We consider the jet cross sections for gluons coupling to quarks with an
anomalous chromomagnetic moment. We then apply this to the deviation and bounds
from QCD found in the CDF and D0 Fermilab data, respectively, to find a range
of possible values for the anomalous moments. The quadratic and quartic terms
in the anomalous moments can fit to the rise of a deviation with transverse
energy. Since previous analyses have been done on the top quark total cross
section, here we assume the same moment on all quarks except the top and find
the range $|\kappa'| \equiv |\kappa/(2 m_q)| = 1.0\pm 0.3$ TeV$^{-1}$ for the
CDF data. Assuming the anomalous moment is present only on a charm or bottom
quark which is pair produced results in a range $|\kappa'_{b,c}| = 3.5 \pm 1.0
$ TeV$^{-1}$. The magnitudes here are compared with anomalous magnetic moments
that could account for $R_b$ and found to be in the same general range, as well
as not inconsistent with LEP and SLD bounds on $\Delta \Gamma_{\text{had}}$.Comment: REVTeX, 11 pages, 2 postscript figure

A.D. Martin

B. Flaugher

B.L. Combridge

D. Atwood

D. Silverman

Dennis Silverman

E. Eichten

F. Abe

G.L. Shaw

J. Reid

K. Cheung

M. Bander

P. Haberl

S.J. Brodsky

T.G. Rizzo

English

arXiv

Crossref

Physical Review D

Anomalous chromomagnetic moments of quarks and large transverse energy jets

We consider the jet cross sections for gluons coupling to quarks with an anomalous chromomagnetic moment. We then apply this to the deviation and bounds from QCD found in the CDF and D0 Fermilab data, respectively, to find a range of possible values for the anomalous moments. The quadratic and quartic terms in the anomalous moments can fit to the rise of a deviation with transverse energy. Since previous analyses have been done on the top quark total cross section, here we assume the same moment on all quarks except the top quark and find the range |κ′|≡|κ(2mq)|=1.0±0.3 TeV-1 for the CDF data. Assuming the anomalous moment is present only on a charm or bottom quark which is pair produced results in a range |κb,c′|=3.5±1.0 TeV-1. The magnitudes here are compared with anomalous magnetic moments that could account for Rb and found to be in the same general range, as well as not inconsistent with CERN LEP and SLD bounds on ΔΓhad

