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WR identification at hadron colliders
Volume 254, number 3,4
PHYSICS LETTERS B
24 January 1991
WR identification at hadron colliders J.-M. Fr~re a,b,1 a n d W . W . R e p k o b a Physique Thkorique, CP225, Universit~ Libre de Bruxelles, B-1050 Brussels, Belgium 2 b Department of Physics andAstronomy, Michigan State University, East Lansing, MI 48824, USA
Received 5 November 1990 We study the process pp (pf~)--*WH~ fit ~ bbWL, where WH is a hypothetical heavy gauge boson. The differential cross section da/dEw is sensitive to the chiral structure of the WHcoupling. In particular, the heavy WRexpected from SU (2)L × SU (2)R X U ( 1) models is clearly distinguishable from an additional W~.
1. M o t i v a t i o n
Left-right symmetric models based on the group SU (2)L × SU (2)R × U ( 1 ) [ 1 ] represent a minimal extension of the standard model. In the charged sector, the salient feature is an additional W-boson whose mixing with the WL is characterized by an angle ~. Although direct experimental constraints are limited, ~ is usually small [ 2 ] and we will refer to WL and WR directly, rather than the mass eigenstates. The only direct limit on WR assumes that the mass o f the corresponding neutrino VR is small [ 3] and yields MR/> 560 GeV. Indirect limits arise from consideration o f non-leptonic matrix elements, most notably K ° - I ( ° mixing. The typical expectation here is [ 4 ] MR i> 1.6 TeV. In general, however, different Cabibbo angles must be allowed for the L and R sectors, which results in a loosely constrained model [ 5 ] with MR>---360 GeV. While a massless VR is possible, a large Majorana mass is usually expected from the symmetry breaking SU(2)LXSU(2)RXU ( 1 ) B _ L - - ' S U ( 2 ) L X U ( 1 ), and mvR is typically of order MR, which either forbids or severely inhibits the decay WR-~ ~V~R. For these reasons, it makes sense to consider a specific search for WR through its non-leptonic decays in the entire mass range MR > 360 GeV. There is also the interesting possibility that WR is responsible for C P violation, in which case one expected [ 6 ] MR < 30 TeV. In this note we make the assumption that the top quark mass mt is larger than the usual WL mass, i.e. m t > Mw. This allows consideration of the process pp(pp) ~
W~ ~
tl~ L~ w~ bb,
with t and W~- on shell. We use WH tO denote a generic heavy W. One of the striking points of this study is that the types o f couplings of WH can be determined even f o r unpolarized pp collisions. In particular, the case where WH is an extra W [ is clearly distinguishable from the case WH = WR. While the detection o f a WR in this channel is obviously harder than in the ~VR channel considered in ref. [ 7 ], it is worth considering since: (i) the ~VR channel, as noted above, may not be open, and (ii) the presence o f a WL in the final state allows the characterization o f the heavy W coupling even if the colliding hadrons are not polarized. t Chercheur qualifi6 du fonds National de le Recherche Scientifique (Bruxelles). 2 Permanent address. 0370-2693/91/$ 03.50 © 1991 - Elsevier Science Publishers B.V. ( North-Holland )
485
Volume 254, number 3,4
PHYSICS LETTERS B
24 January 1991
2. Calculation of ua-~6bW Although the complete amplitude for u a - , b b W by Wn exchange can be calculated directly, it is both more transparent and easier to consider the separate processes ua~tl~ followed t--,bW and to use a density matrix formalism. We follow the approach of ref. [ 8 ], which was developed for leptons but applies equally well to the t quark. The QCD corrections to polarization effects in t quark decay have been studied [ 9 ] and are small if mt ve x/~A'/w. Restricting ourselves to pure left-handed (L) or pure right-handed (R) couplings, the amplitude is expressible in the form [ 8 ] I~lZ=
1 (t2+mZt)2+rn2f,~,
~ (X'V~I,L)(y'v~£u)
(1)
