General Gauge Mediation @ the EW scale
Diego Redigolo
GGI, Florence September 4th
based on 1507.04364 & to appear work with
- S. Knapen and D.Shih
General Gauge Mediation @ the EW scale Diego Redigolo GGI, - - PowerPoint PPT Presentation
General Gauge Mediation @ the EW scale Diego Redigolo GGI, Florence September 4th based on 1507.04364 & to appear work with S. Knapen and D.Shih 2+1 problems for BSM physics -1 -1 s = 7 T eV , L = 5.1 fb s = 8 T eV , L =
(GeV)
m
80 100 120 140 160 180
Events / 3 GeV
2 4 6 8 10 12 14 16
Data Z+X *, ZZ γ Z =125 GeV
H
m
CM S
= 8 T eV , L = 5.3 fb s
= 7 T eV , L = 5.1 fb s
(GeV)
m
120 140 160
Events / 3 GeV
1 2 3 4 5 6 > 0.5
DK
Mass scales [GeV] 200 400 600 800 1000 1200 1400 1600 1800
233 ' λ µ tbt → R t ~ 233 λ t ν τ µ → R t ~ 123 λ t ν τ µ → R t ~ 122 λ t ν e µ → R t ~ 112 '' λ qqqq → R q ~ 233 ' λ µ qbt → q ~ 231 ' λ µ qbt → q ~ 233 λ ν qll → q ~ 123 λ ν qll → q ~ 122 λ ν qll → q ~ 112 '' λ qqqq → g ~ 323 '' λ tbs → g ~ 112 '' λ qqq → g ~ 113/223 '' λ qqb → g ~ 233 ' λ µ qbt → g ~ 231 ' λ µ qbt → g ~ 233 λ ν qll → g ~ 123 λ ν qll → g ~ 122 λ ν qll → g ~ χ ∼ l → l ~ χ ∼ χ ∼ ν τ τ τ → ± χ ∼ 2 χ ∼ χ ∼ χ ∼ ν τ ll → ± χ ∼ 2 χ ∼ χ ∼ χ ∼ H W → 2 χ ∼ ± χ ∼ χ ∼ χ ∼ H Z → 2 χ ∼ 2 χ ∼ χ ∼ χ ∼ W Z → 2 χ ∼ ± χ ∼ χ ∼ χ ∼ Z Z → 2 χ ∼ 2 χ ∼ χ ∼ χ ∼ ν νSummary of CMS SUSY Results* in SMS framework
CMS Preliminary
m(mother)-m(LSP)=200 GeV m(LSP)=0 GeVICHEP 2014
lsp m ⋅ +(1-x) mother m ⋅ = x intermediate m For decays with intermediate mass, Only a selection of available mass limits *Observed limits, theory uncertainties not included Probe *up to* the quoted mass limitLHC bound
LHC bound
N = 1 vector multiplet
(g1, g2, g3) of GSM
msoft ' g2
i
(4π)2 F M
C0
C1/2
C1
Q , m2 U , m2 L}
B1/2
m2
Hu = m2 Hd = m2 L
m2
E = 3
2
U − m2 Q + m2 L
CAVEAT: extensions of the pure GGM will destroy the sum-rules and in some cases even flavor universality: Ex: D-tadpoles, MSSM-messenger-messenger, MSSM-MSSM-messenger couplings…
(Meade, Seiberg, Shih 2008)
CALCULABLE parameter space: i.e. realizable in terms of weakly coupled models (Buican, Meade, Seiberg, Shih 2008)
(Draper, Meade, Reece, Shih 2011)
−Lsoft ⊃ m2
Q3| ˜
Q3|2 + m2
U3| ˜
U3|2 + (AtHu ˜ Q3 ˜ U3 + c.c.) is radiatively sensitive to 3 soft parameters
h
mQ3 ≈ mU3 to keep it simple
2 4 500 1000 1500 2000 2500 3000
êmé eVD
Tuning
pect iggs
D
100 300 500 750 1000 1500 2000 2500
2 4 500 1000 1500 2000 2500 3000
Xtêmt
é
mt
é @GeVD
Lightest Stop Mass
Suspect FeynHiggs
mt1
é
MS
At MS
(Hall, Pinner, Ruderman, 2011)
extensions of the pure GGM can generate large UV A-terms but destroy sum-rules/flavor universality
stops tachyonic to get them light in the IR
16π2 d dtm2
Q = −32
3 g2
3|M3|2 + · · ·
16π2 d dtAt = yt 32 3 g2
3M3 + · · ·
large A-terms from heavy gluino
16π2 d dtm2
Hu = 2|yt|2(m2 Q3 + m2 U3) + 2|At|2 + · · ·
tension with EWSB: tachyonic stops pull mHu up
4 6 8 10 12
2 4 Log10 QêGeV signed value HTeVL
At mQ mu M3 mHu mL3
L slepton tachyon in the IR
m2
Hu = m2 Hd = m2 L GGM sum-rule
m2
E = 3
2
U − m2 Q + m2 L
in the IR
4 6 8 10 12
2 4 6 Log10 QêGeV signed value HTeVL
At mQ mu M3 mHu mL3 mE3
4 6 8 10 12
2 4 6 Log10 QêGeV signed value HTeVL
At mQ mu M3 mHu mL3
µ At . . . M3 . . .
Bµ m2
Hu
m2
Hd
m2
Q3
. . .
