In this talk, given at "RunII QCD and weak boson WS", we report on
calculations of the survival probability of the large rapidity gap (LRG)
processes and its energy behaviour.Comment: 4 pages, 3 figure

Levin, Eugene

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arXiv

Levin, E.

UNT Digital Library

s _ I BNL-67023 Cost of Survival for Large Rapidity Gaps Eugene Levin a b* a HEP Department, School of Physics, Tel Aviv University, Tel Aviv 69978, ISRAEL b Physics Department, Brookhaven National Laboratory, Upton, NY 1.1973 - 5000, USA In this note we report on calculations of the survival probability of the large rapidity gap (LRG) processes and its energy behaviour. 1. INTRODUCTION In this note we consider reaction P+P-+ (1) Xl+@1 (YI,PI,~ +I ~)+[LJZ']+jet2(~2,t << 1_')+x2 , where LRG denotes the large rapidity gap between produced particles and X corresponds to a system of hadrons with masses much smaller than the total en- ergy. The story of LRG processes started from Refs. [l- 31, where it was noticed that these processes give us a unique way to measure high energy asymptotic at short distances. Indeed, at first sight the experimental observable f Sap = CJ( dijet production with LRG ) cinclusive ( di jet production ) (2) is directly related to the so called “hard” Pomeron ex- change. However, this is not the case and the fac- tor ( survival probability (1 S 1”) appears between “hard” Pomeron exchange and the experimental servable. the ob- f o(LRG) =<s2> -'=cJ(INCL) 2 Actually, this factor (1 S 1”) is a product of two survival probabilities (I S I”) = (3) ‘Email: leving@post.tau.ac.il, elevin@quark.phy.bnl.gov (I Sbremssfrohlung @Y = IY~-YzI I">:*(I &pectators(~) 12) which have different meanings. (I SbremSStr&lUng 12) is probability that the LRG will not be filled by emission, of bremsstrahlung gluons ii-om partons, taking part in the “hard” interaSction ( see fig l-a). This factor is certain11 important and has been calculated in pQCD in Refs. [4,5,10]. We are not going to discuss it here; (I Sspectatorl I”) is related to probability that ev- ery ,pa,rion with xi > x1 will have no inelastic interuNction with any parton with x < x2 ( see fig. l-b). The situation with our knowledge of this survival probability is the main goal of this paper. 2. Q&A Q: Have we developed a theory for (I Sspectators (s) I2 )? A: No, there are only models on the market (see Refs. [S-lo]). Q: Can we give a reliable estimates for the value of (I &pectator I") ? A: No, we have only rough estimates based on the Eikonal - type models. Q: Can we give a reliable estimates for the energy behaviour of (1 Sspectator I”) ? A: No, but we understood that (I Sspectator 12) could steeply decreases with energy. Q: Why are you talking about (I Sspectator j2) if you can do nothing ? A: Because dealing with models we learned what questions we should ask experimentalists to improve our estimate *and what problems we need to solve the- oretically to provide reliable estimates. 1 E’ig. l-a Fig. l-b Figure 1. Two sources of survival probability: sion of gluons from the par-tons taking parts (a) emis- in “hard ” interaction and (b) emission due to of spectator quarks (partons ). %oft” interaction 3. EIKONAL-TYPE MODELS 3.1. Eikonal model In eikonal model we assumed that the correct de- grees of freedom at high energies are hadrons, and, therefore, the scattering amplitude is diagonal in the hadron basis. Practically, it means [6] that we assume that the ratio aSD/oel ‘ < 1. In this model the uni- tarity constraint looks simple, namely, lmael(s, b) =I ~(s,b) I2 +Gi,(s,b) , (4) which has solution in terms of arbitrary real function - opacity 0(s, b): [ Wa.b) Q = i 1-e-T 1 ; Gi,(s, b) = 1 - e-o(‘.