Remarks on mass difference between the charged and neutral K*(892) 高 道 能 ICTS, USTC 2017年11月24日-26日， 滁州

Outline Experimental data and motivation Theoretical model analysis Discussions and remarks

Experimental data and motivation At low energies, strong dynamics is dominated by the low-lying mesons like with Chiral pertubation theory

SU(3) vector multiplets: neutral charged In the limit of isospin symmetry, both of neutral and charged particles have equal mass. 矢量介子K*(892)是迄今为止很少的几个实验上测出其同位旋分量间质量劈裂的共振态粒子。

Mass splitting Experimentally, as shown in Particle Data Group 2016: These are some quite old measurements, which have not been updated since PDG 1980. Such measurements, called as direct measurements, are based on the simultaneous production of both charged and neutral K*(892) in the same final states.

 M. Aguilar-Benitez et al.,  Nucl. Phys. B141 (1978) 101 The average value: No systematical error provided

On the other hand, different from the above direct measurements, Particle Data Group also gives the observed values of the neutral and charged K*(892) separately.

No systematical error provided

If combining with the results from the direct measurement, which is also from the hadronic processes, and as a conservation estimation, we may expect that the experimental value of the mass splitting of K*(892) is This indicates a large mass difference. However, this is not the end of the story; PDG 2006 and before …

decay in which the charged K*(892) In 2007 Belle Collaboration reported a precise measurement of the charged K*(892) mass (Belle Collaboration, Phys. Lett. B 654 (2007) 65) by studying decay in which the charged K*(892) can be reconstructed from the final state. This is significantly different from the previous world average value given by PDG extracted from the hadronic processes. Thus, we have It seems that the large mass splitting disappears!

This result somewhat disagrees with the above earlier experiments, which indicates that some inconsistency may exist. Experimentally, in order to extract the resonance parameters, one has to adopt some parametrization, like Breit-Wigner formula to fit the data, which may generate some model dependence. (Belle Collaboration, Phys. Lett. B 654 (2007) 65)

This model dependence has been analyzed by They find, in some earlier experiments, different parametrization of K*(892) resonance from the Belle experiment 2007 was used. They refit the K*(892) signal in these earlier experiments with the same model used by Belle 2007 in fitting the charged K*(892).

They also did refitting for the neutral K They also did refitting for the neutral K*(892) in some earlier experiments. This means still favor the large mass splitting

Thus, from the current data, there would obviously exist some discrepancy. In order to clarify this discrepancy Experimentally, it is urgent to confirm or rule out the Belle result; it is also important to carry out some new measurements of both the charged and the neutral K*(892) masses. Meanwhile, further theoretical investigations on this issue will be very helpful.

Theoretical model analysis

In general, for SU(3) flavor multiplets of hadrons, the mass splittings between their isospin components are caused by two effects: (i) , inequality of u-d quark masses (ii) Electromagnetic interactions inside the hadrons Consequently, the observed K*(892) mass splitting can be expressed as follows These two parts (QM and EM) cannot be measured directly

On the other hand, in general the EM-masses of neutral hadrons are smaller than ones of their charged partners. So it is reasonable to assume that This leads to Thus, a relative large QM part is required for the large mass splitting

Theoretical situation: Unfortunately, it is still an open question to calculate the mass splittings of the low-lying mesons from the first principle of QCD due to the non-perturbative feature of QCD. Therefore, at the present stage, one generally appeals to some phenomenological models. In order to get a consistent evaluation, then to understand the above possible discrepancy, we should adopt the theoretical framework in which both and can be computed systematically.

Earlier works De Rujula, Georgi, Glashow, PRD (1975) Fritzsch, PLB (1977) Non-relativistic quark model Not explicitly calculate QM and EM (iii) controversial

Our work Gao, Li, & Yan,PRD56(1997); Gao & Yan, EPJA 3(1998). In the framework of chiral constituent quark model, have analyzed the EM and QM masses separately. Actually our analysis favors a small value of the K*(892) mass splitting.

