# The LHC as a photon collider

### Eugenio Scapparone

**1 Introduction**

LHC is a powerful, flexible and complex machine; it delivers an impressive luminosity independent of the energy at which it runs and of the type of hadrons circulating in its pipes. World records at CERN largest ring do not hold for long: the LHC itself continuously updates them. The LHC experiments have been analyzing a huge amount of data, collected in proton-proton, proton-ion and ion-ion hadronic interactions, but that is not the end of the story. At TeV energies, hadrons circulating in the machine produce a remarkable number of photons, reaching an energy up to several hundreds of GeV: the LHC is therefore a powerful source of high-energy light too.

After drilling a hole in the upper left-hand corner of the plaster door of Tutankhamun’s tomb, the first thing the archeologist Howard Carter did was to insert a candle and peer into the darkness, looking on with amazement. For a physicist working at the world’s largest hadron accelerator, having a rich source of photons is as valuable as it was for Carter at the Valley of the Kings. The nature of the photon source used at the LHC is, however, quite different from that of a normal candle.

The electromagnetic field observed some distance away from a moving charged particle cannot be distinguished from that of an equivalent flux of photons – this was realized by Enrico Fermi at about the same time as Tutankhamun’s tomb was discovered (1923-24). About ten years later, Weizsacker and Williams extended Fermi’s method to the ultra-relativistic case.

When two hadrons or nuclei pass by each other at the LHC at a distance which is larger than the sum of their two radii, no hadronic interactions will occur, but their electromagnetic field will produce an intense pulse of photons on the beam particle moving in the opposite direction. These interactions are called Ultra Peripheral Collisions (UPC), a domain where photons shed light almost undisturbed on hadrons.

At the LHC, p-p, p-Pb, and Pb-Pb collisions offer the opportunity to illuminate nucleons and heavy nuclei. The number of photons in the field is proportional to $Z^{2}$ ($Z$ being the charge of the projectile) making heavy ions particularly good photon sources. The transverse momentum of the photons is restricted to $ \hbar /R$, whereas the longitudinal momentum is enhanced by the Lorentz factor γ. The latter property, together with the extremely high beam energies, makes LHC the world’s highest-energy photon collider. Photon-induced interactions have been studied by most of the LHC experiments. What did we learn so far?

**2 Vector meson production in nucleus-nucleus collisions**

The first analyses on vector meson photo-production in relativistic heavy-ion collisions date back to STAR and PHENIX: these collaborations studied ρ and J /ψ photo-production in ultra-peripheral Au-Au collisions at $ \sqrt{s_{\mathrm{NN}}} = 200$ GeV. Although RHIC studies have demonstrated the feasibility of these measurements, it was not possible to significantly constrain the nuclear gluon PDFs. The J/ψ analysis was statistically limited, while in UPC-produced ρ, a hard scale cannot be established to perform perturbative QCD calculations.

In fact in photo-production events, the hard scale Q^{2} is set by the particle mass, Q^{2} ~ M^{2} and
therefore the production of J/ψ, ψ(2σ) and ϒ is much more attractive, since it can be treated
perturbatively. Unfortunately heavy vector meson photo-production cross section is quite
small (as an example, the UPC J/ψ cross section is less than 1 mb at RHIC in Au-Au collisions
at $ \sqrt{s_{NN}} = 200$ GeV); it increases with the centre-of-mass energy, so that LHC offers better
opportunities to study these mesons.

The ALICE and the CMS collaborations have studied exclusive photo-production of J/ψ mesons in Pb-Pb collisions at $ \sqrt{s_{\mathrm{NN}}} = 2.76$ TeV. The photon spends part of its time as a virtual q-$\bar{\mathrm{q}}$ pair (fig. 1, left) preserving the spin of the photon ($J =1$). The interaction of the pair with the nuclear field, through the colourless exchange of two (or more) gluons, may produce a real vector meson. The events considered here are characterized by a single J /ψ meson (reconstructed through its di-muon or di-electron decay) but no other particles being produced, giving an event with two tracks in an otherwise empty detector: figure 2 shows a J /ψ candidate in ALICE produced in a hadronic event (left) and a UPC J/ψ candidate (rigth). At leading order, the cross section of this process is proportional to the nuclear gluon distribution function squared, as computed by Ryskin:

