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Hunting the hidden standard Higgs
Volume, 166B, n u m b e r 1
PHYSICS LETTERS
2 January 1986
HUNTING THE HIDDEN STANDARD HIGGS A A A K H U N D O V ~, D Yu B A R D I N and T R I E M A N N Laboratory of Theorettcal Phkstcs, J I N R Dubna, P 0 Box 79 S U 101 000 Moscow, USSR Received 13 August 1985, revised manuscript recewed 25 October 1985
The mass of the Hlggs scalar of the standary theory may be estimated through its influence on radiative correcttons from a preose measurement of M 7 and sm20w at SLC or LEP
The existence of the Hlggs boson H of the GlashowWemberg-Salam (GWS) theory is one of the outstanding miracles of present-day physics, and the search for Hlggs boson production constitutes an essential part of the experimental programmes of all large accelerators However, if its massM H is too large and/or the production cross section is too small, one should seek for indirect signals of its existence, e g, through radiative corrections This is an ambRlous attempt m view of the well-known fact that one-loop radiative corrections depend o n M H only weakly [1-3] Consequently, m most papers on the Higgs boson search the discusslon of radiative corrections is excluded [4] We propose to take this idea seriously and feel encouraged by the foUowmg observations There Is at present no stringent indication that the GWS-theory needs to be modified [5], henceforth, we wall assume that this theory Is completely correct m all Its aspects Further, m recent years a clear procedure has been developed which allows quite accurate predictions for a variety of measurable quantities and has become known as Slrhn's on-mass-shell renormahzation scheme [2] Here the free structure constant a, the Fermi constant of muon decay Gu, and the Z boson massM z are used to fix the gauge boson sector of the theory This allows one to determine the W boson massM w and the weak mLxmg angle sln20w with high accuracy and without reference to other measurable quantxties Of course, one has to take into account the yet free parameters Instmtute of Physics, Academy of Sctences of the Azerba~jan SSR, Baku, USSR
0370-2693/86/$ 03 50 © Elsevier Science Pubhshers B V (North-Holland Physics PubhshmffDlXaslon)
M H and mt, the t-quark mass Based on formulae pubhshed some time ago [6] we have done such a precision calculation Recently, m an article mainly devoted to the study of asymmetries In e+e--annihllatlon [7], M w and sin20w have been tabulated with four-digit precision based on a completely independent calculation The results of both calculations agree within all pubhshed digits, thus proving a high level of rehablllty of the electroweak corrections being obtained To detect one-loop Higgs effects one has to do the following knowing ct and Gu, measure two other parameters ~Ol,2(Mz,Mw, c~, Gu) and confront them with the calculated prediction as functions o f M H Evidently, one has to use those quantities which may be (a) measured and (n) calculated with the highest accuracy accessible These two demands led us to the choices tPl =Mz, ¢2 = sln20w as to be measured at LEP and SLC The calculatxons rely on the well-known formulae of Slrlm M w =A/sin 0w,
M z =Mw/cos 0w,
A = A 0 / ( 1 - Ar) 1/2, a 0 = ('/r0t/N/~ a/.t) 1/2 =
37 218 G e V ,
Ar = ~-~X We define sln20w = 1 - M 2 / M 2, where M w is lteratlvely determined from ct, Gu, M z through 1 + 1 (l_4A2/M2)1/2]l/2, M w = M z [-~ 111
Volume 166B, number 1
PHYSICS LETTERS
2 January 1986
from the above, standard expectations As is evident, they allow to draw some definite conclusions We have estimated that one may distinguish b e t w e e n M H -- 100 GeV and M H = 1000 GeV with 3a confidence level A further factor of 1/2 m both errors would allow one to measure the Hlggs massM H with an accuracy (dependlng on the actual parameters) of, say, -+ 100GeV In conclusion, xfM H >~Mz/2,a determination of the Hlggs boson mass from radlatwe corrections to the dependence of sm20w o n M z , Gu, ct could serve as a best guess during the years up to the operation of the LHC and/or SSC
0222
0 220
G~ 02~8
½
0216
0214 I
I
940
Mz(OeV)
