF23-nlo-as-0114 10-1 MRST2004qed_proton GeV) /

-2 (fb 10

/dM -3

σ 10 d

10-4

3000 4000 5000 6000 7000 M(GeV) M (GeV)

[60]

I. Antoniadis (CERN) 67 / 91 Localized fermions (on 3-brane intersections) => single production of KK modes I.A.-Benakli ’94

f strong bounds indirect effects: R−1 > 3 TeV n_ • ∼ R new resonances but at most n = 1 _ • f

Otherwise KK momentum conservation [70] => pair production of KK modes (universal dims)

f n_ weak bounds R−1 > 500 GeV R • ∼ _ n_ no resonances f - R • lightest KK stable : dark matter candidate • Servant-Tait ’02

I. Antoniadis (CERN) 68 / 91 R−1 = 4 TeV 100

γ + Z 10-1 γ

10-2 Z

10-3

-4

Events / GeV Events 10

10-5

10-6

1500 3000 4500 6000 7500 Dilepton mass - no observation in dijets => R−1 > 20 TeV ; 95% CL ∼ - more than one dimension => stronger limits

I. Antoniadis (CERN) 69 / 91 Universal extra dimensions (UED) : Mass spectrum

Radiative corrections => mass shifts that lift degeneracy at lowest KK level divergent sum over KK modes in the loop => cutoff scale Λ 10/R ≃

I. Antoniadis (CERN) 70 / 91 UED hadron collider phenomenology

large rates for KK-quark and KK-gluon production cascade decays via KK-W bosons and KK-leptons determine particle properties from different distributions missing energy from LKP: weakly interacting escaping detection phenomenology similar to supersymmetry

spin determination important for distinguishing SUSY and UED [60] gluino 1/2 KK-gluon 1 squark 0 KK-quark 1/2 chargino 1/2 KK-W boson 1 slepton 0 KK-lepton 1/2 neutralino 1/2 KK-Z boson 1

I. Antoniadis (CERN) 71 / 91 SUSY vs UED signals at LHC

Example: jet dilepton final state

SUSY UED

I. Antoniadis (CERN) 72 / 91 Extra U(1)’s and anomaly induced terms

masses suppressed by a loop factor

usually associated to known global symmetries of the SM

(anomalous or not) such as (combinations of) Baryon and Lepton number, or PQ symmetry

Two kinds of massive U(1)’s: I.A.-Kiritsis-Rizos ’02

- 4d anomalous U(1)’s: MA gAMs ≃ - 4d non-anomalous U(1)’s: (but masses related to 6d anomalies)

MNA gAMs V (6d 4d) internal space => MNA MA ≃ 2 ← → ≥ or massless in the absence of such anomalies

I. Antoniadis (CERN) 73 / 91 Green-Schwarz anomaly cancellation

X

A 2 = k TrQAQ axion θ : δA = dΛ δθ = mAΛ I ∼ I → −

1 2 1 2 θ A 2 FI (dθ+mAA) + kI Tr FI FI I I −4gI − 2 mA ∧ տcancel the anomaly

string theory: θ = Poincar´edual of a 2-form dθ = dB ∗ 2 Heterotic: single universal axion [38]

D-brane models: U(1)A gauge boson acquires a mass but global symmetry remains in perturbation theory

I. Antoniadis (CERN) 74 / 91 Standard Model on D-branes : SM++

2-Left 1-Right gluon U(3) 3-Baryonic Q L U , D R R

W

#-Leptonic U(1) L

L E ! " L R Sp(1) SU(2) U(1) ≡ R U(1)3 : hypercharge + B, L

I. Antoniadis (CERN) 75 / 91 TeV string scale Anchordoqui-IA-Goldberg-Huang-L¨ust-Taylor ’11

B and L become massive due to anomalies Green-Schwarz terms

the global symmetries remain in perturbation - Baryon number => proton stability - Lepton number => protect small neutrino masses 2 no Lepton number => 1 LLHH Majorana mass: hHi LL Ms → Ms տ GeV B, L => extra Z ′s ∼ with possible leptophobic couplings leading to CDF-type Wjj events Z ′ B lighter than 4d anomaly free Z ′′ B L ≃ ≃ −

