INVESTIGACiÓN REVISTA MEXICANA DE FislCA 44 (1) )9-42

W bosoo weak electric dipole momeot io pp(PP) --+ W:!: ZOX

J. García and A. QueijeiroDepartamento de Física, Escuela Superior de Fúica y Matemáticas

Unidad Profesional Adolfo López Mateos, Instituto Politécnico Nacional07738 México D.F, Mexico

Recibido el 7 de febrero de 1997; aceptado el 18 de abril de 1996

FEBRERO 1998

We introduce ao ancmalcus weak electric dipole moment of the \1/ hosoo lo study lhe process pp(pP) --+ W:t: ZO X. We compute the¡ovariant mass spectrum of the lV Z pair. and the total cross.section production.

Keywords: W bason. total cross-section production

Estudiamos el proceso de producción de bosones pp(pp) --+ n'::!: ZO X introduciendo un momento di polar débil eléctrico anómalo delbosón a'. Presentamos resultados para el espectro de masa invariante del par \.l' Z. y la sección lotal de producción.

Descriptores: bosón VV, sección total de producción

PACS: 14.80.Er; 12.15.1i; 12.50.Fk

is a prolon (anliproton), and X denotes a final slale hadron.We shall show lhal similar results as in [IJ are oblained here.

To ealculale Ihe mass speelrum of Ihe WV pair pro-duced in pp or pp reactions, we write the angular differen-lial eross-seclion al Ihe quark level, q;iji' If O is lhe an-gle of Ihe W boson wilh respeel lo quark qi, we can wrilet = a + bz, where a = -s(1 - e) 2, b = s(3 2, z = cosO,and e = (J'vfrv+ Mt)js, (3 = (1- el' - 4MwMvjs'.Then, splilling in lhe sum of Iwo lerms, Ihe angular differen-tial cross-section at the quark level is given by

1. Inlroduclion

In a previous paper [1 J we sludied lhe effeets of a pos-sible anomalous W boson (weak)-eleelrie dipole momenlKv in ¡.Ji -+ WV, where f¡ and Ji are lwo membersof an SU(2) doublel of elementary fermions in Ihe stan-dard model of eleelroweak unifiealion (SM), and 11 is apholon or a neulral Z boson. We showed lhal lhe angu-lar differential and lhe lolal cross-sections are sensitive toKv and Ihal lhey are of lhe same order of magnitude thanthose contributions coming from the anomalous tV boson(weak) magnelie dipole momen! "v. The purpose of thispaper is to report results for the effects of Kv on the ¡n-variant mass al' the H'V pair and on the total cross-sectionin Ihe hadronie reaetions pp (pp) -+ W ZX, where p(p)

I wilh

da(q,iji -+ WII)

dz(1a)

() , (")'{( j)' [.]. .,dCJ 27TQ j3 GI) sev e 2.'leV" le gJ gl gl - g)-1 = -3- - _ \1' A(s,z) + ,_ \1' --fes. z.b) + -les, z, -b) + (--) E(s, z)(Z SM S e s J w S .J l\/ e e e

(gi)'a' _ b'z' _ M' AI' (gi)'a' - b'z' _ M' M' (gigi) s(M' + M')}+ _ w v + _ w v + 2 __ W v (lb)e (a-bz)' e (a+bz)' e' a'-b'z' '

the SM eonlribution,

(da) 21ro.'(3(Gii)'{ ,[ sevje ]'dz NSM = ~ --;;- ("v -1) 2(s _ M¡;') AI(s,z)

sevje [ g' g' ] 3,[ sevje]' }+ ("v - 1)s _ M¡;' B(s, z) + ~ll (s, Z. b) - -¡ll (s, z, -b) + 2"v 2(s _ M¡;') A,(s, z) , ( le)

40 J. GARCíA AND A. QUElJEIRO

,o',,' pp-W'Z'X. it. (, )pp-W-Z'X ,R. (,) pp - W'Z'X. ié, (b)

">

"~o •lOe

lS1.S 1 e:;; 1 "~ OS ~e 0,0,1 0,0.1 e 'o'

01:;"ClJ lO'

'o'

" '" ro " " o. ,. " " " ",. " ", " ., ro "VS (TeV} v;¡- ( TeV) M{TeV) M (leV)

"' 'o'pi) -W~Z"X, <, pp-W'Z'X . ¡(, pp - W-Z'X .K, (e) pp-W'Z'X. K, (d)

(e) (d)

