Study of h,H,A→ τµ decays in the

context of the MSSM within the Mass

Insertion Approximation

Roberto Morales

Universidad Nacional de La Plata - Instituto de Fısica La Plata - Argentina

IV Postgraduate Meeting on Theoretical Physics, IFT UAM-CSIC - November 18, 2015

Roberto Morales 1/28

Outline

• Motivation

• Experimental Bounds

• MSSM + general slepton mixing

• Mass Insertion Approximation (MIA)

• Lepton Flavor Violation Higgs Decays (LFVHD) processes

• Results

• Phenomenology

• Conclusions

Roberto Morales 2/28

References

Work based on:

• E.Arganda, M. J. Herrero, R. Morales and A. Szynkman,“Analysis of the h,H,A→ τµ decays induced from SUSY loops within the Mass InsertionAproximation”, arXiv:1510.04685[hep-ph].

In continuation to:

• M. Arana-Catania, E.Arganda and M. J. Herrero,“Non-decoupling SUSY in LFV Higgs decays: a window to new physics at the LHC”,JHEP 1309 (2013) 160 [JHEP 1510 (2015) 192] [arXiv:1304.3371 [hep-ph]].

Roberto Morales 3/28

Motivation

• Why Lepton Flavor Violation? LFV occurs in Nature.Neutrino oscillations −→ LFV

• LFV is a window to BSM physics: No LFV within SM.

• SUSY not seen yet at LHC (scale mSUSY at TeV range?)

• Higgs mediated processes are sensitive to SUSY via loops.

Main here:the MIA allows us to derive simple analytical expressions for decay rates. Useful for Pheno!

Roberto Morales 4/28

Experimental BoundsSome searched processes:

LFV process Present Upper Bound (90%CL) Future Sensitivity (?)

BR(µ→ eγ) 5.7× 10−13 (MEG 2013) 5× 10−14 (MEGup)

BR(τ → eγ) 3.3× 10−8 (BaBar 2010) 3× 10−9 (SuperB)

BR(τ → µγ) 4.4× 10−8 (BaBar 2010) 2.4× 10−8 (SuperB)

BR(µ→ eee) 1× 10−12 (SINDRUM 1988) 1× 10−16 (Mu3E-PSI)

BR(τ → eee) 2.7× 10−8 (Belle 2010) 1× 10−9,−10 (Belle2, SuperB)

BR(τ → µµµ) 2.1× 10−8 (Belle 2010) 1× 10−9,−10 (Belle2, SuperB)

BR(τ → µη) 2.3× 10−8 (Belle 2010) 1× 10−9,−10 (Belle2, SuperB)

CR(µ− e, Au) 7× 10−13 (SINDRUM2 2006)

CR(µ− e, Al) 3.1× 10−15 (COMET-I, J-PARC)

2.6× 10−17 (COMET-II, J-PARC)

2.5× 10−17 (Mu2E-FermiLab)

CR(µ− e, Ti) 4.3× 10−12 (SINDRUM2 2004) 1× 10−18 (PRISM, J-PARC)

New input from LHC: LFV Higgs DecaysBR(H → τµ) < 1.51× 10−2 (95%C.L.) [CMS 2015] (2.4σ excess?)

BR(H → τµ) < 1.85× 10−2 (95%C.L.) [ATLAS 2015]

Roberto Morales 5/28

The MSSM with general slepton mixingLow energy parametrization for general slepton mixing (model independent).

LLFVsoft = −L†m2

LL− R∗m2

RR +

(L†AlR∗H1 + h.c.

)

m2L

=

m2L1

δLL12 mL1mL2

δLL13 mL1mL3

δLL21 mL2mL1

m2L2

δLL23 mL2mL3

δLL31 mL3mL1

δLL32 mL3mL2

m2L3

∆

LLmk ≡ (m

2L

)mk = δLLmkmLmmLk

m2R

=

m2R1

δRR12 mR1mR2

δRR13 mR1mR3

δRR21 mR2mR1

m2R2

δRR23 mR2mR3

δRR31 mR3mR1

δRR32 mR3mR2

m2R3

∆

RRmk ≡ (m

2R

)mk = δRRmkmRmmRk

v1Al =

meAe δLR12 mL1

mR2δLR13 mL1

mR3

δLR21 mL2mR1

mµAµ δLR23 mL2mR3

δLR31 mL3mR1

δLR32 mL3mR2

mτAτ

∆LRmk ≡ (v1Al)mk = δ

LRmkv1

√mLmmRk

=⇒ δLRmk = δ

LRmk

v1√mLmmRk

∆RLmk ≡ (v1Al)km = δ

RLmkv1

√mRmmLk

=⇒ δRLmk = δ

RLmk

v1√mRmmLk

v1(2) = 〈H1(2)〉 and tanβ = tβ = v2/v1

⇒ LFV is originated from the off-diagonal real δABmk ’s via SUSY loops.

