Fits on standard model, results on $\alpha(m^{2}_{Z})$ and influence on the Higgs mass

HAL Id: in2p3-00014166

http://hal.in2p3.fr/in2p3-00014166

Submitted on 25 Nov 2003

HAL is a multi-disciplinary open access archive for the deposit and dissemination of sci- entific research documents, whether they are pub- lished or not. The documents may come from teaching and research institutions in France or abroad, or from public or private research centers.

L’archive ouverte pluridisciplinaire HAL, est destinée au dépôt et à la diffusion de documents scientifiques de niveau recherche, publiés ou non, émanant des établissements d’enseignement et de recherche français ou étrangers, des laboratoires publics ou privés.

Fits on standard model, results on α(m ² _Z ) and influence on the Higgs mass

B. Pietrzyk

To cite this version:

B. Pietrzyk. Fits on standard model, results on α(m

_Z ) and influence on the Higgs mass. Work- shop on Hadronic Cross Section at Low Energy SIGHAD03, Oct 2003, Pisa, Italy. pp.97-104,

�10.1016/j.nuclphysbps.2004.02.014�. �in2p3-00014166�

Fits on standard model, results on α(m

) and influence on the Higgs mass

B. Pietrzyk

LAPP-IN2P3-CNRS 9 chemin de Bellevue - BP. 110 F-74941 Annecy-le-Vieux Cedex

Presented at Workshop on Hadronic Cross Section at Low Energy, SIGHAD03

Pisa, Italie, 8-10 Octobre 2003

1

Fits on Standard Model, results on α (m ² _Z ) and influence on the Higgs mass

B. Pietrzyk

a

Laboratoire de Physique des Particules (LAPP), IN2P3-CNRS, F-74019 Annecy-le-Vieux, France

Fits on Standard Model, results onα(m²_Z) and influence on the Higgs mass are presented.

1. Standard Model Fits

The precise electroweak measurements (Fig. 1) are used in the Standard Model (SM) fits which are performed by the LEP Electro Weak Working Group [1].

Measurement Fit |O^meas−O^fit|/σ^meas

0 1 2 3

0 1 2 3

∆α_had(m_Z)

∆α⁽⁵⁾ 0.02761 ± 0.00036 0.02767 m_Z [GeV]

m_Z [GeV] 91.1875 ± 0.0021 91.1875 ΓZ[GeV]

ΓZ[GeV] 2.4952 ± 0.0023 2.4960 σ_had [nb]

σ⁰ 41.540 ± 0.037 41.478 R_l

R_l 20.767 ± 0.025 20.742 A_fb

A^0,l 0.01714 ± 0.00095 0.01636 A_l(P_τ)

A_l(P_τ) 0.1465 ± 0.0032 0.1477 R_b

R_b 0.21638 ± 0.00066 0.21579 R_c

R_c 0.1720 ± 0.0030 0.1723 A_fb

A^0,b 0.0997 ± 0.0016 0.1036 A_fb

A^0,c 0.0706 ± 0.0035 0.0740 A_b

A_b 0.925 ± 0.020 0.935

A_c

A_c 0.670 ± 0.026 0.668

A_l(SLD)

A_l(SLD) 0.1513 ± 0.0021 0.1477 sin²θ_eff

sin²θ^lept(Q_fb) 0.2324 ± 0.0012 0.2314 m_W [GeV]

m_W [GeV] 80.426 ± 0.034 80.385 Γ_W [GeV]

Γ_W [GeV] 2.139 ± 0.069 2.093 m_t[GeV]

m_t[GeV] 174.3 ± 5.1 174.3 sin²θ_W(νN)

sin²θ_W(νN) 0.2277 ± 0.0016 0.2229 Q_W(Cs)

Q_W(Cs) -72.84 ± 0.46 -72.90

Summer 2003

Figure 1. The precise electroweak measurements.

