Y-Unified GUTS: MSSM at large tanβ Archana Anandakrishnan The Ohio State University
January 15, 2014
Based on arXiv:1212.0542 & arXiv:1303.5125 & arXiv:1307.7723 & arXiv:1310.7579 & work in progress
(Phys. Rev. D 87, 055005 (2013)) (Phys.Rev.Lett. 111 (2013) 211801) (Phys.Rev. D88 (2013) 075002)
with Stuart Raby, B. Charles Bryant, Linda Carpenter (OSU), Kuver Sinha (Syracuse), Akın Wingerter(LPSC) Michigan Center for Theoretical Physics 1
Outline
Introduction to SO(10) SUSY GUTS Constraints from Yukawa Unification χ2 Analysis Spectrum and Collider Phenomenology Dark Matter Summary
2
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. 3
SO(10) GUTS and Yukawa Unification SO(10) → 16 →
×
SU(3)C
×
SU(2)L
U(1)Y
×
U(1)(B−L)
(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. 4
Yunification and Boundary Conditions
One can use Yukawa Unification to constrain the GUT scale boundary conditions. Yukawa Unification & Soft SUSY breaking
5
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
6
Recent papers on Yukawa unification (created using wordle) 7
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
8
Higgs vev
Ratio of the Higgs vev is defined as tanβ =
vu hHu i = vd hHd i
Fermion masses are generated by coupling to the Higgs boson ¯ + λτ vd τ¯τ L ⊃ λt vu ¯t t + λb vd bb The value of tanβ is restricted by the requirement of Yukawa unification. tanβ ' 50
9
Yunification and Boundary Conditions
One can use Yukawa Unification to constrain the GUT scale boundary conditions. Yukawa Unification & Soft SUSY breaking tanβ ' 50
10
Bottom quark mass In the large tanβ regime, there are large corrections to the bottom quark mass. δmb /mb '
g32 µMg˜ tanβ λ2t µAt tanβ + 12π 2 32π 2 m˜t2 mb˜2 Hall et. al; Carena et. al; Blazek et. al
In order to fit data, δmb /mb ' −(few )% µMg˜ > 0; ⇒ µAt < 0 Trilinear Coupling A0 < 0
11
Electroweak Symmetry Breaking The RGEs for the up and down-type Higgs mass squared can be written as: 2 dmHd
dt 2 dmHu
dt
= =
3 − g12 M12 − 3g22 M22 − 5 2 3 − g12 M12 − 3g22 M22 + 16π 2 5 2 16π 2
3 2 g S + 3λ2b Xb + λ2τ Xτ 10 1
3 2 g S + 3λ2t Xt + λ2ντ Xντ 10 1
RGE evolution in standard MSSM scenarios SPS1a
600 mQl
(µ2+mHd2)1/2
GeV
400
M3 M2
200
M1 mEr
0 (µ2+mHu2)1/2 -200 2
4
6
SOFTSUSY3.0.5
8 10 12 log10(µ/GeV)
14
16
Fig from SOFTSUSY 12
Electroweak Symmetry Breaking
The RGEs for the up and down-type Higgs mass squared can be written as: 2 dmHd
dt 2 dmHu
dt
= =
3 − g12 M12 − 3g22 M22 − 5 2 3 − g12 M12 − 3g22 M22 + 16π 2 5 2 16π 2
3 2 g S + 3λ2b Xb + λ2τ Xτ 10 1
3 2 g S + 3λ2t Xt + λ2ντ Xντ 10 1
In Yunified models, since, λt = λb = λτ = λν = λ, in order for REWSB, one needs 2 2 mHu < mHd Non-universal Higgs masses!
13
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
14
Bs → Xs γ Exp BR(Bs → Xs γ)Exp = (3.43 ± 0.30) × 10−4 SM NNLO BR(Bs → Xs γ)SM = (3.15 ± 0.23) × 10−4
In MSSM, +
C7χ˜ ∝
µAt tanβ × sign(C7SM ) m ˜2
Data constrains C7eff = C7SM + C7SUSY ' ±C7SM C7SUSY ' −2C7SM , implying light scalars.
C7SUSY ' 0, implying heavy scalars scalars. Which possibility does data accommodate?
15
B → K ∗ µ+ µ−
AFB
Forward-Backward Asymmetry in B → K ∗ µ+ µ− ! If C7eff = +C7SM , then AFB crosses zero at some momentum. If C7eff = −C7SM , then there is no zero-crossing in the AFB . 1
Theory LHCb
Binned theory
0.5
0
LHCb Preliminary
-0.5
-1 0
5
10
15
20
q2 [GeV2/c 4]
2012 Result from LHCb *More new results! Heavy Scalars 16
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 MA4
In MSSM models with large tanβ, MA ≥ 1500 GeV Standard Model like Higgs
17
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
18
The Higgs, at last..
