ELECTROWEAK PHYSICS RESULTS FROM THE SLD

Frank E. Taylor*

Laboratory for Nuclear Science

Massachusetts Institute of Technology

Cambridge, MA 02 139

Representing the SLD Collaboration

ABSTRACT

Data taken by the SLD Collaboration at the Stanford Linear Collider

(SLC) on e+e- -+Z”, obtained with a polarized electron beam, have

enabled many incisive tests of the electroweak sector of the Standard

Model to be performed. We discuss our recent determinations of sin2ew,

derived from the total cross-section asymmetry, and the quark final state

asymmetries, As, AC, A,, and branching ratios, R, and R,. Aspects of the

precision tests of the standard electroweak theory, involving radiative

corrections, are described. Limits on the mass of the Higgs particle are

given.

* Work supported in part by the Department of Energy.

0 1998 by Frank E. Taylor.

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(b) Z” - f f (f = e, v) interactions (NCZ):

(c) W* - ev interactions (CC):

(lb)

(lc)

where GF is the Fermi coupling constant, MZ the Z-boson mass, and gv, gA are NC

vector and axial vector coupling constants, respectively. The two NC interactions,

involving the exchange of y or Z, are characterized by coupling strengths e and g’,

respectively, whereas the charged current (exchange of W ’) has a coupling strength

g - mMw. The coupling constants involving the exchange of massive vector bosons

(W’ and Z”) are related by the Weinberg mixing angle, Bw, with tan& = g’lg and the +

electromagnetic neutral current is “unified” with the W- and Z interactions by

e = g’g/Jg” + g’. The NC interaction for a massive fermion pair coupled to the Z”

has generally unequal right and left terms couplings g& and gh, respectively. The CC

interaction is pure “V-A.”

By the Higgs mechanism the vector boson masses, M, and M,, acquire mass of

magnitude determined by the vacuum expectation value of the Higgs field, given by

(v) = (fiG,)-‘” = 246 GeV, and the coupling constants g and g’. The Fermi

coupling constant, GF, is the only “dimensioned number” in the theory. It is con-

ventional to express the boson masses in terms of the experimentally determined

constants oem, sir?O, and G,, where CX,, is the fine structure constant and is determined

by the quantum hall effect and Thomson scattering at low energies, sin%, is

measured by a number of experiments, and G, = G, by precision muon decay data. In

this convention we have:

(24

(2b)

where c, and <, are radiative correction terms, of order one, to be described later.

The NC vector and axial vector couplings (or right- and left-handed couplings) for

fermion fare given by:

g,, = (g, + g,,) = 1: - 2Q,sin’%, (34

g,, = (SLf -g,, I= 1: 2 (=I

respectively, where 1: is the third component of the weak isospin of fermion f, and Qf

is the corresponding electric charge. Since most of the precision electroweak data are

at the Z pole, it is conventional to take sin28’$r to be the effective value at the pole,4

thereby absorbing the radiation corrections in the gauge boson propagators. As such,

sinZ ,eJfeme = (1-gv,k.d/414,1, (4)

where gvr and gAf are the effective vector and axial vector couplings of fermion f at

the Z0 pole.

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where 8 is the angle of the final fermion with respect to the electron beam direction

ami g Le and gLf are the left-handed electron and final fermion couplings to Z”,

respectively. Averaging over final fermion helicities for an electron beam with a

polarization of P,, the differential cross section has the form

& -(l-Pe A&l +c0se2) +2c0s e (A, - P,) Af (9)

Here, the electron and final fermion coupling asymmetry parameters Ae, Af are given

by Eq. 5b.

Figure 1 shows the differential cross section for the production of (bb)for three

electron beam polarization cases. Note that for left-handed incident electrons the b-

quark tends to go in the forward hemisphere. This large production asymmetry is ex-

ploited by the SLD in b-quark studies in tests of the SM through electroweak coupling

asymmetries and b-quark flavor mixing.

The basis of the measured asymmetries at LEP and SLC is given by Eqs. 10 (a-d).

At LEP the forward-backward asymmetry (Pe= 0), given by

(104

is a measure of the product of coupling asymmetries A,, Ar. The forward-backward

asymmetry is exploited at LEP to obtain lepton and quark couplings.

-1.0 -0.5 0.0 0.5 1.0 case

Figure 1: The differential cross section for efem -+ Z0 -+ bb is shown for P, = + 0.77, corresponding to polarized electron beams at SLC and P, = 0, the operating condition for LEP.