∗pietrzyk@lapp.in2p3.fr

The variation of ∆χ

(m

) as a function of m

for the fit in which all the precise measurements are used is shown in Fig. 2. The value of the Higgs mass obtained from the fit is

m

= 96

GeV

and the 1-sided 95% CL upper limit is 219 GeV.

0 2 4 6

100

20 400

m

[ GeV ]

∆χ

Excluded

∆α_had =

∆α⁽⁵⁾

0.02761±0.00036 0.02747±0.00012 Without NuTeV

theory uncertainty

Figure 2. ∆χ

(m

) as a function of m

.

The highest sensitivity

H)/σO

of the fit

on the Higgs mass comes from the m

, the left-

right asymmetry measurement at SLD A

, and

the forward-backward b asymmetry A

measure-

ments at LEP (Fig. 3).

0 2

ΓZ σhad Rl Afbl Al Rb Rc Afbb Afbc Ab Ac Alr <Q>fb mW ΓW sin2ΘW νN Qw(Cs)

log10(MH) sensitivity

Figure 3. Sensitivity

H)/σO

of the different measurements on the Higgs mass.

The A

and m

push the central value of the Higgs mass towards lower values in the fit (Fig.

4), A

towards higher values. The Higgs mass from the sin

Θ

measurements in the

N scat- tering at NuTeV is even in the overflow (above 1000 GeV) on the Fig. 4.

M

[ GeV ]

Summer 2003

Γ_Z [GeV]

Γ_Z [GeV]

σ_had [nb]

σ⁰ R_l R⁰ A_fb A^0,l A_l(P_τ) A_l(P_τ) R_b R⁰ R_c R⁰ A_fb A^0,b A_fb A^0,c A_b A_b A_c A_c A_l(SLD) A_l(SLD) sin²θ_eff sin²θ^lept(Q_fb) m_W [GeV]

m_W ΓW[GeV] ΓW

sin²θ_W(νN) sin²θ_W(νN) Q_W(Cs) Q_W(Cs)

10 10

10

Figure 4. Higgs mass fits to individual measure- ments.

The

/d.o.f. is 25.4/15 in the SM fit, giv- ing the low probability of 4.5%. The sin

Θ

the Higgs mass, but it has a large contribution to the low probability of the SM fit (Fig. 1). A large contribution to the low probability of the fit comes also from the A

and the A

asymme- try measurements. A comparison of the different asymmetry measurements is shown in Fig. 5.

10² 10³

0.23 0.232 0.234

Final

Preliminary

sin

θ

= (1 − g

/g

)/4 m

[ GeV ]

χ²/d.o.f.: 10.5 / 5

A^0,l_fb 0.23099 ± 0.00053

A_l(P_τ) 0.23159 ± 0.00041

A_l(SLD) 0.23098 ± 0.00026

A^0,b_fb 0.23212 ± 0.00029

A^0,c_fb 0.23223 ± 0.00081

Q^had_fb 0.2324 ± 0.0012

Average 0.23150 ± 0.00016

∆αhad= 0.02761 ± 0.00036

∆α⁽⁵⁾

m_Z= 91.1875 ± 0.0021 GeV m_t= 174.3 ± 5.1 GeV

Figure 5. Comparison of the effective electroweak mixing angle derived from the different measure- ments.

In the SM, all these measurements are sensitive to the same leptonic effective electroweak mixing angle sin

Θ

. However, the two most pre- cise determinations of sin

Θ

deviate by 2.9

. There is no straightforward explanation of this deviation in terms of new physics. The

of combination of sin

Θ

is 10.2/5 d.o.f giving an important contribution to the low probability of the SM fit. If the global fit is performed with the average sin

Θ

, the

/d.o.f becomes 15/10 giving more reasonable probability of 13%. It is important to note that there is a good agreement

2The label ”eff” means that it includes electroweak radia- tive corrections dependant also on mt and mH.

3

between the results obtained by the different LEP experiments on the asymmetry A

(Fig. 6).

