Electroweak symmetry breaking and cold dark matter from hidden sector technicolor
aa r X i v : . [ h e p - ph ] J a n November 1, 2018 4:26 WSPC/INSTRUCTION FILE icfp07˙pko
International Journal of Modern Physics Ac (cid:13)
World Scientific Publishing Company
Electroweak symmetry breaking and cold dark matter from hiddensector technicolors
PYUNGWON KO
School of Physics, Korea Institute for Advanced StudySeoul 130-722, [email protected]
Received Day Month YearRevised Day Month YearWe consider models with a vectorlike confining gauge theory in the hidden sector, anddemonstrate that the origin of the electroweak symmetry breaking (EWSB) is due to thedimensional transmutation in the hidden sector gauge theory, and the lightest mesonsin the hidden sector could be a good cold dark matter (CDM) candidate. There wouldbe more than one neutral Higgs-like scalar bosons, and they could decay mainly into theCDM pair, if that decay channel is kinemtically allowed.
Keywords : electroweak symmetry breaking; cold dark matter; technicolor; hidden sector.PACS numbers:
1. Introduction
Revealing the origin of the electroweak symmtry breaking (EWSB) is the mostpressing question in particle physics in the era of CERN Large Hadron Collider(LHC). Another important problem in particle astrophysics and cosmology is toidentify the nature of cold dark matter (CDM). Also there is a more speculativeissue about the existence of a new hidden sector, which is generic in supersymmetric(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 masslessQCD ? • What is the nature of CDM ? Is it possible to have all the global symmetryas accidental symmetries, as in the standard model (SM) ? • What would be the phenomenological consequences, if there is a hiddensector ?I will present models with a hidden sector where these seemingly unrelated questionsare in fact closely connected with each other. More details and complete list ofreferences can be found in Ref.s 1, 2. ovember 1, 2018 4:26 WSPC/INSTRUCTION FILE icfp07˙pko Pyungwon Ko
Let me remind you that there is a good old example, namely quantum chro-modynamics(QCD), where we can learn many lessons related with the issues listedabove. 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
QCD . In additionpions are stable if electroweak interactions are switched off. It would be nice if wecould have a model for EWSB in the same manner as the dimensional transmutationin QCD, and CDM is stable as pions are stable under strong interaction.The basic features of our models are the following. We assume a vectorlikeconfining gauge theory such as QCD or technicolor in the hidden sector, which wedub as hidden sector technicolor (hTC). Then dimensional transmutation will occurin the hidden sector, and this scale is transmitted to the SM by a messenger, andtriggers EWSB. And the lightest mesons in the hidden sector becomes a CDM.
2. Model I
Let us assume that there is a new strong interaction that is described by SU ( N h,C )guage theory with vectorlike quarks Q i and Q i with N h,f flavors, such as QCD withthe confinement scale Λ h . This scale is presumed to be higher than the electroweakscale by at least an order of magnitude. L hidden = − G µν G µν + N HF X k =1 Q k ( i D · γ − M k ) Q k (1)Then this new strong interaction will trigger chiral symmetry breaking due tononzero hQQi ≡ Λ H,χ . For illustration, we assume that there is an approximate SU (2) L × SU (2) R global symmetry in the hidden sector that breaks down to SU (2) V spontaneously. In the low energy limit of hTC, massless Nambu-Goldstone bosonswill appear, which are dubbed as hidden sector pion π h . Also there would be ascalar resonance like the ordinary σ , and we call it σ h , and ~π h and σ h will form SU (2) L × SU (2) R bidoublet (denoted as H ) and the low energy effective theorywill be the same as the Gelmann-Levy’s linear σ model, except that the mesons arein 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 V ( H , H ) = − µ ( H † H ) + λ H † H ) − µ ( H † H ) + λ H † H ) + λ ( H † H )( H † H ) + av σ h (2)This looks like the potential in the 2-Higgs doublet model, but there are importantdifferences. First, H is a SM singlet, not a SM doublet. W and Z get massesentirely from H VEV. And the a term is new in our model, and necessary togenerate the mass for the hidden sector pion. Note that the λ term connects the SMand the hidden sector, and originates from nonrenormalizable interactions betweentwo sectors, or by some messengers.ovember 1, 2018 4:26 WSPC/INSTRUCTION FILE icfp07˙pko Electroweak symmetry breaking and cold dark matter from hidden sector technicolor -4 -3 -2 -1