Roberto Morales 6/28

Full and MIA approach

Full Calculation

• Work with the mass basis −→ full diagonalization of mass matrix.

• Physical states: 6 sleptons lα and 3 sneutrinos να.

• Dependence on δABmk hidden in physical masses and rotation matrices.

• Numerical results for decay rates.

MIA Calculation

• Work with the EW interaction basis. Gauge states: lLi , lRi and νi where i denotes flavore, µ, τ .

• Non-diagonal elements of the mass matrix are considered as two-field interactions. Forexample, explicit dependence on ∆AB

mk appears in the lepton flavor violation insertions:

lAm lBk

−i∆ABmk

νm νk−i∆LL

mk

• Analytical expressions for decay rates as perturbative expansion of δABmk and other massratios.

Roberto Morales 7/28

LFVHD processes h,H,A→ lklm with m 6= k

In this context, LFV Higgs Decays occur at one-loop order:

Hx

lk

lm

px

pk

pm

∆mk

mSUSY

mEW

Our aim:to get the form factors F as an expansion valid for heavy SUSY

(mSUSY � mh,H,A,mlep,mW )

∆ABmkF (mHx ,mlep,mW ,mSUSY) ∼ ∆AB

mk

(F |mext=0 +O(M2

Hx/m2

SUSY) +O(M2W /m2

SUSY))

F |mext=0 ∼ O(M0Hx/m0

SUSY) −→ Non-Decoupling ND contributions (dominant terms).

O(M2Hx/m2

SUSY),O(M2W /m2

SUSY) −→ Decoupling D contributions (leading and subleading

corrections).

Roberto Morales 8/28

Results for LFVHD in the MIA

In the next slides,

• SUSY scenarios: all heavy masses are proportional to one scale mSUSY.

• All relevant one-loop diagrams for the full and MIA computation.

• Decay rate in terms of the form factors and ∆ABmk .

• Study of the cases ∆LLmk and ∆RR

mk : Non-Decoupling behavior.

• Study of the cases ∆LRmk and ∆RL

mk: Decoupling behavior.

• Perturbativity on δABmk ’s.

• Comparison between MIA/Full calculation and with Effective approach.

• Pheno implications: numerical study of maximum rates allowed by experimental boundsfrom τ → µγ and searches of neutral MSSM Higgs bosons.

Roberto Morales 9/28

SUSY scenarios

• Equal masses scenario: all the relevant parameters involved set to be equal

M1 = M2 = µ = mL = mR = Aµ = Aτ = mSUSY

• GUT approximation scenario: set an approximate GUT relation for the gaugino masses

M2 = 2M1 (GUT relation)

We also relate the soft parameters and the µ parameter to a common scale by choosing:

mL = mR = M2 = Aµ = Aτ = µ/a = mSUSY with a =3

4,

4

3

• Generic scenario: we set different values for all the mass parameters involved

M1 = 2.2mSUSY ,M2 = 2.4mSUSY , µ = 2.1mSUSY

mL1= 2mSUSY ,mL2

= 1.8mSUSY ,mL3= 1.6mSUSY

mR1= 1.4mSUSY ,mR2

= 1.2mSUSY ,mR3= mSUSY

Aµ = 0.6mSUSY , Aτ = 0.8mSUSY

Roberto Morales 10/28

One-loop diagrams for the Full results

Use mass basis for the internal SUSY particles: sleptons, sneutrinos, charginos andneutralinos.

