Strings, SUSY and LHC

Transcription

1 Strings, SUSY and LHC Joseph P. Conlon (Cavendish Laboratory and DAMTP, Cambridge) fpuk, November 2007 Strings, SUSY and LHC p. 1/4

2 The LHC What is the LHC? The greatest experiment on earth! Strings, SUSY and LHC p. 2/4

3 The LHC The LHC: pp collider a collision energy of 14TeV first collisions summer 2008 a design luminosity of 100fb 1 year 1 A cost to the UK of < (1 pint of beer) person 1 year 1 The TeVatron: p p collider a collision energy of 1.8TeV a current total integrated luminosity of 3.5fb 1. Strings, SUSY and LHC p. 3/4

4 The LHC Cross-sections are N events = σ L σ pp b b fb σ pp t t fb σ pp H fb σ pp ZZ fb σ pp susy (1 10) 10 3 fb Design luminosity is L = 100fb 1 year 1 Strings, SUSY and LHC p. 4/4

5 Supersymmetry Supersymmetry is a great solution to the gauge hierarchy problem: t H t t H Λ 2 H H Λ 2 Strings, SUSY and LHC p. 5/4

6 Supersymmetry TeV supersymmetry stabilises the Higgs mass against radiative corrections gives a good dark matter candidate explains gauge symmetry breaking through radiative electroweak symmetry breaking is compatible with LEP I precision electroweak data is the prime candidate for new physics discovered at the LHC Strings, SUSY and LHC p. 6/4

7 Supersymmetry The MSSM soft Lagrangian is L soft = L susy [M 3λ g λ g + M 2 W a W a + M 1 B B + h.c.] + ǫαβ [ bh α d Hβ u H α u Q β i ÃuijŨc j + H α d Q β i Ãdij D c j + H α d L β i ÃeijẼc j + h.c.] +m 2 H d H d 2 + m 2 H u H u 2 + Q α i m 2 Qij + L α i m 2 Lij L α j + Ũc i m 2 UijŨc j + Susy is explicitly broken by: Q α j D c i m 2 Dij D c j + Ẽc i m 2 EijẼc j Strings, SUSY and LHC p. 7/4

8 Supersymmetry The MSSM soft Lagrangian is L soft = L susy [M 3λ g λ g + M 2 W a W a + M 1 B B + h.c.] + ǫαβ [ bh α d Hβ u H α u Q β i ÃuijŨc j + H α d Q β i Ãdij D c j + H α d L β i ÃeijẼc j + h.c.] +m 2 H d H d 2 + m 2 H u H u 2 + Q α i m 2 Qij + L α i m 2 Lij L α j + Ũc i m 2 UijŨc j + Susy is explicitly broken by: scalar masses m 2 φ φ, Q α j D c i m 2 Dij D c j + Ẽc i m 2 EijẼc j Strings, SUSY and LHC p. 7/4

9 Supersymmetry The MSSM soft Lagrangian is L soft = L susy [M 3λ g λ g + M 2 W a W a + M 1 B B + h.c.] + ǫαβ [ bh α d Hβ u H α u Q β i ÃuijŨc j + H α d Q β i Ãdij D c j + H α d L β i ÃeijẼc j + h.c.] +m 2 H d H d 2 + m 2 H u H u 2 + Q α i m 2 Qij + L α i m 2 Lij L α j + Ũc i m 2 UijŨc j + Q α j D c i m 2 Dij D c j + Ẽc i m 2 EijẼc j Susy is explicitly broken by: scalar masses m 2 φ φ, gaugino masses Mλλ, Strings, SUSY and LHC p. 7/4

10 Supersymmetry The MSSM soft Lagrangian is L soft = L susy [M 3λ g λ g + M 2 W a W a + M 1 B B + h.c.] + ǫαβ [ bh α d Hβ u H α u Q β i ÃuijŨc j + H α d Q β i Ãdij D c j + H α d L β i ÃeijẼc j + h.c.] +m 2 H d H d 2 + m 2 H u H u 2 + Q α i m 2 Qij + L α i m 2 Lij L α j + Ũc i m 2 UijŨc j + Susy is explicitly broken by: scalar masses m 2 φ φ, trilinear scalar A-terms A ijk φ i φ j φ k. Q α j D c i m 2 Dij D c j + Ẽc i m 2 EijẼc j gaugino masses Mλλ, Strings, SUSY and LHC p. 7/4

