Block, M.B.

Cahn, R.N.

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Lawrence Berkeley National LaboratoryRecent WorkTitleAN ANALYSIS OF FORWARD AND NEAR FORWARD ELASTIC SCATTERING AMPLITUDES FOR pp AND pp COLLISIONSPermalinkhttps://escholarship.org/uc/item/54h4z99tAuthorsBlock, M.B.Cahn, R.N.Publication Date1983-04-01eScholarship.org Powered by the California Digital LibraryUniversity of CaliforniaLBL-16030 C Lawrence Berkeley Laboratory UNIVERSITY OF CALIFORNIA LAWRENCE Physics, Computer Science 8& Fv Mathematics Division 	JUN15 1983 LIBRARY AND DOCUMENTS SECTiON Presented at the XVIII th  Rencontre de Moriond, Orsay, France, January 23-29, 1983 AN ANALYSIS OF FORWARD AND NEAR FORWARD ELASTIC SCATTERING AMPLITUDES FOR pp AND p COLLISIONS Martin B. Block and Robert N. Cahn April 1983 I n Prepared for the U.S. Department of Energy under Contract DE-AC03-76SF00098 DISCLAIMER This document was prepared as an account of work sponsored by the United States Government. While this document is believed to contain correct information, neither the United States Government nor any agency thereof, nor the Regents of the University of California, nor any of their employees, makes any warranty, express or implied, or assumes any legal responsibility for the accuracy, completeness, or usefulness of any information, apparatus, product, or process disclosed, or represents that its use would not infringe privately owned rights. Reference herein to any specific commercial product, process, or service by its trade name, trademark, manufacturer, or otherwise, does not necessarily constitute or imply its endorsement, recommendation, or favoring by the United States Government or any agency thereof, or the Regents of the University of California. The views and opinions of authors expressed herein do not necessarily state or reflect those of the United States Government or any agency thereof or the Regents of the University of California. April 1983 	LBL-16030 AN ANALYSIS OF FORWARD AND NEAR FORWARD ELASTIC SCATTERING AMPLITUDES FOR pp AND pp COLLISIONS*t Martin B. Block Department of Physics Northwestern University Evanston, 11 60201 and Robert N. Cahn Lcurence Berkeley Laboratory University of California Berkeley, CA 94720 Abstract We will present the results of two recently published (1983) papers by M.M. Block and R.N. Cahn0 ' 2 , which analyze for pp and pp elastic scattering the p values (ratios of the real to the imaginary parts of the forward nuclear scattering amplitudes), the total (hadronic) cross sections c, and the b values, the nuclear slope parameters. The predictions of the analyses, from v's > 5 GeV, is compared with the recently measured values of c and b at the SPS Coflider. The analysis has also been redone to include new ISR data available from R211 at 	= 62.5 GeV, in order to estimate "odderon" contributions, i.e., contributions from odd amplitudes with unconventional (non-Reggeon) energy dependence. Limits of —1% are placed on these amplitudes. Our analysis has been extrapolated up to 100 TeV, to give a, p and b predictions for cosmic ray and future collider energies. * This work was supported in part by the Director, Office of Energy Research, Office of High Energy and Nuclear Physics, Division of High Energy Physics of the U.S. Dept. of Energy under Contract DE-AC03-76SF00098. tTalk presented at the xviiith Rencontre de Moriond, Orsay, France, January 23-29, 1983. -2- The high energy behavior (defined here as (T > 5 Gev) of total cross sections a, cross section differences (a=a(pp)- a(p)), p values (ratio of the real to imaginary portion of the forward hadronic amplitude), and b values, the nuclear slope parameters, for both pp and Tp elastic scattering, have long been one of the central concerns of high energy physics. As we note in our papers analyzing these quantities (1,2),  the recent operation of the ISR with both TO andpp collisions has dramatically extended the energy domain of possible measurements (up to /T = 52.8 Gev at the time of publication). Recently, R211 has measured the cross section, a, p and b at IT = 62.5 Gev for pp, and Tp, and UA4( 4) has measured a (vp)  and b (p)  (at low itt) at IT = 540 Gev, which we heard reported this morning. In this note, we have incorporated