CMS ; ATLAS Mh = 125.3 ± 1 GeV
19
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 20
Higgs and Bottom quark To fit bottom quark mass: δmb /mb '
g32 µMg˜ tanβ λ2t µAt tanβ + 12π 2 32π 2 m˜t2 mb˜2
χ2
Fitting the Higgs mass: 7
95% C.L.
6
5
90% C.L.
4
3
68% C.L. 2
1
0
2010
1436 0
500
1000
1500
2092
2000
2500
M (˜ g ) [GeV]
m16 = 20 TeV
21
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
22
Dermisek-Raby Model Analysis by AA, S.Raby, and A. Wingerter 1212.0542 Sector gauge SUSY (GUT scale) textures neutrino SUSY (EW scale) Total #
Third Family Analysis αG , MG , 3 m16 , M1/2 , A0 , mHu , mHd λ tan β, µ
# 3 5 1 0 2 11
Full three family Analysis αG , MG , 3 m16 , M1/2 , A0 , mHu , mHd , 0 , λ, ρ, σ, ˜, ξ MR1 , MR2 , MR3 tan β, µ
# 3 5 11 3 2 24
(Compared to 32 parameters in the CMSSM)
Wch.fermions = λ 163 10 163 + 16a 10 χa + χ ¯a (Mχ χa + 45
˜a φ φa 163 + 45 16a + A 16a ) ˆ ˆ M M
Effective operators to generate the first two family and off-diagonal Yukawa couplings. 10
~ Φ
45
10
a
MX
163
163
Φa
45
10
MX 16 b
χa
_
χa
χa
162
_
10
A
MX
16c
16b
23
162
χa
χa
_
χa
16c
GUT (24 parameters) 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
RGEs for MSSM w/right-handed neutrinos
RHN Right-handed neutrinos integrated out
RGEs for MSSM
m16 1st and 2nd generation scalars are integrated out
MSUSY SUSY spectrum & flavor observables calculated (susy flavor) RGEs for MSSM w/o 1st and 2nd generation scalars
Mtop Calculate top pole mass
RGEs for MSSM w/o 1st and 2nd generation scalars
RGEs for SM
Corrections
MEW SM spectrum & flavor observables calculated (SuperIso) & tan β, µ, mh , mH , mA , mH ±
Compare
Compare RGEs: 3-loop QCD & 1-loop EW
Gauge & EW sector: MZ , MW , αem , Gµ , α3 , Mh
2 GeV Calculate light masses mu , md , ms
Experiment (36 Observables)
quark
Compare
Quark sector: Mt , mb , mc , ms , md /ms , 1/Q2 , |Vus |, |Vcb |, |Vub |, |Vtd |, |Vts |, sin2β
Lepton sector: Mτ , Mµ , Me , θ12 , θ23 , θ13 , m221 , m231
Flavor observables: ǫK , ∆MBs /∆MBd , ∆MBd , B → Xs γ, Bs → µ+ µ− , Bd → µ+ µ− , B → τ ν, B → K ∗ µ+ µ− (3x)
24
SUSY Spectrum Benchmark Points m16 A0 µ M1/2 χ2 MA m˜t1 mb˜ 1 mτ˜1 mχ˜ 0 1 mχ˜ + 1 Mg˜
10 TeV -20.2 TeV 791 201 49.65 2333 1681 2046 3851 133 260 853
15 TeV -30.6 TeV 513 201 31.02 3662 2529 2972 5576 134 263 850
20 TeV -41.1 TeV 1163 168 26.58 1651 3975 5194 7994 137 279 851
25 TeV -51.3 TeV 1348 158 27.93 2029 4892 6353 9769 149 309 910
SUSY spectrum is predominantly determined by fitting: Third family masses light Higgs mass BR(Bs → Xs γ) and BR(Bs → µ+ µ− ) 25
30 TeV -61.6 TeV 1647 162 29.48 2036 5914 7660 11620 167 351 1004
χ2
SUSY Spectrum 7
95% C.L.
6
5
90% C.L.
