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Andreas Crivellin ITP Bern. Chirally enhanced corrections in the MSSM. Outline:. Self-energies in the MSSM Resummation of chirally-enhanced corrections Effective higgsino and gaugino vertices Effective Higgs vertices Flavor-violation from SUSY. Introduction. - PowerPoint PPT Presentation
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24.03.11 2
Outline:Outline:
Self-energies in the MSSMSelf-energies in the MSSM Resummation of chirally-enhanced Resummation of chirally-enhanced
correctionscorrections Effective higgsino and gaugino verticesEffective higgsino and gaugino vertices Effective Higgs verticesEffective Higgs vertices Flavor-violation from SUSYFlavor-violation from SUSY
24.03.11 3
IntroductionIntroductionSources of flavor-violation in the MSSMSources of flavor-violation in the MSSM
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Quark massesQuark masses Top quark is very Top quark is very
heavy.heavy. Bottom quark rather Bottom quark rather
light, but Ylight, but Ybb can be can be big at large tan(β)big at large tan(β)
All other quark All other quark masses are very masses are very small small
sensitive to sensitive to radiative correctionsradiative corrections
u
d
c
s
tb
tm v
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q LRq 22 LLq q 2
RRq LR †
MM
M
q† 2 q 2(D)q qW M W M
Squark mass matrixSquark mass matrix
q 2LL,RRM
d d0i ij ij
d LRij d
u LR u 0i ii ij ju
uj
v
v
tan Y A
t Y Aco
involves only bilinear terms (in the decoupling involves only bilinear terms (in the decoupling
limit)limit)
hermitianhermitian
::
tan u
d
v
v
The chirality-changing elements are proportional to a The chirality-changing elements are proportional to a
vevvev
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Mass insertion approximationMass insertion approximation(L.J. Hall, V.A. Kostelecky and S. Raby, Nucl. Phys. B 267 (1986) 415.)(L.J. Hall, V.A. Kostelecky and S. Raby, Nucl. Phys. B 267 (1986) 415.)
A,B
q ABij
flavor indices 1,2,3
chiralitys L,R
i, j
off-diagonal element of the squark mass off-diagonal element of the squark mass
matrixmatrix
q ABfii
Afq
Biq
q u,d
Useful to visualize flavor-changes in the squark sector
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SQCD self-energy:SQCD self-energy:
s t
q LR q q* q LR q q* 2 2 2fi s g fs js jl lt it 0 g q q
2m W W W W C m ,m ,m
3
q LR
fii 0
Finite and proportional to at least one power of
decoupling decoupling limitlimit
q LRfi
s
q LR * 2 2fi s g fs i 3,s 0 g q
2m W W B m ,m
3
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Chargino self-energy:Chargino self-energy:
f i
LR
d di 0
id fd
su
3
f t
3
3 s
s
62u *LR u RL u RR d LL 2 2
d d 33 s 33 t 33 0 u u2s,t 1
62 22
2 W 2 0
CKM 0 *d3f
d LLs q 2
s 1f 3
1Y V V C ,m ,m
16
2g sin M M C M
Y V
,V m ,
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Neutralino self-energy:Neutralino self-energy:
d LR
fii 0
id fd
0
d
0
i j i
s
i
R
s
j
L j
LR 2 2 2 2d d 1 1 0 12 d d
232 2 22
u 2 0 2 ds 1
2 2 2 21 u 1 0 1
d LRij
d d LLs ij
d d RRs ijd
Y V
1 2g M C M ,m ,m
16 9
g 1v M C M , ,m 1 2
2 3
1g v M C M , ,m
3Y V
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Decomposition of the self-energyDecomposition of the self-energy(flavour-conserving part)(flavour-conserving part)
into a holomorphic part proportional to an A-term
non-holomorphic part proportional to a Yukawa
d LRii
d LR d LRi Yi ii A
0d LR dg LR d LRfi A fi A fi A
0d LR dg LR d LR d LRfi fi Y fi Y fi
di
i
d LR
ii Ydi d
uv Y
Define dimensionless quantity
which is independent of a Yukawa coupling
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Decomposition of the self-energyDecomposition of the self-energy(flavor-changing part)(flavor-changing part)
into a part independent of the CKM matrix
part proportional to CKM element
d LRfi fi CKM
dd LLR R
fi CM Mfi K KC CKd L M* d3
Rf FCV
fi CKM
0d LR dg LR d LRfi fi fi CKM
d LR
d LR d LRfiCKM fiCKM
d LR3f Yd
FC CKM*b 3fm V
Define dimensionless quantity
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Finite RenormalizationFinite Renormalization
and resummation of chirally enhanced and resummation of chirally enhanced correctionscorrections
AC, Ulrich Nierste, arXiv:0810.1613AC, Ulrich Nierste, arXiv:0908.4404AC, arXiv:1012.4840AC, L. Hofer and J. Rosiek, arXiv:1103.4272
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ii
q LRd ii Ad 0
dd i
mY
v 1 tan
tan(β) is automatically resummed to all orders
Renormalization IRenormalization I All corrections are finite; counter-term not
necessary.