where 2 and/~ refer to the t quark polarization, the Vau are related to helicity projection operators, and t is the t quark momentum. The vectors X u and Yu are obtained, respectively, from the spin summed expressions for the production and decay of the t quark. For t quark production by ud-.bt, Xu is 1 X u = 4 g 4 (s-gn)2 2+MnFH2 2 u ' 6 d u ,
(2)
and the momenta of the various particles are denoted by the corresponding particle symbol. The amplitude for the decay t ~ b W L gives b. w w u Yu = g2 ( b.~.~ + ~u b" ~* - ~. ~*b u + ~ u ~ , a b ~ 6 ) _..g2( _ bu + 2 ~ / ,
)
(3)
where ¢ is the WL polarization vector and the last form results from summing over WE polarizations. Using the explicit form of the Vau, it is possible to perform the summation over X and/~ to obtain - m ~ X. Y / 2
I~I~L=( t 2 + m 2 ) 2 + mt2F~2,
m~ X. Y / 2 + X.t Y.t [J~i[L = ( t2 + m2)2 + m2 F 2 •
(4)
The evaluation of dtr/dEw in the ud center of mass is relatively simple if we assume that the t quark is on shell. Taking the final state variables to be bu, t u = b u + w u and w u, one encounters integrals over d4t of the form
I, Iu, It~, = f d 4 t ( l ' tu, t u t . ) ~ + ( - m 2 - s - 2 t . q ) 6 + ( - m 2 - M 2 - 2 t . w ) 6 ( t 2 + m
(5)
2) ,
with qu = u. + d u. Letting I = ao and expanding I u and Iu~ as Iu =alqu + b l v u ,
(6)
I,~ =a2st~uv + b 2 q u q ~, + c 2 v u v u + d 2 ( q u v u + vuq~) ,
with v u = w u + q" w qu/S so that v"q = 0, the various expansion coefficients are al=Aao,
a2=
(7)
bl=-Bao,
sAZ_v.v B2_m 2 2s ao,
b2--
3sA2_v.v BR_m~ 2S ao,
c2=
- s A Z + 3v.v B2 + mZt 2v'v ao,
d2=-ABao.
(8)
The quantities A and B are A- s+m2 2s '
B = s(m2t + M ~ v ) + q ' w ( s + m 2 ) 2s v.v
(9)
An expression for ao is most easily obtained in the rest frame of q with the W momentum w in the z-direction. 486
Volume 254, n u m b e r 3,4
PHYSICS LETTERS B
24 January 1991
In this frame, ao is ao-41wlv/~
\ 2v/~
)(
-Ew 0 Ew-
(lO)
2mZv/~ j ,
and the angle ot between t and w is constrained by COS O / =
2EtEw - m ~ -M~v 2ltllwl
(11)
In an arbitrary frame, ao is ao=
rC A(s+M2w+q'w)O(--q'w-- m4+M~vs'~ 4~/(q.w)2_M~vs~\ 2 2mtZ 1.
(12)
The remaining integrations over d4w are simple since we sum over W + polarizations. From eq. (3), it is not difficult to retain the l-dependence. However, it is our feeling that, in particular for MR in excess of 1 TeV, the angular features may be hard to observe, since the event will consist essentially of two jets back-to-back in the CM. In fact, the collinearity of the event allows the determination of Ew. The direction ofv from the W + decay cannot differ much from that of the jet and is thus essentially known, allowing the reconstruction of the CM and the W energy. The expressions for do'RL/dEw and deLL/dEw in the ud CM are ~1 de RL Ot3wmt dEw - 48
g
de LL dEw
mZt)(m2t )
[(
Ft (s-M~)2+MZRF~
2-~-J\~ww-2
(sWM2'( Ew+
2x/~
m4t "~] 2 - S-~w]_ ],
(13)
ot3w m t 48 F t (s_MI2)2+MLF
L22
)<[(2- ~-~)(2- ~-)Ew-w/
(s+MZw)2x/~ ( 2 - sMw/~2 ]+(2+\
(mZ-M 2 ) ( 2 +
-~)(s-mZ)2mZtx/~s
~ww,]J rnt2 ) l '
(14,
with Ft, the t quark width, being O/w Ft= _~mt(l_ M2w~2(2 m2t~
m 2 / \ + M-~wJ"
(15)
From these equations, it is evident that the slope of the Ew-dependence changes sign in going from RL to LL. This feature of the constituent cross sections is illustrated in fig. 1. The integration of either of these cross sections over dEw gives the same result, 24
(s--MH) 2 2+MHF 2 H 2 (s-m2t)
1-
2+
(16)
and the yield of W's from t quarks produced by WH exchange is illustrated in fig. 2 for Pl) collisions at x/~=2 TeV (solid) and pp collisions at x/~=40 TeV (dashed). We have assumed a complete reconstruction of the event with only one neutrino emitted. Depending on mass ranges considered, further tagging might be needed (e.g., semileptonic decays of the 6). A complete simulation would then require going back to the first form of eq. (3) because the W polarization will affect its decay parameters.