11 Supersymmetry The MSSM soft Lagrangian is L soft = L susy [M 3λ g λ g + M 2 W a W a + M 1 B B + h.c.] + ǫαβ [ bh α d Hβ u H α u Q β i ÃuijŨc j + H α d Q β i Ãdij D c j + H α d L β i ÃeijẼc j + h.c.] +m 2 H d H d 2 + m 2 H u H u 2 + Q α i m 2 Qij + L α i m 2 Lij L α j + Ũc i m 2 UijŨc j + Susy is explicitly broken by: scalar masses m 2 φ φ, Q α j D c i m 2 Dij D c j + Ẽc i m 2 EijẼc j gaugino masses Mλλ, trilinear scalar A-terms A ijk φ i φ j φ k. B-term bǫ αβ H α u H β d. Strings, SUSY and LHC p. 7/4

12 Supersymmetry The MSSM Spectrum is: Gluino g, squarks q, Sleptons ẽ, µ, τ, sneutrinos ν Neutralinos χ 1, χ 2, χ 3, χ 4 ( B, Z, H1, H2 ) Charginos χ ± 1, χ± 2 Higgs fields: h 0,H 0,A,H ± Strings, SUSY and LHC p. 8/4

13 SUSY Phenomenology SUSY introduces new strongly interacting particles at the TeV scale. Gluon g Gluino g Quark q Squark q A pp machine is a colour collider and a squark/gluino factory p + p g + g, g + q, q + q Squarks and gluinos are abundantly produced and have long decay chains. Strings, SUSY and LHC p. 9/4

14 SUSY Phenomenology LHC SUSY phenomenology is the study of cascade decays of squarks and gluinos. p + p g g + g t + t χ b + W + b χ 1 + W + + b + q + q + b χ 1 + l + + ν l + b + q + q + b SUSY events are complex, with Strings, SUSY and LHC p. 10/4

15 SUSY Phenomenology LHC SUSY phenomenology is the study of cascade decays of squarks and gluinos. p + p g g + g t + t χ b + W + b χ 1 + W + + b + q + q + b χ 1 + l + + ν l + b + q + q + b SUSY events are complex, with multi-jets, Strings, SUSY and LHC p. 10/4

16 SUSY Phenomenology LHC SUSY phenomenology is the study of cascade decays of squarks and gluinos. p + p g g + g t + t χ b + W + b χ 1 + W + + b + q + q + b χ 1 + l + + ν l + b + q + q + b SUSY events are complex, with multi-jets, multi-leptons, Strings, SUSY and LHC p. 10/4

17 SUSY Phenomenology LHC SUSY phenomenology is the study of cascade decays of squarks and gluinos. p + p g g + g t + t χ b + W + b χ 1 + W + + b + q + q + b χ 1 + l + + ν l + b + q + q + b SUSY events are complex, with multi-jets, multi-leptons, missing E T. Strings, SUSY and LHC p. 10/4

18 SUSY Phenomenology q g l + q g q χ 2 l+ q l χ 1 Strings, SUSY and LHC p. 11/4

19 SUSY Spectroscopy χ 2 χ 1 l l + l Max(M l+ l ) = M M χ 2 l M χ 1 1 M 2 χ 2 M 2 l2 This decay chain gives a characteristic edge. Strings, SUSY and LHC p. 12/4

20 SUSY Spectroscopy 400 signal SM backg SUSY backg events/4 GeV/30 fb m ll (GeV) (ATLAS TDR) Strings, SUSY and LHC p. 13/4

21 SUSY Spectroscopy Other sparticle masses can be measured through kinematic edges, thresholds and endpoints. If TeV SUSY is present, the LHC will find it. The LHC will measure the MSSM Lagrangian. Strings, SUSY and LHC p. 14/4

22 SUSY Spectroscopy Other sparticle masses can be measured through kinematic edges, thresholds and endpoints. If TeV SUSY is present, the LHC will find it. The LHC will measure with moderate accuracy combinations of some of the parameters of the MSSM Lagrangian. Strings, SUSY and LHC p. 14/4

23 SUSY Spectroscopy Other sparticle masses can be measured through kinematic edges, thresholds and endpoints. If TeV SUSY is present, the LHC will find it. The LHC will measure with moderate accuracy combinations of some of the parameters of the MSSM Lagrangian. A hadron collider is messy - many MSSM parameters cannot be measured. For example, A-terms and particle spins are very hard to measure. Strings, SUSY and LHC p. 14/4

