Äîêóìåíò âçÿò èç êýøà ïîèñêîâîé ìàøèíû. Àäðåñ îðèãèíàëüíîãî äîêóìåíòà : http://qfthep.sinp.msu.ru/talks/nevzorov-qfthep2010.pdf Äàòà èçìåíåíèÿ: Tue Sep 7 17:04:22 2010 Äàòà èíäåêñèðîâàíèÿ: Mon Oct 1 19:47:50 2012 Êîäèðîâêà:

Nonstandard Higgs decays in the E6SSM
Roman Nevzorov University of Hawaii, USA & ITEP, Moscow, Russia

in collaboration with J. Hall, S. F. King, S. Pakvasa and M. Sher

QFTHEP-2010, Golitsino, Moscow region, Russia, 8-15 September 2010 ­ p. 1/25


Outline
Introduction Exceptional SUSY model Iner t charginos and neutralinos Exotic Higgs decays Conclusions

Based on:
J. S. S. S. Hall, F. Ki F. Ki F. Ki S. ng, ng, ng, F. King, R. S. Moretti S. Moretti S. Moretti Nevzor and R. and R. and R. ov, S. Pakvasa and M. Sher, in preparation; Nevzorov, Phys. Lett. B 650 (2007) 57; Nevzorov, Phys. Rev. D 73 (2006) 035009; Nevzorov, Phys. Lett. B 634 (2006) 278.

QFTHEP-2010, Golitsino, Moscow region, Russia, 8-15 September 2010 ­ p. 2/25


Introduction
SUSY leads to a par tial unification of the SM gauge interactions with gravity within SUGRA models. But MSSM being incorporated in supergravity or GUTs suffers from the µ problem. Indeed
W
S U GRA

^^ ^^ ^ ^^ ^ W0 (hm ) + µ(hm )(Hd Hu ) + ht (QHu )uc + hb (QHd )dc + ...,

where µ(hm ) MP l or µ(hm ) = 0. The correct pattern of EW symmetry breaking requires
µ(hm ) 100 - 1000 GeV .

In the superstring inspired E6 models gauge symmetry forbids any bilinear terms in W allowing interaction
W
E
6

^^^ = S (Hd Hu ) + ... .

QFTHEP-2010, Golitsino, Moscow region, Russia, 8-15 September 2010 ­ p. 3/25


At high energies E6 may be broken to
E6 S U (3)C â S U (2)W â U (1)Y â U (1) , U (1) = U (1) cos + U (1) sin ,
where E6 S O(10) â U (1) , S O(10) S U (5) â U (1) .

= arctan 15 corresponds to U (1)N symmetr y under which right-handed neutrinos have zero charge.



Only in this exceptional SUSY model (E6 SSM) right­handed neutrino may be superheavy shedding light on the origin of lepton mass hierarchy. At the EW scale field S acquires VEV breaking U (1)N and providing natural solution of the µ­problem µef f = < S > .

QFTHEP-2010, Golitsino, Moscow region, Russia, 8-15 September 2010 ­ p. 4/25


Exceptional SUSY model
To ensure anomaly cancellation the par ticle content of the E6 SSM is extended to include three complete 27i representations of E6 . In addition the spectrum of the E6 SSM is supplemented by S U (2) doublet and anti-doublet from extra 27 and 27 (L4 and L4 ) to preserve gauge coupling unification in the one­loop approximation. Together with survivors the par ticle content of the E6 SSM becomes
c 3 â 27i + L4 + L4 = 3 Qi , uc , di , Li , ec + 3(Di , Di )+ i i

+3(Hiu ) + 3(Hid ) + 3(Si ) + 3(Nic ) + L4 + L4 .
Di and Di are exotic quarks. Hid and Hiu are either Higgs or iner t Higgs fields.

