is light pseudoscalar higgs still possible in so(10 ... · -0.04 -0.02 0.00 0.02 0.04 300 400 500...

Is light pseudoscalar Higgs still possible in SO(10)motivated MSSM with large tan 𝛽?

Peter Matak,Tomas Blazek

Comenius University in Bratislava

26.11.2011

Peter Matak,Tomas Blazek (Comenius University in Bratislava)Is light pseudoscalar Higgs still possible in SO(10) motivated MSSM with large tan 𝛽?26.11.2011 1 / 16

Why supersymmetry?

Protect the higgs self-energy from quadratic divergent terms.

f

h0 h0 +

f

h0 h0

𝛿𝑚2 =𝜆𝑓

16𝜋2Λ2𝑈𝑉 −

𝜆2𝑓

16𝜋2Λ2𝑈𝑉 + ... . 1TeV (1)


MSSM - second Higgs doublet

SUSY does not allow complex conjugation of scalar fields in Yukawa terms. Thisforces us to introduce second higgs doublet. Second higgs doublet is also welcomedue to the gauge anomaly cancelation.

ℒ𝑆𝑀𝑌 𝑢𝑘𝑎𝑤𝑎 = −𝛿𝑖𝑗𝑢

𝑐𝑌𝑢𝑄𝑗𝐻𝑖* − ... −→ ℒ𝑀𝑆𝑆𝑀

𝑌 𝑢𝑘𝑎𝑤𝑎 = −𝜖𝑖𝑗𝑢𝑐𝑌𝑢𝑄

𝑗𝐻𝑖𝑢 − ... (2)

𝐻𝑑 =

(𝐻0

𝑑

𝐻−𝑑

)=

(𝑣𝑑 + 1√

2(𝐻0𝑐𝛼 − ℎ0𝑠𝛼 + 𝑖𝐴0𝑠𝛽 − 𝑖𝐺0𝑐𝛽)

𝐻−𝑠𝛽 −𝐺−𝑐𝛽

)(3)

𝐻𝑢 =

(𝐻+

𝑢

𝐻0𝑢

)=

(𝐻+𝑐𝛽 + 𝐺+𝑠𝛽

𝑣𝑢 + 1√2(𝐻0𝑠𝛼 + ℎ0𝑐𝛼 + 𝑖𝐴0𝑐𝛽 + 𝑖𝐺0𝑠𝛽)

)(4)

tan𝛽def=

𝑣𝑢𝑣𝑑

GUT : 𝑦𝑏 ≈ 𝑦𝑡 ⇒ tan𝛽 ≈ 50


Why 𝐵0𝑠 → 𝜇+𝜇−?

In the SM, the flavour changing amplitudes are small. In the SM exensions,their values can be enlarged up to several orders due to extended Higgs sector(large values of tan𝛽). The branching ratio of the 𝐵0

𝑠 → 𝜇+𝜇− process isproportional to the tan6 𝛽.

SM gives branching ratio ℬ(𝐵0𝑠 → 𝜇+𝜇−) = (3.1 ± 1.4) × 10−9 (C.Bobeth,

T.Ewerth, F.Kruger, J.Urban Phys. Rev. D64 (2001)). Experimental boundis ℬ(𝐵0

𝑠 → 𝜇+𝜇−) < 1.1 × 10−8 at 95% CL (LHCb-CONF-2011-047, CMSPAS BPH-11-019).

In the 𝐵0𝑠 → 𝜇+𝜇− process, the renormalization effects (running of the

Wilson coefficients from the electroweak scale to 5 GeV) do not playsignificant role. (A.J.Buras, 1998)

No sign of squarks and gluinos in hadronic jets at LHC...

...but plenty of 𝐵0𝑠 ’s produced.

𝐵0𝑠 → 𝜇+𝜇− can be one of the first signals of the beyond Standard Model

physics.


Sources of the flavour violation

Cabibbo - Kobayashi - Maskawa mixing matrix (Minimal Flavour Violation)

Off-diagonal elements of the squark mass matrix

ℒ𝑚𝑎𝑠𝑠 = . . .−(𝑞†𝐿 𝑞†𝑅

)( ℳ2𝑞,𝐿𝐿 ℳ2

𝑞,𝐿𝑅

ℳ2𝑞,𝑅𝐿 ℳ2

𝑞,𝑅𝑅

)(𝑞𝐿𝑞𝑅

). . . (5)

��𝛼 = 𝑍†𝑢

(��𝐿

��𝑅

), 𝑑𝛼 = 𝑍*

𝑑

(𝑑𝐿𝑑𝑅

)(6)


Relevant mass insertions

Possible off-diagonal elements are often parametrized as

(𝛿𝑞,𝑋𝑌 )𝐽𝐼 =(∆ℳ2

𝑞,𝑋𝑌 )𝐽𝐼

��2𝑞

. (7)

Left-handed squarks ��𝐿, 𝑑𝐿 are members of the same 𝑆𝑈(2)-doublet, hence

ℳ2��,𝐿𝐿 = 𝑉𝐶𝐾𝑀ℳ2

𝑑,𝐿𝐿𝑉 †𝐶𝐾𝑀 . (8)

Mass matrix has to be unitary: ℳ2𝑞 = (ℳ2

𝑞)†.

