Rescattering effect in decay
Peng Guo
Physics Department & NTC Indiana University - Bloomington, U.S.A.
Collaborators: A.P. Szczepaniak, H. Matevosyan, R. Mitchell and M. Shepherd
INT-JLab Workshop on Hadron Spectroscopy ! Seattle, Nov. 2009!
Tuesday, November 10, 2009 Isobar Model: quasi two-body decays
1 1 3 1
(31) (12) 2 1 2 2 + + = (23) 3 2 3 3
Tuesday, November 10, 2009 Outline
Motivation: Rescattering effect (corrections to isobar model) in
Method: Unitarity + Analyticity
Conclusion
Tuesday, November 10, 2009 rho-pi puzzle Experiment measurement PQCD vs
vs
BES Collaboration BES Collaboration Phys.Rev.D70:012005,2004 Phys.Lett.B619:247,2005
Tuesday, November 10, 2009 PHYSICAL REVIEW D VOLUME 55, NUMBER 3 1 FEBRUARY 1997
Possible explanation of the ‘‘ puzzle’’ in J/, decays
Xue-Qian Li Rutherford Appleton Laboratory, Chilton, Didcot, OX11 0QX, United Kingdom and Department of Physics, Nankai University, Tianjin 300071, China
David V. Bugg and Bing-Song Zou Queen Mary and Westfield College, London E1 4NS, United Kingdom Received 9 August 1996 We evaluate the contributions of final state interactions FSI’s to J/ and with vari- → → ous intermediate physical channels. We find that the rescattering of a2 and a1 into can change the production rate substantially, and, therefore, could be an explanation for the long-standing ‘‘ ¯ puzzle.’’ The FSI effects may also play a significant role for other channels, such as K*K and f 2. S0556-28219705703-2 VOLUME 78, NUMBER 25 P H Y S I C A L R E V I E W L E T T E R S 23 JUNE 1997
PACS numbers: 13.25.Gv, 13.75.Lb, 14.40.Gx Intrinsic Charm of Vector Mesons: A Possible Solution of the “rp Puzzle’’
Stanley J. Brodsky* I. INTRODUCTION tion. It turns out that the FSI givesStanford rise to Linear substantial Accelerator Center, contri- Stanford University, Stanford, California 94309 butions. The method for evaluation of hadronic loopsMarek is Karliner† School of Physics and Astronomy, Raymond and Beverly Sackler Faculty of Exact Sciences, Tel-Aviv University, The mysterious suppression puzzle has lingered proved to be reliable and appropriate to practical calcula-69978 Tel-Aviv, Israel for a long while, but remains→ unanswered 1,2. According to tions. Such calculations depend on and are well constrained(Received 28 April 1997) An outstanding mystery of charmonium physics is why the Jc decays prominently to pseudoscalar perturbative QCD, for any specific final hadronic state h, one by the input experimental data.plus There vector meson may channels, be a such factor as Jc of 2–3rp and Jc K K, whereas the c02S does not. We ! ! expects uncertainty for the results. Howevershow that such the decays physical of Jc and their picture suppression is for c02S follow naturally from the existence of intrinsic charm qqcc Fock components of the light vector mesons. [S0031-9007(97)03448-0] usually determined by the order of magnitude.j B h B ee With this understanding inPACS mind, numbers: it 13.25.Gv, is natural 12.39.Ki, to 14.40.–n apply this Qh → → 0.1470.023 3. BJ/ h BJ/ e e method to calculate theOne ofhadronic the basic tenets loop of quantum contributions chromodynamics to the is the quarkonium wave function near the origin, → → that heavy quarkonium states such as the J c, c , and 1 2 1 interesting final states from J/ and decays. Here0 we Bc0 h Bc0 e e Y must decay into light hadrons via the annihilation of ! ! 0.147 6 0.023 , BJc h BJc e1e2 calculate the contributionsthe heavy from quark loop constituents diagrams into gluons, shown as shown in Fig. in ! ! While this is true for many hadronic states 3, it fails for 1. Figure 1a is uniqueFig. 