next-to-leading order contributions to the pole mass of...

Next-to-leading order contributions to the pole mass of gluino in

minimal gauge mediationJHEP05(2012)029[arXiv:1112.3904]

Jae Yong Lee (Korea University)with Yeo Woong Yoon (KIAS)

June 8, 2012Yonsei University

2012 NRF Workshop on Flavor Physics and Collider Physics

1Friday, June 8, 12

• LHC and CMSSM

• Minimal Gauge Mediation(MGM)

• Gluino Pole Mass in MGM

• Numerical Analysis

• Conclusion

Outline

2Friday, June 8, 12

Two muons and two electrons

LHC-ATLAS

3Friday, June 8, 12

u

d

e

νe

c

s

µ

νµ

t

b

τ

ντ

g

γ

W

Z

Forcecarriers

Quarks

Leptons

Elementary particles

I II IIIThree families of matter

4Friday, June 8, 12

u

d

e

νe

c

s

µ

νµ

t

b

τ

ντ

g

γ

W

Z

Forcecarriers

Quarks

Leptons

Elementary particles

I II IIIThree families of matter

u

d

e

νe

c

s

µ

νµ

t

b

τ

ντ

g

γ

W

Z

GauginosSq

uarks

Sleptons

Superparticles

I II IIIThree families of matter

4Friday, June 8, 12

u

d

e

νe

c

s

µ

νµ

t

b

τ

ντ

g

γ

W

Z

Forcecarriers

Quarks

Leptons

Elementary particles

I II IIIThree families of matter

u

d

e

νe

c

s

µ

νµ

t

b

τ

ντ

g

γ

W

Z

GauginosSq

uarks

Sleptons

Superparticles

I II IIIThree families of matter

4Friday, June 8, 12

u

d

e

νe

c

s

µ

νµ

t

b

τ

ντ

g

γ

W

Z

Forcecarriers

Quarks

Leptons

Elementary particles

I II IIIThree families of matter

u

d

e

νe

c

s

µ

νµ

t

b

τ

ντ

g

γ

W

Z

GauginosSq

uarks

Sleptons

Superparticles

I II IIIThree families of matter

4Friday, June 8, 12

u

d

e

νe

c

s

µ

νµ

t

b

τ

ντ

g

γ

W

Z

Forcecarriers

Quarks

Leptons

Elementary particles

I II IIIThree families of matter

u

d

e

νe

c

s

µ

νµ

t

b

τ

ντ

g

γ

W

Z

GauginosSq

uarks

Sleptons

Superparticles

I II IIIThree families of matter

Question:Why are superpartners heavy?

4Friday, June 8, 12

m0, m1/2, A0, tan�, µ(> 0)

constrained minimal supersymmetric standard model

MX = 2.0⇥ 1016 GeV

5Friday, June 8, 12

6Friday, June 8, 12

Direct Search

7Friday, June 8, 12

Direct Search

[GeV]0m500 1000 1500 2000 2500 3000 3500

[GeV

]1/

2m

100

200

300

400

500

600

700

(600)g~

(1000)g~

(1400)g~

(600)q~ (1000)

q ~ (1400)q ~

1± r¾LEP 2

Stau LSPTheoretically excluded

95% C.L. limitssCL

>0µ= 0, 0

= 10, A`MSUGRA/CMSSM: tan -1 = 4.7 fbintL

PreliminaryATLASObservedExpectedObservedExpectedObservedExpected

2-6 jets*0-lepton,

6-9 jets*0-lepton,

3,4 jets*1-lepton,

ATLAS-CONF-2012-033

ATLAS-CONF-2012-037

ATLAS-CONF-2012-041

7Friday, June 8, 12

Including indirect searches and other constraints

8Friday, June 8, 12

Including indirect searches and other constraints

8Friday, June 8, 12

arXiv:1205.2283

Including indirect searches and other constraints

8Friday, June 8, 12

arXiv:1205.2283

Including indirect searches and other constraints

8Friday, June 8, 12

16⇡2 d

dtm2

Q3= Xt +Xb �

32

3g23 |M3|2 � 6g22 |M2|2 �

2

15g21 |M2

1 |+1

5g21S

where

Xt = 2|yt|2(m2Hu

+m2Q3

+m2u3) + 2|at|2

Xb = 2|yb|2(m2Hd

+m2Q3

+m2d3) + 2|ab|2

S = Tr[Yjm2�j]

Renormalization Group Equation

9Friday, June 8, 12

16⇡2 d

dtm2

Q3= Xt +Xb �

32

3g23 |M3|2 � 6g22 |M2|2 �

2

15g21 |M2

1 |+1

5g21S

where

Xt = 2|yt|2(m2Hu

+m2Q3

+m2u3) + 2|at|2

Xb = 2|yb|2(m2Hd

+m2Q3

+m2d3) + 2|ab|2

S = Tr[Yjm2�j]

