Y-Unified GUTS: MSSM at large tan Archana Anandakrishnan The Ohio - - PowerPoint PPT Presentation

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Y-Unified GUTS: MSSM at large tan Archana Anandakrishnan The Ohio State University October 3, 2013 Based on arXiv:1212.0542 (Phys. Rev. D 87, 055005 (2013)) & arXiv:1303.5125 & arXiv:1307.7723 (Accepted in PRD) & work in progress

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Y-Unified GUTS: MSSM at large tanβ

Archana Anandakrishnan

The Ohio State University

October 3, 2013 Based on arXiv:1212.0542 (Phys. Rev. D 87, 055005 (2013)) & arXiv:1303.5125 & arXiv:1307.7723 (Accepted in PRD) & work in progress

with Stuart Raby, B. Charles Bryant, Linda Carpenter (OSU), Kuver Sinha (Syracuse), Akın Wingerter(LPSC) Theory Seminar, Los Alamos National Lab

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Outline

Introduction to SO(10) SUSY GUTS Constraints from Yukawa Unification The Analysis Spectrum and Phenomenology Effective“Mirage” Mediation. Summary

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Supersymmetric GUTS

Dimopoulos, Raby, Wilczek (1981)

(Fig. from Martin’s Primer) Argument in favor of SUSY, independent of the solution to hierarchy problem. Requires some superpartners of around the TeV scale. Unification of couplings at ∼ 1016 GeV.

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SO(10) GUTS and Yukawa Unification

SO(10) → SU(3)C × SU(2)L × U(1)Y × U(1)(B−L) 16 → (3, 2)1/3,1/3 + (¯ 3, 1)−4/3,−1/3 + (1, 1)−2,1 + (¯ 3, 1)2/3,−1/3 + (1, 2)−1,−1 + (1, 1)0,1 Q ¯ u ¯ e ¯ d L ¯ ν

SO(10) GUTS are very economical: 16 dimensional representation. Only renormalizable Yukawa coupling is of the form, W ⊃ λ 16 10 16 allowing for unified Yukawa couplings at the GUT scale. Third family Yukawa Unification is consistent with current data. λt = λb = λτ = λντ = λ Effective higher dimensional operators could generate the first two family hierarchical Yukawa couplings.

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Yunification and Boundary Conditions

One can use Yukawa Unification to constrain the GUT scale boundary conditions. Yukawa Unification & Soft SUSY breaking

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Blazek, Dermisek & Raby PRL 88, 11804; PRD 65, 115004 Baer & Ferrandis PRL 87, 211803 Auto, Baer, Balazs, Belayaev, Ferrandis,& Tata JHEP 0306:023 Tobe & Wells NPB 663,123 Dermisek, Raby, Roszkowski, & Ruiz de Austri JHEP 0304:037; JHEP 0509:029 Baer, Kraml, Sekmen, & Summy JHEP 0803:056; JHEP 0810:079 Badziak, Olechowski & Pokorski JHEP 2011:147 Gogoladze, & Shafi,Un JHEP 2012:028; PLB 704, 201 Ajaib, Gogoladze, Shafi, & Un JHEP 2013:139 AA & Raby arXiv:1303.5125

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Recent papers on Yukawa unification (created using wordle)

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A quick refresher

GUT scale parameters of a ’minimal’ SO(10) SUSY GUT m16 - Universal scalar mass m10 - Universal Higgs mass M1/2 - Universal gaugino mass A0 - Trilinear coupling tanβ - Ratio of the Higgs vev. g - Unified gauge coupling λ - Unified Yukawa coupling at the GUT scale

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Higgs vev

Ratio of the Higgs vev is defined as tanβ = vu vd = Hu Hd Fermion masses are generated by coupling to the Higgs boson L ⊃ λtvu¯ tt + λbvd¯ bb + λτvd ¯ ττ The value of tanβ is restricted by the requirement of Yukawa unification. tanβ ≃ 50

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Yunification and Boundary Conditions

One can use Yukawa Unification to constrain the GUT scale boundary conditions. Yukawa Unification & Soft SUSY breaking tanβ ≃ 50