The left-right total cross section asymmetry, exploited by the SLD Collaboration5 is

given by

(lob)

where o,, are the e+e- + Z0 total cross sections for incident L, R electron

polarizations and is the centerpiece of our precision electroweak tests at the SLC.

Knowledge of the electron polarization IPel allows the electron Z” coupling

asymmetry, Ae, to be directly and quite accurately measured. The polarized forward-

backward asymmetry, given by

&B-LR = - t&R OiR) = f ,pe, A~,

+ &‘R + &R (1Oc)

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Figure 2: The differential cross sections measured at the SLD for e+ e- + Zu + e+ e-, p+p-, and ;r- are shown.

At the end of the ‘97-‘98 run, several important checks of the SLC parameters

were performed which are important to certify the small corrections of y exchange

and r-Z0 interference and to make certain that the SLC positrons are not polarized. In

order to check the energy calibration of the electron and positron spectrometers,

which follow the beam interaction point, the Z” cross section peak was scanned and

matched to the Z” mass determined at LEP-I. It was determined that the energy scale

is known to about 40 MeV, which results in a negligible correction to sir&~

(0.0001 l+ 0.00009). In addition, a putative positron polarization was sought by

directly measuring the positron beam polarization by means of a Moller polarimeter

located in End Station A and found to be consistent with zero (Pe+ = -0.02 + 0.07%).

Finally, the Compton polarimeter, which measures the electron polarization, was

questioned but found to be in good agreement with measurements of the energy

asymmetry of back-scattered Compton gammas detected by a threshold Cherenkov

gas counter and a quartz fiber- tungsten radiator calorimeter.

In Table 3 we summarize the worlds data on lepton coupling asymmetries’.’ (both

SLD’ and LEP’ data are preliminary).

Table 3: Lepton Coupling Asymmetries.

Quantity Asymmetry

SLD: ALR 0.15 10 f 0.0025

SLD: Ae 0.1504 + 0.0072

SLD: Au 0.120 f 0.019

SLD: Ar 0.142 f 0.019

SLD: <Ae,u,T> 0.1459 + 0.0063

SLD: A,, <Ae,u,+ 0.1503 + 0.0023 1 LEP: &ES Cl), Ae,p,-t 0.1469 * 0.0027

SLD+LEP 0.1489 f 0.0018

We note that the LEP-I values and those from the SLC-SLD are in good agreement

with the resulting value of leptonic asymmetries differing by only - 1 cr.

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ratio for Z” to decay into a quark favor, f, determines the combination

Rr = Fr I Fhad - (gZf + gXf). To check theory, the vector and axial vector couplings are

taken from the average value of sin’O:derived from global fits, where the overall

consistency of the data is checked. Or more strictly, the value of sin20:ff is taken from

purely lepton measurements, thereby probing the universality of sin20z across

lepton-quark families. In the case of the Z” + bb vertex (also Z” + Ss), since gL* -

30 g& Rb has a large sensitivity to the left-handed coupling, such as vertex

corrections involving W*, t* exchange, whereas At, has a greater sensitivity to the

right-handed components. We find the following sensitivities for sin*8’: = 0.23

i% - - Rb 3.6 hgLb + 0.7 8gRb ,

iik - - A3 0.3 &Lb + 1.7 6gRb

Thus, R, and At, are complementary measurements and probe different sectors of the

theory.

The SLD brings a number of experimental tools to the study of the electroweak

couplings of s, c, and b quarks. The pixel vertex detector can identify displaced

vertices from the IP as a signature for b and c quark final states, and the Cherenkov

Ring Imaging Detector (CRID) can identify n*, K’, pr particles in the final state.

Various discriminants are used to isolate s-, c-, and b-quark events, which result for

example in a hemisphere b-tag efficiency and purity in the range of 45% and 99%,

respectively.

The most powerful test of the SM for quark final states have come from a study of

the b-system. Several factors conspire to allow this.

(1) The asymmetry parameter At, is expected to be only weakly dependent on

sin20;ff (see the entry for d-quarks in Table 2), thus the measurement of

Araab, given by Eq. lOa, is mostly a determination of Ae.

(2) The b-quark has a large branching ratio (-22%) and thus has a small

statistical error for reasonable detection efficiency.

(3) b-quark events can be separated from other hadronic events by detection

of displaced secondary vertices and various event attributes, such as high

transverse mass.