~t Here, we have includeda factorof ~ for the averageover initial spins and note that the colorfactorin this case is unity. 487
Volume 254, number 3,4
-* -WH
PHYSICS LETTERS B
+ -* t b
I
-~ b b W
I
+
Q-s =
1
24 January 1991
TeV
I m t = 180 GeV
p p ( p p ) ~ Wa+ ~ ~' "~
102
t
101
i"
i00
' ' I ' ' ' I ' ' ' I ' ' ' I ' ' ' ~
m t = 180 GeV
>
~v~ 2x10-4
b I"~
to-1
v~ b
10-4
10-2
200
300
400
500
E, (GeV) Fig. 1. The W energy distribution from t quark decay is shown for t production by the exchange of a heavy WL (LL) and by the exchange of a heavy WR(RL). The heavy W mass was taken to be 800 GeV.
,
400
600 800 1000 WIt Mass (GeV)
,
, [ , , , 1200 1400
Fig. 2. The total cross section for the production of a t quark of mass 180 GeV is shown for pp collisions at x/~=2 TeV (solid) and for pp collisions at x/~ = 40 TeV (dashed).
3. Conclusions T h e e s s e n t i a l p o i n t o f o u r d i s c u s s i o n is t h a t , f o r mt s u f f i c i e n t l y large, t h e d e c a y t ~ b W + c a n b e u s e d t o d e t e r m i n e t h e c h i r a l i t y o f t h e c o u p l i n g s o f h e a v y c h a r g e d gauge b o s o n s . T h i s c a n b e d o n e w i t h u n p o l a r i z e d p p o r p p colliders by e x a m i n i n g the slope o f the W energy distribution.
Acknowledgement O n e o f us ( J . - M . F . ) w i s h e s t o t h a n k t h e D e p a r t m e n t o f P h y s i c s a n d A s t r o n o m y at M i c h i g a n S t a t e U n i v e r s i t y f o r its h o s p i t a l i t y , T h i s r e s e a r c h w a s s u p p o r t e d i n p a r t b y t h e N a t i o n a l S c i e n c e F o u n d a t i o n u n d e r G r a n t 9006117.
References [ 1 ] J.C. Pati and A. Salam, Phys. Rev. Lett. 31 (1973) 661; R.N. Mohapatra and J.C. Pati, Phys. Rev. D 11 ( 1975 ) 2588. [2] J. Donnghue and B. Holstein, Phys. Lett. B 113 (1982) 382; I.I. Bigi and J.M. Fr6re, Phys. Lett. B 110 (1982) 255; L. Wolfenstein, Phys. Rev. D 29 (1984) 2130. [ 3 ] M. Strovink, in: Progress in electroweak interactions (Moriond, 1986 ), ed. J. Tran Thanh Van. [4] G. Beall and A. Soni, Phys. Rev. Lett. 48 (1982) 848. [ 5 ] P. Langacker and S. Urea Sankar, Phys. Rev. D 40 ( 1989 ) 1569. [6] G.C. Branco, J.M. Fr6re and J.-M. G6rard, Nucl. Phys. B 221 (1983) 317; D. Chang, Nucl. Phys. B 214 (1983) 435. [ 7 ] P. Langacker, R.W. Robinett and J.L. Rosner, Phys. Rev. D 30 (1984) 1470. [8IV. Barger, J. Ohnemus and R.J.N. Phillips, Phys. Rev. D 35 (1987) 166. [ 9 ] J. Liu and Y.P. Yao, University of Michigan preprint. 488
PHYSICS LETTERS B
24 January 1991
WR identification at hadron colliders J.-M. Fr~re a,b,1 a n d W . W . R e p k o b a Physique Thkorique, CP225, Universit~ Libre de Bruxelles, B-1050 Brussels, Belgium 2 b Department of Physics andAstronomy, Michigan State University, East Lansing, MI 48824, USA
Received 5 November 1990 We study the process pp (pf~)--*WH~ fit ~ bbWL, where WH is a hypothetical heavy gauge boson. The differential cross section da/dEw is sensitive to the chiral structure of the WHcoupling. In particular, the heavy WRexpected from SU (2)L × SU (2)R X U ( 1) models is clearly distinguishable from an additional W~.