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Bottom quark mass

In the large tanβ regime, there are large corrections to the bottom quark mass. δmb/mb ≃ g 2

3

12π2 µM˜

gtanβ

m2

˜ b

+ λ2

t

32π2 µAttanβ m2

˜ t

Hall et. al; Carena et. al; Blazek et. al

In order to fit data, δmb/mb ≃ −(few)% µM˜

g > 0; ⇒ µAt < 0

Trilinear Coupling A0 < 0

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Electroweak Symmetry Breaking

The RGEs for the up and down-type Higgs mass squared can be written as:

dm2

Hd

dt = 2 16π2

  • − 3

5 g2

1 M2 1 − 3g2 2 M2 2 − 3

10 g2

1 S + 3λ2 bXb + λ2 τXτ

  • dm2

Hu

dt = 2 16π2

  • − 3

5 g2

1 M2 1 − 3g2 2 M2 2 + 3

10 g2

1 S + 3λ2 t Xt + λ2 ντ Xντ

  • RGE evolution in standard MSSM scenarios
  • 200

200 400 600 2 4 6 8 10 12 14 16 GeV log10(µ/GeV) (µ2+mHd

2)1/2

(µ2+mHu

2)1/2

M1 M2 M3 mQl mEr SOFTSUSY3.0.5 SPS1a

Fig from SOFTSUSY 12

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Electroweak Symmetry Breaking

The RGEs for the up and down-type Higgs mass squared can be written as:

dm2

Hd

dt = 2 16π2

  • − 3

5 g2

1 M2 1 − 3g2 2 M2 2 − 3

10 g2

1 S + 3λ2 bXb + λ2 τXτ

  • dm2

Hu

dt = 2 16π2

  • − 3

5 g2

1 M2 1 − 3g2 2 M2 2 + 3

10 g2

1 S + 3λ2 t Xt + λ2 ντ Xντ

  • In Yunified models, since, λt = λb = λτ = λν = λ, in order for

REWSB, one needs m2

Hu < m2 Hd

Non-universal Higgs masses!

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Yunification and Boundary Conditions

One can use Yukawa Unification to constrain the GUT scale boundary conditions. Yukawa Unification & Soft SUSY breaking tanβ Corrections to bottom mass Non-universal Higgs mass

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Bs → Xsγ

Exp BR(Bs → Xsγ)Exp = (3.43 ± 0.30) × 10−4 SM NNLO BR(Bs → Xsγ)SM = (3.15 ± 0.23) × 10−4

In MSSM, C ˜

χ+ 7

∝ µAt ˜ m2 tanβ × sign(C SM

7

) Data constrains C eff

7

= C SM

7

+ C SUSY

7

≃ ±C SM

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C SUSY

7

≃ −2C SM

7

, implying light scalars. C SUSY

7

≃ 0, implying heavy scalars scalars. Which possibility does data accommodate?

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B → K ∗µ+µ−

Forward-Backward Asymmetry in B → K ∗µ+µ−! If C eff

7

= +C SM

7

, then AFB crosses zero at some momentum. If C eff

7

= −C SM

7

, then there is no zero-crossing in the AFB.

]

4

c /

2

[GeV

2

q

5 10 15 20

FB

A

  • 1
  • 0.5

0.5 1 Theory Binned theory LHCb

Preliminary LHCb

2012 Result from LHCb Heavy Scalars

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Breaking News!

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Bs → µ+µ−

2012 LHCb BR(Bs → µ+µ−)Exp = (3.2 ± 1.5) × 10−9 SM BR(Bs → µ+µ−)SM = (3.37 ± 0.31) × 10−9

MSSM contributions are enhanced in the large tanβ limit. BR(Bs → µ+µ−) ∝ (tanβ)6 M4

A

In MSSM models with large tanβ, MA ≥ 1500 GeV Standard Model like Higgs

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Yunification and Boundary Conditions

One can use Yukawa Unification to constrain the GUT scale boundary conditions. Yukawa Unification & Soft SUSY breaking tanβ Corrections to bottom mass Non-universal Higgs mass Flavor Physics

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Discovery of the millenia

CMS ; ATLAS Mh = 125.3 ± 1 GeV

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Light Higgs Mass

Boundary conditions consistent with minimal Yukawa unification: m16 > few TeV; m10 ∼ √ 2m16; A0 ∼ −2m16; µ, M1/2 << m16; tanβ ∼ 50

Bagger, Feng, et al

Maximal mixing region - easy to get ∼ 125 GeV Higgs.