4
3
68% C.L. 2
1
0
2010
1436 0
500
1000
1500
2092
2000
2500
M (˜ g ) [GeV]
SUSY spectrum is predominantly determined by fitting: Third family masses light Higgs mass BR(Bs → Xs γ) and BR(Bs → µ+ µ− ) 26
m16 = 20 TeV
Topologies T1bbbb
T1tttt
800 -1
600
10
400 10-2
200
0 400
-3
600
800
1000
1200
1400
0 pp → ~ g~ g, ~ g→ tt∼ χ NLO+NLL exclusion 1
700 600
Observed ± 1 σtheory Expected ± 1 σexperiment
1
500 10-1
400 300 10-2
200 100 0 400
10
m~g (GeV)
-3
600
800
1000
1200
1400
95% CL upper limit on cross section (pb)
1
800
1
Observed ± 1 σtheory Expected ± 1 σexperiment
95% CL upper limit on cross section (pb)
1
1000
m∼χ0 (GeV)
CMS , L = 19.4 fb-1, s = 8 TeV
0 pp → ~ g~ g, ~ g → b b∼ χ NLO+NLL exclusion
1
mχ∼0 (GeV)
CMS , L = 19.4 fb-1, s = 8 TeV
1200
10
m~g (GeV)
BR(˜ g → b b¯χ ˜01 ) = 100%
BR(˜ g → t ¯t χ ˜01 ) = 100% Results from CMS wiki 27
Not so simplified model AA, Bryant, Raby, and Wingerter: arXiv:1307.7723, arXiv:1308.2232 Benchmark point with m16 = 20 TeV , Mg˜ = 1.06 TeV BR(˜ g → b¯t χ ˜+ 1) − ¯ BR(˜ g → t bχ ˜ ) 1
BR(˜ g → t ¯t χ ˜02 ) BR(˜ g → gχ ˜01 )
=
27%
=
27%
=
22%
=
15%
Compare with data from LHC Analysis SS di-lepton
Luminosity 10.5
αT analysis (for Simplified models) (for the benchmark models)
11.7
∆φ analysis
19.4
Signal Region Njet ≥ 4, Nb−jet ≥ 2, miss ET > 120, HT > 200 Njet ≥ 4, Nb−jet = 3, HT > 875 Njet ≥ 4, Nb−jet = 2, 775 < HT < 875 miss > 350, H > 1000 Nb−jet ≥ 3, ET T
28
Reference CMS-SUS-12-017
CMS-SUS-12-028 CMS-SUS-12-024
Yunified vs Simplified From Hadronic ∆φˆ analysis: Benchmark Model
∆φ analysis: L = 19.4 fb−1 , M (χ˜01 ) = 200 GeV, B(˜ g → χ˜01 tt¯) = 100%
Number of events passing all cuts
Number of events passing all cuts
T1tttt 40
35
30
25
20
15
10
35
30
25
20
15
10
NUL = 8.0
5
0
∆φ analysis: L = 19.4 fb−1 , Benchmark models
40
NUL = 8.0
5
600
800
1000
1200
0
1400
M (˜ g ) [GeV]
380
526
666
801
932
0 6 9 0 0 5 9 0 0 2 106 118 130 143 155 166 177 189 201 210
M (˜ g ) [GeV]
Mg˜ ≥ 1100GeV
Mg˜ ≥ 1000GeV
MATON → SDECAY → PYTHIA → DELPHES
29
Neutrino sector Observables in the neutrino sector: sin2 θ12
=
2
sin θ23
=
sin2 θ13
=
2 ∆m21 2 ∆m31
= =
0.27 − 0.34 0.34 − 0.67
0.016 − 0.030
(7.00 − 8.09) × 10−5 eV2
(2.27 − 2.69) × 10−3 eV2
(3σ range) from Nu-fit Collaboration exp θ13 DR−model θ13
=
9◦ (7.29 − 9.96)
. 6◦
DayaBay; Reno
30
Predictions Rare Processes e EDM ×1028 µ EDM ×1028 τ EDM ×1028 BR(µ → eγ) × 1012 BR(τ → eγ) × 1012 BR(τ → µγ) × 108
Current Limit < 10.5 e cm (−0.1 ± 0.9) × 109 e cm −0.220 − 0.45 × 1012 e cm < 2.4 < 3.3 × 104 < 4.4
sin δ
10 TeV −0.224 34.6 −2.09 5.09 58.8 1.75 -0.60
20 TeV −0.0173 3.04 −0.185 0.211 2.40 0.0837 -0.27
30 TeV −0.0084 1.20 −0.0732 0.0447 0.502 0.0182 -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).
31
Dark Matter AA, Kuver Sinha arXiv:1310.7579
Bino-Higgsino Dark matter in tension with other observables. 600
Best fit region and Relic abundance with α = 0 2000.000
0.0 8
0
550
00
1700.000
0. 2
M1/2, in GeV
500
450
400 1500.000
350
300 1200.000
250 300
350
400
450
500
µ, in GeV
32
550
600
650
700
Effective “Mirage” Mediation
arXiv:1303.5125 AA and Stuart Raby
Non-universal gaugino masses with mirage pattern. gG2 bi α MPl Mi = 1 + M1/2 log 16π 2 m16 Choi,Nilles
where M1/2 and α are free parameters and bi = (33/5, 1, −3) For small α, there are small non-universalities to the gaugino masses. The gaugino spectrum is compressed.
