The $W$ Boson Loop Background to H - ZZ at Photon-photon Colliders
a r X i v :h e p -p h /9307259v 1 13 J u l 1993
University of Wisconsin Madison
MAD/PH/771July 1993
The W Boson Loop Background to H →ZZ
at Photon-photon Colliders
M.S.Berger
Physics Department,University of Wisconsin,Madison,WI 53706,USA
ABSTRACT
We have performed a complete one-loop calculation of γγ→ZZ in the Standard Model,including both gauge bosons and fermions in the loop.We con?rm the large irreducible continuum background from the W -boson loop found by Jikia.We have included the photon-photon luminosity,and ?nd that the continuum background of transverse Z boson pairs prohibits ?nding a heavy Higgs with mass ～>350GeV in this decay mode.
I.INTRODUCTION
The search for the mechanism of electroweak symmetry breaking is one of the most im-portant challenges facing particle physics today.Detailed studies of the feasibility of signal for Higgs bosons have been undertaken in this area for both hadron and for e+e?collid-ers.The possibility of creating a photon-photon collider by Compton backscattering laser beams o?electron beams has attracted much attention recently.These machines would provide collisions of photons at energies almost as high as the parent e+e?colliders,lead-ing to recent interest in the possibility of detecting Higgs bosons at photon-photon colliders [1–3].This also o?ers the possibility that the Higgs-photon-photon coupling can be mea-sured,and so provides an indirect probe of new physics because any new charged particle that couples to the Higgs will contribute[4].While the photon-photon luminosity via the Weizsacker-Williams spectrum falls rapidly with increasing diphoton mass,the possibility of using backscattered laser beams provides a?at luminosity or even a luminosity which grows with energy almost all the way to the energy of the parent e+e?collider.
The W loop contribution toγγ→ZZ has been calculated recently in a nonlinear gauge by Jikia[5]who found a large cross section for transverse Z’s.We have performed an independent calculation of this process in the Feynman gauge(Rξwithξ=1).We?nd a total cross section as well as contributions from individual helicity modes to be in good numerical agreement with the results of Jikia.We are also in good numerical and analytic agreement with Glover and van der Bij who have calculated and published the matrix elements for gg→ZZ[6].This result can be immediately translated into the fermion loop contribution forγγ→ZZ with the appropriate coupling replacements for the quarks and including the charged leptons.
Most studies of Higgs detection at photon-photon colliders have neglected the irreducible continuum background of Z pairs that arise from W boson and fermion loops.The signal obtains its largest contribution from W loops,and the explicit calculation of the continuum background presented here and in Ref.[5]indicates that the contribution to the background
from almost all the helicity modes is dominated by the W boson loops as well.
The calculation required is straightforward but very lengthy.There are188one-loop diagrams with W-boson loops in the Rξgauge.These are shown in Figure1;the mixed coupling between the photon,the charged Goldstone boson,and the W boson is present in this gauge.The Higgs pole appears in the diagrams in Figure1b.We have performed the calculation with the symbolic manipulation programs FORM and MATHEMATICA using the tensor integral reduction algorithm of van Oldenborgh and Vermaseren[7].We obtain analytic expressions for each helicity amplitude,o?ering the possibility of including the full spin correlations of the decay products of the Z bosons as well as arbitrary polarization of the incident photon beams.The result was derived for on-shell Z bosons,so it can be used for any energy above threshold√
boson loops and the top quark loops to the Higgs peak is more severe.The other amplitudes are independent of the Higgs mass.There is interference between the Higgs pole and the continuum background that is constructive below the Higgs peak and destructive above.