Carena, Quiros, Wagner

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Higgs and Bottom quark

To fit bottom quark mass: δmb/mb ≃ g 2

3

12π2 µM˜

gtanβ

m2

˜ b

+ λ2

t

32π2 µAttanβ m2

˜ t

Fitting the Higgs mass:

500 1000 1500 2000 2500

M(˜ g) [GeV]

1 2 3 4 5 6 7

χ2 95% C.L. 2092 90% C.L. 2010 68% C.L. 1436

m16 = 20 TeV

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Yunification and Boundary Conditions

One can use Yukawa Unification to constrain the GUT scale boundary conditions. Yukawa Unification & Soft SUSY breaking tanβ Corrections to bottom mass Non-universal Higgs mass Flavor Physics Higgs Mass

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Neutrino sector

Observables in the neutrino sector: sin2 θ12 = 0.27 − 0.34 sin2 θ23 = 0.34 − 0.67 sin2 θ13 = 0.016 − 0.030 ∆m2

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= (7.00 − 8.09) × 10−5 eV2 ∆m2

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= (2.27 − 2.69) × 10−3 eV2 (3σ range) from Nu-fit Collaboration θexp

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= 9◦(7.29 − 9.96) θDR−model

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  • 6◦

DayaBay; Reno Flavor violating corrections to the K¨ ahler potential. Chen, Fallbacher et al

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Yunification and Boundary Conditions

One can use Yukawa Unification to constrain the GUT scale boundary conditions. Yukawa Unification & Soft SUSY breaking tanβ Corrections to bottom mass Non-universal Higgs mass Flavour Physics Higgs Mass Neutrino masses and mixing angles

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Dermisek-Raby Model

Recent analysis by AA, S.Raby, and A. Wingerter 1212.0542 Sector Third Family Analysis # Full three family Analysis # gauge αG , MG , ǫ3 3 αG , MG , ǫ3 3 SUSY (GUT scale) m16, M1/2, A0, mHu , mHd 5 m16, M1/2, A0, mHu , mHd 5 textures λ 1 ǫ, ǫ′, λ, ρ, σ, ˜ ǫ, ξ 11 neutrino MR1, MR2, MR3 3 SUSY (EW scale) tan β, µ 2 tan β, µ 2 Total # 11 24

(Compared to 32 parameters in the CMSSM)

Wch.fermions = λ 163 10 163 + 16a 10 χa + ¯ χa (Mχ χa + 45 φa ˆ M 163 + 45 ˜ φa ˆ M 16a + A 16a) Effective operators to generate the first two family and off-diagonal Yukawa couplings.

16 10 16

3 3

45 Φa MX 10 16 χa χa

_

~

162 2 45 Φa MX 10 16 χa χa

_

16

a c b

MX 10 16 χa A χa

_

16 b c

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Model defined in terms of 24 real parameters: αG, MG, ǫ3, m16, M1/2, A0, mHu, mHd, λ, ǫ, ǫ′, ρ, σ, ˜ ǫ, ξ, MR1, MR2, MR3, tan β, µ

GUT (24 parameters)

Right-handed neutrinos integrated out

RHN

1st and 2nd generation scalars are integrated out

m16

SUSY spectrum & flavor observ- ables calculated (susy flavor)

MSUSY

Calculate top pole mass

Mtop

SM spectrum & flavor observables cal- culated (SuperIso) & tan β, µ, mh, mH, mA, mH±

