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The Gaugino Code Hans Peter Nilles Bethe Center for Theoretical Physics Universit at Bonn Stringpheno, Philadelphia, May 2008 p.1/38 Outline Mediation schemes in string theory Recent progress Mirage Mediation Distinct

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SLIDE 1

The Gaugino Code

Hans Peter Nilles Bethe Center for Theoretical Physics Universit¨ at Bonn

Stringpheno, Philadelphia, May 2008 – p.1/38

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Outline

Mediation schemes in string theory Recent progress Mirage Mediation Distinct “compressed” pattern of soft terms Some remarks on the MSSM hierarchy problem Robust prediction for gaugino masses The Gaugino Code Identification of string schemes Uncertainties Conclusions and outlook

Stringpheno, Philadelphia, May 2008 – p.2/38

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Mediation schemes

Supersymmetry is broken in a hidden sector and we have a variant of so-called gravity mediation tree level dilaton/modulus mediation

(Derendinger, Ibanez, HPN, 1985; Dine, Rohm, Seiberg, Witten, 1985)

radiative corrections in case of a sequestered hidden sector (e.g. anomaly mediation)

(Ibanez, HPN, 1986; Randall, Sundrum, 1999)

Stringpheno, Philadelphia, May 2008 – p.3/38

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Mediation schemes

Supersymmetry is broken in a hidden sector and we have a variant of so-called gravity mediation tree level dilaton/modulus mediation

(Derendinger, Ibanez, HPN, 1985; Dine, Rohm, Seiberg, Witten, 1985)

radiative corrections in case of a sequestered hidden sector (e.g. anomaly mediation)

(Ibanez, HPN, 1986; Randall, Sundrum, 1999)

The importance of the mechanism to adjust the cosmological constant has only been appreciated recently

(Choi, Falkowski, HPN, Olechowski, Pokorski, 2004)

Stringpheno, Philadelphia, May 2008 – p.3/38

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Basic Questions

  • rigin of the small scale?

stabilization of moduli?

Stringpheno, Philadelphia, May 2008 – p.4/38

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Basic Questions

  • rigin of the small scale?

stabilization of moduli? Recent progress in moduli stabilization via fluxes in warped compactifications of Type IIB string theory

(Dasgupta, Rajesh, Sethi, 1999; Giddings, Kachru, Polchinski, 2001)

generalized flux compactifications of heterotic string theory

(Becker, Becker, Dasgupta, Prokushkin, 2003; Gurrieri, Lukas, Micu, 2004)

combined with gaugino condensates and “uplifting”

(Kachru, Kallosh, Linde, Trivedi, 2003; Löwen, HPN, 2008)

Stringpheno, Philadelphia, May 2008 – p.4/38

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Fluxes and gaugino condensation

Is there a general pattern of the soft mass terms? We always have (from flux and gaugino condensate)

W = something − exp(−X)

where “something” is small and X is moderately large.

Stringpheno, Philadelphia, May 2008 – p.5/38

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Fluxes and gaugino condensation

Is there a general pattern of the soft mass terms? We always have (from flux and gaugino condensate)

W = something − exp(−X)

where “something” is small and X is moderately large. In fact in this simple scheme

X ∼ log(MPlanck/m3/2)

providing a “little” hierarchy.

(Choi, Falkowski, HPN, Olechowski, Pokorski, 2004)

Stringpheno, Philadelphia, May 2008 – p.5/38

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Mixed Mediation Schemes

The contribution from “Modulus Mediation” is therefore suppressed by the factor

X ∼ log(MPlanck/m3/2) ∼ 4π2.

Stringpheno, Philadelphia, May 2008 – p.6/38

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Mixed Mediation Schemes

The contribution from “Modulus Mediation” is therefore suppressed by the factor

X ∼ log(MPlanck/m3/2) ∼ 4π2.

