In this note we investigate the production of charged heavy particles via
\gaga\ fusion at high energy pp colliders. We revise previous claims that the
\gaga\ cross section is comparable to or larger than that for the corresponding
Drell-Yan process at high energies. Indeed we find that the \gaga\ contribution
to the total production cross section at pp is far below the Drell-Yan cross
section. As far as the individual elastic, semi-elastic and inelastic
contributions to the \gaga\ process are concerned we find that they are all of
the same order of magnitude.Comment: REVTEX, 12 pages, two uuencoded figures appended at the end of the
  fil

Drees, M.

Godbole, R. M.

Nowakowski, M.

Rindani, S. D.

English

arXiv

In this Brief Report we investigate the production of charged heavy particles via γγ fusion at high energy pp colliders. We revise previous claims that the γγ cross section is comparable to or larger than that for the corresponding Drell-Yan process at high energies. Indeed we find that the γγ contribution to the total production cross section at pp is far below the Drell-Yan cross section. As far as the individual elastic, semielastic, and inelastic contributions to the γγ process are concerned we find that they are all of the same order of magnitude

Drees, Manuel

Godbole, Rohini M.

Nowakowski, Marek

Rindani, Saurabh D.

Publications of the IAS Fellows

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March 1994
γγ PROCESSES AT HIGH ENERGY pp COLLIDERS
Manuel Drees∗
Physics Department, University of Wisconsin, Madison, WI 53706, USA
Rohini M. Godbole
Physics Department, University of Bombay, Vidyanagari, Bombay 400098, India
Marek Nowakowski† and Saurabh D. Rindani
Theory Group, Physical Research Laboratory, Navrangpura, Ahmedabad 380 009,India
Abstract
In this note we investigate the production of charged heavy particles
via γγ fusion at high energy pp colliders. We revise previous claims that the
γγ cross section is comparable to or larger than that for the corresponding
Drell-Yan process at high energies. Indeed we find that the γγ contribution
to the total production cross section at pp is far below the Drell-Yan cross
section. As far as the individual elastic, semi-elastic and inelastic contributions
to the γγ process are concerned we find that they are all of the same order of
magnitude.
∗Heisenberg Fellow
†Feodor-Lynen Fellow
1
The detection of a fundamental charged scalar particle would certainly lead beyond
the realm of the Standard Model (SM). These particles can arise either in the context of
supersymmetric models, as superpartners of quarks and leptons [1], or in extended Higgs
sectors, e.g. in two-Higgs-doublet models [2] (with or without supersymmetry) or in models
with triplet Higgses [3]. In general, the different charged scalars will have different interac-
tions at tree level. For instance, sleptons do not couple to quarks in contrast to H± in the
two Higgs doublet model, while one charged Higgs boson in triplet models does not couple
to matter at all but has an unconventional H+W−Z0 vertex. Hence a model independent
production mechanism is welcome. Such a model independent interaction is clearly given by
the scalar QED part of the underlying theory. For example the γγ fusion processes:
γγ → H+H−, l˜+l˜−, ... (1)
are uniquely calculable for given mass of the produced particles. At pp colliders we also
have, however, the possibility of the qq annihilation Drell–Yan processes
qq → H+H−, l˜+l˜− ... (2)
There has been a claim in the literature that the γγ fusion exceeds the Drell–Yan (DY)
cross sections at pp by orders of magnitude [4]. This would be an interesting possibility of
producing charged heavy scalars at hadronic colliders or for that matter any charged particle
which does not have strong interactions.
Apart from the charged scalars mentioned above there exist various candidates for
charged fermions. These fermions can be either fourth generation leptons, charginos or exotic
leptons in extended gauge theories like E6 [5]. Current limits on the masses of all exotic
charged particles which couple to the Z with full strength are ∼ MZ/2. In the case of H±
there exist additional constraints (clearly model dependent) from the experimental studies
of the b → sγ decay. In one variation of the model mH± < 110 GeV is ruled out for large
values of tanβ and for mt = 150 GeV [6]. However, in the two-Higgs-doublet models with
SUSY these constraints are much weaker [7]. (The same analysis also shows that there are
2
no limits on the chargino masses from the b → sγ rate.) The calculation for γγ → L+L−
at pp colliders has been done recently [8]. The result in [8] is that the γγ cross section is