LEP

Summer 2003 <A

FB 0,bb

_

> =0.0997 ± 0.0016

OPAL

inclusive 1991-2000 0.1000 ± 0.0034 ± 0.0018

L3

jet-ch 1994-95 0.0954 ± 0.0101 ± 0.0056

DELPHI

inclusive 1992-2000 0.0984 ± 0.0030 ± 0.0015

ALEPH

inclusive 1991-95 0.1015 ± 0.0025 ± 0.0012

OPAL

leptons 1990-2000 0.0983 ± 0.0038 ± 0.0018

L3

leptons 1990-95 0.1007 ± 0.0060 ± 0.0035

DELPHI

leptons 1991-95 0.1031 ± 0.0051 ± 0.0024

ALEPH

leptons 1991-95 0.1009 ± 0.0038 ± 0.0017

0.09 0.1 0.11

A FB 0,bb

_

Figure 6. Comparison of the A

measurements by the different LEP experiments.

W-Boson Mass [ GeV ]

m

[ GeV ]

80 80.2 80.4 80.6

χ²/DoF: 0.3 / 1

pp⁻-colliders 80.454 ± 0.059

LEP2 80.412 ± 0.042

Average 80.426 ± 0.034

NuTeV 80.136 ± 0.084

LEP1/SLD 80.373 ± 0.033

LEP1/SLD/m_t 80.378 ± 0.023

Figure 7. Comparison of different measurements of W mass.

The sin

Θ

measurement in the

N scatter- ing at NuTeV makes another large contribution to the low probability of the SM fit. This mea- surement can also be interpreted in term of the W mass measurement using the relation sin

Θ

= 1- m

. The large deviation of the NuTeV result from the SM prediction (Fig. 1) can also be seen in the figure showing the comparison of different W mass measurements (Fig. 7). We see again that the NuTeV measurements show 2.9

deviation from the SM prediction. There is no

straightforward explanation for this deviation in terms of new physics. However, an explanation for this deviation was recently proposed within the SM as being due to the strange sea asymme- try present in the new CTEQ fits [2]. A global SM fit without NuTeV gives a probability of 28%.

0.231 0.2315 0.232 0.2325 0.233

83.6 83.8 84 84.2 ∆α

Preliminary 68% CL

Γ

[ MeV ] sin

θ

m_t= 174.3 ± 5.1 GeV m_H= 114...1000 GeV

m_t m_H

Figure 8. Contour curve of 68% probability in the sin

Θ

Γ

plane.

0.231 0.2315 0.232 0.2325 0.233

80 80.2 80.4 80.6

∆α

Preliminary 68% CL

M

[ GeV ] sin

θ

m_t= 174.3 ± 5.1 GeV m_H= 114...1000 GeV

m_t m_H

Figure 9. Contour curve of 68% probability in the sin

Θ

m

plane.

In conclusion, the low probability of the SM

fit is related to the large

/d.o.f. of the com-

Figure 10. The shift of ∆χ

fit distribution when the ∆α

(m

) and m

are changed by one stan- dard deviation.

bination of sin

Θ

measurements and to the deviation of NuTeV measurement from the SM prediction.

2. α

(

)

The Figs 8 and 9 show the contour curves of 68% probability in the sin

Θ

Γ

and sin

Θ

m

planes. The dot shows the predic- tion of a theory based on Born and QED with running

due to hadronic vacuum polarization. The shaded region shows the SM prediction with the values of m

and m

varied in the ranges indicated. m

is obtained in the fit from the measurement of gen- uinely electroweak radiative corrections which are observed as a difference between the dot and the shaded region. Clearly, as seen from Figs 8 and 9, the changes of the input values of ∆α

(m

) and m

affect the value of m

obtained from the fit.

These changes are potentially important. Fig.

10 shows the shift of ∆

fit distribution when the

∆

(m

) and m

are changed by one standard deviation.

