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New Results from GRACE/SUSY at 1-loop
J.Fujimoto, T.Ishikawa, M.Jimbo, T.KanekoT.Kon, Y.Kurihara,
M.Kuroda
Y.Shimizu(Susy group @ Minami-Tateya Collaboration)
RADCOR05Shonan Village, Japan October 6, 2005
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Outline
Introduction
Renormalization scheme
Physical results
Summary
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Introduction
Precise O(1%) measurement at LCSame accuracy of Theoretical
predictions
Why RC is important?
RC in MSSM renormalization, mass spectrum, decays, production
(Higgs, chargino / neutralino, sfermion)
Fritzsche, Hollik / Eberl, Majerotto, Yamada et al. /Denner /
Öller, Eberl, Majerotto /Hollik, Rzehak / Arhrib, Hollik /Kovarik,
Weber, Eberl, Majerotto /Freitas, Miller, von Manteuffel, Zerwas
/Guasch, Hollik, Solà etc.
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Many possible processes for SUSY particle production
a large number of Feynman diagrams
Why automatic calculation is needed?
SUSY Models
FeynArts & FormCalc Küblbeck, Böhm, Denner / Hahn,
Perez-Victoria / Hahn / Hahn, SchappacherCompHEP & LanHEP
Moscow group / Boudjema, Bèlanger, Semenov ... see Boudjema’s
talk
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Tree level GRACE/SUSY
GRACE/SUSY at 1-loop
"GRACE/SUSY AUTOMATIC GENERATION OF TREE AMPLITUDES IN THE
MINIMAL SUPERSYMMETRIC STANDARD MODEL"
KEK-CP-129, Aug 2002, hep-ph/0208036 Comput.Phys.Commun. 153
(2003) 106
http://minami-home.kek.jp/
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Renormalization scheme
Gauge symmetric & On-shell scheme
Renormalization of tanβ
€
δ tanβ = −12tanβ δZH1 −δZH2 − 2
δv1v1
+ 2δv2v2
€
δv1v1
≠δv2v2
On-shell conditions
€
(A0,H 0)Gauge bosons, Fermions, Scalar fermions
€
( ˜ χ 10, ˜ χ 1
+, ˜ χ 2+)
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Renormalization of sfermions
€
δm ˜ ν l2 = 2cosθl sinθlδθl m˜ l 2
2 −m˜ l 12( ) + cos2θlδm˜ l 12 + sin2θlδm˜ l 22
€
+δ MW2 cos2β −ml
2( )€
δm ˜ f 2 = −ReΣ ˜ f ̃ f (m ˜ f
2 )
€
sin2θuδm ˜ u 22 = 2cosθd sinθdδθd m ˜ d 2
2 −m ˜ d 12( ) + cos2θdδm ˜ d 12 + sin2θdδm ˜ d 22
€
−2cosθu sinθuδθu m ˜ u 22 −m ˜ u 1
2( )− cos2θuδm ˜ u 12
€
+δ MW2 cos2β +mu
2 −md2( )
€
δθu =12Σ ˜ u 1 ˜ u 2 (m ˜ u 2
2 )+Σ ˜ u 2 ˜ u 1 (m ˜ u 12 )
m ˜ u 22 −m ˜ u 1
2
€
δθl
€
δθd
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Mass shifts
€
mh : 89.30�→�118.53 GeV
example : SPA1a’
€
mH+ : 438.43�→�438.76 GeV
€
€
mχ20 : 184.55�→�184.43 GeV
€
mχ30 : 404.99�→�405.15 GeV
€
mχ40 : 420.35�→�422.15 GeV
€
€
msphys( )2 = ms2 + ˆ Σ s (ms2 )for h0, H+