comparable to the corresponding Drell–Yan process at high energies, e.g. at
√
s = 40 TeV
for mL ∼ 100 GeV. At LHC energies the γγ cross section in the same mass range was found
to be [8] one order of magnitude smaller than the DY cross section.
We have repeated the calculations for scalar and fermion pair production, and find
that in both cases the γγ cross sections are well below the Drell–Yan contribution [9]. In
what follows we outline briefly the basic tools and approximations in the calculation.
In order to calculate the pp cross section we have used the Weizsa¨cker-Williams
approximation [10] for the inelastic case (γpX vertex) and a modified version of this approx-
imation [11,12] for the elastic case (γpp vertex). In the latter case the proton remains intact.
The inelastic (inel.) total pp cross section for H+H− as well as L+L− production reads
σinel.pp (s) =
∑
q, q′
∫
1
4m2/s
dx1
∫
1
4m2/sx1
dx2
∫
1
4m2/sx1x2
dz1
∫
1
4m2/sx1x2z1
dz2 e
2
qe
2
q′
· fq/p(x1, Q2) fq′/p(x2, Q2)fγ/q(z1) fγ/q′(z2) σˆγγ(x1x2z1z2s) (3)
where m is the mass of either H± or L±, eu = 2/3, ed = −1/3 and σˆγγ is the production
subprocess cross section with the center of mass energy
√
sˆ =
√
x1x2z1z2s. The structure
functions have the usual meaning: fq/p is the quark density inside the proton, fγ/q is the
photon spectrum inside a quark. We use the the MRSD
′
− parameterization for the partonic
densities inside the proton [13]. The scale Q2 has been chosen throughout the paper to be
sˆ/4. With
fγ(z) ≡ fγ/q(z) = fγ/q′(z) =
αem
2pi
(1 + (1− z)2)
z
ln(Q21/Q
2
2) (4)
we can write (3) in a more compact form as
σinel.pp (s) =
∫
1
4m2/s
dx1
∫
1
4m2/sx1
dx2
∫
1
4m2/sx1x2
dz1
∫
1
4m2/sx1x2z1
dz2
1
x1
F p2 (x1, Q
2)
· 1
x2
F p2 (x2, Q
2)fγ(z1) fγ(z2) σˆγγ(x1x2z1z2s) (5)
3
where F p2 is the deep-inelastic proton structure function. There is a certain ambiguity about
the choice of the scales Q2i in the argument of the log in eq. (4). We choose Q
2
1 to be the
maximum value of the momentum transfer given by sˆ/4−m2 and the choice of Q22 = 1 GeV2
is made such that the photons are sufficiently off–shell for the Quark–Parton–Model to be
applicable.
The semi-elastic (semi-el.) cross section for pp→ H+H−(L+L−)pX is given by
σsemi−el.pp (s) = 2
∫
1
4m2/s
dx1
∫
1
4m2/sx1
dz1
∫
1
sm2/sx1z1
dz2
1
x1
F p2 (x1, Q
2)
· fγ(z1) f el.γ/p(z2) σˆγγ(x1z1z2s) (6)
The subprocess energy now is given by
√
sˆ =
√
sx1z1z2. The elastic photon spectrum f
el.
γ/p(z)
has been obtained in the form of an integral in [11]. However, we use an approximate analytic
expression given in [12] which is known to reproduce exact results to about 10%. The form
we use is given by
f el.γ/p(z) =
αem
2piz
(1 + (1− z)2)
[
lnA− 11
6
+
3
A
− 3
2A2
+
1
3A3
]
(7)
where
A = 1 +
0.71(GeV)2
Q2min
(8)
with
Q2min = −2m2p +
1
2s
[
(s+m2p)(s− zs +m2p)
− (s−m2p)
√
(s− zs−m2p)2 − 4m2pzs
]
(9)
At high energies Q2min is given to a very good approximation by m
2
pz
2/(1 − z). Since the
relevant values of the scaled photon energy zi can in general take smaller values in the elastic
case as compared to the inelastic case, eqs. (9),(8) and (7) imply that even in the elastic
case there is a logarithmic enhancement of the photon densities.
Finally the pure elastic contribution wherein both the photons remain intact and
hence can in principle give rise to clean events, can be written as
4
σel.pp(s) =
∫
1
4m2/s
dz1
∫
1
4m2/z1s
dz2 f
el.
γ/p(z1) f
el.
γ/p(z2) σˆγγ(sˆ = z1z2s) (10)
Defining βˆL, H = (1− 4m2L, H/sˆ)1/2 the γγ subcross sections take the simple form
σˆ(γγ → H+H−) = 2piα
2
em(M
2
W )
sˆ
βˆH
[
2− βˆ2H −
1− βˆ4H
2βˆH
ln
1 + βˆH
1− βˆH
]
, (11)
and for lepton production
σˆ(γγ → L+L−) = 4piα
2
em(M
2
W )
sˆ
βˆL
[
3− βˆ4L
2βˆL
ln
1 + βˆL
1− βˆL
− (2− βˆ2L)
]
. (12)
Note that we have used αem = 1/137 in (4) and (7) and αem(M
2
W ) = 1/128 in the subcross
sections (11) and (12).
For completeness we also give here the Drell-Yan qq annihilation cross section to
H+H− including Z0 exchange, for the case that H± resides in an SU(2) doublet:
σˆ(qq → H+H−) = 4piα
2
em(M
2
W )
3sˆ
(βˆH)
3/2
4
[
e2q + 2eqgVq
cot 2θW
sin 2θW
sˆ(sˆ−m2Z)
(sˆ−m2Z)2 + Γ2Zm2Z
+ (g2Vq + g
2
Aq)
cot2 2θW
sin2 2θW
sˆ2
(sˆ−m2Z)2 + Γ2Zm2Z
]
(13)
In the above gVq , gAq are the standard vector and axial vector coupling for the quark.
The results of our calculations are presented in Fig. 1 for H+H− production and
in Fig. 2 for the lepton case. As far as the H+H− production in γγ fusion is concerned
we differ from the results given in [4] by roughly three orders of magnitude: our γγ cross
section is far below their results and also approximately two orders of magnitude smaller
