Electroweak symmetry breaking and cold dark matter from hidden sector technicolor

0.32 MB·English

by  Pyungwon Ko

February 4, 2008 7:34 WSPC/INSTRUCTION FILE icfp07˙pko
International JournalofModernPhysicsA
(cid:13)c WorldScientificPublishingCompany
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2 Electroweak symmetry breaking and cold dark matter from hidden

n sector technicolors
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2 PYUNGWONKO
School of Physics, Korea Institute for Advanced Study

] Seoul 130-722, Korea
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[email protected]
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p ReceivedDayMonthYear
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We consider models with a vectorlike confining gauge theory in the hidden sector, and

1 demonstratethattheoriginoftheelectroweaksymmetrybreaking(EWSB)isduetothe
v dimensional transmutation in the hidden sector gauge theory, and the lightest mesons
4 in the hidden sector could be a good cold dark matter (CDM) candidate. There would
8 bemorethanoneneutralHiggs-likescalarbosons,andtheycoulddecaymainlyintothe
2 CDMpair,ifthatdecaychannel iskinemticallyallowed.
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. Keywords:electroweaksymmetrybreaking;colddarkmatter;technicolor;hiddensector.
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: 1. Introduction
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X Revealing the origin of the electroweak symmtry breaking (EWSB) is the most
r pressing question in particle physics in the era of CERN Large Hadron Collider
a
(LHC). Another important problem in particle astrophysics and cosmology is to
identify the nature of cold dark matter (CDM). Also there is a more speculative
issueabouttheexistenceofanewhiddensector,whichisgenericinsupersymmetric
(SUSY) model buildings or superstring theories.
In this talk, I would like to consider three seemingly unrelated questions:
• Can all the masses arise (mostly) from quantum mechanics, as in massless
QCD ?
• Whatisthe natureofCDM?Isitpossibletohaveallthe globalsymmetry
as accidental symmetries, as in the standard model (SM) ?
• What would be the phenomenological consequences, if there is a hidden
sector ?
Iwillpresentmodelswithahiddensectorwheretheseseeminglyunrelatedquestions
are in fact closely connected with each other. More details and complete list of
references can be found in Ref.s 1, 2.
1
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2 Pyungwon Ko
Let me remind you that there is a good old example, namely quantum chro-
modynamics(QCD), where we can learnmany lessons related with the issues listed
above. QCD has many nice features: renormalizability, asymptotic freedom, con-
finement and chiral symmetry breaking, dynamical generation of hadron masses,
natural hierarchy between the Planck scale and the QCD scale Λ . In addition
QCD
pions are stable if electroweak interactions are switched off. It would be nice if we
couldhaveamodelforEWSBinthesamemannerasthedimensionaltransmutation
in QCD, and CDM is stable as pions are stable under strong interaction.
The basic features of our models are the following. We assume a vectorlike
confining gauge theory such as QCD or technicolor in the hidden sector, which we
dubashiddensectortechnicolor(hTC).Thendimensionaltransmutationwilloccur
in the hidden sector, and this scale is transmitted to the SM by a messenger, and
triggers EWSB. And the lightest mesons in the hidden sector becomes a CDM.
2. Model I
Letusassumethatthereis anewstronginteractionthatisdescribedbySU(N )
h,C
guagetheorywithvectorlikequarksQ andQ withN flavors,suchasQCDwith
i i h,f
the confinement scaleΛ . This scale is presumedto be higher thanthe electroweak
h
scale by at least an order of magnitude.
1 NHF
Lhidden =− GµνGµν + X Qk(iD·γ−Mk)Qk (1)
4
k=1
Then this new strong interaction will trigger chiral symmetry breaking due to
nonzero hQQi ≡ Λ3 . For illustration, we assume that there is an approximate
H,χ
SU(2) ×SU(2) globalsymmetryinthehiddensectorthatbreaksdowntoSU(2)
L R V
spontaneously. In the low energy limit of hTC, massless Nambu-Goldstone bosons
will appear, which are dubbed as hidden sector pion π . Also there would be a
h
scalar resonance like the ordinary σ, and we call it σ , and ~π and σ will form
h h h
SU(2) ×SU(2) bidoublet (denoted as H ) and the low energy effective theory
L R 2
willbe the sameasthe Gelmann-Levy’slinearσ model,exceptthatthe mesonsare
in the hidden sector, so that SM singlets. They are all neutral.
The potential for the SM Higgs and the hidden sector H is given by
2
λ λ
V(H ,H )= −µ2(H†H )+ 1(H†H )2−µ2(H†H )+ 2(H†H )2
1 2 1 1 1 2 1 1 2 2 2 2 2 2
av3
+ λ (H†H )(H†H )+ 2σ (2)
3 1 1 2 2 2 h
This looks like the potential in the 2-Higgsdoublet model, but there areimportant
