is light pseudoscalar higgs still possible in so(10 ... · -0.04 -0.02 0.00 0.02 0.04 300 400 500...
TRANSCRIPT
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)
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 2 / 16
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
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 3 / 16
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.
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 4 / 16
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)
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 5 / 16
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.
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 6 / 16
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).
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 7 / 16
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)).
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 8 / 16
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
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 9 / 16
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.
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 10 / 16
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
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 11 / 16
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
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 12 / 16
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
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 13 / 16
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
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 14 / 16
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
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 15 / 16
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.
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 16 / 16