- Email: [email protected]
Scaling violation through squark and light gluino production
11 June 1998
Physics Letters B 429 Ž1998. 51–54
Scaling violation through squark and light gluino production L. Clavelli 1, I. Terekhov
2
Department of Physics and Astronomy, UniÕersity of Alabama, Tuscaloosa, AL 35487, USA Received 27 August 1997; revised 12 March 1998 Editor: H. Georgi
Abstract In the light gluino scenario, squarks in the 100 GeV mass region can be copiously produced at the Tevatron without a second heavy particle. Their subsequent dijet decay into quark plus gluino leads to non-scaling structure in the inclusive jet X T distribution. The expected behavior is similar to recent observations. q 1998 Published by Elsevier Science B.V. All rights reserved. PACS: 11.30.Pb; 14.80.Ly
Recent anomalies in the production of jets in pp annihilation have stimulated significant interest as a possible sign of physics beyond the standard model. A case in point is the inclusive jet transverse energy cross section which was reported by CDF as exhibiting a dip at low ET and a rise at high ET relative to the standard model predictions w1x. This behavior was cited as a possible indication of quark substructure or of various other non-standard-model effects w2x. Among these latter was the suggestion that the jet ET distribution could be due, in the light gluino scenario, to extra jet activity from production of gluino pairs and to the expected slower running of a s w3,4x. In addition to these two effects, the possible production of a squark in association with a light gluino could explain one of the several possible bumps visible in the CDF data. ŽFor a discussion of other indications of a light gluino see w5x and for a
1 2
E-mail: [email protected]. E-mail: [email protected].
discussion of direct phenomenological signals in future searches see w6x.. On the other hand it was also found possible w7x to fit the data, apart from the low Ž- 50 GeV. ET values, by readjusting the gluon distribution function in the proton in a way still consistent with other data or by changing the renormalization scheme w8x. Thus, whether or not new physics is contained in the Fermilab data must await further analysis. It is significant that the angular distributions of the jets in various dijet mass bins are consistent with that expected from the standard model w9x. This would seem to rule out many non-standardmodel explanations of the data. However, it has been shown that the light gluino hypothesis would lead to dijet angular distributions in practice indistinguishable from the standard model expectations except in dijet mass bins containing an up squark or down squark w13,14x. This is due to the fact that the structure of light gluino production amplitudes is quite similar to that of other light partons dominated by massless particle exchanges in the t and s channels. However a squark, once produced, will, in the
0370-2693r98r$19.00 q 1998 Published by Elsevier Science B.V. All rights reserved. PII: S 0 3 7 0 - 2 6 9 3 Ž 9 8 . 0 0 4 8 4 - 5
L. ClaÕelli, I. TerekhoÕr Physics Letters B 429 (1998) 51–54
52
light gluino case, decay into dijets with an isotropic angular distribution in its rest frame. The light gluino hypothesis, therefore, seems viable only if the valence squarks are below about 150 GeV or above 650 GeV since currently analyzed data does not constrain the lower or higher mass regions w15,4,14x. The possible bump at about 550 GeV seen by CDF and discussed in the light gluino case in w15x might, therefore, be a statistical fluctuation. This interpretation is supported by the failure of the later analysis w16,17x to confirm a bump in this region. On the other hand the angular distributions have not been published in the vicinity of a possible particle near 100 GeV suggested by the ET data. w3x. Furthermore D0 has not published data spanning the relevant low ET region. Assuming it is relatively less attractive to have squarks above 650 GeV, the study of jet angular distributions in the 100 GeV to 150 GeV dijet mass region could therefore be crucial to the light gluino hypothesis. The parton distribution functions Žpdf’s. in the standard model must presently be treated as theoretically arbitrary functions; the primary constraints are from data on deep inelastic scattering and from direct photon production. This freedom eliminates the necessity of, although not the possibility of, new physics in explaining the Fermilab results for the jet transverse energy cross sections at high ET . It does not at present, however, allow for an understanding of the behavior below 50 GeV ET . In addition, it is possible to study suitably defined scaling distributions whose ratio at two different Fermilab energies is relatively insensitive to modifications of the parton distributions. Such a quantity is the scaled inclusive jet transverse energy cross section, which is predicted to have the form s
ds dXT
2
ž
s a s Ž m . F XT ,
L ,
m
's 's
/
Ž 1.
with XT s
2 ET
's
.