than the DY cross section. The logarithmic enhancement of the photon densities is simply
not enough to overcome completely the extra factor α2em in the γγ process. Even if the Higgs
is doubly charged (such a Higgs appears in triplet models [3]) the ratio of DY to γγ cross
section changes only by a factor 1/4 as compared to the singly charged Higgs production.
We also find that contributions from elastic, semi-elastic and inelastic processes to the total
γγ cross section are of the same order of magnitude. The elastic process contributes ∼ 20%
of the total γγ cross–section at smaller values of mH going up to 30% at the high end. This
can be traced to the logarithmic enhancement of the photon density even in the elastic case
5
mentioned earlier. Assuming the l˜L, l˜R to be degenerate in mass the cross–section for γγ
production of sleptons (for one generation) will be twice the corresponding H+H− cross–
sections.
Our results for leptons are given in Fig.2. Here again we find that at LHC energies
DY exceeds γγ by two orders of magnitude even for relatively small mL masses in the range
of 50− 100 GeV [9]. In general the L+L− cross–sections are higher than the corresponding
H+H− cross–sections (both for γγ and DY) by about a factor of 5–7. This can be traced to
the different spin factors and the different βˆ dependence of the subprocess cross–section for
the fermions and scalars. The cross–section for the γγ production of charginos will again be
the same as that of the charged leptons.
One might think that by sacrificing rate for ‘cleanliness’ the purely elastic processes
might prove useful. Moreover, even inelastic or semi–elastic γγ events might be characterized
by “rapidity gaps”, where the only hadrons at central rapidities are due to the decay of
the heavy particles produced. However, at the LHC one expects about 16 minimum bias
events per bunch crossing at luminosity L = 1034 cm−2 sec−1; even the elastic γγ events
will therefore not be free of hadronic debris. These “overlapping events” will fill the entire
rapidity space with (mostly soft) hadrons, thereby obscuring any rapidity gap. Notice also
that in the purely elastic events the participating protons only lose about 0.1% of their
energy, making it very difficult to detect them in a forward spectrometer of the type now
being installed at HERA detectors. We are therefore forced to conclude that most likely
one will not be able to distinguish experimentally between DY and γγ events if the LHC is
operated anywhere near its design luminosity. The clean elastic events might be detectable
at luminosities well below 1033 cm−2 sec−1, where event overlap is not expected to occur.
However, our results show that at such a low luminosity one is running out of event rate at
masses not much above the limit that can be probed at LEP200; moreover, there might be
sizable backgrounds, e.g. due to the process γγ →W+W−.
At this point it might be instructive to compare the γγ cross–sections with other
6
(model dependent) possible production mechanisms for various weakly interacting charged
particles. Studies [14] have shown that search for charginos in hadronically quiet multilepton
events due to associated production of a chargino with a neutralino (via DY) at LHC might
be feasible up to mχ± ≃ 250 GeV. The detection of sleptons with mass up to ∼ 250 GeV
also seems possible [15]. Hence the DY process still seems to be the dominant mode for
production for sleptons, charginos as well as heavy leptons. For larger masses the DY cross–
section falls off and in some cases the gluon induced production (which we discuss below)
will take over.
For the charged Higgses the situation is somewhat different. The question of
DY/γγ/gg production becomes relevant in this case only for mt < mH±. If mt > mH±
the charged Higgs can be produced in the decay of the top quark and the strong production
of top quarks gives large rates allowing one to probe at LHC upto mH± ∼ mt−20 GeV [16].
Even when mt < mH± production of a single charged Higgs in association with a t quark
via the process
gb→ tH− (14)
might provide a measurable signal in the decay channel
tH+ → ttb→ b(bqq¯′)(blν). (15)
The cross–section is ∼ 15 pb for mH± ∼ 150 GeV and could provide a feasible signal up to
mH± ∼ 200 GeV over a wide range of parameter space, if b quarks can be tagged with high
purity and not too low efficiency [17]. Fig.1 shows that even for the DY process the charged
Higgs cross–section is only a few tens of fb or less if mH+ > mt.
Another process that contributes to the pair production of Higgs bosons and charged
leptons is one loop gluon fusion:
gg→ H+H−
gg→ L+L− (16)
7
These contributions will only be competitive with ordinary DY production if some couplings