Thus the contribution due to radiative corrections becomes competitive, leading to mixed mediation schemes. The simplest case for radiative corrections leads to anomaly mediation competing now with the suppressed contribution of modulus mediation. For reasons that will be explained later we call this scheme MIRAGE MEDIATION

(Loaiza, Martin, HPN, Ratz, 2005)

Stringpheno, Philadelphia, May 2008 – p.6/38

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The little hierarchy

mX ∼ Xm3/2 ∼ X2msoft

is a generic signal of such a scheme moduli and gravitino are heavy gaugino mass spectrum is compressed

(Choi, Falkowski, HPN, Olechowski, 2005; Endo, Yamaguchi, Yoshioka, 2005; Choi, Jeong, Okumura, 2005)

such a situation occurs if SUSY breaking is e.g. “sequestered” on a warped throat

(Kachru, McAllister, Sundrum, 2007)

Stringpheno, Philadelphia, May 2008 – p.7/38

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Mirage Unification

Mirage Mediation provides a characteristic pattern of soft breaking terms. To see this, let us consider the gaugino masses

M1/2 = Mmodulus + Manomaly

as a sum of two contributions of comparable size.

Manomaly is proportional to the β function,

i.e. negative for the gluino, positive for the bino thus Manomaly is non-universal below the GUT scale

Stringpheno, Philadelphia, May 2008 – p.8/38

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Evolution of couplings

3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 log10ΜGeV 0.02 0.03 0.04 0.05 0.06 0.07 0.08 0.09 Αi

Stringpheno, Philadelphia, May 2008 – p.9/38

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The Mirage Scale

3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 log10ΜGeV 600 800 1000 1200 1400 1600 MiGeV

M3 M2 M1

(Lebedev, HPN, Ratz, 2005)

Stringpheno, Philadelphia, May 2008 – p.10/38

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The Mirage Scale (II)

The gaugino masses coincide above the GUT scale at the mirage scale

µmirage = MGUT exp(−8π2/ρ)

where ρ denotes the “ratio” of the contribution of modulus

  • vs. anomaly mediation. We write the gaugino masses as

Ma = Ms(ρ + bag2

a) = m3/2

16π2 (ρ + bag2

a)

and ρ → 0 corresponds to pure anomaly mediation.

Stringpheno, Philadelphia, May 2008 – p.11/38

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Constraints on the mixing parameter

2 4 6 8 10 Ρ 20 40 60 80 100 120 m32 TeV tan Β 5 sign Μ 1 mt 172 GeV TACHYONS ALLOWED t

  • 1 LSP

mh 114 GeV

(Löwen, HPN, Ratz, 2006)

Stringpheno, Philadelphia, May 2008 – p.12/38

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Constraints on ρ

2 4 6 8 10 Ρ 20 40 60 80 100 120 m32 TeV tan Β 30 sign Μ 1 mt 172 GeV TACHYONS ALLOWED t

  • 1 LSP

mh 114 GeV

(Löwen, HPN, Ratz, 2006)

Stringpheno, Philadelphia, May 2008 – p.13/38

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The “MSSM hierarchy problem”

The scheme predicts a rather high mass scale heavy gravitino rather high mass for the LSP-Neutralino

Stringpheno, Philadelphia, May 2008 – p.14/38

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The “MSSM hierarchy problem”

The scheme predicts a rather high mass scale heavy gravitino rather high mass for the LSP-Neutralino One might worry about a fine-tuning to obtain the mass of the weak scale around 100 GeV from

m2

Z

2 = − µ2 + m2

Hd − m2 Hu tan2 β

tan2 β − 1 ,

and there are large corrections to m2

Hu......

(Choi, Jeong, Kobayashi, Okumura, 2005)

Stringpheno, Philadelphia, May 2008 – p.14/38

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The “MSSM hierarchy problem”?

The influence of the various soft terms is given by

m2

Z

≃ −1.8 µ2 + 5.9 M2

3 − 0.4 M2 2 − 1.2 m2 Hu + 0.9 m2 q(3)

L +

+ 0.7 m2

u(3)

R −0.6 At M3 + 0.4 M2 M3 + . . .

Stringpheno, Philadelphia, May 2008 – p.15/38

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The “MSSM hierarchy problem”?

The influence of the various soft terms is given by

m2

Z

≃ −1.8 µ2 + 5.9 M2

3 − 0.4 M2 2 − 1.2 m2 Hu + 0.9 m2 q(3)

L +

+ 0.7 m2

u(3)

R −0.6 At M3 + 0.4 M2 M3 + . . .