1(a). to This assumption. Here is motivated stands by the for Okubo- the (1) Zweig-Iizuka (OZI)→ rule which postulates suppression of (see Refs. [5,6]), where h denotes a given hadronic and K*K final states 1,2; the present experimental lim- low-energy S-wavetransitions amplitude between hadrons9. If without this contribution valence quarks in is channel. The JS.J.Brodsky,c rp andG.P.LepageJc &KK S.T.Tuan decays also ! ! its 2 for and K*K¯ final states are one to two orders of large, it could give acommon. natural A explanation central feature of for the the perturbative difference quantum of Phys.Rev.Lett. 59:621,1987 chromodynamics (PQCD) analysis is the fact that the an- magnitude smaller: production ratesnihilation from amplitudeJ/ and for quarkonium. Unfortunately, decay into gluons oc- we find its contribution tocurs be at relatively negligible short distances comparedr 1m toQ, the thus allowing experi- Q 0.0028 and Q ¯ 0.011. 2 mental value, due toa perturbative the exchanged expansion in pion a small being QCD coupling too farasm off-Q . K*K Glueball nearIn this the Letter wemass shall challenge of theJ/Psi assumption that shell for the on-shellquarkoniumJ/ and states intermediate necessarily decay state. via intermediate The rea- Brodsky, Lepage, and Tuan 4 proposed that there might gluon states. We shall argue, in analogy with the analysis son for considering[1,2] Fig. of 1 theb nucleonis the strangeness following. content, The that the largest wave be a gluonium intermediate state with a mass very close to hadronic decay channelfunctions of observed the light hadrons, for particularlyJ/ vectordecays mesons is M , so that the resonance effect greatly enhances the rate Intrinsic 0 charmsuch as the rcomponentand K, have a non-negligible of probability rho (J/) 2( ) , whereto its have largest higher Fock contributions state components come containing from heavy in- of J/ compared to . However, the recent data termediate a2 statesquark3 pairsand [3]. possibly The presence also of from intrinsica1 charm states and of the→ Beijing Electron-Positron→ Collider BEPC seem not bottom in the light hadron wave functions then allows which may not havetransitions been identified between heavy due quarkonium to the large and light width hadrons of to support the existence of glueballs within this mass range 2S-1D wave mixing in Psi’ the a1. Both a2(1320)by rearrangement and a1(1230) of the have underlying quarkas their lines, domi- rather 2, so one has to search for other explanations of the than by annihilation. nant decay mode, andOne can of rescatter the most dramatic into problems by confronting exchanging the suppression. the lightest meson, thestandard pion; picture they of quarkonium may therefore decays is make the Jc sub- → Hybrid rp puzzle [4]. This decay occurs with a branching! Generally, before claiming probable new physics apply- stantial contributions to the final states. Our results con- ratio of 1.28 6 0.10% [5], and it is the largest two- FIG. 1. (a) The decay JcJz 1 rp via the standard ing to a process which seems exotic, one should try all well- firm this expectation.body Their hadronic contributions branching ratio of to the Jc.have The J thec PQCD cc annihilationS.J.Brodsky mechanism. & M.Karliner A! light quark helicity flip is assumed to be a cc bound state pair in the C1S is required, since thePhys.Rev.Lettr must be 78:4682,1997 produced with helicity 61. known mechanisms and see if the mystery can be interpreted (b) A connected quark rearrangement diagram which induces same order of magnitudestate. One as then the expects experimentally the c0 C2S to decay