of the produced particles grow with their mass. Accordingly the first process will be large
[18] if mt > mH+ (in which case H
+ production from t decays will have even larger rates) but
is expected to decrease for mH+ > mt. Since the coupling of chiral leptons to Higgs bosons
and longitudinal Z bosons grows with the lepton mass, graphs containing the (1–loop) ggH0∗
and ggZ0∗ couplings dominate the production of both charged [19] and neutral [20] chiral
leptons of sufficiently large mass.
In summary, we have shown that the cross section for the pair production of heavy
charged scalars or fermions via γγ fusion amounts to at best a few % of the corresponding
Drell–Yan cross section; in many cases there are additional production mechanisms with even
larger cross sections. Moreover, at the LHC overlapping events prevent one from isolating
γγ events experimentally unless the machine is run at a very low luminosity, in which case
the accessible mass window is not much larger than at LEP200. We do therefore not expect
γγ fusion processes at the LHC to be competitive with more traditional mechanisms for the
production of new particles.
While writing this note we have received a preprint [21] which treats the same subject
of γγ processes in pp colliders and gets similar results. However we differ somewhat in the
details which is most probably due to the different treatment of the photon luminosity
functions.
Acknowledgments
We thank the Department of Science and Technology (India) and the organizers of
the WHEPP-III workshop held in Madras (India) where this work was partially done. The
work of M.D. was supported by a grant from the Deutsche Forschungsgemeinschaft under
the Heisenberg program, as well as in part by the U.S. Department of Energy under contract
No. DE-AC02-76ER00881, by the Wisconsin Research Committee with funds granted by the
Wisconsin Alumni Research Foundation, and by the Texas National Research Laboratory
Commission under grant RGFY93–221. R.M.G. wishes to thank the Theory Group at PRL
8
for hospitality. M.N. wishes to thank the Alexander von Humboldt foundation for financial
support under the Feodor-Lynen fellowship program.
9
REFERENCES
[1] For a review see J.F. Gunion, H. Haber, G.L. Kane and S. Dawson, “The Higgs Hunter’s
Guide”, Addison-Wesley, Reading, MA, 1990.
[2] T.D. Lee, Phys.Rev. D8 (1973)1226; H. Georgi, Hadronic J. 1 (1978) 155
[3] J.F. Gunion, R. Vega and J. Wudka Phys. Rev. D42 (1990) 1673 and references therein.
[4] S.K. Oh et al., Z.Phys. C46 (1990)267
[5] J.L. Hewett and T.G. Rizzo, Phys.Rep. 183 (1989) 193
[6] J.L. Hewett, Phys. Rev. Lett. 70 (1993) 1045; V. Barger, M.S. Berger and R.J.N.
Phillips, Phys. Rev. Lett. 70 (1993) 1368.
[7] R. Barbieri and G.F. Guidice, Phys. Lett. B309 (1993) 86. For a detailed analysis of
the subject see: F. Borzumati, DESY 93-090.
[8] G. Bhattacharya, P.A. Kalyniak and K.A. Peterson, Carleton University preprint,
OCIP/C-93-12.
[9] On reexamination the authors of [8] agree with our conclusions for the lepton case
(private communication).
[10] E.J. Williams, Phys.Rev. 45 (1934) 729(L); C.F. Weizsa¨cker, Z.Phys. 88 (1934) 612.
[11] B.A. Kniehl, Phys.Lett.B254 (1991) 267.
[12] M. Drees and D. Zeppenfeld, Phys.Rev. D39 (1989) 2536.
[13] A.D. Martin, R.G. Roberts and W.J. Stirling, Phys. Lett. B306 (1993) 306; Erratum
ibid 309 (1993) 492.
[14] R. Barbieri, F. Caravaglios, M. Frigeni and M.L. Mangano, Nucl. Phys. B367 (1991)
28.
10
[15] F. del Aguila and L. Ametller, Phys. Lett. B261 (1991) 326; H. Baer, C. Chen, F. Paige
and X. Tata, Florida State Univ. preprint FSU–HEP–931104.
[16] D.P. Roy, Phys. Lett. B283 (1992) 403.
[17] V. Barger, R.J.N. Phillips and D.P. Roy, University of Wisconsin preprint
MAD/PH/790.
[18] S.S.D. Willenbrock, Phys.Rev. D35 (1987) 173.
[19] S.S.D. Willenbrock and D.A. Dicus, Phys.Lett. B156 (1985) 429.
[20] D.A. Dicus and P. Roy, Phys.Rev. D44 (1991) 1593; A. Datta and A. Pilaftsis,
Phys.Lett. B278 (1992) 162; D. Choudhury, R.M. Godbole and P. Roy, Phys.Lett.
B308 (1993) 394; erratum ibid 314 (1993) 482.
[21] J. Ohnemus, T.F. Walsh and P.M. Zerwas, DESY-preprint 93-173.
11
FIGURES
FIG. 1. Cross section in fb for DY and γγ production of the charged Higgs at LHC energies,
as a function of the Higgs mass. The dashed, dash-dotted and long-dashed lines show the el., inel.
and semi-el. contributions (as defined in the text) to the γγ cross sections. The total γγ cross
section and the DY contributions are shown by the labeled solid lines.
FIG. 2. Cross section in fb for DY and γγ production of the charged Leptons at LHC energies,
as a function of the Lepton mass. The convention is the same as in 1.
12