MEW

Calculate light quark masses mu, md, ms

2 GeV

Gauge & EW sector: MZ, MW, αem, Gµ, α3, Mh Quark sector: Mt, mb, mc, ms, md/ms, 1/Q2, |Vus|, |Vcb|, |Vub|, |Vtd|, |Vts|, sin2β Lepton sector: Mτ, Mµ, Me, θ12, θ23, θ13, m2

21, m2 31

Flavor observables: ǫK, ∆MBs/∆MBd, ∆MBd, B → Xsγ, Bs → µ+µ−, Bd → µ+µ−, B → τν, B → K∗µ+µ− (3x)

Experiment (36 Observables)

RGEs for MSSM w/right-handed neutrinos RGEs for MSSM RGEs for MSSM w/o 1st and 2nd generation scalars RGEs for MSSM w/o 1st and 2nd generation scalars Corrections Compare Compare Compare RGEs for SM RGEs: 3-loop QCD & 1-loop EW

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SUSY Spectrum

Benchmark Points

m16 10 TeV 15 TeV 20 TeV 25 TeV 30 TeV A0

  • 20.2 TeV
  • 30.6 TeV
  • 41.1 TeV
  • 51.3 TeV
  • 61.6 TeV

µ 791 513 1163 1348 1647 M1/2 201 201 168 158 162 χ2 49.65 31.02 26.58 27.93 29.48 MA 2333 3662 1651 2029 2036 m˜

t1

1681 2529 3975 4892 5914 m˜

b1

2046 2972 5194 6353 7660 m˜

τ1

3851 5576 7994 9769 11620 m ˜

χ0

1

133 134 137 149 167 m ˜

χ+

1

260 263 279 309 351 M˜

g

853 850 851 910 1004

SUSY spectrum is predominantly determined by fitting: Third family masses light Higgs mass BR(Bs → Xsγ) and BR(Bs → µ+ µ−)

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SUSY Spectrum

500 1000 1500 2000 2500

M(˜ g) [GeV]

1 2 3 4 5 6 7

χ2

95% C.L. 2092 90% C.L. 2010 68% C.L. 1436

m16 = 20 TeV SUSY spectrum is predominantly determined by fitting: Third family masses light Higgs mass BR(Bs → Xsγ) and BR(Bs → µ+ µ−)

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Topologies

T1bbbb

(GeV)

g ~

m

400 600 800 1000 1200 1400

(GeV)

1

χ ∼

m

200 400 600 800 1000 1200

  • 3

10

  • 2

10

  • 1

10 1 = 8 TeV s ,

  • 1

CMS , L = 19.4 fb NLO+NLL exclusion

1

χ ∼ b b → g ~ , g ~ g ~ → pp

theory

σ 1 ± Observed

experiment

σ 1 ± Expected

95% CL upper limit on cross section (pb)

BR(˜ g → b¯ b˜ χ0

1) = 100%

T1tttt

(GeV)

g ~

m

400 600 800 1000 1200 1400

(GeV)

1

χ ∼

m

100 200 300 400 500 600 700 800

  • 3

10

  • 2

10

  • 1

10 1 = 8 TeV s ,

  • 1

CMS , L = 19.4 fb NLO+NLL exclusion

1

χ ∼ t t → g ~ , g ~ g ~ → pp

theory

σ 1 ± Observed

experiment

σ 1 ± Expected

95% CL upper limit on cross section (pb)

BR(˜ g → t¯ t ˜ χ0

1) = 100%

Results from CMS wiki

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Not so simplified model

AA, Bryant, Raby, and Wingerter: arXiv:1307.7723, arXiv:1308.2232 Benchmark point with m16 = 20 TeV , M˜

g = 1.06 TeV

BR(˜ g → b¯ t ˜ χ+

1 )

= 27% BR(˜ g → t¯ b˜ χ−

1 )

= 27% BR(˜ g → t¯ t ˜ χ0

2)

= 22% BR(˜ g → g ˜ χ0

1)

