Naturalness and string phenomenology in the LHC era

Transcription

1 Naturalness and string phenomenology in the LHC era I. Antoniadis String Phenomenology 2014 ICTP, Trieste, 7-11 July 2014 LHC: where do we stand? where do we go? Low energy SUSY after the Higgs discovery Non-linear SUSY and MSSM Non-linear SUSY and Starobinsky inflation I. Antoniadis (CERN) 1 / 43

2 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) 2 / 43

3 Entrance of a Higgs Boson in the Particle Data Group 2013 particle listing I. Antoniadis (CERN) 3 / 43

4 Combined mass measurement 37 [CMS-PAS-HIG ]! Float 3 signal strengths to not depend on yields.! % ## and H ZZ 4 results compatible at 1.6" I. Antoniadis (CERN) 4 / 43

5 @+);5A+B+,K'EJ'K<+'#.::;'IE;E,'B);;' F),D';.:,)*';KA+,:K<;G' = GeV)) H (m Signal yield (σ/σ SM 4 ATLAS -1 s = 7 TeV 3.5 Ldt = 4.5 fb s = 8 TeV Ldt = 20.3 fb Combined γγ+zz* H γγ H ZZ* 4l Best fit 68% CL 95% CL TEK+'B+);5A+'-<),,+*;' ;.:,)*';KA+,:K<' γγ µ (m H=125.98GeV ) ZZ µ (m H=124.51GeV ) =1.29 ± = H*D'A+;5*KQ' T+WQ' [GeV] m H ± 0.2 (stat) (syst) GeV ± 0.37 (stat) ± 0.18 (syst) GeV 7caq'%A+-.;.E,'B+);5A+B+,K'F;K)L;L-)*'5,-+AK).,K6'DEB.,),KG' H*D' \\'),D'γγ'-EB0)LI.K6' m=2.3±0.9 '"EB0)LI.*.K6''1c9σ'' m=1.47±0.72 "EB0)LI.*.K6''8c3lσ'' 8m' I. Antoniadis (CERN) 5 / 43

6 ATLAS Prelim. m H = GeV H γγ µ = H ZZ* 4l µ = H WW* lνlν µ = Combined H γγ, ZZ*, WW* µ = σ(stat.) sys inc. σ( theory ) σ(theory) Total uncertainty ± 1σ on µ W,Z H bb +0.7 µ = H ττ (8 TeV data only) +0.5 µ = Combined H bb, ττ µ = Combined µ = s = 7 TeV Ldt = fb -1 s = 8 TeV Ldt = 20.3 fb ±0.5 ±0.4 < Signal strength (µ) =;;5B+;'/@'IA),-<.,:'JA)-LE,;' ),D'0AED5-LE,'BED+;' "EB0)LI*+'W.K<'/@'F)K'89qG'' µ=1.30±0.12 (stat) ± 0.10 (th) ± 0.09 (syst) =**'-<),,+*;'-E50*.,:;'50D)K+D';EE,' /K)6'K5,+D'U'' a1' I. Antoniadis (CERN) 6 / 43

7 Signal strength 53 [CMS-PAS-HIG ]! Grouped by production tag and dominant decay:! - 2 /dof = 10.5/16! p-value = 0.84 (asymptotic)! tth-tagged 2.0" above SM.! Driven by one channel. a.david@cern.ch Same I. Antoniadis (CERN) 7 / 43

8 The value of its mass 125 GeV consistent with expectation from precision tests of the SM favors perturbative physics quartic coupling λ = mh 2 /v2 1/8 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 Dark matter, neutrino masses, baryon asymmetry, flavor physics, axions, electroweak scale hierarchy, early cosmology,... I. Antoniadis (CERN) 8 / 43

9 Beyond the Standard Theory of Particle Physics: 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) 9 / 43

10 I. Antoniadis (CERN) 10 / 43

11 I. Antoniadis (CERN) 11 / 43

12 What is next? I. Antoniadis (CERN) 12 / 43

13 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) 13 / 43

14 LS1 Machine Consolidation The LHC timeline LS2 Machine upgrades for high Luminosity Collimation Cryogenics Injector upgrade for high intensity (lower emittance) Phase I for ATLAS : Pixel upgrade, FTK, and new small wheel LS3 Machine upgrades for high Luminosity Upgrade interaction region Crab cavities? Phase II: full replacement of tracker, new trigger scheme (add L0), readout electronics. Europe s top priority should be the exploitation of the full potential of the LHC, including the high-luminosity upgrade of the machine and detectors with a view to collecting ten times more data than in the initial design, by around FFP% 7F.EH.I%!"#$"%&'%()*% +,-%./%012%345/%678% 9. %:-";%<,=:% *&<<4D"%6EF%9. %?4$% G4#$%#"%.EH.I%345%% 7F.2% >J#A4K.%,?B$#@4%%!"%$,<L=#"4%<,=:% 67F77% 67FEF%!"#$%&'()*'$ 3M:D4%-&=:-#<%<,=:% #"%.I%345/%% 6.FF%9. %?4$%G4#$% >J#A4K7%,?B$#@4% "&%)(K()*% 6EFF%9. %?4$%G4#$/% $,-%,?%"&%N%E%#O.% D&<<4D"4@% E2% #####!"#$!"&$ I. Antoniadis (CERN) 14 / 43