€
/ q −m ˜ χ i0− ˆ Σ ii ( / q ) = 0
for neutralinos (i=2,3,4)
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Nonlinear gauge (NLG) fixing terms in MSSM
€
FW ±
= (∂µ ±ie ˜ α Aµ ±igcW ˜ β Zµ )W±µ
€
±iξWg2
(v+ ˜ δ HH0 + ˜ δ hh
0 ±i ˜ κ G 0 )G ±
€
FZ = ∂µZµ +ξZ
gZ2
(v+ ˜ ε HH0 + ˜ ε hh
0 )G 0
Fγ = ∂µAµ
€
( ˜ α , ˜ β , ˜ δ h , ˜ δ H , ˜ κ , ˜ ε h , ˜ ε H ) : NLG
parameters
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Physical results
2-body decay widths (Higgs & sparticles)
Chargino pair production at LC
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2-body decay widths
€
H 0 → bb
€
Γ0(GeV )parameter set : SPA1a’
€
δΓ /Γ0
€
1.80
€
H+ →νττ+
€
8.75×10-2
€
+16%
€
+9.7%
€
H+ → ˜ χ 10 ˜ χ 1
+
€
1.21×10-1
€
+4.0%
€
˜ e 1− → e− ˜ χ 1
0
€
7.80×10-2
€
+7.8%
€
˜ χ 1+ →ντ ˜ τ 1
+
€
2.93×10-2
€
+9.0%
€
˜ χ 2+ → Z 0 ˜ χ 1
+
€
7.53×10-1
€
−2.8%
€
˜ χ 30 →W − ˜ χ 1
+
€
1.47
€
−4.2%
€
˜ χ 30 → Z 0 ˜ χ 1
0
€
4.42×10-1
€
+2.5%
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€
H 0 → bb How to CalculateTree
%%%%%%%%%%%%Model=”mssm.mdl”;%%%%%%%%%%%%Process; ELWK={1};
Initial={higgs2}; Final={b b-bar}; Kinem=”1201”;Pend;
Tree+photon%%%%%%%%%%%%Model=”mssm.mdl”;%%%%%%%%%%%%Process;
ELWK={2}; Initial={higgs2}; Final={photon b b-bar};
Kinem=”1301”;Pend;
1-loop%%%%%%%%%%%%Model=”mssm.mdl”;%%%%%%%%%%%%Process; ELWK={3,
1}; Initial={higgs2}; Final={b b-bar}; Kinem=”1201”;Pend;
Feynman diagram generation numerical calculation event
generation
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€
H 0 → bb Graph 1
0H0
1b
2ab
H0b
bH+
W+t
Graph 2
0H0
1b
2ab
H0b
bX+
W+t
Graph 3
0H0
1b
2ab
H0b
b
W+W+
t
Graph 4
0H0
1b
2ab
H0b
b
H+W+
t
Graph 5
0H0
1b
2ab
H0b
b
H+H+
t
Graph 6
0H0
1b
2ab
H0b
bX+
H+t
Graph 7
0H0
1b
2ab
H0b
b
X+W+
t
Graph 8
0H0
1b
2ab
H0b
b
X+H+
t
Graph 9
0H0
1b
2ab
H0b
bX+
X+t
Graph 10
0H0
1b
2ab
H0b
bA0
Z0b
Graph 11
0H0
1b
2ab
H0b
bX3
Z0b
Graph 12
0H0
1b
2ab
H0b
b
Z0Z0
b
Graph 13
0H0
1b
2ab
H0b
b
A0Z0
b
Graph 14
0H0
1b
2ab
H0b
b
A0A0
b
Graph 15
0H0
1b
2ab
H0b
b
A0X3
b
Graph 16
0H0
1b
2ab
H0b
b
X3Z0
b
Graph 17
0H0
1b
2ab
H0b
bA0
X3b
Graph 18
0H0
1b
2ab
H0b
b
X3X3
b
Graph 19
0H0
1b
2ab
H0b
b
tt
W+
Graph 20
0H0
1b
2ab
H0b
b
tt
H+
Graph 21
0H0
1b
2ab
H0b
b
tt
X+
Graph 22
0H0
1b
2ab
H0b
b
bb
Z0
Graph 23
0H0
1b
2ab
H0b
b
bb
A
Graph 24
0H0
1b
2ab
H0b
b
bb
h0
Graph 25
0H0
1b
2ab
H0b
b
bb
H0
Graph 26
0H0
1b
2ab
H0b
b
bb
A0
Graph 27
0H0
1b
2ab
H0b
b
bb
X3
Graph 28
0H0
1b
2ab
H0b
b
~t1~t1
~w1+
Graph 29
0H0
1b
2ab
H0b
b
~t1~t1
~w2+
Graph 30
0H0
1b
2ab
H0b
b
~t1~t2
~w1+
Graph 31
0H0
1b
2ab
H0b
b
~t1~t2
~w2+
Graph 32
0H0
1b
2ab
H0b
b
~t2~t2
