Contributions of off-shell top quarks to decay processes

Volume 251, number 2

PHYSICS LETTERS B

15 November 1990

Contributions of off-shell top quarks to decay processes A. G r a u t, G. P a n c h e r i 2 Laboratori Nazionali di Frascati dell'INFN, Frascati, 1-00044, Italy and R.J.N. Phillips Rutherford Appleton Laboratory, Chilton, Didcot Oxon OXI 10QX, UK Received 14 April 1990

We quantify the contributions of decay channels proceeding through off-shell top quarks in the decay of the standard model Higgs boson and the Z boson. These contributions turn out to be very small compared to the dominant decay modes except when nearly on-shell.

1. Introduction Decays into heavy quark pairs are potentially important modes for both the standard model Higgs boson H ° and the Z ° boson. It is customary to ignore such channels below the threshold for decay into real quarks; however, the possibility o f decay via virtual heavy quarks into light final particles remains open and could in principle be significant. With new limits on the top quark mass [ 1 ] ( m , > 8 9 GeV at 95% CL), it appears that m t > Mw allowing decay into real W bosons, giving a large width to the top quark and making top decays an important background to W production mechanisms. In the present work we first derive explicit formulae for H--,t*t*--, (all), where t* denotes a generic top quark that may be either on or off-shell. We compare the partial width for this process with the total width and with other important off-shell decay channels, in particular H--, Z'Z*--, 4Ix and H--, W ' W * . We also derive formulae for Z--,ti* decay, which is a possible background in the search for Z - d e , etc., that could arise in models with enhanced flavour-changing neutral current couplings [ 2 ].

2. Virtual contributions to Higgs decay 2.1. H--,ti-* decays

If the Higgs mass exceeds m r + rob, H--,t*t* decay will be dominated by configurations where either t or t is on the mass-shell. As a first step, we therefore examine the process

H -. t~*-, t6ff', where t is a real on-shell top quark and f, ]" are light fermions (u, d, s, c, e, Ix, x, v). Universitat Autbnoma de Barcelona, Bellaterra (Barcelona), Spain. 2 University of Palermo, Palermo, Italy. 0370-2693/90/$ 03.50 © 1990 - Elsevier Science Publishers B.V. ( North-Holland )

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15 November 1990

The decay rate can be obtained as the product of the following three factors: (i) phase space for the decay H~t6f~': dO 2

dPS(H~tbf-f' ) = d P S ( H ~ t t * ) dPS(t*~l~f]" ) 2n ' where Q2 is the squared invariant mass of i*. (ii) Initial state factors, which are given by 1

2mH

1

for H--*t ({--,all),

1

1

2mr. 2 - 4Q

for i*--,6ff' .

(iii) Squared matrix element for the process H ~ t 6 f ] " , which will contain a factor analogous to the squared matrix element for the decay H ~ ti, one for the decay t--,13ff' and then extra factors like the top-quark propagator. The matrix element is written as

({-m,) a ( f )Tu(1 -ys)v(f' ) M=gtgZwa(t) (QZ-m2t) +iFt.m, yu( 1 -Ts)V(6) ((~Z_M2w) +iFwMw with g, = (g/2Mw)m, and gw =g/2x/'2. The calculation of the squared matrix element together with the phase space factors leads to the expression (mH --mr) 2

F ( H - , t all (off-shell {) ) =

f

QdQ 2 P(t*--*6f~' )F(h ~ t t * ) n (Q2-m2)2+(F,.mt) 2'

(1)

where the width into one real and one virtual quark t*, is defined as F ( H - - , t t * ) = 3g221/2t~2 ~ 2 Q2 ) ( t,,,__~n,,,,,,

8ztm 3

(m~-Q2-3m2)

+

m2, - Q 2 2Q2

(m~-m~-Q

2)

)

(2)

with 2(a, b, c) = a 2+ b 2+ c2- 2ab- 2ac- 2bc. The decay width of an off-shell top quark of mass Q has the form

G2Q5 r ~ = 9 1--~-~

forQ<
or [3-5]

Grmw 2 4 f dk 2 2 ,/2( Q2, rn~,, k 2) r__,e=996n3Q3 J (kZ-m2w) 2+ F w2m w2 [ ( Q2-m~)Z +k2( Q2 + m~,) - 2k4]

(3)

in the case in which the finite mass of the W-boson compares to that of the quark Q. Here we assume [ Vtb[ = 1. The factor 9 comes from summing all W*~fl" channels neglecting final fermion masses and QCD corrections. Using the narrow width approximation for the quark propagator, one can easily check that the above expression reduces to the known formula for Higgs decay into a fermion-antifermion pair [ 6 ]. A plot of the Higgs decay width for various top masses, as a function of the Higgs mass, is shown in fig. 1. it is interesting to see the opening of the W-threshold, in the if' channel occurring at mH = mt at-mr,+ Mw. A similar formula describes H--,t*t decay, with i on-shell and t off-shell instead; these contributions are not included in fig. 1, which is therefore slightly misleading. Fig. 1 and eq. ( 1 ) give the correct on-shell limit, but 294

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Fig. I. Dependence of F(H--,tt*), the decay width of the standard model Higgsboson into one on-shell t plus one possibly offshell t* quark, versus the Higgs mass ran. The cases mr= 90, 120, 200 GeV are illustrated.

only half o f the off-shell contributions for mH < 2mr, because t has been artificially constrained to be on-shell throughout. This deficiency is remedied in the next section.