(4) The b-quark charge can be determined by a variety of experimental

signatures, such as a high Pt charged lepton, jet charge, kaon charge and,

in the SLD, initial state tagging through the incident electron beam

polarization.

(5) A, varies with center-of-mass energy, and when measured below and

above the Z” peak at LEP, has a larger asymmetry, thereby adding

information to the small asymmetry at the pole.

Similar arguments hold for s-quark and c-quark final states (no flavor mixing), al-

though the c-quark final state is more sensitive to sin2ew, thereby making the test of

the SM more involved. Further, c-quarks are more difficult to separate from back-

ground and their detection frequently exploits “charm counting” where all charm

hadrons which eventually decay via Do, Df, D,, and A, are summed, or by the

reconstruction of D*s, yielding a clean sample of events. A lepton fit is also used to

separate c (and b) events from background.

The coupling constant asymmetry measurements are not sensitive to the detection

efficiency, although the background dilution in the asymmetry is. For the branching

ratio analysis the detection efficiency critically enters and it is highly beneficial to

achieve high detection efficiency since, for example, 6R, - l&.

-267-

-89Z-

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9v pue ‘3~ ‘sv JO fquawamsaaly T’S

Each of the two hemispheres, defined by the perpendicular plane bisecting the thrust

axis, was required to have at least one identified strange particle. Overall, the purity of

the sS final state was estimated to be 69% with 107 o uii, 9% dd, 11% CC, and 1% bb

contamination. A binned maximum likelihood fit was performed to determine A,. The

procedure included particle detection efficiencies and acceptances.

Taking sin*8’: = 0.23155, the SM predicts As = 0.935, a value which is slowly

varying with sin*8’:. The table indicates that the preliminary SLC value of As is

1 .O (J low with respect to the SM and the LEP value is 0.1 (T low (with Ae correction

made). The SLD+LEP average is dominated by the SLC value and is 1.0 cr low

The SLD brings excellent vertex detector and particle identification to the isolation

of CT events. From the ensemble of hadronic events, secondary vertices possibly 12

signifying CF events are identified by means of a topological algorithm, which

searches for space points in three dimensions where the reconstructed tracks overlap.

Tracks, in this algorithm, are considered probability “tubes.” The method finds

secondary vertices in 84% of b, 38% of c, and 2% of light quark events under the

requirement that the secondary vertex be displaced from the IP by at least 1 mm.

Further refinement of the charm sample is obtained by reconstructing the mass of the

tracks associated with the secondary vertex-a calculation aided by the well-defined

IP of the SLC and our high resolution pixel vertex detector. The mass is defined as

M=q+lPd. where I& is the mass of the ensemble of charged tracks

associated with the secondary vertex and Pt is the net transverse momentum with

respect to the line connecting the secondary vertex and the IP. Charm candidates

were required to have a vertex mass in the range 0.55 < M,< 2 GeV/c2. By vetoing on

b-events and imposing momentum cuts, charm events are isolated with 81% purity.

Several methods are employed to determine the direction of the charm quark needed

for the AFBmLR evaluation, such as vertex charge, k tag, lepton tag and D*, d

identification. These tags have different efficiencies in the range of - 30%. A

maximum likelihood fit to all tagged events is used to determine A,.

Referring to Table 6, the A, LEP-SLC average is in good agreement (only 0.6 o)

with the SM value of A, = 0.668 for sin*ft~ = 0.23155 with the preliminary SLD

value lower than the SM by about 0.5 (J and the LEP value low by 0.9 6. The LEP

values are derived from measurements which average to <A,a.c > = 0.0714 f 0.0044,

which is then corrected by 4/(3 A,).

Table 6: Ac measurements from LEP and SLC (Summer 1998).

-269-

large uncertainties of a direct calculation of the single tag efficiency. The b-tagging

efficiency is typically &b - 35% with a hemisphere correlation of &, - 0.6%.

The R world average is within 0.2 CT of the SM value of R, = 0.1723. The

SLC values are considered preliminary. The Rb world average of Table 9 is within

1.4 (T of the SM value of Rt, = 0.2155. Hence the interesting 4 d discrepancy with the

SM of the summer 1995 has dissolved into fairly good agreement.

Table 8: Measurements of R (Winter 1998).

Table 9: Measurements of R, (Summer 1998).