Silverman, Dennis

eScholarship - University of California

UC IrvineUC Irvine Previously Published WorksTitleAnomalous chromomagnetic moments of quarks and large transverse energy jetsPermalinkhttps://escholarship.org/uc/item/8gp9f6v5JournalPhysical Review D, 54(9)ISSN2470-0010AuthorSilverman, DennisPublication Date1996-11-01DOI10.1103/physrevd.54.5563Copyright InformationThis work is made available under the terms of a Creative Commons Attribution License, availalbe at https://creativecommons.org/licenses/by/4.0/ Peer reviewedeScholarship.org Powered by the California Digital LibraryUniversity of CalifornianeopPHYSICAL REVIEW D 1 NOVEMBER 1996VOLUME 54, NUMBER 90556-2Anomalous chromomagnetic moments of quarks and large transverse energy jetsDennis SilvermanDepartment of Physics and Astronomy, University of California, Irvine, Irvine, California 92717-4575~Received 15 May 1996!We consider the jet cross sections for gluons coupling to quarks with an anomalous chromomagneticmoment. We then apply this to the deviation and bounds from QCD found in the CDF and D0 Fermilab data,respectively, to find a range of possible values for the anomalous moments. The quadratic and quartic terms ithe anomalous moments can fit to the rise of a deviation with transverse energy. Since previous analyses havbeen done on the top quark total cross section, here we assume the same moment on all quarks except the tquark and find the rangeuk8u[uk/(2mq)u51.060.3 TeV21 for the CDF data. Assuming the anomalousmoment is present only on a charm or bottom quark which is pair produced results in a rangeukb,c8 u53.561.0 TeV21. The magnitudes here are compared with anomalous magnetic moments that couldaccount forRb and found to be in the same general range, as well as not inconsistent with CERN LEP and SLDbounds onDGhad. @S0556-2821~96!05821-3#PACS number~s!: 13.87.Ce, 13.40.Em, 14.65.2qsasad-tict---I. INTRODUCTIONThere are several higher-dimensional operators thatbe used to evaluate structure from a theory beyond the sdard model @1#. In this paper we use the time-honoreanomalous magnetic moment as the indicator@2–5#, appliedto the quark-gluon vertex, or the anomalous chromomagnmoment. Several papers have been written analyzingcontribution of such a moment to the top production crosection @6–10#. In this paper, we assume such a momecould apply to any or all of the mainly annihilated, scatteror produced quarks other than the top quark. The resultthis will be different from those of the four-Fermion containteraction operators, and also should be included in evations of possible structure. Along with the exchange of a s3/2 excited quark state@11#, theET dependence and angulatwo-jet behavior could help further limit or establish a composite mechanism, or new interactions from higher mscales. The same theory that gives an anomalous chromagnetic moment also may give a four-Fermion contactteraction, but here we analyze only the anomalous mommechanism in a general context. For a complete analysiall color current contributions in a particular model, we refto the recent analysis of the Minimal Supersymmetric Stdard Model@12#. The key point in our analysis is that thanomalous moment termk8smnqn, when compared to theDirac currentgm , grows at highET asO(k8ET).In the top production papers, gluon fusion or quark fusito a virtual gluon are calculated to produce the-t̄ pair. Herewe include all quark gluon hadronic processes since quacommonly present in protons and antiprotons could havesmall anomalous moments.Since next-to-leading order QCD corrections have nbeen calculated for this general set of anomalous momprocesses, to compare with the data we follow the ColliDetector at Fermilab Collaboration~CDF! @13,14# proced-ure of calculating the ratio of the theory with structure dvided by lowest order QCD and comparing it with the rat54821/96/54~9!/5563~4!