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Implications of new deep inelastic scattering data for light neutrino and top quark mass limits
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IMPLICATIONS OF NEW DEEP INELASTIC SCATTERING DATA FOR LIGHT NEUTRINO AND TOP QUARK MASS LIMITS A.D. MARTIN,
W.J. STIRLING
Department of Physics, University ofDurham, Durham DHI 3LE, UK
and R.G. ROBERTS Rutherford-Appleton Laboratory, Chilton, Didcot, Oxon OX1 I OQX, UK Received
9 March
1988
Recent measurements of the structure function F,(p) from the BCDMS and EM Collaborations are in apparent disagreement. We study the implications of this for the limits on the number of light neutrinos and on the top quark mass derived from precision measurements of W and Z cross sections at pp colliders. Patton distributions derived from the recent high statistics BCDMS data imply larger W and Z cross sections and tend to weaken the upper limits obtained previously on m, from CERN collider data. The theoretical ambiguities in predicting the ratio of W and Z cross sections are shown to be significantly smaller for the PNAL pp collider energy, and more precise limits should obtain.
tio of W and Z cross sections, both quantities being sensitive to the ratio of d to u parton distributions. Since the work of refs. [ 2,3 ] was completed, the situation with regard to structure functions has changed quite dramatically. New muon scattering dataonF,(p) andonF,(n)/F,(p) fromtheBCDMS Collaboration [ 61 have become available, which in the relevant x-region are in apparent disagreement with previously published data on the same quantities from the EM Collaboration [ 71. Although the differences are, in absolute terms, not large they have a sizeable impact on the extraction of N, and m, limits using the above method. We have repeated [8] our next-to-leading order structure function analysis of a wide range of deep inelastic data, using in turn the EMC and BCDMS data for the uN structure functions. We concluded that both data sets were compatible with neutrino scattering data - apart from an overall renormalisation factor which is significant when using EMC data - and also with perturbative QCD. Accordingly we derived two sets of parton distributions, which we shall call here MRSE and MRSB. It is impossible to say categorically which of these sets
One of the most important current methods for obtaining limits on the number of light neutrinos and the top quark mass involves considering the ratio R, of the W and Z production cross sections in pp collisions [ 11. The method is based on the simple relation R=
#(w+ev) #(Z+e+e-) =R;ReR
.
crw BR(W+ev) = z BR(Z+e+e-) (1)
In two recent papers [ 2,3 1, we have presented a detailed study of the limits which are obtained using the UA 1 [ 41 and UA2 [ 5 ] measurements for R. A central feature of the analysis concerns the accuracy with which the quantity R, can be calculated. The uncertainty on this quantity ultimately determines the precision of the limits on N, and m,. In refs. [2,3], we argued that the then available muon and neutrino deep inelastic data put quite stringent constraints on the parton distributions and consequently on the predicted W and Z cross sections. In particular, we showed how the muon structure function ratio F2 (n) /F2 (p ) gave a rather direct measure of the ra0370-2693/88/S (North-Holland
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is correct, although an upwards renormalisation of the low-x EMC data by 10% or more is suggested [ 8 ] not only by comparison with the neutrino data but also by Drell-Yan data. The most significant difference between the two sets is in the valence quark distributions (see fig. 4 of ref. [S]). In the x-range 0.1-0.4 the valence up-quark distribution of MRSB is significantly larger than that of MRSE, reflecting the difference in the measured values of F2 (p) in the same range. There is less difference in the valence down quark distribution and in the sea. As was remarked in ref. [ 81 this has important implications for W and Z cross sections in pp collisions. The purpose of this paper is to study these implications in detail. The curves denoted by E and B in fig. 1 are the MRSE and MRSB descriptions of the F2 (n) IF2 (p) EMC [ 71 and BCDMS [ 61 data respectively in the crucial low-x region, as obtained in the structure function analysis of ref. [ 8 1. We should remark here that the MRSE parton distributions are similar, but not identical, to the MRS 1 distributions presented in ref. [ 3 1. The latter were fitted to a slightly different set of deep inelastic data which included no BCDMS F2 (p) data and an earlier set of preliminary BCDMS F*(n)/F*(p) data. This explains the small differences between the MRSE W and Z cross sections calculated below and those labelled MRS 1 in ref. [ 3 1. Before