ITP-9O-29B L.L.Jenkovszky, E.S,Martynov, HOW FAST DO CROSS SECTIONS RISE?
Academy of Sciences of the Ukrainian SSR Institute for Theoretical Physios Preprint ITP-90-29E L.L.Jenkovszky, E.S.Martynov, B.V.Struminsky HOW PAST DO GROSS SECTIONS RISE? К1«т - 1990
УДК 539.125.17 Л.Л.Енконский, Е.С.Мартынов, Б.Б.Струминекии О росте полных сечений Недлвние измерения полного сечения рр-расееяния на Тэватроне указывает на логарифмическую асимптотику 61, характерную для дипольного померона с единичным мнтереептом. Асимптотика отношения S'et/^t отстает от асимптотики 6" t L.L.Jenkovszky, E.S.Martynov, B.V.Struminsky How Faat do Croas Sections Rise? V:i argue that the reoeat luminooity-in^ependent meaaurement of tlxe pp total oross seotion at the Tevatron iadicatee the approach to the logaritbmio aaymptotics of 6^.., typical of a dipole Pomeron with a unit intercept. The ratio ^ел/^ь approaches its aaymptotio oonatant limit more elowely than 1990 Институт теоретической физики АН УССР
-3- The recent luminocity-independent measurement of the pp total сгозэ section at /s =1.8 TeV, 6^ =72.1^3.3 mb performed by the Е-7Ю Collaboration [O might shed new light on the longstanding prob?..em posed in the title of thia note. Kver since the vx.ao of the cross sections was established in early 70-icu, the rno.-з^. popular model of high-energy elastic scattering was baaed on a "oupercritical" Pomeron exchange, with Д =oi(o)-а У О, which after unitarization, results in the Proiesart saturation of the total cross section, 6 t - LvV (1) Moat uuthora argued that the data support the fast increase of 6^, the only difference between different versions of the models being the value of the parameter Д and the related question of tiow close the data are to the asymptotic regime (1). Parallel to thia general trend, there was an alternative and lesa popular approach, based on a double Pomeron (DP) pole exchange [^2-4]. In the dipole Pomeron DP model, with a unit Pomeron intercept, is the maximally allowed growth of the total cross section (provided the trajectory <*.( ) ia not singular at t-=o ). The relevant invariant scattering amplitude is where and GCt) = e e>t Various versions of the DP model as well as detailed fits to data (including also contributions from secondary reggeons (f,to,..,) and the odderon) can be found e.g. in Ке*.[з]. At the Tevatron, /5 M1.8 TeV and small )*tl the odderon, f,<-o and other terms oontribute by at moat a few percents as oompared to the Pomeron oontribution. In other words, at the Tevatron for the first tine we have the opportunity to see the Pomeron clearly - other contributions being below the level of the experimental error bars.
-4- A representative fit to pp total and elastio cross eeotion data from [з] is shown in figs.1,2. The dipole Poraeron contribution ia shown in fig.1 by a dotted line. Prom (3) with the norm & =83rImA(s,o), ~~ we get asymptotically: Im A(s>o) 2 Ьп. ц. and 2 S* -. X,, (8) where a Ji <. 1. ^ 2 is restricted by unitarity. The constant asymptotic limit (7) ia typical of geometrioal soaling (GS) shared by the DP model. Interestingly, the limit (8) ia delayed with respect to C> t. In other words, while the asymptotic regime (5) ia already reached at the Tevatson this is not the case for 5et/<5 t, which at,/g = «1.8 TeV still increases almost logarithmically, acoording to (fig.3) where [ 3] tvt Ъ. + ЪМр - *1S The fits presented in figs.1-3 are illustrative; they were made [з] prior to the publication [1}. Tha value fj ( {% «1.8 TeV)-O.i45, used in ref.[i]. Is olose to our prediction* [3] made in the context of the odderoa problem (we do not expeot a large value of p ). Finally, we would like to streae that the virtue of the OP
