General Gauge Mediation @ the EW scale Diego Redigolo GGI, - - PowerPoint PPT Presentation

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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 =


slide-1
SLIDE 1

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
slide-2
SLIDE 2

2+1 problems for BSM physics

Why is the Higgs @ 125 GeV? Is the EW scale natural at all?

(GeV)

  • 4

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

  • 1

= 8 T eV , L = 5.3 fb s

  • 1

= 7 T eV , L = 5.1 fb s

(GeV)

  • 4

m

120 140 160

Events / 3 GeV

1 2 3 4 5 6 > 0.5

D

K

Where is everybody? SM & nothing else or BSM around the corner?

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 ν
  • l
+ l →
  • χ
+ χ ∼ χ ∼ χ ∼ ν lll → ± χ ∼ 2 χ ∼ χ ∼ bZ → b ~ χ ∼ tW → b ~ χ ∼ b → b ~ ) H 1 χ ∼ t → 1 t ~ ( → 2 t ~ ) Z 1 χ ∼ t → 1 t ~ ( → 2 t ~ H G) → χ ∼ ( χ ∼ t b → t ~ ) χ ∼ W → + χ ∼ b( → t ~ χ ∼ t → t ~ χ ∼ q → q ~ )) χ ∼ W → ± χ ∼ t( → b ~ b( → g ~ ) χ ∼ W → ± χ ∼ qq( → g ~ ) χ ∼ t → t ~ t( → g ~ χ ∼ tt → g ~ χ ∼ bb → g ~ χ ∼ qq → g ~ SUS-13-006 L=19.5 /fb SUS-13-008 SUS-13-013 L=19.5 /fb SUS-13-011 L=19.5 /fb x = 0.25 x = 0.50 x = 0.75 SUS-14-002 L=19.5 /fb SUS-13-006 L=19.5 /fb x = 0.05 x = 0.50 x = 0.95 SUS-13-006 L=19.5 /fb SUS-12-027 L=9.2 /fb SUS-13-007 SUS-13-013 L=19.4 19.5 /fb SUS-12-027 L=9.2 /fb SUS 13-019 L=19.5 /fb SUS-14-002 L=19.5 /fb SUS-12-027 L=9.2 /fb SUS-13-003 L=19.5 9.2 /fb SUS-13-006 L=19.5 /fb SUS-12-027 L=9.2 /fb EXO-12-049 L=19.5 /fb SUS-14-011 L=19.5 /fb SUS-12-027 L=9.2 /fb SUS-13-008 L=19.5 /fb SUS-12-027 L=9.2 /fb EXO-12-049 L=19.5 /fb SUS-12-027 L=9.2 /fb SUS-12-027 L=9.2 /fb SUS-13-024 SUS-13-004 L=19.5 /fb SUS-13-003 L=19.5 /fb SUS-12-027 L=9.2 /fb SUS-13-019 L=19.5 /fb SUS-13-018 L=19.4 /fb SUS-13-014 L=19.5 /fb SUS-14-011 SUS-13-019 L=19.3 19.5 /fb SUS-13-008 SUS-13-013 L=19.5 /fb SUS-13-024 SUS-13-004 L=19.5 /fb SUS-13-013 L=19.5 /fb x = 0.20 x = 0.50 SUS-12-027 L=9.2 /fb SUS-13-003 L=19.5 9.2 /fb SUS-12-027 L=9.2 /fb SUS-13-008 SUS-13-013 L=19.5 /fb SUS-12-027 L=9.2 /fb SUS-14-002 L=19.5 /fb SUS-12-027 L=9.2 /fb SUS-13-013 L=19.5 /fb SUS-13-006 L=19.5 /fb x = 0.05 x = 0.50 x = 0.95 SUS-13-006 L=19.5 /fb RPV gluino production squark stop sbottom EWK gauginos slepton

Summary of CMS SUSY Results* in SMS framework

CMS Preliminary

m(mother)-m(LSP)=200 GeV m(LSP)=0 GeV

ICHEP 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 limit

BSM physics vs strong bounds from flavor

  • bservables
slide-3
SLIDE 3

minimal: consistent UV completions BUT issues with fine-tuning non-minimal: hard UV completions BUT better fine-tuning

has far reaching implications for SUSY mh = 125 GeV Run I hints at an heavier scale for SUSY states

minimal: no light states at Run I are expected once the Higgs mass is imposed non-minimal: LHC bounds are dominating the tuning minimal non-minimal:

LHC bound

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SLIDE 4

Maybe in minimal SUSY the Higgs mass is already telling us that SUSY was not expected at Run I?