/$10.00cantan-deticthessntedofctlua-pinr-ssmo-in-entofern-eonrkstheotenteri-ioof data divided by next to leading order~NLO! QCD. Wefind that an anomalous chromomagnetic coefficientuk8u5uk/(2mq)u51.0 TeV21 fits the CDF rise, and would beroughly upper bounded by 1.3 TeV21, and lower boundedby 0.7 TeV21. The central value for the rise in CDF is notdirectly supported by the D0@15# data, but is within the onesigma systematic energy calibration error curve for D0,which rises to 120% atET5450 GeV.We usek8 since in the general case the internal diagramor dynamics might not involve the light external quark, and anew physics model calculation will givek8 directly. The useof the breakup into a vector current (gm) and an anomalouschromomagnetic moment term (ik8smn) includes all anoma-lous moment vertex corrections ink8 including those ofQCD. However, at the very large momentum transfers weare considering here, there are form factors on the QCD vertex corrections making up the anomalous chromomagneticmoment either for virtual gluons or for highET virtualquarks~‘‘sidewise form factors’’@16#!, which will damp like@kQCD8 5O(mq /p'2 )# and become irrelevant. At someq2, theanomalous moment from new or composite interactions alsowill evidence a form factor. That is automatically included inthe analysis by consideringk8(q2) as a function ofq2, but inthe comparison to the data, we do not need to invoke thadependence yet. We test whether an anomalous magnetmoment equal to the anomalous chromomagnetic momenpossibly indicated here would be in conflict with theGhadaccuracy at the CERNe1e2 collider LEP, and find it wouldnot be.Because of discrepancies in the total hadronic cross sections for charm and bottom production at LEP and the SLACLarge Detector~SLD!, Rc andRb , we also find a separaterange for either the charm or bottom quark only having ananomalous chromomagnetic moment, using the quarkantiquark production cross sections. The range for the CDFdata isukb,c8 u53.561 TeV21. We note that if theRb dis-crepancy is accounted for by an anomalous magnetic mo5563 © 1996 The American Physical Societygr-et-rn5564 54DENNIS SILVERMANment, it is the same order of magnitude as the anomalchromomagnetic moment found here.AFBb is not inconsistentwith this interpretation and rules out one of two possibanomalous magnetic moment values. For comparison wresults from the top quark total cross section from Ref.@8#,we note from their Fig. 3, using present CDF and D0 datas top, that 0<k tg<0.35. This corresponds to 0<k t8g<1TeV21, and is better than the inclusive jet limits for theb orc quark alone calculated here.II. ANOMALOUS CHROMOMAGNETIC MOMENTCROSS SECTIONSThe top gluon fusion production@7,9,10# with anomalouschromomagnetic moments has been calculated already.use the simplifications of these for the case of zero qumass in the various channels in which quark-quark-gluogluon processes occur. For completeness, we repeat tformulas here for the massless case along with the massQCD contribution. We also present here the result wanomalous chromomagnetic moments for quark-antiquannihilation and scattering to the same quark-antiquark winterference, and its crossed quark-quark scattering. We tpresent the cross sections for different quarks scatteringannihilating. The cross sections are even in powers ofk8 dueto the zero quark mass limit being used. This is becausezero mass only gamma matrices occur in the QCD tracesubstitution of an anomalous momentsmn term for a gmwould give an odd number of gamma matrices and resultin a zero trace, unless accompanied by an additionalsmnterm. In other terms, at zero quark mass, there is no interence between helicity conserving and helicity flip processhelicity conserving ones have either no anomalous momterms or two such terms; helicity flip ones have one anomlous moment for each helicity flipped quark line, and thgets squared in the cross section. Neglect of the masspropagator term could give an error of ordermb /ET'2.3%in the amplitude atET5200 GeV, or 4.5% in the cross section.A. Gluon processesThe well-known result@17# for gluon-gluon scattering isdŝdt̂5pas2ŝ292 S 32 t̂ ûŝ2 2ûŝt̂2 2 ŝt̂û2D . ~1!For quark-antiquark to gluon-gluon@18,17,7,9#, the crosssection isdŝdt̂5pas2ŝ21672F83 S ût̂ 1 t̂ûD 112t̂ ûŝ2 261 283 k82ŝ1163 k84t̂ ûG .