2.5 5 7.5

10²

2.5 5 7.5

2 2.5

m_Higgs[GeV500]

∆χ2 ∆χ2

EXCLUDED BY DIRECT SEARCHES

PREL. Summer 2000

standard using BES R measurements

minimum moves to 90 GeV, upper limit moves to 210 GeV

↑very preliminary↑

July 28, 2000 The global fit to EW data Bolek Pietrzyk

Figure 11. Transparency presented during ICHEP 2000 conference at Osaka showing the change of the SM fit results with the new BES data.

In fact, the minimum of ∆χ

fit distribution has moved from 60 to 88 GeV and the 1-sided 95% CL upper limit has moved from 165 to 210 GeV when BES data arrived during ICHEP 2000 conference in Osaka [3] (Fig 11).

3. Our evaluation of α(m²_Z

)

The value of the hadronic contribution

∆α

(m

) to the running of

used in the SM fit (Fig. 2) comes from the 2001 analysis made by H.Burkhardt and the author [4] (Fig. 12). The uncertainty of this analysis has been reduced from 0.0007 to 0.00036 mainly due to the use of BES [5]

measurements in 2-5 GeV c.m.s. region. It is im- portant to note, however, that this region gives still the most important contribution to the to- tal uncertainty together with the 1-2 GeV region (Fig. 13).

In our analysis we integrate R

represented

by a simple parametrization, like broad averages

and straight lines in the continuum and rely,

whenever available, on published world averages.

5

0 1 2 3 4 5 6 7

0 1 2 3 4 5 6 7 8 9 10

Bacci et al.

Cosme et al.

Mark I Pluto Cornell,DORIS Crystal Ball MD-1 VEPP-4 VEPP-2M ND DM2 BES 1999 BES 2001 BES 2001

Burkhardt, Pietrzyk 2001

15 % 5.9 % 6 % 1.4 %

rel. err. cont.

Rhad

ρ,ω,φ Ψ's Υ's

√s in GeV

Figure 12. R

used in our analysis of hadronic contribution to the QED vacuum polarization.

We adapt the analysis to make the best possi- ble use of experimental data. In the 2001 paper we connected and integrated directly 91 points measured by BES. The systematic uncertainties were treated as fully correlated, in contrast to the statistical errors. The information from the older measurements was kept. This was achieved by a slight rescaling of the BES contribution (Fig. 14).

In the

region (Fig. 15) we used the ”hid- den local parametrization” given by the CMD2 Collaboration with a small extra bump at 1.2 GeV. A check made with the direct integration of CMD2 data and the tails from the parametriza- tion gave compatible results. The 2001 result was obtained using preliminary CMD2 data [6]. It was not necessary to update our 2001 result with the published CMD2 data [7] since this would result in shift of our result by only 10% of its

> 12 GeV

7 - 12 GeV 5 - 7 GeV 2.0 - 5 GeV

1.05 - 2.0 GeV narrow resonanc ρ es

> 12 GeV 7 - 12 GeV

5 - 7 GeV

2.0 - 5 GeV 1.05 - 2.0 GeV

narrow resonances ρ

contributions at m_Z

in magnitude

in uncertainty

Burkhardt, Pietrzyk 2001

Figure 13. Relative contribution to ∆α

(m

) in magnitude and uncertainty.

uncertainty (Fig. 16). The recent improvement in the treatment of radiative corrections by the CMD2 collaboration [8] shifts our result by 18%

of its uncertainty giving the value of hadronic contribution ∆α

(m

) to the running of

of 0.02768±0.00036.

Our uncertainty reflects correctly the uncer- tainty of data, improvement will come using new measurements from KLOE, CMD2, BES, CLEO, BABAR and BELLE.

Improvement is also possible using currently

available data. In the c.m.s. region of 2-5 fully

correlated systematic uncertainty of BES points

is used. The uncertainty on ∆

(m

) can be

improved when the BES Collaboration will give

R without resonances

Bacci et al.