The cross sections for the helicity amplitudes with unequal photon helicities is shown in Figures2d.The contributions from the other helicity modes to the cross section are related by
σ+++?=σ++?+,(1)
σ+?++=σ+???,(2)
σ+++0=σ++0+,(3)
σ++?0=σ++0?,(4)
σ+?+0=σ+?0?,(5)
σ+?0+=σ+??0.(6) The cross sectionsσ+?+?andσ+??+are not strictly equal,but the numerical agreement is very close.A similar statement applies toσ+?+0andσ+??0.The large cross section from the W boson loop arises in the helicity modesσ++++,σ+?+?,andσ+??+.These contributions reproduce the large cross sections for transverse Z pairs at large√
sγγ>>M W)by
M++++=8e2g2cos2θW s2γγ[D(sγγ,tγγ)+D(sγγ,uγγ)+D(uγγ,tγγ)],(7) where D(sγγ,tγγ)and D(sγγ,uγγ)are the two straight scalar boxes and D(tγγ,uγγ)is the
crossed scalar box(see e.g.the?rst paper in Ref.[6]for the functional form of these scalar
integrals in terms of dilogarithms and elementary functions).This amplitude is concentrated in the forward-backward directions at large energies,and is also logarithmically growing at large energies at?xed scattering angles.
The total cross section is the sum of the contribution from the individual modes.Branch-ing fractions for the subsequent decays of the Z bosons have not been included in the Figures or Tables.For unpolarized photons there is a factor of one half from averaging over the initial helicities.In Figures3and4the sum of the contributions from all helicity modes is shown for unpolarized photons with an angular cut|cosθ|<0.9on the Z bosons.We emphasize
that the angular cut is not particularly e?ective at reducing the continuum background at √
sγγ～>700GeV,unlike the process γγ→W+W?where a modest cut can reduce the transverse W background by an order of magnitude[9].The prominence of the Higgs peak is reduced as the Higgs mass increases; coupled with the rapid rise of the T T background,the viability ofγγ→H→ZZ for detecting a heavy Higgs boson deteriorates rapidly with increasing Higgs mass.
The peak cross section of the signal after subtracting out the underlying background is in close agreement with the approximate form given by the pole approximation
8πΓ(H→γγ)Γ(H→ZZ)
σ(γγ→H→ZZ)=
must multiply by the Z appropriate branching fractions and include the photon-photon luminosity distribution.However,one can already deduce that for a Higgs as heavy as400 GeV,one needs a large number of events since the background is over three times the size of the peak at its maximum.
A brief comment can be made here about the Higgs bosons of extended Higgs sectors and about supersymmetric Higgs bosons.Extra contributions enter into the loop,e.g.the charged Higgs loops,the squark loops,and chargino loops must be included.These contri-butions,however,can be deduced from subsets of the calculation already performed in the Standard Model.This will be the subject of future work.In such cases,we believe this background is still typically large.
III.PHOTON-PHOTON COLLIDERS
The results of the previous section were presented with respect to the invariant mass of the photons.To understand the event rates at a realistic photon-photon collider one must incorporate the spectrum of photons obtained from Compton backscattering a laser beam o?the electron beam.We assume the photon beams obtained are unpolarized,thus giving a broad and largely?at luminosity distribution up to approximately80%of the energy of the e+e?collider.We consider three such electron colliders with energies of E≡√
dz =2
√
x
Fγ/e(x,ξ)Fγ/e(τ/x,ξ),(9)
where z2=τ=sγγ/s e+e?and for unpolarized photons
Fγ/e(x,ξ)=1
1?x?
4x
ξ2(1?x)2 ,(10)
D(ξ)= 1?4ξ2 ln(1+ξ)+1ξ?1
ξ=
2
√m 2e
.(12)
We take the conversion coe?cient k to be one.The energy of the laser beam cannot be too large,or it would be possible to create electron-positron pairs from an interaction between the laser beam and the backscattered photon.So we take the dimensionless parameter ξis taken be 4.82as usual (ωo ?1.26eV for a 500GeV e +e ?collider)The maximum value of the fraction of the incident electrons’s energy carried by the back-scattered photon,x ,is then
x m =
ξ
2k 2z
dL γγ
(1+
ξ)ξ4D (ξ)2
(?4ξ4?4ξ5+ξ6)+(4ξ2+20ξ3+27ξ4+9ξ5?4ξ6)z 2
+(?8ξ?40ξ2?63ξ3?41ξ4?5ξ5+6ξ6)z 4+(8+32ξ+54ξ2+48ξ3+21ξ4?ξ5?4ξ6)z 6
+(?2ξ2?5ξ3?3ξ4+ξ5+ξ6)z 8
(?ξ+z 2+ξz 2)?1(?1+z 2)?2
+
1
(?ξ+z 2+ξz 2)2
(?1+z 2)?3
+
2
(1+
ξ)2z 2
.
