- Email: [email protected]
Where are the missing V0V0′ in γγ reactions?
Volume 215, number 2
PHYSICS LETTERS B
15 December 1988
W H E R E A R E T H E M I S S I N G V°V °' IN 77 R E A C T I O N S ?
Aharon LEVY School of Physics and Astronomy, Raymond and Beverly Sackler Faculty of Exact Sciences, Tel-Aviv University, 69978 Tel-Aviv, Israel
Received 14 October 1988
The measured cross sections o f y T ~ V ° V °' are inconsistent with the measurements of the 77 total hadronic cross section above 2 GeV. Higher cross sections for 77 ~ p ° p ° or additional V°V°' final states are needed to solve this inconsistency.
There exists now information about all the nine possible combinations of vector-vector meson production in photon-photon interactions ,l. The recent measurements of ARGUS, CELLO and TPC/27, together with the earlier results of MARK II, PLUTO and TASSO have supplied full measurements of six 77 ~VV' reactions and upper limits of the remaining three. The six neutral-neutral non-strange vector meson cross sections can be compared via the optical model and the vector dominance model (VDM) to the 77 hadronic total cross section [ 12]. In this note we show that this comparison gives inconsistent results for 77 energies W> 2 GeV, indicating that we are missing 77--'V°V°' events in this energy range. The relation between the VDM part of the 77 total hadronic cross section, a VDM ( 7 7 ) and the V°V°'production cross section is given by [ 12 ] aVDM(77)
4zc 4zt =aV/~v~v,~-v~v, [Bvv, a(77)--*V°V°')]'/2,
(1)
where a = ~7, Yv is the direct photon-vector meson coupling constant and Bvv, is the slope of the exponential differential cross section of the reaction 77-'V°V°'. It is assumed that the scattering amplitude A (77 - ' V °V°') is imaginary in the forward direc-
tion. The effective direct photon-vector meson couplings are taken as [13]: 72/4n =0.55, 5.9, 4.6 for p, co, and ~, respectively. The slope Bvv, is estimated by using factorization [ 14]: Bvv, =Bvv +Bvv,-Bpp, where Bvv is the slope of the reaction 7P--' Vp and Bpp is the slope of the elastic pp reaction. For the calculation of the RHS of expression (1) we have used the measurements of 77-,p°p ° [3], y7--,p°(o [4], 77-~o(o [6], and the upper limits for the reactions 77~pO~ [5], 77~co~ [7] and 7 7 ~ [ 8]. In order to obtain the LHS of expression (1), namely a vDM (77), we assume that the VDM contribution to the total hadronic 77 cross section, aT (77), can be calculated by subtracting the point-like part aP (77) from av(77): GVDM ( 7 7 ) = aT ( 7 7 ) -- aTP ( 7 7 ) •
The point-like part is calculated using the quark-parton model (QPM)[ 15]. Only two groups have published their measurements of aT (77) [ 16,17 ]. These measurements have been well described by a factorization model [ 14], which relates av(Y7) to the forward Compton scattering and forward pp elastic scattering, taking into account the correct kinematic flux factors. The W dependence obtained from this factorization model is aT(77) =
~ See refs. [1,2] for recent reviews. For measurements of yT-*p°p° see ref. [3], ofyy~p°o~ see ref. [4], of 7 7 ~ p ° ~ see ref. [5], of 77--,o~co see ref. [6], of 7 7 ~ t o ~ see ref. [7], of y y - - . ~ see ref. [8], o f 7 7 - , p + p - see ref. [9], o f y y ~ K * ° K *° see ref. [ 1 0 ] , o f y y - - , K * + K *- see ref. [11].
0370-2693/88/$ 03.50 © Elsevier Science Publishers B.V. (North-Holland Physics Publishing Division)
(2)
187+ 702/W.
