The implications of recent electroweak data for mt and MH

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PHYSICS LETTERS B

23 November 1989

T H E I M P L I C A T I O N S O F R E C E N T E L E C T R O W E A K DATA F O R mt A N D M s John ELLIS CERN, Ctl- 1211 Geneva 23, Switzerland

and G.L. F O G L I Dipartimento di Fisica, Universit~ di Bari, and lNFlV. Sezione di Bari, 1-70126 BarL Italy

Received 1 September 1989

We report the results of a new global fit to electroweak data, including the recent SLC, CDF and UA2 measurements of Mz, the new CDF and UA2 values of Mw/Mz, and the new CHARM II measurement of a(x,ae)/a(vue). The precision measurement of Mz enforces a strong negative correlation between sin20w and rn,, and we find sinZ0w=0.2276+o°o~, _. rrh=~'32 -37 ÷3t GeV. The electroweak data also prefer Mt~< Mz, but not at a high level of significance.

Experimental probes o f the electroweak sector o f the S t a n d a r d Model are entering a new era with the advent o f precision data from the Z ° peak. However, it should not be forgotten that useful information can still be obtained by comparing these data with lowenergy neutral current measurements. There have been two global analyses o f e l e c t r o w e a k data, mainly on ncutral currents [ 1 ], and we have discussed how these data can be used to constrain the top quark mass rn~ [2], taking into account both cxperimental and theoretical uncertainties such as those in the charm quark mass rnc and the Higgs boson mass MH. More recently [3 ], we have discussed the interesting constraint on the top quark mass m, that could be obtained by c o m b i n i n g a future high-precision measurement o f M z with the existing low-energy neutral current data. We showed that if MZ were measured with an error _+50 MeV, then m , = 9 5 G e V + 6 6 (91.6 G e V - M z ) + 0 ( 3 5 ) GeV. Since our p a p e r was written, several new electroweak measurements have been published, including ( a ) a new m e a s u r e m e n t o f sin2Ow from c o m p a r i n g v~c and ~,~e scattering [4], ( b ) new m e a s u r e m e n t s o f Mw/-'v/z by the C D F [ 5 ] and UA2 [ 6 ] collaborations, and most i m p o r t a n t l y (c) new m e a s u r e m e n t s of-'v/z by the Mark II collaboration at SLC [7 ], by

the C D F collaboration [ 5 ], and by the UA2 collaboration [6]. In this paper wc report the results o f a new global analysis o f electroweak data, including all the new measurements. Since they are crucial for the interpretation o f the low-energy data, we also review briefly the systematic errors in the analysis o f deepinelastic vN scattering. Even though the present SLC errors on -'dz are still considerably larger than the conjectural ones wc assumed in ref. [3], wc find a qualitatively similar conclusion, namely that mt is fixed with an error o f less than 40 GeV, if one assumes the m i n i m a l standard model to be correct: m, = 132_+3~ G e V .

( 1)

We also c o m m e n t on the mass o f the Higgs boson MH in the light o f our analysis. As in our previous papers, we group the available electroweak data into 4 sectors (i) v-q, (it) v-e, (iii) e - q , and ( i v ) Mw,z. We now discuss cach o f thcse sectors in turn, pointing out key features and new developments. v - q sector. Hcre there arc no ncw data, and we use again the complete analysis o f neutral currents in deep-inelastic vN scattering reported in [ 8 ]. Since it is the almost mr-independent value o f sinZz~w ex-

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tracted from these data that dominates the comparison with the mr-dependent high-energy data, we discuss in some detail the uncertainties in the v-q sector. The estimates of the four (squared) chiral couplings u[, d 2, u~, d~ in ref. [8] include both the experimental errors and all theoretical uncertainties due to the parametrization of deep-inelastic scattering within the parton model with QCD effects. In particular, the effect was considered of varying me, which influences the threshold of charm production in the chargedcurrent sector. A fit to the deep-inelastic charged and neutral current vN scattering data alone does not constrain mc very tightly: mc=1.54+0.33 GeV. However, there is independent information on me from the perturbative QCD analysis of other hard processes and a recent review [9] quotes me= 1.35 +_0.05 GcV. Accordingly we have assumed me= 1.45 GeV, which is the value for which we found the best value Z 2 in the sin 2 0w analysis of all sectors in rcf. [2]. Values ofrnc between 1.35 and 1.55 GeV would give results well within the errors we quote. The other theoretical uncertainties include the paramctrization of the deep-inelastic structure functions, the value of as (or equivalently A~:D), and the generalized Cabibbo angles. Structure function parametrizations similar to those discussed by Buras and Gaemers were used in ref. [ 8 ]. They are adequate for our purposes: parametrizations incorporating all leading and next-to-leading order QCD effects would bc too cumbersome for convenient fitting and would not change the results outside the quoted errors. The most important contributions to these include the uncertainty in the strange sea quoted in ref. [8], an allowance for a deviation from the perturbative QCD value o f a L / a T by +0.1, and errors in the MINUIT fit parameters. We take AQCD=0.25 +_0.18 GeV to cover a wide range of values. As for the generalized Cabibbo angles, we assume effective unitarity among the first two generations, in which case all matrix elements can be expressed in terms of the Cabibbo angle, for which we take cos 0k= 0.9744 +_0.0010. v-e sector. Here the most significant new development has been a determination of sin 2 Ow from the ratio a(9~e)/a(v,e) by the CHARM II collaboration [4]: sin 2 0w =0.233 ± 0.012+_0.008,