Mirage mediation improves the situation especially for small ρ because of a reduced gluino mass and a “compressed” spectrum of supersymmetric partners

(Choi, Jeong, Kobayashi, Okumura, 2005)

explicit model building required

(Kitano, Nomura, 2005; Lebedev, HPN, Ratz, 2005; Pierce, Thaler, 2006; Dermisek, Kim, 2006; Ellis, Olive, Sandick, 2006; Martin, 2007)

Stringpheno, Philadelphia, May 2008 – p.15/38

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Explicit schemes I

The different schemes depend on the mechanism of uplifting: uplifting with anti D3 branes

(Kachru, Kallosh, Linde, Trivedi, 2003)

ρ ∼ 5 in the original KKLT scenario leading to

a mirage scale of approximately 1011 GeV This scheme leads to pure mirage mediation: gaugino masses and scalar masses both meet at a common mirage scale

Stringpheno, Philadelphia, May 2008 – p.16/38

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Constraints on ρ

2 4 6 8 10 Ρ 20 40 60 80 100 120 m32 TeV tan Β 30 sign Μ 1 mt 172 GeV TACHYONS ALLOWED t

  • 1 LSP

mh 114 GeV

(Löwen, HPN, Ratz, 2006)

Stringpheno, Philadelphia, May 2008 – p.17/38

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The Mirage Scale

3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 log10ΜGeV 600 800 1000 1200 1400 1600 MiGeV

M3 M2 M1

(Lebedev, HPN, Ratz, 2005)

Stringpheno, Philadelphia, May 2008 – p.18/38

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Explicit schemes II

uplifting via matter superpotentials

(Lebedev, HPN, Ratz, 2006)

allows a continuous variation of ρ leads to potentially new contributions to sfermion masses

Stringpheno, Philadelphia, May 2008 – p.19/38

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Explicit schemes II

uplifting via matter superpotentials

(Lebedev, HPN, Ratz, 2006)

allows a continuous variation of ρ leads to potentially new contributions to sfermion masses gaugino masses still meet at a mirage scale soft scalar masses might be dominated by modulus mediation similar constraints on the mixing parameter

Stringpheno, Philadelphia, May 2008 – p.19/38

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Constraints on the mixing parameter

2 4 6 8 10 Ρ 10 20 30 40 50 m32 TeV tan Β 5 sign Μ 1 mt 175 GeV Below LEP No EWSB g LSP Χ

(V. Löwen, 2007)

Stringpheno, Philadelphia, May 2008 – p.20/38

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Constraints on the mixing parameter

2 4 6 8 10 Ρ 10 20 30 40 50 m32 TeV tan Β 5 sign Μ 1 mt 175 GeV

100 300 500 700 900

(V. Löwen, 2007)

Stringpheno, Philadelphia, May 2008 – p.21/38

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Constraints on the mixing parameter

2 4 6 8 10 Ρ 10 20 30 40 50 m32 TeV tan Β 5 sign Μ 1 mt 175 GeV Below LEP No EWSB g LSP Χ

(V. Löwen, 2007)

Stringpheno, Philadelphia, May 2008 – p.22/38

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Constraints on the mixing parameter

2 4 6 8 10 12 10 20 30 40 50 60

  • m32 TeV

tan Β 30 Η 4 Η 6

g LSP No EWSB Below LEP Χ LSP

WMAP WMAP

(V. Löwen, HPN, 2008)

Stringpheno, Philadelphia, May 2008 – p.23/38

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Explicit schemes III

This “relaxed” mirage mediation is rather common for schemes with F-term uplifting

(Intriligator, Shih, Seiberg; Gomez-Reino, Scrucca; Dudas, Papineau, Pokorski; Abe, Higaki, Kobayashi, Omura; Lebedev, Löwen, Mambrini, HPN, Ratz ,2006)

although “pure” mirage mediation is possible as well

Stringpheno, Philadelphia, May 2008 – p.24/38

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Explicit schemes III

This “relaxed” mirage mediation is rather common for schemes with F-term uplifting