[Arganda, Curiel, Herrero, Temes; 2005]

Hx

lk

lmχ−j

χ−i

να

(1)

Hx

lk

lm

χ−i

να

νβ(2)

Hx

lm

lk

χ−i

να

lm

(3)

Hx

lm

lk

χ−i

ναlk

(4)

Hx

lk

lmχ0j

χ0i

lα

(5)

Hx

lk

lm

χ0i

lα

lβ(6)

Hx

lm

lk

χ0i

lα

lm

(7)

Hx

lm

lk

χ0i

lαlk

(8)

Roberto Morales 11/28

Relevant one-loop diagrams for ∆LLmk

Use gauge basis for the internal SUSY particles: flavor sleptons, flavor sneutrinos, Bino,Winos, Higgsinos.

Hx

lk

lmW−, H−

H−, W−

νm

νk

(1a,1b)

Hx

lm

lk

H−

W−

νkνm

lm

(3a)

Hx

lm

lk

W−

νkνm

lm

(3b)

Hx

lm

lk

W−, H−H−, W−

νkνmlk

(4a,4b)

Hx

lm

lk

W−

νkνmlk

(4c)

Hx

lk

lmB, W3

H1

H2:1

lLm

lLk

(5a,5b:5c,5d)

Hx

lk

lm

B, W3

H1

H2:1lLm

lLk

(5e,5f:5g,5h)

Hx

lk

lm

B

lRk

lLk

lLm(6a)

Hx

lk

lm

B

lRm

lLm

lLk

(6b)

Roberto Morales 12/28

Relevant one-loop diagrams for ∆LLmk

Hx

lm

lk

H1

H2:1B, W3

lLklLm

lm

(7a,7b:7c,7d)

Hx

lm

lk

B, W3

lLklLm

lm

(7e,7f)

Hx

lm

lk

B

lRklLk

lLmlm

(7g)

Hx

lm

lk

B, W3 H1

H2:1

lLklLmlk

(8a,8b:8c,8d)

Hx

lm

lk

B, W3

lLklLmlk

(8e,8f)

Hx

lm

lk

B

lLk

lLm

lRmlk

(8g)

Hx

lm

lk

B, W3

H1

H2:1

lLklLmlk

(8h,8i:8j,8k)

Hx

lm

lk

B

lRk

lLk

lLmlk

(8l)

Other diagrams suppressed by extra factors of (MEW /mSUSY)n and/or (mlep/mSUSY)m.

Roberto Morales 13/28

Relevant one-loop diagrams for ∆LRmk and ∆RL

mk

• Case ∆LRmk

Hx

lk

lm

B

lRk

lLm(6c)

Hx

lm

lk

B

lRklLmlk

(8m)

• Case ∆RLmk

Hx

lk

lm

B

lLk

lRm(6d)

Hx

lm

lk

B

lLklRmlk

(8n)

Roberto Morales 14/28

Relevant one-loop diagrams for ∆RRmk

Hx

lk

lmB

H1

H2:1

lRm

lRk

(5i:5j)

Hx

lk

lm

B

H1

H2:1lRm

lRk

(5k:5l)

Hx

lk

lm

B

lLk

lRk

lRm(6e)

Hx

lk

lm

B

lLm

lRm

lRk

(6f)

Hx

lm

lk

H1

H2:1B

lRklRm

lm

(7h:7i)

Hx

lm

lk

B

lRklRm

lm

(7j)

Hx

lm

lk

B

lLklRk

lRmlm

(7k)

Hx

lm

lk

B

H1

H2:1

lRklRmlk

(8o:8p)

Hx

lm

lk

BH1

H2:1

lRklRmlk

(8q:8r)

Hx

lm

lk

B

lRklRmlk

(8s)

Hx

lm

lk

B

lLk

lRk

lRmlk

(8t)

Hx

lm

lk

B

lRk

lRm

lLmlk

(8u)

Roberto Morales 15/28

Analytical results in the MIA

The amplitude of Hx(p1)→ lk(−p2)lm(p3) for Hx = h,H,A is

iM = −igulk (−p2)(F(x)L PL + F

(x)R PR)vlm (p3)

The decay rate reads as follows:

Γ(Hx → lk lm) =g2

16πmHx

√√√√(1−(mlk +mlm

mHx

)2)(

1−(mlk −mlm

mHx

)2)

×(

(m2Hx−m2

lk−m2

lm)(|F (x)

L |2 + |F (x)R |2)− 4mlkmlmRe(F

(x)L F

(x)∗R )

)where the form factors are linear in ∆AB

mk

F(x)L,R = ∆LL

mkF(x)LLL,R + ∆LR

mkF(x)LRL,R + ∆RL

mkF(x)RLL,R + ∆RR

mkF(x)RRL,R

• All of them are UV convergent: they are expressed in terms of the loop functions C0, C2,D0, D0 of three and four points because there are 2 scalar and 1 fermionic propagators atleast.