considering the impact of fig. 1 on R, we first consider the total W-+ev and Z-+e+e- cross sections from the two sets. These are shown at two pp collider energies, 630 GeV and 1.8 TeV, in fig. 2 together with the combined UAl and UA2 data points [ 4,5 ] as derived in ref. [ 3 1. The curves correspond to N, = 3 and are shown as a function of m, in the appropriate range. It is immediately apparent that the MRSB set (curve B) gives significantly higher cross sections - about 9% higher for the W and 16% higher for the Z at 630 GeV, and about 16% higher for both at 1.8 TeV. It is not possible to derive any significant conclusion from fig. 2 because the 0( a:) QCD corrections are unknown. Since the 0 (01,) corrections, which have been included, increase the cross sections by about 30% it is reasonable to expect the higher order corrections to be of order ? lo%, which therefore obscures the differences between the two sets and also the differences arising from the variation of m,. Further uncer206
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n F2 P Fz
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Fig. 1. The structure function ratio Fz(un)/Fz(up) as measured by BCDMS [ 61 (closed dots) and EMC [ 71 (open circles). The average Q* at which the measurements are made is also shown. The statistical and systematic errors are shown by continuous and dashed error bars respectively. (They are added in quadrature in the tits.) The continuous curves labelled E and B are the results of global tits to the EMC and BCDMS muon scattering data respectively, combined with deep inelastic neutrino data. The dashed curves labelled A, C and F correspond to other tits designed to span the range of F,(n)/F,(p) measurements, as described in the text. The values of x relevant for W and 2 production at 630 GeV and 1.8 TeV are also indicated.
tainties from the allowed variation of Mw and Mz are of order + 2% and are not shown. Many of the experimental and theoretical uncertainties cancel in the ratio of W and Z cross sections defined in eq. ( 1). The focus of attention then switches to the theoretical calculation of the quantity R,. It is already apparent from the curves denoted by E and B of fig. 2 that the MRSE and MRSB parton distributions give different values for R,. Choosing values for Mw and Mz of 8 1 GeV and 92.3 1 GeV, respectively (which corresponds to sin’& = 0.23 ), we find R,( 630 GeV) = 3.42 ~3.22
[ MRSE]
,
[MRSB]
.
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Fig. 2. W( +ev) and Z( +ee) cross sections in pp collisions at 630 GeV and 1.8 TeV. The average of the UAl [ 41 and UA2 [ 51 measurements at 630 GeV is shown. The curves labelled E and B are the predictions using the MRSE and MRSB parton distributions respectively, as functions of r-n,. In computing the Z branching ratio a value of N,= 3 is assumed.
The
corresponding predictions for the ratio (with N,=3,5) are shown in fig. 3 as a function of m,, together with the combined UAl and UA2 measurement and 90% CL upper limit [ 4,5]. Apart from the possibility of Z+vLVL we assume that the fourth and higher generations do not contribute to W or Z decay. Fig. 3 can be compared with our previous version, fig. 18 of ref. [ 3 1. The MRSE prediction (curve E) falls within the previous band of uncertainty, which corresponded to R,= 3.36 ? 0.09, while the MRSB curve is substantially lower and gives a weaker top quark mass upper limit. The smaller value of R, for the BCDMS-inspired parton distributions is due to the lower value of the d/u ratio in the appropriate x-range. This lower ratio is due partly to the lower values of F2 (n) /F2 (p) and partly to the constraint from simultaneously fitting to the individual vN and uN structure functions. Even if the data on the ratio F,(n) /F,(p) are omitted from the fit-
R=Ro.RBR
30
50
70
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mt (GeV) Fig. 3. Ratio of the W and Z cross sections at 630 GeV and 1.8 TeV. The combined UAl [4] and UA2 (51 measurement and 90% CL upper limit are shown. At 630 GeV the shaded bands are the theoretical predictions defined by the MRSE and MRSB parton distributions (E,B). Also shown, to the right of the bands, are the predictions corresponding to the other sets of parton distributions described in the text and shown in fig. 1 (A,C,F). At 1.8 TeV the predictions corresponding to E and F are the same. The dashed lines correspond to the + 0.04 variation in R,arising from the If-O.005 uncertainty in sin*&