Renormalization Group Equation

9Friday, June 8, 12

16⇡2 d

dtm2

Q3= Xt +Xb �

32

3g23 |M3|2 � 6g22 |M2|2 �

2

15g21 |M2

1 |+1

5g21S

where

Xt = 2|yt|2(m2Hu

+m2Q3

+m2u3) + 2|at|2

Xb = 2|yb|2(m2Hd

+m2Q3

+m2d3) + 2|ab|2

S = Tr[Yjm2�j]

Renormalization Group Equation

9Friday, June 8, 12

16⇡2 d

dtm2

Q3= Xt +Xb �

32

3g23 |M3|2 � 6g22 |M2|2 �

2

15g21 |M2

1 |+1

5g21S

where

Xt = 2|yt|2(m2Hu

+m2Q3

+m2u3) + 2|at|2

Xb = 2|yb|2(m2Hd

+m2Q3

+m2d3) + 2|ab|2

S = Tr[Yjm2�j]

Renormalization Group Equation

Gluino

9Friday, June 8, 12

Leading Order NLO NNLO

Tree One-loop Two-loop

NNLO corrections

NLO< 10%

10Friday, June 8, 12

fate of cMSSM?

11Friday, June 8, 12

fate of cMSSM?

Dead or Alive

11Friday, June 8, 12

• Ingredients of SUSY breaking

• A bunch of messenger superfields which are charged under the SM gauge symmetry.

• A SM singlet chiral superfield which has vacuum expectaction values in both zero and theta^2 components.

(Minimal) Gauge Mediation

12Friday, June 8, 12

W � X��

hXi = Mmess + ✓2FX

13Friday, June 8, 12

fermion

scalar

Messenger fields

�+ ��

14Friday, June 8, 12

fermion

scalar

Messenger fields

�+ ��

Mmess

Mmess

s

1± FX

M2mess

14Friday, June 8, 12

fermion

scalar

Messenger fields

gauge interactions Yukawa interactions

�+ ��

Mmess

Mmess

s

1± FX

M2mess

14Friday, June 8, 12

fermion

scalar

Messenger fields

gauge interactions Yukawa interactions

fundamental

�+ ��

Mmess

Mmess

s

1± FX

M2mess

14Friday, June 8, 12

fermion

scalar

Messenger fields

gauge interactions Yukawa interactions

fundamental

anti-fundamental

�+ ��

Mmess

Mmess

s

1± FX

M2mess

14Friday, June 8, 12

fermion

scalar

Messenger fields

gauge interactions Yukawa interactions

fundamental

anti-fundamental

g

�+ ��

Mmess

Mmess

s

1± FX

M2mess

14Friday, June 8, 12

fermion

scalar

Messenger fields

gauge interactions Yukawa interactions

fundamental

anti-fundamental

g

�g

�+ ��

Mmess

Mmess

s

1± FX

M2mess

14Friday, June 8, 12

Many Yukawa interactions

ψ

ψ†

ψ

ψ

ψ†

ψ†

φ∗± i

φ± j

φ− j

φ+ j

φ∗− i

φ∗+ i

β

β

β

β β

β

j

i

i

i

j

j

a

a

a

a

a

a

α

α

α

α

α

α

−ig(T a) ji δ

βα

−ig(T a) ji δ

βα

ig(T a) ji δ

βα

−ig(T a) ji δ

βα

ig(T a) ji δ

αβ

−ig(T a) ji δ

αβ

(a) (b)

(c) (d)

(e) (f)

15Friday, June 8, 12

What mass are we talking about?

bare mass

running mass

(physical) pole mass

16Friday, June 8, 12

ps =

⌦

1� ⌅

= ⌦(1) +⇥⌦(1)⌅(1) + ⌦(2)

⇤+ · · ·

⌦ = ⌦(1) + ⌦(2) + ⌦(3) + · · ·⌅ = ⌅(1) + ⌅(2) + ⌅(3) + · · ·

Gluino pole mass in perturbation theory

17Friday, June 8, 12

gluino mass at one-loop order

⌦(1)(s)|x! 0 =

✓↵s

4⇡

◆⇤Nmess 2C(R)

"r ln(r)

(r � 1)2+ (r $ r)

#.