• We perform a systematic expansion in powers of pext and keep: the leading contributionsO(p0

ext) and the next-to-leading O(p2ext).

Roberto Morales 16/28

Non-decoupling contributions for ∆LLmk and ∆RR

mk(∆LL

23 F(x)LLL

)ND

=

(g2

16π2

mτ

2MW

)[σ

(x)2 + σ

(x)∗

1 tβ

cβ

](δLL23 mL2

mL3

)

×[

3

2µM2D0(0, 0, 0,m

L2,m

L3, µ,M2)

− t2W

2µM1D0(0, 0, 0,m

L2,m

L3, µ,M1)

−t2WµM1D0(0, 0, 0,mL2,m

L3,m

R3,M1)

]

O(M0

Hx/m0

SUSY)

(∆RR

23 F(x)RRR

)ND

=

(g2t2W16π2

mτ

2MW

)[σ

(x)∗

2 + σ(x)1 tβ

cβ

](δRR23 m

R2mR3

)

×[µM1D0(0, 0, 0,m

R2,m

R3, µ,M1)

−µM1D0(0, 0, 0,mR2,m

R3,m

L3,M1)

]

O(M0

Hx/m0

SUSY)

whereHx = (h,H,A) , σ

(x)1 = (sα,−cα, isβ) , σ

(x)2 = (cα, sα,−icβ)

⇒ Simple analytical expressions: we factorized the contributions of the loops and the rest ofMSSM parameters (tβ and mA).

Roberto Morales 17/28

Non-decoupling contributions for ∆LLmk and ∆RR

mk

10-9

10-8

10-7

10-6

10-5

10-4

0.5 1 1.5 2 2.5 3 3.5 4 4.5 5

BR(φ

→ τ µ

)

mSUSY [TeV]

mA = 800 GeV, tan β = 40, δ23LL = 0.5

GUT approx. µ = 3/4 mSUSY h → τ µ FullA → τ µ Fullh → τ µ MIAA → τ µ MIA

10-12

10-11

10-10

10-9

10-8

10-7

10-6

0.5 1 1.5 2 2.5 3 3.5 4 4.5 5

BR(φ

→ τ µ

)

mSUSY [TeV]

mA = 800 GeV, tan β = 40, δ23RR = 0.5

Generic scenario

h → τ µ FullA → τ µ Fullh → τ µ MIAA → τ µ MIA

• Non-Decoupling behavior of BR(Hx → τµ) ∼ m0SUSY in contrast with the decoupling

behavior of BR(τ → µγ) ∼ m−4SUSY.

• First order MIA approximates the full calculation very well.

• Largest rates for LL and large tβ : BR(Hx → τµ) ∼ t2β .

• Similar results in other scenarios.

Roberto Morales 18/28

Decoupling contributions for ∆LRmk and ∆RL

mk(∆LR23 F

(x)LRL

)D

=

(g2t2W16π2

M1

2MW

)[σ(x)∗1

](δLR23 v

√mL2

mR3)

×[−C0(p2, p1,M1,mR3

,mL2) + C0(p3, 0,M1,mL2

,mR3)]O(M

2Hx/m

2SUSY)

⇒ Simple analytical expressions: we factorized the contributions of the loops and the rest ofMSSM parameters (tβ and mA).

10-17

10-16

10-15

10-14

10-13

10-12

10-11

10-10

10-9

10-8

0.5 1 1.5 2 2.5 3 3.5 4 4.5 5

BR(φ

→ τ µ

)

mSUSY [TeV]

mA = 800 GeV, tan β = 40, δ~23LR = 0.5

GUT approx. µ = 4/3 mSUSY

h → τ µ FullA → τ µ Fullh → τ µ MIAA → τ µ MIA

10-18

10-17

10-16

10-15

10-14

10-13

10-12

10-11

10-10

10-9

0.5 1 1.5 2 2.5 3 3.5 4 4.5 5

BR(φ

→ τ µ

)mSUSY [TeV]

mA = 800 GeV, tan β = 40, δ~23LR = 0.5

Generic scenario

h → τ µ FullA → τ µ Fullh → τ µ MIAA → τ µ MIA

• Exact cancellations between Non-Decoupling terms.

