Decays of Higgs scalars into vector mesons and photons

Abstract Decays of a neutral Higgs scalar (H) into a neutral vector meson (V) and a photon ( γ ) are discussed. The width for H → V + γ is related to the leptonic width V → l + l − . The rate for H → V + V is also estimated using a Phenomenological quark interaction with vector mesons supplemented by form factors.

Higgs scalars are an important ingredient in the construction of unified gauge theories of weak and electromagnetic interactions.Recent results from a wide variety of experiments support the simple SU(2) X U(1) gauge theory constructed by Weinberg and Salam [1].In principle one can develop unified models which are phenomenological in nature and which are also consistent with experiments.Higgs scalars have no place in such alternatives to gauge models [2].Discovery of Higgs scalars with prescribed couplings would therefore constitute a most important verification of spontaneously broken gauge theories.The mass of the Higgs scalar, being a free parameter in the theory [1], may be less than the mass of the W or Z boson and therefore the Higgs meson may well be accessible, while the W or Z bosons are not, to existing machines or those that are to come in operation soon.As a result, considerable effort is being directed towards understanding the phenomenology of these particles [3-71.
Detection of Higgs scalars is likely to be a formidable experimental problem.Their coupling to fermions (f of mass mf) gf = G 1/2 2l/4mf suggests that their decays to ~-(or heavier) leptons would be important and perhaps relatively clean ,1.However, in practice the ~leptons from Higgs decay may not be appreciable compared to the "background" production of r+r -.For Supported in part by the National Science Foundation.+1 For definiteness we will concern ourselves with the simplest spontaneously broken gauge theory of Weinberg-Salam [ 1 ] which involves a single neutral physical Higgs boson.
example, in pp collision where the Higgs cross section is appreciable [6] the rate for pp -+ ~-+r-X through virtual photons [8] is many times more than the r's from pp -+ H + X followed by H -+ ~-+r-.Missing-mass techniques [4,5,7] may have the best chance of revealing an H.Its detailed properties may have to be studied for confirmation that it is indeed a Higgs particle.Twobody decays and/or decay modes in which all the products are detectable could be particularly useful in this regard.One is thus led to consider neutral Higgs decays into 7 + 7, 7 + V, V + V, where 7 is the photon and V a neutral vector meson.Unfortunately H ~ ~, + 7 turns out to be small because of a subtle cancellation arising from the contributions of fermions and weak boson loops [3].Such a cancellation can be avoided if one replaces one or both photons with strongly interacting vector mesons.We are thus motivated to investigate H -+V + 7and H-~ V + V.These decays proceed through the quark loop as shown in fig. 1.We will concern ourselves with the case where the vector meson (V) is a pure orthoquarkonium bound state of the particular quark flavor (of charge leql) in the loop.For m H ~ m v one can calculate the width FHV v for the reaction H -+ V + 7 in terms of 14(0)12 , where 4(0) is the radial wave function of the V at the origin ,2 : FHbv,y = 48g2~eq21~(0)12(l --r)/m21(l +r) ,2 Superscripts b and g in eqs.
(1) and (3) are used to distinguish the bound state calculation from the perturbative one.