Cosme et al.

Mark I VEPP-2M ND DM2 FENICE BES 1999 BES 2001

R

0 0.5 1 1.5 2 2.5 3 3.5

1 1.5 2 2.5 3 3.5

QCD pred.

Burkhardt, Pietrzyk 2001

√s in GeV

Figure 14. Direct integration of BES points. The line used in the integration follows the shape of BES points but it is slightly shifted up in order to take into account the older measurements.

correlations between different points. In the

re- gion the uncertainty of 2.3% is used in our 2001 result. The total uncertainty would be reduced a little bit using the overall (stat. and sys. com- bined) uncertainty of 0.9% of CMD2 results.

Fig. 17 shows the values of the different esti- mates of ∆α

(m

) since 1989. The only im- portant changes appeared in 1995 when Crystal Ball data were used for the first time and in 2000 when BES data arrived. The central value of our result is in agreement with the one obtained by F. Jegerlehner (FJ) and the HMNT analysis. The uncertainty of our result is in agreement with FJ but it is larger than the one obtained by HMNT [9].

The participants of this workshop know that it is very important to improve the precision of R

1 10

0.4 0.6 0.8 1 1.2 1.4

VEPP-2M TOF VEPP-2M OLYA VEPP-2M CMD ACO DM1 Quenzer et al.

VEPP-2M Koop et al.

VEPP-2M CMD-2

√s in GeV

| Fπ(s)

Figure 15. The pion form factor.

measurements. It is also, however, important to remeasure R

in a given c.m.s region with sim- ilar precision to the one presently available. A change of an experimental result by one standard deviation happens often in physics. The Table 1 gives the shift of the central value of the Higgs mass m

obtained from the Standard Model fits made with the modified value of ∆α

(m

) ob- tained with the R

shifted by the uncertainty of its measurement in different c.m.s. regions. m

shifts of about 15 GeV are obtained when R

is modified in the region of 2-5 GeV, recently mea- sured by the BES collaboration, and also for the region of 1-2 GeV where precise measurement are not available.

The modification of our result due to the recent

improvement in the treatment of radiative correc-

tions by the CMD2 Collaboration has a small ef-

fect on the SM fit as seen in Fig. 18. On the other

7

Table 1

Shift of central value of the Higgs mass m

obtained from the Standard Model fits made with the modified value of

obtained with the R

shifted by uncertainty of its measurement in different c.m.s. regions.

c.m.s. region uncertainty (%) m

shift main experiment

ρ

2.3 -4.9,5.0 CMD2

narrow resonances 3.1 -3.1,3.6

1-2 GeV 15 -13.6,15.2

2-5 GeV 5.9 -13.1,14.2 BES

5-7 GeV 6 -6.7,7.3 Crystal Ball

7-12 GeV 1.4 -2.5,2.7

>12 GeV

0.2 -1.2,1.3

Burkhardt, Pietrzyk 2001 published 2003 preliminary 0.02761±0.00036 0.02768±0.00036

∆α_had

1999

2001 2003

prelimary

published revised

-10% +18%

of total uncertainty on ∆α_had CMD2

Figure 16. Changes of the value of ∆

(m

) caused by improvements in calculations of radia- tive corrections by the CMD-2 Collaboration in units of the total uncertainty of ∆α

(m

).

hand, some large effects are expected in the near future due to a possible change of the top mass.

In fact the top mass combination used in the SM fit does not take into account the improved analy- sis of run I data made by the D0 Collaboration as seen in Fig. 19. The combination using all avail- able data could shift the combined top mass by about one standard deviation which would have a major impact on the SM fit results as seen in Fig. 18.