Minimal renormalization scheme is simplest.
i
i
i i
i
d d LR0d d ii
d dq LR0 0d ii A d d
m v Y
v Y v tan Y
Mass renormalizationMass renormalization
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Renormalization IIRenormalization II
Flavour-changing correctionsimportant two-important two-
looploopcorrectionscorrectionsA.C. Jennifer Girrbach A.C. Jennifer Girrbach
2010 2010
2 2 3
2 3
3
2
2 3 3
q LR q LR12 13
q q
q L q RL q LR21 23
2q LR12
2q
2q LR12
2q
q RL q RL32 21
q q
q q
q RL q RL31 32
q q
2m
2m
m m
1 11
m m
1 1U 1
m m
1 11
m m
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Renormalization IIIRenormalization III Renormalization of the CKM matrix:
Decomposition of the rotation matrices
Corrections independent of the CKM matrix
CKM dependent corrections
† u L d LCKM CKMU VU
†0 u L d LV U V U
q L
CKMU U q L q L
CKMU
CKM
V U 0†u L
CKMV U d L
0 13,2313,23 1
FC
VV
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Effective gaugino Effective gaugino and higgsino verticesand higgsino vertices
No enhanced genuine vertex corrections.No enhanced genuine vertex corrections.
Calculate Calculate Determine the bare Yukawas and bare CKM matrixDetermine the bare Yukawas and bare CKM matrix Insert the bare quantities for the vertices.Insert the bare quantities for the vertices. Apply rotations to the external quark fields.Apply rotations to the external quark fields. Similar procedure for leptons (up-quarks)Similar procedure for leptons (up-quarks)i i
dd FC ii Y
, , q LRii CKM
,q LR
,q L RfiU
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Chiral enhancementChiral enhancement
dq LR
d LR ijddfi 0fi i ij
SUSY SUSY
Av1tan Y
100 M 100 M
d LR d22 A 22 SUSY
d LR d11 A 11 SUSY
O A M1
1O A M1
25
tanO
100
For the bottom quark For the bottom quark only the term only the term proportional to tan(proportional to tan(ββ) is ) is important.important.
tan(tan(ββ) ) enhancementenhancement
For the light quarks also For the light quarks also the part proportional to the part proportional to the A-term is relevant.the A-term is relevant.
d LR b 033 Y d b
1v tan Y m
100
Blazek, Raby, Pokorski, hep-Blazek, Raby, Pokorski, hep-ph/9504364ph/9504364
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Flavor-changing correctionsFlavor-changing corrections
max f ,i
q LRCKMfifi
q
Vm
A.C., Ulrich Nierste, A.C., Ulrich Nierste, hep-ph/08101613hep-ph/08101613
CKM qcb 23 SUSY
CKM q 1ub 13 SUSY
CKM q 1us 12 SUSY
V : A M
V : A M 10
V : A M 10
Flavor-changing A-term can Flavor-changing A-term can easily lead to order one easily lead to order one correction.correction.
24.03.11 20
Bren
B
M
M
Effect of including the self- Effect of including the self- energies in energies in ΔΔF=2 F=2 processesprocesses
for gm 1000GeV
AC, Ulrich Nierste, arXiv:0908.4404
24.03.11 21
b→sb→sγγ
experimentally allowed range
bm tan( ) 0TeV
bm tan( ) 30TeV
bm tan( ) 30TeV
d LR23Behavior of the branching ratio for
Two-loop effects enter only if also mTwo-loop effects enter only if also mbbμμ··tan(tan(ββ) is ) is
large.large.
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Effective Higgs verticesEffective Higgs verticesAC, arXiv:1012.4840AC, L. Hofer and J. Rosiek, arXiv:1103.4272
24.03.11 23
Higgs vertices in the EFT IHiggs vertices in the EFT I
d LLfi
id
idY d RRfi
uH
idY
fdY
dH
uH
idY id
uH
id id
id fdid fd
new
fd
dH
id
dfiA
24.03.11 24
Higgs vertices in the EFT IIHiggs vertices in the EFT II
d LRfi Yd
fiu
Ev
id dd dfi d u fifi fi
m v v EY E
ddfif
eff a b a*dY f L ba d u i Ri fi i
L H dEQ E HY
Non-holomorphic corrections Non-holomorphic corrections
Holomorphic corrections Holomorphic corrections
The quark mass matrix The quark mass matrix is no longer diagonal in the same basis as the Yukawa is no longer diagonal in the same basis as the Yukawa couplingcoupling
Flavor-changing neutral Higgs Flavor-changing neutral Higgs couplingscouplings
d LRfi Ad
fid
Ev
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i
d Ld effij d ij
d
Rij Y
1Y m
v
2 3
2 3
3 3
d LR d LR12 13
d d
d L* d R d LR d LRjf ki 2
d LR d LR22 Y 33 Y
d LR d LR22
1 23d q
d LR d LR31 3
Y 33 Y
2d q
d LR d LR d LRjk Y jk Y fi Y
d LR d LR33 Y 33 Y
0m m
U U 0m m
0m m
Effective Yukawa couplingsEffective Yukawa couplings
withwith
Final result:Final result:
Diagrammatic explanation in the full theory:Diagrammatic explanation in the full theory:
0d LR dg LR d LR d LRfi Y fi Y fi fi Y
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Higgs vertices in the full theoryHiggs vertices in the full theory
32d LR 0
kH
3
3
dd dv Y m2d
32d LRA
3d
3d
dv3dY
3d
32d LRA
dv
0kH
2d
32dA
Cancellation incomplete since Cancellation incomplete since Part proportional to is left over.Part proportional to is left over.