these new ISR results, which represent the end of a 25 year era in comparing pp and Tp elastic data, into our analysis in order to test for the possible presence of Isoddero n sla. The "odderon", a name coined by Prof. Nicolescu, is an odd amplitude (of a non-Reggeon variety) with an unconventional energy dependence, and we will come back to It later on. Analyticity is a central theme of asymptotic energy behavior, and is of course essential to our analysis. However, rather than introducing artalyticity via the form of dispersion relations, we exploit it in a more direct and simple fashion by writing out explicit amplitudes of the proper analytic behavior and syninetry (in the high energy domain,where the amplitudes, far from poles, are smooth functions of the center-of-mass energy, li). As shown In Fig. 1, it is convenient to introduce even and odd amplitudes, M.. Our goals are three-fold: To parameterize a, p , b concisely and precisely, for both Tp and pp data, from /1 > 5 Gev to /1 62.5 Gev. To extrapolate these fits to collide energies (/T = 540 Gev (a = 71 mb) and the Tevatron collider IT P. 2000 Gev (a = 100 mb) and indeed, to IT- 20 1ev (a = 175 mb), the cosmic ray domain that will be discussed later by Prof. Yodh(3)). -3- (3) To see if the forward (hadronic) pp and Tp amplitudes become equal at very high energies. For example, how well do the data of today exclude the possibility of a constant cross section difference? As detailed in our paper( 1 ), we get an excellent fit to all available date, putting in Fig. 2, C 	a = 0. C Is the equivalent of a subtraction constant in dispersion relations, and turns out to be negligible, whereas setting a=0 means the cross section asymptotically continues to rise with a £n2 s behavior, its limiting value due to the Froissart bound. All data are fitted( 1 ) with the 5 constants A, B, so, 0, a given in Table 1, Fit 1. The explicit formulae for a and p are given in Fig. 2. This note has updated our published analysis by Including the recent experimental results at /T = 62.5 Gev, presented by R211( 4) this morning. The values of A,B, so, 0, a given by Fit 2, Table 1, remain unchanged, with a new 2 /d.f. = 88.7/76. The predlctions( 1 ) for a and p are shown in Fig. 3 and 4, respectively, compared to the experimental data and are the upper curves. In Fig. 3, the total cross section value at IT = 540 Gev, (1 + p 2 ) a = 71±7 mb, as reported this morning by tJA4( 5 ),, is shown. We used the value of p = 0.2 (Fig. 4) in appending the value a = 68.3 ± 7 mb to Fig. 3. Also shown in Fig. 3 and 4 are the dotted curves (lower) corresponding to a non-zero value of a in Fig. 1. It is an attempt to see if the measured values of a at today's energies, which are dominated by a £n2 s behavior, are indeed compatible with a total cross section that even-tually will flatten and go to a constant value. Its parameters are given in Table 1, Fit 2. Clearly, the present experimental results are too inaccurate now to decide. A much more sensitive place to look is in the p value, and a reason-able measurement of p at the SPS might soon settle this important issue. The prediction of 175 mb for /T - 20 TO also allows cosmic ray data to verify whether cross sections continue fj5jflg*  as £n2 s. The nuclear slope parameter b(p) has been measured at small t by LJA4( 5 ) and UA1( 6 ), and was also presented *The prediction for a*0 is —110mb at this energy. -4- this morning. They obtained the values b = 17.6 ± 1.0 and 17.1 ± 1.0 (Gev/c) 2 . We show in Fig. 4 our parameterization of the nuclear slopes b(pp) and b(p), in terms of even and odd slopes b+ = C. + D+ Lns + E+ £n2 s and b- = C_ + D_ Lns, for very small Iti. By fitting the low energy data up to ISR energies( 2 ), we we obtain the values C+ = 10.94 ± .53, D+ = -.09 ± .18, E+ = 0.44 t .016, C- 	23.2 ± 1.6 and D- 	.94 ± .16. Our analysis predicts bp p = 16.7 ± 0.9 (Gev/c) 2 at IT = 540 Gev, and it is excellent agreement with the new measure-ments. The fitted curve is shown in Fig. 5, along with the experimental values. We now turn our attention the "odderons", the non-Reggeon odd amplitudes whose strengths are denoted by E( 0 ), E( 1 ) and E( 2 ) in Fig. 1. We note that odderon( 0) gives no contribution to the total cross section as