I. Antoniadis (CERN) 76 / 91 microgravity experiments

change of Newton’s law at short distances detectable only in the case of two large extra dimensions new short range forces light scalars and gauge fields if SUSY in the bulk or broken by the compactification on the brane I.A.-Dimopoulos-Dvali ’98, I.A.-Benakli-Maillard-Laugier ’02 such as radion and lepton number 2 −4 volume suppressed mass: (TeV) /MP 10 eV mm range ∼ → can be experimentally tested for any number of extra dimensions

- Light U(1) gauge bosons: no derivative couplings => for the same mass much stronger than gravity: > 106 ∼

I. Antoniadis (CERN) 77 / 91 Experimental limits on short distance forces

m1m2 −r/λ V (r)= G r 1+ αe 10 10 − Lamoreaux  10 9 gauged B# 10 8 Excluded by 10 7 Stanford 1 experiment 10 6

10 5 Yukawa messengers Stanford 3

4 α 10 dilaton strange Stanford 2 3 10 modulus

2 10 gluon U.Colorado modulus 10 1 KK gravitons U.Washington 2 10 0 U.Washington 1 heavy q 10 -1 moduli 10 -2 1 10 100 1000 λ (µm)

I. Antoniadis (CERN) 78 / 91 Adelberger et al. ’06

α =1=> λ < 55 µm ∼ dark-energy length scale 85µm • ≈

I. Antoniadis (CERN) 79 / 91 improved bounds from Casimir effect in the nm range Decca-Fischbach et al ’07, ’08

5: Colorado 4: Stanford 3: Lamoureaux 1: Mohideen et al.

I. Antoniadis (CERN) 80 / 91 LIMITS ON EXTRA YUKAWA FORCE mass [eV] 105 104 103 102 10 1 | Neutron scattering: 2 -8 antiprotonic atoms bounds in the range log|g -10 EXCLUDED 1pm - 1nm REGION ∼ Unseen extra UCN gravitational level -12 Nesvizhevsky-Pignol- -14 Electroweak scale new boson Protasov ’07 Ederth -16

-18

Random potential model -20 Comparing forward and backward scattering Mohideen Comparing forward scattering and total X-section Asymmetry of scattering on noble gases -22

gauge boson -24 in extra dimensions Purdue

-26 10-12 10-11 10-10 10-9 10-8 10-7 λ [m]

I. Antoniadis (CERN) 81 / 91 I. Antoniadis (CERN) 82 / 91 More general framework: large number of species

2 2 N particle species => lower scale : M∗ = Mp /N Dvali ’07, Dvali, Redi, Brustein, Veneziano, Gomez, L¨ust ’07-’10 derivation from: black hole evaporation or quantum information storage

M 1 TeV => N 1032 particle species ! ∗ ≃ ∼ 2 ways to realize it lowering the string scale

1 Large extra dimensions SM on D-branes [51]

n n N = R l : number of KK modes up to energies of order M Ms ⊥ s ∗ ≃ 2 Effective number of string modes contributing to the BH bound 1 N g −16 = 2 with s 10 SM on NS5-branes gs ≃ I.A.-Pioline ’99, I.A.-Dimopoulos-Giveon ’01

I. Antoniadis (CERN) 83 / 91 More general framework: large number of species

2 2 N particle species => lower quantum gravity scale : M∗ = Mp /N Dvali ’07, Dvali, Redi, Brustein, Veneziano, Gomez, L¨ust ’07-’10 derivation from: black hole evaporation or quantum information storage

Pixel of size L containing N species storing information:

localization energy E > N/L ∼ → 2 Schwarzschild radius Rs = N/(LMp )

no collapse to a black hole : L > Rs => L > √N/Mp = 1/M∗ ∼ ∼ M 1 TeV => N 1032 particle species ! ∗ ≃ ∼

I. Antoniadis (CERN) 84 / 91 What is LST ? Decouple gravity from NS5-branes

Analogy from D3-branes : decouple gravity => Ms , gs fixed →∞ (conformal) Field Theory (CFT) → simplest case: 4d = 4 super Yang Mills SU(N) N parameters: number of branes N, gauge coupling gYM

