Andreas CrivellinITP Bern

Chirally enhanced corrections in the MSSM

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

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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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Self-energiesSelf-energiesin the MSSMin the MSSM

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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.

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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

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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

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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

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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

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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

qq

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

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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

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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

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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

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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

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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

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Effects in Effects in K→K→ππνννν

Verifiable Verifiable predictions predictions for NA62for NA62

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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.