This figure "fig1-1.png" is available in "png"
 format from:
http://arXiv.org/ps/hep-ph/9403368v1
This figure "fig1-2.png" is available in "png"
 format from:
http://arXiv.org/ps/hep-ph/9403368v1


γγ processes at high energy pp colliders

Indian Academy of Sciences

ar
X
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:h
ep
-p
h/
94
03
36
8v
1 
 2
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M
ar
 1
99
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MAD/PH/824
PRL-TH-94/10
BU-TH-94/3
March 1994
γγ PROCESSES AT HIGH ENERGY pp COLLIDERS
Manuel Drees∗
Physics Department, University of Wisconsin, Madison, WI 53706, USA
Rohini M. Godbole
Physics Department, University of Bombay, Vidyanagari, Bombay 400098, India
Marek Nowakowski† and Saurabh D. Rindani
Theory Group, Physical Research Laboratory, Navrangpura, Ahmedabad 380 009,India
Abstract
In this note we investigate the production of charged heavy particles
via γγ fusion at high energy pp colliders. We revise previous claims that the
γγ cross section is comparable to or larger than that for the corresponding
Drell-Yan process at high energies. Indeed we find that the γγ contribution
to the total production cross section at pp is far below the Drell-Yan cross
section. As far as the individual elastic, semi-elastic and inelastic contributions
to the γγ process are concerned we find that they are all of the same order of
magnitude.
∗Heisenberg Fellow
†Feodor-Lynen Fellow
1
The detection of a fundamental charged scalar particle would certainly lead beyond
the realm of the Standard Model (SM). These particles can arise either in the context of
supersymmetric models, as superpartners of quarks and leptons [1], or in extended Higgs
sectors, e.g. in two-Higgs-doublet models [2] (with or without supersymmetry) or in models
with triplet Higgses [3]. In general, the different charged scalars will have different interac-
tions at tree level. For instance, sleptons do not couple to quarks in contrast to H± in the
two Higgs doublet model, while one charged Higgs boson in triplet models does not couple
to matter at all but has an unconventional H+W−Z0 vertex. Hence a model independent
production mechanism is welcome. Such a model independent interaction is clearly given by
the scalar QED part of the underlying theory. For example the γγ fusion processes:
γγ → H+H−, l̃+l̃−, ... (1)
are uniquely calculable for given mass of the produced particles. At pp colliders we also
have, however, the possibility of the qq annihilation Drell–Yan processes
qq → H+H−, l̃+l̃− ... (2)
There has been a claim in the literature that the γγ fusion exceeds the Drell–Yan (DY)
cross sections at pp by orders of magnitude [4]. This would be an interesting possibility of
producing charged heavy scalars at hadronic colliders or for that matter any charged particle
which does not have strong interactions.
Apart from the charged scalars mentioned above there exist various candidates for
charged fermions. These fermions can be either fourth generation leptons, charginos or exotic
leptons in extended gauge theories like E6 [5]. Current limits on the masses of all exotic
charged particles which couple to the Z with full strength are ∼ MZ/2. In the case of H±
there exist additional constraints (clearly model dependent) from the experimental studies
of the b → sγ decay. In one variation of the model mH± < 110 GeV is ruled out for large
values of tanβ and for mt = 150 GeV [6]. However, in the two-Higgs-doublet models with
SUSY these constraints are much weaker [7]. (The same analysis also shows that there are
2
no limits on the chargino masses from the b → sγ rate.) The calculation for γγ → L+L−
at pp colliders has been done recently [8]. The result in [8] is that the γγ cross section is
comparable to the corresponding Drell–Yan process at high energies, e.g. at
√
s = 40 TeV
for mL ∼ 100 GeV. At LHC energies the γγ cross section in the same mass range was found
to be [8] one order of magnitude smaller than the DY cross section.
We have repeated the calculations for scalar and fermion pair production, and find
that in both cases the γγ cross sections are well below the Drell–Yan contribution [9]. In
what follows we outline briefly the basic tools and approximations in the calculation.
In order to calculate the pp cross section we have used the Weizsäcker-Williams
approximation [10] for the inelastic case (γpX vertex) and a modified version of this approx-
imation [11,12] for the elastic case (γpp vertex). In the latter case the proton remains intact.