,,' >e •1.S 1.S lO

" 1. 1~ S S ee0,0.1 "0,01 ~ 1.S

O 'o' e 1

.gl~'o' OS 50.1. 01O O

'o' ,,", " '" ro " ro '" ro '" " " ,. " " " "' ,. " "vs (leV) vs (leY)

Figure l. Invariant mass spectrum oC the W Z pair for (a) pp -+w- ZOX. (b) pp -+ w+ ZOX, (e) pp -+ w- ZOX, and (d)

pp -+ ~V+ ZOX . We use IVI ~ 2.5. and the centcr oCmass energyis ..;s = 20 Te V. Labels on curves denote values oC;:¿z.

M (TeV) M (leV)

Figure 2. Total cross-section as a function of ..;s Cor (a) pp -+W-ZoX. lb) pp -+ W+ZoX. (e) pp -+ W-ZoX, and (d)pp -+ lV+ ZOX . Labcls on curves denote values oC Kz.

fm the non-slandard model eonlribulion. In Appendix A wegive all the funetions and parameters appearing in Eqs. (1al!O (le).

Tbe invariant mass oflbe Wt; pair (V = "(or Z) is de-I

lined hy M = ,)(1'1 + 1'2)2. wilh pi = Ml,., and p~= M~.DenoIing by VS the tOlal energy in the pp(pp) eenter ofrnass rcfercnce systcm, wc have that 0.2 TeV :::; Al <VS. Then ¡he differenlial eross-seetion fm pp(pp) -+W ZX is given by [2]

d<7{ab-+ WZX) _ 2M" fY d [¡I"I( '[2)¡(b)( ... '[')------- - L- Yb i X(¡, i~ ..,- Xb •. Hdl,[ S .. _y )'.1

¡("i( '[2)¡lbl(.. ')]+ J Xn,'~ i .[b,'\l f'O d"(q;q -+ WV)dz ) .

-Zo dz(2)

Here ¡;I") (x"' M') is the quark '1; disIribution funeIioninside hadron a, ¡~bl(Xb, M') the eorresponding one forquark qj inside hadion b; s = TS, where T is the scale fac-tor defined by Xa,b = e:::!:Yb JT. The inlegralion over Yb isperformed assuming an inlerva! (Y, -Y), where Y is Ihe 50-

eaHed rapidily en\.

Inlegration in the variable z in Eq. (2) can be done ana-litically, bUI lhe one in Yb is pcrforrned numerically, sincethe quark distributions funclions, given in Appendix B, arequile complicated. The results are shown in Fig. l for thecase V = Z; we have used the Set I of Duke-Owens [31 fmlhe distribution functions. and considered contributions fromvalence and sea u, d. e, and s quarks only. Fig. I shows that

Ithe contributions from /{,Z are similar than those coming from"z, in the same inlerval 01'valucs [4J.

Intcgrating Eq. (2) over Al yields the total cross-scclion,and as a funetion of VS is plolled in Fig. 2 for 2 :s VS :s100 in TeV. and 11'1 :s 2.5 . Here again our results for Kz aresimilar to [hose coming from Kz.

In summary. in this work we have complemented pre.vious results by us, for the posible effects 01' an anomalous(weak) electric dipole momcnl 01' the HT boson. From theabovc results we observe that the contributions [rom Kv are0'- the sallle order of magnitude than the corresponding re.sults for "'y, whcn both are in Ihe range (-2,2). A final

Rev. Mex. Fís. 44 (1) (19lJR) 39-42

W BOSON WEAK ELECTRIC IJIPOLEMOMENT IN PP(PP) -+ 11'" ZoX 41

comenl on this range of values is as follows. Thc origin of~v is relatcd lO the violation of (he CP syrnmelry, and in the51\1 this comes [rom (he interactions of the Ur hoson withthe quarks. Thcn a {erm like Kv arise via radiativc corrcc-tioos. starting al lhe thrcc-Ioop level [5]. which IIlcans a vcrysmall value. Sincc ~l' is related lo a CP-even propcrty oflheIV 0050n, radiative corrections to its \'alue at Ircc.lcvcl(ti" = 1 )star! conlrihuting from the one-Ioop level, leadinglo a valllc oiggcr than ~v. Then, within SM, the contrihutionsfrom Kv arc slIpprcsscd compared to thc contrihulions fromti'" for the kind of ohservables computed in this work [6].A diffcrent situatian occurs in the mini mal supcrsymmctricSM, wherc Ihe U' boson couId have a non-vanishing eleclricdipole moment through a one loop diagram medialed hy theheavy massive charginas and neutratinos [7]. In compositemodels the situation can be less restrictive, since as is shownin [81 for f'-¿v, simple model calculations give a signifkativc