-5- model with a unit intercept io that it ia able to reproduce all the observed phenomena in elastic diffraction at the "Born level", i.e. without reacattering corrections (in a sense, the model reproduces itself against these corrections [2]). The basic properties of the DP model are (for a review and earlier references see 4]): 1. asymptotically the DP obeys geometrical scaling (G3) with er.e, ~ er t ~ б\ ~ B(s) - R 2 (s) - w s 2. positive real part, 9(s,o)>O and dip-bump structure at the "Born level" [4]; 3. the mean multiplicity of produced particles in the DP model is [5] <* > ~tv\ 2 S. Note that the dipole is the only alternative to a single pole - higher order poles (e.g. tripoles) violate unitary (for nonaingular trajectories at t =O ). This simplicity makes the DP anaatz particularly attractive for phenomenological applications. Formally, unitarity corrections to the DP should be taken into account. This prooedure for an arbitrary Д = о<(р)-1 ia reviewed in ref.[6]. The formalism does not exclude the utilization, of a supercritical DP whioh seems to be the only alternative to the above model with Д«О. Contrary to the oase of a simple supercritical pomeron pole model (which disagrees with the earlier and the new [1} data), the parameter Д in the dipole оаэе is amall and the log 2 s regime sets on [7] Гаг beyond the range of the future accelerators. Bven though the option A > O in the DP cannot be ruled out, the simple and eoonomio dipole ansatz with «*(?) =1 [2-4] is- preferable as a reliable and feasable model of high-energy elastio diffraction sinoe it does not require the calculation of resoattering corrections at email t. REFERENCES 1. N.A.Amoa et al. A Luminooity-Independent Measurement of the Total Cross Section at Vs "1.8 TeV. Cornell UniTsrslty prepr. CLNS 981. 2. R.J.N.Phillip». A Dipole Pomeron Ansatz. Rutherford Lab. Prupr.
RL-74-03, 1974. -6-3«N.A.Kobylinaky, A.I.Kosenko, E.S.f.Iartynov, V.V.Timokhin, Lfkr. Phys.Journ. 2&> 1 989, 167 (in Russian), prepr. ГЛР-86-47Е, Kiev, 1936; N.A.Kobylinaky, E.S.Martynov: Z.Physics 044, 1989, 681; L.L.Jenlcov3zky, Nuc.l.Physics B(Pi'oo.Suppl). T2 (1990) 317. 4. L.L.Jenkovszky. Fortachritte Phys. 2Л (1986) 791. 5. N.A.Kobylinsky, E.S.Martynov, V.P.Sheleat. Z.Phys. _C28, J_ (1985) 143-6. A.K.V/all, L.L..Jenkovszky, B.V.Struminsky. Particles and Wuole 19 (1988) 183-7. L.L.Jenkovazky, B.V.Struminsky, A.H.Wall. Yad.JPiz. ^6 (1967) 1519. 8. M.Bozzo et al. Phys.Letters 147B (1984) 392. Heceived June 1, 1990 FIGURE CAPTIONS Pig.1. Л representative fit to pp total cross aeotions (for details see ref[3]). The dipole Pomeron contribution is aaown by a broken line. The compilation of the data is frora ref. ij with an additional data point at -^5 = -546 GeV from [в]. Pig.2. Elastic differential стова section in the DP model. ffig.3. The ratio в^/я^, for pp scattering. The curve is an earlier DP prediction, (see (9) in the text and ref.[3] for more details) (here, the secondary trajectories and the oddaron were not included).
-7- о Corroll etal д Amos et Ambrosio et al Bernard et ol x Alner et al v Arnibon et al This Experiment и EWzo et al 10 I 1 I 11 ll I ' ' ' '! i i " ' " i'ig.1, о Ayres etol Ашоь et ol 0 Ambrosfo «f al Bozzo et al Arnison ctal This I 'I Ю 4 Ю 5 s(gev 2 ) " ig.2.
1 i т-гттгп г i г i-гттту -8- l i т i i i \ I I 1П1 1 1 1 I 114.26 2A.гг о Ayres et al л Amos et al О Ambrosio et al a Etozzo et QI V Ami son et al Tbis Experiment.20.18.16.15 I I I 1 I I J II I I I 1 I I Ill ll 1 1 1 10 s 10 io r Pig.3.
Ласло Ласлович Енковский Евгений Сергеевич Мартынов Борис Владимирович Сгруминский О росте полных сечений Утверждено к печати ученым советом Института теоретической физики АН УССР Редактор А.А.Храброва Техн.редактор Е.А.Бунькова Зак. //^ Формат 60x84/16. Уч.-иэд.л. 0,46 Подписано к печати 1.0G.1990 года. Тира» 200. Цена 3 коп. Полиграфический участок Института теоретической физики АН УССР
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