Higgs detection via Z0 polarisation

Volume 179, number 4

PHYSICS LETTERS B

30 October 1986

H I G G S D E T E C T I O N VIA Z ° P O L A R I S A T I O N M.J. D U N C A N Department of Ph)'stc~, Unwerstty of Penns~,lvama, Phtladelphm, PA 19104, USA Received 9 June 1986, revised manuscript received 28 July 1986

It Is demonstrated that ff one determines the polarlsatmn of the Z° final states from pp ~ Z°Z° --* charged leptons, then one can rehably detect the presence of a Hlggs boson m the range 300 GeV < mH < 1 TeV at the SSC. This is m contrast to other methods for Hlggs detection which are susceptible to QCD backgrounds, severe cuts, or uncertainties m the Z° continuum. For one year's running at the nominal SSC luminosity of 1033 cm-2 s-1 and energy 40 TeV there are sufficient numbers of such events to perform the straightforward analysis.

A certain amount of concern has arisen as to whether the existence of a standard Higgs particle heavier than a few hundred GeV could ever be experimentally verified [ 1 - 6 ] . It is imperative that we understand more clearly the underlying physics of the electroweak scale, since it provides an example of the principle of hidden symmetry which is so central to our present way of thinking The next generation of supercolliders should place us in just the right energy region for testing this. Unfortunately, these machines generate copious backgrounds which can mimic the very processes we wish to study. A Hlggs particle decays predominantly into a pair of longitudinally polarlsed gauge vector bosons and its foremost production mechanism at a hadron collider (if its mass is ), 300 GeV) is via vector boson fusion [7]. Thus the analysis of the Hlggs proceeds in the context of WW physics. This can be treated perturbatlvely provided the Hlggs is also lighter than a TeV or so [8]. Otherwise the electroweak interactions become strong, which is certainly another intriguing possibility [61. Each W from any W+W- final state can decay into two jets or lepton + neutrino. The former has a huge QCD background [ 1] which might be reduced somewhat by rather stringent kinematic restrictions, which drastically reduce the event rate, whilst for the latter there is an ambiguity in the neutrino four-momentum. It Is not clear whether one could definitively distinguish 0370-2693/86/$ 03.50 © Elsevier Science Publishers B.V. (North-Holland Physics Publishing Division)

the charged W channels, and this question is currently under Investigation by means of Monte Carlo simulations :~1 Avoiding the hadronlc backgrounds can be accomphshed by focussing on the Z0Z 0 final states decaying into four charged leptons This is a distinct signature but the rate is reduced by the small (~3.4%) branching ratio for Z 0 ~ £+J~- The only known potential background for these modes is from the cascade decay of heavy quarks, which can be removed by rather lax kinematic cuts [9]. For a hadron colhder we can estimate the Z0Z 0 spectrum expected from the presence of a Hlggs. As usual we treat the hadrons as consisting of quark-partons with certain distribution functions which are determined experimentally at currently accessible mom e n t u m transfers and which can be confidently evolved up to the much higher momenta probed at supercolliders [ 10,11 ]. Moreover, we can consider these quarks as effectively consisting of W± , Z 0 partons [7] The latter then undergo vector boson scattering to the final Z 0 pairs, and have the capability of having a Hlggs as an intermediate state. Thus we examine first the patton chain pp ~ q(~) -~ W+W- ' Z0Z 0 ~ Z0Z 0 depicted in fig. la. The distribution of a vector boson Inside a quark with m o m e n t u m fraction x is given by [7] ,1 For a progress report see ref. [2] 393

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Volume 179, number 4

The collider center of mass energy lS~ with 7.0 =m2Z/S and ov 1s the cross section for the vector scatterlng VxV x, -+ Z0Z 0 . The two luminosities are the usual one for quarks,

A (0) P

L

(~) . ~

Z

d.L?qq,

-ln

aT. (7.)= f In

dyfq(x/~eY)fq,(X/r-re-Y),

(3)

,/7

where the f are the quark distribution functions inside the proton, evaluated at momentum transfer Q2 = 7.s, and for the vectors

(b) Zo

1

vq~,(7.) = f ~ Fq(x)Fq:(7./x).