~2!For gluon-gluon to quark-antiquark, we use the above,placing the coefficient 16/72 by 16/256, for either the quaor antiquark being observed.For gluon-quark to gluon-quark with the gluon observe~or gluon-antiquark to gluon-antiquark!, the cross section isousleithonWearkn-heselessitharkithhenandatandingfer-es:enta-isin a-re-rkddŝdt̂52pas2ŝ21696F83 S ŝû1 ûŝD 112ûŝt̂2 261 283 k82t̂1163k84ûŝG . ~3!For gluon-quark to gluon-quark with the quark observed~orgluon-antiquark to gluon-antiquark!, we interchanget̂ withû in the above equation.B. Quark processesFor quark antiquark to the same quark antiquark includint-channel exchange as well ass-channel annihilation withtheir interference, and observing the quark, we havedŝdt̂5pas2ŝ21636H ~ û21 t̂2!ŝ2 1 ~ ŝ21û2!t̂2 2 23 û2ŝt̂1k82F4ŝt̂ ûS 1ŝ211t̂2D 1 13 ûS 91 ŝt̂ 1 t̂ŝD G112k84S ~ t̂2û!21~ ŝ2û!22 13 ~ t̂2û!~ ŝ2û!D J .~4!For the above process observing the antiquark, we intechanget̂ and û in the above formula. For identical quarksscattering to the same identical quarks, we interchangeŝ andû in the above equation, and add a factor of 1/2 for thidentical final state quarks.For a quark-antiquark annihilation to a virtual gluon cre-ating a different quark-antiquark pair, as in charm and botom production, summing over identical cross sections foeither quark or antiquark observed~which will later be mul-tiplied by 4 for four other light quarks being created!, wehave for thes-channel gluon exchangedŝdt̂5pas2ŝ21636S ~ û21 t̂2!ŝ2 14k82ŝt̂ û 1ŝ2 1 12 k84~ t̂2û!2D .~5!For q1q̄8→q1q̄8 observing the final quark, we have forthe t-channel gluon exchangedŝdt̂5pas2ŝ21636S ~ ŝ21û2!t̂2 14k82ŝt̂ û 1t̂2 1 12 k84~ ŝ2û!2D .~6!For observing the final antiquark, we use the above equatiowith t̂ and û exchanged. Forq1q8 to q1q8 observing thequark, we use the above formula and interchangeŝ and û inthe large parentheses. Forq1q8 to q1q8 observingq8, wevass54 5565ANOMALOUS CHROMOMAGNETIC MOMENTS OF QUARKS . . .interchanget̂ and û in the large parentheses of the aboformula.III. COMPARISON WITH POSSIBLE ANOMALOUSMAGNETIC MOMENTS IN Z COUPLINGSThe possibility of anomalous magnetic momentsquarks appearing at LEP and SLD at theZ peak and theirforward-backward asymmetry has been considered@4,8#.Here we just get values to indicate the order of magnitureferring the reader to the more careful and complete ansis by T.G. Rizzo@8#, which gives20.012<kbe<20.002 at95% CL, updated to Moriond 1996 data@19#. With ananomalous electric dipole moment as well, it allows positikbe<0.025. Using the integrated cross section@4,8# for bproduction at theZ peak, we find withmb54.5 GeV ~andwith F285kbe)s}@vb21ab213vbkbe1mZ2kbe2/~8mb2!#, ~7!s}~0.36521.03kbe151.1kbe2!. ~8!Letting the kbe terms account for the discrepancy@20#,DRb /Rb50.026 gives two solutions,kbe50.027, andkbe520.0069, corresponding tokb8e53.0 TeV21 andkb8e520.77 TeV21.AFBb isolates the cosu term in theZ cross section, whichcan be partly due to the anomalous magnetic moment@4,8#@AbSM[2vbab /(vb21ab2)#AFBb 534AbSMAe~11kbe/gV!/~11DRb /Rb!, ~9!where the inverse power term has been taken here to m11DRb /Rb . Using the SM value forAbSM the positivekbe50.027 gives a 3.1s discrepancy with @20#AFBb 50.100260.0028, and is eliminated. The negativkbe520.0069 (kb8e520.77 TeV21) value only gives a0.4s deviation and is consistent. The error oAb5AbSM(11kb3/vb)/(11DRb /Rb) is about 6%, and it is11% below theory. The correction of the anomalous momonly lowers theory by 0.5%.Our calculated CDF jet cross sections do not dependthe sign ofk8g, and for the case of only theb quark havingthe anomalous chromomagnetic momentukb8gu53.561TeV21 is not inconsistent with theDRb anomalous magneticmoment since there will be a numerical factor dependinghow the electric and color charges are distributed amonginternal constituents with different masses.For the case where all quarks except top are givenanomalous chromomagnetic moment, allowing an eqanomalous magnetic moment for each, we find changeDGhad/Ghad of 0.0017, 0.0005, and20.0005, correspondingto thek851.3, 1.0, and 0.7 TeV21 cases, respectively. Thiis at most a ones discrepancy since the fractional error@20#on DGhad/Ghad is 60.0019.eofde,ly-veatchenentononthetheualinIV. RESULTS AND CONCLUSIONSIn calculating the jet transverse energy distributions, wehave used the parton distribution functions