24 SUSY Breaking Susy phenomenology is the study of supersymmetry breaking What is the origin and underlying structure of the MSSM soft parameters? How is supersymmetry broken? Strings, SUSY and LHC p. 15/4

25 SUSY Breaking Gravity exists - SUSY is a local symmetry. Phenomenology of susy breaking is classified by gravitino mass m 3/2 = e K/2 W m 3/2 1TeV : gravity mediation, moduli mediation, anomaly mediation m 3/2 1TeV : gauge mediation Focus on gravity (moduli) mediation: natural in string theory Higgs potential automatically at weak scale only need to solve the hierarchy problem once! Strings, SUSY and LHC p. 16/4

26 Supersymmetry We need m 3/2 = e K/2 W 1 Big question: Why is m 3/2 so small? Does the hierarchy come from e K/2 or W? Strings, SUSY and LHC p. 17/4

27 Strings and SUSY Low-energy supersymmetry is a great channel to connect string theory to experiment The compactification geometry can break supersymmetry The compactification geometry determines the sparticle masses The existence of low energy supersymmetry can be correlated to very different physics (such as axions). Strings, SUSY and LHC p. 18/4

28 Strings and SUSY How to realise the Standard Model - heterotic, IIA, IIB? How to break supersymmetry? How to generate the hierarchy? Strings, SUSY and LHC p. 19/4

29 Strings and SUSY How to go from this... Strings, SUSY and LHC p. 20/4

30 Strings and SUSY...to this? Strings, SUSY and LHC p. 21/4

31 Strings and SUSY 1. Compactify. 2. Work out effective four-dimensional theory. 3. Minimise the moduli potential. 4. Compute the moduli F-terms in vacuo. 5. Compute the moduli couplings to Standard Model. 6. Compute the high-scale soft breaking terms. 7. Run soft terms to low energy and compute MSSM Lagrangian. 8. Feed Lagrangian into a Monte Carlo and study the collider phenomenology. Strings, SUSY and LHC p. 22/4

32 Strings and SUSY To study the moduli potential and supersymmetry breaking: W = Ŵ(Φ) + µ(φ)cα C β Y αβγ(φ)c α C β C γ +..., K = ˆK(Φ, Φ) + K Φ)C [ ] α β(φ, α C β + ZC α C β + h.c. +..., f a = f a (Φ). V = e ˆK( ˆK i j D i ŴD j Ŵ 3 Ŵ 2 ) Strings, SUSY and LHC p. 23/4

33 Strings and SUSY Moduli scalar potential is ( ) V = K F i F j i j 3m 2 3/2 M2 P Supersymmetry breaking occurs if F i = e K/2 K i j ( j W + ( j K)W) 0. F-terms parametrise supersymmetry breaking. No phenomenological restriction on nature of minimum. Strings, SUSY and LHC p. 24/4

34 Strings and SUSY We know V = e K ( K i j D i WD j W 3 W 2). On physics grounds we expect ( ) V = Ms 4 stuff. and M s = e φ M P Vs. Holomorphy prevents T, S appearing in W, suggesting K = 2 ln(v s ) 4 ln(g s ) Strings, SUSY and LHC p. 25/4

35 Strings and SUSY Fields must be written in holomorphic variables: IIB(D3/D7): T = e φ Vol(Σ 4 ) + ic 4, U = Ω, S = e φ + ic 0 Σ 3 The moduli space Kähler potential is ( ) ˆK = 2 ln(v E ) ln i Ω Ω ln(s + S) This can be rigorously derived through dimensional reduction. Strings, SUSY and LHC p. 26/4

36 Flux Compactifications Flux compactifications can generate potentials for the moduli Fluxes source an energy density that depends on the size of cycles. In IIB, fluxes generate a superpotential W = G 3 Ω(U) Strings, SUSY and LHC p. 27/4

37 Moduli Stabilisation: Fluxes ˆK = 2 ln ( V(T + T) ) ln W = V = e ˆK = e ˆK G 3 Ω (U). U,S U,S ( i ˆK α βd α WD β W + ˆK α βd α WD β W ) Ω Ω(U) T ln ( S + S ), ˆK i j D i WD j W 3 W 2 Stabilise S and U by solving D S W = D U W = 0. Strings, SUSY and LHC p. 28/4