(4)

"r

The latter are readily evaluated from (1), Zo

vqq'(r) :(aw/47r)2QqQ ~ X (1/7.)[2(7.-

Fig. 1. (a) WW scattering producing Z° pairs. The mitml vectors are treated as partons reside the quark by the effective W approximation. (b) Continuum production of Z0 parrs from quark fusion.

1) - ( 1 + 7.)In r ] ,

=(C~w/47r)

x

QqQq ln(m2z/4m2 )

+37. +,~7.2 -2(1+7.)1n7.),

qq' _ 2 q q' 2 2 2 V~T (7") - (~W/8rr) QvQv in (mzz/4m V) C~w

Fq(x ) = ~ Q q 1 x-X ~w

Fq(x) =-~n Qq 1

X (1/7.)(2(r + 3)(r - 1) - (2 + 021n 7.)

+ (1 - x ) 2

x

ln(p2/m2v)

(1)

for longitudinal and transverse polarisations, respectively. For the various quark and vector flavours Q~d,s,.. = 1 , ,nu,c,t d s,b = 0.508.The ~Z = 0.486 and Qz' transverse momentum cutoff, p~ is for convenience taken to be half the invariant mass of the final Z0Z 0 pair, m z z . Hence for the considered scattering process, the mvariant mass distribution is found to be d°l dm2z

-_

fdT.[V_W1

1 s q,q, V,h,h' r0

v 2 X oxx,(mzz),

1

,

d./2qq, (7")1 vqq'(7.0/7.)

Using (2) and (5) we can evaluate the cross section for all helicity channels. Since the Hlggs couples most strongly to its partners m the weak scalar lsodoublet, which have been transmuted to the longitudinal degrees of freedom of the vectors, it appears largely as an s-channel resonance m the scatterings ~LWL Z °L Z °L and Z9L Z9L + Z L ° Z 0L" However, the above chain has to compete with the direct continuum production of the final state Z 0's from quark-antNuark annihilation, pp -~ q~l ~ zOz0 depicted in fig. lb, which has a large cross section in comparison [4,10,12]. This is evaluated m the standard manner, dm2zd°2_ 3s L .~q _ _ ~Vrd't2q~l l (7.0) 1 ~q(m2z).

(6)

(2)

summed over participating quark flavours (q, q'), vector flavours (V = W± , Z 0) and vector hellcities (X, X'). 394

(5)

The factor of 1/3 is for colour averaging and the notation is as above. 6q is the cross section for qC:l~ Z0Z 0,

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2 +s3 c [f '2+4]ln(s-~-~)-2s3] 6q(S) = - S2COS40w q D ---Z--2-! s -

(7) and henceforth we scale the energies wlth respect to the Z0 mass for conciseness, s -+ s/m2z . The constants are C u c t = 1.605 X 10 . 2 and Cd, s b = 3.317 X 10-2,'with/3 = (1 - 4/s) 1/2 the velocity of the outgoing vectors m their center of mass frame. Eqs. (2), (3) and (6) can be modified in a straightforward manner +2 to implement cuts on rapidity ( y ) which is used to reject the low transverse m o m e n t u m debris from the hadronlc collisions. In fig. 2 we plot a typical mvanant mass distribution at SSC energies (x/}--= 40 TeV) for three values of the Hlggs mass. We have employed the EHLQ quark distributions [10]. We wash to measure the Z 0 decays into leptons in order to circumvent the QCD background. Muons are relatively straightforward to identify in most detectors. Electrons, on the other hand, can only be efficiently discriminated if there are no *2 See for example refs. [5,10] I

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jets close by and they are away from the forward region. We impose a cut of 2.5 on the Z0's rapidity to aid in any electron identification. This also favours the Z0's from the lsotroplc scalar decays over the highly forward peaked Z°'s from the qC:t annihilations. At first glance the signals appear quite pronounced. However, the branching raUo of Z0Z 0 to muons and electrons is only (~6.8%) 2. Assume the nominal SSC luminosity [13] of 1033 cm - 2 s -1 or equivalently 104 events/(pb of cross section)/(year of running). Integrating each curve over a bin centered on m H and whose width is PH, we find 97, 44 and 28 events per year for rn H = 500,750 and 1000 GeV, respectively (PH = 6 3 , 2 1 0 , 5 0 0 GeV). The continuum accounts for 28, 20 and 16 of these, respectively. In practice, however, uncertainties in the normallsation of the continuum would make effective identification of the peaks difficult [3], and so simply looking for a fluctuation above the expected rate could be misleading. Nevertheless, there is a method [5] by which one can significantly enhance the signal and it relies on the result that the continuum Z0's are almost purely transversely polarlsed whereas, as stated above, those from the Hlggs decay are almost purely longitudinal. The quantity one uses to characterise this is denoted bYfL, the proportion of the .Z0's winch are longitudinal, fL = do(LL) + ½do(LT) do