I

Appendix A

enhancement al' one or two orders 01' magnitude for lhe ra-diative corrections. Thus, if the n' hoson tum out to be non-eicmentary, one can cxpecl a Kv al' the order 10-1 and itscontributions he nal much supressed. Nevertheless, a~ wehave shown in this work. only if ~v is as big as in Figs. 1 and2 its conlrihutions are cOlllpelilive regarding lo the physicalohservables considered here. Por smaller values 01'Kv it isrequired a very great acculllulation 01'data than is expectedfrom the expcriments now running in Ihe Tevatron, and inlhe analogous expcrimcnts at LEP callider. As we have com-mented aboye a diffcrcnt situation emerges when we studythe helicity amplitudes althe elemenlary fermion level [6).

Acknowledgement~

Authors wishes to thank Ihe Comisión de Operación y Fo-mento de las Actividades Académicas dellPN for partial sup-por!.

The various funetions appearing in Eqs, (1h)-( Ic) are:

[(I_E)2 2M;"M~] 82E [1 (M;" - M~)2] [(I_E)2 2M;"M~] 2

.4(8, z) = (co- 1) -2- + 82 + M,~M~ 2 - E + 282 +C2 -2- + 52 z ,

(co - 1 S2E 1) (3 ('2(1 - E) 2 52, + M~.M~

/(.u.b) = -.1- + 2\/2 \./2 +;¡ (I-E) +:,z + 4 z + ..( b-) ,j w' v ~ - .:> II + .•

~/'é CO - 1 e2 :2£(8,Z) = 2M?vM~+ -4--:¡-z ,

(. _ _ 8(3' (2M~. - M~ + s )M~ ( . . .')Al 8, -) - --o '-2 + :2 (o - 1 + C2_ ,

2Afw 28

(M;" - jH~+ s)M~. 2B(s,z) = A¡(8,Z) + 22 ('0 -1 +('2Z ),s

s(l - E) 5(32 (12M;") ( 2) M~l¡(s,z) = -----+ --2- +--- 1 - z - --,2M~. 8Mw a+bz a+bz

\/' 2 \/2 .(:J2 (3 (32( .2 . 2 . 2)1 ".v+ 1.w8.'i .2 ... 2 2'):2.:2 ,2:2 ay s +AlwAlv 2A2(,'i.:) = ;;At(s.z) + ') :2 --,- + J\lwAf\, - S _1\1w.l.\I,,," (J +:-- + .:2.2 Z,

_ .S 2'\/1\' 28 4MwM"

and

(A.I)

(A.2)

(A.3)

(AA)

(A.S)

(A.6)

(A.7)

Ca = .,'(1 - 0)'4Afa Af~ '(A.S)

Appendix H

To cvaluatc Eq. (2) we use Ihe following set 01'valcncc quarkdistribulion funclions:

Iwhere

(B.I)

(82)

Xurl =3{B('I¡"12 + 1)[1+ "Y"d'l1 ]}-¡ (B.3)(1 + 'I¡ +'/2)

;Yd = {B('I¡"I¡ + 1)[1 + (1 +~;:/:ry.¡J}-1 (BA)

Rev. Mex. Fí.>.44 (1) (1998) 39-42

42 J. GARCiA ANO A. QUEIJEIRO

B(x,y) is the Euler heta funClion. The sea quark distribu-tion function are:

u, ::;:Us::;: ds = d, = ss::;: Ss = (~)A8Xll-l(1 - X)b

X (1 + ox + ¡3x2 + I'X'), (B.5)

- A 0'-1(1 lb'C, ::: es::;: eX - X

[ (11')/ (Q')]r ::;: ln In '.\2 In A~ .

where A' = 0.04 GeV'. and Q6 = 4.0 GeV'.is related lo Yb by

:0 = min[13¡¡1 tanlt(l' - YbJ.I],

(B.7)

In Eq. (2) :0

x (1 + o'x + ¡3'x' + )'x'). (B6) with

Here ry, (i = 1,2,3, 4),) ••d, )d. A" A,. a, b, a', b', o, ¡3, ),o', (J. anu,' are functions uf

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Rev. Mex. Fú. 44 (1) (1998) 39--42