latter decrease the l~referred value of sin 2 0w as a function of mt when it exceeds -~ 50 GeV, in a manner qualitatively similar to their effect on sin 2 0w as derived from the vector boson masses, and therefore do not provide a long lever arm for determining m, by comparison with the vector boson masses. However, we remind the reader that this determination of sin 2 0w is immune to the type of vexing theoretical uncertainties discussed above in connection with vN scattering. The new result of CHARM II [4] has been combined with the previous estimate of the chiral lcptonic couplings considered in ref. [3] and discussed in ref. [ 10 ]. e-q sector. Apart from a recent estimate of sin 2 0w from the forward-backward asymmetry for I~P-~ ( Z °--' e +e - ) + X for which radiative corrections are not available, there has been no significant new experimental development since the high-precision measurement of parity violation in cesium by the Boulder group [ 11 ]. We use the analysis of these and other c-q neutral current data made in ref. [ 12 ]. Mw,z sector. It is here that the most dramatic new experimental developments have occurred. The most precise has been a new measurement of Mz by the Mark II collaboration at the SLC [ 7 ]: M z = 9 1 . 1 7 + 0 . 1 8 GeV,

(3)

including systematic errors of 0.04 GcV due to the absoluteenergy scale uncertainty and 0.05 GeV due to the uncertainty in the miniSAM efficiency. Also significant has been a new measurement of Mz by the CDF collaboration at the FNAL Tevatron collider

[5]: Mz =90.9+_0.3+_0.2 GcV,

(4)

where the former error includes both statistics and systematics, and the latter is an energy scale error. There has also been a new measurement of-lCz by the UA2 collaboration [ 6 ], Mz =90.2+_0.6+_ 1.4 GeV.

(5)

In our analysis we take into account all the above measurements, evidently dominated by the estimate (3) of the Mark II collaboration: by combining all the errors in quadrature we obtain

(2) Mz =91.09+_0.16 GeV.

bcfore the application of radiative corrections. The 140

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Two new m e a s u r e m e n t s o f Mw have also been made, by the C D F collaboration [ 5 ]: Mw = 80.0 + 0.2 (star) + 0.5 (syst) _+0.3(scale) G e V ,

(7)

and by the UA2 collaboration [ 6 ]: My,, =

80.0 + 0.4 (stat) + 0.4 (syst)

+ 1.2(scale) G c V .

(8)

They not only contribute to the analysis o f sin 2 Ow in terms o f mt in the VBM sector, but, more importantly, they allow through the ratio M w / M z a rather accurate d e t e r m i n a t i o n o f sin 2 tgw i n d e p c n d e n t l y o f mt (see fig. 1 ), since the overall energy scale errors drop out o f the ratio, which is d o m i n a t e d by statistical errors and by systematic errors in the procedure

.240

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v-e

u-q

o~

.220 L

.210 I

50

"

I

1()0 ",50 rn (GeV)

200

Fig. I. The dependences on rr~ of the central values of sin 2 0w extracted from present data in the different sectors considered: v-q, v--c,e-q and the vector boson masses (VBM). The error on sin2 0w from measurements OfMw/Mz is shown as a vertical error bar as well as being included in the VBM sector. Note the differences between the sectors at large mr. We have assumed me= 1.45 GeV and MH=Mz. This figure updates fig. 1 of ref. [31.

