Cosmological vacuum selection

Transcription

1 Cosmological vacuum selection and metastable susy breaking Zygmunt Lalak ITP Warsaw Corfu Summer Institute 2010 with Y. Dalianis, S. Pokorski, K. Turzyński, J. Pawełczyk, T. Jeliński JHEP 0810 (2008) 016 [hep-ph ], PLB 689 (2010) 186 [hep-ph ], hep-ph

2 References R. Kitano D. Shih C. Cheung, A. Fitzpatrick, D. Shih R. Kitano, Y. Nomura gauge mediation G. Giudice, R. Rattazzi S. Kachru, R. Kallosh, A. Linde, S. Trivedi R. Kallosh, A. Linde flux stabilisation H. P. Nilles, M. Ratz M. Gomez-Reino, C, Scrucca E. Dudas, C. Papineau, S. Pokorski F-term uplifting H. Abe, T. Higaki, T. Kobayashi, Y. Omura S. Abel, V. Khoze, J. Jaeckel, C. Durnford M. Cvetic, T. Weigand E. Dudas, A. Romagnoni, M. Trapletti, S. Pokorski W. Buchmuller, K. Hamaguchi, O. Lebedev, M. Ratz M. Ibe, R. Kitano L. Anguelova, V. Calo high T F. Schaposnik ISS sourcing gauge mediation charged moduli

3 !"#$%&'(($)%'*+%$,-./0* 0,"0$*./)$%,123/&4* 0%,5.)'4* 6*

4 gauge mediation: natural suppression of flavour changing processes, works in the flat limit but: light gravitino, problematic c.c. cancellation, problems with correct electroweak breaking gauge and gravity mediation - can one mix them arbitrarily? or: to what extent the hidden sector needs to be separated from the observable one? degree of cosmological tuning?

5 (&)*+,-.$-/$012&30455&634$73&+8*.9$ w = λx φφ 0*.9:&6;$73&+80$0104$ 5, 5 of SU(5) F X =0 M i = α i 4π N F X X!" # $%&'$ m 2 s =2 i αi 4π 2 C (i) s N 2 FX X

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7 K = XX + n i=1 φi φi + φ i φ i 1 16π 2 f 4 ( XX) 2 Λ π 2 f 6 ( XX) 3 Λ c

8 condensation + retrofitting in string models: string instantons gauge instantons supersymetry breakdown

9 V V M P V X V V X X M P < X X!"#$%!&''$(%&)*%$+,-./)%$0+($1) (2)!#2.(+.$2"!)R)!&''$(%&) *%$+,-./)!"#$%!&''$(%&)*%$+,-./)%$0+($1) (2)!23)R)!&''$(%&)*%$+,-./) (%+.!'-4$1)(5%2"/5)/%+6-(&)

10 Solutions X = Λ 2 f 4 M P if f 4 > 0 and dominant X 2 = 8 f 4 9f 6 Λ2 if f 4 < 0 and f 6 > 0 X 3 = 16π2 9 Λ4 3f 6 M P if f 4 0 in all cases solutions exist if X 10 3 M P above this value of X the gravitational term gives to large negative slope

11 Gauging the hidden sector - introducing moduli K = X 2 X 4 Λ 2 + m2 V 2 (T + T V ) 2, W = W 0 + fxe T X = D =( X 2 2 X 4 Λ 2 ) m2 V (T + T ) Λ 2 2 3(1 + 3Λ2 2m 2 V ), T = Λ 4 24m 2 3Λ2 V (1 + 2m 2 V ) 2 ( 2 2f Λ masses of (Re(X),Im(X),Re(T)): 1+ 3Λ2 2 2f ), 2m 2 Λ 1+ 3Λ2 V 2m 2 V ), 2 m V ) D f 2 m 3/2 f

12 Adding untwisted moduli

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14 A way out: (Problematic, with S. de Alwis)

15 Cosmological vacuum selection X q q X

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17 X T >> Λ X = q T 2 cr = 4µ2 λ >> T 2 S = µ3 λ 3 δw = λxq q q q X

18 The second cri*cal temperature at which the susy breaking minima are formed: 1) g 4 > 0 T S µ 3 λ 3 1/2 = T 3/2 cr 2) g 4 < 0 and g 6 > 0 3) g 4 0 T S µ2 λ T S µ2 λ 1 Λ 1 1 Λ 2/3 2 For all the cases we find that this second cri1cal temperatur is lower than the first cri1cal temperature which drives the system to the susy minima. non-supersymmetric vacua disfavoured!