33
Neutralino Dark Matter α = 1.5
α = 2.0
Best fit region and Relic abundance with α = 1.5
600
600
550
550 1000.000
1200.000
500
M1/2, in GeV
500
M1/2, in GeV
Best fit region and Relic abundance with α = 2.0
450 1100.000
400 1000.000
350
80
0.0
450 900.000
400
350
800.000
00 0.2
80
0.0
900.000
300
250 300
350
400
450
500
µ, in GeV
550
600
650
250 300
700
350
400
LSP is an admixture of Bino-Wino-Higgsino. Gluino is within reach of 14 TeV LHC.
34
00
0.2
300
450
500
µ, in GeV
550
600
650
700
Effective “Mirage” Mediation
arXiv:1303.5125 AA and Stuart Raby
Non-universal gaugino masses with mirage pattern. g 2 bi α MPl Mi = 1 + G 2 log M1/2 16π m16
Choi,Nilles
where M1/2 and α are free parameters and bi = (33/5, 1, −3)
For large α, 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 → Xs γ) and (iii) anomalous magnetic moment of muon*.
Badziak, Olechowski, Pokorski
* Now, ruled out after the Higgs result.
35
Scalar Masses Two different cases for non-universal Higgs masses [NUHM] with “just so” Higgs splitting 2 2 mH = m10 − (+)2D u(d)
or, D-term Higgs splitting, in addition, squark and slepton masses are given by 2 ¯ ma2 = m16 + Qa D, {Qa = +1, {Q, u¯, e¯}; −3, {L, d}}
with the U(1) D-term, D, and SU(5) invariant charges, Qa . Sector gauge SUSY (GUT scale) textures SUSY (EW scale) Total #
Third Family Analysis αG , MG , 3 m16 , M1/2 , α, A0 , m10 , D λ tan β, µ 12
36
SUSY Spectrum NUHM m16 A0 µ M1/2 α MA m˜t1 mb˜1 mτ˜1 mχ˜ 0 1 mχ˜ + 1 ∆M ≡ Mχ˜ + − Mχ˜ 0 Mg˜
“Just-so” 5.00 TeV 8.07 TeV -615 GeV -105 GeV 11.59 1558 1975 2049 2473 231.98 232.05 519 MeV 882
D-term 5.00 TeV 5.59 TeV -1.29 TeV -100 GeV 11.99 1236 2920 2158 3601 219.11 219.11 434 MeV 874
Very different spectrum from the minimal Yukawa unification scenario. Heavier gluino, degenerate charginos and neutralinos. 37
Topologies
Pion pT (GeV)
LARGE IMPACT PARAMETER
KINKS
DISAPPEARING CHARGED TRACKS 1 GeV
10 cm
Chargino Decay length (cm)
38
Degenerate Chargino-Neutralino NUHM mχ˜01 mχ˜+1 ∆M ≡ Mχ˜+ − Mχ˜0
“Just-so” 231.98 232.05 519 MeV
D-term 219.11 219.11 434 MeV
Signatures: χ ˜± → χ ˜0 π ± Disappearing charged tracks, kinks, large impact parameter. Associated photon and Z production Work in progress with Linda Carpenter & Stuart Raby
39
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 accommodated.
40
Thank you!
41
EXTRA SLIDES
42
Benchmark Point
GUT scale parameters EW parameters Spectrum
m16 µ m˜t1 mχ˜ 0
20 .8 3.695 0.172
1
Gluino Branching Fractions
mu˜,d,˜ ˜ e gχ e04 0 gχ e2
20 38% 8%
43
M1/2 tanβ mb˜ 1 mχ˜ +
0.25 50 4.579 0.342
A0
mc˜,˜s ,µ˜ gχ e03 t ¯t χ e01
20 35% 1.2%
MA tb χ e± 1 ¯χ bb e01
1
mτ˜1 Mg˜
-41 7.834 1.061 2.2 14% 0.006%
SUSY Spectrum 12
11
10 0 .00 00 30 0 0 .0 00
α
9
8 .0
0 50
7 10
6
00
00
00
20
5 00 2
.0
1
.0
00
5
4
0
−200
−400
−600
M1/2, in GeV
−800
−1000
Very different spectrum from the minimal Yukawa unification scenario. Heavier gluino, degenerate charginos and neutralinos. 44
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 χ ˜02 ) = 8% BR(˜ g → gχ ˜0 )
=
63%
Branching Ratios for the D-term splitting scenario BR(˜ g → b¯t χ ˜+ 1 ) = 38% − ¯ BR(˜ g → t bχ ˜1 ) = 38% BR(˜ g → t ¯t χ ˜01 ) = 14% BR(˜ g → b b¯χ ˜01 ) = 4% Work in progress with Charles Bryant & Stuart Raby
45