⇒ For the 𝐵0𝑠 decay only 𝛿23��,𝐿𝐿, 𝛿

23��,𝑅𝑅, 𝛿

23��,𝐿𝑅, 𝛿

32��,𝐿𝑅, 𝛿

23𝑑,𝑅𝑅

, 𝛿23𝑑,𝐿𝑅

, 𝛿32𝑑,𝐿𝑅

are

relevant.


Structure of penguin diagrams for 𝐵0𝑠 → 𝜇+𝜇−

µ+ µ+µ− µ−

A0 A0

s sb b1PI

Z1/2bs

In the large tan𝛽 region, dominant contribution to the 𝐵0𝑠 → 𝜇+𝜇− comes from

Higgs penguin diagrams - 1PI vertex corrections and 𝑍1/2-factors (LSZ reduction).


Dominant contributions to 𝑏− 𝑠− 𝐴0 vertex

b

s

A0 A0 A0

s s

b b

= +χ

u

u

d

d

g ±

± i sin β√2vd χ

b

s

u± i sin β√

2vd

b

s

g d

’Chargino’ diagrams due to extra tan𝛽.

’Gluino’ diagrams due to strong coupling - only in the NMFV case(P.H.Chankowski, L.Slawianowska (2000)).


In our numerical analyses we used following values of SUSY parameters

tan𝛽 𝑀2 𝑀3 𝜇50 600 GeV 2 TeV 110 GeV

𝑚𝑄1 𝑚𝑄3 𝑚𝑢1 𝑚𝑢3

500 GeV 300 GeV 500 GeV 200 GeV

𝑚𝑑1 𝑚𝑑3 𝐴 𝑓𝐵500 GeV 180 GeV -300 GeV 210 MeV


Light pseudoscalar Higgs scenario

Thanks to the Higgs propagator all the considered diagrams depend on theHiggs mass as ∝ 𝑚−2.

In the MFV the Minimal Supersymmetric Standard Model predicts too largedecay rate of the 𝐵0

𝑠 → 𝜇+𝜇− decay. We can solve this by putting𝑚𝐴0 & 800GeV.

In our work we study the allowed MSSM parameter space where non-minimalflavour violation (𝛿23��,𝐿𝑅, . . .) significantly affect the CKM contribution andreduces it, so that lower values of the pseudoscalar higgs mass can be OK inthe 𝐵0

𝑠 → 𝜇+𝜇− amplitude.


𝑚𝐴0 − 𝛿23𝑢,𝐿𝐿

1.´10-8

2.5´10-

3.´10-8

3.5´10-8

4.´10

-0.04 -0.02 0.00 0.02 0.04300

400

500

600

700

∆uLL

23

mA0HG

eVL


𝑚𝐴0 − 𝛿23𝑢,𝐿𝑅

1.5´10-8

2.´10-8

2.5´10-8

3.´10-8

3.5´10-8

4.´10-8

-0.04 -0.02 0.00 0.02 0.04450

500

550

600

650

700

∆uLR

23

mA0HG

eVL


𝑚𝐴0 − 𝛿23𝑑,𝐿𝑅

5.´10-9

5.´10-9

1.´10-8

1.5´10-8

1.5´10-8

2.´10-8

2.5´10-8

2.5´

3.´10-8

3.5´10-8

4.´10-8

4.´10

-0.015-0.010-0.005 0.000 0.005 0.010 0.015200

300

400

500

600

700

∆dLR

23

mA0HG

eVL


𝑚𝐴0 − 𝛿32𝑑,𝐿𝑅

5.´10-9

´10-8

1.´10-8

1.5´10-8

2.´10-8

2.5´10-8

3.´10-8

3.´10-8

10-8

3.5´10-8

10-8

4.´10-8

-0.015-0.010-0.005 0.000 0.005 0.010 0.015200

300

400

500

600

700

∆dLR

32

mA0HG

eVL


𝑚𝐴0 − 𝛿23𝑑,𝑅𝑅

´10-8

1.5´10-8

2.5´10-8

3.´10-8

3.5´10-8

´10-8

-0.04 -0.02 0.00 0.02 0.04300

400

500

600

700

∆dRR

23

mA0HG

eVL


Conclusion

Conclusions

In the MSSM with large value of tan𝛽 the light pseudoscalar higgs 𝐴0 is stillallowed.

For suppression of the large CKM matrix contribution off-diagonal massinsertions in the squark mass matrices can be used.


is light pseudoscalar higgs still possible in so(10 ... · -0.04 -0.02 0.00 0.02 0.04 300 400 500...

Documents