1. M o t i v a t i o n
Left-right symmetric models based on the group SU (2)L × SU (2)R × U ( 1 ) [ 1 ] represent a minimal extension of the standard model. In the charged sector, the salient feature is an additional W-boson whose mixing with the WL is characterized by an angle ~. Although direct experimental constraints are limited, ~ is usually small [ 2 ] and we will refer to WL and WR directly, rather than the mass eigenstates. The only direct limit on WR assumes that the mass o f the corresponding neutrino VR is small [ 3] and yields MR/> 560 GeV. Indirect limits arise from consideration o f non-leptonic matrix elements, most notably K ° - I ( ° mixing. The typical expectation here is [ 4 ] MR i> 1.6 TeV. In general, however, different Cabibbo angles must be allowed for the L and R sectors, which results in a loosely constrained model [ 5 ] with MR>---360 GeV. While a massless VR is possible, a large Majorana mass is usually expected from the symmetry breaking SU(2)LXSU(2)RXU ( 1 ) B _ L - - ' S U ( 2 ) L X U ( 1 ), and mvR is typically of order MR, which either forbids or severely inhibits the decay WR-~ ~V~R. For these reasons, it makes sense to consider a specific search for WR through its non-leptonic decays in the entire mass range MR > 360 GeV. There is also the interesting possibility that WR is responsible for C P violation, in which case one expected [ 6 ] MR < 30 TeV. In this note we make the assumption that the top quark mass mt is larger than the usual WL mass, i.e. m t > Mw. This allows consideration of the process pp(pp) ~
W~ ~
tl~ L~ w~ bb,
with t and W~- on shell. We use WH tO denote a generic heavy W. One of the striking points of this study is that the types o f couplings of WH can be determined even f o r unpolarized pp collisions. In particular, the case where WH is an extra W [ is clearly distinguishable from the case WH = WR. While the detection o f a WR in this channel is obviously harder than in the ~VR channel considered in ref. [ 7 ], it is worth considering since: (i) the ~VR channel, as noted above, may not be open, and (ii) the presence o f a WL in the final state allows the characterization o f the heavy W coupling even if the colliding hadrons are not polarized. t Chercheur qualifi6 du fonds National de le Recherche Scientifique (Bruxelles). 2 Permanent address. 0370-2693/91/$ 03.50 © 1991 - Elsevier Science Publishers B.V. ( North-Holland )
485
Volume 254, number 3,4
PHYSICS LETTERS B
24 January 1991
2. Calculation of ua-~6bW Although the complete amplitude for u a - , b b W by Wn exchange can be calculated directly, it is both more transparent and easier to consider the separate processes ua~tl~ followed t--,bW and to use a density matrix formalism. We follow the approach of ref. [ 8 ], which was developed for leptons but applies equally well to the t quark. The QCD corrections to polarization effects in t quark decay have been studied [ 9 ] and are small if mt ve x/~A'/w. Restricting ourselves to pure left-handed (L) or pure right-handed (R) couplings, the amplitude is expressible in the form [ 8 ] I~lZ=
1 (t2+mZt)2+rn2f,~,
~ (X'V~I,L)(y'v~£u)
(1)
where 2 and/~ refer to the t quark polarization, the Vau are related to helicity projection operators, and t is the t quark momentum. The vectors X u and Yu are obtained, respectively, from the spin summed expressions for the production and decay of the t quark. For t quark production by ud-.bt, Xu is 1 X u = 4 g 4 (s-gn)2 2+MnFH2 2 u ' 6 d u ,
(2)