LHC bound

What about Run II? Have we learn everything we can from Run I? We will try to answer these questions for ALL the possible gauge mediation models with the MSSM @ low energy

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SLIDE 5

In the MSSM, SUSY-breaking terms are problematic for flavor Gauge mediation automatically gives flavor bind SUSY-breaking

Hidden Sector

N = 1 vector multiplet

(g1, g2, g3) of GSM

M, √ F

Visible Sector

msoft ' g2

i

(4π)2 F M

SM gauge interactions are flavor blind!

Why gauge mediation?

It also provides a COMPLETE theory of SUSY breaking It is consistent up to the Planck scale It accommodates unification of gauge couplings

slide-6
SLIDE 6

C0

C1/2

C1

sfermion masses:

{m2

Q , m2 U , m2 L}

+

B1/2

{M1 , M2 , M3}

gaugino masses:

+

“by-hand”

µ + Mmess Bµ ≈ 0 A-terms ≈ 0

All the other (non-zero) soft masses are fixed by UV sum-rules/flavor universality

m2

Hu = m2 Hd = m2 L

m2

E = 3

2

  • m2

U − m2 Q + m2 L

  • ex:

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…

General Gauge Mediation (GGM) gives a model independent definition of “pure” gauge mediation

(Meade, Seiberg, Shih 2008)

8 PARAMETERS

CALCULABLE parameter space: i.e. realizable in terms of weakly coupled models (Buican, Meade, Seiberg, Shih 2008)

slide-7
SLIDE 7

(Draper, Meade, Reece, Shih 2011)

zero A-terms

Heavy stops: High-scale SUSY, Split-SUSY

The low energy theory for GGM is the MSSM:

mtree

h

≤ mZ

How do we get mh = 125 GeV?

−Lsoft ⊃ m2

Q3| ˜

Q3|2 + m2

U3| ˜

U3|2 + (AtHu ˜ Q3 ˜ U3 + c.c.) is radiatively sensitive to 3 soft parameters

m2

h

mQ3 ≈ mU3 to keep it simple

multi-TeV A-terms

Maximal Mixing delivers light stops (possibly accessible at LHC)

  • 4
  • 2

2 4 500 1000 1500 2000 2500 3000

êmé eVD

Tuning

pect iggs

D

100 300 500 750 1000 1500 2000 2500

  • 4
  • 2

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)

slide-8
SLIDE 8

extensions of the pure GGM can generate large UV A-terms but destroy sum-rules/flavor universality

in (pure) GGM At = 0

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

  • 4
  • 2

2 4 Log10 QêGeV signed value HTeVL

At mQ mu M3 mHu mL3

An intuitive picture I: mQ ≈ mU

Can we generate large A-terms in pure GGM? What is the min stop mass after mh = 125 GeV is imposed?

L slepton tachyon in the IR

m2

Hu = m2 Hd = m2 L GGM sum-rule

slide-9
SLIDE 9

Splitting the stops soft masses GGM sum-rule

m2

E = 3

2

  • m2

U − m2 Q + m2 L

  • E slepton tachyon

in the IR

4 6 8 10 12

  • 4
  • 2

2 4 6 Log10 QêGeV signed value HTeVL

At mQ mu M3 mHu mL3 mE3

mU ⌧ mQ light right-handed stop

4 6 8 10 12

  • 4
  • 2

2 4 6 Log10 QêGeV signed value HTeVL

At mQ mu M3 mHu mL3

light left-handed stop mU mQ

slide-10
SLIDE 10

A systematic approach:

We expect boundaries @ low stop masses to be produced by the convergence of the tensions discussed

The main technical difficulty to get a complete picture is that

  • EWSB+Higgs constraints are imposed @ EW scale
  • GGM boundary conditions are defined @ Mmess

We completely characterize GGM with mh = 125 GeV We understand its features in a simple analytical approximation We can use these results to study the LHC coverage on GGM after Higgs Similar techniques can possibly be used in other frameworks

slide-11
SLIDE 11

We trade UV parameters for IR ones once and for all!

T T 0 T 00 depend on Mmess , MS , tan β ONLY

  • A =

        µ At . . . M3 . . .        

  • m2 =

       Bµ m2

Hu

m2

Hd

m2

Q3

. . .       