= 15% Compare with data from LHC

Analysis Luminosity Signal Region Reference SS di-lepton 10.5 Njet ≥ 4, Nb−jet ≥ 2, CMS-SUS-12-017 Emiss T > 120, HT > 200 αT analysis (for Simplified models) 11.7 Njet ≥ 4, Nb−jet = 3, HT > 875 (for the benchmark models) Njet ≥ 4, Nb−jet = 2, 775 < HT < 875 CMS-SUS-12-028 ∆φ analysis 19.4 Nb−jet ≥ 3, Emiss T > 350, HT > 1000 CMS-SUS-12-024 31

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Yunified vs Simplified

From Hadronic ∆ˆ φ analysis:

T1tttt Benchmark Model

600 800 1000 1200 1400

M(˜ g) [GeV]

5 10 15 20 25 30 35 40

Number of events passing all cuts NUL = 8.0 ∆φ analysis: L = 19.4 fb−1, M(˜ χ0

1) = 200 GeV, B(˜

g → ˜ χ0

1t¯

t) = 100%

M˜

g ≥ 1100GeV

3 8 5 2 6 6 6 6 8 1 9 3 2 1 6 1 1 8 6 1 3 9 1 4 3 1 5 5 1 6 6 5 1 7 7 9 1 8 9 2 1 2 1 2

M(˜ g) [GeV]

5 10 15 20 25 30 35 40

Number of events passing all cuts NUL = 8.0 ∆φ analysis: L = 19.4 fb−1, Benchmark models

M˜

g ≥ 1000GeV

MATON → SDECAY → PYTHIA → DELPHES

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Predictions

Rare Processes

Current Limit 10 TeV 20 TeV 30 TeV e EDM ×1028 < 10.5 e cm −0.224 −0.0173 −0.0084 µ EDM ×1028 (−0.1 ± 0.9) × 109 e cm 34.6 3.04 1.20 τ EDM ×1028 −0.220 − 0.45 × 1012 e cm −2.09 −0.185 −0.0732 BR(µ → eγ) × 1012 < 2.4 5.09 0.211 0.0447 BR(τ → eγ) × 1012 < 3.3 × 104 58.8 2.40 0.502 BR(τ → µγ) × 108 < 4.4 1.75 0.0837 0.0182 sin δ

  • 0.60
  • 0.27
  • 0.53

BR(µ → e γ) ∼ 10−12 − 10−13 for values of m16 = 15 − 25 TeV. Latest result from MEG BR(µ → eγ) < 0.57 × 10−12. Neutrinos obey a normal hierarchy. PROBLEMS: Bino LSP - over-abundant dark matter. (Axions Baer, Haider, et al.) (g − 2)µ too small, due to heavy scalars (sleptons).

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PART II

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Effective “Mirage” Mediation

arXiv:1303.5125 AA and Stuart Raby

We investigate a new set of boundary conditions at the GUT scale, consistent with Yukawa unification. Non-universal gaugino masses with mirage pattern. Mi =

  • 1 + g 2

Gbiα

16π2 log MPl m16

  • M1/2

Choi,Nilles

where M1/2 and α are free parameters and bi = (33/5, 1, −3) We choose µ < 0, M1/2 < 0 such that M3 > 0 and M1,2 < 0 Simultaneously satisfy (i) corrections to bottom quark mass (ii) BR(Bs → Xsγ) and (iii) anomalous magnetic moment of muon*.

Badziak, Olechowski, Pokorski

* Now, ruled out after the Higgs result.

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Scalar Masses

Two different cases for non-universal Higgs masses [NUHM] with “just so” Higgs splitting m2

Hu(d) = m2 10 − (+)2D

  • r,

D-term Higgs splitting, in addition, squark and slepton masses are given by m2

a = m2 16 + QaD, {Qa = +1, {Q, ¯

u, ¯ e}; −3, {L, ¯ d}} with the U(1) D-term, D, and SU(5) invariant charges, Qa.