NS-5 branes: Ms finite, gs 0 (little) String Theory without gravity → → simplest case: 6d LST (chiral IIA or non-chiral IIB)

massless sector: 6d SU(N) of tensors (IIA) or vectors (IIB)

at a non-trivial fixed point

parameters: number of branes N, string scale Ms

I. Antoniadis (CERN) 85 / 91 How to study LST ? Using gauge/gravity duality

Gravity background : near horizon geometry (holography) Maldacena ’98

Analogy from D3-branes : AdS S5 5 × parameters: AdS radius rAdS Ms , gs N, gYM ↔ 2 validity: rAdS Ms >> 1, gs << 1 => large N, gYM N model independent part : AdS → 5 NS-5 branes : ( R ) SU(2) S3 M6 ⊗ + × ≡ linear dilaton background↑ in 7d flat string-frame metric Φ= α y − | | Aharony-Berkooz-Kutasov-Seiberg ’98 3 parameters: Ms , α (or S radius) N ↔ sugra validity: small α => large N

compactify to d = 4 ( ) => gYM 2d volume M6 → M4 ∼ model independent part : linear dilaton → I. Antoniadis (CERN) 86 / 91 Put gravity back but weakly coupled

“cut” the space of the extra dimension => gravity on the brane

Toy 5d bulk model

rc 4 −Φ 3 3 2 Sbulk = d x dy√ g e M R + M ( Φ) Λ − 5 5 ∇ − Z Z0  S = d 4x√ g e−Φ L T vis(hid) − SM(hid) − vis(hid) Z    Tuning conditions: Tvis = Thid Λ < 0 [89] − ↔

I. Antoniadis (CERN) 87 / 91 Constant dilaton and AdS metric : Randal Sundrum model

spacetime = slice of AdS : ds2 = e−2k|y|η dxµdxν + dy 2 k2 Λ/M3 5 µν ∼ 5 bulk

′ IR-brane UV-brane T Λ T −| |

y = 0 y = πrc

−2krc 2 3 exponential hierarchy: MW = MP e M M /k M MGUT P ∼ 5 5 ∼ 4d gravity localized on the UV-brane, but KK gravitons on the IR

−2krc mn = cn k e TeV cn (n + 1/4) for large n ∼ ≃ => spin-2 TeV resonances in di-lepton or di-jet channels

I. Antoniadis (CERN) 88 / 91 Linear dilaton background IA-Arvanitaki-Dimopoulos-Giveon ’11

dilaton Φ = α y and flat metric => − | | 2 −α|y| 2 2 α|y| µ ν 2 g = e ; ds = e 3 (η dx dx + dy ) Einstein frame s µν ← z eαy/3 => polynomial warp factor + log varying dilaton ∼ bulk

Planck-brane SM-brane MW Λ MP −| |

y = 0 y = rc

3 2 −α|y| 2 M5 αrc exponential hierarchy: g = e M e α kRS s P ∼ α ≡ 4d graviton flat, KK gravitons localized near SM

I. Antoniadis (CERN) 89 / 91 LST KK graviton phenomenology

nπ 2 α2 KK spectrum : m2 = + ; n = 1, 2,... n r 4  c  => mass gap + dense KK modes α 1 TeV r −1 30 GeV ∼ c ∼ 1 1 couplings : Λn ∼ (αrc )M5

=> extra suppression by a factor (αrc ) 30 ≃ 2 width : 1/(αrc ) suppression 1 GeV ∼ => narrow resonant peaks in di-lepton or di-jet channels

extrapolates between RS and flat extra dims (n = 1)

=> distinct experimental signals

I. Antoniadis (CERN) 90 / 91 Conclusions

Discovery of a Higgs scalar at the LHC: important milestone of the LHC research program

Precise measurement of its couplings is of primary importance

Hint on the origin of mass hierarchy and of BSM physics

natural or unnatural SUSY? low string scale in some realization? something new and unexpected? all options are still open

LHC enters a new era with possible new discoveries

Future plans to explore the 10-100 TeV energy frontier

I. Antoniadis (CERN) 91 / 91