0 50 100 150 200 250 300 B r ( h ) m π h bb ττ ggcc γ Z γγ ss µµπ h π h tan β = 1m h = 120 GeVm H = 300 GeV 10 -4 -3 -2 -1
0 50 100 150 200 250 300 350 400 B r ( H ) m π h [GeV] hhWWZZbbgg ττπ h π h tan β = 1m h = 120 GeVm H = 300 GeV Fig. 1. Branching ratios of (a) h and (b) H as functions of m π h for tan β = 1, m h = 120 GeVand m H = 300 GeV. -54 -52 -50 -48 -46 -44 -42 -40
10 100 1000 σ ( π h N → π h N ) [ c m ] m π h [GeV] Ω h < 0.096 0.096 < Ω h < 0.122 CDMS II CDMS 2007 projectedXENON 10 2007XMASSsuper CDMS-1 ton [GeV] h π M ] [ c m S I σ -49 -46 -43 -40 -37 -34 < 0.096 h Ω ≤ h Ω ≤ = 1 TeV h v = 500 GeV h v Fig. 2. σ SI ( π h p → π h p ) as functions of m π h for (a) tan β = 1 in Model I, and (b) Model II. It is straightforward to analyze phenomenology from this scalar potential. Thegeneric predictions of our models are the following: • The origin of the EWSB, namely the negative Higgs mass parameter couldbe the chiral symmetry breaking in the hTC. • The electroweak precision test does not put strong constraints unlike in theordinary technicolor models, since H does not contribute to the W and Z masses at tree level. And no Higgs-mediated FCNC problem since H doesnot couple to the SM fermions. • There are more than one neutral Higgs-like scalar bosons, and they candecay into the π h with a large invisible branching ratio. This makes rela-tively difficult to produce and discover these Higgs-lilke neutral scalars atcolliders. See Fig. 1 (a) and (b). • The hidden sector pion ( π h ) is stable due to the flavor conservation in thehTC, and could be a good CDM candidate. Direct detection rate of the π h isin a promising sensitivity of the current/future DM detection experimentssuch as CDMS, XENON10 or XMASS (Fig. 2 (a)).ovember 1, 2018 4:26 WSPC/INSTRUCTION FILE icfp07˙pko Pyungwon Ko
3. Model II with classical scale invariance
The Model I has a few drawbacks, since the hidden sector quark masses M k ’sare given by hand, and the Model I is not renormalizable. These can be cured byintroducing a real singlet scalar S and making the following replacement, M k → λ k S in Eq. (1). Then L hidden has classical scale symmetry. With a real singlet S , the SMlagrangian is implemented into L SM = L kin + L Yukawa − λ H H † H ) − λ SH S H † H − λ S S (3)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 allthe 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 sectorquarks.Dimensional transmutation in the hidden sector will generate the hidden QCDscale and chiral symmetry breaking with developing nonzero h ¯ Q k Q k i . Then the λ k S term generate the linear potential for the real singlet S , leading to nonzero h S i . Thisin turn generates the hidden sector current quark masses through λ k terms as wellas the EWSB through λ SH term. The π h will get nonzero masses, and becomesa good CDM candidate. Due to the presence of the messenger S , the CDM pairannihilation into the SM particles occurs more efficiently in Model II than in ModelI, and it is easy to accommodate the WMAP data on Ω CDM h . Direct detectionrates are in the interesting ranges (see Fig. 2 (b)). All the qualitative features ofthis model is similar to the Model I. See Ref. 2 for more details.
4. Conclusions
In this talk, I presented models where the origin of EWSB and CDM lie in the hiddensector technicolor interaction. In the Model II, all the masses including the CDMmass arise quantum mechanically from dimensional transmutation in the hiddensector. One can enjoy many variations of these models by considering differentgauge groups and matter fields in the hidden sector. If we include the radiativecorrections to the scalar potential, the details could change, but the qualitativefeatures described in this talk would remain untouched.
Acknowledgments
I thank Dr. Chun Liu for invitation to this nicely organized conference. I am gratefulto Taeil Hur, D.W. Jung and J.Y. Lee for collaborations. This work is supported inpart by KOSEF through CHEP at Kyungpook National University.