ting procedure, a lower value of d/u is preferred in the BCDMS case. Superimposed on fig. 1 are the xvalues corresponding to M/G for W and Z production at 630 GeV and 1.8 TeV. In the 630 GeV range of x-values, the BCDMS F2( n) /F2( p) ratio is systematically lower. Since a smaller value of F2 (n) /F2 (p) evidently corresponds to a weaker m, upper limit, it is the lowest allowed value of F,(n) /F,(p) which is important. To gauge this we have performed some more tits to deep inelastic data, deliberately forcing the F2 (n) /F2 (p) ratio to be first smaller and then larger than our “best tits” in the important x-range. In particular we have obtained two more BCDMS fits, labelled A and C in fig. 1, which roughly correspond to the variation allowed by the 207
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experimental errors #I. We have also obtained another EMC fit, labelled F, which roughly corresponds to the upper end of the error bars on the EMC data. In each case, we have calculated the corresponding values of R,: [ “MRSE”
(curve F) 1,
=3.30
[“MRSB”
(curve C)],
=3.09
[“MRSB”
(curveA)],
R,( 630 GeV) = 3.5 1
(3)
and displayed the predictions for R on the “scale” at the side of fig. 3. It is clear that, as first pointed out in ref. [ 2 1, there is an almost linear relation between the value for F2 (n) /F2(p) at the appropriate x-value and the value of R obtained from the W and Z cross sections, even though the latter correspond to pat-ton distributions which have been evolved to much higher values of the scale. We do not therefore wish to present any definitive value, or range of values, for R,. Instead, we leave the reader to judge from figs. 1 and 3 what the “most likely” theoretical value for R might be, taking into account the differences between the two data sets and the systematic and statistical errors on each. We can however conclude that the possibility of there being IZOlimit on m, from this method cannot be ruled out at this stage. In this sense the new BCDMS data on Fz(n)/Fz(p) has changed the picture considerably. At this point it is appropriate to comment on other recent analyses of the same quantity. Based on an independent structure function study (not including the new BCDMS data), Diemoz et al. [ 9 ] have obtained R,= 3.28 !c 0.15 #2. In view of the above discussion, this is a not unreasonable range, corresponding more to the BCDMS rather than EMC data on F2(n)/F2(p). In contrast, Halzen et al. [lo] have presented a value of R, of 3.42 with an error due to structure function uncertainties of only & 0.01 (again not including the new BCDMS data). This is based on a weighted average of a range of u/d measurements at the appropriate value of x. We would argue that only a global structure function tit makes sense, RIThe constraints
of other data are such that curve C represents an upper limit for an acceptable fit including BCDMS data. *’ The reason why R, obtained from EMC data is so low is because d/u is too tightly constrained by the parametrisation chosen in ref. [ 91.
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in view of the overall systematic errors and differences between the data sets. For example, in our view it would not be appropriate to take a weighted average of the BCDMS and EMC data points on F2 (n) /F2(p) just in a narrow band of x and translate this into a value for R,. The fact that our “best fit” for MRSB does not in fact go through the middle of the data points around x=0.15 illustrates the importance of the other (e.g. neutrino scattering) data sets and also the constraints from sum rules on the parton distributions which affect a wider x-range. Considering the current state of the deep inelastic data, there is little hope of much improvement in the theoretical precision on the evaluation of R at 630 GeV. Perhaps suprisingly, the situation at the 1.8 TeV FNAL collider will be significantly better. The reason for this is that as smaller x-values are probed, the valence quarks have less influence on the W and Z cross sections and the processes become sea-quark dominated. In fact in the limit &cc the ratio R, is essentially fixed by the ratio of the W and Z fermionic couplings. One can see this behaviour in fig. 1, where the various curves for F2(n) /F2(p) come together at small x. Also in this small-x region the approximate Q2 independence of the ratio breaks down and the one-to-one correspondence between F2(n) /F2(p) and R, is lost. Therefore, although the actual deep inelastic data becomes less well-determined at small x, the differences in the predictions for R, from the different parton distributions become smaller. Explicitly, we find #3 R,(1.8TeV)=3.27
[MRSE (curveE)],
~3.27
[MRSB (curveB)],
~3.29
[“MRSE”
(curveF)],
=3.29
[“MRSB”
(curvec)],
= 3.25
[ “MRSB”
(curve A) 1.
(4)
We can therefore with some confidence derive predictions for the value of R at 1.8 TeV. The curves displayed in fig. 3 correspond to the MRSE and MRSB values in eq. (4). (Note that the small differences in the third decimal place in the R, values are not shown in eq. (4).) Again the other values are shown as a 113 The prediction should be 3.26.
given for R,( 2 TeV) in ref.