Y(V)
V + exchonge Fig. 1.Dia~ams for tt ~ V + 9"(V).H is Higgs, A, B, C are internal lines of a particular quark flavor that V is composed of.
2 2 where r = mv/m H and PV£~ is the leptonic width V -* ee or V-+p/l [9,10].This calculation for the width of H -+ V + 3' in terms of ~(0) corresponds to taking the quark lines B and C on-shell.As m H grows larger, the contribution from the real part of the loop becomes increasingly important and thus Pg, would HV"/ be expected to be a lower bound to the actual width for m H >2> m V.
For calculating I'HV s for m H >> m V we imagine tfiat the vector meson has an effective interaction with quarks of the form -igv~-q3'u ~q Vu.Setting 2mq = m V we are led to: where a v = g2/4~ and Is(r ) is the loop integral: Several remarks are in order.First we will content ourselves with six quark flavors with the sixth t quark of charge eq = +2/3 ,a.Secondly, we will, following Sakurai's observation [12], assume that Pw~/e2q 1.3 keV is a constant for all quark flavors.This constancy with the assumed quark-vector meson interaction implies (from dimensional considerations) that av oc 1/m v.The constant of proportionality is fixed by normalizing the width (3) with the bound state result (2) in a region where the latter is expected to hold best, that is for rn H ~ m v.For definiteness, we did the normalization at rn H = v~rne for H -+ t~ + 3'.In this way we find: a v ~ 3.9 GeV/rn V . ( $3 We assume that T (9.46) is composed of b quarks of charge -l/3.See ref. [11].
where Cf = 3 for quarks and Cf = I for leptons.RVA is thus the upper bound on the branching ratio for H V + A + s.Fig, 2 shows Rvv for various vector mesons as a function of mn.Notice that for m n <~ 4 GeV, H ~ p + 7 is dominant, for 4 GeV <~ m H <~ 25 GeV dominates, for m n ~> 25 GeV decays into "f' are slightly more than into f and with m T = 30 GeV decays H -+ T + 3` are dominant for rn H ~ 40 GeV.
For m H ~ m v the bound state result (2) for H -+ V + % in terms of the leptonic width of the vector mesons is quite reliable.For mtl >> m v the partial width ['nV-r depends somewhat (but not too appreciably) on the value of mH/m V that one chooses to normalize ~v at.However, the ratio of decay rates for H V + 3` into any two vector mesons is independent of the normalization for ~V and is, therefore, reliable.The decays H -+ V + V, on the other hand, cannot be calculated accurately.These modes may be quite important and even rough estimates for them (which can be obtained rather easily from our previous calculation) could be of experimental use.For this purpose we have adopted a purely phenomenological approach and estimated the partial width PHVV by supplementing the effective quark-vector meson interaction with form factors F n (q2n) leading to x II v (r)12G (q2mn)/2567r3, (9) where #s For numerical computations we have assumed quark mass !x the mass of the corresponding vector meson.In prac-2 rice, the effective quark mass (mq) for the decay H ~ q6~ may be somewhat more.This could appreciably change the value of 2P(tt ~ ff-) and consequently the ratio RVA in the range rn V < m H < 2mq.
Here q2 n is the minimum of the squared momentum of quark line C (fig. 1) when lines A and B are on their mass shell and is given by 2 It may be worth pointing out that qmn is timelike for H -+ V + 3' and space-like for H -+ V + V. Now as line C goes away from mass shell F n (with 1l > 1) would tend to bring about the suppression of the decay mode.For m H ~ my, q2nn is ~-3rn2,i and for rn H >~ ?nV , .) q~nn --9m4/m~I, so that near threshold F n -+ 5 -n and asymptotically b n -~ 2 -n.For n = 2 the resulting suppression ranges from 1/25 to 1/4.It may be worth mentioning that since ffV ~ 3.9 GeV/m V, for m V ~4 GeV, ~v <~ 1, consequently for large values ofm V a perturbative calculation for H -+ V + V may turn out to be reasonable anyway.Fig. 3 shows the numerical results for the partial width (EHVV) and RVV, defined by eq. ( 7) with A = V for p, ~, T, and T with a mass of 30 GeV.For m H < 8 GeV decays into p, co, ~p are dominant, for 10 <~ m H ~< 28 GeV decays into a pair #6 The decay H -~ V + V depends on the quark mass and not on its charge.4~ and 03 are, therefore, omitted to avoid overcrowding fig. 3 as their curves are not appreciably different from that for p.Let us finally discuss, in brief, how these decay modes and this calculation may be put to use.First consider the V + V mode.Here one possible final signature for a Higgs could be ~+{~-X via (~ = e or u): X (no £) where the X contains no £.The final signal ~+£-X would be additionally suppressed by the leptonic branching ratio of V. From fig. 3 we see that the rates for H ~ V + V (at least for m H <~ 30 GeV and perhaps even for larger rnH) may be large enough to allow its experimental observation through reaction (13).
Next consider H ~ V + 3`.In principle, one would like to see the V through its leptonic decay mode and then search for a peak in ~+£-3` mass distribution where rn~.~-= rn v.The numbers in fig. 2 are already small enough that, by the time one folds in the leptonic branching ratio of the V, searching for a Higgs peak in £+~-~, may become almost impossible.Somewhat more realistic, but still difficult, may be the search for 3' rays resulting from a two-body decay H ~ 3` + V followed by V --* X.That is, one has to select 3` + x events such that rn x = m V.
The most likely role that these decay modes may play lies in confirming or refuting that a given candidate discovered through, say, a missing-mass technique is a Higgs scalar or not.The point is that any spin-zero boson can in principle decay to a V + 3` or V + V. Since the theoretical uncertainty in H -* V + 3`, especially in the ratio of the rates of the decays into two different vector mesons, is minimal, if the measured rates of a given candidate for Higgs are (say) too large compared to theoretical expectations, then it simply cannot be a Higgs scalar.
Discussions with Gordon Shaw and Dennis Silverman are gratefully acknowledged.

Fig. 2 .
Fig.2.Decay width VHVy for H --+ V + y and RVs as defined by eq.(7) are shown for various vector mesons as a function of m H.

Fig. 3 .
Fig. 3. Decay width PHVVfor H ~ V + V and RVV defined by eq.(7) are shown for various vector mesons as a function Of MH +6.