Collective hadronic Higgs production in heavy-ion collisions

Nuclear Physics A544 (1992) 585c-5 North-Holland, Amsterdam

Collective hadronic Higgs production in heavy-ion collisio s Hans-Thomas Elze and Johann Rafelski Institut fûr Theoretische Physik der Universitàt Frankfurt a.M., Germany, and Department of Physics, University of Arizona, Tucson, AZ 85721, USA Abstract We study co"lective and subthreshold Higgs production due to the formation of high energy density matter (QGP) associated with a rapid change of the scalar density < ** > . The rapidity spectra of Higgs particles are discussed in the Bjorken colli sion scenario and for a spherically expanding fireball . We briefly consider options for experiments . 1. COLLECTIVE HADRONIC HIGGS PRODUCTION In this work [1] we investigate, if hadronic Higgs production could be observed in the forthcoming generation of experiments involving high-energy collisions of heavy nuclei in association with the search for the quark-gluon plasma (QGP). The Higgs boson, which constitutes a key cornerstone of the Standard Model, has not been observed to date. The problem is related to its intrinsically weak coupling and unfavorably large backgrounds for the production processes studied so far. - We refer the reader to Ref.[2] for extensive reviews of this subject including further references. We observe that during a central collision a rapid change by orders of magnitude of the scalar density < i%F > occurs. As the Higgs is a scalar particle coupling to matter via the scalar density, the rapid change of this "source" leads withoull doubt to production of Higgs particles by the collective action of all constituents, and we address this process here by the theoretical means available today. While each microscopic component of the scalar density, i.e. each quark, carries much less energy than the mass of the Higgs, the total energy e.g. in CERN-SPS Pb-Pb colilsiarls by far exceeds the energy necessary to produce the Higgs assuming 60 GeV< mH < 2mtiy . Therefore, we must consider processes driven by the collective action of a large fraction of all constituents . Considering production by the "macroscopic" region filled with dense matter and having the characteristic size of an atomic nucleus, the momentum scale will be -20 MeV, the inverse of the size of the system, R - 10 fm. It corresponds to production of a 60 GeV or heavier Higgs practically at rest. The total CM energy contained in the strongly interacting system created during the course of a central high-energy collision by itself presents no guarantee that it can be put collectively into the excitation of a single "microscopic mode", such as the emission 0375-9474/92/$05 .00 © 1992 - Elsevier Science Publishers B .V. All rights reserved .

586c

H.-ë'. Elze, .I. Rafelski / Collective hadronic Higgs production in heavy-ion collisions

of a iggs. Recall that the ®ßbauer effect essentially consists in the reverse phenomenon : the recoil energy of a single atom/ion in a solid is transferred in a coherent one-step (one scattering amplitude) process into a collective longwavelength excitation of the whole system. The mechanism we presently have in mind (in distinction to e.g. 7r+7r' -), iggs annihilation) consists in a scattering process with all participating pions (or partons in a deconfined environment) recoiling and delivering each a tiny fraction of the energy (mH/N, on average) at a negligible three-momentum of the Higgs. The energy has to be transferred by strong interactions to a virtual or real heavy particle, which couples weakly to the Higgs . Note that the collective production mechanism is insensitive to a possible Higgs form factor (up to the scale of a few fm) .

Figure 1. Collective Higgs production by multiple scattering of a) pions, b) partons. Presently we consider pions only, because they allow us effectively to keep track of the rapidly changing scalar density. Since the particle (pion) multiplicity in a heavyion collision carries practically all the energy, the same fraction of energy has to be extracted from each pion as from the entire collision, which amounts to a few percent at most. With the pion energy, roughly 3T with T 200 - 250 MeV (source temperature), the energy transferred from each pion to the Higgs is of the order of 10 MeV, which is similar to the momentum transfer. Thus, many pions undergo low-energy scatterings contributing to the built-up of the Higgs amplitude. 11,n additional complication is due to the strongly time- dependent and rapidly rising number of pions . In Fig.1a we illustrate schematically the approximations to be studied in order to justify our model calculations . The basic process presumably consists in multiple "soft" pion scattering via colorless two- gluon (pomeron, glueball, .. .) exchange coupling to a heavy virtual quark (generally = heavy particle) loop coupling to the Higgs. Secondly, the high phase-space density of pions implied by the observed multiplicities and spectra allows the replacement of individual pions by a semi-classical collective, i.e . strongly selfinteracting pion field Fr (similar to recoilless scattering of M®ßbauer photons off an entire crystal), and finally, by a classical scalar source emitting the Higgs. This approximation will be performed in Section 2. Simple uncertainty principle considerations indicate that there exists an optimal number or not-too-soft initial scatterings, i.e. presumably not