[ 21 is in error and
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scale on the right-hand side. Since the differences due to the structure function uncertainties are SO small, we must return to other sources of uncertainties, as described in ref. [2]. The largest of these is the uncertainty on sin28w. The reason is that the ratio of the W. and Z cross sections depends to a good approximation only on the ratio Mw and M,, and therefore only on sin’8w. All of the above numbers have been evaluated using the value of 0.23 for the latter, with the absolute value of Mw adjusted to lie roughly at its measured value. If we instead introduce a “world average” value and error [ 111 sin*& = 1 -M&,/M;
=0.230?0.005,
we find this leads to an uncertainty
(5)
AR,=O.O4. We can summarise the results of our study as follows. It is difficult to predict accurately the value of R, at 630 GeV. There is a rather large experimental uncertainty in the value of F2 (n) /F2 (p) in the relevant range of x, due primarily to the systematic differences in the EMC and BCDMS data sets. We should remark that in this study, as in ref. [ 8 1, we have taken the EMC and BCDMS data at face value, and used the spread in the experimental measurements to determine the uncertainty in the theoretical predictions. Of course, since the two measurements of F2 (p) are in contradiction - at least at the level of the statistical errors - we can only assume that the situation will change with an eventual reconciliation of the measurements. If and when this happens we must again perform a new global fit to the deep inelastic scattering data to determine a new set of parton distributions and an improved determination of R,. At present, however, the theoretical uncertainty on R, combined with the experimental uncertainty on the value of R, make it impossible to obtain a definitive upper limit on m,. However the situation would improve dramatically if the F2 (n ) /F2 (p ) ratio could be measured to high precision, In view of the importance of obtaining as much information on the allowed values of m, as possible, we believe that such a measurement should be given serious consideration. Perhaps suprisingly, the situation appears much better for the FNAL collider at 1.8 TeV. The dominance of the sea quarks at small x means that the value of R, is much more tightly constrained at this higher en-
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ergy. In fact we have shown that the larger uncertainty comes instead from the uncertainty on sin2Bw. Considering the variation arising from the parton distributions, as summarised in eq. (4), and that arising from sin28w given in eq. ( 5 ), we conclude that R,( 1.8 TeV) = 3.27 2 0.03 (pat-ton distributions)
kO.04 (sin’f?,)
.
(6)
The corresponding predictions for R are displayed in fig. 3. We can summarise the situation by saying that a measured value for R ( 1.8 TeV) greater than about 10.5 would imply at least four light neutrinos. A value between 8.8 and 10.5 would imply either three, four or five light neutrinos and a corresponding value of m, for each, and (perhaps most interesting of all) a value less than about 8.8 would signal a breakdown of the standard model. We wish to thank Alain Milsztajn, Terry Sloan and Gerard Smadja for helpful discussions concerning the deep inelastic muon data.
References [ 1] F. Halzen and M. Mursula, Phys. Rev. Lett. 5 1 ( 1983) 857; K. Hikasa, Phys. Rev. D 29 (1984) 1939; N.G. Deshpande et al., Phys. Rev. Lett. 54 (1985) 1757; D. Dicus et al., Phys. Rev. Lett. 55 (1985) 132; F. Halzen, Phys. Lett. B 182 (1986) 388; F. Halzen, C.S. Kim and S. Willenbrock, University of Wisconsin-Madison preprint MAD/PH/342 (1987). [2] A.D. Martin, R.G. Roberts and W.J. Stirling, Phys. Lett. B 189 (1987) 220. [ 31 A.D. Martin, R.G. Roberts and W.J. Stirling, RAL preprint RAL-87-052 (1987), Phys. Rev. D, to be published. [4] UAl Collab., E. Locci, in: Proc. Intern. Europhysics Conf. on High energy physics (Uppsala, 1987 ) ed. 0. Botner, p. 8. [ 51 UA2 Collab., R. Ansari et al., Phys. Lett. B 186 (1987) 440. [6] BCDMS Collab., A. Milsztajn, private communication. [7] EM Collab., J.J. Aubert et al., Nucl. Phys. B 272 (1986) 158; B 293 (1987) 704. (81 A.D. Martin, R.G. Roberts and W.J. Stirling, RAL preprint RAL-88-002 (1988). [9] M. Diemoz, F. Ferroni, E. Longo and G. Martinelli, preprint CERN-TH-4751/87 (1987), Z. Phys. C, to be published. [ lo] F. Halzen, C.S. Kim and S. Pakvasa, University of Wisconsin-Madison preprint MAD/PH/394 (1987). [ 111 See e.g., U. Amaldi et al., Phys. Rev. D 36 (1987) 1385.
