Low-lying scalars in an extended linearσmodel

Abstract

We formulate an extended linear σ model of a quarkonia nonet and a tetraquark nonet as well as a complex iso-singlet (glueball) by virtue of chiral symmetry SUL(3) × SUR(3) and UA(1) symmetry. In the linear realization formalism, we study the mass spectra and components of the low-lying scalars and pseudo scalars in this model. The mass matrices for physical staes are obtained and the glueball candidates are examined. We find that the model can accommodate the mass spectra of low-lying states quite well. Our fits indicate that the most glueball like scalar should be 2 GeV or higher while the glueball pseudoscalar is η(1756). We also examine the parameter region where the lightest iso-scalar f0(600) can be the glueball and quarkonia dominant but find such a parameter region may be confronted with the problem of the unbounded vacuum from below.PACS numbers: I. INTRODUCTIONThe pseudoscalar, vector and axial-vector as well as tensor mesons of light quarks have been well-understood in the naive quark model in terms of the chiral symmetry. Despite of its success, the naive quark model can not explain the scalar meson sector, which have the same quantum numbers as the vacuum. There are about 19 states which are twice more than the expectedqq nonet as in vector and tensor sectors, while the mass and decay pattern of these low-lying scalars are different from the expectation of the naive quark model. To understand the nature of these scalars has been the focus of recent studies e.g. see Refs. [1][2][3][4] and references therein.Among the low-lying scalar mesons, the lightest scalar f 0 (600) or σ attracts a lot of interests. It is widely believed that f 0 (600) is like the Higgs boson which plays a crucial role in the spontaneous chiral symmetry breaking. Confirmation of existence of the elusive f 0 (600) from ππ scattering processes settles down a controversy last for more than a few decades [2,5]. The πK scattering [6] and analysis from D decay D + → K − π + π − [7] revealed that κ should also exist. BES II also found such a κ like structure in J/Ψ decays [8]. Combined with the well determined sharp resonances, i.e. isoscalar f 0 (980) and isotriplet a(980) from ππ and πη as well as KK scattering processes, now it is accepted in literature that these low-lying scalar mesons (say less than 1 GeV) can be cast into a chiral nonet. The next important issue is what is the nature of this nonet.There are a couple of viewpoints on the nature of this nonet. For example,the tetraquark model [9] can explain the mass hierarchy and decay pattern of this nonet quite successfully and is further supported from other experimental data, like the photon-photon collision data, which prefer the tetraquark interpretation for the lowest scalar meson nonet [10] (where it is demonstrated that f 0 (980) should be a tetraquark dominant state with great details). An alternative interpretation is that this nonet is bound state of the meson-meson molecule [11]. In any way, this nonet challenges a self-consistent interpretation in the naive quark mod...

Soft drop groomed jet angularities at the LHC

“…Power corrections ∼ O(R 2 ) to Eq. (4) are generally expected to be small, even for a relatively large jet radius R ∼ 1, see for example Refs [7,44]. On the other hand, the advantages of working in the small-R limit are for example the possibility to define quark-gluon fractions perturbatively orderby-order in QCD through Eq.…”

Lepton-Jet Correlations in Deep Inelastic Scattering at the Electron-Ion Collider

“…In the process (1), soft gluon radiation associated with the jet will also contribute to the imbalance q ⊥ . This contribution depends on the jet size R [34][35][36][37], which we compute using the narrow jet approximation [38]. We also introduce a subtraction to define the soft factor associated with the jet,…”

Jet angularities in photoproduction at the Electron-Ion Collider

“…(3) holds up to power corrections of order O(R 2 ). It was found that these power corrections are typically small even for large values of the jet radius, both for inclusive jet cross sections as well as jet substructure observables [48,49]. The jet functions also have the advantage that one may directly calculate quark/gluon fractions beyond leading-order, and they allow for a convenient calculation of jet angularities at the EIC as discussed in the next section.…”