Chiral constituent quark model In the limit of the vanishing light current quark masses, QCD lagragian has chiral symmetry: with , respectively. Nonzero current quark masses will explicitly break chiral symmetry

A simple constituent quark model is proposed by At low energies, chiral symmetry is spontaneously broken to with the appearance of eight Goldstone bosons, and the quarks become massive with mass about 300~400 MeV, called as constituent quark mass. A simple constituent quark model is proposed by Manohar & Georgi, NPB(1984): where : Goldstone bosons : Gell-Mann matrices is chiral invariant chiral constituent quark model (ChQM) m: constituent quark mass

contains only Goldstone bosons (pseudoscalar-mesons): The meson Lagrangian : contains only Goldstone bosons (pseudoscalar-mesons): This can generate the kinetic terms for Goldstone bosons

ChQM Including Vector- and Axial-vector Mesons ChQM can be extended to include vector and axial-vector mesons: Li, Yan & Liu PRD(1991); Li,PRD(1995). Here and mass terms for and are allowed

Similarly Now we can get the meson lagrangian including pseudoscalar, vector, and axial-vector mesons. To parameterize the model: parameter fixed from data Li, PRD52; Zhuang, Wang, &Yan, PRD62; Wang & Yan PRD62, etc The phenomenology of this model is quite well.

Li, PRD52

Zhuang, Wang, &Yan, PRD62

Electromagnetic form factor of pion Electromagnetic interactions have been included in , after integration over the quark field, the electromagnetic interaction of the mesons including pseudoscalar,vector,axial-vectors has been established in , so EM masses of hadrons can be evaluated in this framework. VMD proposed by J.J. Sakurai Electromagnetic form factor of pion

Electromagnetic self-energy of pion Gao, Li, & Yan, PRD56(1997) Quark mass (current quark) matrix: which represents the explicit chiral symmetry breaking in this model, has been introduced into to get quark mass effects

B parametrizes the quark condensate in ChQM The nonzero quark masses will yield new terms in addition to the effective lagrangian in the chiral limit. At the leading order in quark mass expansion, the masses of the pseudoscalar mesons will be no longer zero These are the well-known Gell-Mann-Oakes-Renner formulas B parametrizes the quark condensate in ChQM

For the vector mesons, to the first order of Gao & Yan, EPJA3 (1998) the vector meson masses in the chiral limit

mixing and quark mass parameters

The prediction from the ChQM is Recall the model independent requirement: The value from hadronic process: inconsistent The value from tau lepton decays: consistent

The electromagnetic mass splitting of K*(892): Gao, Li, & Yan, PRD56(1997) Totally, the prediction of the mass splitting of K*(892) in ChQM: Gao & Yan, CPC 32 (2008) which obviously favors the small mass splitting

Discussions and remarks 1. We reexamine the mass splitting between the neutral and the charged K*(892). Our analysis shows that there might exist some discrepancy from the current data: a large mass splitting is expected from the old hadronic data; which a small value is favored from the tau decay data. In the framework of ChQM, we give a theoretical estimation as which seems to support the tau decay data by the Belle Collaboration.

2. It has been pointed out in the 2007 Belle’s paper that: None of the previous mass measurements of the charged K*(892) listed in PDG06, all of which were performed more than twenty years ago, present the systematic uncertainties for their measurements; more importantly, all those earlier mass measurements listed there come from analysis of hadronic reactions and include the effects of final state interaction. Belle Collaboration presents the measurement based on decays, where decay products of are the only hadrons involved.

3. Thanks to the works by LHCB and BESIII, there are some interesting changes in First result with systematical error

This indicates that the most recent data prefer to the small value of the mass splitting , which is consistent with our model estimation. Explicitly, if we only consider the most recent data by LHCB and BESIII for the K* masses: 4. Future dedicated measurements of the K* (including both charged and neutral ones) masses with high precision are necessary to clarify the discrepancy. We therefore urge our experimental colleagues to produce more data in order to get a solid and more meaningful conclusion.

Thank you !

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