Ž 2.
Here m is conventionally taken to be ETr2, L is the QCD dimensional transmutation parameter, and m represents any particle mass appearing in the theory. Since the lowest order cross sections in QCD are
proportional to a s2 , this has been factored out, although it also could be written as a function of the first two arguments of the scaling function F. If all masses in the theory are negligible compared to 's , F depends on s only through its second argument coming from scaling deviations in the parton distribution functions and from logarithmic scaling violations due to higher order terms in a s both of which effects are expected to be small. The ratio of the scaling distribution at two different Žhigh. energies is therefore expected to be approximately constant in X T Žfor X T R 0.05. independent of small modifications of the pdf’s. The CDF collaboration w18x has presented preliminary results for the ratio
r Ž XT . s
sd srdXT sd srdXT
Ž 's s 630. . Ž 's s 1800.
Ž 3.
In the standard model r Ž X T . departs from unity due to the running of the coupling constant in Ž1. and due to logarithmic scaling violations in the pdf’s. This leads to a predicted value for r near 1.8 approximately independent of X T . The data show a systematic tendency to be below this prediction. In the light gluino case a s runs more slowly than in the standard model leading to a value for r near 1.6 again approximately constant if the squarks are too high in mass to be copiously produced. These values depend somewhat on the assumed scale m s ETr2 which seems to be preferred by the CDF study of the separate ET distributions. The current data for the ratio of the transverse energy distributions at two energies are preliminary. Although systematic errors are still under study and could raise the overall normalization of the scaling curve, it is difficult to imagine systematic errors seriously affecting the point-to-point errors in such a way as to produce the observed structure. The reported structure in r Ž X T . is, therefore, a tantalizing suggestion of the existence of strongly interacting particles whose masses are not negligible compared to 630 GeV and which then lead to a strong effect from the third argument in the F of Ž1.. Weakly interacting particles, such as the W and Z bosons, do not have a sufficiently high production cross section compared to QCD jet production to affect the r parameter significantly. Similarly the top quark or
L. ClaÕelli, I. TerekhoÕr Physics Letters B 429 (1998) 51–54
the prevalent supersymmetry hypothesis with pair produced heavy squarks and gluinos have production cross sections too low to be helpful in the current context. In addition, such states are not expected to have prominent dijet decay modes. On the other hand, in the light gluino scenario, which can be obtained in the context of the constrained supergravity related SUSY breaking model by setting the universal gaugino mass m1r2 to zero, a single heavy squark can be produced in association with a light gluino leading to greatly enhanced squark production cross sections as discussed in w15,3x. In the light gluino case, but not in the standard SUSY picture, a squark will have a predominantly dijet decay into quark plus gluino. Such a squark would produce a dip in the r ratio Žbefore smearing due to experimental resolution and hadronization. at approximately X T s mŽGeV.r1800 followed by a peak at mŽGeV.r630. There is in fact some indication in the data for such a low X T dip followed by a peak at roughly three times higher X T . In this letter we explore this basic signature which should be preserved independent of details such as the choice of renormalization scale, assumptions about squark degeneracy splitting, hadronization smearing effects, etc. These latter effects will be studied in a full length paper to follow. Our present purpose is not to present a definitive fit but to illustrate the size of the dip-bump structure that might appear for simple choices of parton distribution functions and various preliminary assumptions about renormalization scale and squark width enhancement. In the current work we adopt the light gluino hypothesis and consider as in w15,3,14x the lowest order standard model processes together with the effect of sparticle production processes
˜˜ GG ™ GG
Ž 4.
˜˜ QQ™ GG
Ž 5.
˜˜ QG ™ QGG.
Ž 6.