s., but does not allow Ap to go to zero as s. Odderon( 1 ) gives both finite &a and Ap as whereas odderon( 3 ) actually causes Aa to diverge as £ns as s+. Of course, all 3 possibilities are allowed by the Pomeranchuk theorem, which for cross sections rising as Ln2 s, only states that the ratio of a pp lapp + 1 as The statement that a cross section, rising asymptotically as £n2 s, "saturates the Froissart bound" is perhaps semantically misleading. Although the energy rise due to the Froissart bound can go no faster than £n 2 s, the (experimental) coefficient of £n2 s is only -1% of the allowed strength of the tn 2 s term. This perhaps is one of the deeper mysteries remaining in our understanding of strong interactions in the high energy domain. Our original analysis( 1 ), as shown In Table I, indicates that all 3 coefficients E( 0 ), E( 1 ) and E( 2 ) of the odderons are only about two standard deviations from zero (each taken separately). When compared to the dominant even amplitude, the odderon amplitude is at most -1%. Of course, if compared 	ti to the odd Reggeon amplitude, which vanishes with increasing /, they will become large by definition since they do not vanish with increasing energy. In particular, to give a scale to these results, it is instructive to examine the constant &a arising from odderon(l), i.e., Aa = 	E( 1 ) 	- .16 ± .06 nib., as s+. This would suggest that there is a crossover in pp and Op cross -5- sections at very high energies, with the pp cross section eventually .16 (±.06)mb higher. Since IT = 62.5 Gev is the upper and of the ISR and is the highest energy where, for the next decade or so, one can compare elastic pp and p scattering, we refit all of the experimental data at lower energies along with the new R21.1 data( 4), for odderon( 1 ). The result is essentially indistinguishable from that given In Table I, with only the coefficient D changing from -40.8± 1.8 to -40.9 ± 1.8, and 2 /d.f. = 80.6/75. Thus, our original conclusions( 1 ' 2 ) that the odderon contributions are exceedingly small is reinforced by the new experimental data. There is currently discussion underway to plan for an ultra-high energy collider of 20 Tev on 20 Tev, using Tp collisions. If the cross section continues to rise as Ln2 s, we predict a= 200 mb, p= .16 and b= 29 (Gev/c) 2 . Dafaeanrae M.M. Block and Robert N. Cahn, Phys. Lett. 120B, 224 (1983). M.M. Block and Robert N. Cahn, Phys. Lett. 120B, 229 (1983). G. Yodh, Cosmic Ray Results, this conference. M. Bottje, R211 results, this conference. Sanguinetti - IJA4 results, this conference. Hodges, IJA1 results, this conference. Acknowled ginent s This work was supported by the Director, Office of Energy Research, Office of High Energy and Nuclear Physics, Division of High Energy Physics of the U.S. Department of Energy under Contract DE-AC03-76SF00098. . • cv, CJ CJ C4 C4 CJ • r. - I. r. '4- -•-. • C UD — co • . . . . . 04 cv, — C C '.0 	• C • C CC I I I •+4 41 84I C C I I I - '.0 . .0C.4 © C.-' S I •44 S I I CC "'C CC C C C C C C • 0% CO• '.0 	• • C . ow C C C C Ln C d' d 4 d d•' I '.0 . co  C • r- c%J — N- -4 S C\I C4 '+4 +4 4-I •+4 +4 +I en C., I I I I I I • • . . . C LD +I +I 44 544 +4 '+4 14) 14) o C', C', C' C') C') C') U) C C C C C C CO• ON 	• C.' 	• '0 	• 0 C +4 C • +4 C • +4 C • +4 C • +4 C • +4 C 14) C C C C C C N- 	• • t-.. 	• N. 	• • C. .0 N- C r- C r C i.. C i'.. 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Any conclusions or opinions expressed in this report represent solely those of the author(s) and not necessarily those of The Regents of the University of California, the Lawrence Berkeley Laboratory or the Department of Energy. Reference to a company or product name does not imply approval or recommendation of the product by the University of California or the U.S. Department of Energy to the exclusion of others that may be suitable. ot ti tn 0 NO 4-11 I tn tn 0 0 tTj C) 0 z 

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AN ANALYSIS OF FORWARD AND NEAR FORWARD ELASTIC SCATTERING AMPLITUDES FOR pp AND pp COLLISIONS

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AN ANALYSIS OF FORWARD AND NEAR FORWARD ELASTIC SCATTERING AMPLITUDES FOR pp AND pp COLLISIONS

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