15 We must fully explore the TeV energy range Linear Colliders - ILC project Circular Colliders I. Antoniadis (CERN) 15 / 43

16 I. Antoniadis (CERN) 16 / 43

17 I. Antoniadis (CERN) 17 / 43

18 I. Antoniadis (CERN) 18 / 43

19 I. Antoniadis (CERN) 19 / 43

20 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) 20 / 43

21 I. Antoniadis (CERN) 21 / 43

22 I. Antoniadis (CERN) 22 / 43

23 126 GeV Higgs compatible with supersymmetry Upper bound on the lightest scalar mass: [ mh 2 < mz 2 cos2 2β + 3 mt 4 (4π) 2 v 2 ln m2 t mt 2 + A2 t m 2 t ( 1 A2 t 12m 2 t m h 126 GeV => m t 3 TeV or A t 3m t 1.5 TeV => % to a few %0 fine-tuning )] < (130GeV ) 2 minimum of the potential: m 2 Z = 2m1 1 m2 2 tan2 β tan 2 β 1 2m RG evolution: m 2 2 = m2 2 (M GUT) 3λ2 t 4π 2m2 t ln M GUT m t + [37] m 2 2 (M GUT) O(1)m 2 t + I. Antoniadis (CERN) 23 / 43

24 Reduce the fine-tuning minimize radiative corrections M GUT Λ : low messenger scale (gauge mediation) δm 2 t = 8α s 3π M2 3 ln Λ M 3 + 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 [25] I. Antoniadis (CERN) 24 / 43

25 Non-linear supersymmetry => goldstino mode χ Volkov-Akulov 73 Effective field theory of SUSY breaking at low energies m χ << m susy e.g. gauge mediation dominant vs gravity mediation χ: longitudinal gravitino with m χ m2 susy M Planck < m soft << m susy M Planck : SUGRA decoupled massless χ coupled to matter 1/m susy Non-linear SUSY transformations: δχ α = ξ α κ + κλµ ξ µχ α Λ µ ξ = i ( χσ µ ξ ξσµ χ ) κ: goldstino decay constant (susy breaking scale) κ = ( 2m susy ) 2 I. Antoniadis (CERN) 25 / 43

26 Constrained superfields Rocek-Tseytlin 78, Lindstrom-Rocek 79, Komargodski-Seiberg 09 spontaneous global SUSY : no supercharge but still conserved supercurrent => superpartners exist in operator space (not as 1-particle states) => constrained superfields: eliminate superpartners Goldstino: chiral superfield X NL satisfying X 2 NL = 0 => L NL = X NL (y) = χ2 2F + 2θχ + θ 2 F y µ = x µ + iθσ µ θ = FΘ 2 Θ = θ + χ 2F d 4 θx NL XNL 1 { } d 2 θx NL + h.c. = L Volkov Akulov 2κ F = 1 2κ +... I. Antoniadis (CERN) 26 / 43

27 Goldstino couplings to matter supermultiplets replace spurion superfield S = m soft θ 2 by goldstino constrained superfield => Non-linear MSSM S 2κm soft X NL = m soft m susy X NL F-auxiliary in X NL : dynamical field with no derivatives to be solved F = msusy 2 + Bµ msusy 2 h 1 h 2 + A u msusy 2 ũ R qh 2 + => compact form for all goldstino couplings at linear and non-linear level I. Antoniadis (CERN) 27 / 43

28 Phenomenological analysis I.A.-Dudas-Ghilencea-Tziveloglou 10 Higgs potential is modified: V = V MSSM + 2κ 2 m 2 1 h m 2 2 h Bµh 1 h O(κ 4 ) => m 1,2,Bµ: soft mass parameters, µ: higgsino mass Classical value of light higgs mass can be increased significantly for m susy a few TeV large tanβ limit: m 2 h = m2 Z + v2 2msusy 2 (2µ 2 + m 2 Z )2 + Quartic higgs coupling increases for large soft masses => MSSM little fine tuning of the EW scale is alleviated I. Antoniadis (CERN) 28 / 43

29 m h m A = GeV µ = 900 GeV; tanβ = m susy µ = GeV m A = 150 GeV; tanβ = m susy I. Antoniadis (CERN) 29 / 43

30 Validity of perturbative expansion: m 2 i v2 /m 4 susy << 1 m 2 1 v2 m 4 susy µ = 900 GeV; tanβ = 50 m A = GeV m 2 2 v2 m 4 susy m susy m susy I. Antoniadis (CERN) 30 / 43