Processes Ž4. and Ž5., while increasing the jet activity by some 6% do not have a significant effect on the r ratio. The possibility of a squark intermediate state in process Ž6. leads however to structure in r as discussed above. The effect is shown in Fig. 1 in the
53
Fig. 1. CDF data on the XT scaling distribution compared to a. the standard model prediction Ždashed line., b. light gluino with decoupled Žeffectively infinitely massive. squarks Ždot-dashed line., and c. light gluino plus 133–135 GeV valence squarks Žsolid lines.. See text.
higher solid curve for a squark mass of 135 GeV. The structure shown in the r parameter theory as a function of X T is due to an intermediate squark in the process of Ž6.. This process has a collinear logarithmic mass singularity as the gluino mass approaches zero. Although this feature is not problematic at present energies, the summation of these singularities would be expected to build an intrinsic gluino distribution in the proton due to gluon splitting. Such a gluino distribution would decrease the gluon distribution in the proton. Several fits to pdf’s including light gluino effects have been published w10,11x. As an example illustrating the effect of intrinsic gluinos, in Fig. 1 we also plot for comparison the scaling curve resulting from the Ruckl-Vogt ¨ pdf set where the 2 to 3 process of 6 is replaced by ˜ Other Žnon-resonant. the 2 to 2 process QG˜ ™ QG. gluino initiated processes are also included here. The process of 6 would of course still occur Žat a reduced level. together with other O Ž a s3 . effects which will partially cancel in the scaling ratio. A complete study of these higher order effects awaits further calcula-
54
L. ClaÕelli, I. TerekhoÕr Physics Letters B 429 (1998) 51–54
tion. In Fig. 1the lower solid line corresponds to the intrinsic gluino pdf set with a squark mass of 133 GeV and the renormalization scale chosen as the parton CM energy. The higher solid line corresponds to the standard w12x CTEQ3 pdf set with scale set as ETr2. In lowest order QCD, the squark width is predicted to be
GQ˜ s 2 MQ˜ a sr3.
Ž 7.
This width would be increased somewhat by electroweak decays of the squark and by QCD corrections to the hadronic decays. In addition the four valence squark states would be split in mass Žby some 10 to 20 GeV in the simple Supergravity related model. To roughly exemplify these effects, in the upper solid curve of Fig. 1 we have increased the squark width by a factor of 1.3. The width of the observed structure is not grossly inconsistent with the expected squark width. A more detailed study, including the effects on the separate ET distributions will be part of the later paper which will also provide space for detailed consideration of resolution and hadronization smearing effects. Since the peaks, if they exist, sit on a steeply falling background, the effect of resolution might be to move the observed peak upward. Given the preliminary nature of the data and uncertainties in the actual amount of smearing present in the data we would not consider any squark mass between 100 GeV and 140 GeV as definitively counter-indicated at present. The possible bump in the data near X T ; 0.28 could be fit by a squark of mass 180 GeV but such a mass is disfavored by dijet angular distribution measurements w13,14x. Our main conclusion at this point is that the light gluino hypothesis together with valence squarks in the 100 GeV to 140 GeV region is in qualitative agreement with current experimental indications as exemplified in Fig. 1. An attempt to present a precise fit must await further understanding of systematic uncertainties in both the experiment and the theory. It seems unlikely that the current magnitude of the observed structure could be fit in any model involving pair production of two heavy particles with coupling strength a s or less or in any model with additional gauge bosons in the electroweak sector.