QFTHEP-2010, Golitsino, Moscow region, Russia, 8-15 September 2010 ­ p. 5/25


In the E6 SSM two­loop corrections to i (µ) are large and could spoil gauge coupling unification. However it was argued that within the E6 SSM gauge coupling unification can be achieved for any value of 3 (MZ ) which is in agreement with current data [S.F.King, S.Moretti, RN, Phys.Lett.B 650 (2007) 57].
Two­loop RG flow of i (µ) in the E6 SSM and MSSM
0.14 0.12 0.1 0.08 0.06 0.04 0.02 -60 -50 -40 -30 -20 -10 0 0.14 0.12 0.1 0.08 0.06 0.04 0.02 -60 -50 -40 -30 -20 -10 0

2 log[µ/MX ]

2 log[µ/MX ]

QFTHEP-2010, Golitsino, Moscow region, Russia, 8-15 September 2010 ­ p. 6/25


To prevent rapid proton decay the invariance under some discrete symmetry should be imposed. To suppress baryon number violating and flavour H changing processes one can postulate Z2 symmetry under which all superfields except Hd H1,3 , Hu H and S S3 are odd. H The Z2 symmetry reduces the structure of Yukawa interactions to:
W
E6 SSM

2,3

~^^ +f S (H

^^^ S (H u H d ) +
d

^ +h4j (H

u

^ ^d ^u ^^^ ^ ^^ S (H H ) + i S (Di Di ) + f S (Hd H 1 ^ ^ ^c ^^ ^ ^^ Hu ) + hEj (Hd L4 )ec + µ (L4 L4 ) + Mij Nic Nj 4 j 2 ^ ^c ^ ^ ^c L4 )Nj + hij (Hu Li )Nj + WM S S M (µ = 0) ,

u

where , = 1, 2 and i = 1, 2, 3 . ^^ ^ Hu , Hd and S play the role of Higgs superfields.

QFTHEP-2010, Golitsino, Moscow region, Russia, 8-15 September 2010 ­ p. 7/25


s v1 v2 At the physical vacuum Hd = , Hu = , S = , 2 2 2 2 2 where v 2 = v1 + v2 = (246 GeV )2 and tan = v2 /v1 .

At the tree level CP is preserved in the Higgs sector of the E6 SSM so that the Higgs spectrum contains
­ one pseudoscalar ­ two charged states ­ three scalars m2 , A
2 m2 ± = m2 + O(MZ ) , A H 2 Z


2 m2 3 = m2 + O(MZ ), m2 2 = M A h h

2 + O (M Z ) .

The upper limit on the lightest Higgs mass mh1 in the E6 SSM is considerably larger than in the MSSM and NMSSM. In the two­loop approximation the upper bound on m does not exceed 150 - 155 GeV.
h
1

QFTHEP-2010, Golitsino, Moscow region, Russia, 8-15 September 2010 ­ p. 8/25


H The Z2 symmetry can only be approximate since it ensures that the lightest exotic quark is stable.

If D­quarks were stable they would be confined in heavy hadrons which relative concentrations would be 10-10 per nucleon. The experimental limits on the abundances of such stable relics vary from 10-15 to 10-30 per nucleon [T.K. Hemmick et al. Phys.Rev.D 41 (1990) 2074.]

,

There are two different ways to impose an appropriate Z2 symmetr y leading to the bar yon and lepton number conservation which imply
­ exotic quarks are diquarks, i.e. BD
,D

= 2/3 ;
,D

­ exotic quarks are leptoquarks, i.e. BD

= ±1/3, LD

,D

= ±1 .

QFTHEP-2010, Golitsino, Moscow region, Russia, 8-15 September 2010 ­ p. 9/25


The terms which allow D and D to decay are given by
Q q W1 = gij k Di (Qj Qk ) + gij k Di dc uc . jk

if exotic quarks are diquarks and
E D W2 = gij k ec Dj uc + gij k (Qi Lj )Dk , i k

if exotic quarks are leptoquarks.

Since Z

H 2

symmetry violating operators give rise to
0

In the E6 SSM lepton asymmetry can be dynamically c generated via the decay of N1 and then gets conver ted into baryon asymmetry due to sphaleron interactions.

FCNC processes (K 0 - K oscillations, µ e- e+ e- and etc.) the corresponding Yukawa couplings are expected to be small ( 10-4 - 10-3 ).