⇤ =FX

Mmess

x = � p

2

M

2mess

= � s

M

2mess

,

r =m

2�+

M

2mess

= 1 +⇤

Mmess,

r =m

2��

M

2mess

= 1� ⇤

Mmess,

18Friday, June 8, 12

Search for supersymmetry in events with photons and missing energy

SUS-12-001

Abstract

We have performed a search for supersymmetry in a gauge-mediation scenario with the gravitino as the lightest supersymmetric particle. The data sample corresponds to an integrated luminosity of 4.7 fb^-1 of pp collisions at sqrt(s) = 7 TeV, recorded by the CMS experiment at the LHC.We compare the missing transverse energy distribution in events containing either at least two photons plus at least one hadronic jet or at least one photon plus at least two hadronic jets to the spectra expected from standard model processes. No excess of events at high missing transverse energy is observed and upper limits on the signal production cross sections of order 0.01 pb (0.1 pb) at the 95% confidence level for the bino-like (wino-like) scenarios are determined for a range of squark, gluino, and neutralino masses. This analysis is also re-interpreted as a search for Universal Extra Dimensions leading to 95% exclusion values of 1/R < 1335 GeV for NLEDs = 6.

19Friday, June 8, 12

g

q

q

q′

χ01

γ

G

20Friday, June 8, 12

g

q

q

q′

χ01

γ

G

20Friday, June 8, 12

95% C.L. exclusion contours in gluino-squark mass space for bino-like neutralinos for the diphoton analysis. The shaded uncertainty band around the exclusion contours correspond to the NLO renormalization and PDF uncertainties of the signal cross section.

)2 (GeV/cq~m500 1000 1500 2000

)2 (G

eV/c

g~m

500

1000

1500

2000

0χ∼GGM bino-like )2 = 375 (GeV/c0

χ∼mAt least 1 jet requirementNLO Limits

Observed (theory)σ1±

Expected (theory)σ1± (experimental)σ1±

CMS Preliminary = 7 TeVs, -1dt = 4.7 fbL ∫

Excluded

21Friday, June 8, 12

)2 (GeV/c0χ∼m

500 1000 1500

)2 (G

eV/c

g~m

500

1000

1500

2000

)2 = 2500 (GeV/cq~mAt least 1 jet requirementNLO Limits

Observed (theory)σ1±

Expected (theory)σ1± (experimental)σ1±

CMS Preliminary = 7 TeVs, -1dt = 4.7 fbL ∫

Excluded NLSPg~

95% C.L. exclusion contours in gluino-bino mass space for bino-like neutralinos for the diphoton analysis. The shaded uncertainty band around the exclusion contours correspond to the NLO renormalization and PDF uncertainties of the signal cross section.

22Friday, June 8, 12

Jump to the two-loop order contributions

23Friday, June 8, 12

⌅(1)(s)|x!0 =

✓↵s

4⇡

◆"C(R)

Nmess

✓r ln(r)

r � 1+

r ln(r)

r � 1� 2� 2 ln

✓µ2

M2mess

◆◆

+2Nf

✓ln

✓�s

µ2

◆� 2

◆!+ C2(G)

✓ln

✓�s

µ2

◆� 2

◆#.

Gaugino wavefunction renormalization

= + +

ψ(ψ)

φ±

24Friday, June 8, 12

Two-loop Feynman diagrams

⌦(2)(s)|x!0 =

✓↵s

4⇡

◆2

⇤Nmess 2C(R)

"C2(G)

ln(r)

(r � 1)2

✓8r � 4r ln

⇣�s

µ2

⌘

+⇣2r +

1

r � 1

⌘ln(r) + ln(r)

◆+

4r � 2

(r � 1)2Li2(1� r) +

2

r � 1Li2

✓2r � 2

r

◆!

+ C2(R)ln(r)

(r � 1)2

6r + 2 + 2(r + 1) ln

⇣ µ2

M2mess

⌘� r(r � 3)

r � 1ln(r) + ln(r)

!

+ (r $ r)

#.

25Friday, June 8, 12

One-loop corrections for a propagator

= + +

= +

++

+

One-loop vertex corrections

26Friday, June 8, 12

m

I1

q2

I21

q2

m2

m1

I22

m1

m2I31

q2m1

m1I32

q2m1

m1I33

q2

m1

m1I34

q2m1

m2I35

q2m1

m2I36

q2

m1

m2I37

q2

m1

m1m2

I41

q2

m2

m3m1

I42

q2

m1

m2

m2

I51

q2

m1m1

m2 m2

I52

q2

m1m2

m1 m2

I53

q2

m1m3

m1 m2

I5427Friday, June 8, 12

28Friday, June 8, 12

Numerical Analysis

29Friday, June 8, 12

30Friday, June 8, 12

31Friday, June 8, 12

32Friday, June 8, 12

Benchmark Points

33Friday, June 8, 12

ConclusionThe NLO corrections to the gluino pole mass in the MGM is 20% or more of the LO pole mass.

The large corrections should be reckoned with for precision studies on the SUSY parameters.

The NLO corrections to the squark pole mass are anticipated to be large as well.

The study on the gluino pole mass of the anomaly mediation presently gets under way.

34Friday, June 8, 12