The inelastic (inel.) total pp cross section for H+H− as well as L+L− production reads
σinel.pp (s) =
∑
q, q′
∫
1
4m2/s
dx1
∫
1
4m2/sx1
dx2
∫
1
4m2/sx1x2
dz1
∫
1
4m2/sx1x2z1
dz2 e
2
qe
2
q′
· fq/p(x1, Q2) fq′/p(x2, Q2)fγ/q(z1) fγ/q′(z2) σ̂γγ(x1x2z1z2s) (3)
where m is the mass of either H± or L±, eu = 2/3, ed = −1/3 and σ̂γγ is the production
subprocess cross section with the center of mass energy
√
ŝ =
√
x1x2z1z2s. The structure
functions have the usual meaning: fq/p is the quark density inside the proton, fγ/q is the
photon spectrum inside a quark. We use the the MRSD
′
− parameterization for the partonic
densities inside the proton [13]. The scale Q2 has been chosen throughout the paper to be
ŝ/4. With
fγ(z) ≡ fγ/q(z) = fγ/q′(z) =
αem
2π
(1 + (1 − z)2)
z
ln(Q21/Q
2
2) (4)
we can write (3) in a more compact form as
σinel.pp (s) =
∫
1
4m2/s
dx1
∫
1
4m2/sx1
dx2
∫
1
4m2/sx1x2
dz1
∫
1
4m2/sx1x2z1
dz2
1
x1
F p2 (x1, Q
2)
· 1
x2
F p2 (x2, Q
2)fγ(z1) fγ(z2) σ̂γγ(x1x2z1z2s) (5)
3
where F p2 is the deep-inelastic proton structure function. There is a certain ambiguity about
the choice of the scales Q2i in the argument of the log in eq. (4). We choose Q
2
1 to be the
maximum value of the momentum transfer given by ŝ/4−m2 and the choice of Q22 = 1 GeV2
is made such that the photons are sufficiently off–shell for the Quark–Parton–Model to be
applicable.
The semi-elastic (semi-el.) cross section for pp → H+H−(L+L−)pX is given by
σsemi−el.pp (s) = 2
∫
1
4m2/s
dx1
∫
1
4m2/sx1
dz1
∫
1
sm2/sx1z1
dz2
1
x1
F p2 (x1, Q
2)
· fγ(z1) f el.γ/p(z2) σ̂γγ(x1z1z2s) (6)
The subprocess energy now is given by
√
ŝ =
√
sx1z1z2. The elastic photon spectrum f
el.
γ/p(z)
has been obtained in the form of an integral in [11]. However, we use an approximate analytic
expression given in [12] which is known to reproduce exact results to about 10%. The form
we use is given by
f el.γ/p(z) =
αem
2πz
(1 + (1 − z)2)
[
lnA − 11
6
+
3
A
− 3
2A2
+
1
3A3
]
(7)
where
A = 1 +
0.71(GeV)2
Q2min
(8)
with
Q2min = −2m2p +
1
2s
[
(s + m2p)(s − zs + m2p)
− (s − m2p)
√
(s − zs − m2p)2 − 4m2pzs
]
(9)
At high energies Q2min is given to a very good approximation by m
2
pz
2/(1 − z). Since the
relevant values of the scaled photon energy zi can in general take smaller values in the elastic
case as compared to the inelastic case, eqs. (9),(8) and (7) imply that even in the elastic
case there is a logarithmic enhancement of the photon densities.
Finally the pure elastic contribution wherein both the photons remain intact and
hence can in principle give rise to clean events, can be written as
4
σel.pp(s) =
∫
1
4m2/s
dz1
∫
1
4m2/z1s
dz2 f
el.
γ/p(z1) f
el.
γ/p(z2) σ̂γγ(ŝ = z1z2s) (10)
Defining β̂L, H = (1 − 4m2L, H/ŝ)1/2 the γγ subcross sections take the simple form
σ̂(γγ → H+H−) = 2πα
2
em(M
2
W )
ŝ
β̂H
[
2 − β̂2H −
1 − β̂4H
2β̂H
ln
1 + β̂H
1 − β̂H
]
, (11)
and for lepton production
σ̂(γγ → L+L−) = 4πα
2
em(M
2
W )
ŝ
β̂L
[
3 − β̂4L
2β̂L
ln
1 + β̂L
1 − β̂L
− (2 − β̂2L)
]
. (12)
Note that we have used αem = 1/137 in (4) and (7) and αem(M
2
W ) = 1/128 in the subcross
sections (11) and (12).
For completeness we also give here the Drell-Yan qq annihilation cross section to
H+H− including Z0 exchange, for the case that H± resides in an SU(2) doublet:
σ̂(qq → H+H−) = 4πα
2
em(M
2
W )
3ŝ
(β̂H)
3/2
4
[
e2q + 2eqgVq
cot 2θW
sin 2θW
ŝ(ŝ − m2Z)
(ŝ − m2Z)2 + Γ2Zm2Z
+ (g2Vq + g
2
Aq)
cot2 2θW
sin2 2θW
ŝ2
(ŝ − m2Z)2 + Γ2Zm2Z
]
(13)
In the above gVq , gAq are the standard vector and axial vector coupling for the quark.
The results of our calculations are presented in Fig. 1 for H+H− production and
in Fig. 2 for the lepton case. As far as the H+H− production in γγ fusion is concerned
we differ from the results given in [4] by roughly three orders of magnitude: our γγ cross
section is far below their results and also approximately two orders of magnitude smaller
than the DY cross section. The logarithmic enhancement of the photon densities is simply
not enough to overcome completely the extra factor α2em in the γγ process. Even if the Higgs
is doubly charged (such a Higgs appears in triplet models [3]) the ratio of DY to γγ cross
section changes only by a factor 1/4 as compared to the singly charged Higgs production.
We also find that contributions from elastic, semi-elastic and inelastic processes to the total
γγ cross section are of the same order of magnitude. The elastic process contributes ∼ 20%
of the total γγ cross–section at smaller values of mH going up to 30% at the high end. This