  • AIR = T

AUV

  • m2

IR =

AUV T 0 AUV + T 00 m2

UV

  • Transfer matrix (TM) method: RGE’s are bilinear in soft masses

(common in high-scale scenarios)

From GGM UV b.c. we get relations among IR quantities

Ex: At(Mmess) = 0

M3 ≈ p0At + q0M2

Key ingredient to handle the RG evolution

slide-12
SLIDE 12

parameter counting GGM in the IR : 8 parameters

M1, M2, At, m2

Q3, m2 U3, m2 L3, µ and Mmess

all the rest of the spectrum is fixed by IR relations @ the weak scale

3 parameters m2

Q3, m2 U3, M2

+ signµ

has little impact on the RGEs

  • 2 parameters

∼ g2

1

“high”, “medium”, “low”

M1 = 1 TeV

Mmess = 1015, 1011, 107 GeV

IR constraints: mh = 123 GeV

m2

Z = −2(m2 Hu + |µ|2) + · · ·

sin 2β = 2Bµ 2|µ|2 + m2

Hu + m2 Hd

+ · · ·

{

2 EWSB conditions

  • 3 parameters

(tan β = 20)

(accounting conservatively for theory error Allanach & co. 2004)

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SLIDE 13

A bird's-eye view of the results from the scan:

(TM to trade UV & IR) (EWSB conditions + Higgs mass computed by SoftSUSY)

µ < 0 µ > 0 µ < 0 µ > 0 µ < 0 µ > 0

mU3 > 1.5 TeV

mU3 > 2 TeV

mU3 > 2.5 TeV

the M2

  • mL3

|At| M3 1 2 3 4

  • 1

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)

(mQ3 mU3) fixed

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SLIDE 14

The plan of the TALK is to explain a number of features of these plots…

4) How the

mU3

lower bound on is produced? 1) How the Higgs mass constraint acts on the stop mass plane? 5) How the physics depend on the stop mass plane? 6) What is the role of

signµ ?

3) How boundaries of the M2-interval arise? 2) What is the role of ?

Mmess

slide-15
SLIDE 15

The role of the Higgs constraint

Approximations:

  • 1-loop RGEs
  • neglecting
  • tree-level EWSB
  • leading order in

yb, yτ, g1 effects

tan β → ∞

Rt ≡ |At| q m2

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

Rt rises One of the EWSB conditions in GGM

e (δM2 + d At)2 + a m2

L3 + µ2 ≈ m2

where m2

0 ≡ b (m2 Q3 + m2 U3) − c A2 t

m2

0 > 0

R2

t < b/c

implies

15 11 7 1.01 0.85 0.69

p b/c

Mmess

the bounds gets more strict for low Mmess

slide-16
SLIDE 16

no-tachyon constraints

Can we understand them in general?

LHS RHS E tachyons

L tachyons

Q tachyons

1 2 3 4 5 1 2 3 4 5 mQ3 (TeV) mU3 (TeV)

m2

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 .

m2

A = m2 L3 + µ2

Extra boundaries in GGM

1 2 3 4 5 1 2 3 4 5 mQ3 HTeVL mU3 HTeVL

1.2 1 0.8 0.6 0.4

M

mess

= 1

15

G e V

Rt < 1 . 1

D quarks don’t matter CP-odd Higgs doesn’t matter

slide-17
SLIDE 17

Each tachyon characterizes a boundary

the allowed range of Rt (in the M2-interval) shrinks to a point almost constant for

Rt

µ < 0

varies a lot for µ > 0

L-R COMMON FEATURES:

(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

  • 1(TeV)

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)

slide-18
SLIDE 18

the allowed range of Rt (in the M2-interval) shrinks to a point

L-R COMMON FEATURES:

is a monotonic function of

µ < 0

M2

The upper end of

M2-interval is bounded by µ → 0

The lower end of M2-interval is bounded by

mL3 → 0 mE3 → 0

(it is true also for the upper end)

The lower end can be understood analytically! (black line)

slide-19
SLIDE 19

We define: m2 ≡ m2

0 − 3

4a(m2

Q3 − m2 U3)θ(m2 Q3 − m2 U3)

In terms of this quantity we get from EWSB

mL3 → 0 mE3 → 0

µ = − r m2 − e d2A2

t

a0

µ = − q m2 − e d2A2

t

m2 = ed2At

describes the boundary quite well!

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

We can get a complete description of the GGM boundary analytically for µ < 0

slide-20
SLIDE 20

A new feature for µ < 0

almost constant for

Rt

µ < 0

varies a lot for µ > 0

M2 ≈ 0 has a large effect

Rt drops

min[mQ] has M2 ≈ 0 min[mQ] has µ ≈ 0

From EWSB:

−g δM2 µ tan β ≈ m2

L3 + µ2

δM2 ≡ M2 + f At

signµ signδM2 and are correlated! Only for µ > 0 M2 = 0 is allowed

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SLIDE 21

What happens for µ ≈ M2 ≈ 0 ?