Fig 1 Graph of sm20w versus MZ, mfluenced by MH through radiative correctxons The thickness corresponds to the range 30 GeV 6 m t ~<40 GeV, the error bars m&cate the accuracy expected at Z boson factones. and X(a, M z , Mw, mf, MH) has been taken from ref [6] We used the complete expressions for A r as functions o f m t a n d M H m our calculation *I To be specific, we assumed 3 generations of flavor and choose m t = (35 -+5) GeV close to UA1 prehmmary data [9] Fig 1 shows a theoretical prediction of the sm20w, M z Interdependence The scales have been chosen under the assumption that expertmentally the folowIng preclsions can be obtained AM Z ~ 100 MeV - this limit is determined by the energy resolution which depends on machine parameters .2 , A sln20w = 0 001 - this error stems from theoretical and experimental uncertainties The former ( ~ 0 0006) IS mainly due to the hadronIc vacuum polarization [ 11], the latter ( ~ 0 0008) may be obtained from measuring the polarization asymmetry at resonance assuming half a million o f Z bosons produced [10] The error bars are drawn to indicate the possibly resulting hmits o n M n .1 Of course, the common influence of bothM H and mt on quantities like MZ, MW has been studied by several authors, see e g refs [2,3,7,8] Here we exphcitly search for quanlatatxve conclusions on Mr~ from expenmental data .2 See any review on LEP and SLC physics, e g ref [10]
112
We are deeply indebted to Professor D V Shlrkov who strongly enforced us to study the problem raised in this letter
References [1] M Veltman, ActaPhys Pol B8 (1977)475 [2] A Strhn, Phys Rev D22 (1980)971 [3] W J Marcmno and A Slrhn, Phys Rev D22 (1980) 2695 [4] B Cox and F J Gttman, Contrlb 1984 Summer Study on Desagn and ultfllzataon of SSC (Snowmass, CO, 1984) FERMILAB, Conf - 85/33 (1985), A S Schwarz, SLAC-PUB-3665 (1985), and references thereto [5] Contnb Intern EurophyslcsConf on High-energy physxcs (Ban, Italy, July 1985) [6] D Yu Bardm, P Ch Chnstova and O M Fedorenko, Nucl Phys B197 (1982) 1, D Yu Bardm and V A Dokuchaeva, NueL Phys B246 (1984) 221 [7] B W Lynn and R G Stuart, Nuel. Phys B253 (1985) 216 [8] M Consoh, S Lo PrestI and L Mmam, NucL Phys B223 (1983) 474, WJ Marcaanoand A Slrlm, Phys Rev D29 (1984) 945, D Bardln and V Khovansky, preprlnt ITEP-61 (1984) [9] UA1 CoUab, contnb Proc XXII Intern Conf on High energy physics (Leipzig, 1984), Vol II, p 2 [10] J M Dorfan, Lectures Theoretical Advanced Study Institute on Elementary particle physics (Ann Arbor, Michigan, 1984), SLAC-Pub-3407 (1984) [11] C Verzegnassl, Phys Lett 147B (1984) 455
PHYSICS LETTERS
2 January 1986
HUNTING THE HIDDEN STANDARD HIGGS A A A K H U N D O V ~, D Yu B A R D I N and T R I E M A N N Laboratory of Theorettcal Phkstcs, J I N R Dubna, P 0 Box 79 S U 101 000 Moscow, USSR Received 13 August 1985, revised manuscript recewed 25 October 1985
The mass of the Hlggs scalar of the standary theory may be estimated through its influence on radiative correcttons from a preose measurement of M 7 and sm20w at SLC or LEP
The existence of the Hlggs boson H of the GlashowWemberg-Salam (GWS) theory is one of the outstanding miracles of present-day physics, and the search for Hlggs boson production constitutes an essential part of the experimental programmes of all large accelerators However, if its massM H is too large and/or the production cross section is too small, one should seek for indirect signals of its existence, e g, through radiative corrections This is an ambRlous attempt m view of the well-known fact that one-loop radiative corrections depend o n M H only weakly [1-3] Consequently, m most papers on the Higgs boson search the discusslon of radiative corrections is excluded [4] We propose to take this idea seriously and feel encouraged by the foUowmg observations There Is at present no stringent indication that the GWS-theory needs to be modified [5], henceforth, we wall assume that this theory Is completely correct m all Its aspects Further, m recent years a clear procedure has been developed which allows quite accurate predictions for a variety of measurable quantities and has become known as Slrhn's on-mass-shell renormahzation scheme [2] Here the free structure constant a, the Fermi constant of muon decay Gu, and the Z boson massM z are used to fix the gauge boson sector of the theory This allows one to determine the W boson massM w and the weak mLxmg angle sln20w with high accuracy and without reference to other measurable quantxties Of course, one has to take into account the yet free parameters Instmtute of Physics, Academy of Sctences of the Azerba~jan SSR, Baku, USSR
0370-2693/86/$ 03 50 © Elsevier Science Pubhshers B V (North-Holland Physics PubhshmffDlXaslon)
