next-to-leading order contributions to the pole mass of...
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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
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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?
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m0, m1/2, A0, tan�, µ(> 0)
constrained minimal supersymmetric standard model
MX = 2.0⇥ 1016 GeV
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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
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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
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Benchmark Points
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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