‘) ; (6) 1 Q(s, b) = zj(s)e-&C; (7) where Eq. (7) is Pomeron-like parameterization that has been used for numerical estimates. The formula Figure 2. Survival probability in the eikonal model. for survival probability looks as [3] [S] where R& is radius for the hard processes. In Ref. [6] the values of RL and R2(s) were discussed in details. The main observation is that the experimental value of the ration uel/utot depends only on the value of V. This gives us a way to find the value of u directly from the experimental data. The result is plotted in Fig.2 and shows both the small value of the survival probability and its sharp energy dependence. 3.2. Three channel model. The assumption that oSD/uel ’ < 1 is in contradic- tion with the experimental data, therefore, it is inter- esting to generalize the eikonal model to include pro- cesses of the diffractive dissociation. It was done in Ref.[7], where the ri.ch diffractive final state was de- scribed by one wave function orthogonal to the hadron XQ hadron - -(YQ~+p~Ilz; *j, = -Be, +a*‘2, (9) where cy2 + p2 = 1. The scattering amplitude is diag- onal with respect functions ki,z and we used Eq. (5)- Eq. (7) -type parameterization to describe it. The re- sult of our calculation is given in Fig.3. 4. CONCLUSIONS The experimentally observed value of the survival probability appear naturally in these two models. 2 The parameters that have been used are in agree- ment with the more detailed fit of the experimental data. It turns out that the scale of (1 Sspectator 12) is given by ratios R,l = z, RSD = z and RDD = z, but not the ratio RD = i7=, + (T?D + %TDD otot , which does not show any energy dependence. The further measurement all ratios mentioned above will specify the model and will provide a better predic- tions for the survival probability. For example, new data on RDI, [ll] will specify the value of /3 which will lead to more definite predictions for (1 Sspectator 12) (see Fig. 3). Acknowledgements: I am very grateful to A. Gotsman and U. Maor for encouraging optimism and their permanent efforts in hard business of LRG survival. My special thanks goes to Larry McLerran and his mob at the BNL for very creative atmosphere and hot discussion on the subject. This research was supported in part by the Israel Sci- ence Foundation, founded by the Israeli Academy of Science and Humanities, and BSF # 9800276. This manuscript has been authorized under Contract No. DEAC02-98CH10886 with the U.S. Department of Energy. REFERENCES 1. 2. 3. 4. 5. 6. 7. 8. 9. Yu.L. Dokshitser,- V. Khoze and S.I. Troyan,Sov.J.Nucl.Phys. 46 (1987) 116. Yu.L. Dokshitser, V.A. Khoze and T. Sjostrand, Phys.Lett. B274 (1992 )116. J.D. Bjorken, Phys.Rev. D45 ( 1992 ) 4077; D47 ( 1993 ) 101. A.D. Martin, M.G. Ryskin and V.A. Khoze, Phys.Rev.D56 ( 1997 ) 5867; Phys. Lett B401 ( 1997 ) 330. G. Oderda and G. Steman, Phys.Rev. Lett. 81 ( 1998 ) 359; Talk at ISMD’99, Providence,RI, 9-13 Aug 1999, hep-ph/9910414; E. Gotsman, E. Levin and U. Maor, Phys.Rev.D48 ( 1993 ) 2097; Nucl.PhysB493 (1997 ) 354; Phys. Lett. B438 (1998) 229. E. Gotsman, E. Levin and U. Maor, Phys.Rev. D60 (1999) 094011; Phys. Lett. B438 (1998) B452 (1999) 387, B438 (1998) 229-234. R.S. Fletcher, Phys.Rev.D48 ( 1993 ) 5162; Phys.Lett.B320 (1994) 373. A. Rostovtsev and M.G. Ryskin, Phys. Lett. B390 ( 1997 ) 375 ). 10. E. Levin, A.D. Martin and M.G. R.yskin. J.Phys.G25 (1999) 1507. 11. K. Goulianos, talk at this WS. Q.. *--...._ -... 30 .’ r 1%. ---.___ L -... < I s I2 >* a... 0%. *... ‘-.. %. \_ *... --.. --.. -.. --,. . . . . . . . . . . . -. $0 * r Fig.S-a 2 75 25 P 25 --- Fig. 3-b Fig. 3-c Figure 3. The value of survival probability (Fig.3-a), its energy dependence (Fig.3-b) and prediction for the ratio of doublt: diffraction dissociation to the total cross section (Fig.3-c) versus p. 3 

Cost of Survival for Large Rapidity Gaps

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Cost of Survival for Large Rapidity Gaps

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