0.026 0.027 0.028 0.029 0.03

Burkhardt, Jegerlehner, Verzegnassi,Penso 1989 Jegerlehner 1992

Nevzorov 1994 Geshkenbein, Morgunov 1994

Martin, Zeppenfeld 1994 Swartz 1994 Geshkenbein, Morgunov 1995

Eidelman, Jegerlehner 1995 Burkhardt, Pietrzyk 1995

Swartz 1995 Adel, Yndurain 1995

Alemany, Davier, H cker 1997 Davier, H cker 1997 K hn, Steinhauser 1998 Groote, K rner 1998 Davier, H cker 1998 Jegerlehner 1999 Erler 1999

Osaka 2000 update of Burkhardt, Pietrzyk 1995

Martin,Outhwaite,Ryskin 2000 Burkhardt, Pietrzyk 2001 Jegerlehner 3/01 Jegerlehner 3/01 Troconiz, Yndurain 11/01

Jegerlehner 03/03 Zeuthen 2003 presentation

Burkhardt, Pietrzyk 2003 Aachen 2003

HMNT 2003 incl. Aachen 2003

Jegerlehner 08/03 Zeuthen 2003 proceedings

Jegerlehner 8/03 Zeuthen 2003 proceedings

Figure 17. Comparison of different estimates of

∆

(m

) since 1989.

In conclusion, the measurements discussed in

this workshop are very important for fundamen-

tal physics questions. A new more precise value

of ∆α

(m

) will come with new measurements

from CDM2, KLOE, BES, CLEO, BABAR and

BELLE.

0 2 4 6

10

m

[ GeV ]

∆χ

Excluded

∆α_had =

∆α⁽⁵⁾

0.02761±0.00036 0.02768±0.00036 M_T = 179.4±5.1 GeV

Figure 18. ∆χ

(m

) with modified ∆α

(m

) and m

.

I would like to thank the organizers for inviting me to come to this very interesting and important workshop and also H. Burkhardt, S. Eidelman, P. Gambino, M. Gr¨ unevald, G. Quast, P. Wells and T. Teubner for helping me in the preparation of this talk.

REFERENCES

1. LEP Electroweak Working Group, http://lepewwg.web.cern.ch/LEPEWWG/;

see also presentation during summer 2003 conferences: P. Wells and G. Quast, HEP2003 Europh. Conf. in Aachen, Germany, http://eps2003.physik.rwth- aachen.de/, P. Gambino, XXI Int. Symp.

on Lepton and Photon Int., Fermilab, http://conferences.fnal.gov/lp2003/index.htm.

2. see P. Gambino’s presentation at XXI Int.

Symp. on Lepton and Photon Int., Fermilab, http://conferences.fnal.gov/lp2003/index.htm.

150. 200.

M_top[GeV]

D∅ dilepton 168.4±12.8

D∅ lepton+jets OLD 173.3±7.8 D∅ lepton+jets NEW 180.1±5.4

D∅ combined 172.1±7.1

(Excluding New)

CDF dilepton 167.4±11.4

CDF lepton+jets 176.1±7.4

CDF All hadronic 186.0±11.5

CDF Combined 176.1±6.6

CDF/D∅ combined 174.3±5.1 (Excluding New)

Figure 19. Top mass combination.

3. B. Pietrzyk,

27 July-2 August 2000, Ed. C.S. Lim and T.

Yamanaka, page 710.

4. H. Burkhardt and B. Pietrzyk, Phys. Lett.

B513 (2001)46.

5. BES Collaboration, J.Z. Bai, Phys.Rev.Lett.

88:101802,2002.

6. R.R. Akhmetshin et al., CMD-2 Collabora- tion, hep-ex/9904027.

7. R.R. Akhmetshin et al., CMD-2 Collabora- tion, Phys. Lett. B527 (2002)161.

8. R.R. Akhmetshin et al., CMD-2 Collabora- tion, hep-ex/0308008.

9. T. Teubner, these proceeding, see

also his presentation at HEP2003 Eu-

roph. Conf. in Aachen, Germany,

http://eps2003.physik.rwth-aachen.de/.