and the momenta of the various particles are denoted by the corresponding particle symbol. The amplitude for the decay t ~ b W L gives b. w w u Yu = g2 ( b.~.~ + ~u b" ~* - ~. ~*b u + ~ u ~ , a b ~ 6 ) _..g2( _ bu + 2 ~ / ,
)
(3)
where ¢ is the WL polarization vector and the last form results from summing over WE polarizations. Using the explicit form of the Vau, it is possible to perform the summation over X and/~ to obtain - m ~ X. Y / 2
I~I~L=( t 2 + m 2 ) 2 + mt2F~2,
m~ X. Y / 2 + X.t Y.t [J~i[L = ( t2 + m2)2 + m2 F 2 •
(4)
The evaluation of dtr/dEw in the ud center of mass is relatively simple if we assume that the t quark is on shell. Taking the final state variables to be bu, t u = b u + w u and w u, one encounters integrals over d4t of the form
I, Iu, It~, = f d 4 t ( l ' tu, t u t . ) ~ + ( - m 2 - s - 2 t . q ) 6 + ( - m 2 - M 2 - 2 t . w ) 6 ( t 2 + m
(5)
2) ,
with qu = u. + d u. Letting I = ao and expanding I u and Iu~ as Iu =alqu + b l v u ,
(6)
I,~ =a2st~uv + b 2 q u q ~, + c 2 v u v u + d 2 ( q u v u + vuq~) ,
with v u = w u + q" w qu/S so that v"q = 0, the various expansion coefficients are al=Aao,
a2=
(7)
bl=-Bao,
sAZ_v.v B2_m 2 2s ao,
b2--
3sA2_v.v BR_m~ 2S ao,
c2=
- s A Z + 3v.v B2 + mZt 2v'v ao,
d2=-ABao.
(8)
The quantities A and B are A- s+m2 2s '
B = s(m2t + M ~ v ) + q ' w ( s + m 2 ) 2s v.v
(9)
An expression for ao is most easily obtained in the rest frame of q with the W momentum w in the z-direction. 486
Volume 254, n u m b e r 3,4
PHYSICS LETTERS B
24 January 1991
In this frame, ao is ao-41wlv/~
\ 2v/~
)(
-Ew 0 Ew-
(lO)
2mZv/~ j ,
and the angle ot between t and w is constrained by COS O / =
2EtEw - m ~ -M~v 2ltllwl
(11)
In an arbitrary frame, ao is ao=
rC A(s+M2w+q'w)O(--q'w-- m4+M~vs'~ 4~/(q.w)2_M~vs~\ 2 2mtZ 1.
(12)
The remaining integrations over d4w are simple since we sum over W + polarizations. From eq. (3), it is not difficult to retain the l-dependence. However, it is our feeling that, in particular for MR in excess of 1 TeV, the angular features may be hard to observe, since the event will consist essentially of two jets back-to-back in the CM. In fact, the collinearity of the event allows the determination of Ew. The direction ofv from the W + decay cannot differ much from that of the jet and is thus essentially known, allowing the reconstruction of the CM and the W energy. The expressions for do'RL/dEw and deLL/dEw in the ud CM are ~1 de RL Ot3wmt dEw - 48
g
de LL dEw
mZt)(m2t )
[(
Ft (s-M~)2+MZRF~
2-~-J\~ww-2
(sWM2'( Ew+
2x/~
m4t "~] 2 - S-~w]_ ],
(13)
ot3w m t 48 F t (s_MI2)2+MLF
L22
)<[(2- ~-~)(2- ~-)Ew-w/
(s+MZw)2x/~ ( 2 - sMw/~2 ]+(2+\
(mZ-M 2 ) ( 2 +
-~)(s-mZ)2mZtx/~s
~ww,]J rnt2 ) l '
(14,
with Ft, the t quark width, being O/w Ft= _~mt(l_ M2w~2(2 m2t~
m 2 / \ + M-~wJ"
(15)
From these equations, it is evident that the slope of the Ew-dependence changes sign in going from RL to LL. This feature of the constituent cross sections is illustrated in fig. 1. The integration of either of these cross sections over dEw gives the same result, 24
(s--MH) 2 2+MHF 2 H 2 (s-m2t)
1-
2+
(16)
and the yield of W's from t quarks produced by WH exchange is illustrated in fig. 2 for Pl) collisions at x/~=2 TeV (solid) and pp collisions at x/~=40 TeV (dashed). We have assumed a complete reconstruction of the event with only one neutrino emitted. Depending on mass ranges considered, further tagging might be needed (e.g., semileptonic decays of the 6). A complete simulation would then require going back to the first form of eq. (3) because the W polarization will affect its decay parameters.