38 Moduli Stabilisation: Fluxes = 0 No-scale model : ˆK = 2 ln ( V(T i + T i ) ), W = W 0. ( ) V = e ˆK ˆK i j D i WD j W 3 W 2 T vanishing vacuum energy broken susy (F T 0,F U = 0) T unstabilised Goldstino is breathing mode g µν λ 2 g µν Strings, SUSY and LHC p. 29/4

39 Moduli Stabilisation: KKLT ˆK = 2 ln (V), W = W 0 + i A i e a it i. Non-perturbative ADS superpotential. T -moduli are stabilised by solving D T W = 0. Supersymmetric minimum: needs extra energy to break susy. No hierarchy in m 3/2. Strings, SUSY and LHC p. 30/4

40 Moduli Stabilisation: Large-Volume ˆK = 2 ln ( W = W 0 + i V+ ξ g 3/2 s ), A i e a it i. Add the leading α corrections to the Kähler potential. This leads to dramatic changes in the large-volume vacuum structure. Strings, SUSY and LHC p. 31/4

41 Moduli Stabilisation: Large-Volume The simplest model P 4 [1,1,1,6,9] has two Kähler moduli. V = ( Tb + T ) 3/2 b 2 ( Ts + T s 2 ) 3/2 ( ) τ 3/2 b τs 3/2. If we compute the scalar potential, we get for V 1, V = τs a 2 s A s 2 e 2a sτ s V a s A s W 0 τ s e a sτ s V 2 + ξ W 0 2 g 3/2 s V 3. Strings, SUSY and LHC p. 32/4

42 Moduli Stabilisation: Large-Volume V = τs a 2 s A s 2 e 2a sτ s a s A s W 0 τ s e a sτ s } V {{ V 2 } Integrate out τ s + ξ W 0 2 g 3/2 s V 3. V = W 0 2 (ln V) 3/2 A minimum exists at V 3 + ξ W 0 2 V W 0 e a sτ s, τ s ξ2/3 g s. This minimum is non-supersymmetric AdS and at exponentially large volume. g 3/2 s V 3. Strings, SUSY and LHC p. 33/4

43 Moduli Stabilisation: Large-Volume BULK BLOW UP U(2) Q L e L U(3) U(1) Q R U(1) e R Strings, SUSY and LHC p. 34/4

44 Moduli Stabilisation: Large-Volume The stabilised volume is exponentially large. The large volume lowers the string scale and gravitino mass through m s = M P V, m 3/2 = M P V. To solve the gauge hierarchy problem, need V The vacuum is pseudo no-scale and breaks susy... Strings, SUSY and LHC p. 35/4

45 Moduli Stabilisation: Large-Volume The stabilised volume is exponentially large. The large volume lowers the string scale and gravitino mass through m s = M P V, m 3/2 = M P V. To solve the gauge hierarchy problem, need V The vacuum is pseudo no-scale and breaks susy... Can generate the hierarchy and compute the moduli F-terms F Ti 0,F U j = 0. Strings, SUSY and LHC p. 35/4

46 Soft Terms W = Ŵ(Φ) + µ(φ)h 1H Y αβγ(φ)c α C β C γ +..., K = ˆK(Φ, Φ) + K Φ)C α β(φ, α C β + [ZH 1 H 2 + h.c.] +..., f a = f a (Φ). Couplings to visible matter determine the soft terms. Strings, SUSY and LHC p. 36/4

47 Soft Terms Soft scalar masses m 2 i j and trilinears A αβγ are given by m 2 α β = (m 2 3/2 + V 0) K α β F m F n ( m n Kα β ( m Kα γ ) K γδ ( n Kδ β) ) A αβγ M a = e ˆK/2 F m[ ˆKm Y αβγ + m Y αβγ ( ( m Kα ρ ) K ) ] ρδ Y δβγ + (α β) + (α γ). = F m m f a Re(f a ) Similar expressions hold for µ and Bµ. Strings, SUSY and LHC p. 37/4

48 Soft Terms The matter metrics K α β can be computed if we know where the Standard Model is realised. For example, in the large-volume models with the Standard Model on D7 branes wrapping a blow-up cycle, K α β = τ1/3 s V 2/3k α β (U,Ū), f a = T s + h a (F)S Strings, SUSY and LHC p. 38/4