H.-T. Eke, J. Rafelski / Collective hadronic Higgs production in heavy-ion collisions 587c

all pions available need to participate . In Fig.1b we depict an alternative, completely microscopic process involving only partons and their fusions . It represents the inverse of Higgs decay via multiple branchings into partons. Such a process gains from any coherence or enhancement in the parton distributions as they evolve during a nuclear collision. As in Fig.1a, the heavy particle pair fusing into the Higgs may exist only in a virtual loop and does not necessarily have to be present in the initial state. - A truly microscopic calculation of collective Higgs production following the above outline has not yet been performed . In the Standard Model the equation of motion for the scalar Higgs field is, in the tree approximation, (a,,a,, + mH)H = J,

(1)

where we introduced the "classical" collective Higgs source (v=246 GeV), -v_i J = mq < *q@q > , q representing the rapidly changing scalar quark density in colliding matter .

(2)

r

2. MODEL CONSIDERATIONS With the conservative assumption that the produced matter consists of individual hadrons, predominantly pions, the effective Higgs-pion coupling, CTH = 9TH7r - !rH [3], amounts to the "source" J~ = 9~H

f(

d3p

27r) 32E r (P)

g(P)

< n.(P)

>

where g,H !:~-, -84MeV - m r /v [3] and g(p) allows for momentum dependence of the coupling constant or indicates a form factor sensitive to the Higgs mass. We set g(p) .^.: 1, since we expect only a negligible four-momentum transfer from each pion as discussed in Section 1. The expectation value of the pion number operator nA is given by the pion spectrum, which will be strongly space-time dependent . For simplicity we characterize the magnitude of J'r by its integrated asymptotic strength S and its switch-on function f(t), S - f(t) -

f dix J".

f(tfo)

= 0(tjro) - (1 - e-'/"0)

with f(oo) = 1 and ro ;~s 1 fm. Assumptions implied by this Ansatz are discussed in Ref.[1]. The strength of the Higgs source is related to the observed rapidity spectrum, i.e. growing with the number of pions produced : - - 84MeV f(t) S f(t) v

%+Y

dN = dy = f (t) l' y dy

f

+Y dy Y

dS(y) dy

2Y is the rapidity gap between target and projectile. For further comments see Ref.[1] . Then, from eq.(1) one obtains the number of Higgs particles produced per collision:

~33~

®~°.

lde~ .l .

r~ elski 1 ~oPlcc°five hadronic 1-~i~gs production in heavy-ion collisions

.r( , ) enotes the Fourier transform of the source function . ere ® ~)1~ an t re a real switchin -o of e conversion of incoming beam energy into matter (quarks nti-guar s~ is of crucial i portance in order to obtain relevant Fourier frequencies ~_ . ® e calculate the rapidity spectra of produced ~Iiggses in two scenarios of central ig - er y envy-ion collisions: rlcal a i re all . The source function is [1] :

with ~(t) = Ao ~-,Qt, a ® = 1 . " 1ls fm for a central +A collision, and Q ~ 1, which may represent a nearly fully stopping collision . It yields the rapidity spectrum of produced eggs particles for the ,ire l et ( ~ [1] : -`- .S ( ér~r® ®

c®S116t,/)-1

e-~®m~ainh~y

~ ~2 (3i2T~ ~ÛmH)

-1

,

~~ ô(y) ~OmH

he spectrugn is completely centered at zero Chi rapiditr~ within an interval of Dy - 10-~ (as well at negligible pi before integration) . Eq.(3) implies the scaling formula : = 2.3 . 1 -19 (