23 November 1989

for extracting MW from the observed lepton Prdistribution. We now discuss the results o f our global fit to the elcctroweak data. Fig. 1 shows the mr-dependence o f the central values o f sin 2 Ow inferred from the various sectors above, which can be c o m p a r e d with our previous figures o f this type. Two significant effects are noticeable. One is that Mz (cq. ( 6 ) ) is now somewhat below the previous central value, although well within the errors stated previously [2 ]. This increases the value o f sin 2 0w extracted from the vector boson mass sector for any fixed value o f m,. Since the value o f sin 2 Ow extracted from the v - q sector is not strongly d e p e n d e n t on mr, the net effect is to shift the optimal value o f mt to a higher value. The error in sin 2 0w inferred from the direct measurement o f M w / Mz is much larger than that inferred from M z alone, and is shown as an error bar on the left-hand side o f the figure. However, it goes in the direction o f decreasing sin 2 flw and hence increasing the preferred value o f mr. We also observed that the VBM and v - e central values o f sin 2 0w ar now coincident for m r - 200 GeV, although the errors in the latter sector still do not p e r m i t a definite conclusion to be drawn from this comparison alone. As advertized above, the principal constraint on rnt comes from the comparison between the v - q and VBM sectors, by virtue o f their smaller errors and the different mr-dependences o f the inferred values o f sin 2 0w. Fig. 2 plots again their central values o f sin 2 tgw, together with their error bands. It is the limited range o f overlap between these bands that is the driving force behind our bounds ( 1 ) on m,. The extent o f this overlap is almost independent o f the error in the VBM sector due to the uncertainty in measuring Mz, as soon as this error becomes significantly less than that frown the v - q sector. This e x p l a i n s why our b o u n d s ( 1 ) are very similar to those given in ref. [ 3 ] for the same central value o f Mz, even though the present error in Mz is considerably larger than what we had assumed previously. We have already discussed why we believe the errors we quote on sin 2 Ow in the v - q sector to be realistic. It is clear from figs. 2 and 3 that even if the v - q errors were somewhat increased, e.g. to reflect uncertainty on me, the essential features o f significant lower and upper bounds on rn, would be maintained. On the one hand, we see in fig. 2 that the C D F and UA2 141

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.240 L

I v-q

t

.230 t

i ' v-e

,...-...

.230

?~_

.220

~20

.2!0

210

I

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I

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150 (GeV)

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Fig. 2. Allowed regions in the (mr, sin2 Ow) plane showing the 1 - a limit on each of the two variables separately for the VBM and v-q sectors. Note that the measured value of Mw/Mz favours mr>95 GeV. We continue to take m¢=1.45 GeV and

measurements of M w / M z would prevent mt from being much smaller than 100 GeV. On the other hand, we see in fig. 3 that consistency in the low-energy sectors between v-q, e - q and v - e data would prevent m t from being much greater than 180 GeV, and that consistency between the VBM and v - q sectors could not long be m a i n t a i n e d because of their divergent dependences of sin 2 0w on rn~. As an exercise, we nevertheless made a notional global fit in which the v - q errors in the chiral quark couplings were arbitrarily inflated by 50%. We found that the central value of m, was increased by 8 GeV, because of the strongcr relative weights of the VBM, v-e and e - q sectors that prefer large m,. The upper (lower) b o u n d of mt is increased (decreased) by 8 ( 11 ) GeV. Using the preferred errors quoted earlier and combining all 4 sectors we obtain the final contour in the (mr, sin ~ Ow) plane and z2-distribution as a function of mr shown in fig. 4. In the top part of the figure we 142

I

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I

100 150 m: (GeV)

J

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Fig. 3. Allowed regions in the (rnt, sin2 Ow) plane showing the 1 - a limit on each of the two variables separately for the VBM and low-energy (v--q, v--eand e--q) sectors. Note that the latter ",done favour mr< 180 GeV. We continue to take me= 1.45 GeV and Mri= Mz. see again the strong negative correlation between mt and sin z Ow which has been imposed by the precision measurement of Mz. Leaving m t as a frce parameter, we find s i n 2 ~a _ n o o 7 A~+- -00.. 00003 34 9 t/W --~.x.z~

,

(9)

whose central value is very close to that we quoted previously [ 3 ] before Mz was measured so precisely. As for m,, we find m~ = 132 +_3 137 G e V ,

(10)

as already reported in eq. ( 1 ). It is a non-trivial check on the consistency of the Standard Model, including radiative corrections, that this favoured range of mt is compatible with the lower bounds established by the pp colliders at FNAL and CERN ( m , > 78 GeV at 90% CL from C D F [ 13], m , > 6 7 GeV at 95% CL from UA2 [ 14], mr> 65 GeV at 95% CL from UA1 [151).

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' 2.5

.230 . a

.z

2.0

.226

zz

.222

/° I

1.5 I

Zz 2.0

~0[

b

1.5

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mt {GeVI Fig. 5. The X2distributionsas a function of m, for different choices 2 of,,):= M 2H/Mz.