2.2. H--. t*i-* decays For m . < m, + mb, neither t nor t can be on-shell and it is necessary to consider the full decay process H ~ t * t * ~ (bf, ~'2) (6f3]'4) as shown in fig. 2. The calculation proceeds in a way rather similar to one outlined above, although the squared matrix element is not immediately factorizable into a product o f separate factors as before. The matrix element now is given by

(Q, +m,)

(Q2-m,)

M=g,g~va(b)y"( l -~'5) (Q~ _mZ) +iF,.m, (QZ _m2t ) +iF,.m, ~,u( 1-ys)v(g) a ~ )~,,~( l - :,~ ) v ~ ) a ~

)~,. ( 1 - ~ ) v ( f . )

× [(K~_M2w)+iFwMw] [(K~-M2w)+iFwMw] • After integration over phase space we get the following expression for the Higgs width: ( m H

F(H-~t*i*~bf,]'26f3]'4) = ( m H

×

- Q 1

--re'o)

~

2

Q, dQ~

F(t*-~bf,~'2)

( Q~-m2t )2 + (F,.rnt) 2

)2

f

Qz d Q ,2

n

r(~*~fffl4)

(Q~-m2t)2+(Fi.mt)

2r(H-,t*i*)

(4)

where the width into both t and i off the mass shell is defined as F(S-,t*t*)=3

m~gZt 2'/2(m~' Q~'Q2) [[m~(Q2t +QZ,)-½(Q~ +,qz~z ~2s - 2,q2,q21 ~,~2J ,

8rim 3

(5)

Q~Q~

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15 November 1990

mto p = 160 Gev

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Fig. 2. Feynman diagram describing Higgs boson decay via a pair of real or virtual top quarks.

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Higgs Mass (Gev) Fig. 3. The partial width for Higgs boson decay via a pair of real or virtual top quarks; the solid curve shows the complete result from eq. (4); the dotted curve shows the partial result from eq. ( 1), where one final quark is constrained to be on-shell. Results are plotted versus the Higgs boson mass m., for the illustrative case m, = 160 GeV.

which reduces to eq. ( 2 ) when the quark t is p r o d u c e d on the mass shell ( Qt = mr). We show in fig. 3 the decay width into two virtual t and t together with the decay probability into one real t and one virtual i*. When m t + m b < r n H < 2 m , the integrand o f e q . ( 4 ) is d o m i n a t e d by configurations where either t or t is on-shell; in this region the t ' t * formula correctly gives twice the contribution o f the tt* formula, remedying the deficiency o f fig. 1.

2.3. H ~ W W or Z Z decays Above the threshold for p r o d u c t i o n o f two i n t e r m e d i a t e vector bosons ( I V B ) , the search for the Higgs boson relies on the possibility o f observing its decay into a pair o f Z ° bosons [7 ]. A much grayer search area is the one below the two Z ° threshold and in that region, the possibility o f using the same signature, i.e. H --, (la+t~- ) (la+la - ) has been advanced. The decay width for Higgs into a pair o f real or virtual Z ° bosons can be written as [ 8 ] ~t

-*~ F ( H - - ' a l l Z°Z°) =

f

(,n~-Or)2 d O t2 m z F z

n[(Q~-m~):+(mzFz):]

0

f

dQ~ r n z r z

n [ ( Q ~ - m 2 z ) Z + ( m z F z ) 2]

F(H-,Z*Z*)

'

(6)

0

where F ( H ~ Z * Z * ) represents the decay width o f a Higgs boson into a pair o f virtual bosons o f masses Q~ and Q2 and it is given by

F(H--,Z*Z*)=~GFm3 21/2( 1 , 2 , ,

22) ( 1 +).~ +2~ + 102122-2)t, - 2 2 2 )

(7)

with 2,=QZ,/m~. A similar formula holds for the decay H--,W + W - , with ~t The expression in this paper differs slightly from ours probably because of typing errors. We thank R. Cahn for sharing with us his numerical results. 296

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G~m 3 F ( H - - , W * W * ) - 8n----~ ).,/2( 1, ).1, ).2) ( 1 + ) . ] +).2 + 10).1).2 -2).1 - 2 ) . 2 ) •

(8)

