Aspects of string phenomenology I. Antoniadis CERN New Perspectives in String Theory: opening conference Galileo Galilei Institute, Florence, 6-8 April 2009 main questions and list of possibilities 1 phenomenology of low string scale 2 general issues of high string scale 3 string GUTs 4 framework of magnetized branes 5 I. Antoniadis (CERN) 1 / 27
Are there low energy string predictions testable at LHC ? What can we hope from LHC on string phenomenology ? I. Antoniadis (CERN) 2 / 27
Very different answers depending mainly on the value of the string scale M s - arbitrary parameter : Planck mass M P − → TeV - physical motivations = > favored energy regions: � M ∗ P ≃ 10 18 GeV Heterotic scale High : M GUT ≃ 10 16 GeV Unification scale Intermediate : around 10 11 GeV ( M 2 s / M P ∼ TeV) SUSY breaking, strong CP axion, see-saw scale Low : TeV (hierarchy problem) I. Antoniadis (CERN) 3 / 27
Low string scale = > experimentally testable framework - spectacular model independent predictions perturbative type I string setup - radical change of high energy physics at the TeV scale explicit model building is not necessary at this moment but unification has to be probably dropped particle accelerators - TeV extra dimensions = > KK resonances of SM gauge bosons - Extra large submm dimensions = > missing energy: gravity radiation - string physics and possible strong gravity effects : · string Regge excitations · production of micro-black holes ? [9] microgravity experiments - change of Newton’s law, new forces at short distances I. Antoniadis (CERN) 4 / 27
Universal deviation from Standard Model in jet distribution M s = 2 TeV Width = 15-150 GeV Anchordoqui-Goldberg- L¨ ust-Nawata-Taylor- Stieberger ’08 I. Antoniadis (CERN) 5 / 27
Tree N -point superstring amplitudes in 4 dims involving at most 2 fermions and gluons: completely model independent for any string compactification any number of supersymmetries, even none No intermediate exchange of KK, windings or graviton emmission Universal sum over infinite exchange of string Regge (SR) excitations: k 1 k 3 masses: M 2 n = M 2 s n maximal spin: n + 1 | k ; n � k 2 k 4 I. Antoniadis (CERN) 6 / 27
Cross sections |M ( gg → gg ) | 2 q ) | 2 , |M ( gg → q ¯ model independent for any compactification q → gg ) | 2 |M ( qg → qg ) | 2 |M ( q ¯ , L¨ ust-Stieberger-Taylor ’08 � 1 |M ( gg → gg ) | 2 s 2 + 1 t 2 + 1 g 4 � = YM u 2 � 3 ( sV s + tV t + uV u ) 2 � 9 − 1 � s 2 V 2 s + t 2 V 2 t + u 2 V 2 � × 4 u � M s = 1 t 2 + u 2 � 1 tu ( tV t + uV u ) 2 − 3 1 q ) | 2 = g 4 |M ( gg → q ¯ 8 V t V u YM s 2 6 3 π 2 tu + . . . V s = − tu s B ( t , u ) = 1 − 2 V t : s ↔ t V u : s ↔ u YM limits agree with e.g. book ” Collider Physics ” by Barger, Phillips I. Antoniadis (CERN) 7 / 27
In addition we need: q ) | 2 , |M ( qq → qq ) | 2 |M ( q ¯ q → q ¯ model dependent: geometry, KK, windings however they are suppressed: • QCD color factors favor gluons over quarks in the initial state • Parton luminosities in pp above TeV are lower for qq , q ¯ q than for gg , gq [5] I. Antoniadis (CERN) 8 / 27
Energy threshold for black hole production : E BH ≃ M s / g 2 ← string coupling s Horowitz-Polchinski ’96, Meade-Randall ’07 weakly coupled theory = > P ≃ M s / g 2 / (2+ d ⊥ ) strong gravity effects occur much above M s , M ∗ s ↑ ր higher-dim Planck scale bulk dimensionality Regge excitations : M 2 n = M 2 g s ≃ α YM ∼ 0 . 1 ; s n = > տ gauge coupling s ∼ 10 4 string states before reach E BH production of n ∼ 1 / g 4 I. Antoniadis (CERN) 9 / 27
Newton constant: G N ∼ g 2 s in string units string size black hole: r H ∼ 1 > black hole mass: M BH ∼ 1 / G N ≃ 1 / g 2 = s ↑ r d / 2 − 1 valid in any dimension d : H s ∼ √ n : string entropy black hole entropy S BH ∼ 1 / G N ∼ 1 / g 2 I. Antoniadis (CERN) 10 / 27
Intermediate string scale : not directly testable but interesting possibility with several implications → ‘large volume’ compactifications High string scale : perturbative heterotic string : the most natural for SUSY and unification prediction for GUT scale but off by almost 2 orders of magnitude g 2 M s = g H M P ≃ 50 M GUT H ≃ α GUT ≃ 1 / 25 introduce large threshold corrections or strong coupling → M s ≃ M GUT but loose predictivity I. Antoniadis (CERN) 11 / 27