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IMPLICATIONS OF NEW DEEP INELASTIC SCATTERING DATA FOR LIGHT NEUTRINO AND TOP QUARK MASS LIMITS A.D. MARTIN,
W.J. STIRLING
Department of Physics, University ofDurham, Durham DHI 3LE, UK
and R.G. ROBERTS Rutherford-Appleton Laboratory, Chilton, Didcot, Oxon OX1 I OQX, UK Received
9 March
1988
Recent measurements of the structure function F,(p) from the BCDMS and EM Collaborations are in apparent disagreement. We study the implications of this for the limits on the number of light neutrinos and on the top quark mass derived from precision measurements of W and Z cross sections at pp colliders. Patton distributions derived from the recent high statistics BCDMS data imply larger W and Z cross sections and tend to weaken the upper limits obtained previously on m, from CERN collider data. The theoretical ambiguities in predicting the ratio of W and Z cross sections are shown to be significantly smaller for the PNAL pp collider energy, and more precise limits should obtain.
tio of W and Z cross sections, both quantities being sensitive to the ratio of d to u parton distributions. Since the work of refs. [ 2,3 ] was completed, the situation with regard to structure functions has changed quite dramatically. New muon scattering dataonF,(p) andonF,(n)/F,(p) fromtheBCDMS Collaboration [ 61 have become available, which in the relevant x-region are in apparent disagreement with previously published data on the same quantities from the EM Collaboration [ 71. Although the differences are, in absolute terms, not large they have a sizeable impact on the extraction of N, and m, limits using the above method. We have repeated [8] our next-to-leading order structure function analysis of a wide range of deep inelastic data, using in turn the EMC and BCDMS data for the uN structure functions. We concluded that both data sets were compatible with neutrino scattering data - apart from an overall renormalisation factor which is significant when using EMC data - and also with perturbative QCD. Accordingly we derived two sets of parton distributions, which we shall call here MRSE and MRSB. It is impossible to say categorically which of these sets
One of the most important current methods for obtaining limits on the number of light neutrinos and the top quark mass involves considering the ratio R, of the W and Z production cross sections in pp collisions [ 11. The method is based on the simple relation R=
#(w+ev) #(Z+e+e-) =R;ReR
.
crw BR(W+ev) = z BR(Z+e+e-) (1)
In two recent papers [ 2,3 1, we have presented a detailed study of the limits which are obtained using the UA 1 [ 41 and UA2 [ 5 ] measurements for R. A central feature of the analysis concerns the accuracy with which the quantity R, can be calculated. The uncertainty on this quantity ultimately determines the precision of the limits on N, and m,. In refs. [2,3], we argued that the then available muon and neutrino deep inelastic data put quite stringent constraints on the parton distributions and consequently on the predicted W and Z cross sections. In particular, we showed how the muon structure function ratio F2 (n) /F2 (p ) gave a rather direct measure of the ra0370-2693/88/S (North-Holland
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is correct, although an upwards renormalisation of the low-x EMC data by 10% or more is suggested [ 8 ] not only by comparison with the neutrino data but also by Drell-Yan data. The most significant difference between the two sets is in the valence quark distributions (see fig. 4 of ref. [S]). In the x-range 0.1-0.4 the valence up-quark distribution of MRSB is significantly larger than that of MRSE, reflecting the difference in the measured values of F2 (p) in the same range. There is less difference in the valence down quark distribution and in the sea. As was remarked in ref. [ 81 this has important implications for W and Z cross sections in pp collisions. The purpose of this paper is to study these implications in detail. The curves denoted by E and B in fig. 1 are the MRSE and MRSB descriptions of the F2 (n) IF2 (p) EMC [ 71 and BCDMS [ 61 data respectively in the crucial low-x region, as obtained in the structure function analysis of ref. [ 8 1. We should remark here that the MRSE parton distributions are similar, but not identical, to the MRS 1 distributions presented in ref. [ 3 1. The latter were fitted to a slightly different set of deep inelastic data which included no BCDMS F2 (p) data and an earlier set of preliminary BCDMS F*(n)/F*(p) data. This explains the small differences between the MRSE W and Z cross sections calculated below and those labelled MRS 1 in ref. [ 3 1. Before considering the impact of fig. 1 on R, we first consider the total W-+ev and Z-+e+e- cross sections from the two sets. These are shown at two pp collider