(14)
valid in the region 0
dσ=
1
dz
d ?σ(++)+d ?σ(+?)
,
(15)
where z ?and z +are the minimum and maximum of the energy range to be integrated over.To increase the statistical signi?cance of the Higgs peak we integrate over from M H ?ΓH <
sγγ A factor of one-half is included to convert these contributions from each helicity mode for unpolarized photon beams because of averaging over the photon helicities.On the other hand for perfectly polarized photons,one would consider only the modes with equal photon helicities(++λ3λ4)yielding an extra factor of2in the signal[1].Unfortunately this also yields a factor two in the largest part of the T T background,namelyσ++++.However we expect some improvement from the unpolarized case since the backgroundσ+?+?and σ+??+would be reduced.Another improvement arises from the fact that the polarized photon-photon luminosity can peak more strongly than the unpolarized luminosity. The cross sections in femtobarns is given in Tables1-4with the angular cut on the Z’s of|cosθ|<1,0.9,0.8,and0.7in the center-of-mass system.Three value of the Higgs mass are considered:M H=300,350,and400GeV).This range of masses completely covers the region where the Higgs signal is much larger than the continuum background(M H=300 GeV)to the region where the signal is much smaller than the background(M H=400GeV. Both the signal and background for the400GeV Higgs is somewhat reduced at the500GeV e+e?collider,since part of the peak extends past the range of the photon-photon luminosity, z～<0.83. The event rates can be obtained from the?gures by incorporating the branching fractions of the Z pairs to some?nal state.The four-jet decay may be di?cult because of the huge γγ→W+W?process at tree level,so one can have one of the Z’s decay leptonically.For example,consider the decay mode[3]ZZ→q qZ,andγγ→t Using the results of Ref.[3]we can estimate that the irreducible continuum background is larger than the sum of these backgrounds for M H～>350GeV with a reasonable angular cut. A higher energy collider will not improve the situation.While the reach of the collider would be greater,less of the photon-photon luminosity would be devoted to the region of the Higgs peak M H?ΓH<√ sγγ≈300?400GeV.For larger√ s>>M W.The same helicity amplitudes should eventually grow with energy.We are currently incorporating the decay density ma-trices for the Z bosons. IV.CONCLUSION We have con?rmed the large Z T Z T production from photon-photon collisions at high energy.An angular cut on the Z bosons is ine?ective at reducing this background.The search for the heavy Higgs boson or for physics beyond the standard model such as new states should take this background into consideration.The large size of the T T background casts doubt on the viability of the processγγ→ZZ as a“quantum counter,”since any signal is probably buried beneath the Standard Model W boson loop contribution.The bene?ts of polarized photon beams and cuts on the decay products of the Z bosons in detecting a heavy Higgs including the continuum background considered here is a subject for future study. ACKNOWLEDGMENTS We wish to thank