MRSA8 @21#.Since we are taking ratios of anomalous moment contribu-tions to strict QCD, both in leading order, most variance withparton distribution functions~PDFs! drops out, only beingabout 2% atET5450 GeV among the Martin-Roberts-Stirling ~MRS! set of PDFs, or between MRSA8 andCTEQ3M. Assuming all quarks except the top have the sameanomalous chromomagnetic moment, we find in Fig. 1 thatthe range uk8u51.060.3 TeV21 will fit the CDF data@13,14#, and be in the allowed systematic error range of theD0 data@15#. The quadratic and quartic terms ink8 give anatural fit to the possible curvature in the data, and indicateFIG. 2. The ratio of the anomalous chromomagnetic momentcontribution of either a bottom or charm quark-antiquark pair cre-ated to the lowest order QCD jet distribution in transverse energy.The dashed, solid, and dotted curves are forukb,c8 u54.5, 3.5, and2.5 TeV21, respectively. The data are as in Fig. 1.FIG. 1. The ratio of the anomalous chromomagnetic momentcontribution to the lowest order QCD jet distribution in transverseenergy. The dashed, solid, and dotted curves are foruk8u51.3,1.0, and 0.7 TeV21, respectively. The crossed data are from CDFrun 1a, and the circle data from run 1b~preliminary!.ithons.oneirS.up-on-5566 54DENNIS SILVERMANwhy the corrections do not show up significantly unET>200 GeV. It is not inconsistent with an equal anomalomagnetic moment being present for the quarks at theZ p ak.If the charm or bottom quark alone among the lightquarks possesses a sizable anomalous chromomagneticment, we find in Fig. 2 the rangeukb,c8 u53.561 TeV21 willfit the CDF data, and be in the allowed range of the D0 daIt is not inconsistent with a comparable anomalous magnmoment explanation@8# of Rb .tilusermo-ta.eticACKNOWLEDGMENTSThe author thanks Professor Myron Bander for help wthe conceptual framework and numerous helpful discussiWe also thank W. Giele for supplying the structure functiprogram. The author thanks the SLAC theory group for thhospitality and acknowledges discussions with S. Drell,Brodsky, L. Dixon, and T.G. Rizzo. This research was sported in part by the U.S. Department of Energy under Ctract No. DE-FG03-91ER40679.@1# E. Eichten, K. Lane, and M. Peskin, Phys. Rev. Lett.50, 811~1983!.@2# S.J. Brodsky and S.D. Drell, Phys. Rev. D22, 2236~1980!.@3# G.L. Shaw, D. Silverman, and R. Slansky, Phys. Lett.94B, 57~1980!.@4# D. Silverman and G.L. Shaw, Phys. Rev. D27, 1196~1983!.@5# J. Reid, M. Samuel, K.A. Milton, and T.G. Rizzo, Phys. RevD 30, 245 ~1984!.@6# D. Atwood, A. Aeppli, and A. Soni, Phys. Rev. Lett.69, 2754~1992!.@7# D. Atwood, A. Kagan, and T.G. Rizzo, Phys. Rev. D52, 6264~1995!.@8# T.G. Rizzo, Phys. Rev. D53, 2326~1996!.@9# P. Haberl, O. Nachtmann, and A. Wilch, Phys. Rev. D53,4875 ~1996!.@10# K. Cheung, Phys. Rev. D53, 3604~1996!.@11# M. Bander, Phys. Rev. Lett.77, 601 ~1996!.@12# J. Ellis and D.A. Ross, Report No. CERN-TH/96-108, hep-p9604432~unpublished!.@13# CDF Collaboration, F. Abeet al., Phys. Rev. Lett.77, 438~1996!..h/@14# CDF Collaboration, B. Flaugher, talk given at DPF,Indianapolis, 1996 ~unpublished!, webpage: http://wwwcdf.fnal.gov/physics/new/qcd/qcd_plots/inclusive_jets/public/inclusive_jet_1b.html@15# D0 Collaboration, J. Blazey, talk given at Recontre de Mori-ond, 1996, Report No. FERMILAB-CONF-96-132-E,199 ~unpublished!, webpage: http://d0sgi0.fnal.gov/public/inclusive_jets.html@16# Shown for QED in D. Silverman, Ph.D. thesis, Stanford Uni-versity, 1968.@17# E. Eichten, I. Hinchliffe, K. Lane, and C. Quigg, Rev. Mod.Phys.56, 599 ~1984!.@18# B.L. Combridge, Nucl. Phys.B151, 429 ~1979!.@19# T.G. Rizzo~private communication!.@20# LEP Electroweak Working Group and SLD Heavy FlavorGroup, Report No. LEPEWWG/96-01, 1996~unpublished!@SLD Physics Note 47~unpublished!#.@21# A.D. Martin, W.J. Stirling, and R.G. Roberts, Phys. Lett. B354, 155 ~1995!.

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Anomalous Chromomagnetic Moments of Quarks and Large Transverse Energy
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Anomalous Chromomagnetic Moments of Quarks and Large Transverse Energy Jets

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