1'0t I

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1

100

I

150 mt (GeV|

I

2O0

Fig. 4. (a) Allowed region in the ( mr, sin2 Ow) plane showing the 1 - r y limit on each of the two variables separately when data from all sectors are included, and (b) the Z2 distribution as a function of re. both for me= 1.45 GeV and MH=Mz. In all the a b o v e analysis, we have taken as o u r default o p t i o n "P[~=Mz. We have previously reported [2] o n a very slight preference for small "I4H on the basis o f t h c electroweak d a t a available last year. T h i s very slight preference is m a i n t a i n e d this year, b u t is still n o t significant. Fig. 5 c o m p a r e s the Z 2 d i s t r i b u tions for ~ = (:t/[tl/tVIz)2=O.O1 (dotted line), 1 (solid l i n e ) a n d 100 ( d a s h e d l i n e ) . T h e shifts in the optimal value o f mt are + 5 GeV for 3 = 0 . 0 1 a n d - 1 0 G e V tbr d = 100, which are still small c o m p a r c d with the o t h e r sources o f error in mt i n c l u d e d in the range q u o t e d in the cqs. ( 1 ) a n d ( 1 0 ) . F u r t h e r a d v a n c e s in the m e a s u r e m e n t o f electroweak p a r a m e t e r s will m a i n l y c o m e from high-precision m e a s u r e m e n t s at the Z ° peak in e+e - a n n i h i l a tion, although precision low-energy m e a s u r e m e n t s in v - e scattering a n d a t o m i c physics parity violation will also be i m p o r t a n t . As noted above, it is alrcady a n o n trivial c o n s i s t e n c y check o n the s t a n d a r d clectroweak theory that the high values o f m t favoured by this

analysis o f radiative corrections are c o n s i s t e n t with the lower l i m i t s o n mt reccntly established by the lOp collidcrs. It is quite possible that o u r i n f o r m a t i o n a b o u t m t will c o n t i n u e for s o m e t i m e to be indirect, although discovery o f the top q u a r k at the F N A L fop collider or at LEP II still appears possible. We would like to t h a n k G. Altarelli a n d L. M a i a n i for useful discussions a b o u t the subject.

References

[ 1 ] U. Amaldi, A. B6hm, L.S. Durkin, P. l_angacker,A.K. Mann, W.J. Marciano, A. Sirlin and H.H. Williams, Phys. Rev. D 36 (1987) 1385; G. Costa, J. Ellis, G.L. Fogli, D.V. Nanopoulos and F. Zwirner, Nucl. Phys. 13297 (1988) 244. [ 2 ] J. Ellis and G.L. Fogli, Phys. Left. B 213 ( 1988 ) 526. [3] J. Ellis and G.L. Fogli, Phys. Lett. B 231 (1989) 189. [41 CHARM I1 Collab., D. Geiregat et al., CERN EP preprint; and presentation by J. Panman, in: Proc. XW Intern. Syrup. on Lepton and photon interactions (Stanford, 1989), to appear. [ 5 ] CDF Collab., F. Abe et al., Phys. Rev. Lett. 63 (1989) 720; and presentation by M.K. Campbell, in: Proc. XIV Intern. Symp. on Lepton and photon interactions (Stanford, 1989), to appear. [6] UA2 Collab., presented by A. Weidberg, in: Proc. XIV Intern. Symp. on Lepton and photon interactions (Stanford, 1989), to appear. 143

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[7] Mark II CoUab., G.S. Abrams et al., Phys. Rcv. Lett. 63 (1989) 724; and presentation by G. Feldman, in: Proc. XIV Intern. Symp. on Lepton and photon interactions (Stanford, 1989), to appear. [ 8 ] G.L. Fogli and D. Haidt, Z. Phys. C 40 ( 1988 ) 379. [9] J. Gasser and H. Leutwyler, Phys. Rep. 87 (1982) 77. [ I 0 ] G.L. Fogli, Europhys. Lett. 4 ( 1987 ) 527. [ 11 ] M.C. Noccker, B.P. Masterson and C.E. Wieman, Phys. Rev. Left. 61 (1988) 310.

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[ 12] G.L. Fogli, Z. Phys. C 43 (1989) 229. [ 13 ] CDF Collab., presented by P. Sinervo, in: Proc. XIV Syrup. on Lepton and photon interactions (Stanford, to appear. [ 14] UA2 Collab., presented by L. Di Lella, in: Proc. XIV Symp. on Lepton and photon interactions (Stanford, to appear. [ 15] UA1 Collab., presented by K. Eggert, in: Proc. XIV Symp. on Lepton and photon interactions (Stanford, to appear.

Intern. 1989), Intern. 1989), Intern. 1989),