~t Here, we have includeda factorof ~ for the averageover initial spins and note that the colorfactorin this case is unity. 487
Volume 254, number 3,4
-* -WH
PHYSICS LETTERS B
+ -* t b
I
-~ b b W
I
+
Q-s =
1
24 January 1991
TeV
I m t = 180 GeV
p p ( p p ) ~ Wa+ ~ ~' "~
102
t
101
i"
i00
' ' I ' ' ' I ' ' ' I ' ' ' I ' ' ' ~
m t = 180 GeV
>
~v~ 2x10-4
b I"~
to-1
v~ b
10-4
10-2
200
300
400
500
E, (GeV) Fig. 1. The W energy distribution from t quark decay is shown for t production by the exchange of a heavy WL (LL) and by the exchange of a heavy WR(RL). The heavy W mass was taken to be 800 GeV.
,
400
600 800 1000 WIt Mass (GeV)
,
, [ , , , 1200 1400
Fig. 2. The total cross section for the production of a t quark of mass 180 GeV is shown for pp collisions at x/~=2 TeV (solid) and for pp collisions at x/~ = 40 TeV (dashed).
3. Conclusions T h e e s s e n t i a l p o i n t o f o u r d i s c u s s i o n is t h a t , f o r mt s u f f i c i e n t l y large, t h e d e c a y t ~ b W + c a n b e u s e d t o d e t e r m i n e t h e c h i r a l i t y o f t h e c o u p l i n g s o f h e a v y c h a r g e d gauge b o s o n s . T h i s c a n b e d o n e w i t h u n p o l a r i z e d p p o r p p colliders by e x a m i n i n g the slope o f the W energy distribution.
Acknowledgement O n e o f us ( J . - M . F . ) w i s h e s t o t h a n k t h e D e p a r t m e n t o f P h y s i c s a n d A s t r o n o m y at M i c h i g a n S t a t e U n i v e r s i t y f o r its h o s p i t a l i t y , T h i s r e s e a r c h w a s s u p p o r t e d i n p a r t b y t h e N a t i o n a l S c i e n c e F o u n d a t i o n u n d e r G r a n t 9006117.
References [ 1 ] J.C. Pati and A. Salam, Phys. Rev. Lett. 31 (1973) 661; R.N. Mohapatra and J.C. Pati, Phys. Rev. D 11 ( 1975 ) 2588. [2] J. Donnghue and B. Holstein, Phys. Lett. B 113 (1982) 382; I.I. Bigi and J.M. Fr6re, Phys. Lett. B 110 (1982) 255; L. Wolfenstein, Phys. Rev. D 29 (1984) 2130. [ 3 ] M. Strovink, in: Progress in electroweak interactions (Moriond, 1986 ), ed. J. Tran Thanh Van. [4] G. Beall and A. Soni, Phys. Rev. Lett. 48 (1982) 848. [ 5 ] P. Langacker and S. Urea Sankar, Phys. Rev. D 40 ( 1989 ) 1569. [6] G.C. Branco, J.M. Fr6re and J.-M. G6rard, Nucl. Phys. B 221 (1983) 317; D. Chang, Nucl. Phys. B 214 (1983) 435. [ 7 ] P. Langacker, R.W. Robinett and J.L. Rosner, Phys. Rev. D 30 (1984) 1470. [8IV. Barger, J. Ohnemus and R.J.N. Phillips, Phys. Rev. D 35 (1987) 166. [ 9 ] J. Liu and Y.P. Yao, University of Michigan preprint. 488