(8)

c

where da = da I + do 2 for both of the Z 0 longitudinal, or for one longitudinal and the other transverse. In the continuum case one has to integrate

E

~-~ (qcl -+ zOzO')

g

b

(3s

7r~2 1~6'

-.-%. I

I

I

400

600

800

I

[

1000 1200 1400

ALL

mzz (GeV) ATT Fig. 2. Mass distribution for pp --+ Z ° Z ° m nb/GeV at the SSC, as a funcUon o f the Z ° pair mvaxlant mass, for Higgs masses of 500 GeV, 750 GeV and 1 TeV. The dashed line is the c o n t i n u u m co ntrib ution. The final Z ° rapidity is restricted to [Yl < 2.5

(9)

m the notation of (7), between the relevant limits should one impose rapidity cuts. The A are _

200

- 2s2c°S40w C q A ~ ,

4(ut - 1) -~S--2)2 ( 1 - - 1 ) 2 ,

_ (ut

-

1)

~S--4~ 12(1-

(1

+(U2 + t 2 -- 2) U +

1)2

(10)

395

Volume 179, number 4 _ (u 2 + t 2 -

PHYSICS LETTERS B S

2)

X (u 2 + t 2 + 4ut + 4u +4t + 2 ) .

(10 cont'd)

Together these add up to the cross section for all final state polarisations, (11)

and one can check that this reproduces (7) when the hrnlts are t± = ½(2 - s + s3). One can also verify that most of the Z °'s are transversely polarlsed as stated above. The calculated fL as a function of the Z 0 pair lnvarlant mass is plotted In fig. 3 and one can clearly witness the enhancement of the Higgs signal over the continuum. There are a few methods by which one can experimentally determine a value f o r f L, all of them relying on an examination of the leptons which emerge as the Z 0 decay products. We will consider the most straightforward [5].

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Boost each Z 0 to its rest frame and extract +z*, the cosine of the angle between the tmal lepton momenta and the boost direction. (This variable can also be directly obtained from laboratory measurements.) The distribution of z* is different for longitudinally or transversely polarlsed vectors. Given a sample of Z°'s with a fixed fractlonf L of them longitudinal, the average value and the variance of z .2 are related to f L by (z .2) = { ( 2 - - S L ) , [o(z*2)] 2 = ~s(3 _ 2/L) _ ~ ( 2 - - / L )2,

(12)

which- are depicted in fig. 4. Conversely, a sufficiently accurate measurement of (z .2) should yield an estimate o f f L. Given N samples of the decays the variance in the esttmate of the mean (z .2) is o 2 / N . If one wtshes to obtain an empirical graph akin to the theoretical graph of fig. 3 one has to have the error l n f L smaller t h a n f L itself. To dxstlngulshfL1 from another value fL2 at the 20 level requires N samples such that *2 *2 (Z~2} _ (Z 1.2)• O(Z2 V) ~+ O(zl )

0 4 •~ 1

I

'

I

'

(13)

I

i

I

'

1000-500

0,7

750

--

0,3

1000

N

0.6

N

0.5

b 0.2

\

lOO N

\

\\(c)

fL 04 S 01

03

10

0.2 0.0 O0

0.1 oo

200

400

~----b-, ,----d-----

600

800

1000 1200 1400

m z z (GeV) Fig. 3. The longitudinal fractions for each Hlggs mass. The dashed line is the contmuum

396

,

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O2

i

1

,

04

I

06

,

I

08

,

0

fL

Fig. 4. Mean (z .2) (a) and standard deviation o(z . 2 ) (b) as a

function offL. Also plotted (c) is the mlmmum number of events requxred to be able to distinguish fL from zero at the 2o level.