5.3 Comment on Ab and sin2Wff

An itself shows the same difference as we observed in the sin’8” value derived from

AFBOb above-namely AmOb measured is smaller than the prediction of the SM,

resulting in a larger value of sin2Vwff from the LEP measurements. Remember that we

have used the pure leptonic determination of A, to correct the LEP forward-backward

asymmetries in order to obtain the value of Ah by the factor 4/(3Ae). Also note that

the SLD measures Ah directly by means of the forward-backward left-right

asymmetry.

Examining the factors involved, we conclude that the discrepancy in sin’t3:

between LEP and the SLD is consistent with a discrepancy of the value of Ah from

the SM. In fact, if we take the direct measurement of At, from the SLD to derive the

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8 g. a

In order to check the theory beyond the “tree level” radiative corrections must be

included. This process is usually performed by fitting all the measured quantities at

the Z” pole with radiative corrections to derive the top quark mass and the Higgs

mass, or constraining the top quark mass by the measured value at FNAL and

deriving the Higgs mass. The consistency of the theory is measured by the quality of

the fit. Sensitivities to Mt and Ml, arise from different measured quantities having

different dependencies on the parameters of the radiative corrections. We have

already absorbed the vertex corrections for leptons (but not for quarks) by defining an

effective mixing angle determined by A,, the electron coupling constant asymmetry.

There have been a number of theoretical treatments which make the comparison of

theory to data less model-dependent.18 Here we adopt a more pedestrian approach and

use “experimental” parameters, such as Mt and Ml, to obtain an estimate of the

magnitude of various terms. The need for radiative corrections is easily demonstrated

in a naive evaluation of Eq. 2 using the value of sin28’wff determined above, &, given

by atomic physics experiments, and GF from muon decay. This naive exercise

predicts Mz = 88.38 + 0.03 GeV and M w = 71.48 + 0.04 GeV, values which are

embarrassingly discrepant with the measured values of 9 1.1867 k 0.002 1 GeV and

80.37 + 0.090 GeV, respectively [Vancouver 1998].8

Radiative corrections are grouped into two general types: (1) electromagnetic

corrections, which include initial and final state radiation, vertex diagrams, etc., and

the running of I&,,, for the atomic energy scale q2 = 0 to the q2 = Mx*; and (2)

electroweak corrections where some of the corrections are absorbed in the definition

of sin ‘Cl~fi , isospin-breaking loop terms in W and Z propagators, running of the Z

self-energy, corrections to the Z + bb vertex, and corrections to the W mass.

7.1 Hadronic Vacuum Polarization

Much of the discrepancy in the vector boson mass relations is corrected by the

running of cr.&Q*). The QED coupling at the M, scale is related to its value at low

energy, given precisely in atomic physics experiments by

aem 0%) = aem (0) 1 - Aa,, (Mz) ’

(13)

where Aaem (Mz) = - II, is the photon self-energy. The photon self-energy is evaluated

quite accurately for leptons, but not for quarks. In order to evaluate the quark

contribution, the measured e+e- hadronic cross section is employed to determine the

value of a dispersion integral. Ironically, the data in the 1.05 to 5 GeV region, well

beneath the scale of the Z” pole, contribute a large fraction of the integral as well as a

large part of the uncertainty. Much of the data in this energy region are old and have

large normalization errors. Further, above the charm threshold, many channels with

different properties exist, complicating the evaluation of the integral. A number of

evaluations have been performed. 19

The result adopted by the LEP EW-WG is

a,,(M;) = l/(128.896+0.090), which is an evolution of Aala - 0.063. In this

formulation GF does not run. 20

7.2 Electroweak Radiative Corrections

The radiative corrections are furnished by the terms < in Eqs. 2 and 5 above. At the

one-loop level the correction terms for the MZ mass relation given by Eq. 2a is

-273-

-PLZ-

(391)

(991)

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(WI) 9 8Zo’O- - dVF =MaJv

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(WI)

P”

‘suual /C%aua-3las 2 pm? s~ole%doJd z pm? TM aql 01 suog3arro3 door %uyaJq

-u!dsos! aq$ ‘Aaf) 091 = Sfl pun hag SLI = $q q]!M lapJo %mpeaI 103 ‘a1aqt.t

s! ‘q%j ‘uog3auo3 xavaa aqL ‘~1.0 = (zZ~)% ~03

@PI) ‘(%+ I) (dv+ I,)=~>

Table 10: Results of a fit to electroweak data at Z” pole.