( 1 fm)2 ( 7.1 fm )3 ( 100 GeV ~ )s 1000 )2 r® A® mH

dependent ®n total ultiplicity of secondary hadrons (pions), initial fireball radius normalize by aim = .1 fns, and lliggs mass (in GeV). For the scaling 1~~ oc Ai+a with 1.2-1.6" Numerical results for Pb-f-Pb _ .1 - .3 and ~~, a A1/s we find dNH ~ collisions are presented in the Table. ® e sce ari®. The jorken scenario of central high-energy heavy-ion collisions is quasi one-dimensional and has asymptotic boost invariance along the longitudinal direction . Together with the longitudinally causal structure of matter production this leads t® a larger I-Iiggs production (by a factor a aomH) as compared to the fireball o el. The source function is now given by [1] :

[GeV]) . SP (17) S (30)* (77)** IC (200) L C (6250)

Y

dN dy

1~IH " 101~

NH " 1014

2 .9 3 .5 4 .4 5 .4 3 .3

500 - 350 51.0 - 900 560 - 1000 670 - 2000 1400 - 3000

.6 - 1 .8 1.2 - 10.7 14 .2 - 962 .

.4 - 1 .4 .8 - 6 .9 5.9 - 193 .

Table: Number of collectively produced I~iggs particles per event in Pb+Pb collisions for the fireball ( ) and jorken ( ) scenarios (ro = 1 fm, mH = 100 GeV ; ~ GSI high lu in ity collider under discussion; *~ fixed target mode of LIiC) .

H.-T. Elze, J. Rafelski / Collective hadronic Higgs production in heavy-ion collisions 589c JW =

/

dS(y)

6( x0 - rcosh e_x1 Aa dr dy ,f ( r l r0) y) «2II - rsinh y) . 2 7r1a10 0 dy

Note that there now exists a strong correlation between time and rapidity and longitudinal position and rapidity of matter formation . - We obtain the rapidity spectrum of produced Higgs particles for the Bjorken scenario (B) [11 : dNB

dy

ti Sv2(27r2rÛ aômH)_1(1 - 2e-2Y coshY)2 ,

for 7'0MH » 1 and for sufficiently large Y > JyJ . A cross section can be obtained by multiplying eq .(11) by 7rA2 , i.e. by 1/4 of the geometric nuclear cross section : uH

dy

v-°

= 2.3 10 -15 b

( dNA 1 fm 2 100 GeV ~ dy /1000)2 (r0) ( ) mH

.

(

)

Furthermore, eq .(11) implies the scaling formula : NH

= 1.9 . 10-15 (2Y - 1.5) ( dNA /1000)2 ( 1 fm)2 ( ?. 1 fm )2 ( 100 GeV )4

(13)

for dNR /dy .; const . We find here that the yield of Higgs particles per collision scales like dNH cu A1 .5-1 .9 and duH oc A2 .2-2 .s . Numerical results for Pb+Pb collisions from eq.(13) are also presented in the Table . The numbers for the Bjorken scenario, presumably a realistic picture at sufficiently high energy, seem very interesting, because they may largely underestimate the actual production rate due to two important effects: I) The scalar density probably is much higher during the reaction than given by the number of constituent quarks plus antiquarks bound in final state mesons; a QGP intermediate state could considerably enhance the strength of the scalar source, perhaps by an order of magnitude. - II) With increasing CM energy we expect a strongly increasing contribution from strange quarks (e.g. Higgs-kaon coupling = 4 " grH [3]) . 3.

BRI

ENTS

Observation of Higgs particles in deep-inelastic nuclear reactions in the subthreshold kinematic region poses a different problem in comparison to the usual production at LHC and SSC, as the background is considerably different. We will focus on the Higgs mass region of 60-160 GeV, which is hardly accessible to all presently planned particle accelerators, due to dominant background processes . Given the small production cross section from our mechanism, viz. the time change of the scalar density, we have to identify the process with little, if any, background. Consider central collisions in a collider : compared to the Higgs production rate there will be numerous sideways jets of hadronic matter, with energies easily up to mH/2 . Consequently, hadronic decay modes, dominant at mH <_ 160 GeV, will be hidden in hadronic background . The process H --+ ZZ -* l+l®l+l® has a channel ratio comparable to the direct branching ratio H -+ -y-y, varying between 4 .10®4 and 2 . 10°a as a function

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