energies, 630 GeV and 1.8 TeV, in fig. 2 together with the combined UAl and UA2 data points [ 4,5 ] as derived in ref. [ 3 1. The curves correspond to N, = 3 and are shown as a function of m, in the appropriate range. It is immediately apparent that the MRSB set (curve B) gives significantly higher cross sections - about 9% higher for the W and 16% higher for the Z at 630 GeV, and about 16% higher for both at 1.8 TeV. It is not possible to derive any significant conclusion from fig. 2 because the 0( a:) QCD corrections are unknown. Since the 0 (01,) corrections, which have been included, increase the cross sections by about 30% it is reasonable to expect the higher order corrections to be of order ? lo%, which therefore obscures the differences between the two sets and also the differences arising from the variation of m,. Further uncer206
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n F2 P Fz
h'f(FNAL) 1 -
W Z (CERN)
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$ EMC f BCOMS (prelim. I
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30
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O-3
Fig. 1. The structure function ratio Fz(un)/Fz(up) as measured by BCDMS [ 61 (closed dots) and EMC [ 71 (open circles). The average Q* at which the measurements are made is also shown. The statistical and systematic errors are shown by continuous and dashed error bars respectively. (They are added in quadrature in the tits.) The continuous curves labelled E and B are the results of global tits to the EMC and BCDMS muon scattering data respectively, combined with deep inelastic neutrino data. The dashed curves labelled A, C and F correspond to other tits designed to span the range of F,(n)/F,(p) measurements, as described in the text. The values of x relevant for W and 2 production at 630 GeV and 1.8 TeV are also indicated.
tainties from the allowed variation of Mw and Mz are of order + 2% and are not shown. Many of the experimental and theoretical uncertainties cancel in the ratio of W and Z cross sections defined in eq. ( 1). The focus of attention then switches to the theoretical calculation of the quantity R,. It is already apparent from the curves denoted by E and B of fig. 2 that the MRSE and MRSB parton distributions give different values for R,. Choosing values for Mw and Mz of 8 1 GeV and 92.3 1 GeV, respectively (which corresponds to sin’& = 0.23 ), we find R,( 630 GeV) = 3.42 ~3.22
[ MRSE]
,
[MRSB]
.
(2)
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R=uwB(W-ev)
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Fig. 2. W( +ev) and Z( +ee) cross sections in pp collisions at 630 GeV and 1.8 TeV. The average of the UAl [ 41 and UA2 [ 51 measurements at 630 GeV is shown. The curves labelled E and B are the predictions using the MRSE and MRSB parton distributions respectively, as functions of r-n,. In computing the Z branching ratio a value of N,= 3 is assumed.
The
corresponding predictions for the ratio (with N,=3,5) are shown in fig. 3 as a function of m,, together with the combined UAl and UA2 measurement and 90% CL upper limit [ 4,5]. Apart from the possibility of Z+vLVL we assume that the fourth and higher generations do not contribute to W or Z decay. Fig. 3 can be compared with our previous version, fig. 18 of ref. [ 3 1. The MRSE prediction (curve E) falls within the previous band of uncertainty, which corresponded to R,= 3.36 ? 0.09, while the MRSB curve is substantially lower and gives a weaker top quark mass upper limit. The smaller value of R, for the BCDMS-inspired parton distributions is due to the lower value of the d/u ratio in the appropriate x-range. This lower ratio is due partly to the lower values of F2 (n) /F2 (p) and partly to the constraint from simultaneously fitting to the individual vN and uN structure functions. Even if the data on the ratio F,(n) /F,(p) are omitted from the fit-
R=Ro.RBR
30
50
70
50
70
90
mt (GeV) Fig. 3. Ratio of the W and Z cross sections at 630 GeV and 1.8 TeV. The combined UAl [4] and UA2 (51 measurement and 90% CL upper limit are shown. At 630 GeV the shaded bands are the theoretical predictions defined by the MRSE and MRSB parton distributions (E,B). Also shown, to the right of the bands, are the predictions corresponding to the other sets of parton distributions described in the text and shown in fig. 1 (A,C,F). At 1.8 TeV the predictions corresponding to E and F are the same. The dashed lines correspond to the + 0.04 variation in R,arising from the If-O.005 uncertainty in sin*&