There has been a recent attempt to understand the anomalies in the scaling data from a Regge point of view w19x. Current fits from this point of view do succeed in reducing the theoretical scaling curve by some 10% from the standard QCD prediction in the region X T - 0.1. This is still far from observations and does not, at present, predict the observed structure. If one ignores the structure apparent in the current experimental analysis, the light gluino fit with squarks far above the 100–200 GeV mass range, shown in the dot-dashed line of Fig. 1 seems to be also preferred by the data over the standard model fit. This work was supported in part by the Department of Energy under grant DE-FG02-96ER40967. References w1x F. Abe et al., CDF Collaboration, Phys. Rev. Lett. 77 Ž1996. 438. w2x R.S. Chivukula, A.G. Cohen, E.H. Simmons, Phys. Lett. B 380 Ž1996. 92. w3x L. Clavelli, I. Terekhov, Phys. Rev. Lett. 77 Ž1996. 1941. w4x Z. Bern, A.K. Grant, A.G. Morgan, Phys. Lett. B 387 Ž1996. 804. w5x L. Clavelli, in: Proceedings of the Workshop on the Physics of the Top Quark, IITAP, Iowa State Univ., Ames Ia, 1995, World Scientific Press. w6x G. Farrar, Phys. Rev. D 51 Ž1995. 3904; Phys. Rev. Lett. 76 Ž1996. 4115. w7x H.L. Lai, J. Huston, S. Kuhlmann, F. Olness, J. Owens, D. Soper, W.K. Tung, H. Weerts, Phys. Rev. D 55 Ž1997. 1280. w8x M. Klasen, G. Kramer, Phys. Lett. B 386 Ž1996. 384. w9x F. Abe et al., CDF Collaboration, Phys. Rev. Lett. 77 Ž1996. 5336. w10x R.G. Roberts, W.J. Stirling, Phys. Lett. B 313 Ž1993. 453. w11x R. Ruckl, A. Vogt, Z. Phys. C 64 Ž1994. 431. ¨ w12x H.L. Lai et al., CTEQ Collaboration, Phys. Rev. D 51 Ž1993. 4763. w13x J. Hewett, T. Rizzo, M. Doncheski, Phys. Rev. D 56 Ž1997. 5703, hep-phr9612377. w14x I. Terekhov, Phys. Lett. B 412 Ž1997. 86, hep-phr9702301. w15x I. Terekhov, L. Clavelli, Phys. Lett. B 385 Ž1996. 139. w16x D0 Collaboration, S. Abachi et al., Phys. Rev. Lett. 75 Ž1995. 618. w17x CDF Collaboration, F. Abe et al., Fermilab-PUB-97r023-E. w18x A. Bhatti, Fermilab-Conf-96r352-E, presented at the DPF conference, Minneapolis, August 1996. w19x V.T. Kim, G.B. Pivovarov, J.P. Vary, hep-phr9709303; V.T. Kim, G.B. Pivovarov, hep-phr9709304.
Physics Letters B 429 Ž1998. 51–54
Scaling violation through squark and light gluino production L. Clavelli 1, I. Terekhov
2
Department of Physics and Astronomy, UniÕersity of Alabama, Tuscaloosa, AL 35487, USA Received 27 August 1997; revised 12 March 1998 Editor: H. Georgi
Abstract In the light gluino scenario, squarks in the 100 GeV mass region can be copiously produced at the Tevatron without a second heavy particle. Their subsequent dijet decay into quark plus gluino leads to non-scaling structure in the inclusive jet X T distribution. The expected behavior is similar to recent observations. q 1998 Published by Elsevier Science B.V. All rights reserved. PACS: 11.30.Pb; 14.80.Ly
Recent anomalies in the production of jets in pp annihilation have stimulated significant interest as a possible sign of physics beyond the standard model. A case in point is the inclusive jet transverse energy cross section which was reported by CDF as exhibiting a dip at low ET and a rise at high ET relative to the standard model predictions w1x. This behavior was cited as a possible indication of quark substructure or of various other non-standard-model effects w2x. Among these latter was the suggestion that the jet ET distribution could be due, in the light gluino scenario, to extra jet activity from production of gluino pairs and to the expected slower running of a s w3,4x. In addition to these two effects, the possible production of a squark in association with a light gluino could explain one of the several possible bumps visible in the CDF data. ŽFor a discussion of other indications of a light gluino see w5x and for a
1 2
E-mail: [email protected]. E-mail: [email protected].