• Decoupling behavior of BR(Hx → τµ) ∼ m−4SUSY like BR(τ → µγ).

• First order MIA for H and A approximates the full calculation better than the h.

• Very small rates for LR and RL.

• Similar results in other scenarios.

Roberto Morales 19/28

Limitations of the MIA results

10-12

10-11

10-10

10-9

10-8

10-7

10-6

10-5

10-4

10-3

-1 -0.5 0 0.5 1

BR(φ

→ τ µ

)

δ23LL

mA = 800 GeV, tan β = 40, mSUSY = 5 TeVGUT approx. µ = 4/3 mSUSY

h → τ µ FullA → τ µ Fullh → τ µ MIAA → τ µ MIA

10-14

10-13

10-12

10-11

10-10

10-9

10-8

10-7

10-6

10-5

-1 -0.5 0 0.5 1

BR(φ

→ τ µ

)

δ23RR

mA = 800 GeV, tan β = 40, mSUSY = 5 TeVGUT approx. µ = 4/3 mSUSY

h → τ µ FullA → τ µ Fullh → τ µ MIAA → τ µ MIA

10-21

10-20

10-19

10-18

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10-14

10-13

10-12

-1 -0.5 0 0.5 1

BR(φ

→ τ µ

)

δ23LR

mA = 800 GeV, tan β = 40, mSUSY = 5 TeVGUT approx. µ = 4/3 mSUSY

~

h → τ µ FullA → τ µ Fullh → τ µ MIAA → τ µ MIA

10-21

10-20

10-19

10-18

10-17

10-16

10-15

10-14

10-13

10-12

-1 -0.5 0 0.5 1

BR(φ

→ τ µ

)

δ23RL

mA = 800 GeV, tan β = 40, mSUSY = 5 TeVGUT approx. µ = 4/3 mSUSY

~

h → τ µ FullA → τ µ Fullh → τ µ MIAA → τ µ MIA

Perturbativity works reasonably well within |δAB23 | ≤ O(1).

Roberto Morales 20/28

Equal masses scenario: form factors

Dominant contributions for each δ:

F(x)L,R = δLL23 F

(x)LLL,R + δLR23 F

(x)LRL,R + δRL23 F

(x)RLL,R + δRR23 F

(x)RRL,R

As in the generic scenario, for δLL23 we get

F(x)LLL =

g2

16π2

mτ

2MW

[σ

(x)2 + σ

(x)∗

1 tβ

cβ

]1− t2W

4

}ND

For δLR23 , δRL23 , δRR23 , strong cancellations produce

F(x)LRL =

gt2W16π2

1

24√

2

[σ

(x)∗

1

] m2Hx

m2S

F(x)RLR =

gt2W16π2

1

24√

2

[σ

(x)1

] m2Hx

m2S

F(x)RRR =− g2t2W

16π2

mτ

2MW

[2σ

(x)∗

2 + σ(x)1

120cβ

]m2Hx

m2S

D

Roberto Morales 21/28

Equal masses scenario: simplest effective vertices

The most relevant mixing for phenomenology is δLL23 .

For this case, we can write the dominant effective vertex −igV effHxτµPL

V effHxτµ

=g2

16π2

mτ

2MW

[σ

(x)2 + σ

(x)∗

1 tβ

cβ

](1− t2W

4

)δLL23

In the large tβ limit:

V effhτµ|tβ�1 = − g2

16π2

mτ

MW

M2Z

m2A

tβ

(1− t2W

4

)δLL23

V effHτµ|tβ�1 = −iV eff

Aτµ|tβ�1 = − g2

16π2

mτ

2MWt2β

(1− t2W

4

)δLL23

We deduce:

• For light Higgs: effective vertex suppressed by M2Z/m

2A (mA →∞, h is SM-like).