(common in high-scale scenarios)
Q3, m2 U3, m2 L3, µ and Mmess
1
“high”, “medium”, “low”
m2
Z = −2(m2 Hu + |µ|2) + · · ·
sin 2β = 2Bµ 2|µ|2 + m2
Hu + m2 Hd
+ · · ·
(tan β = 20)
(accounting conservatively for theory error Allanach & co. 2004)
(TM to trade UV & IR) (EWSB conditions + Higgs mass computed by SoftSUSY)
mU3 > 1.5 TeV
mU3 > 2 TeV
mU3 > 2.5 TeV
the M2
|At| M3 1 2 3 4
1 2 3 4 5 M2 (TeV) TeV
interval is divided in two disconnected segments with different
signµ
The gray dots are physical stop masses (including 1-loop thresholds)
Q3 + m2 U3
1 2 3 4 5 1 2 3 4 5 mQ3 HTeVL mU3 HTeVL
1.2 1 0.8 0.6 0.4
L3 + µ2 ≈ m2
0 ≡ b (m2 Q3 + m2 U3) − c A2 t
p b/c
Mmess
LHS RHS E tachyons
L tachyons
Q tachyons
1 2 3 4 5 1 2 3 4 5 mQ3 (TeV) mU3 (TeV)
E3 , m2 L3 , m2 Q3 ARE THE ONLY RELEVANT TACHYONS
ONLY 3rd generations matter
m2
Q1,2
≈ m2
Q3 + 1
3(m2
L3 − m2 Hu)
m2
U1,2
≈ m2
U3 + 2
3(m2
L3 − m2 Hu)
m2
L1,2
≈ m2
L3
m2
D1,2,3 ≈ 1
2(m2
Q3 + m2 U3) − 1
2m2
Hu
m2
E1,2,3 ≈ 2m2 L3 − 1
2m2
Hu + 3
2(m2
U3 − m2 Q3)
m2
E3 <
✓3 2 + 2b a ◆ m2
U3 −
✓3 2 − 2b a ◆ m2
Q3 − 2c
a A2
t .
A = m2 L3 + µ2
1 2 3 4 5 1 2 3 4 5 mQ3 HTeVL mU3 HTeVL
1.2 1 0.8 0.6 0.4
mess
15
D quarks don’t matter CP-odd Higgs doesn’t matter
(L) (E) (Q) LHS RHS E tachyons
L tachyons
Q tachyons
1 2 3 4 5 1 2 3 4 5 mQ3 (TeV) mU3 (TeV)
1 2 3 4 1 2 3 4 (Q) mt
MMess=1011 GeV mQ3 (TeV)
1-loop thresholds from heavy gluino
(BPMZ 1997)
<0 >0 1.5 2.0 2.5 3.0 3.5 0.2 0.3 0.4 0.5 0.6 0.7 (E) Rt Mmess=1015 GeV mU3 (TeV)
(it is true also for the upper end)
t
t
1 2.5 5 10
1 2 3 4 5 1 2 3 4 5 mQ3 HTeVL mU3 HTeVL
Mmess=1011 GeV m<0
1 2.5 5 10
1 2 3 4 5 1 2 3 4 5 mQ3 HTeVL mU3 HTeVL
Mmess=1015 GeV m<0
L3 + µ2
µ(M2 = 0) = m2
0 − e(d + f)2A2 t
agf(−At) tan β + . . . m2
E3(M2 = 0) = 2
m2
0 − e(d + f)2A2 t − 3 4a(m2 Q3 − m2 U3)
a + . . .
1 2 3 4 5 1 2 3 4 5 mQ3 HTeVL mU3 HTeVL
Mmess=107 GeV m>0
1 2 3 4 5 1 2 3 4 5 mQ3 HTeVL mU3 HTeVL
Mmess=1011 GeV m>0
1 2 3 4 5 1 2 3 4 5 mQ3 HTeVL mU3 HTeVL
Mmess=1015 GeV m>0
m2
E3(M2 = 0) → 0
µ ( M
2
= ) → µ(M2 = 0) → 0
µ(M2 = 0) → 0
m2
E3(M2 = 0) → 0
m
2 E
3(M
2
= 0) → 0
Q3 , m2 L3 , m2 E3
m˜
tL < m ˜ Q3
m˜
tL < m ˜ Q3
(Riotto & Roulet 1995)
(Giudice & Rattazzi review 1998)
(Espinosa & Navarro 2001)
(extensive class of models…)
ÊÊÊÊÊÊÊÊÊÊÊÊÊÊÊÊÊÊÊÊÊÊÊÊÊÊÊ Ê Ê Ê Ê Ê Ê Ê Ê
1 2 3
1 2 3 m HTeVL M2 HTeVL
mh
123.5 124 124.5 125 125.5
2 4 6
Ê Ê Ê ÊÊ Ê Ê Ê Ê Ê Ê Ê Ê ÊÊÊÊÊÊÊÊÊÊÊÊÊ Ê ÊÊÊÊÊÊÊÊÊÊÊÊÊÊÊÊÊÊÊÊÊÊÊÊÊÊÊÊÊ
¯
1 2 3 4 2.0 2.2 2.4 2.6 2.8 M2 HTeVL
Mmess=1011 GeV mQ3= 1.5 TeV mU3= 3 TeV
(already noticed of course see for example Vega & Villadoro 2015)
Mmess M1 mQ3, mU3, M2 At mL3, µ 107, 1011, 1015 GeV 1 TeV fine scan mh = 123 GeV EWSB conditions
1700 1800 1900 2000 2100
500 1000 1500 M3@UVD HGeVL signed mL@UVD HGeVL mQ=1000, mU=3000, smu=1, M2=1300
snutau tachyon mHu
2>0
50 100 150 200 1 10 100 1000 104 105 mU3 (GeV)
100 200 10 100 1000 104 105 mQ3 (GeV)
100 200 300 400 1 10 100 1000 104 105 B (Mmess) (GeV) 122.8 122.9 123.0 123.1 123.2 123.3 1 10 100 1000 104 105 mh (GeV)
IR thresholds to gauge & yukawa couplings iterative determination