(1) $ \frac{\mathrm{d}\sigma}{\mathrm{d} t} (\gamma^{*} p \rightarrow \psi p)|_{0} = \frac{\Gamma_{ee} M_{\psi}^{3} \pi^{3}}{48\alpha} \frac{\alpha_{S} ( \bar{Q}^{2} )^{2}}{\bar{Q}^{8}} [ xg ( x,\bar{Q}^{2} ) ]^{2} ( 1+ \frac{Q^{2}}{M_{\psi}^{2}} ) $ .

J/ψ produced at a given rapidity y is sensitive to the gluon distribution at Bjorken-*x*,
$ x = (M_{J/\Psi} /\sqrt{s} ) \cdot e^{\pm y}$, at a hard scale $Q^{2} \sim M^{2}_{J/\Psi} /4 $. The relevant values of $x$ that can be explored at
the LHC are in the 10^{–2} to 10^{–5} range, a region where the nuclear gluon PDF are poorly known:
that is why the study of J/ψ photo-production in Pb-Pb
collisions is a very important measurement.

The exclusive photo-production can be either coherent,
where the photon couples coherently to almost all the
nucleons, or incoherent, where the photon couples to a
single nucleon. Coherent production is characterized by low
transverse momentum of vector mesons (〈 p_{T} 〉 ~ 60 MeV/*c*)
where the nucleus normally does not break up by the J /ψ
production.

However the exchange of additional photons may lead to
the nucleus break-up, estimated by the simulation models
at the level of 20-30% of the events. Incoherent production,
corresponding to quasi-elastic scattering off a single nucleon,
is characterized by a somewhat higher transverse momentum
(〈 p_{T} 〉 ~ 500 MeV/c).

ALICE performed an analysis selecting di-muon events
at forward rapidity, using the muon spectrometer and
another analysis at mid rapidity using both the $\mu^{+} \mu^{-}$ and
$e^{+} e^{-} J/ \Psi$ decay channels. The J/ψ’s selected in the first
analysis correspond to Bjorken-*x* ~10^{–2}, while those selected
in the second one to *x* ~10^{–3}. At mid rapidity the events were
triggered by the coincidence of the Silicon Pixel detector
and the Time of Flight detector, while the forward plastic
scintillator detector (VZERO) was used as a veto, to reject
hadronic events. The obtained coherent cross sections for
the process Pb+Pb → J/ψ+Pb+Pb were 1.00 ± 0.18 (stat)
${}^{+0.24}_{-0.26}$ (syst) mb at $–3.6 < y < –2.6$ and $2.38^{+0.34}_{-0.24}$ (stat+syst) mb at
$–0.9 < y < 0.9$ (fig. 3).

These results clearly showed the nuclear gluon structure
function at *x* ~10^{–2}–10^{–3} and Q^{2} ~ 2.2 GeV2/*c*^{2} is below
that expected by a simple superposition of the proton
and neutron structure functions. This is the so-called
“impulse approximation”, where the q-$\bar{\mathrm{q}}$ pair interacts
with the gluons radiated by just a single nucleon of the
Pb nucleus with a probability enhanced by a factor *A*. The
impulse approximation prediction uses data from exclusive
J/ψ photo-production in γ-p interactions to estimate the
coherent J/ψ cross section in γ-Pb collisions. By using γ-p
data, the impulse approximation calculation neglects all
nuclear effects such as the expected modification of the
gluon density in the lead nuclei compared to that of the
proton.

The CMS measurement, obtained at $1.8 < |y| < 2.3$ nicely complements the ALICE data, collected at $–0.9 < y < 0.9$ and –3.6 < y < –2.6, allowing to investigate a different Bjorken-x region. CMS candidates were triggered requiring an energy deposit consistent with at least one neutron in either of the ZDCs; low signal in at least one of the beam scintillator counters (BSC); the presence of at least one single muon, and at least one track in the pixel detector. These results confirmed the evidence that the nuclear gluon density is below that expected for a simple superposition of protons and neutrons in the nucleus.

