ContributionJl ReviJlta Mexicana de Fúica 39, No. Suplemento 1 (1993) 523-530

Searching for signals of charged supersymmetric Higgsbosons in pp collisions at SSC energies

A. FERNÁNDEZ

Departamento de FísicaFacultad de Ciencias Físco Matemáticas Universidad A utónoma de Puebla

Apartado postal 1152, 72000 Puebla, Pue., México

M.A. PÉREZ

Departamento de FísicaCentro de Investigación y de Estudios Avanzados Instituto Politécnico Nacional

Apartado postal 14-740, 07000 México, D.F.

AND

A. ROSADO

Instituto de Física, Universidad Autónoma de PueblaApartado postal ).48, 72570 Puebla, Pue., México

ABSTRACT. We calculate the production oC charged scalar and vector bosons in the process pP ~BX ~ TVX ~ AX(B = W'", JI'"; A = e,p,'Ir,p) in tbe context oC the minimal supersymmetricstandard model, at energies available at SSC accelerator. We find that the energy spectrum oCthe outgoing A-particle, obtained through the charged Higgs boson, is similar to that obtainedvia W¡:i: production, but different Crom the spectrum expected from wj production. However,the spectrum oC the charged Higgs bosons is supressed by two or three orders oC magnitude withrespect to the spectrum oC the W,'". We conclude that the Cormerprocess is not appropiated toanalize the physics oC the charged Higgs particle.

RESUMEN. Se estudia la producción.de bosones escalares y vectoriales cargados en el proceso pjJ-BX + TVX ~ AX(B = W'", JI'", A = c,P, 'Ir, p) en el marco del modelo mínimo supersimétrico alas energías que estarán disponibles en el acelerador sse. Se encuentra que el espectro de energíade la partícula saliente A, generada a partir del bosón cargarlo escalar, es similar al obtenido enla producción de Wf, pero diCerentedel obtenido en producción de W;. Sin embargo, el espectrode los bosones JI'" está suprimido por dos o tres órdenes de magnitud con respecto al de W,'".En conclusión, se tiene que este tipo de reacciones no es apropiada para analizar la física de losbosones cargados H:i:.

PACS: l4.80.Gt; 12.15.Cc

l. INTRODUCTION

The Supercondllcting Super Collider (SSC) will provide us with the possibility to observepp-collisions with a maximal center oC mass energy EI!!Mx = 40 TeV [1). The majn goal oCthis accelerator is to look Corphysics beyond the standard mode!. Qne oC the interestingexperiments at SSC will be the search oC signals oC charged Higgs bosons El'". The existence

24 A. FERNÁNDEZ ET AL.

of these partides is a necessary ingredient of most of the minimal Higgs extensions of thestandard model [2].On the other hand, the PT-spectrum of the partides produced via the decay of gauge

bosons and fermions is a good tool to loo k for "new physics" (physics beyond the standardmodel). For example, it was pointed out [3] that the PT-spectrum of the partide A allowsto distinguish between the helicity L or R of the charged boson W" produced in thereactions:

pp --+ wt RX --+ TI/X --+ AX

where A stands for e, JI, 'Ir, or p.Our aim in this work is to analize the PT-spectrum of the partide A in the reactions

pp --+ Wt,RX, H" X --+ TI/X, T --+ AX, (1)

with A = e, 1', 'Ir or p, in order to ¡¡nd out whether it is possible to discriminate betweenthe production of WtR and lI;", i.e. the spin of the produced boson.We discuss the pr¿cesses (1) in the context of a minimal supersymmetric standard

model [4], using thy parto n model [6] which take into account scaling violations and thecharm contribution.Our paper is organized as follows. In Sect. 2, we perform the analytical calculations

for the difTerential cross section of processes (1). In Sect. 3, we present and discuss ournumerical results, and give our condusions.