49 Soft Terms High-scale soft terms are M i = F s M, 2τ s m α β = M Kα β, 3 A αβγ = M Ŷαβγ, B = 4M 3. Strings, SUSY and LHC p. 39/4

50 Soft Terms High-scale soft terms are M i = F s M, 2τ s m α β = M Kα β, 3 A αβγ = M Ŷαβγ, B = 4M 3. Big question: How is the Standard Model realised? Strings, SUSY and LHC p. 39/4

51 Strings and Flavour Physics The MSSM has a flavour problem: we need mũ = m c,m d = m s,... Squark mass universality to 0.5% is constrained by K 0 K 0 mixing. Strings, SUSY and LHC p. 40/4

52 Strings and Flavour Physics The MSSM has a flavour problem: we need mũ = m c,m d = m s,... Squark mass universality to 0.5% is constrained by K 0 K 0 mixing. SUSY breaking involves high-scale physics. Flavour physics (Yukawa couplings) also involve high scale physics. Strings, SUSY and LHC p. 40/4

53 Strings and Flavour Physics The MSSM has a flavour problem: we need mũ = m c,m d = m s,... Squark mass universality to 0.5% is constrained by K 0 K 0 mixing. SUSY breaking involves high-scale physics. Flavour physics (Yukawa couplings) also involve high scale physics. Why isn t susy breaking sensitive to flavour physics? Strings, SUSY and LHC p. 40/4

54 Strings and Flavour Physics For flavour universality, we require m 2 α β = m 2 K α β, A αβγ = AY αβγ, φ M1 = φ M2 = φ M3 = φ A. Soft terms must be family-independent and insensitive to flavour. Strings, SUSY and LHC p. 41/4

55 Strings and Flavour Physics Sufficient conditions for flavour universality: 1. Hidden sector factorises Φ hidden = Ψ susy χ flavour. 2. The kinetic terms are decoupled K(Φ, Φ) = K 1 (Ψ + Ψ) + K 2 (χ, χ), 3. The superpotential Yukawas depend only on χ flavour : Y αβγ (Ψ,χ) = Y αβγ (χ). 4. The gauge kinetic functions depend only on Ψ fields: f a (Ψ,χ) = i λ i Ψ i. Strings, SUSY and LHC p. 42/4

56 Strings and Flavour Physics 4. The visible metric factorises. K α β(ψ, Ψ,χ, χ) = h(ψ + Ψ)k α β(χ, χ) 5. Ψ breaks susy, χ does not: D Ψi W 0,D χj W = 0. If all these assumptions hold, susy breaking generates flavour universal soft terms. Strings, SUSY and LHC p. 43/4

57 Strings and Flavour Physics 4. The visible metric factorises. K α β(ψ, Ψ,χ, χ) = h(ψ + Ψ)k α β(χ, χ) 5. Ψ breaks susy, χ does not: D Ψi W 0,D χj W = 0. If all these assumptions hold, susy breaking generates flavour universal soft terms. Totally ad hoc in effective field theory! Strings, SUSY and LHC p. 43/4

58 Strings and Flavour Physics String theory knows this structure! Calabi-Yau moduli space factorises in precisely this fashion. Kähler (T ) and complex structure (U) moduli have factorised moduli spaces IIB : Ψ susy T,χ flavour U, IIA : Ψ susy U,χ flavour T. In flux compactifications susy breaking factorises: F T 0, F U = 0. Strings, SUSY and LHC p. 44/4

59 Strings and Flavour Physics The structure of Calabi-Yau moduli space provides a solution to the flavour problem of the MSSM Naturalness in string theory Naturalness in effective field theory Strings, SUSY and LHC p. 45/4

60 Open Problem Find a compactification with: The Standard Model matter content and Yukawa couplings All moduli stabilised in a controlled fashion Hierarchically low susy breaking m 3/2 1TeV Known moduli-matter couplings Strings, SUSY and LHC p. 46/4

61 Open Problem Find a compactification with: The Standard Model matter content and Yukawa couplings All moduli stabilised in a controlled fashion Hierarchically low susy breaking m 3/2 1TeV Known moduli-matter couplings Predict all soft terms and MSSM spectrum, and compare with experiment! Strings, SUSY and LHC p. 46/4

62 Conclusions Strings, SUSY and LHC p. 47/4