In this report an exponential trajectory for the Pomeron is introduced for better description of the inclusive differential cross-section of single diffraction at high 4-momentum transfers

Baishev, I S

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EUROPEAN ORGANIZATION FOR NUCLEAR RESEARCHCERN-SL-2000-077 APSingle diffraction at high momentumtransfersI. BaishevAbstractIn this report an exponential trajectory for the Pomeron is intro-duced for better description of the inclusive differential cross-sectionof single diffraction at high 4-momentum transfers.Geneva, SwitzerlandNovember 2000∗ Also IHEP, Protvino, RussiaThe single diffractive collisions in the interaction points of the LHC can beimportant for beam loss studies [1], [2]. Each of the two high luminosity inter-action points will produce up to 1.5  108 diffractive protons per second. Thelocation of such proton losses in the machine depends on 4-momentum transfer tand on the fraction of the momentum loss ξ = 1− p/p0.The majority of the measured differential cross-sections covers the range ofjtj  1GeV2 and the parameters of theoretical and phenomenological models werefitted in the same range of t. The most recent comprehensive analysis of singlediffraction data is given in [3] for the widest possible range of the center of massenergy squared s. The formula for the differential cross-section proposed in [3]can be written asd2 σsddξ dt= 5.865(1s)F 2(t) ξ1+−2αP (t) [mbGeV2] , (1)where αP (t) is the Pomeron Regge trajectory andF (t) =4m2 − 2.8t4m2 − t(1− t0.71)−2is the proton form factor, m is the mass of the proton.All the experimental data at small t are described successfully by the expres-sion (1) with the linear Pomeron trajectoryαP (t) = 1 +  + α0t (2)with  = 0.104 , α0 = 0.25 GeV−2. However the higher is jtj the worse is theagreement with the measured data. This can be clearly seen in Figure 1 wherethe case of linear αP (t) is shown by the dashed curves.The analysis [6] of single diffraction atps = 630 GeV measured by UA8collaboration shows that αP (t) is not linear for jtj > 1GeV2. A quadratic termin t is introduced in [6] for the best fit of their data measured in the range2GeV2 > jtj > 0.8GeV2. Such an approach means that if new data at higher twould appear then, more cubic, biquadratic etc. terms with corresponding freeparameters should be added to the linear trajectory of Pomeron.We therefore propose to replace the linear trajectory by the exponential oneαP (t) =  + eα′t (3)without introducing any new parameters. This empirical trajectory improvesthe agreement of formula (1) with the experimental data at the highest mea-sured t (see solid lines in Figure 1) while the good agreement at lower t remainsunchanged.We would like to thank J.B. Jeanneret for his helpful comments.2Figure 1: The inclusive differential cross-sections of the single diffraction. Pointswith errorbars show the experimental data: ISR [5] - a),b) and UA8 [6] - c).Dashed lines represent the formula (1) with linear αP (t) as given by the expression(2). Solid lines represent the same formula (1) with the proposed nonlinearexpression (3) for αP (t).3References[1] LHC Conceptual Design, CERN/AC/95-05, (1995), p.48.[2] I. Ajguirei et al., LHC Project Report 398, 2000.[3] K. Goulianos and J. Montanha, Phys.Rev. D59, 114017(1999)[4] A. Donnachie and P.V. Landshoff, Nucl.Phys. B303, 634(1988)[5] M.G. Albrow et al., Nucl.Phys. B108, 1(1976)[6] A. Brandt et al., Nucl.Phys. B514, 3(1998)4

Single diffraction at high momentum transfers

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