1. 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

2. Outline Experimental data and motivation Theoretical model analysis
Discussions and remarks

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

4. 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。

5. 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.

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

7. 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.

9. No systematical error provided

10. 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 …

11. 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!

12. 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)

13. 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).

14. 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

15. 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.

16. Theoretical model analysis

17. 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

18. 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

19. 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.

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

22. 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.

23. 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

24. 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

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

26. 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

27. 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.

28. Li, PRD52

29. Zhuang, Wang, &Yan, PRD62

30. 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

31. 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

32. 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

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

34. mixing and quark mass parameters

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

36. 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

37. 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.

38. 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.

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

41. 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.

42. Thank you !

43. Back up