We show that the correction to the Paschos-Wolfenstein relation associated
with charge symmetry violation in the valence quark distributions is
essentially model independent. It is proportional to a ratio of quark momenta
that is independent of Q^2. This result provides a natural explanation of the
surprisingly good agreement found between our earlier estimates within several
different models. When applied to the recent NuTeV measurement, this effect
significantly reduces the discrepancy with other determinations of the Weinberg
angle.Comment: 7 pages, no figures; expanded discussion of N.ne.Z correction

A. W. Thomas

A.I. Signal

E. Sather

E.A. Paschos

E.N. Rodionov

F.G. Cao

G.P. Zeller

H.L. Lai

J. T. Londergan

J.T. Londergan

S. Davidson

S.A. Kulagin

Physical Review D

English

arXiv

Crossref

Charge symmetry violation corrections to determination of the Weinberg angle in neutrino reactions

We show that the correction to the Paschos-Wolfenstein relation associated with charge symmetry violation in the valence quark distributions is essentially model independent. It is proportional to a ratio of quark momenta that is independent of Q². This result provides a natural explanation of the surprisingly good agreement found between our earlier estimates within several different models. When applied to the recent NuTeV measurement, this effect significantly reduces the discrepancy with other determinations of the Weinberg angle

Londergan, J.

Thomas, A.