can be traced to the logarithmic enhancement of the photon density even in the elastic case
5
mentioned earlier. Assuming the l̃L, l̃R to be degenerate in mass the cross–section for γγ
production of sleptons (for one generation) will be twice the corresponding H+H− cross–
sections.
Our results for leptons are given in Fig.2. Here again we find that at LHC energies
DY exceeds γγ by two orders of magnitude even for relatively small mL masses in the range
of 50 − 100 GeV [9]. In general the L+L− cross–sections are higher than the corresponding
H+H− cross–sections (both for γγ and DY) by about a factor of 5–7. This can be traced to
the different spin factors and the different β̂ dependence of the subprocess cross–section for
the fermions and scalars. The cross–section for the γγ production of charginos will again be
the same as that of the charged leptons.
One might think that by sacrificing rate for ‘cleanliness’ the purely elastic processes
might prove useful. Moreover, even inelastic or semi–elastic γγ events might be characterized
by “rapidity gaps”, where the only hadrons at central rapidities are due to the decay of
the heavy particles produced. However, at the LHC one expects about 16 minimum bias
events per bunch crossing at luminosity L = 1034 cm−2 sec−1; even the elastic γγ events
will therefore not be free of hadronic debris. These “overlapping events” will fill the entire
rapidity space with (mostly soft) hadrons, thereby obscuring any rapidity gap. Notice also
that in the purely elastic events the participating protons only lose about 0.1% of their
energy, making it very difficult to detect them in a forward spectrometer of the type now
being installed at HERA detectors. We are therefore forced to conclude that most likely
one will not be able to distinguish experimentally between DY and γγ events if the LHC is
operated anywhere near its design luminosity. The clean elastic events might be detectable
at luminosities well below 1033 cm−2 sec−1, where event overlap is not expected to occur.
However, our results show that at such a low luminosity one is running out of event rate at
masses not much above the limit that can be probed at LEP200; moreover, there might be
sizable backgrounds, e.g. due to the process γγ → W+W−.
At this point it might be instructive to compare the γγ cross–sections with other
6
(model dependent) possible production mechanisms for various weakly interacting charged
particles. Studies [14] have shown that search for charginos in hadronically quiet multilepton
events due to associated production of a chargino with a neutralino (via DY) at LHC might
be feasible up to mχ± ≃ 250 GeV. The detection of sleptons with mass up to ∼ 250 GeV
also seems possible [15]. Hence the DY process still seems to be the dominant mode for
production for sleptons, charginos as well as heavy leptons. For larger masses the DY cross–
section falls off and in some cases the gluon induced production (which we discuss below)
will take over.
For the charged Higgses the situation is somewhat different. The question of
DY/γγ/gg production becomes relevant in this case only for mt < mH±. If mt > mH±
the charged Higgs can be produced in the decay of the top quark and the strong production
of top quarks gives large rates allowing one to probe at LHC upto mH± ∼ mt −20 GeV [16].
Even when mt < mH± production of a single charged Higgs in association with a t quark
via the process
gb → tH− (14)
might provide a measurable signal in the decay channel
tH+ → ttb → b(bqq̄′)(blν). (15)
The cross–section is ∼ 15 pb for mH± ∼ 150 GeV and could provide a feasible signal up to
mH± ∼ 200 GeV over a wide range of parameter space, if b quarks can be tagged with high
purity and not too low efficiency [17]. Fig.1 shows that even for the DY process the charged
Higgs cross–section is only a few tens of fb or less if mH+ > mt.
Another process that contributes to the pair production of Higgs bosons and charged
leptons is one loop gluon fusion:
gg→ H+H−
gg→ L+L− (16)
7
These contributions will only be competitive with ordinary DY production if some couplings
of the produced particles grow with their mass. Accordingly the first process will be large
[18] if mt > mH+ (in which case H
+ production from t decays will have even larger rates) but
is expected to decrease for mH+ > mt. Since the coupling of chiral leptons to Higgs bosons
and longitudinal Z bosons grows with the lepton mass, graphs containing the (1–loop) ggH0∗
and ggZ0∗ couplings dominate the production of both charged [19] and neutral [20] chiral