(3)
Fig. 1 shows the published 77 total cross section measurements of PLUTO [ 16 ] and TPC/27 [ 17 ]. The dotted line is the factorization model expression (3). The solid line is the result of (2), namely sub421
PHYSICS LETTERS B
Volume 215, number 2
800 600
"
I
"I'""'"V''""V"'""I"'""! oPLUTC *TPC
~. 400
b~ 200
oo ..... , h , , . , , , d , . . . , , ,
2
h,,,,,,,,h,,.,,,
3 4 5 w(o~v)
6
Fig. 1.7*/total hadronic cross section (see text).
tracting the point-like contribution, by using Q P M [ 13 ], from expression (3) a n d thus representing the L H S o f expression (1). The open squares are the contributions to the total cross section coming from the V°V °' measurements, using the optical m o d e l as described by the R H S o f expression (1). As can be seen, there is good agreement between the LHS a n d R H S o f (1) up to 2 GeV. Between 2 a n d 3 G e V however, the measured V°V °' cross sections are too low a n d fail the consistency check. A b o v e 3 GeV, there are no m e a s u r e m e n t s o f pOpOa n d p°to final states, which are the m a i n contributors to the R H S o f (1). The inconsistency described above could be the result o f the fact that the m e a s u r e d pOpO cross section above 2 G e V is quite low. In fact there is an appreciable pOn + n - cross section [ 18] which, for W > 2 GeV, is even higher t h a n the pOpO cross section [ 3 ]. However, the pOn+n- cross section was o b t a i n e d without taking into account charge conjugation ( C ) conservation which forces the n + n - system recoiling against the pO to have the q u a n t u m n u m b e r s o f a vector meson [ 19 ]. Therefore the discrepancy shown in fig. 1 would indicate that one has to reanalyze the 3'3'--+2r~+ 2 ~ - final state taking into account the C conservation constraint. A n o t h e r possible solution could be that we are missing some V°V °' state above 2 GeV. Since the m a i n c o n t r i b u t i o n to the total 3'3' cross section, using the optical model, comes from p°V°' final states, the first reaction that comes in m i n d is 3'3' ~ popo, (1600). The pO, (1600) decays m a i n l y through pon + n - , therefore one should look for this final state in the reaction 77--->3~+3n - . Both A R G U S [2] a n d C E L L O [20] have m e a s u r e d this final state a n d the p r e l i m i n a r y cross section m e a s u r e m e n t s show a sharp rise just at the pOpO, (1600) threshold. 422
15 December 1988
In conclusion, we have shown that the m e a s u r e d cross sections o f 77 ~ V°V°' are inconsistent with the m e a s u r e m e n t s o f the total h a d r o n i c 3'7 cross section above 2 GeV. This could come either from the fact that the 3'7--> pOpO cross sections are too low above 2 G e V because o f an inadequate analysis o f the 2rt ÷ 2~ channel, or from the fact that some V°V °' final states have eluded their detection in 3'7 reactions. Therefore one would like to see a reanalysis o f the reaction 3'3'--,2n + 2 n - , taking into account constraints from C conservation, and searches for reactions such as 73'-,p°p °' (1600) are needed.
Acknowledgement I would like to thank U r i M a o r for helpful discussions.
References [ 1] U. Maor, Vector meson production in 77 reactions, invited talk VIIth Intern. Workshop on photon-photon collisions (Shoresh, Israel, April 1988); [ 2 ] A. Levy, Two-photon production of exclusive final states, Rapporteur talk Rochester Conf. ( Munich, August 1988). A.W. Nilsson, Exclusive final states - continuum (experimental). Argus Collab., invited talk Vllth Intern. Workshop on Photon-photon collisions (Shoresh, Israel, April 1988); [3] CELLO Collab., H.J. Behrend et al., Z. Phys. C 21 (1984) 205; MARK II Collab., D.L. Burke et al., Phys. Lett. B 103 (1981 ) 153; PLUTO Collab., Ch. Berger et al., Z. Phys. C 38 (1988) 521; TASSO Collab., R. Brandelik et al., Phys. Len. B 97 (1980) 448; M. Althoffet al., Z. Phys. C 16 (1982) 13; TPC/27 Collab., H. Aihara et al., Phys. Rev. D 37 (1988) 28. [4 ] ARGUS Collab., H. Albrecht et al., Phys. Lett B 196 (1987) 101; CELLO Collab., H.J. Behrend et al., contrib. Rochester Conf. (Munich 1988); TPC/27 Collab., W. Hofmann et al., contrib. Rochester Conf. (Munich, 1988). [5] ARGUS Collab., H. Albrecht et al., Phys. Lett. B 198 (1987 ) 577; TASSO Collab., M. Althofet al., Z. Phys. C 23 (1986) 11; TPC/27 Collab., H. Aihara et al., Phys. Rev. D 37 (1988) 28.