• For heavy Higgs: effective vertex enhanced by t2β (in agreement with [Brignole, Rossi;

2003])

Roberto Morales 22/28

Phenomenology

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20

30

40

50

60

mSUSY HTeVL

tanb

BRHhÆtmLê»d23LL 2

Equal masses 1.¥10-6

5.¥10-6

0.00001

0.00002

0.000030.00005

0.00007

0.0001

1 2 3 4 5

10

20

30

40

50

60

mSUSY HTeVLtanb

BRHAÆtmLê»d23LL 2

Equal masses

• Shaded pink area: excluded by BR(τ → µγ) < 4.4× 10−8.• Shaded blue area: excluded by negative searches by ATLAS and CMS of neutral MSSM

Higgs bosons decaying to tau pairs.

⇒ Maximum allowed rates are ∼ 5× 10−5 for H and A (below LHC sensitivity).

Roberto Morales 23/28

Phenomenology

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200 400 600 800 1000

10

20

30

40

50

60

mA HGeVL

tanb

BRHhÆtmLê»d23LL 2

Equal masses 1.¥10-6

0.00001

0.00005

0.0001

0.00015

0.00020.00025

0.00030.00035

200 400 600 800 1000

10

20

30

40

50

60

mA HGeVLtanb

BRHAÆtmLê»d23LL 2

Equal masses

• We can set mSUSY = 4 TeV (ND terms) −→ no constraints by τ → µγ.• Shaded blue area: excluded by negative searches by ATLAS and CMS of neutral MSSM

Higgs bosons decaying to tau pairs.

⇒ Maximum allowed rates are ∼ 3.5× 10−4 for H and A.Taking in account both channels τµ and τµ, BR∼ 10−3 closer to LHC sensitivity!

Roberto Morales 24/28

h,H,A→ τµ at LHC

• Shaded gray area: excluded by τ → µγ.

• Shaded blue area: excluded by negative searches by ATLAS and CMS.

⇒ Most promising for H and A: in the region tβ ∼ 40− 60, mA ∼ 900− 1000 GeV and

mSUSY > 4 TeV, for√s = 14 TeV and L ∼100 fb−1 we predict O(1-10) events.

Roberto Morales 25/28

Conclusions

• We performed a diagramatic computation of LFVHD within the MIA. We found simpleanalytical expressions for the form factors. They are very useful for phenomenology andcomparison with data.

• We compared MIA vs Full results: good agreement in most cases, in particular for theNon-Decopling terms (phenomenological important ones).

• Also, we compared with the effective vertices approach: in accordance with previousresults in the literature.

• We understood the BR behavior with the MSSM parameters tβ and mA.

• We concluded that H,A→ τµ are promising channels at the LHC.

Roberto Morales 26/28

Back-up

Roberto Morales 27/28

Subleading corrections: O(M2W/m

2SUSY)

10-20

10-18

10-16

10-14

10-12

10-10

10-8

5 10 15 20 25 30 35 40

BR(h

→ τµ

)

tan β

Equal massesmA = 800 GeV, mSUSY = 5 TeV, δ23

XY = 0.5M1 = M2 = µ = mL = mR = Aµ,τ = mSUSY

LL FullLL MIA

RR FullRR MIA

LR FullLR MIA

10-18

10-16

10-14

10-12

10-10

10-8

10-6

10-4

5 10 15 20 25 30 35 40

BR(A

→ τµ

)

tan β

Equal massesmA = 800 GeV, mSUSY = 5 TeV, δ23

XY = 0.5M1 = M2 = µ = mL = mR = Aµ,τ = mSUSY

LL FullLL MIA

RR FullRR MIA

LR FullLR MIA

F(x)RRR =

g2t2W16π2

mτ

2MW cβ

M2W

m2S

t2β

1 + t2β

[(σ(x)1

60

(3t

2W + 13− 4t

2W tβ − 12tβ

)

−σ(x)∗1

5−

4σ(x)2

15−

2σ(x)∗2

15+σ(x)3

√1 + t2β

12tβ

(1 + t

2W

)

+

1 + t2W60tβ

(−8σ

(x)1 + 4σ

(x)∗1 + σ

(x)2 + σ

(x)∗2

)+σ(x)3

√1 + t2β

12t2β

(−1 + 5t

2W

)+

(1 + t2W30t2β

(−σ(x)

1 + σ(x)∗1 + σ

(x)2 − σ(x)∗

2

))]Roberto Morales 28/28