~w1+
Graph 33
0H0
1b
2ab
H0b
b
~t2~t2
~w2+
Graph 34
0H0
1b
2ab
H0b
b
~t2~t1
~w1+
Graph 35
0H0
1b
2ab
H0b
b
~t2~t1
~w2+
Graph 36
0H0
1b
2ab
H0b
b
~b1~b1
~sz1
Graph 37
0H0
1b
2ab
H0b
b
~b1~b1
~sz2
Graph 38
0H0
1b
2ab
H0b
b
~b1~b1
~sz3
Graph 39
0H0
1b
2ab
H0b
b
~b1~b1
~sz4
Graph 40
0H0
1b
2ab
H0b
b
~b1~b2
~sz1
Graph 41
0H0
1b
2ab
H0b
b
~b1~b2
~sz2
Graph 42
0H0
1b
2ab
H0b
b
~b1~b2
~sz3
Graph 43
0H0
1b
2ab
H0b
b
~b1~b2
~sz4
Graph 44
0H0
1b
2ab
H0b
b
~b2~b2
~sz1
Graph 45
0H0
1b
2ab
H0b
b
~b2~b2
~sz2
Graph 46
0H0
1b
2ab
H0b
b
~b2~b2
~sz3
Graph 47
0H0
1b
2ab
H0b
b
~b2~b2
~sz4
Graph 48
0H0
1b
2ab
H0b
b
~b2~b1
~sz1
Graph 49
0H0
1b
2ab
H0b
b
~b2~b1
~sz2
Graph 50
0H0
1b
2ab
H0b
b
~b2~b1
~sz3
Graph 51
0H0
1b
2ab
H0b
b
~b2~b1
~sz4
Graph 52
0H0
1b
2ab
H0b
b
~w1+~w1+
~t1
Graph 53
0H0
1b
2ab
H0b
b
~w1+~w1+
~t2
Graph 54
0H0
1b
2ab
H0b
b
~w1+~w2+
~t1
Graph 55
0H0
1b
2ab
H0b
b
~w1+~w2+
~t2
Graph 56
0H0
1b
2ab
H0b
b
~w2+~w2+
~t1
Graph 57
0H0
1b
2ab
H0b
b
~w2+~w2+
~t2
Graph 58
0H0
1b
2ab
H0b
b
~w2+~w1+
~t1
Graph 59
0H0
1b
2ab
H0b
b
~w2+~w1+
~t2
Graph 60
0H0
1b
2ab
H0b
b
~sz1~sz1
~b1
Graph 61
0H0
1b
2ab
H0b
b
~sz1~sz1
~b2
Graph 62
0H0
1b
2ab
H0b
b
~sz1~sz2
~b1
Graph 63
0H0
1b
2ab
H0b
b
~sz1~sz2
~b2
Graph 64
0H0
1b
2ab
H0b
b
~sz1~sz3
~b1
-
Graph 65
0H0
1b
2ab
H0b
b
~sz1~sz3
~b2
Graph 66
0H0
1b
2ab
H0b
b
~sz1~sz4
~b1
Graph 67
0H0
1b
2ab
H0b
b
~sz1~sz4
~b2
Graph 68
0H0
1b
2ab
H0b
b
~sz2~sz2
~b1
Graph 69
0H0
1b
2ab
H0b
b
~sz2~sz2
~b2
Graph 70
0H0
1b
2ab
H0b
b
~sz2~sz1
~b1
Graph 71
0H0
1b
2ab
H0b
b
~sz2~sz1
~b2
Graph 72
0H0
1b
2ab
H0b
b
~sz2~sz3
~b1
Graph 73
0H0
1b
2ab
H0b
b
~sz2~sz3
~b2
Graph 74
0H0
1b
2ab
H0b
b
~sz2~sz4
~b1
Graph 75
0H0
1b
2ab
H0b
b
~sz2~sz4
~b2
Graph 76
0H0
1b
2ab
H0b
b
~sz3~sz3
~b1
Graph 77
0H0
1b
2ab
H0b
b
~sz3~sz3
~b2
Graph 78
0H0
1b
2ab
H0b
b
~sz3~sz1
~b1
Graph 79
0H0
1b
2ab
H0b
b
~sz3~sz1
~b2
Graph 80
0H0
1b
2ab
H0b
b
~sz3~sz2
~b1
Graph 81
0H0
1b
2ab
H0b
b
~sz3~sz2
~b2
Graph 82
0H0
1b
2ab
H0b
b
~sz3~sz4
~b1
Graph 83
0H0
1b
2ab
H0b
b
~sz3~sz4
~b2
Graph 84
0H0
1b
2ab
H0b
b
~sz4~sz4
~b1
Graph 85
0H0
1b
2ab
H0b
b
~sz4~sz4
~b2
Graph 86
0H0
1b
2ab
H0b
b
~sz4~sz1
~b1
Graph 87
0H0
1b
2ab
H0b
b
~sz4~sz1
~b2
Graph 88
0H0
1b
2ab
H0b
b
~sz4~sz2
~b1
Graph 89
0H0
1b
2ab
H0b
b
~sz4~sz2
~b2
Graph 90
0H0
1b
2ab
H0b
b
~sz4~sz3
~b1
Graph 91
0H0
1b
2ab
H0b
b
~sz4~sz3
~b2
Graph 92
0H0
1b
2ab
H0b
b
h0h0
b
Graph 93
0H0
1b
2ab
H0b
b
h0H0
b
Graph 94
0H0
1b
2ab
H0b
bh0
H0b
Graph 95
0H0
1b
2ab
H0b
b
H0H0
b
Graph 96
0H0
1b
2ab
H0b
b
Graph 97
0H0
1b
2ab
H0 b
bh0
Graph 98
0H0
1b
2ab
H0 b
bH0
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How to check results?