19 Conditions for thermal equilibrium Messengers: σvn α SM T T up GeV T q m q /20 δw = λsq q λ 2 S 2 q 2 T λ 2 S 2 T 2

20 Spurion: For T > m q the thermally averaged cross section for 2-2 processes with two spurions is of the order of equilibrium possible below Γ int =< σvn > T λ4 α 2 16π 2 T T eq λ4 α 2 16π 2 g = O(10 3 )λ 4 α 2 for T < m q, the thermalization could also be achieved and the relevant averaged cross section becomes σvn T α 2 λ 4 T 5 /m 4 q This gives a lower bound for the equilibrium window For the case of mixed gauge/gravity mediation spurion doesn t achieve equilibrium

21 Conditions for the selection of the susy breaking vacuum Biased initial conditions: Λ 2 <S init < Λ 1) W = W I (1 ξq I S +...) V 3H S 2 2 O S 4 +3H 2 1 ξq I S 2 Λ 2 (for instance Q I = I e I 0 ) 2) δk = q qi I S Q I and T reheating <m q λs or, for sufficiently small λ, m q <T reheating <T S

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23 0.01 Unstable S direction 10 5 gauge domination mixed gravity domination Λ 10 8 T m Unstable messenger direction

24 Moving vacua around W = µ 2 S λsq q ± Mq q + c In the global susy the theory has a susy minimum at and a susy breaking minimum at S = M λ, q q = µ2 λ, In sugra hence S = q = q =0 V 0 2cµ 2 (S + S )+4µ 4 S 2 Λ 2 S cλ 2 /(2µ 2 )

25 Finite temperature potential, assuming a temperature higher than the messenger scale M is V T = T µ4 Λ 2 +4µ2 c S + S Λ 2 +3 λs ± M 2 +3λ 2 ( q 2 + q 2 ) m 2 q 2λµ T 2 λ 2 T cr 2µ/ λ Note: δw = D 2 (λs Γ) leads to λs Γ if Γ M since δv T T 2 (λs Γ) 2 Ellis, Llewellyn Smith and Ross 82

26 Moduli at finite temperature scaling by moduli dependent factors: λ λe K(T, T )/2 µ 2 µ 2 e K(T, T )/2 c ce K(T, T )/2 Λ Λ e K(T, T )/2 where e.g. e K(T, T )/2 = 1 (T + T ) 3/2 all critical temperatures are moduli independent e.g. T c = µ λ µek/4 λ e K/2

27 Backreaction of the temperature effects on moduli V tot (t) =V 0 + V T emp + F (T,g 2 = 1 2t ) V tot = 2 (t t 0 ) (S 2 +2q 2 )λ 2 T 2 (2t) π2 T 4 24 a 2 2t where = 1 N e t/n, a 2 3N 3 8π 2 conditions: V tot = 0 and t t 0 t 0 give new critical temperature T : 2 t 0 = 3 16t 4 (S 2 +2q 2 )λ 2 T 2 + π2 a t 2 T 4 0 additional condition: T R <T

28 Summary Thermalization usually makes metastable supersymmetry breaking cosmologically disfavoured Biased initial conditions and low reheating temperature help to drive the system towards the susy breaking vacuum Cosmological history of susy breakdown is rather sensitive to the nature of the hidden/ transmission sectors

29 Backup

30 Vacua of microscopic O R models

31 this assumes sugra corrections null

32 if: the term linear in X, sourced by sugra, becomes important, and : <X> 10 3 M P