discussion of direct phenomenological signals in future searches see w6x.. On the other hand it was also found possible w7x to fit the data, apart from the low Ž- 50 GeV. ET values, by readjusting the gluon distribution function in the proton in a way still consistent with other data or by changing the renormalization scheme w8x. Thus, whether or not new physics is contained in the Fermilab data must await further analysis. It is significant that the angular distributions of the jets in various dijet mass bins are consistent with that expected from the standard model w9x. This would seem to rule out many non-standardmodel explanations of the data. However, it has been shown that the light gluino hypothesis would lead to dijet angular distributions in practice indistinguishable from the standard model expectations except in dijet mass bins containing an up squark or down squark w13,14x. This is due to the fact that the structure of light gluino production amplitudes is quite similar to that of other light partons dominated by massless particle exchanges in the t and s channels. However a squark, once produced, will, in the
0370-2693r98r$19.00 q 1998 Published by Elsevier Science B.V. All rights reserved. PII: S 0 3 7 0 - 2 6 9 3 Ž 9 8 . 0 0 4 8 4 - 5
L. ClaÕelli, I. TerekhoÕr Physics Letters B 429 (1998) 51–54
52
light gluino case, decay into dijets with an isotropic angular distribution in its rest frame. The light gluino hypothesis, therefore, seems viable only if the valence squarks are below about 150 GeV or above 650 GeV since currently analyzed data does not constrain the lower or higher mass regions w15,4,14x. The possible bump at about 550 GeV seen by CDF and discussed in the light gluino case in w15x might, therefore, be a statistical fluctuation. This interpretation is supported by the failure of the later analysis w16,17x to confirm a bump in this region. On the other hand the angular distributions have not been published in the vicinity of a possible particle near 100 GeV suggested by the ET data. w3x. Furthermore D0 has not published data spanning the relevant low ET region. Assuming it is relatively less attractive to have squarks above 650 GeV, the study of jet angular distributions in the 100 GeV to 150 GeV dijet mass region could therefore be crucial to the light gluino hypothesis. The parton distribution functions Žpdf’s. in the standard model must presently be treated as theoretically arbitrary functions; the primary constraints are from data on deep inelastic scattering and from direct photon production. This freedom eliminates the necessity of, although not the possibility of, new physics in explaining the Fermilab results for the jet transverse energy cross sections at high ET . It does not at present, however, allow for an understanding of the behavior below 50 GeV ET . In addition, it is possible to study suitably defined scaling distributions whose ratio at two different Fermilab energies is relatively insensitive to modifications of the parton distributions. Such a quantity is the scaled inclusive jet transverse energy cross section, which is predicted to have the form s
ds dXT
2
ž
s a s Ž m . F XT ,
L ,
m
's 's
/
Ž 1.
with XT s
2 ET
's
.
Ž 2.
Here m is conventionally taken to be ETr2, L is the QCD dimensional transmutation parameter, and m represents any particle mass appearing in the theory. Since the lowest order cross sections in QCD are
proportional to a s2 , this has been factored out, although it also could be written as a function of the first two arguments of the scaling function F. If all masses in the theory are negligible compared to 's , F depends on s only through its second argument coming from scaling deviations in the parton distribution functions and from logarithmic scaling violations due to higher order terms in a s both of which effects are expected to be small. The ratio of the scaling distribution at two different Žhigh. energies is therefore expected to be approximately constant in X T Žfor X T R 0.05. independent of small modifications of the pdf’s. The CDF collaboration w18x has presented preliminary results for the ratio
r Ž XT . s
sd srdXT sd srdXT
Ž 's s 630. . Ž 's s 1800.
Ž 3.
