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Register a new userFrom Higgs to pions and Back -- the Unbearable Lightness of a Composite Scalar Boson at 125 GeV in Purely Vectorial Theories
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Authors
Shmuel Nussinov
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We argue that the $125 GeV$ Higgs particle is unlikely to arise as a fermion- antifermion composite if the underlying dynamics is a vectorial gauge theory. The reason is that the lightest scalar in such theories is heavier than the lightest pseudo-scalar with the mass difference being fixed by the scale of the theory. LHC searches suggest that the scale of any new physics, including that of a putative new theory dynamically generating the 125 GeV Higgs particle, is relatively high $sim{(1/2TeV-1TeV)}$. Also the LHC analysis suggests that it is {it scalar} namely $J^P = 0^+$ rather than pseudo-scalar. Thus it is unlikely that the Higgs could arise as a composite in such theories- though it will arise in special cases when the underlying binding gauge group is real as a fermion-fermion bound state. The direct considerations of the various two point functions in the large $N_c$ limit presented below- suggest that massless pseudo-scalars, but not any other anomalously light meson, arise as composites of massless fermions say the massless u and $bar{d}$ quarks in QCD. These massless pions manifest the spontaneous breaking of the global axial symmetry in QCD with the pions being (pseudo) Nambu Goldstone Bosons. This offers a different insight into SXSB in QCD and most other confining non-abelian gauge vectorial gauge theory. Specifically we consider the euclidean two point functions $F_I|x-y|$ for asymptotic $|x-y|$ expressed as a sum over fermionic paths. We conjecture that for the pseudo-scalar two point function - and for that case only- self retracing paths and closely related paths make in this limit a positive, coherent and dominant contribution, a contribution which evades the generic asymptotic exponential fall-off and allows the lightest pseudoscalars to be massless. The same arguments imply that the scalars are very massive.
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Assuming that the 125 GeV particle observed at the LHC is a composite scalar and responsible for the electroweak gauge symmetry breaking, we consider the possibility that the bound state is generated by a non-Abelian gauge theory with dynamically generated gauge boson masses and a specific chiral symmetry breaking dynamics motivated by confinement. The scalar mass is computed with the use of the Bethe-Salpeter equation and its normalization condition as a function of the SU(N) group and the respective fermionic representation. If the fermions that form the composite state are in the fundamental representation of the SU(N) group, we can generate such light boson only for one specific number of fermions for each group. In the case of small groups, like SU(2) to SU(5), and two fermions in the adjoint representation we find that is quite improbable to generate such light composite scalar.
While the properties of the 125 GeV Higgs boson-like particle observed by the ATLAS and CMS collaborations are largely compatible with those predicted for the Standard Model state, significant deviations are present in some cases. We, therefore, test the viability of a Beyond the Standard Model scenario based on Supersymmetry, the CP-violating Next-to-Minimal Supersymmetric Standard Model, against the corresponding experimental observations. Namely, we identify possible model configurations in which one of its Higgs bosons is consistent with the LHC observation and evaluate the role of the explicit complex phases in both the mass and diphoton decay of such a Higgs boson. Through a detailed analysis of some benchmark points corresponding to each of these configurations, we highlight the impact of the CP-violating phases on the model predictions compared to the CP-conserving case.
We discuss NMSSM scenarios in which the lightest Higgs boson $h_1$ is consistent with the small LEP excess at about 98 GeV in $e^+e^- to Zh$ with $hto banti b$ and the heavier Higgs boson $h_2$ has the primary features of the LHC Higgs-like signals at 125 GeV, including an enhanced $gammagamma$ rate. Verification or falsification of the 98 GeV $h_1$ may be possible at the LHC during the 14 TeV run. The detection of the other NMSSM Higgs bosons at the LHC and future colliders is also discussed, as well as dark matter properties of the scenario under consideration.
We investigate the effects of messenger-matter mixing on the lightest CP-even Higgs boson mass m_h in gauge-mediated supersymmetry breaking models. It is shown that with such mixings m_h can be raised to about 125 GeV, even when the superparticles have sub-TeV masses, and when the gravitino has a cosmologically preferred sub-keV mass. In minimal gauge mediation without messenger-matter mixing, realizing m_h = 125 GeV would require multi-TeV SUSY spectrum. The increase in $m_h$ due to messenger-matter mixing is maximal in the case of messengers belonging to 10+bar{10} of SU(5) unification, while it is still significant when they belong to $5+bar{5}$ of SU(5). Our results are compatible with gauge coupling unification, perturbativity, and the unification of messenger Yukawa couplings. We embed these models into a grand unification framework with a U(1) flavor symmetry that addresses the fermion mass hierarchy and generates naturally large neutrino mixing angles. While SUSY mediated flavor changing processes are sufficiently suppressed in such an embedding, small new contributions to K^0-bar{K^0} mixing can resolve the apparent discrepancy in the CP asymmetry parameters sin2beta and epsilon_K.
The Composite Particles Model (CPM) is characterized by composite Higgs, composite top quark, cancelation of the scalar leading quadratic divergences, and a particular ground state such that top anti-top channel is neither attractive or repulsive at tree level at the Z pole mass. The radiatively generated scalar mass in 2D is m_H=sqrt((6m_t^2 -M_Z^2-2M_w^2)/3(1+{pi}/k))= 113 GeV/c^2,143 GeV/c^2,...,230 GeV/c^2 for k = 1,2,...infty. As first proposed by Nambu in the simplest models with dynamical mass generation and fermion condensate in 4D, one expects the Higgs mass on the order of twice the heaviest fermion mass. Hence, if this is applied to the CPM one could expect scalar mass dynamically generated by top constituent quarks and composite top quarks to be equal to 2 m_t/3 and 2m_t respectively. When Bose-Einstein statistics for kT cong M_W c^2 is applied to the two lowest energy states in 2D (113 GeV and 143 GeV) and 4D (115 GeV and 346 GeV), the CPM suggests physical Higgs mass equal to m_H cong 125 GeV/c^2 in both 2D and 4D.
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