QFTHEP-2010, Golitsino, Moscow region, Russia, 8-15 September 2010 ­ p. 10/25


New exotic par ticles predicted by the E6 SSM contribute to the generation of lepton asymmetry. In the E6 SSM the substantial lepton CP asymmetries can be induced even for M1 106 GeV that may allow to avoid gravitino problem [S.King,R.Luo,D.Miller,RN, JHEP 12 (2008) 042]. New par ticles may be produced at future colliders. At the LHC the Z boson can be discovered if it has a mass below 4 - 4.5 TeV [A.Leike, Phys.Rept. 317 (1999) 143; J.Kang, P.Langacker, Phys.Rev.D 71 (2005) 035014].
Diagrams that contribute to the generation of lepton asymmetr y
H N
~ L N
1

u i

L N
1

y

H N H
u k j

u i

L N
1

y

H N
j

u i

1

L
y

L

x

x

H

u k

L
~ dk H
u i

x

H N ~ H
u k j

u i

~ L N
1

y

H ~ Nj

u i

d N
1

k

H N ~ Dl
j

u i

L

x

~ H

u k

N

1

N Dl

j

L

x

L

x

L

x

QFTHEP-2010, Golitsino, Moscow region, Russia, 8-15 September 2010 ­ p. 11/25


If exotic quarks are light their production cross section ¯ at the LHC can be comparable with (pp tt + X ). Assuming that D and D couple most strongly with the third family quarks and leptons light exotic quark will result in the enhancement of the cross sections of
m pp ttbb + ET iss + X if exotic quarks are diquarks; m pp ttll + ET iss + X if new quark states are leptoquarks.

Cross sections for pair production of exotic par ticles at the LHC

QFTHEP-2010, Golitsino, Moscow region, Russia, 8-15 September 2010 ­ p. 12/25


Inert charginos and neutralinos
H In our analysis we assume that Z2 symmetry violating couplings are small and can be neglected so that neutralino and Iner t neutralino states as well as chargino and Iner t chargino states do not mix. ~d ~u ~ ~d ~u ~ In the field basis (H2 0 , H2 0 , S2 , H1 0 , H1 0 , S1 ) the mass matrix of the Iner t neutralino sector takes a form

M

IN

A

1 = - 2



A2 = A1 0 s



2 2

A21 , A11


s

~ f v sin f




0

~ f v sin f v cos

v cos , 0



QFTHEP-2010, Golitsino, Moscow region, Russia, 8-15 September 2010 ­ p. 13/25


In the basis of Iner t chargino interaction states ~d ~d ~u ~u (H2 + , H1 + , H2 - , H1 - ) the corresponding mass matrix is given by
M
IC

0 CT = , C0

1 C = 2



s.

We require
all Iner t charginos to be heavier than 100 GeV to satisfy LEP constraints; s to be large enough to avoid lower experimental bound on MZ 860 GeV (s 2400 GeV); the validity of per turbation theory up to the GUT scale that constrains the allowed range of all Yukawa couplings.

QFTHEP-2010, Golitsino, Moscow region, Russia, 8-15 September 2010 ­ p. 14/25


Our numerical analysis indicates that
the lightest and second lightest Iner t neutralinos are always light (m1 , 2 60 - 65 GeV); two lightest Iner t neutralinos are predominantly Iner t singlinos; four other Iner t neutralinos, which are basically linear superpositions of neutral components of Iner t Higgsinos, are normally heavier than 100 GeV; the lightest and second lightest Iner t neutralinos may have rather small couplings to Z -boson so that they could escape detection at LEP; the couplings of the two lightest Iner t neutralinos to the SM-like Higgs boson are always large if they have appreciable masses.

QFTHEP-2010, Golitsino, Moscow region, Russia, 8-15 September 2010 ­ p. 15/25


In order to clarify the obtained results let us consider a simple scenario when



=



,

f = f



,

~ ~ f = f



.

In the considered case the mass matrix of Iner t neutralinos becomes block diagonal while the masses of the Iner t charginos are given by
m± = s. 2

~ In the limit when s f v , f v the mass matrix of the Iner t neutralinos can be approximately diagonalised.