In the standard model r Ž X T . departs from unity due to the running of the coupling constant in Ž1. and due to logarithmic scaling violations in the pdf’s. This leads to a predicted value for r near 1.8 approximately independent of X T . The data show a systematic tendency to be below this prediction. In the light gluino case a s runs more slowly than in the standard model leading to a value for r near 1.6 again approximately constant if the squarks are too high in mass to be copiously produced. These values depend somewhat on the assumed scale m s ETr2 which seems to be preferred by the CDF study of the separate ET distributions. The current data for the ratio of the transverse energy distributions at two energies are preliminary. Although systematic errors are still under study and could raise the overall normalization of the scaling curve, it is difficult to imagine systematic errors seriously affecting the point-to-point errors in such a way as to produce the observed structure. The reported structure in r Ž X T . is, therefore, a tantalizing suggestion of the existence of strongly interacting particles whose masses are not negligible compared to 630 GeV and which then lead to a strong effect from the third argument in the F of Ž1.. Weakly interacting particles, such as the W and Z bosons, do not have a sufficiently high production cross section compared to QCD jet production to affect the r parameter significantly. Similarly the top quark or
L. ClaÕelli, I. TerekhoÕr Physics Letters B 429 (1998) 51–54
the prevalent supersymmetry hypothesis with pair produced heavy squarks and gluinos have production cross sections too low to be helpful in the current context. In addition, such states are not expected to have prominent dijet decay modes. On the other hand, in the light gluino scenario, which can be obtained in the context of the constrained supergravity related SUSY breaking model by setting the universal gaugino mass m1r2 to zero, a single heavy squark can be produced in association with a light gluino leading to greatly enhanced squark production cross sections as discussed in w15,3x. In the light gluino case, but not in the standard SUSY picture, a squark will have a predominantly dijet decay into quark plus gluino. Such a squark would produce a dip in the r ratio Žbefore smearing due to experimental resolution and hadronization. at approximately X T s mŽGeV.r1800 followed by a peak at mŽGeV.r630. There is in fact some indication in the data for such a low X T dip followed by a peak at roughly three times higher X T . In this letter we explore this basic signature which should be preserved independent of details such as the choice of renormalization scale, assumptions about squark degeneracy splitting, hadronization smearing effects, etc. These latter effects will be studied in a full length paper to follow. Our present purpose is not to present a definitive fit but to illustrate the size of the dip-bump structure that might appear for simple choices of parton distribution functions and various preliminary assumptions about renormalization scale and squark width enhancement. In the current work we adopt the light gluino hypothesis and consider as in w15,3,14x the lowest order standard model processes together with the effect of sparticle production processes
˜˜ GG ™ GG
Ž 4.
˜˜ QQ™ GG
Ž 5.
˜˜ QG ™ QGG.
Ž 6.
Processes Ž4. and Ž5., while increasing the jet activity by some 6% do not have a significant effect on the r ratio. The possibility of a squark intermediate state in process Ž6. leads however to structure in r as discussed above. The effect is shown in Fig. 1 in the
53
Fig. 1. CDF data on the XT scaling distribution compared to a. the standard model prediction Ždashed line., b. light gluino with decoupled Žeffectively infinitely massive. squarks Ždot-dashed line., and c. light gluino plus 133–135 GeV valence squarks Žsolid lines.. See text.
higher solid curve for a squark mass of 135 GeV. The structure shown in the r parameter theory as a function of X T is due to an intermediate squark in the process of Ž6.. This process has a collinear logarithmic mass singularity as the gluino mass approaches zero. Although this feature is not problematic at present energies, the summation of these singularities would be expected to build an intrinsic gluino distribution in the proton due to gluon splitting. Such a gluino distribution would decrease the gluon distribution in the proton. Several fits to pdf’s including light gluino effects have been published w10,11x. As an example illustrating the effect of intrinsic gluinos, in Fig. 1 we also plot for comparison the scaling curve resulting from the Ruckl-Vogt ¨ pdf set where the 2 to 3 process of 6 is replaced by ˜ Other Žnon-resonant. the 2 to 2 process QG˜ ™ QG. gluino initiated processes are also included here. The process of 6 would of course still occur Žat a reduced level. together with other O Ž a s3 . effects which will partially cancel in the scaling ratio. A complete study of these higher order effects awaits further calcula-
54
L. ClaÕelli, I. TerekhoÕr Physics Letters B 429 (1998) 51–54
tion. In Fig. 1the lower solid line corresponds to the intrinsic gluino pdf set with a squark mass of 133 GeV and the renormalization scale chosen as the parton CM energy. The higher solid line corresponds to the standard w12x CTEQ3 pdf set with scale set as ETr2. In lowest order QCD, the squark width is predicted to be
GQ˜ s 2 MQ˜ a sr3.
Ž 7.