ting procedure, a lower value of d/u is preferred in the BCDMS case. Superimposed on fig. 1 are the xvalues corresponding to M/G for W and Z production at 630 GeV and 1.8 TeV. In the 630 GeV range of x-values, the BCDMS F2( n) /F2( p) ratio is systematically lower. Since a smaller value of F2 (n) /F2 (p) evidently corresponds to a weaker m, upper limit, it is the lowest allowed value of F,(n) /F,(p) which is important. To gauge this we have performed some more tits to deep inelastic data, deliberately forcing the F2 (n) /F2 (p) ratio to be first smaller and then larger than our “best tits” in the important x-range. In particular we have obtained two more BCDMS fits, labelled A and C in fig. 1, which roughly correspond to the variation allowed by the 207
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experimental errors #I. We have also obtained another EMC fit, labelled F, which roughly corresponds to the upper end of the error bars on the EMC data. In each case, we have calculated the corresponding values of R,: [ “MRSE”
(curve F) 1,
=3.30
[“MRSB”
(curve C)],
=3.09
[“MRSB”
(curveA)],
R,( 630 GeV) = 3.5 1
(3)
and displayed the predictions for R on the “scale” at the side of fig. 3. It is clear that, as first pointed out in ref. [ 2 1, there is an almost linear relation between the value for F2 (n) /F2(p) at the appropriate x-value and the value of R obtained from the W and Z cross sections, even though the latter correspond to pat-ton distributions which have been evolved to much higher values of the scale. We do not therefore wish to present any definitive value, or range of values, for R,. Instead, we leave the reader to judge from figs. 1 and 3 what the “most likely” theoretical value for R might be, taking into account the differences between the two data sets and the systematic and statistical errors on each. We can however conclude that the possibility of there being IZOlimit on m, from this method cannot be ruled out at this stage. In this sense the new BCDMS data on Fz(n)/Fz(p) has changed the picture considerably. At this point it is appropriate to comment on other recent analyses of the same quantity. Based on an independent structure function study (not including the new BCDMS data), Diemoz et al. [ 9 ] have obtained R,= 3.28 !c 0.15 #2. In view of the above discussion, this is a not unreasonable range, corresponding more to the BCDMS rather than EMC data on F2(n)/F2(p). In contrast, Halzen et al. [lo] have presented a value of R, of 3.42 with an error due to structure function uncertainties of only & 0.01 (again not including the new BCDMS data). This is based on a weighted average of a range of u/d measurements at the appropriate value of x. We would argue that only a global structure function tit makes sense, RIThe constraints
of other data are such that curve C represents an upper limit for an acceptable fit including BCDMS data. *’ The reason why R, obtained from EMC data is so low is because d/u is too tightly constrained by the parametrisation chosen in ref. [ 91.
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in view of the overall systematic errors and differences between the data sets. For example, in our view it would not be appropriate to take a weighted average of the BCDMS and EMC data points on F2 (n) /F2(p) just in a narrow band of x and translate this into a value for R,. The fact that our “best fit” for MRSB does not in fact go through the middle of the data points around x=0.15 illustrates the importance of the other (e.g. neutrino scattering) data sets and also the constraints from sum rules on the parton distributions which affect a wider x-range. Considering the current state of the deep inelastic data, there is little hope of much improvement in the theoretical precision on the evaluation of R at 630 GeV. Perhaps suprisingly, the situation at the 1.8 TeV FNAL collider will be significantly better. The reason for this is that as smaller x-values are probed, the valence quarks have less influence on the W and Z cross sections and the processes become sea-quark dominated. In fact in the limit &cc the ratio R, is essentially fixed by the ratio of the W and Z fermionic couplings. One can see this behaviour in fig. 1, where the various curves for F2(n) /F2(p) come together at small x. Also in this small-x region the approximate Q2 independence of the ratio breaks down and the one-to-one correspondence between F2(n) /F2(p) and R, is lost. Therefore, although the actual deep inelastic data becomes less well-determined at small x, the differences in the predictions for R, from the different parton distributions become smaller. Explicitly, we find #3 R,(1.8TeV)=3.27
[MRSE (curveE)],
~3.27
[MRSB (curveB)],
~3.29
[“MRSE”
(curveF)],
=3.29
[“MRSB”
(curvec)],
= 3.25
[ “MRSB”
(curve A) 1.
(4)
We can therefore with some confidence derive predictions for the value of R at 1.8 TeV. The curves displayed in fig. 3 correspond to the MRSE and MRSB values in eq. (4). (Note that the small differences in the third decimal place in the R, values are not shown in eq. (4).) Again the other values are shown as a 113 The prediction should be 3.26.
given for R,( 2 TeV) in ref.