2. TIIE PROCCESSES pp --+ W;;,LX, H" X --+ TI/X, T --+ AX

The dilferential cross section d~p¡; for (1) is calculated in the parto n model from the crosssection d~ of the parto n subprocesses

qlq2 --+ B --+ TI/,T --+ AX

with B = wt R' H"; A = e, 1', 'Ir, P and the parto n distribution functions ¡.;(Xi, Q2)(i =1,2), which are the probabilities to ¡¡nd a parton qi with the fraction X; of the nudeonmomentum (q; = X;P~) in a scattering process with momentum transfer square Q2.The general expression of the cross-section for the process q¡ q2 --+ TI/ and T --+ AX is

given by [7]

1 J 2dPTdPLX~= 4q,5I/2 IT(q¡q2 --+ TI/)I 27r (S,P~,PT)

IT(T --+ AX)J2dPLX(PTPX)x-----------(m~ - Pi) +m~q

(2)

SEARCIIING FOR S¡GNALS, " 25

(Pxstand,Jor(P¡, Pz, "" Pn), the momentum ofthe ereated particles through the r deeay),with S = (q¡ + qz)Z and qo = (1¡ + qz)Z gives the energy of the eolliding quarks at theeenter of mass system, The Lorentz invaraint phase spaee is defined by

n 3 4[ I4-3n TI d P.S Pa + Pb - "PidPLX(S; PI, PZ, "" Pn) = (2rr) 2E-'

.=1 I

Using the narrow width approximation for the I3reit- Wigner propagator

and integrating over STo we obtain

Let us define

(3)

(4)

(5)

2ETdr(r - 1,2, "" n) = IT(r - 1,2, "" n)lzdPLx(ST; PI, Pz, Pn,) (6)

so we can rewrite (5) as follows

d - 1 ¡T( )IZ2E dr(r - 1,2, ,." n),,- 617TZS q¡,qz - rv T rTmT

(7)

From Eq, (7) we observe that the amplitude of proeesses (1) can be expressed as theproduet of the amplitudes of two simple proeesses: the eollision q¡qz - rv and the deeayr - AX, The kinematieal variables of the last two proccsses are rclaled through theeorresponding difTerential elements in the phase space,The previous results enables us to ealculate the following subproeesses

26 A. FERNÁNDEZET AL.

al

bl

e,/'-

\\ ,.,rr,p

FIGURE 1. Feynman diagrams which conlribule lo lowesl order in " lo lhe elemenlary processesa) q,q. - Wt,R' H% - TI' - e%vev(J'%v~v), b) q,q. - Wt,R' H% - TI' - ".%v(p%v)

which are required for our analysis. The corresponding Feynman diagrams are depictedin figure 1.Using the coupling of the scalar and vectorial bosons to fermions provided by the

minimal supersymmetric standard model [41, we get

IT(ud -> ¡¡- -> T-V )12 = (1/12)(g2/8M ) (A¡ + B?HA~ + B?)S - m~) (10)T 11 (m2 _ S)2 + ó2 m2

11 11 11

where S = (Pu + Pd)2, Pd is the momentum of the quark d, k is lhe momentum of lheT,g = e/sin8w and

Al = md tan f3 +mu cot f3

BI = md tan f3 + mu col f3

Furthermore, since the T is produced via the decay of the WL.R or ll, we can neglectits mass. Thus, the T has purely left or righl handed helicily. In this case, we can use theexpression for the decay rate of the muon [81 with spin S:

SEARCHlNG FOR SIGNALS. • • 27

with P the electron momentum and E. its energy, q = k - P and ET is the energy of T.Becase T has a defined helicity, then we can write its 4-vector spin 5 as follows

where >. = 1:.1/2 defines a positive or negative helicity of the T.

Substituting (9)-(11) in (7), we get [9]

(12)

dlTWLdeos B•.udE •.u

1l'O2v's(1 + COS Bc)2B.,u[1 - (2£./ v's)3]36 sin4 Bwl(mw - 5)2 + mwrw]

(13)

dlTWR _ lI'o2v's(1 + cos Bc)2B•.ull + 2E./v's][1 - 2E./v's)]dcosB.,udE.,u 36sin4 Bwl(mw - 5)2 + m~,rw]

M¡¡ _ lI'o2v's(A; + BiJ(A~ + BiJB •.u(1/8mW)i1 - (2E./v's)3]dcosB •.udE.,u - 72sin4 Bwl(m¡¡ - 5)2 + m¡/r¡¡)

where

B. = r(T -+ e¡¡.¡¡~)/rlot

B.rtol = G~.m;/79211'3and

"'X (d- ¡Id - -)Un L,R = (J U -+ L,R -+ TV -+ evTv

For the case in which T decays to 11".we obtain

dlTWX _ G}m1vv's(1 1:.co.B.)2(BlI'/3)(1 - X)dE.deo.B. - 4811'1(mw- 5)2 + rwmwJ3

(14)

(15)