Adelaide Research & Scholarship

PUBLISHED VERSION  Londergan, J. Timothy; Thomas, Anthony William  Charge symmetry violation corrections to determination of the Weinberg angle in neutrino reactions Physical Review D, 2003; 67(11):111901   © 2003 American Physical Society http://link.aps.org/doi/10.1103/PhysRevD.67.111901            http://link.aps.org/doi/10.1103/PhysRevD.62.093023                        http://hdl.handle.net/2440/11124           PERMISSIONS http://publish.aps.org/authors/transfer-of-copyright-agreement   “The author(s), and in the case of a Work Made For Hire, as defined in the U.S. Copyright Act, 17 U.S.C. §101, the employer named [below], shall have the following rights (the “Author Rights”): [...] 3. The right to use all or part of the Article, including the APS-prepared version without revision or modification, on the author(s)’ web home page or employer’s website and to make copies of all or part of the Article, including the APS-prepared version without revision or modification, for the author(s)’ and/or the employer’s use for educational or research purposes.”    10th April 2013  RAPID COMMUNICATIONSPHYSICAL REVIEW D 67, 111901~R! ~2003!Charge symmetry violation corrections to determinationof the Weinberg angle in neutrino reactionsJ. T. Londergan*Department of Physics and Nuclear Theory Center, Indiana University, Bloomington, Indiana 47405, USAA. W. Thomas†Department of Physics and Mathematical Physics, and Special Research Center for the Subatomic Structure of Matter,University of Adelaide, Adelaide 5005, Australia~Received 6 March 2003; published 23 June 2003!We show that the correction to the Paschos-Wolfenstein relation associated with charge symmetry violationin the valence quark distributions is essentially model independent. It is proportional to a ratio of quarkmomenta that is independent of Q2. This result provides a natural explanation of the surprisingly goodagreement found between our earlier estimates within several different models. When applied to the recentNuTeV measurement, this effect significantly reduces the discrepancy with other determinations of the Wein-berg angle.DOI: 10.1103/PhysRevD.67.111901 PACS number~s!: 11.30.Hv, 12.15.Mm, 12.38.Qk, 13.15.1gIn 1973, Paschos and Wolfenstein @1# derived an expres-sion using the ratio of neutral-current and charge-changingneutrino interactions on isoscalar targets. This ratio isR2[1r02 ~^sNCnN0&2^sNCn¯N0&!^sCCnN0&2^sCCn¯N0&512 2sin2uW . ~1!In Eq. ~1!, ^sNCnN0& and ^sCCnN0& are, respectively, the neutral-current and charged-current inclusive, total cross sections forneutrinos on an isoscalar target. The quantity r0[M W /(M Zcos uW) is one in the standard model. From thisratio, one can obtain an independent measurement of theWeinberg angle (sin2uW).The NuTeV group recently measured neutrino charged-current and neutral-current cross sections on iron @2#. Fromthe ratios of these cross sections for neutrinos and anti-neutrinos they extracted sin2uW50.227760.0013 (stat)60.0009 (syst). This value is three standard deviationsabove the measured fit to other electroweak processes,sin2uW50.222760.00037 @3#. The discrepancy between theNuTeV measurement and the determination of the Weinbergangle from electromagnetic measurements is surprisinglylarge, and it may be evidence of physics beyond the standardmodel.As the NuTeV experiment did not strictly involve thePaschos-Wolfenstein relation, Eq. ~1!, there are a number ofadditional corrections that need to be considered, such asdifferences in shadowing for photons, W6 and Z0’s @4#,asymmetries in s and s¯ distributions @5# and so on—Ref. @6#summarizes corrections to the NuTeV result from within andoutside the standard model. In addition, Eq. ~1! is valid onlyfor an isoscalar target and it is based upon the assumption of*Electronic address: tlonderg@indiana.edu†Electronic address: athomas@physics.adelaide.edu.au0556-2821/2003/67~11!/111901~3!/$20.00 67 1119charge symmetry. There is thus a premium on knowing thecorrections as accurately as possible.Let us first review the corrections due to the fact that NÞZ for the iron target. The corrections take the form @6#DRI52F3Du21Dd21 4as9p ~g¯ L22g¯R2 !G S N2ZA D FUv2DvUv1DvG~2!whereDq2[~gLq !22~gRq !2, 3Du21Dd251273 sin2uW ,g¯ L22g¯R2 5~gLu !21~gLd !22~gRu !22~gRd !2512 2sin2uW ,Qv[E01xqv~x !dx . ~3!The additional QCD radiative term in Eq. ~2! was calculatedby Davidson et al., Ref. @6#; it is quite small at the Q2 for theNuTeV experiment. The final term in Eq. ~2! involves theratio of momentum carried by up and down valence quarks.Since both the numerator and the denominator involve thesame moments of QCD non-singlet parton distributions, theyevolve identically, so this ratio can be evaluated at any con-venient value of Q2. Using the CTEQ3D parton distributions@7# in Eq. ~2!, one obtains dRI520.0126. The NuTeV grouphas emphasized @2,8# that they do not actually measure thePaschos-Wolfenstein ratio, but instead combine separatemeasurements of ratios of neutral to charged-current crosssections for neutrinos and anti-neutrinos with a full MonteCarlo simulation of their experiment. Using their simulation,the NuTeV group reports an isoscalar correction of20.0080. This represents a 36% reduction from the Paschos-Wolfenstein correction, and the NuTeV