A-terms generate flavor-changing Higgs A-terms generate flavor-changing Higgs couplingscouplings
33d LRY
3
3
dd dv Y m
0kH
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Radiative generation of Radiative generation of light quark masses and light quark masses and
mixing angelsmixing angels
AC, Ulrich Nierste, arXiv:0908.4404AC, Jennifer Girrbach, Ulrich Nierste, arXiv:1010.4485AC, Ulrich Nierste, Lars Hofer, Dominik Scherer arXiv:1104.XXXX
24.03.11 28
SU(2)³ flavor-symmetry in SU(2)³ flavor-symmetry in
the MSSM superpotential:the MSSM superpotential:
CKM matrix is the unit CKM matrix is the unit matrix.matrix.
Only the third generation Only the third generation Yukawa coupling is Yukawa coupling is different from zero.different from zero.
0CKM
1 0 0
V 0 1 0
0 0 1
3
q
0 0 01
Y 0 0 0v
0 0 m
All other elements are generated All other elements are generated radiatively using the trilinear A-terms!radiatively using the trilinear A-terms!
Radiative flavor-violationRadiative flavor-violation
24.03.11 29
Features of the modelFeatures of the model Additional flavor symmetries in the superpotential.Additional flavor symmetries in the superpotential. Explains small masses and mixing angles via a loop-Explains small masses and mixing angles via a loop-
suppression.suppression. Deviations from MFV if the third generation is Deviations from MFV if the third generation is
involved.involved. Solves the SUSY CP problem via a mandatory phase Solves the SUSY CP problem via a mandatory phase
alignment. (Phase of μ enters only at two loops)alignment. (Phase of μ enters only at two loops)Borzumati, Borzumati, Farrar, Polonsky, Thomas 1999.Farrar, Polonsky, Thomas 1999.
The SUSY flavor problem reduces The SUSY flavor problem reduces to the elements to the elements
Can explain the BCan explain the Bss mixing phase mixing phase32 31,q LR q LR
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CKM generation in the down-CKM generation in the down-sectorsector!
d LR13 b ub
!d LR23 b cb
m V
m V
d LR32
Constraints from b→sγ.Constraints from b→sγ.Chirally enhanced Chirally enhanced corrections importantcorrections important
less constrained less constrained since they contribute to since they contribute to C7‘,C8‘.C7‘,C8‘.
can explain the CPcan explain the CP
phase in Bphase in Bss mixing. mixing.
(not possible in MFV)(not possible in MFV)
d LR d LR31 32,
2bm tan 0.12TeV
2bm tan 0TeV
2bm tan 0.12TeV
24.03.11 31
Higgs effects: BHiggs effects: Bss→→μμμμ
b 0.005
b 0.005
b 0.01
b 0.01
23d LR
b cbm V
Constructive Constructive contribution due tocontribution due to
24.03.11 32
Higgs effects: BHiggs effects: Bss mixing mixing
tan 11
tan 17
tan 20
tan 14
Contribution only if Contribution only if
due to Peccei-Quinn due to Peccei-Quinn symmetrysymmetry
2323 0
d RLR
b
Vm
24.03.11 33
Correlations between Correlations between BBss mixing and mixing and BBss→→μμμμ
H
tan 12
M 400GeV
910 sBr B
2323
d RLR
b
Vm
Allowed region from Bs mixing
24.03.11 34
CKM generation in the up-CKM generation in the up-sector:sector:
!u LR *13 t td
!u LR *23 t cb
m V
m V
u LR31
Constraints from Kaon Constraints from Kaon mixing.mixing.
unconstrained unconstrained from FCNC processes.from FCNC processes.
can induce a sizable can induce a sizable right-handed W coupling.right-handed W coupling.A.C. 2009A.C. 2009
u LR u LR31 32,
2M 800GeV2M 400GeV2M 200GeV
2M 400GeV
24.03.11 35
Effects in Effects in K→K→ππνννν
Verifiable Verifiable predictions predictions for NA62for NA62
24.03.11 36
ConclusionsConclusions Self-energies in the MSSM can be of order one.Self-energies in the MSSM can be of order one.
Chirally enhanced corrections must be taken into Chirally enhanced corrections must be taken into
account in FCNC processes.account in FCNC processes.
A-terms generate flavor-changing neutral Higgs A-terms generate flavor-changing neutral Higgs
couplings.couplings.
Radiative generations of light fermion masses Radiative generations of light fermion masses
and mixing angles solves the and mixing angles solves the SUSY flavorSUSY flavor and and
the the SUSY CPSUSY CP problem. It can explain B problem. It can explain Bss mixing. mixing.