observed to rp Final state interaction the gJcrp coupling, via the higher Fock state of the r, udcc. in the existing theoretical framework. Motivated by this idea, rate. The relativewith phases a comparable between branching loop ratio, diagrams scaled by a and factor the of The 12 signs on the quark lines denote the helicitiesj of the 0.15, due to the ratio of the C2S to C1S wave corresponding quarks. In the dominant intrinsic charm Fock we try to analyze the contributions of the final state interac- 2 functions squared at the origin. In fact, Bc0 rp , state of the r, the ud and cc components of the r are in 0 tions FSI’s to the suppression. 3.6 3 1025 [6], more than a factor of 50! below the and 12 states, respectively, thus generating maximal overlap → expected rate. Most of the branching ratios for exclusive with the p and Jc spin wave functions. (c) A “twisted” The FSI plays a very important, sometimes crucial, role in connected diagram, schematically indicating the suppression of hadronic channels allowed in both Jc and c decays 0 c0rp coupling due to the mismatch between the nodeless wave many exclusive processes. Isgur et al. 5 considered the indeed scale with their lepton pair branching ratios, as function of the cc in the udcc Fock state of the r and the 1 j FSI to explain the I rule in K decays. Lipkin would be expected from decay amplitudes controlled by one-node 2S cc wave function of the c0. 2 → et al. 6 suggested that hadronic loops may result in Okubo- X.Q.Li, D.V.Bugg & B.S.Zou 4682 0031-90079778(25)4682(4)$10.00 © 1997 The American Physical Society Zweig-Iizuka OZI-rule violation for (uu¯dd¯)-ss¯ mixing Phys.Rev.D 55:1421,1997 and some production rates. Anisovich et al. 7 studied Tuesday, FIG.November 1. 10, a2009 Triangle diagram for with standing → → FSI effects in many three-body decay channels. Locher et al. for the S-wave system; b triangle diagram for production 8 established a practical way to evaluate the contribution of from J/ and through a2(1320) and a1(1230) intermediate hadronic loops to and f 2 productions from pp¯ annihila- states.
0556-2821/97/553/14214/$10.0055 1421 © 1997 The American Physical Society I.J.R.Aithison & R.Pasquier Phys.Rev.152:1274,1966 Corrections to naive isobar model I.J.R.Aithison & J.J.Brehm Phys.Rev.D.17:3072,1978
J.A.Oller & E.Oset Phys.Rev.D60:074023,1999
Tuesday, November 10, 2009 Tuesday, November 10, 2009 Subenergy Unitarity
3 1 1’ 1 (1’2’) 1’ (31’) 1 2’ 2 Disc T 2 + 1’ + (12) = 2’ 2 (2’3) 2’ 3 3
Tuesday, November 10, 2009 3 1 1’ 1 (1’2’) 1’ (31’) 1 2’ 2 Disc T 2 + 1’ + (12) = 2’ 2 (2’3) 2’ 3 3
s
Dispersion Relation s th
Tuesday, November 10, 2009 Single integral equation: suitable for data fitting
+ ( )*
# # $%!"& ' !" R.Pasquier & J.Y.Pasquier Phys.Rev.170:1294,1968 + * '( )#
$%!"& # $%*"& # !"# *
Tuesday, November 10, 2009 Tuesday, November 10, 2009 J/^"<#"l$%%&'/"<#"(/
1 Breit-Wigner Rescattering
0.5 )] ij (s,s ! l 0 Re[T
-0.5
-1 J/^"<#"l$%%&'/"<#"(/ 0.5 1 1.5 2 2.5 3 1/2 s ij (GeV) 2 Breit-Wigner Rescattering
1.5 )] ij (s,s ! l 1 Im[T
0.5
0
0.5 1 1.5 2 2.5 3 1/2 s ij (GeV)
Tuesday, November 10, 2009 ^"#S)$<%$l"&&'(/$<%$)/
0.08 Breit-Wigner Rescattering
0.04 )] ij (s,s ! l 0 Re[T
-0.04
-0.08 123 1/2 ^"2S)#<$#l"%%&'/#<$#(/ s ij (GeV) 0.2
Breit-Wigner 0.15 Rescattering )] ij
(s,s 0.1 ! l Im[T
0.05
0 123 1/2 s ij (GeV)
Tuesday, November 10, 2009 Tuesday, November 10, 2009 Summary
Short distance Long distance
Long distance final states rescattering cannot be the cause of rho-pi puzzle.
Interference between rho(770) and rho(2150) might be important.
BES Collaboration Phys.Lett.B619:247,2005
Tuesday, November 10, 2009