There is a 1-loop threshold correction from Winos-Higgsinos enhancing the Higgs mass (see backup)

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 + . . .

(dashed) (solid)

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

mh = 123 GeV

This effect becomes crucial to get at low messenger scale (for Mmess = 107 GeV µ < 0 mQ3/U3 > 4 TeV)

Boundary well described by taking M2 ≈ 0

slide-22
SLIDE 22

tachyons determines the boundary

m2

Q3 , m2 L3 , m2 E3

Mmess

Absolute lower bound on mU3 (stronger for lower

)

˜ tL ,˜ bL arbitrarily light (driven lighter by large gluino thresholds)

µ > 0 threshold from light wino-higgsino (crucial for lower Mmess ) mQ3 ∼ mU3 ∼ |At|/ √ 6 ruled out SUMMARY

µ < 0 µ > 0 µ < 0 µ > 0 µ < 0 µ > 0

E L Q Q L E E L Q

tL < m ˜ Q3

tL < m ˜ Q3

slide-23
SLIDE 23

SKETCHES OF LHC Phenomenology

(a detailed study is work in progress…) We have a full dataset of allowed points with mh imposed

(mQ3 mU3) fixed the behavior of the M2 interval

tells which particle can be light

NLSP types & production channels in the stop mass plane Which are the most relevant simplified models to probe GGM at Run II?

slide-24
SLIDE 24

COLORED xsec: l.h squarks & stop/bottom from the L.H.S EW xsec: Higgsinos & Winos from the bottom

(µ > 0)

LEP

@ LOW SCALE: most of the parameter space can be probed with Wino-Higgsino simplified model!

An interesting example:

slide-25
SLIDE 25

What is next?

Are there extra constraints? Vacuum metastability (tachyons along the flow) previous studies show that these constraints are mild

(Riotto & Roulet 1995)

Gravitino overabundance Dangerous effects of NLSP decays on BBN need of a very low reheating temperature

(Giudice & Rattazzi review 1998)

Doing better with the Higgs mass computation

ex: EFT for mQ3 ⌧ mU3 < M3

(Espinosa & Navarro 2001)

Beyond pure GGM? No results presented can be extrapolated Similar techniques can be useful

(extensive class of models…)

slide-26
SLIDE 26

Thanks for your attention Break a leg for Run II

slide-27
SLIDE 27

BACKUP SLIDES I

ÊÊÊÊÊÊÊÊÊÊÊÊÊÊÊÊÊÊÊÊÊÊÊÊÊÊÊ Ê Ê Ê Ê Ê Ê Ê Ê

  • 3
  • 2
  • 1

1 2 3

  • 3
  • 2
  • 1

1 2 3 m HTeVL M2 HTeVL

mh

123.5 124 124.5 125 125.5

  • 6
  • 4
  • 2

2 4 6

Higgsino-Wino threshold corrections

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

  • At HTeVL

Mmess=1011 GeV mQ3= 1.5 TeV mU3= 3 TeV

we get a shift of around 2.5 GeV when

µ ≈ M2 ≈ 0

this corresponds to an almost 1 TeV shift in

At

Are there other “forgotten” thresholds like this one in the MSSM?

(already noticed of course see for example Vega & Villadoro 2015)

slide-28
SLIDE 28

BACKUP SLIDES II

More details on the scan

Mmess M1 mQ3, mU3, M2 At mL3, µ 107, 1011, 1015 GeV 1 TeV fine scan mh = 123 GeV EWSB conditions

Because of SoftSUSY there is a particular ordering we are forced to solve constraints

mHu , mHd µ , Bµ , mh

1700 1800 1900 2000 2100

  • 1500
  • 1000
  • 500

500 1000 1500 M3@UVD HGeVL signed mL@UVD HGeVL mQ=1000, mU=3000, smu=1, M2=1300

snutau tachyon mHu

2>0

SoftSUSY:

mQ3 , mU3 , M2

µ At , mL3

mh = 123 GeV

Bµ(Mmess) = 0

scan given

cannot do a flat scan! iterative method around a seed guess it is crucial to get a good initial guess!

slide-29
SLIDE 29

Algorithm convergence

Accuracy of transfer matrix in getting the stop masses vs SoftSUSY

  • 50

50 100 150 200 1 10 100 1000 104 105 mU3 (GeV)

  • 100

100 200 10 100 1000 104 105 mQ3 (GeV)

Accuracy of the seeding algorithm

  • 200-100

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

  • f MS

TM does not capture