M H and mt, the t-quark mass Based on formulae pubhshed some time ago [6] we have done such a precision calculation Recently, m an article mainly devoted to the study of asymmetries In e+e--annihllatlon [7], M w and sin20w have been tabulated with four-digit precision based on a completely independent calculation The results of both calculations agree within all pubhshed digits, thus proving a high level of rehablllty of the electroweak corrections being obtained To detect one-loop Higgs effects one has to do the following knowing ct and Gu, measure two other parameters ~Ol,2(Mz,Mw, c~, Gu) and confront them with the calculated prediction as functions o f M H Evidently, one has to use those quantities which may be (a) measured and (n) calculated with the highest accuracy accessible These two demands led us to the choices tPl =Mz, ¢2 = sln20w as to be measured at LEP and SLC The calculatxons rely on the well-known formulae of Slrlm M w =A/sin 0w,
M z =Mw/cos 0w,
A = A 0 / ( 1 - Ar) 1/2, a 0 = ('/r0t/N/~ a/.t) 1/2 =
37 218 G e V ,
Ar = ~-~X We define sln20w = 1 - M 2 / M 2, where M w is lteratlvely determined from ct, Gu, M z through 1 + 1 (l_4A2/M2)1/2]l/2, M w = M z [-~ 111
Volume 166B, number 1
PHYSICS LETTERS
2 January 1986
from the above, standard expectations As is evident, they allow to draw some definite conclusions We have estimated that one may distinguish b e t w e e n M H -- 100 GeV and M H = 1000 GeV with 3a confidence level A further factor of 1/2 m both errors would allow one to measure the Hlggs massM H with an accuracy (dependlng on the actual parameters) of, say, -+ 100GeV In conclusion, xfM H >~Mz/2,a determination of the Hlggs boson mass from radlatwe corrections to the dependence of sm20w o n M z , Gu, ct could serve as a best guess during the years up to the operation of the LHC and/or SSC
0222
0 220
G~ 02~8
½
0216
0214 I
I
940
Mz(OeV)
Fig 1 Graph of sm20w versus MZ, mfluenced by MH through radiative correctxons The thickness corresponds to the range 30 GeV 6 m t ~<40 GeV, the error bars m&cate the accuracy expected at Z boson factones. and X(a, M z , Mw, mf, MH) has been taken from ref [6] We used the complete expressions for A r as functions o f m t a n d M H m our calculation *I To be specific, we assumed 3 generations of flavor and choose m t = (35 -+5) GeV close to UA1 prehmmary data [9] Fig 1 shows a theoretical prediction of the sm20w, M z Interdependence The scales have been chosen under the assumption that expertmentally the folowIng preclsions can be obtained AM Z ~ 100 MeV - this limit is determined by the energy resolution which depends on machine parameters .2 , A sln20w = 0 001 - this error stems from theoretical and experimental uncertainties The former ( ~ 0 0006) IS mainly due to the hadronIc vacuum polarization [ 11], the latter ( ~ 0 0008) may be obtained from measuring the polarization asymmetry at resonance assuming half a million o f Z bosons produced [10] The error bars are drawn to indicate the possibly resulting hmits o n M n .1 Of course, the common influence of bothM H and mt on quantities like MZ, MW has been studied by several authors, see e g refs [2,3,7,8] Here we exphcitly search for quanlatatxve conclusions on Mr~ from expenmental data .2 See any review on LEP and SLC physics, e g ref [10]
112
We are deeply indebted to Professor D V Shlrkov who strongly enforced us to study the problem raised in this letter
References [1] M Veltman, ActaPhys Pol B8 (1977)475 [2] A Strhn, Phys Rev D22 (1980)971 [3] W J Marcmno and A Slrhn, Phys Rev D22 (1980) 2695 [4] B Cox and F J Gttman, Contrlb 1984 Summer Study on Desagn and ultfllzataon of SSC (Snowmass, CO, 1984) FERMILAB, Conf - 85/33 (1985), A S Schwarz, SLAC-PUB-3665 (1985), and references thereto [5] Contnb Intern EurophyslcsConf on High-energy physxcs (Ban, Italy, July 1985) [6] D Yu Bardm, P Ch Chnstova and O M Fedorenko, Nucl Phys B197 (1982) 1, D Yu Bardm and V A Dokuchaeva, NueL Phys B246 (1984) 221 [7] B W Lynn and R G Stuart, Nuel. Phys B253 (1985) 216 [8] M Consoh, S Lo PrestI and L Mmam, NucL Phys B223 (1983) 474, WJ Marcaanoand A Slrlm, Phys Rev D29 (1984) 945, D Bardln and V Khovansky, preprlnt ITEP-61 (1984) [9] UA1 CoUab, contnb Proc XXII Intern Conf on High energy physics (Leipzig, 1984), Vol II, p 2 [10] J M Dorfan, Lectures Theoretical Advanced Study Institute on Elementary particle physics (Ann Arbor, Michigan, 1984), SLAC-Pub-3407 (1984) [11] C Verzegnassl, Phys Lett 147B (1984) 455