UV (Cuv) independence
Soft photon mass (λ) independence
cut off photon energy (kc) independence
Nonlinear gauge parameter independence
check for physical finite contribution
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€
H 0 → bb
€
Γ0 =1.8019(GeV )
€
Γ1loop+soft = 0.122658203244395(GeV )
€
CUV = 0,λ =10−24 ,kc = 0.1GeV
€
CUV =103,λ =10−24 ,kc = 0.1GeV
€
Γ1loop+soft = 0.122658203244395(GeV )
€
CUV = 0,λ =10−27,kc = 0.1GeV
€
Γ1loop+soft = 0.122658203244395(GeV )
€
CUV = 0,λ =10−24 ,kc = 0.1GeV
€
( ˜ α , ˜ β , ˜ δ h , ˜ δ H , ˜ κ , ˜ ε h , ˜ ε H ) = (0,L,0)⇒
(2,3,4,5,6,7,8)
€
Γ1loop+soft = 0.122658203244395(GeV )
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€
H 0 → bb (γ )
€
H 0 → bb
€
CUV = 0,λ =10−24 ,kc = 0.001GeV
€
Γ1loop+soft = 0.0880604496742621(GeV )
€
Γhard (kc = 0.1GeV ) = 0.05140388(GeV )
€
Γhard (kc = 0.001GeV ) = 0.08605922(GeV )
€
Γ1loop+soft+hard (kc = 0.001GeV ) = 0.1741(GeV )
€
Γ1loop+soft+hard (kc = 0.1GeV ) = 0.1741(GeV )
€
= δΓ
€
δΓΓ0
= 9.66%
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Chargino pair production at LC
parameter set : SPA1a’
0.00
0.05
0.10
0.15
0.20
400 600 800 1000 1200 1400
W [GeV]
σ [pb]
Born
1-lp corr
€
e+e− → ˜ χ 1+ ˜ χ 1
−
-
-25.0
-20.0
-15.0
-10.0
-5.0
0.0
5.0
10.0
400 600 800 1000 1200 1400
W [GeV]
Δσ/σ[%]€
e+e− → ˜ χ 1+ ˜ χ 1
−
Weak = 1-loop + soft - BORN*QED
GRACEWien group
(hep-ph/0504109)
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SummaryGRACE/SUSY@1-loop : developed
gauge symmetric & on-shell scheme
full automatic calculation
various check system
useful tools for precise phenomenologies
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SPA1a’mSUGRA values
low energy inputs
M1/2 = 250 GeV sign(μ) = +1M0 = 70 GeV tanβ = 10A0 = -300
GeV
M2 = 197.5 GeV μ = 399.2 GeVM1 = 100.1 GeV tanβ = 10mse1 = 123.2
GeV mse2 = 187.4 GeV θe = 0.50 msτ1 = 110.1 GeV msτ2 = 190.4 GeV θτ
= 0.41msu1 = 506.5 GeV msu2 = 534.1 GeV θu =-0.50msd1 = 506.5 GeV
θd =-0.50mst1 = 347.4 GeV mst2 = 556.8 GeV θt =-0.31msb1 = 469.4
GeV θb = 0.12MA = 431.0 GeV
