aa r X i v : . [ nu c l - e x ] S e p Physics of h ′ → p + p − h and h ′ → p + p − p decays Benedykt R. Jany Nuclear Physics Division of the Jagiellonian University, 30059 Cracow POLANDIKP-2 Forschungszentrum-Jülich, 52428 Jülich GERMANY
Abstract.
The article describes experimental status of the h ′ → p + p − h and h ′ → p + p − p decays.A theoretical framework used for description of the decays mechanism is also reviewed. Thepossibilities for the measurements with WASA-at-COSY are mentioned. Keywords:
Hadronic Decays of h ′ , U ( ) axial anomaly, WASA-at-COSY PACS:
EXPERIMENTAL OVERVIEW
The h ′ → p + p − h decay with branching ratio (BR) 44 .
5% [1] is the main decay modeof the h ′ ( ) meson. The experimental studies of the reaction mechanism are based onthe following data samples: 1400 events from [2] (1974), 6700 events from [3] (2000).The most recent results are from VES experiment with two data sets of 14600 and7000 events collected in two different h ′ production reactions [4] (2006). The decay h ′ → p + p − p is rare since it violates isospin. There exists only a weak limit BR ≤ SYMMETRIES
The physical h ′ , h and p mesons are not pure isospin states e h ′ , e h ( I =
0) and e p ( I = p − h mixing, relatedto light quark mass difference ( m d − m u ), one can write: p = cos ( q ph ) e p − sin ( q ph ) e hh = sin ( q ph ) e p + cos ( q ph ) e h where q ph is the mixing angle between p and h . The mixing angle is expressed interms of the quark masses: sin ( q ph ) = √ m d − m u m s − b m , e-mail: [email protected], [email protected] ith b m = ( m d + m u ) /
2. One proposed way to extract the mixing angle is in hadronicdecays of h ′ [6]. In the paper it is argued that the ratio R = G ( h ′ → p + p − p ) / G ( h ′ → p + p − h ) can be related to q ph in a very simple way: R = P sin ( q ph ) , where P is thephase-space factor. To extract q ph there should be two conditions fulfilled: • The decay h ′ → p + p − p should follow via intermediate state p + p − h and subse-quent h − p mixing. • The amplitudes of both decays must be constant over the phase space.Recent analysis within Chiral Unitary Approach [7] shows that the decay does notfollow entirely via h − p mixing. Moreover the decay amplitudes are not constantsince resonances in the final state interaction are important. Therefore the mixing angle q ph and quark mass difference cannot be extracted in this simple way. In the followingsection a brief overview of the Chiral Effective Field Theory is given and in particularChiral Unitary Approach as the physical tool to describe the hadronic decays of h ′ isintroduced. CHIRAL EFFECTIVE FIELD THEORY
Chiral Symmetry [8, 9] is connected with transformation of left and right handed quarkfields. It holds for QCD Hamiltonian when masses of the quarks are put to zero (chirallimit). It is spontaneously broken i.e the ground state does not posses the symmetry ofthe Hamiltonian itself. The consequence is the existence of the massless mode, so calledGoldstone Bosons – the octet of the pseudoscalar mesons. Nevertheless h ′ in chiral limitremains massive as a consequence of U ( ) axial anomaly [10] and it is close related toit. Chiral symmetry is also explicitly broken by the masses of the quarks what leads tothe non-zero masses of the pseudoscalar mesons. with help comes Partially ConservedAxial Current (PCAC) hypothesis, which says that the quark mass scale is small incomparison to the hadron mass scale. The symmetry breaking effects are small and onecan use a perturbative approach at low energy. One can use Effective Field Theory [11]and construct the Chiral Effective Field Theory - Chiral Perturbation Theory (CHPT).We know that low energy QCD should be independent of the short distance physics.So, one derives an effective Hamiltonian which consists of: a long range part withultraviolet cutoff - to exclude high momentum states and a set of contact terms - tomimic the short distance behavior. Each such contact term, derived by the symmetryconstrains, consists of a local coupling constant multiplied by the local operator. Now wecan mimic with arbitrary precision the low energy data sets. But a problem arises whenone want to generate resonances – the perturbative series just breaks down and does notconverge. One possible way to generate resonances is to use non perturbative relativisticcoupled channels via Bethe-Salpeter Equation (BSE) as it is done in the Chiral UnitaryApproach [12]. The h ′ meson is included in this approach as a dynamical degree offreedom explicitly.Based on the described framework and on the available data, from which one has toextract the chiral parameters, one can predict distributions of the products of the hadronic h ′ decays. In the Fig. 1 a predicted shape of the Dalitz plot for the h ′ → pph decay ishown. Influence of a ( ) ( I =
1) Fig. 1a or f ( ) / s ( I =
0) Fig. 1b in the finalstate can be observed by different population of the Dalitz plot. The limited statistics ofthe existing experimental data does not allow to distinguish between the two possiblescenarios since the difference is small (the total variation of the Dalitz plot densities isonly 20%).The fits to all existing data on hadronic h and h ′ decays, including the latest VES data[4], lead to predictions of surprisingly large branching ratio of the isospin violating decay h ′ → p + p − p . The predicted value of 1 .
