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Home , Weak charge

Probing with Scattering Experiments

A. Kurylov*, MJ. Ramsey-Musolf S.Sud *an *

* California Institute of Technology, Pasadena, CA 91125 USA ^ Department of , University Connecticut,of Storrs, CT 06269USA

Abstract. We compute the supersymmetric contributions to the weak charges of the (<2Jy) and proton (Q^) in the framework of Minimal Supersymmetric Standard Model. We also consider the ratio of neutral current to charged current cross sections, R v and R^ at v (v)-nucleus deep inelastic scattering compard an , supersymmetrie eth c corrections wit deviatione hth thesf so e quantities fro Standare mth d Model predictions implie recene th y dtb NuTeV measurement.

INTRODUCTION

2 Standare th n I d Model (SM particlf )o e physics predictee ,th d runnin f singo 9W from 2 2 energyZ-polw lo o :et sin 0w(0 )- sin 0w(M z0.007)= neves ha , r been established experimentally to a high precision. sirr6w(Mz) can be obtained through the Z-pole 2 precision measurements with very small error. However, no determination of sin 9W energw alo t y with similar precisio availables ni . More recently resulte th , f cesiuo s m atomic -violation (APV) [1] and v- (v-) nucleus deep inelastic scattering (DIS)[2] 2 have been interpreted as determinations of the scale-dependence of sin 9W. The cesium APV result appears to be consistent with the SM prediction for q2 « 0, whereas the DIS measurement implies a H-3

CP698, Intersections of Particle and : 8th Conference, edited by Z. Parsa © 2003 American Institute of Physics 0-7354-0169-1/03/$20.00 168

Downloaded 31 Mar 2006 to 131.215.225.175. Redistribution subject to AIP license or copyright, see http://proceedings.aip.org/proceedings/cpcr.jsp precision observables experience SUSY onl looa yvi p effects involving virtual super- symmetric particles. Tree level corrections appear once ^-parity is broken explicitly. We studies both the PV (PVES) and v (v)-nucleus DIS processes. Details calculatione oth f s presente dfoun[7]e d b her .an Refn n di ] e ca [6 .

RADIATIVE CONTRIBUTION TO WEAK CHARGE

The weak charge of a particle / is defined as the strength of the effective A(e) x V(f)

interaction: <^ = "Q^^f^f- With higher-order corrections included, the

weak charge can be written as Q^ — p\2T^ - 4Qj-K sin 92 + Kj. The quantities pv pv W ppv and KPV are universal, while the correction A ,, on the other hand, does depend on

the species tree-levelt p .A whils , pv A0 d ha K,= one-loo t = e PVea an 1 ,on p

orde 1= r + similapd 8p ™8p,an + y SY r formulae A,, d appl.an Ko yt p p PV

The counterterpv m SG^ determined by life time and the Z° boson self-energy are combined into ppv (expresse obliquterme n di th f so e parameters 5[8])T , : -I. 5^ ,n (Q) *Wo) n (Q) _ _& Ppv0 zz 2 + zz SIL 1L +&T ai m(L) ~ ~~ ~ "~2 — ui °vB~ ^ °VB'

The quantity 8& denotes the the electroweak vertex, external leg, and box graph correc- tions to the muon decay amplitude. — Z mixin7 paritygand - violating electron- coupling F^(0) contribut Keto PV :

The shift 5£in S follows from the definition of S in terms of a, G^, and Af[6].

w e z

2 2

non-universae Th 2 l contributio weae n th Ako t , charg determines ei e sue th f mth o y db the renormalized vertex corrections and the box graphs.

SUSY CORRECTION TO WEAK CHARGES

In order to evaluate the potential size of SUSY loop corrections, a set of about 3000 different combinations of SUSY-breaking parameters was generated. Fig. l(a) shows the shift in the weak charge of the , SQL = 25<2Jy -f <5<2^, versus the corresponding electron'e shifth n i t s weak charge, 5g^, normalize respective th o dt valuesM eS e Th . corrections in the MSSM (with ^-parity conserved) can be as large as ~ 4% (<2(P and ~ 8% (<2w) ~ roughly the size of the proposed experimental errors for the two PVES

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FIGURE 1. Plot(a) shows the relative shifts in electron and proton weak charges due to SUSY effects. Plot(b) show MSSe sth M contributio R^.d Ro nt an v Dots indicate MSSM loop correction ~r sfo 300 0 randomly -generated SUSY-breaking parameters. Interior of truncated elliptical region gives possible shifts due to RPV SUSY interactions (95% confidence).