The masses of four heaviest Iner t neutralino states are
m± ~ f f v 2 sin 2 - , 4m± -m± ~ f f v 2 sin 2 - . 4m±

QFTHEP-2010, Golitsino, Moscow region, Russia, 8-15 September 2010 ­ p. 16/25


The masses of four heaviest Iner t neutralinos are set by the masses of Iner t chargino states. The masses of two lightest Iner t neutralinos are
m ~ f f v 2 sin 2 . 2m±

The masses of the lightest Iner t neutralino states decrease with increasing tan and chargino masses. They are determined by the values of the Yukawa couplings ~ f and f . The requirement of validity of per turbation theory up to the ~ GUT scale sets stringent bounds on f and f . In the simplest case ~ ~ f1 = f1 = f2 = f2 < 0.6 - 0.65 .

QFTHEP-2010, Golitsino, Moscow region, Russia, 8-15 September 2010 ­ p. 17/25


Since the masses of the two lightest Iner t neutralinos are determined by v the couplings of these states to the SM-like Higgs boson are set by their masses, i.e. gh m /v . The Lagrangian that describes interactions of the Z-boson with 1 and 2 can be written as
g ¯ LZ = Zµ µ 5 RZ , 4 v2 2 ~2 RZ = RZ = RZ , f cos2 - f sin2 . 2m2 ± ~ and f can be chosen so that RZ become Couplings f rather small. RZ are always small when Iner t charginos are rather ~ heavy or f and f are small (m 0).

QFTHEP-2010, Golitsino, Moscow region, Russia, 8-15 September 2010 ­ p. 18/25


Exotic Higgs decays
Since in the E6 SSM the lightest Iner t neutralino has mass which is less than 60 GeV it tends to be the LSP, that forms dark matter in the Universe. We restrict our consideration by the scenarios that result in the dark matter density which is not greater than the observed one: C DM h2 = 0.1099 ± 0.0062. This requires annihilation cross-section of (1 1 any thing ) to be large enough.
1

When m1 MZ /2 the lightest Iner t neutralino has rather small couplings and (1 1 any thing ) is too small leading to the extremely large value of h2 . The reasonable dark matter density can be obtained for m1 MZ /2 when the s-channel annihilation through the Z-boson is the dominant annihilation channel.

QFTHEP-2010, Golitsino, Moscow region, Russia, 8-15 September 2010 ­ p. 19/25


This scenario implies that two lightest Iner t neutralinos have large couplings to the SM-like Higgs boson. As a result the lightest Higgs boson in the E6 SSM decays predominantly into 1 1 and 2 2 whereas the branching ratios of ordinary Higgs decays are small. ¯ Since 2 1 + f f the decays of the lightest Higgs boson into l+ l- + X might be observed at the LHC if m2 - m1 is large enough.

The considered scenario is realized only when ± , 3 1 and 4 have masses below 200 GeV and tan is close to 1.5 (tan < 2). So light Iner t chargino and neutralino states, which are predominantly Iner t Higgsinos, can be discovered at the LHC in the nearest future.

QFTHEP-2010, Golitsino, Moscow region, Russia, 8-15 September 2010 ­ p. 20/25


Benchmark point A (All mass parameters are given in GeV):
Parameters : tan = 1.5, m
Q,U

s = 2400,

= MS = 700,

22

= 0.094,

f11 = f22 Spectrum: m m Couplings : h
2 ± 2 ± 1

11 = 0.059, 12 = 21 = 0, ~ ~ ~ ~ = f11 = f22 = 0.53, f12 = f21 = f12 = f21 = 0.053. m6 201.7, RZ m5 162.0,
2

= ki = g1 = 0.468, A = 600, Xt = 6MS , mh1 116,

159.5, 100.1,

m4 152.7, m1 35.42, -0.288,

m3 105.3, m
1 2

51.77, RZ
2 2

R

Z 1 1

-0.115,

0.091,

0.107, B r(h1 2 2 ) 20.3%, B r(h1 ) 0.30%, ¯ B r(h1 2 1 ) 0.25%, B r(h1 1 1 ) 76.3%, B r(h1 b¯) 2.82%, b
ot

Higgs Decay rates:

t

0.0817.

QFTHEP-2010, Golitsino, Moscow region, Russia, 8-15 September 2010 ­ p. 21/25


Benchmark point B (All mass parameters are given in GeV):
Parameters : tan = 1.5, m
Q,U

s = 2400,

= MS = 700,
11

22

=

f11 = f22 Spectrum: m m Couplings : h
2 ± 2 ± 1

= 0.001, 12 = 21 = 0.095, f12 = f21 = 0.69, ~ ~ ~ ~ = f11 = f22 = 0.001, f12 = f21 = 0.49. m6 208.4, RZ m5 205.4,
2

= ki = g1 = 0.468, A = 600, Xt = 6MS , mh1 116,

162.9, 159.5,

m4 163.0, m1 45.44,

m3 159.6, m
1 2

45.80, RZ
2 2

R

Z 1 1

-0.0203,

0,

-0.0206,

0.1017, B r(h1 2 2 ) 48.0%, B r(h1 2 1 ) 0%, B r(h1 ) 0.24%, ¯ B r(h1 1 1 ) 49.5%, B r(h1 b¯) 2.25%, b t
ot

Higgs Decay rates:

0.102.

QFTHEP-2010, Golitsino, Moscow region, Russia, 8-15 September 2010 ­ p. 22/25


Benchmark point C (All mass parameters are given in GeV):
Parameters : tan = 1.5, m
Q,U

s = 2400,

= MS = 700,
11

22

=

f11 = f22 Spectrum: m m Couplings : h
2 ± 2 ± 1

= 0.001, 12 = 21 = 0.08, f12 = f21 = 0.68, ~ ~ ~ ~ = f11 = f22 = 0.04, f12 = f21 = 0.49. m6 192.9, RZ m5 179.0,
2

= ki = g1 = 0.468, A = 600, Xt = 6MS , mh1 116,

137.5, 134.1,

m4 137.7, m1 44.91,

m3 134.1, m
1 2

55.15, RZ
2 2

R

Z 1 1

-0.0214,

0,

-0.0517,

0.0312, B r(h1 2 2 ) 13.3%, B r(h1 2 1 ) 0%, B r(h1 ) 0.41%, ¯ B r(h1 1 1 ) 82.5%, B r(h1 b¯) 3.84%, b t
ot

Higgs Decay rates:

0.060.

QFTHEP-2010, Golitsino, Moscow region, Russia, 8-15 September 2010 ­ p. 23/25


Benchmark point D (All mass parameters are given in GeV):
Parameters :
= ki = g1 = 0.468, A = 600, mQ,U = MS = 700, Xt = 6MS , mh1 116, ~ 22 = 0.468, 11 = 0.08, 12 = 21 = 0.05, f11 = 0.65, ~ ~ ~ f11 = f12 = f21 = f22 = 0.002, f22 = f12 = 0.05, f21 = 0.9,

tan = 1.5,

s = 2400,

Spectrum:

m m

± 2 ± 1

805.0, 125.0,

m6 805.4, RZ

m5 805.4,
2

m4 171.4, m1 46.24,
2 2

m3 171.1, m
1 2

46.60, RZ

Couplings : h
2

R

Z 1 1

-0.0224,

-0.426,

-0.0226,

0.00005, B r(h1 2 2 ) 47.9%, B r(h1 2 1 ) 0, B r(h1 ) 0.27%, ¯ B r(h1 1 1 ) 49.3%, B r(h1 b¯) 2.56%, b t
ot

Higgs Decay rates:

0.0898.

QFTHEP-2010, Golitsino, Moscow region, Russia, 8-15 September 2010 ­ p. 24/25


Conclusions
The E6 SSM leads to the presence of two light Iner t neutralinos with masses below 60-65 GeV that tend to be the lightest SUSY par ticles in the spectrum. The lightest Iner t neutralino with mass MZ /2 can play the role of dark matter. In this case the lightest Higgs boson decays into 1 and 2 2 mainly while the total branching ratio of its decays into SM par ticles varies from 2% to 4%.
1

This scenario implies the presence of relatively light Iner t chargino and neutralino states with masses below 200 GeV that can be discovered at the LHC. In the considered case the decays of the lightest Higgs boson into l+ l- + X might play an essential role in the Higgs searches.

QFTHEP-2010, Golitsino, Moscow region, Russia, 8-15 September 2010 ­ p. 25/25