Volume 215, number 2
PHYSICS LETTERS B
[ 6 ] ARGUS Collab., H. Albrecht et al., Phys. Lett. B 198 (1987) 255. [ 7 ] ARGUS Collab., H. Albrecht et al., contrib. Rochester Conf. (Munich, 1988); [ 8 ] ARGUS Collab., H. Albrecht et al., contrib. Rochester Conf. (Munich, 1988); "lASSO Collab., M. Althoffet al., Z. Phys. C 32 (1966) 11; TPC/27 Collab., H. Aihara et al., Phys. Rev. D 37 (1988) 28. [ 9 ] ARGUS Collab., H. Albrecht et al., contrib. Rochester Conf. (Munich, 1988); CELLO Collab., H.J. Behrend et al., contrib. Rochester Conf. (Munich, 1988). [ 10 ] ARGUS Collab., H. Albrecht et al., Phys. Lett. B 198 (1987) 577.
15 December 1988
[ 11 ] ARGUS Collab., H. Albrecht et al., contrib. Rochester Conf. (Munich, 1988) [12] A. Levy, Phys. Lett. B 181 (1986) 401. [13] T.H. Bauer et al., Rev. Mod. Phys. 50 (1978) 261. [ 141 A. Levy, Phys. Lett. B 177 (1986) 106. [ 15] V.M. Budnev et al., Phys. Rep. 15 (1975) 181. [ 16 ] PLUTO Collab., Ch. Berger et al., Phys. Lett. B 149 (1984) 421. [ 17 ] TPC/27 Collab., D. Bintiger et al., Phys. Rev. Lett. 54 (1985 ) 763. [ 18 ] G. Alexander, A. Levy, S. Nussinov and J. Grunhaus, Phys. Rev. D 37 (1988) 1328. [ 19 ] N.N. Achasov and G.N. Shestakov, Phys. Lett. B 203 (1988) 309. [20] CELLO Collab., H.J. Behrend et al., contrib. Rochester Conf. (Munich, 1988).
423
PHYSICS LETTERS B
15 December 1988
W H E R E A R E T H E M I S S I N G V°V °' IN 77 R E A C T I O N S ?
Aharon LEVY School of Physics and Astronomy, Raymond and Beverly Sackler Faculty of Exact Sciences, Tel-Aviv University, 69978 Tel-Aviv, Israel
Received 14 October 1988
The measured cross sections o f y T ~ V ° V °' are inconsistent with the measurements of the 77 total hadronic cross section above 2 GeV. Higher cross sections for 77 ~ p ° p ° or additional V°V°' final states are needed to solve this inconsistency.
There exists now information about all the nine possible combinations of vector-vector meson production in photon-photon interactions ,l. The recent measurements of ARGUS, CELLO and TPC/27, together with the earlier results of MARK II, PLUTO and TASSO have supplied full measurements of six 77 ~VV' reactions and upper limits of the remaining three. The six neutral-neutral non-strange vector meson cross sections can be compared via the optical model and the vector dominance model (VDM) to the 77 hadronic total cross section [ 12]. In this note we show that this comparison gives inconsistent results for 77 energies W> 2 GeV, indicating that we are missing 77--'V°V°' events in this energy range. The relation between the VDM part of the 77 total hadronic cross section, a VDM ( 7 7 ) and the V°V°'production cross section is given by [ 12 ] aVDM(77)
4zc 4zt =aV/~v~v,~-v~v, [Bvv, a(77)--*V°V°')]'/2,
(1)
where a = ~7, Yv is the direct photon-vector meson coupling constant and Bvv, is the slope of the exponential differential cross section of the reaction 77-'V°V°'. It is assumed that the scattering amplitude A (77 - ' V °V°') is imaginary in the forward direc-
tion. The effective direct photon-vector meson couplings are taken as [13]: 72/4n =0.55, 5.9, 4.6 for p, co, and ~, respectively. The slope Bvv, is estimated by using factorization [ 14]: Bvv, =Bvv +Bvv,-Bpp, where Bvv is the slope of the reaction 7P--' Vp and Bpp is the slope of the elastic pp reaction. For the calculation of the RHS of expression (1) we have used the measurements of 77-,p°p ° [3], y7--,p°(o [4], 77-~o(o [6], and the upper limits for the reactions 77~pO~ [5], 77~co~ [7] and 7 7 ~ [ 8]. In order to obtain the LHS of expression (1), namely a vDM (77), we assume that the VDM contribution to the total hadronic 77 cross section, aT (77), can be calculated by subtracting the point-like part aP (77) from av(77): GVDM ( 7 7 ) = aT ( 7 7 ) -- aTP ( 7 7 ) •