(Intriligator, Shih, Seiberg; Gomez-Reino, Scrucca; Dudas, Papineau, Pokorski; Abe, Higaki, Kobayashi, Omura; Lebedev, Löwen, Mambrini, HPN, Ratz ,2006)

although “pure” mirage mediation is possible as well Main message predictions for gaugino masses are more robust than those for sfermion masses mirage (compressed) pattern for gaugino masses rather generic

Stringpheno, Philadelphia, May 2008 – p.24/38

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Obstacles to D-term uplifting

In supergravity we have the relation

D ∼ F W

which implies that KKLT AdS minimum cannot be uplifted via D-terms.

(Choi, Falkowski, HPN, Olechowski, 2005)

Stringpheno, Philadelphia, May 2008 – p.25/38

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Obstacles to D-term uplifting

In supergravity we have the relation

D ∼ F W

which implies that KKLT AdS minimum cannot be uplifted via D-terms.

(Choi, Falkowski, HPN, Olechowski, 2005)

Moreover in these schemes we have

F ∼ m3/2MPlanck and D ∼ m2

3/2.

So if m3/2 ≪ MPlanck the D-terms are irrelevant.

(Choi, Jeong, 2006)

Stringpheno, Philadelphia, May 2008 – p.25/38

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The string signatures

Schemes to consider: Type IIB string theory Type IIA string theory Heterotic string theory M-theory on manifolds with G2 holonomy Heterotic M-theory

Stringpheno, Philadelphia, May 2008 – p.26/38

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The string signatures

Schemes to consider: Type IIB string theory Type IIA string theory Heterotic string theory M-theory on manifolds with G2 holonomy Heterotic M-theory Questions: are there distinct signatures for the various schemes? can they be identified with LHC data?

(Choi, HPN, 2007)

Stringpheno, Philadelphia, May 2008 – p.26/38

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The Gaugino Code

First step to test these ideas at the LHC: look for pattern of gaugino masses Let us assume the low energy particle content of the MSSM measured values of gauge coupling constants

g2

1 : g2 2 : g2 3 ≃ 1 : 2 : 6

The evolution of gauge couplings would then lead to unification at a GUT-scale around 1016 GeV

Stringpheno, Philadelphia, May 2008 – p.27/38

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Formulae for gaugino masses

Ma g2

a

  • TeV

= ˜ M(0)

a

+ ˜ M(1)

a |anomaly + ˜

M(1)

a |gauge + ˜

M(1)

a |string

˜ M(0)

a

= 1 2F I∂If(0)

a

˜ M(1)

a |anomaly =

1 16π2ba F C C − 1 8π2

  • m

Cm

a F I∂I ln(e−K0/3Zm)

˜ M(1)

a |string =

1 8π2F I∂IΩa

Stringpheno, Philadelphia, May 2008 – p.28/38

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The Gaugino Code

Observe that evolution of gaugino masses is tied to evolution of gauge couplings for MSSM Ma/g2

a does not run (at one loop)

This implies robust prediction for gaugino masses gaugino mass relations are the key to reveal the underlying scheme 3 CHARACTERISTIC MASS PATTERNS

(Choi, HPN, 2007)

Stringpheno, Philadelphia, May 2008 – p.29/38

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mSUGRA Pattern

Universal gaugino mass at the GUT scale mSUGRA pattern:

M1 : M2 : M3 ≃ 1 : 2 : 6 ≃ g2

1 : g2 2 : g2 3

as realized in popular schemes such as gravity-, modulus-, gauge- and gaugino-mediation This leads to LSP χ0

1 predominantly Bino

Mgluino/mχ0

1 ≃ 6

as a characteristic signature of these schemes.

Stringpheno, Philadelphia, May 2008 – p.30/38

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Anomaly Pattern

Gaugino masses below the GUT scale determined by the β functions anomaly pattern:

M1 : M2 : M3 ≃ 3.3 : 1 : 9

at the TeV scale as the signal of anomaly mediation. For the gauginos, this implies LSP χ0

1 predominantly Wino

Mgluino/mχ0

1 ≃ 9

Pure anomaly mediation inconsistent, as sfermion masses are problematic in this scheme (tachyonic sleptons).