31 Fine-tuning analysis I.A.-Babalic-Ghilencea 14 Fine-tuning measures: Ellis-Enqvist-Nanopoulos-Zwirner 86 Barbieri-Giudice 88, Anderson-Castano 94 m = max γ 2, q = { γ = {m 0,m 12,A t,b 0,µ 0 }, γ 2 γ 2 } 1/2, with γ 2 lnv2 lnγ 2 v = EW scale I. Antoniadis (CERN) 31 / 43

32 The Constrained Non-Linear MSSM m 400 q m h GeV m h GeV Minimal values of m (left) and q (right) for tanβ = 10 and m susy from the lowest to the top curve: 2.8 TeV (red), 3.2 TeV (orange), 3.9 TeV (brown), 5 TeV (green), 5.5 TeV (dark green), 6.3 TeV (cyan), 7.4 TeV (blue), 8 TeV (dark blue), 8.7 TeV (black). m susy 3 TeV => NL /10 I. Antoniadis (CERN) 32 / 43

33 Non-liner SUSY in supergravity I.A.-Dudas-Ferrara-Sagnotti 14 K = 3log(1 X X) 3X X ; W = f X + W 0 X X NL => V = 1 3 f 2 3 W 0 2 ; m 2 3/2 = W 0 2 V can have any sign contrary to global NL SUSY NL SUSY in flat space => f = 3m 3/2 M p Dual gravitational formulation: R 2 = 0 chiral curvature superfield Minimal SUSY extension of R 2 gravity I. Antoniadis (CERN) 33 / 43

34 Starobinsky model of inflation L = 1 2 R + αr2 equivalent to a scalar field with exponential potential: L = 1 2 R 1 2 ( φ)2 M2 12 Note that the two metrics are not the same supersymmetric extension: (1 e q 2 3 φ ) 2 M 2 = 3 4α add D-term R R because F-term R 2 does not contain R 2 => brings two chiral multiplets I. Antoniadis (CERN) 34 / 43

35 SUSY extension of Starobinsky model K = 3ln(T + T C C) ; W = MC(T 1 2 ) T contains the inflaton: ReT = e C R is unstable during inflation q 2 3 φ => add higher order terms to stabilize it e.g. C C h(c, C) = C C ζ(c C) 2 Kallosh-Linde 13 SUSY is broken during inflation with C the goldstino superfield Minimal SUSY extension that evades stability problem: replace C by the non-linear multiplet X I. Antoniadis (CERN) 35 / 43

36 Non-linear Starobinsky supergravity K = 3ln(T + T X X) ; W = M XT + f X + W 0 => L = 1 2 R 1 2 ( φ)2 M2 12 q ) (1 e φ 1 q 2 e φ ( a) 2 M2 18 e 2 q 2 3 φ a 2 axion a much heavier than φ during inflation, decouples: m φ = M 3 e q 2 3 φ 0 << m a = M 3 inflation scale M independent from NL-SUSY breaking scale f => compatible with low energy SUSY string realization? [43] I. Antoniadis (CERN) 36 / 43

37 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 M s 1 TeV => volume R n = 1032 ls n (R mm for n = 2 6) - 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 [23] Λ a few TeV and m 2 H = a loop factor Λ2 New Dark Matter candidates e.g. in the extra dims But unification has to be probably dropped I. Antoniadis (CERN) 37 / 43

38 Accelerator signatures: 4 different scales Gravitational radiation in the bulk => missing energy present LHC bounds: M > 3 5 TeV Massive string vibrations => e.g. resonances in dijet distribution [40] M 2 j = M M2 s j ; maximal spin : j + 1 higher spin excitations of quarks and gluons with strong interactions present LHC limits: M s > 5 TeV Large TeV dimensions => KK resonances of SM gauge bosons I.A. 90 Mk 2 = M2 0 + k 2 /R 2 ; k = ±1, ±2,... experimental limits: R 1 > TeV (UED - localized fermions) extra U(1) s and anomaly induced terms masses suppressed by a loop factor from M s [41] I. Antoniadis (CERN) 38 / 43

39 I. Antoniadis (CERN) 39 / 43

40 String Resonances production at Hadron Colliders I.A.-Anchordoqui-Dai-Feng-Goldberg-Huang-Lüst-Stojkovic-Taylor in prep dσ/dm (fb/gev) 10 0 cteq6l1 CT10nlo NNPDF23-nlo-as MRST2004qed_proton M (GeV) I. Antoniadis (CERN) 40 / 43

41 Standard Model on D-branes : SM ++ 3-Baryonic 2-Left Q L gluon 1-Right U R, D R U(3) W #-Leptonic Sp(1) L L SU(2) U(1) R E! " R U(1) U(1) 3 : hypercharge + B, L L I. Antoniadis (CERN) 41 / 43

42 TeV string scale Anchordoqui-IA-Goldberg-Huang-Lüst-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 no Lepton number => 1 M s LLHH Majorana mass: B,L => extra Z s H 2 M s LL տ GeV with possible leptophobic couplings leading to CDF-type Wjj events Z B lighter than 4d anomaly free Z B L I. Antoniadis (CERN) 42 / 43

43 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 TeV energy frontier I. Antoniadis (CERN) 43 / 43