[ 21 is in error and
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scale on the right-hand side. Since the differences due to the structure function uncertainties are SO small, we must return to other sources of uncertainties, as described in ref. [2]. The largest of these is the uncertainty on sin28w. The reason is that the ratio of the W. and Z cross sections depends to a good approximation only on the ratio Mw and M,, and therefore only on sin’8w. All of the above numbers have been evaluated using the value of 0.23 for the latter, with the absolute value of Mw adjusted to lie roughly at its measured value. If we instead introduce a “world average” value and error [ 111 sin*& = 1 -M&,/M;
=0.230?0.005,
we find this leads to an uncertainty
(5)
AR,=O.O4. We can summarise the results of our study as follows. It is difficult to predict accurately the value of R, at 630 GeV. There is a rather large experimental uncertainty in the value of F2 (n) /F2 (p) in the relevant range of x, due primarily to the systematic differences in the EMC and BCDMS data sets. We should remark that in this study, as in ref. [ 8 1, we have taken the EMC and BCDMS data at face value, and used the spread in the experimental measurements to determine the uncertainty in the theoretical predictions. Of course, since the two measurements of F2 (p) are in contradiction - at least at the level of the statistical errors - we can only assume that the situation will change with an eventual reconciliation of the measurements. If and when this happens we must again perform a new global fit to the deep inelastic scattering data to determine a new set of parton distributions and an improved determination of R,. At present, however, the theoretical uncertainty on R, combined with the experimental uncertainty on the value of R, make it impossible to obtain a definitive upper limit on m,. However the situation would improve dramatically if the F2 (n ) /F2 (p ) ratio could be measured to high precision, In view of the importance of obtaining as much information on the allowed values of m, as possible, we believe that such a measurement should be given serious consideration. Perhaps suprisingly, the situation appears much better for the FNAL collider at 1.8 TeV. The dominance of the sea quarks at small x means that the value of R, is much more tightly constrained at this higher en-
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ergy. In fact we have shown that the larger uncertainty comes instead from the uncertainty on sin2Bw. Considering the variation arising from the parton distributions, as summarised in eq. (4), and that arising from sin28w given in eq. ( 5 ), we conclude that R,( 1.8 TeV) = 3.27 2 0.03 (pat-ton distributions)
kO.04 (sin’f?,)
.
(6)
The corresponding predictions for R are displayed in fig. 3. We can summarise the situation by saying that a measured value for R ( 1.8 TeV) greater than about 10.5 would imply at least four light neutrinos. A value between 8.8 and 10.5 would imply either three, four or five light neutrinos and a corresponding value of m, for each, and (perhaps most interesting of all) a value less than about 8.8 would signal a breakdown of the standard model. We wish to thank Alain Milsztajn, Terry Sloan and Gerard Smadja for helpful discussions concerning the deep inelastic muon data.
References [ 1] F. Halzen and M. Mursula, Phys. Rev. Lett. 5 1 ( 1983) 857; K. Hikasa, Phys. Rev. D 29 (1984) 1939; N.G. Deshpande et al., Phys. Rev. Lett. 54 (1985) 1757; D. Dicus et al., Phys. Rev. Lett. 55 (1985) 132; F. Halzen, Phys. Lett. B 182 (1986) 388; F. Halzen, C.S. Kim and S. Willenbrock, University of Wisconsin-Madison preprint MAD/PH/342 (1987). [2] A.D. Martin, R.G. Roberts and W.J. Stirling, Phys. Lett. B 189 (1987) 220. [ 31 A.D. Martin, R.G. Roberts and W.J. Stirling, RAL preprint RAL-87-052 (1987), Phys. Rev. D, to be published. [4] UAl Collab., E. Locci, in: Proc. Intern. Europhysics Conf. on High energy physics (Uppsala, 1987 ) ed. 0. Botner, p. 8. [ 51 UA2 Collab., R. Ansari et al., Phys. Lett. B 186 (1987) 440. [6] BCDMS Collab., A. Milsztajn, private communication. [7] EM Collab., J.J. Aubert et al., Nucl. Phys. B 272 (1986) 158; B 293 (1987) 704. (81 A.D. Martin, R.G. Roberts and W.J. Stirling, RAL preprint RAL-88-002 (1988). [9] M. Diemoz, F. Ferroni, E. Longo and G. Martinelli, preprint CERN-TH-4751/87 (1987), Z. Phys. C, to be published. [ lo] F. Halzen, C.S. Kim and S. Pakvasa, University of Wisconsin-Madison preprint MAD/PH/394 (1987). [ 111 See e.g., U. Amaldi et al., Phys. Rev. D 36 (1987) 1385.
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