V.Barger,G.Bhattacharya,D.Bowser-Chao,M.Chanowitz,K.Che-ung,A.Djouadi,and C.Kao for useful discussions.This research was supported in part by the University of Wisconsin Research Committee with funds granted by the Wisconsin Alumni Research Foundation,in part by the U.S.Department of Energy under contract no.DE-AC02-76ER00881,and in part by the Texas National Laboratory Research Commis-sion under grant no.RGFY93-221. REFERENCES [1]J.F.Gunion and H.E.Haber,“Proceedings of the1990Summer Study on High Energy Physics,”Snowmass(1990);J.F.Gunion and H.E.Haber,University of California preprint UCD-92-22(1992);J.F.Gunion,University of California preprint UCD-93-8 (1993). [2]D.L.Borden,D.A.Bauer,D.O.Caldwell,SLAC preprint SLAC-PUB-5715(1992). [3]K.Cheung and D.Bowser-Chao,Phys.Rev.D48,89(1993);K.Cheung,Talk given at the“Workshop on Physics and Experiments with Linear e+e?Collider,”Northwestern University preprint NUHEP-TH-93-15. [4]M.Chanowitz,Phys.Rev.Lett.69,2037(1992). [5]G.V.Jikia,Phys.Lett.B298,224(1993). [6]E.W.N.Glover and J.J.van der Bij,Phys.Lett.B219,488(1989);Nucl.Phys.B321, 561(1989).See also D.A.Dicus,C.Kao,and W.W.Repko,Phys.Rev.D361570 (1987);D.A.Dicus,Phys.Rev.D38394(1988). [7]G.J.van Oldenborgh and J.A.M.Vermaseren,Z.Phys.C46,425(1990). [8]O.P.Sushkov,V.V.Flambaum,and I.B.Khriplovich,Sov.J.of Nucl.Phys.20,537 (1975);I.F.Ginzburg,G.L.Kotkin,S.L.Pan?l,and V.G.Serbo,Nucl.Phys.228 285(1983). [9]See e.g.G.B′e langer and F.Boudjema,Phys.Lett.B288,210(1992)and references therein. [10]I.F.Ginzburg,G.L.Kotkin,V.G.Serbo and V.I.Telnov,Nucl.Instrum.and Methods 205,47(1983);ibid219,5(1984);V.I.Telnov,Nucl.Instrum.and Methods A294,72 (1990) [11]It is interesting to note that the luminosity integral in Eq.(9)can be performed analyt- ically even for polarized beams. 0.5TeV1TeV1.5TeV 300GeV11.6/3.5 6.7/2.0 4.0/1.2 400GeV 1.6/8.8 1.4/11.80.90/7.7 Table1:The cross section for the signal and background(S/B)in the mass range M H?ΓH<√ s e+e? 350GeV 4.5/7.5 2.9/4.9 1.8/3.1 sγγ M H√ 0.5TeV1TeV1.5TeV 300GeV9.5/2.65.5/1.53.3/0.90 400GeV1.3/6.11.1/8.10.74/5.3 Table3:The cross section for the signal and background(S/B)in the mass range M H?ΓH<√ 0.5TeV1TeV1.5TeV 300GeV8.3/2.14.7/1.22.9/0.74 400GeV1.1/4.91.0/6.40.65/4.2 Table4:The cross section for the signal and background(S/B)in the mass range M H?ΓH<√ Figures Fig.1.Generic diagrams in the W boson loop contribution toγγ→ZZ.The loops consist of all possible combinations of W bosons,Goldstone bosons and ghosts,and the number of nonzero diagrams in each class(in a linear Rξgauge)is indicated.The dashed line is the Higgs boson. Fig. 2.The cross sections for each independent helicity amplitude is shown versus the diphoton mass,√ (a) (b) Figure 1 108 32 8 2 8 4 24 20 s γγ / \ [GeV] σ[f b ] 10 10 10 10 10 10 10 10 σ[f b ]s γγ / \ __ [GeV] 10 10 10 10 10 10 10 10 σ[f b ]s γγ / \ [GeV] σ[f b ]s γγ / \ __ [GeV] Figure 2 100 200 300 400 500 1000 M = 300 GeV H 500 800 Figure 3 m =150 GeV t |cos | < 0.9 θ σ[f b ]s γγ / \ __ [GeV] 200 40 80 120 160 200 200 300 400 500 600 M = 300 GeV H 400 500 s γγ / \ __ [GeV] σ[f b ]Figure 4 m =150 GeV t |cos | < 0.9 θ