This width would be increased somewhat by electroweak decays of the squark and by QCD corrections to the hadronic decays. In addition the four valence squark states would be split in mass Žby some 10 to 20 GeV in the simple Supergravity related model. To roughly exemplify these effects, in the upper solid curve of Fig. 1 we have increased the squark width by a factor of 1.3. The width of the observed structure is not grossly inconsistent with the expected squark width. A more detailed study, including the effects on the separate ET distributions will be part of the later paper which will also provide space for detailed consideration of resolution and hadronization smearing effects. Since the peaks, if they exist, sit on a steeply falling background, the effect of resolution might be to move the observed peak upward. Given the preliminary nature of the data and uncertainties in the actual amount of smearing present in the data we would not consider any squark mass between 100 GeV and 140 GeV as definitively counter-indicated at present. The possible bump in the data near X T ; 0.28 could be fit by a squark of mass 180 GeV but such a mass is disfavored by dijet angular distribution measurements w13,14x. Our main conclusion at this point is that the light gluino hypothesis together with valence squarks in the 100 GeV to 140 GeV region is in qualitative agreement with current experimental indications as exemplified in Fig. 1. An attempt to present a precise fit must await further understanding of systematic uncertainties in both the experiment and the theory. It seems unlikely that the current magnitude of the observed structure could be fit in any model involving pair production of two heavy particles with coupling strength a s or less or in any model with additional gauge bosons in the electroweak sector.
There has been a recent attempt to understand the anomalies in the scaling data from a Regge point of view w19x. Current fits from this point of view do succeed in reducing the theoretical scaling curve by some 10% from the standard QCD prediction in the region X T - 0.1. This is still far from observations and does not, at present, predict the observed structure. If one ignores the structure apparent in the current experimental analysis, the light gluino fit with squarks far above the 100–200 GeV mass range, shown in the dot-dashed line of Fig. 1 seems to be also preferred by the data over the standard model fit. This work was supported in part by the Department of Energy under grant DE-FG02-96ER40967. References w1x F. Abe et al., CDF Collaboration, Phys. Rev. Lett. 77 Ž1996. 438. w2x R.S. Chivukula, A.G. Cohen, E.H. Simmons, Phys. Lett. B 380 Ž1996. 92. w3x L. Clavelli, I. Terekhov, Phys. Rev. Lett. 77 Ž1996. 1941. w4x Z. Bern, A.K. Grant, A.G. Morgan, Phys. Lett. B 387 Ž1996. 804. w5x L. Clavelli, in: Proceedings of the Workshop on the Physics of the Top Quark, IITAP, Iowa State Univ., Ames Ia, 1995, World Scientific Press. w6x G. Farrar, Phys. Rev. D 51 Ž1995. 3904; Phys. Rev. Lett. 76 Ž1996. 4115. w7x H.L. Lai, J. Huston, S. Kuhlmann, F. Olness, J. Owens, D. Soper, W.K. Tung, H. Weerts, Phys. Rev. D 55 Ž1997. 1280. w8x M. Klasen, G. Kramer, Phys. Lett. B 386 Ž1996. 384. w9x F. Abe et al., CDF Collaboration, Phys. Rev. Lett. 77 Ž1996. 5336. w10x R.G. Roberts, W.J. Stirling, Phys. Lett. B 313 Ž1993. 453. w11x R. Ruckl, A. Vogt, Z. Phys. C 64 Ž1994. 431. ¨ w12x H.L. Lai et al., CTEQ Collaboration, Phys. Rev. D 51 Ž1993. 4763. w13x J. Hewett, T. Rizzo, M. Doncheski, Phys. Rev. D 56 Ž1997. 5703, hep-phr9612377. w14x I. Terekhov, Phys. Lett. B 412 Ž1997. 86, hep-phr9702301. w15x I. Terekhov, L. Clavelli, Phys. Lett. B 385 Ž1996. 139. w16x D0 Collaboration, S. Abachi et al., Phys. Rev. Lett. 75 Ž1995. 618. w17x CDF Collaboration, F. Abe et al., Fermilab-PUB-97r023-E. w18x A. Bhatti, Fermilab-Conf-96r352-E, presented at the DPF conference, Minneapolis, August 1996. w19x V.T. Kim, G.B. Pivovarov, J.P. Vary, hep-phr9709303; V.T. Kim, G.B. Pivovarov, hep-phr9709304.