The point-like part is calculated using the quark-parton model (QPM)[ 15]. Only two groups have published their measurements of aT (77) [ 16,17 ]. These measurements have been well described by a factorization model [ 14], which relates av(Y7) to the forward Compton scattering and forward pp elastic scattering, taking into account the correct kinematic flux factors. The W dependence obtained from this factorization model is aT(77) =
~ See refs. [1,2] for recent reviews. For measurements of yT-*p°p° see ref. [3], ofyy~p°o~ see ref. [4], of 7 7 ~ p ° ~ see ref. [5], of 77--,o~co see ref. [6], of 7 7 ~ t o ~ see ref. [7], of y y - - . ~ see ref. [8], o f 7 7 - , p + p - see ref. [9], o f y y ~ K * ° K *° see ref. [ 1 0 ] , o f y y - - , K * + K *- see ref. [11].
0370-2693/88/$ 03.50 © Elsevier Science Publishers B.V. (North-Holland Physics Publishing Division)
(2)
187+ 702/W.
(3)
Fig. 1 shows the published 77 total cross section measurements of PLUTO [ 16 ] and TPC/27 [ 17 ]. The dotted line is the factorization model expression (3). The solid line is the result of (2), namely sub421
PHYSICS LETTERS B
Volume 215, number 2
800 600
"
I
"I'""'"V''""V"'""I"'""! oPLUTC *TPC
~. 400
b~ 200
oo ..... , h , , . , , , d , . . . , , ,
2
h,,,,,,,,h,,.,,,
3 4 5 w(o~v)
6
Fig. 1.7*/total hadronic cross section (see text).
tracting the point-like contribution, by using Q P M [ 13 ], from expression (3) a n d thus representing the L H S o f expression (1). The open squares are the contributions to the total cross section coming from the V°V °' measurements, using the optical m o d e l as described by the R H S o f expression (1). As can be seen, there is good agreement between the LHS a n d R H S o f (1) up to 2 GeV. Between 2 a n d 3 G e V however, the measured V°V °' cross sections are too low a n d fail the consistency check. A b o v e 3 GeV, there are no m e a s u r e m e n t s o f pOpOa n d p°to final states, which are the m a i n contributors to the R H S o f (1). The inconsistency described above could be the result o f the fact that the m e a s u r e d pOpO cross section above 2 G e V is quite low. In fact there is an appreciable pOn + n - cross section [ 18] which, for W > 2 GeV, is even higher t h a n the pOpO cross section [ 3 ]. However, the pOn+n- cross section was o b t a i n e d without taking into account charge conjugation ( C ) conservation which forces the n + n - system recoiling against the pO to have the q u a n t u m n u m b e r s o f a vector meson [ 19 ]. Therefore the discrepancy shown in fig. 1 would indicate that one has to reanalyze the 3'3'--+2r~+ 2 ~ - final state taking into account the C conservation constraint. A n o t h e r possible solution could be that we are missing some V°V °' state above 2 GeV. Since the m a i n c o n t r i b u t i o n to the total 3'3' cross section, using the optical model, comes from p°V°' final states, the first reaction that comes in m i n d is 3'3' ~ popo, (1600). The pO, (1600) decays m a i n l y through pon + n - , therefore one should look for this final state in the reaction 77--->3~+3n - . Both A R G U S [2] a n d C E L L O [20] have m e a s u r e d this final state a n d the p r e l i m i n a r y cross section m e a s u r e m e n t s show a sharp rise just at the pOpO, (1600) threshold. 422
15 December 1988
In conclusion, we have shown that the m e a s u r e d cross sections o f 77 ~ V°V°' are inconsistent with the m e a s u r e m e n t s o f the total h a d r o n i c 3'7 cross section above 2 GeV. This could come either from the fact that the 3'7--> pOpO cross sections are too low above 2 G e V because o f an inadequate analysis o f the 2rt ÷ 2~ channel, or from the fact that some V°V °' final states have eluded their detection in 3'7 reactions. Therefore one would like to see a reanalysis o f the reaction 3'3'--,2n + 2 n - , taking into account constraints from C conservation, and searches for reactions such as 73'-,p°p °' (1600) are needed.