As in the top quark case, when the threshold for real production o f one intermediate vector boson is reached, the decay into two virtual IVB will be d o m i n a t e d by the production o f one real and one virtual IVB [9-11 ]. Unlike the virtual top case, the decay o f the Higgs boson into a pair o f off-shell IVB can be a significant fraction o f the total width, at least for Higgs bosons with a mass just below the threshold. This can be seen from fig. 4 where we compare the decay width for the three processes H--,Z*Z*,

H--,(W+)*(W-) * ,

H~t*i*

above and below the IVB threshold wit the total Higgs width, for the cases m t - - 9 0 and 200 GeV; the total width shown refers to the case m t = 90 GeV. The H--, Z ' Z * and H--, W ' W * contributions do not cut off so sharply below threshold as the H--, t ' t * contribution because Fw and Fz>>Ft (for m r = 9 0 G e V ) . In fact H--,W*W* remains the d o m i n a n t decay channel down to about m n = 150 GeV, where H - , b b finally takes over.

3. Virtual top contributions to Z boson decay

3.1. Z°-. t t * decays Finally we consider Z ° decays into one real, one virtual top quark. There is interest in looking for F C N C decays Z--, t~, etc. that would lead to a final state with a real top quark plus very little hadronic activity (assuming m, < Mz, which cannot yet be excluded completely). We note that Z--, tt*, t*t decays would lead to very similar final states, and must be considered as a potential source o f background. We show in fig. 5 a plot o f the Z ° boson width as a function o f the top mass, which is given by

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Higgs Mass (GeV) Fig. 4. Decay widths of the standard model Higgsboson into pairs of real or virtual W-bosons, Z-bosons or top quarks. The solid curve denotes the total width (for the case rn, = 90 GeV ); the dotdashed curve denotes F(H--,W*W*); the dashed curve denotes F(H-,Z'Z*); the dotted curves show F(H--,t*t* ) for the cases mr=90 and 200 GeV.

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Top Mass (Gev) Fig. 5. Partial width for Z decay via a real top quark t and a virtual (off-shell) [ quark, versus top quark mass mr. 297

Volume 251, number 2

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15 November 1990

( M z - mr) 2

F(Z--*t all(off-shell i ) ) =

fg

Q dQ 2 F([*~I~'

rt

)F(Z~t[*) (9)

(Q2-mZt)2+(Ft.m,)2'

where the width into one real and one virtual quark t*, is defined as

r(z~t~*)=3

g 2z

12nM3z

z 2

2

1 (2MZz_Q2_m

I3mt(gv--gA)+ ~5

~

(m2-72)2'~[

-M--'-fzz I ~(Q2+m2)(g2+g2A)

q

+½(m2t-Q 2 )gvgA] l

J

2 I / 2 ( M z2, m 2, Q2)

(10)

with gz = g / c o s 0w, gA = -- ~ and gv = 41-- ] sin20w to indicate the usual couplings o f the Zo bosons to the top quark. Fig. 5 shows that, with present limits on the top mass, this process has a totally negligible width and cannot be expected to contribute any observable rate o f background events to FCNC.

4.

Conclusions

We have shown that for values o f the top mass a b o v e the present C D F limits, the contribution o f virtual top exchanges in the decay o f the Higgs boson or o f the Zo boson is negligible c o m p a r e d to other d o m i n a n t processes, except when nearly on-shell.

Acknowledgement One o f us ( G . P . ) is indebted to C. R u b b i a for stimulating our interest in the problem o f virtual decay processes o f the Higgs boson.

References [ 1] CDF Collab., F. Abe et al., Phys. Rev. Lett. 64 (1990) 142, 147; K. Sliwa, report to Rencontre de Moriond (1990). [2] W. BuchmiJller and M. Gronau, Phys. Lett. B 220 (1990) 641; H. Fritzsch, Phys. Len. B 224 (1990) 423. [3] V. Barger, H. Baer and R.J.N. Phillips, Phys. Rev. D 30 (1984) 947. [4] I. Bigi, Y. Dokshitzer, V. Khoze, J. Kuhn and P. Zerwas, Phys. Lett. B 181 (1986) 157. [5] S. Geer, G. Pancheri and Y.N. Srivastava, Phys. Len. B 192 (1987) 223. [6} J. Ellis, M.K. Gaillard and D. Nanopoulos, Nucl. Phys. B 106 (1976) 292. [7]C. Rubbia, Future physics with accelerators, in: Proc. European particle accelerator Conf. (EPAC, June 1988), ed. S. Tazzari (World Scientific, Singapore, 1989). [8] R.N. Cahn, Rep. Prog. Phys. 52 (1989) 389. [ 9 ] J.F. Gunion, H.E. Haber, G.L. Kane and S. Dawson, The Higgs hunter's guide, report UCD-89-4, SCIPP-89/13, BNL-41644, (June 1989). [ 10] W.Y. Keung and W.J. Marciano, Phys. Rev. D 30 (1984) 248. [ I I ] T. Rizzo, Phys. Rev. D 22 (1980) 722.

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