The fitted value of Mt is in agreement with the direct observation at FNAL21 of Mt =

173.8 + 5.0 GeV. The limits on Mh are > 90 GeV from direct searches and < 280 GeV 24

at 95% CL.

It is interesting to note that the SLD value of sm 8, ’ eff implies a Minimal Standard

Model (MSM) Higgs scalar of - 40 GeV and is - 1 (T in contradiction with the present

direct search limit of > 90 GeV at the 95% CL, whereas the LEP value is consistent

with Ml, - 220 GeV and is not excluded by direct searches.

A more sophisticated way of looking at the data is shown in Figure 5 as a 25

comparison of the worlds data with the variables S and T of Peskin and Takeuchi.

The variables S and T are normalized to (0,O) at a nominal SM pointAetermined by

the measured value of Mt and a nominal value of Mh. The contributions to isospin-

violating mass differences beyond the set point are described by T, which is roughly

quadratic in Mt and logarithmic in Ml, (see Eqs. 14 and 15 above). The parameter S is

sensitive to isospin-independent terms which would grow systematically with the size

of a new sector. The Peskin-Takeuchi variable U is assumed to be 0 in this

application. The 68% confidence region of the LEP and SLD data is indicated by the

oval region in the figure.

Figure 5: The S and T constraints provided by LEP, SLD, and FNAL arr indicated. The SLD measurement of ALn seems to prefer the MSSM of Pierce et al.

The S-T region predicted by the MSM is indicated by the banana-region centered

about the (0,O) point of the figure. In that region, the right-hand edge corresponds to

Mh = 88 GeV and Mt = 173.9 f 5.2 GeV. Increasing the Higgs mass up to 1 TeV is

displayed by the width of the region. An indication of supersymmetry would be a shift

of the experimental overlap region from the expectations of the MSM with S 26

becoming slightly negative and T positive. The MSSM of Pierce et al. is indicated

by the ensemble of dots in the figure-each representing a choice of the live 21

parameters of the model. We note the SLD data favors a supersymmetric world,

whereas LEP data disfavors the model by about 2 cr.

-275-

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Quark Couplings to the Z”, presented at the XVIII International Symposium on

Lepton Photon Interactions (1997), Hamburg, Germany.

[ 121 D. Jackson, Nucl. Instrum. and Meth., A 338, (1997) 247.

[13] See for example: A. Blonde1 and C. Verzegnassi, Phys. Lett. B 311(1993) 346-

356.

[14] ALEPH: I. R. Tomalin, in Proceeding of ICHEP96, Warsaw, Poland, p. 1340

(1996).

[15] SLD Rc: K. Abe et al., SLAC-PUB-7880 (1998).

[ 161 SLD Rb: K. Abe et al., Phys. Rev. Lett. 80 (1997) 660.

[ 171 T. Takeuchi, A. Grant and J. Rosner, p. 123 1 in Proceedings of gth Meeting of

the DPF (Albuquerque, N.M. 1994), edited by S. Seidel.

[18] G. Altarelli, R. Barbieri, and S. Jadach, Nucl. Phys. B 369, 3 (1992); W.

Marciano, these proceedings.

[19] M. Swartz, Phys. Rev. D 53 (1996) 5268; H. Burkhardt and B. Pietrzyk , Phys.

Lett. B 356 (1995) 398.

[20] R. D. Peccei, DESY 89-060.

[21] G. Degrassi et al., hep-pN9412380.

[22] The fit uses ZFITTER, D. Bardin et al., CERN-TH 6443/92 (May 1992);

hep-pN9412201.

[23] See R. Brock, in Proceedings of Fund. Particles and Interactions, p. 189,

Nashville, TN, edited by R. S. Panvini and T. J. Weiler (1997); J. Kotcher, in

these proceedings.

[24] D. Karlen, in Proceedings of the 1998 ht. ConJ: on High Energy Physics,

ICHEP’98, Vancouver, BC (1998).

[25] M. Peskin and T. Takeuchi , Phys. Rev. D 46,381-409 (1992).

[26] D. Pierce et al., Nucl. Phys. B 491 (1997) 3-67.

[27] “Request for SLD Run Extension,” SLD Collaboration (Aug. 1998).

[28] An earlier comparison of LEP-SLC data can be found in F. E. Taylor, in

Proceedings of Fund. Particles and Interactions, p. 166, Nashville, TN, edited by

R. S. Panvini and T. J. Weiler (1997).

-277-