Acknowledgement I would like to thank U r i M a o r for helpful discussions.
References [ 1] U. Maor, Vector meson production in 77 reactions, invited talk VIIth Intern. Workshop on photon-photon collisions (Shoresh, Israel, April 1988); [ 2 ] A. Levy, Two-photon production of exclusive final states, Rapporteur talk Rochester Conf. ( Munich, August 1988). A.W. Nilsson, Exclusive final states - continuum (experimental). Argus Collab., invited talk Vllth Intern. Workshop on Photon-photon collisions (Shoresh, Israel, April 1988); [3] CELLO Collab., H.J. Behrend et al., Z. Phys. C 21 (1984) 205; MARK II Collab., D.L. Burke et al., Phys. Lett. B 103 (1981 ) 153; PLUTO Collab., Ch. Berger et al., Z. Phys. C 38 (1988) 521; TASSO Collab., R. Brandelik et al., Phys. Len. B 97 (1980) 448; M. Althoffet al., Z. Phys. C 16 (1982) 13; TPC/27 Collab., H. Aihara et al., Phys. Rev. D 37 (1988) 28. [4 ] ARGUS Collab., H. Albrecht et al., Phys. Lett B 196 (1987) 101; CELLO Collab., H.J. Behrend et al., contrib. Rochester Conf. (Munich 1988); TPC/27 Collab., W. Hofmann et al., contrib. Rochester Conf. (Munich, 1988). [5] ARGUS Collab., H. Albrecht et al., Phys. Lett. B 198 (1987 ) 577; TASSO Collab., M. Althofet al., Z. Phys. C 23 (1986) 11; TPC/27 Collab., H. Aihara et al., Phys. Rev. D 37 (1988) 28.
Volume 215, number 2
PHYSICS LETTERS B
[ 6 ] ARGUS Collab., H. Albrecht et al., Phys. Lett. B 198 (1987) 255. [ 7 ] ARGUS Collab., H. Albrecht et al., contrib. Rochester Conf. (Munich, 1988); [ 8 ] ARGUS Collab., H. Albrecht et al., contrib. Rochester Conf. (Munich, 1988); "lASSO Collab., M. Althoffet al., Z. Phys. C 32 (1966) 11; TPC/27 Collab., H. Aihara et al., Phys. Rev. D 37 (1988) 28. [ 9 ] ARGUS Collab., H. Albrecht et al., contrib. Rochester Conf. (Munich, 1988); CELLO Collab., H.J. Behrend et al., contrib. Rochester Conf. (Munich, 1988). [ 10 ] ARGUS Collab., H. Albrecht et al., Phys. Lett. B 198 (1987) 577.
15 December 1988
[ 11 ] ARGUS Collab., H. Albrecht et al., contrib. Rochester Conf. (Munich, 1988) [12] A. Levy, Phys. Lett. B 181 (1986) 401. [13] T.H. Bauer et al., Rev. Mod. Phys. 50 (1978) 261. [ 141 A. Levy, Phys. Lett. B 177 (1986) 106. [ 15] V.M. Budnev et al., Phys. Rep. 15 (1975) 181. [ 16 ] PLUTO Collab., Ch. Berger et al., Phys. Lett. B 149 (1984) 421. [ 17 ] TPC/27 Collab., D. Bintiger et al., Phys. Rev. Lett. 54 (1985 ) 763. [ 18 ] G. Alexander, A. Levy, S. Nussinov and J. Grunhaus, Phys. Rev. D 37 (1988) 1328. [ 19 ] N.N. Achasov and G.N. Shestakov, Phys. Lett. B 203 (1988) 309. [20] CELLO Collab., H.J. Behrend et al., contrib. Rochester Conf. (Munich, 1988).
423