leptons of sufficiently large mass.
In summary, we have shown that the cross section for the pair production of heavy
charged scalars or fermions via γγ fusion amounts to at best a few % of the corresponding
Drell–Yan cross section; in many cases there are additional production mechanisms with even
larger cross sections. Moreover, at the LHC overlapping events prevent one from isolating
γγ events experimentally unless the machine is run at a very low luminosity, in which case
the accessible mass window is not much larger than at LEP200. We do therefore not expect
γγ fusion processes at the LHC to be competitive with more traditional mechanisms for the
production of new particles.
While writing this note we have received a preprint [21] which treats the same subject
of γγ processes in pp colliders and gets similar results. However we differ somewhat in the
details which is most probably due to the different treatment of the photon luminosity
functions.
Acknowledgments
We thank the Department of Science and Technology (India) and the organizers of
the WHEPP-III workshop held in Madras (India) where this work was partially done. The
work of M.D. was supported by a grant from the Deutsche Forschungsgemeinschaft under
the Heisenberg program, as well as in part by the U.S. Department of Energy under contract
No. DE-AC02-76ER00881, by the Wisconsin Research Committee with funds granted by the
Wisconsin Alumni Research Foundation, and by the Texas National Research Laboratory
Commission under grant RGFY93–221. R.M.G. wishes to thank the Theory Group at PRL
8
for hospitality. M.N. wishes to thank the Alexander von Humboldt foundation for financial
support under the Feodor-Lynen fellowship program.
9
REFERENCES
[1] For a review see J.F. Gunion, H. Haber, G.L. Kane and S. Dawson, “The Higgs Hunter’s
Guide”, Addison-Wesley, Reading, MA, 1990.
[2] T.D. Lee, Phys.Rev. D8 (1973)1226; H. Georgi, Hadronic J. 1 (1978) 155
[3] J.F. Gunion, R. Vega and J. Wudka Phys. Rev. D42 (1990) 1673 and references therein.
[4] S.K. Oh et al., Z.Phys. C46 (1990)267
[5] J.L. Hewett and T.G. Rizzo, Phys.Rep. 183 (1989) 193
[6] J.L. Hewett, Phys. Rev. Lett. 70 (1993) 1045; V. Barger, M.S. Berger and R.J.N.
Phillips, Phys. Rev. Lett. 70 (1993) 1368.
[7] R. Barbieri and G.F. Guidice, Phys. Lett. B309 (1993) 86. For a detailed analysis of
the subject see: F. Borzumati, DESY 93-090.
[8] G. Bhattacharya, P.A. Kalyniak and K.A. Peterson, Carleton University preprint,
OCIP/C-93-12.
[9] On reexamination the authors of [8] agree with our conclusions for the lepton case
(private communication).
[10] E.J. Williams, Phys.Rev. 45 (1934) 729(L); C.F. Weizsäcker, Z.Phys. 88 (1934) 612.
[11] B.A. Kniehl, Phys.Lett.B254 (1991) 267.
[12] M. Drees and D. Zeppenfeld, Phys.Rev. D39 (1989) 2536.
[13] A.D. Martin, R.G. Roberts and W.J. Stirling, Phys. Lett. B306 (1993) 306; Erratum
ibid 309 (1993) 492.
[14] R. Barbieri, F. Caravaglios, M. Frigeni and M.L. Mangano, Nucl. Phys. B367 (1991)
28.
10
[15] F. del Aguila and L. Ametller, Phys. Lett. B261 (1991) 326; H. Baer, C. Chen, F. Paige
and X. Tata, Florida State Univ. preprint FSU–HEP–931104.
[16] D.P. Roy, Phys. Lett. B283 (1992) 403.
[17] V. Barger, R.J.N. Phillips and D.P. Roy, University of Wisconsin preprint
MAD/PH/790.
[18] S.S.D. Willenbrock, Phys.Rev. D35 (1987) 173.
[19] S.S.D. Willenbrock and D.A. Dicus, Phys.Lett. B156 (1985) 429.
[20] D.A. Dicus and P. Roy, Phys.Rev. D44 (1991) 1593; A. Datta and A. Pilaftsis,
Phys.Lett. B278 (1992) 162; D. Choudhury, R.M. Godbole and P. Roy, Phys.Lett.
B308 (1993) 394; erratum ibid 314 (1993) 482.
[21] J. Ohnemus, T.F. Walsh and P.M. Zerwas, DESY-preprint 93-173.
11
FIGURES
FIG. 1. Cross section in fb for DY and γγ production of the charged Higgs at LHC energies,
as a function of the Higgs mass. The dashed, dash-dotted and long-dashed lines show the el., inel.
and semi-el. contributions (as defined in the text) to the γγ cross sections. The total γγ cross
section and the DY contributions are shown by the labeled solid lines.
FIG. 2. Cross section in fb for DY and γγ production of the charged Leptons at LHC energies,
as a function of the Lepton mass. The convention is the same as in 1.
12


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$\gamma \gamma$ Processes at High Energy pp Colliders

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γγ\gamma \gamma γγ Processes at High Energy pp Colliders

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$\gamma \gamma$ Processes at High Energy pp Colliders