G}mtvv's(11:. eo.B.)2(BlI'/3)X4811'1(mw- 5)2 + rWmW]

dlT¡¡,,- _ G}m1vv's(A; + Bn(A~ + B~)(n7T/3)XdE.deo.B. - 4811'1(m¡¡- 5)2 + r¡/m¡/]

28 A. FERNÁNDEZET AL.

pp-> W(L,R), H->eXdSIGTOT / dEdCOS(TET A)

001

1 DOOE-03

1 000E-04

1 000E-05

1000E-06

1 OOOE-O?

¡OOOE-OB

1000E-09

lOODE-IO

I DOOE -11

y = O

M(H'r) ;;; 50Dee V

M(/ft) =B3Cev

M(H) ::: ZOOG£V

1000E-12O 200 400 600 BOO 1000 1200 1400 1600

Pl(GeV)

-- WR -+- WL ~ H

FIGURE 2. PT-speetrum oCprocesses (1), wilh rapidily Y = Oand A = e.

Similar expresions are oblained when the T decays to p' s.

3. RESULTS AND CONCLUSIONS

Now we analyze the spectrum distribution of the transverse momentum of the A-particlein the reaction (1.1). This spectrum is called secondary, because JI comes from the decayoC the T, which is produced via the process W, JI ....• TV. It has a very smalllifetime, henceits decay may be observed in the detector. This means that the secondary spectrum cangive information on the T polarization and this information can be related to the natureof the boson which produces the lepton T.

When JI = e, 1", it is necessary to put a lower bound to the transversal momentum of theelectron (muon) PT beca use we have lo distinguish between the electrons coming from IheT decay and those produced through the direct process w ....• evo Putting P'f > 2.5GeV, weeliminate also the background oC electrons produced through the decays oC heavy qllarks.

In Figs. (2-4) we can observe that the Pr-distribution may be used to distinguishbetween the processes in which a WL or a WR is produced. This effect can be observedclearly in the case JI = rr (see Fig. 4). This means that the process (1) allows us lo knowthe helicity of the charged veclor boson, as Gunion and Haber poinled oul in Ref. [:l). \Vecan obtain analytically Ihe same result by comparing expressions (13) and (14) for theelementary processes qij ....• IVL.R ....• TV,T ....• lVevv. lI is imporlant to remark Ihal Iheprimary spectrum for bolh e and l' is not sensible to the helicity of the IV'".

The analytical expressions Cor the cross sections of the processes in which a charged

SEARCHING FOR SIGNALS... 29

pp- > W(H,L),H - >eP

y = 3/J(WR)=ITpV

001I OOOE-D3

1 OOOE-Q4 ~

1 000E-05 ~I 000E-06.1 000E-07 ~

1 OOOE-OB ••

1 000E-09 ¡1 000E-10 ~1 000E-11 ~1 000E-12 ••1 OOOE-13 ~

1 OOOE-l'Ó !"

1 OOOF.-15;1 DODE-IB ~

O 200 400 600 eoo 1000

-*- ;q~ -1-- WL --- H

FIGURE 3. Pr-speclrum oCprocesses (1 l.wilh rapidily Y = 3 and A = e.

PP->W(R,L),H->piX

.V(It'R) :: lTrY

y:: I

800 1000 I ;~OO 1400 1600600.•00

-~-----..¡..._----- .....~- ------ -----

200

"Ol~o 01 ~

1 OOOE -03 ~

1 OOOf:-O" ~1 000 E -o~•.I 000E06 ~1 aODE-O?;

"1 OOOE--Oll ••,1 DODE-O!)

1000E ]0;';

1 OOOE II ~1 aODE 12;,1oom: IJ~

1 OOOE 1.;.O

FIGURE~. PT-speclrum oCprocesses (1), wilh lhe rapidily Y = I and JI = 'r.

scalar ll" is prodllced differs essentially form those in which a charged vector IV" is pro-dllced by a factor (1 :l:cos8)2. 1I0wever, in the physical regio n in which we are interestedthis factor is essentially constant; therefore the PT-distributions for the prodllced ll" orIVt have the same behavior (see Figs. 2-4).

From t he previolls discllssion we conclude that it will be very dimclllt to distingllishbetween the prodllction of a sllpersymmetric ll" boson ami a standard model IVt viathe reaction pfi - wt.Rll+ - T X - AX at SSC energies.

30 A. FERNÁNDEZ ET AL.

REFERENCES

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