8% is more than one order of magnitude largerthan the neutral mode h ′ → p p p . Such large branching ratio is explained by r ± ( ) dominance and can be observed also in the Dalitz plot in Fig. 2. The experimentalsearch for h ′ → p + p − p is difficult due to three pion background which accompaniesproduction of h ′ . -1.5 -1 -0.5 0 0.5 1 1.5 x -1-0.500.51 y -1.5 -1 -0.5 0 0.5 1 1.5 x -1-0.500.51 y a) b) FIGURE 1.
Predicted Dalitz Plot for the h ′ → pph decay: a) with a ( ) dominance, b) with f ( ) / s dominance [13]. → -1.0 -0.5 0.0 0.5 1.0 x -1.0-0.50.00.5 y s π + π − s π π + s π π − m ρ m ρ Γ = 3 1 keV Γ = 330 eV
FIGURE 2.
Predicted Dalitz Plot for the h ′ → p + p − p , one sees r ± ( ) dominance [12]. SUMMARY AND OUTLOOK
The h ′ → p + p − h and h ′ → p + p − p decays, as described above, give unique scientificopportunity to study symmetries in nature and to provide experimental verification ofthe sophisticated theoretical predictions as the Chiral Unitary Approach and to reveal thedriving mechanism of the decays. The experimental situation of the considered decaysas also reviewed. The need for the further data was indicated. When running WASA-at-COSY[14] at its designed luminosity of L = cm − s − one could get 90000 acceptedevents per day for the h ′ → p + p − h decay – more than the present world statistics.Newly commissioned WASA-at-COSY experiment is on the way to take exclusive dataon h ′ decays. REFERENCES
1. W. M. Yao, et al.,
J. Phys.
G33 , 1–1232 (2006).2. G. R. Kalbfleisch,
Phys. Rev.
D10 , 916 (1974).3. R. A. Briere, et al.,
Phys. Rev. Lett. , 26–30 (2000).4. V. Dorofeev, et al. (2006), hep-ph/0607044 .5. A. Rittenberg (1969), URL http://repositories.cdlib.org/lbnl/UCRL-18863 .6. D. J. Gross, S. B. Treiman, and F. Wilczek, Phys. Rev.
D19 , 2188 (1979).7. B. Borasoy, U.-G. Meissner, and R. Nissler,
Phys. Lett.
B643 , 41–45 (2006), hep-ph/0609010 .8. S. Scherer, and M. R. Schindler (2005), hep-ph/0505265 .9. V. Koch,
Int. J. Mod. Phys. E6 , 203–250 (1997), nucl-th/9706075 .10. R. Kaiser, and H. Leutwyler (1998), hep-ph/9806336 .11. G. P. Lepage (2000), nucl-th/9706029 .12. B. Borasoy, and R. Nissler, Eur. Phys. J.
A26 , 383–398 (2005), hep-ph/0510384 .13. B. Borasoy, and R. Nissler, private communication (2007), URL [email protected],[email protected] .14. H. H. Adam, et al. (2004), nucl-ex/0411038nucl-ex/0411038