group cited a verysmall error for this correction @9#. Kulagin @10# claimed thatthe uncertainty in this correction is likely to be considerably©2003 The American Physical Society01-1RAPID COMMUNICATIONSJ. T. LONDERGAN AND A. W. THOMAS PHYSICAL REVIEW D 67, 111901~R! ~2003!larger. The largest uncertainty in Eq. ~2! is the momentumcarried by up and down valence quarks, and according toDavidson et al. @6#, these quantities are known rather accu-rately.Davidson et al. @6# noted that, although charge symmetryviolating ~CSV! corrections are likely to be small, these ef-fects could in principle generate a substantial correction tothe NuTeV result. Recently, we calculated CSV contributionsto the NuTeV experiment arising from the small difference ofu and d quark masses @11#. Following earlier work on CSVin parton distributions @12,13#, our method involved calcu-lating CSV distributions at a low momentum scale, and usingQCD evolution to generate the CSV distributions at the Q2values appropriate for the NuTeV experiment. We obtained aCSV correction to the NuTeV result DRCSV;20.0015. TheNuTeV group also reported an estimate of the CSV partondistributions, using a rather different procedure @8#; they ob-tained a much smaller correction than ours, DRCSV;10.0001. The large discrepancy between these two resultssuggested that the CSV correction might be strongly depen-dent on the starting scale, Q02, the phenomenological valenceparton distribution chosen, or other details of the calculation.Here, we will demonstrate that one can obtain firm pre-dictions for the CSV corrections, and that the CSV contribu-tions to the Paschos-Wolfenstein ratio are essentially modelindependent. The charge symmetry violating contribution tothe Paschos-Wolfenstein ratio has the formDRCSV5F3Du21Dd21 4as9p ~g¯ L22g¯R2 !GF dUv2dDv2~Uv1Dv!G ~4!wheredQv5E01xdqv~x !dxddv~x !5dvp~x !2uvn~x !, duv~x !5uvp~x !2dvn~x !. ~5!The denominator in the final term in Eq. ~4! gives the totalmomentum carried by up and down valence quarks, whilethe numerator gives the charge symmetry violating momen-tum difference, e.g., dUv is the total momentum carried byup quarks in the proton minus the momentum of downquarks in the neutron. As for the isoscalar correction, thisratio is completely independent of Q2 and can be evaluatedat any convenient value of Q2.In our paper @11# we used an analytic approximation tothe charge symmetry violating valence parton distributionsthat was initially proposed by Sather @12#. His equationswereddv~x !52dMMddx @xdv~x !#2dmMddx dv~x !duv~x !5dMM S 2 ddx @xuv~x !#1 ddx uv~x ! D . ~6!In Eq. ~6!, M is the average nucleon mass, dM51.3 MeV isthe neutron-proton mass difference, and dm5md2mu11190;4 MeV is the down-up quark mass difference. Equation ~6!is valid for a low scale, Q02, appropriate for a ~valence domi-nated! quark or bag model @14#.Sather’s approximation allows us to evaluate directly therelevant integrals of the CSV distributions. For dDv , weobtaindDv5E01xF2 dMM ddx xdv~x !2 dmM ddx dv~x !Gdx5dMM E01xdv~x !dx1dmM E01dv~x !dx5dMM Dv1dmM . ~7!The second line of Eq. ~7! is obtained by integrating by parts,using the fact that there is one down valence quark in theproton. In an analogous fashion, the integral of the up quarkCSV distribution isdUv5dMM E01xS 2 ddx @xuv~x !#1 ddx uv~x ! D dx5dMM S E01xuv~x !dx2E01uv~x !dx D5dMM ~Uv22 !. ~8!Using Sather’s approximation relating CSV distributionsto valence quark distributions, Eqs. ~7! and ~8! show that theCSV correction to the Paschos-Wolfenstein ratio dependsonly on the fraction of the nucleon momentum carried by upand down valence quarks. At no point do we have to calcu-late specific CSV distributions. At the bag model scale, Q02’0.5 GeV2, the momentum fraction carried by down va-lence quarks, Dv , is between 0.2 and 0.33, and the totalmomentum fraction carried by valence quarks is Uv1Dv; .80. From Eqs. ~7! and ~8! this gives dDv’0.00463,dUv’20.00203. Consequently, evaluated at the quarkmodel scale, the CSV correction to the Paschos-Wolfensteinratio isDRCSV’@3Du21Dd2#dUv2dDv2~Uv1Dv!’20.00203. ~9!Once the CSV correction has been calculated at some quarkmodel scale, Q02, the ratio appearing in Eq. ~4! is indepen-dent of Q2 because both the numerator and the denominatorinvolve the same moment of non-singlet distributions @in Eq.~9! we have dropped the QCD radiative correction, which isvery small at the Q2 appropriate to the NuTeV measure-ments#.We stress that both Eqs. ~7! and ~8! are only weakly de-pendent on the choice of quark model scale—through themomentum fractions Dv and Uv , which are slowly varyingfunctions of Q02, and are not the dominant terms in those1-2RAPID COMMUNICATIONSCHARGE SYMMETRY VIOLATION CORRECTIONS TO . . . PHYSICAL REVIEW D 67, 111901~R! ~2003!equations. This, together with the Q2 independence of thePaschos-Wolfenstein ratio, Eq. ~4!, under QCD evolution,explains why our previous results, obtained with differentmodels at different Q2 values @11#, were so similar. For ex-ample, the result of Eq. ~9! DRCSV520.00203, at Q0250.5 GeV2, is virtually identical with results using theRodionov CSV distribution (20.0020) and the Sather CSVdistribution (20.0021), at Q2510 and 12.6 GeV2, respec-tively. Using Eqs. ~7! and ~8!, we also calculated a CSVdistribution using the CTEQ4LQ phenomenological partondistribution @15# at Q250.49 GeV2, evolved this to20 GeV2, and obtained DRCSV520.0021 @16#.Cao and Signal @5# point out some limitations of Sather’sapproximation, Eq. ~6!. However, we have compared dUv2dDv obtained by Sather @12#, and by Rodionov et al. @13#,who did not use Sather’s approximation, and they differ byonly a few percent.As noted earlier, the NuTeV group @2,8# do not measurethe Paschos-Wolfenstein ratio, but combine separate mea-surements of neutrinos and anti-neutrinos with a MonteCarlo simulation of their experiment. They have producedfunctionals giving the sensitivity of their observables to vari-ous effects, including parton charge symmetry violation.These are summarized in a single integralDE5E01F@E,d;x#d~x !dx . ~10!Equation ~10! gives the change in the extracted quantity Eresulting from the symmetry violating quantity d(x). Thefunctionals appropriate for the observable sin2uW and the par-ton CSV distributions were provided in Ref. @8#.11190In our previous paper we found that including the NuTeVfunctional with evolved distributions decreased the CSV cor-rection by about 33% from the Paschos-Wolfenstein result.This is very similar to the 36% reduction obtained by NuTeVfor the isoscalar correction. After applying this reduction, theCSV correction to the NuTeV experiment is 20.0015. Whenthe NuTeV measurement is adjusted accordingly, the dis-agreement between the NuTeV and electromagnetic resultsfor sin2uW is reduced from 0.0050 to 0.0035—a 30% de-crease in that discrepancy.In conclusion, we have a robust prediction for the CSVcontribution to the Paschos-Wolfenstein ratio, and also to theNuTeV measurement of the Weinberg angle. The Sather ap-proximation allows us to write integrals of xdqv in terms ofthe total momentum carried by valence quarks. These inte-grals can be calculated without ever specifying the CSV dis-tributions. The Paschos-Wolfenstein ratio involves ratios ofintegrals that behave identically under QCD evolution, sothese ratios are independent of Q2. Despite the fact that par-ton charge symmetry violation has not been directly mea-sured experimentally, and that parton CSV effects are pre-dicted to be quite small, we have strong theoreticalarguments regarding both the sign and magnitude of thesecorrections. The CSV effects should make a significant con-tribution to the value for the Weinberg angle extracted fromthe NuTeV neutrino measurements.This work was supported in part by the Australian Re-search Council. One of the authors ~J.T.L.! was supported inpart by National Science Foundation research contract PHY-0070368. The authors wish to thank G.P. Zeller and K. Mc-Farland of the NuTeV Collaboration, and W. Melnitchouk,for useful discussions regarding these issues.@1# E.A. Paschos and L. Wolfenstein, Phys. Rev. D 7, 91 ~1973!.@2# G.P. Zeller, K.S. McFarland, T. Adams, A. Alton, S. Avvaku-mov, L. de Barbaro, P. de Barbaro, R.H. Bernstein, A. Bodek,T. Bolton, J. Brau, D. Buchholz, H. Budd, L. Bugel, J. Conrad,R.B. Drucker, B.T. Fleming, R. Frey, J.A. Formaggio, J. Gold-man, M. Goncharov, D.A. Harris, R.A. Johnson, J.H. Kim, S.Koutsoliotas, M.J. Lamm, W. Marsh, D. Mason, J. McDonald,C. McNulty, D. Naples, P. Nienaber, A. Romosan, W.K. Saku-moto, H. Schellman, M.H. Shaevitz, P. Spentzouris, E.G.Stern, N. Suwonjandee, M. Tzanov, M. Vakili, A. Vaitaitis,U.K. Yang, J. Yu, and E.D. Zimmerman, Phys. Rev. Lett. 88,091802 ~2002!.@3# D. Abbaneo et al., CERN Report CERN-EP/2001-098,hep-ex/0112021.@4# G.A. Miller and A.W. Thomas, hep-ex/0204007.@5# F.G. Cao and A.I. Signal, Phys. Lett. B 559, 229 ~2003!.@6# S. Davidson, S. Forte, P. Gambino, N. Rius, and A. Strumia, J.High Energy Phys. 02, 037 ~2002!.@7# H.L. Lai, J. Botts, J. Huston, J.G. Morfin, J. Owens, J.W. Qiu,W.K. Tung, and H. Weerts, Phys. Rev. D 51, 4763 ~1995!.@8# G.P. Zeller, K.S. McFarland, T. Adams, A. Alton, S. Avvaku-mov, L. de Barbaro, P. de Barbaro, R.H. Bernstein, A. Bodek,T. Bolton, J. Brau, D. Buchholz, H. Budd, L. Bugel, J. Conrad,R.B. Drucker, B.T. Fleming, R. Frey, J.A. Formaggio, J. Gold-man, M. Goncharov, D.A. Harris, R.A. Johnson, J.H. Kim, S.Koutsoliotas, M.J. Lamm, W. Marsh, D. Mason, J. McDonald,C. McNulty, D. Naples, P. Nienaber, A. Romosan, W.K. Saku-moto, H. Schellman, M.H. Shaevitz, P. Spentzouris, E.G.Stern, N. Suwonjandee, M. Tzanov, M. Vakili, A. Vaitaitis,U.K. Yang, J. Yu, and E.D. Zimmerman, Phys. Rev. D 65,111103~R! ~2002!.@9# G.P. Zeller ~private communication!.@10# S.A. Kulagin, Phys. Rev. D 67, 091301~R! ~2003!.@11# J.T. Londergan and A.W. Thomas, Phys. Lett. B 558, 132~2003!.@12# E. Sather, Phys. Lett. B 274, 433 ~1992!.@13# E.N. Rodionov, A.W. Thomas, and J.T. Londergan, Mod. Phys.Lett. A 9, 1799 ~1994!.@14# A.I. Signal and A.W. Thomas, Phys. Rev. D 40, 2832 ~1989!.@15# H.L. Lai, J. Huston, S. Kuhlmann, F. Olness, J. Owens, D.Soper, W.K. Tung, and H. Weerts, Phys. Rev. D 55, 1280~1997!.@16# This value is not correct in Table II of Ref. @11#, but is cor-rected in our eprint, J.T. Londergan and A.W. Thomas,hep-ph/0301147.1-3

Charge Symmetry Violation Corrections to Determination of the Weinberg
  Angle in Neutrino Reactions

Charge Symmetry Violation Corrections to Determination of the Weinberg Angle in Neutrino Reactions

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