measurements. The shifts 8Q^p are dominated by 5Kp^SY, which is nearly always 2 2 2 2 negative, corresponding to a reduction in the value of sin 9^ (q ) = KPV (q ) sin 6W for PVEe th S experiments. Since this effec identicas i t botr lfo h <2^ d Q^dominane an th , t

effect of &KPV produces a linear correlation between the two weak charges, As evident from Fig. 1 (a), the relative sign of the loop corrections to both Q^ and Qw is nearly always the same and positive. This correlation is significant, since the effects of other new physics scenarios can display different signatures. For example, for the general class of theories based on E6 gauge group, with neutral gauge bosons Z' having mas 100s< 0 GeV effecte th ,Q^ d Q^n o san also correlate t 8Q%>,bu p/Q%>n ca p have either sign in this case[9,10]. In contrast, leptoquark interactions would not lead to discernible effect coult Q^n i sbu d induce sizable shift , 10] Qn [9 si p . corollarya s A alse ,w o find that SUSY loop correction weae th ko st charg cesiuf eo m is suppressed: SfiSVGw8 < 0.2% and is equally likely to have either sign, which is smaller than the presently quoted uncertainty for the cesium nuclear weak charge of about 0.6% [11]. Therefore presene th , t agreemen f Q^ o predictiot M S wit e th h n does not preclude significant shifts in Q^ arising from SUSY. The situation is rather p f p different r examplefo , Ee 6th Zn i , scenario, where sizable shift (X>n i s would also imply observable deviations of g^ from the SM prediction. New tree-level SUSY contribution weae sth ko st charge generatee b n sca d wheR e nth parit MSSn y i t conserved no Ms i effecte Th . s of/^-parity violating (RPV) contribution e parametrizeb n ca positivey db , semi-definite, dimensionless quantities A.d -kan (f) A'.-£(/)[ 12], whic constrainee har d fro existine mth g precision datC% La 95 [12] e Th . region allowed in the SQ^/Q^ vs. SQ^/Qw plane is shown by the closed curve in Fig. 1 (a). We observe that the prospective effects of RPV are quite distinct from SUSY

loops. The value of SQ^/Qw is never positive in contrast to the situation for SUSY loop effects, whereas 8Q^/Q havn ca e eitheP r sign. Thus, a comparison of the two PVES measurements could help determine which extension of the MSSM is to be favored over other new physics scenarios [10],

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Recently NuTee th , V collaboratio performes nha precisda e determinatio ratie th of no Rv (Ry) of neutral and charged current deep-inelastic v^ (vjU)-nucleus cross sections[2], expressewhice b n hca effectivterme n di th f so —ev hadroni q c couplings (g/ #) : tt 2

_

where r = o^/a^. Comparing the SM predictions[13] for (g/f#)2 with the values e obtained by the NuTeV Collaboration yields deviations SRy(-} = R *v - R®*)9 SRV = -0.0029 ±0.0015, SRy = -0.0015 ±0.0026. Tlie numerical result SUSr sfo Y contribution correctioe th a e R^d Rvi th o s t an v o nt effective hadronic couplings (#f#) shown in Fig. 1 (b). For detailed analysis, see Ref. [7]. SUSY loop contribution smalle e R^d ar Ran o st r 2tha observeare neth d deviations.

More significantly, the sign of thev SUSY loop corrections is nearly always positive, in contrasNuTee sige th f th n o V o t anomaly. Tree-leve contributionV RP l R^d Ro st an v are by and large positive. While small negative corrections are also possible, they are numericall smalinterestingo e yb to o lt .

CONCLUSION

In summary, we have studied the SUSY corrections to the weak charge of the electron protond an , which coul scatterinp measuree de b d eeV an P t gda experiments core Th .- relation between thes quantitieo etw s coul usbe db distinguiso dt h variou physicsw sne . alse W o examine SUSe dth Y contribution NuTee th o st V measurement found san d that hars i t explaii o dt NuTee nth V anomal framewore th n yi MSSMf ko .

REFERENCES

1. S.C. Bennet C.Ed an t . Wieman, Phys. Rev. Lett , 24882 . 4 (1999); C.S. Woo t al,de Science 275, 1759 (1997). 2. G.P. Teller et al NuTeV Collaboration, Phys. Rev. Lett. 88:091802 (2002). . 3 SLAC Experiment E-158 Hughes. W . ,E Kumar. K , , P.A. Souder, spokespersons. 4. JLab experiment E-02-020, R. Carlini, J.M. Finn, S. Kowalski, and S. Page, spokespersons. . 5 H.E. Haber KaneL G. , , Phys. Rep. 117 (1985)4 ,7 . 6. A. Kurylov, M. J. Ramsey-Musolf, and S. Su, hep-ph/0303026, to appear in Phys. Rev. D. 7. A. Kurylov, M. J. Ramsey-Musolf, and S. Su, hep-ph/0301208, to appear in Nucl. Phys. B. 8. G. Degrassi, B. A. Kniehl, and A. Sirlin, Phys. Rev. D 48, 3963 (1993). 9. MJ. Ramsey-Musolf, Phys. Rev. C 60:015501 (1999). Erler. J . Ramsey-Musolf . ,MJ 10 . KurylovA d an , , [hep-ph/0302149] (2003). .MilsteinI . 11A . , O.P. Sushkov I.Sd .an , Terekhov, hep-ph/0212072. 12. MJ. Ramsey-Musolf, Phys. Rev. D 62:056009 (2000). . HagiwarK . 13 . a/.aet , Revie f Particlwo e Physics, Phys , .1000 Rev66 D 1. (2002) . ErlerJ ; , private communication.

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