differences. First, H is a SM singlet, not a SM doublet. W and Z0 get masses
2
entirely from H VEV. And the a term is new in our model, and necessary to
1
generatethemassforthehiddensectorpion.Notethattheλ termconnectstheSM
3
and the hidden sector, and originatesfrom nonrenormalizableinteractions between
two sectors, or by some messengers.
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Electroweak symmetry breaking and cold dark matter from hidden sector technicolor 3
100 tan β = 1 bb 100 tan β = 1 hh
mmhH == 132000 GGeeVV mmhH == 132000 GGeeVV WZZW
10-1 ττ 10-1
gg
cc
Br(h) 10-2 Br(H) 10-2 πhπh
πhπh
10-3 γγZγ 10-3
ss
µµ bggb
10-4 10-4 ττ
0 50 100 150 200 250 300 0 50 100 150 200 250 300 350 400
mπh mπh [GeV]
Fig. 1. Branching ratios of (a) h and (b) H as functions of mπh for tanβ =1, mh =120 GeV
andmH =300GeV.
10-40 10-34
Ωh2 < 0.096
10-42 0.096 ≤ Ωh2 ≤ 0.122
2→πσπ N N) [cm] ( hh 1111100000-----5544420864 C0D.0M96XS E <2 N0ΩΩ0O 7hhCN 22pD <<rX1Mo0 M00j eS2..A01c0 t92IS0eI62Sd7 σ2][cmSI11110000----44436307 CXCXsuDEDMpNMMeArOSSS CN--SI2Dv1vI0(M0h0h2( 7 01S== 03p- 416 r51+ kot02 ogjTe0n-0cd0et )5eGV)deV
super CDMS-1 ton 10-49
10-54 10 100 1000 10 102 103
mπh [GeV] Mπh[GeV]
Fig.2. σSI(πhp→πhp)asfunctionsofmπh for(a)tanβ=1inModelI,and(b)ModelII.
It is straightforward to analyze phenomenology from this scalar potential. The
generic predictions of our models are the following:
• TheoriginoftheEWSB,namelythenegativeHiggsmass2 parametercould
be the chiral symmetry breaking in the hTC.
• Theelectroweakprecisiontestdoesnotputstrongconstraintsunlikeinthe
ordinarytechnicolormodels,sinceH doesnotcontributetotheW andZ0
2
masses attree level.And no Higgs-mediatedFCNC problem since H does
2
not couple to the SM fermions.
• There are more than one neutral Higgs-like scalar bosons, and they can
decay into the π with a large invisible branching ratio. This makes rela-
h
tively difficult to produce and discover these Higgs-lilke neutral scalars at
colliders. See Fig. 1 (a) and (b).
• The hidden sector pion (π ) is stable due to the flavor conservation in the
h
hTC,andcouldbeagoodCDMcandidate.Directdetectionrateoftheπ is
h
in a promising sensitivity of the current/future DM detection experiments
such as CDMS, XENON10 or XMASS (Fig. 2 (a)).
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4 Pyungwon Ko
3. Model II with classical scale invariance
The Model I has a few drawbacks, since the hidden sector quark masses M ’s
k
are given by hand, and the Model I is not renormalizable. These can be cured by
introducingarealsingletscalarSandmakingthefollowingreplacement,M →λ S
k k
inEq.(1).ThenL hasclassicalscalesymmetry.WitharealsingletS,theSM
hidden
lagrangianis implemented into
λ λ λ
L =L +L − H (H†H)2− SH S2 H†H − S S4 (3)
SM kin Yukawa
4 2 4
assuming classical scale symmetry. Since there are no mass parameters in this la-
grangain, this is a suitable starting point to investigate if it is possible to have all
the masses from quantum mechanical effects. Note that the real singlet scalar S
plays the role of messenger connecting the SM Higgs sector and the hidden sector
quarks.
Dimensional transmutation in the hidden sector will generate the hidden QCD
scaleandchiralsymmetrybreakingwithdevelopingnonzerohQ¯ Q i.Thentheλ S
k k k
termgeneratethelinearpotentialfortherealsingletS,leadingtononzerohSi.This
in turn generates the hidden sector current quark masses through λ terms as well
k
as the EWSB through λ term. The π will get nonzero masses, and becomes
SH h
a good CDM candidate. Due to the presence of the messenger S, the CDM pair
annihilationintotheSMparticlesoccursmoreefficientlyinModelIIthaninModel
I, and it is easy to accommodate the WMAP data on Ω h2. Direct detection
CDM
rates are in the interesting ranges (see Fig. 2 (b)). All the qualitative features of
this model is similar to the Model I. See Ref. 2 for more details.
4. Conclusions
Inthistalk,IpresentedmodelswheretheoriginofEWSBandCDMlieinthehidden
sector technicolor interaction. In the Model II, all the masses including the CDM
mass arise quantum mechanically from dimensional transmutation in the hidden
sector. One can enjoy many variations of these models by considering different
gauge groups and matter fields in the hidden sector. If we include the radiative
corrections to the scalar potential, the details could change, but the qualitative
features described in this talk would remain untouched.
Acknowledgments
IthankDr.ChunLiuforinvitationtothisnicelyorganizedconference.Iamgrateful
to TaeilHur,D.W. JungandJ.Y.Lee forcollaborations.Thisworkis supportedin
part by KOSEF through CHEP at Kyungpook National University.
References
1. T. Hur,D. W. Jung, P.Ko and J. Y.Lee, arXiv:0709.1218 [hep-ph].
2. T. Hur,D. W. Jung, P.Ko and J. Y.Lee, in preparation.