Sector Third Family Analysis gauge αG , MG , ǫ3 SUSY (GUT scale) m16, M1/2, α, A0, m10, D textures λ SUSY (EW scale) tan β, µ Total # 12 36

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SUSY Spectrum

NUHM “Just-so” D-term m16 5.00 TeV 5.00 TeV A0 8.07 TeV 5.59 TeV µ

  • 615 GeV
  • 1.29 TeV

M1/2

  • 105 GeV
  • 100 GeV

α 11.59 11.99 MA 1558 1236 m˜

t1

1975 2920 m˜

b1

2049 2158 m˜

τ1

2473 3601 m ˜

χ0

1

231.98 219.11 m ˜

χ+

1

232.05 219.11 ∆M ≡ M ˜

χ+ − M ˜ χ0

519 MeV 434 MeV M˜

g

882 874

Very different spectrum from the minimal Yukawa unification scenario. Heavier gluino, degenerate charginos and neutralinos.

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SUSY Spectrum

−1000 −800 −600 −400 −200

M1/2, in GeV

4 5 6 7 8 9 10 11 12

α

1000.000 1500.000 2000.000 2 5 . 3 .

Very different spectrum from the minimal Yukawa unification scenario. Heavier gluino, degenerate charginos and neutralinos.

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Degenerate Chargino-Neutralino

NUHM “Just-so” D-term m ˜

χ0

1

231.98 219.11 m ˜

χ+

1

232.05 219.11 ∆M ≡ M ˜

χ+ − M ˜ χ0

519 MeV 434 MeV Signatures: ˜ χ± → ˜ χ0π± Disappearing charged tracks, kinks, large impact parameter. Associated photon and Z production

Work in progress with Linda Carpenter & Stuart Raby Linda’s talk at SUSY

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Topologies

Chargino Decay length (cm) Pion pT (GeV)

1 GeV 10 cm LARGE IMPACT PARAMETER KINKS DISAPPEARING CHARGED TRACKS

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Decay Rates

Branching Ratios for the ”Just-so” Higgs splitting scenario BR(˜ g → b¯ t ˜ χ+

1 )

= 14% BR(˜ g → t¯ b˜ χ−

1 )

= 14% BR(˜ g → t¯ t ˜ χ0

2)

= 8% BR(˜ g → g ˜ χ0) = 63% Branching Ratios for the D-term splitting scenario BR(˜ g → b¯ t ˜ χ+

1 )

= 38% BR(˜ g → t¯ b˜ χ−

1 )

= 38% BR(˜ g → t¯ t ˜ χ0

1)

= 14% BR(˜ g → b¯ b˜ χ0

1)

= 4%

Work in progress with Charles Bryant & Stuart Raby

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Summary

Yunified SUSY GUTS - tan β ≈ 50, CP odd Higgs mass, mA ≫ MZ. Light Higgs is predicted to be Standard Model-like. In the minimal Yukawa-unified scenario: I, II family of scalars are of the order m16 > 10TeV , third family scalars are naturally much lighter. Upper bound on the gluino mass, in order to fit the Higgs mass. Cannot be described by a simple ’simplified model’. In the effective mirage mediation scenario: Very different ‘lighter’ spectrum. Degenerate charginos and neutralinos. Wino-like LSP. Interesting signatures at the LHC. Well tempered neutralinos can be accomodated.

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SLIDE 43

Thank you!

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EXTRA SLIDES

44

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Benchmark Point

GUT scale parameters m16 20 M1/2 0.25 A0

  • 41

EW parameters µ .8 tanβ 50 Spectrum m˜

t1

3.695 m˜

b1

4.579 m ˜

τ1

7.834 m ˜

χ0 1

0.172 m ˜

χ+ 1

0.342 M˜

g

1.061 m˜

u,˜ d,˜ e

20 m˜

c,˜ s, ˜ µ

20 MA 2.2 Gluino Branching Fractions g χ0

4

38% g χ0

3

35% tb χ±

1

14% g χ0

2

8% t¯ t χ0

1

1.2% b¯ b χ0

1

0.006%

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Dark Matter

Universal Yunified models - bino LSP Effective Mirage scenario - wino LSP Well Tempered neutralinos in Yukawa unified models:

300 350 400 450 500 550 600 650 700

µ, in GeV

250 300 350 400 450 500 550 600

M1/2, in GeV

0.080 0.200 900.000 1 . 1 1 . 1200.000

Best fit points and Relic abundance

Work in progress with Kuver Sinha

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