Volume 179, number 4

PHYSICS LETTERS B

Also in fig. 4 we plot the n u m b e r needed to differentiate b e t w e e n f L = 0 and t h e f L value on the axis. It is precisely deviations f r o m zero which will herald the presence o f the Higgs. F r o m fig. 3 we typically require to discriminate f L = 0.5 at the most. Hence, from fig. 4 we ought to have at least 36 events if we are to be c o n f i d e n t about this value. Recall that under the peaks there are 97, 44 and 28 Z 0 pairs yielding 194, 88 and 56 m e a s u r e m e n t s o f a single Z 0 polarisatlon. Thus we have enough events to render the polarlsation test effective. Moreover, since the c o n t i n u u m value o f f L ts entirely neghglble, any u n c e r t a i n t y in it should not slgntficantly alter our conclusions. We have presented the outlmes o f a simple m e t h o d for detecting Hlggs bosons o f mass below 1 TeV. It has the advantages over o t h e r tests in that it is not susceptible to QCD backgrounds, uncertainties in the Z 0 pair c o n t i n u u m normallsatlon, or draconian kinematic cuts. It should be a straightforward test to p e r f o r m w i t h any d e t e c t o r that can efficiently identify and measure charged leptons. It is a pleasure to thank N. L o c k y e r and F.E. Paige for helpful discussions. This w o r k was supported an part by the US D e p a r t m e n t o f Energy.

[2]

[3]

[4] [5] [6]

[7]

[8]

[9] [10] [11] [12]

References [ 1 ] E. Fernandez et al., Identification of W pairs at the SSC, Proc. 1984 Summer Study on the Design and utihsation of the SSC (Snowmass, CO), eds. R Donaldson and J.G. Morfm, p. 107; W.J Sttrlmg, R. Kleiss and S.D. Ellis, Phys. Lett. B 163 (1985) 261,

[13]

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J.F. Gunion, Z. Kunszt and M. Soldate, Phys. Lett. B 163 (1985) 389; J F. Gunlon and M. Soldate, Davis preprmt UCD-86-09. J.F. Gunion and A. Savoy-Navarro, Report UCLA Workshop on Supercollider physics, Davis preprint UCD86-11. J F. Gunion and M. Soldate, Davis preprmt UCD-85-13; R.N. Cahn and M.S. Chanowltz, Phys. Rev. Lett. 56 (1986) 1327. M J. Duncan, G.L Kane and W.W. Repko, Phys Rev Lett. 55 (1985) 773. M.J. Duncan, G.L. Kane and W.W Repko, Michigan preprint UM TH 85-18, to be published m Nuel Phys. B. M S Chanowitz and M.K. Galliard, Nucl. Phys. B 261 (1985) 379, M. Claudson, E. Fahri and R.L. Jaffe, Caltech preprint CTP 1331. R.N. Cahn and S. Dawson, Phys. Lett. B 136 (1984) 196, G L Kane, W.W. Repko and W.B Rolnick, Phys. Lett. B 148 (1984) 367, S. Dawson, Nucl. Phys B 249 (1985) 42. D. DIcus and V. Mathur, Phys. Rev. D 7 (1973) 3111, M. Veltman, Acta Phys. Pol. B 8 (1977) 475; B.W Lee, C. Qulgg and H. Thacker, Phys. Rev. D 16 (1977) 1519 F E. Palge, private commumcation. E Elchten, I. Hmchliffe, K. Lane and C. Quigg, Rev. Mod. Phys. 56 (1984) 367. D. Duke and J. Owens, Phys Rev. D 30 (1984) 49. W. AUes, G. Boyer and A. Buras, Nucl. Phys. B 19 (1977) 125, R W. Brown and K. Mlkaehan, Phys. Rev. D 19 (1979) 922; K J.F. Gaemers and G.J. Gounarls, Z. Phys C 1 (1979) 259 R. Diebold and D.E. Johnson, pp interaction regions, Proc. 1984 Summer Study on the Design and utihsation of the SSC (Snowmass, CO), eds. R. Donaldson and J G. Morfm, p 399.

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