High string scale: M s ∼ M GUT Appropriate framework for SUSY + unification: intersecting branes in extra dimensions: IIA, IIB, F-theory Heterotic M-theory internal magnetic fields in type I 2 approaches: - Standard Model directly from strings - ‘orbifold’ GUTs: matter in incomplete representations Main problems: - gauge coupling unification is not automatic different coupling for every brane stack - extra states: vector like ‘exotics’ or worse they also destroy unification in orbifold GUTs I. Antoniadis (CERN) 12 / 27
Maximal predictive power if there is common framework for : moduli stabilization model building (spectrum and couplings) SUSY breaking (calculable soft terms) computable radiative corrections (crucial for comparing models) Possible candidate of such a framework: magnetized branes [23] I. Antoniadis (CERN) 13 / 27
From string inspired to string derived inspired : impose general constraints from a particular string framework → phenomenological analysis e.g. heterotic (KM level-1): no adjoints, extra U (1)’s, . . . = > flipped SU (5), Pati-Salam, orbifold GUTs, etc local : V 6 , M p → ∞ , gauge couplings fixed (decoupled gravity) → only a few local constraints (anomaly cancellation) e.g. intersecting branes at singularities, F-theory GUTs derived : ‘complete’ models taking into account global/string constraints e.g. heterotic: modular invariance type IIA/B orientifolds: tadpole cancellation I. Antoniadis (CERN) 14 / 27
string inspired/local models advantages : simplicity, Field-theory framework disadvantages : miss (important) consequences of the global constraints not every local → global e.g. swampland no information on the hidden sector do not address moduli stabilization = > predictivity is weak no control on extra states: chiral or non-chiral exotics, fractional electric charges, extra U (1)’s conditions for dynamical SUSY breaking: gravity or gauge mediation? cannot do precise computations: couplings, thresholds, radiative corrections [22] → examples: Heterotic orbifold GUTs, Intersecting branes, F-theory GUTs I. Antoniadis (CERN) 15 / 27
Heterotic models revived: Orbifold GUTs string constructions based on Z ′ 6 = Z 3 × Z 2 orbifold groups in Munich, Bonn, Hamburg, Ohio, U Penn GUT breaking to SM by discrete Wilson lines on non-contractible cycles 2 ‘large’ dimensions = > M GUT = compactification scale solve GUT scale problem: need universal thresholds above M GUT Higgs from untwisted sector = > gauge-Higgs unification λ top = g GUT = > m top ∼ IR fixed point ≃ 170 GeV I. Antoniadis (CERN) 16 / 27
Yukawa couplings: hierarchies ` a le Froggatt-Nielsen discrete symmetries = > couplings allowed with powers of a singlet field λ n ∼ Φ n � Φ � ∼ 0 . 1 M s → hierarchies A single anomalous U (1) = > � Φ � � = 0 to cancel the FI D-term R-neutrinos: natural framework for see-saw mechanism > m R ∼ M ; m L ∼ v 2 / M � h � ν L ν R + M ν R ν R � h � = v << M = proton decay: problematic dim-5 operators in general need suppression higher than M s or small couplings SUSY breaking in a hidden sector from the other E 8 → gravity mediation I. Antoniadis (CERN) 17 / 27
Intersecting branes: ‘perfect’ for SM embedding gauge group and representations but no unification → hypercharge normalization GUTs: problematic no perturvative SO (10) spinors no top-quark Yukawa coupling in SU (5): 10 10 5 H SU (5) is part of U (5) = > U (1) charges : 10 charge 2 ; 5 H charge ± 1 = > cannot balance charges with SU (5) singlets can be generated by D-brane instantons but . . . no Majorana neutrino masses same reason but instantons can do or alternatively generate exp suppressed Dirac masses I. Antoniadis (CERN) 18 / 27
Minimal Standard Model embedding General analysis using 3 brane stacks = > U (3) × U (2) × U (1) antiquarks u c , d c (¯ 3 , 1) : antisymmetric of U (3) or bifundamental U (3) ↔ U (1) > 3 models: antisymmetric is u c , d c or none = I.A.-Dimopoulos ’04 I. Antoniadis (CERN) 19 / 27
U(3) U(3) U(2) U(2) U(3) U(2) Q Q Q c ν c u c c ν c d U(1) U(1) l U(1) c L L L u c d u c c d c ν c c l l Model A Model B Model C Y A = − 1 3 Q 3 + 1 6 Q 3 − 1 1 Y B , C = 2 Q 2 2 Q 1 � � 1 = 3 1 6 sin 2 θ W = � � = � � 2 + 2 α 2 / 3 α 3 8 1 + α 2 / 2 α 1 + α 2 / 6 α 3 7 + 3 α 2 /α 1 � � α 2 = α 3 α 2 = α 3 I. Antoniadis (CERN) 20 / 27
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