Stringpheno, Philadelphia, May 2008 – p.31/38

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Mirage Pattern

Mixed boundary conditions at the GUT scale characterized by the parameter ρ (the ratio of anomaly to modulus mediation).

M1 : M2 : M3 ≃ 1 : 1.3 : 2.5

for ρ ≃ 5

M1 : M2 : M3 ≃ 1 : 1 : 1

for ρ ≃ 2 The mirage scheme leads to LSP χ0

1 predominantly Bino

Mgluino/mχ0

1 < 6

a “compact” gaugino mass pattern.

Stringpheno, Philadelphia, May 2008 – p.32/38

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Uncertainties

String thresholds

˜ M(1)

a |string =

1 8π2F I∂IΩa

Kähler corrections

˜ M(1)

a |anomaly =

1 16π2ba F C C − 1 8π2

  • m

Cm

a F I∂I ln(e−K0/3Zm)

Intermediate thresholds

˜ M(1)

a |gauge =

1 8π2

  • Φ

CΦ

a

F XΦ MΦ

Stringpheno, Philadelphia, May 2008 – p.33/38

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Various String Schemes

Type IIB with matter on D7 branes: mirage mediation Type IIB with matter on D3 branes: anomaly mediation? Heterotic string with dilaton domination: mirage mediation Heterotic string with modulus domination: string thresholds might spoil anomaly pattern M theory on “G2 manifold”: Kähler corrections might spoil mirage pattern

(Acharya, Bobkov, Kane, Kumar, Shao, 2007)

Stringpheno, Philadelphia, May 2008 – p.34/38

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Summary

In the calculation of the soft masses we get the most robust predictions for gaugino masses Modulus Mediation: (fWW with f = f(Moduli)) If this is supressed we might have loop contributions, e.g. Anomaly Mediation as simplest example

Stringpheno, Philadelphia, May 2008 – p.35/38

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Summary

In the calculation of the soft masses we get the most robust predictions for gaugino masses Modulus Mediation: (fWW with f = f(Moduli)) If this is supressed we might have loop contributions, e.g. Anomaly Mediation as simplest example How much can it be suppressed?

log(m3/2/MPlanck)

So we might expect a mixture of tree level and loop contributions.

Stringpheno, Philadelphia, May 2008 – p.35/38

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Conclusion

Gaugino masses can serve as a promising tool to disentangle various string schemes Rather robust predictions 3 basic and simple patterns (mSugra, anomaly, mirage) Mirage pattern rather generic Is pure modulus mediation possible? Main uncertainties from “string threshold corrections” With some luck we might test these ideas at the LHC!

Stringpheno, Philadelphia, May 2008 – p.36/38

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Conclusion

Mirage Mediation naturally appears in string theory models with background fluxes and gaugino condensation. It predicts heavy moduli and a heavy gravitino reduces the fine tuning of the weak scale gives a consistent neutralino dark matter candidate Mirage mediation avoids the problems of conventional schemes like anomaly and modulus mediation is the correct way to implement anomaly mediation gives a consistent picture with very few parameters

Stringpheno, Philadelphia, May 2008 – p.37/38

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Conclusion

The source of Mirage Mediation is the appearance of a small parameter

X−1 ∼ log(m3/2/MPlanck)

that leads to a (heavy) superpartner spectrum exhibiting a little hierarchy

mX ∼ Xm3/2 ∼ X2msoft

a rather heavy gravitino mass and a mirage pattern of the gaugino masses.

Stringpheno, Philadelphia, May 2008 – p.38/38

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Conclusion

The source of Mirage Mediation is the appearance of a small parameter

X−1 ∼ log(m3/2/MPlanck)

that leads to a (heavy) superpartner spectrum exhibiting a little hierarchy

mX ∼ Xm3/2 ∼ X2msoft

a rather heavy gravitino mass and a mirage pattern of the gaugino masses. Mirage Mediation provides a distinct (compressed) pattern

  • f soft terms that could be tested at the LHC!

Stringpheno, Philadelphia, May 2008 – p.38/38