Considering both the ALICE and the CMS results, the impulse approximation over-predicts the ALICE and CMS J /ψ UPC cross section by more than 5σ (fig. 3).

According to these results, the gluon field of each nucleon is therefore screened by the presence of the other nucleon fields. This effect is usually named “gluon shadowing” and it is quantified by the ratio

(2) $ R ( x,Q^{2} ) = G_{N} ( x,Q^{2} ) / ( A \cdot G_{n} ( x,Q^{2} ) ) ,$

where $G_{N} ( x,Q^{2} )$ represents the nuclear gluon PDF and $G_{n} ( x,Q^{2} )$ are the nucleon gluon PDF.

Data show a good agreement with the prediction of
the “leading twist approximation” model, developed by
V. Guzey, M. Strikman and M. Zhalov. This is a calculation
at the partonic level that uses a diffractive proton PDF as an
input and implements a gluon recombination mechanism.
It is based on the combination of the generalization of
the Gribov-Glauber theory with the QCD factorization
theorem, resulting in an effective nuclear gluon shadowing.
The theoretical uncertainty band for the leading twist
approximation result, shown in fig. 3, is ~12% and is due to
the uncertainty in the strength of the gluon recombination
mechanism. This uncertainty is uncorrelated with the photon
flux uncertainty (about 5%). This model foresees a gluon
shadowing $R ( x,Q^{2} ) $ of about 50% at Bjorken-*x* ~10^{−3}.

The ultra-peripheral collisions studies performed at the LHC provided the first direct evidence for nuclear gluon shadowing. Nevertheless the use of these measurements to constrain the gluon shadowing is not trivial.

As an example a NLO prediction (used in most of the PDF
fit analyses) for this cross section is not available yet. A first
attempt to extract $R ( x,Q^{2} )$ from these data was made by
Guzey *et al.* obtaining $R ( x,Q^{2} ) = 0.61^{+0.05}_{-0.04} $.

Recently ALICE presented at the Quark Matter 2017
conference a new analysis based on the 2015 Pb-Pb run
data collected at $\sqrt{s_{NN}} = 5.02$ TeV. The results show a good agreement with models predicting a gluon shadowing
compatible with that predicted by Guzey *et al.* (2014).

**3 Vector meson production in pp and p-A collisions**

The process e+p → e+p+J/ψ was studied in detail at
HERA. As a result the cross section of the process γ+p → J/
ψ+p as a function of the photon-proton centre-of-mass
energy ($W_{\gamma p}$) was found to grow as a power law. The fit to a
power law, $\sigma \propto W_{\gamma p}^{\delta} $, in the range $ 20 < W_{\gamma p} < 300$ GeV, gave
δ = 0.69 ± 0.02 (stat) ± 0.03 (syst) (ZEUS) and δ =0.67 ±
0.03 (stat+syst) (H1). The growth of the cross section was
interpreted by pQCD-inspired models as an increase of the
gluon density approaching smaller Bjorken-*x*.

ALICE studied the J/ψ photo-production up to $W_{\gamma p} \sim 700$ GeV, using p-Pb data collected at $\sqrt{s_{NN}}=5.02 $ TeV. In this case the Pb nucleus acts as photon emitter in more than 95% of the events. This allows to give an unambiguous determination of the event rapidity y and therefore of $W_{\gamma p}$. During the 2013 p-Pb run, the beam direction was reversed, allowing the study of two different rapidity ranges.

The obtained cross section was σ(p+Pb → J /ψ+p+Pb)= 6.42 ± 0.43 (stat) ± 0.61 (syst) μb at 2.5 < y < 4 and
σ (p+Pb → J/ψ+p+Pb) = 2.46 ± 0.31 (stat)${}^{+0.24}_{-0.28}$ (syst) μb at
−3.6 < y < −2.6. The above cross section is related to the
photon-proton cross section γ +p → J/ψ+p through the
photon flux, d*n*/d*k*, where *k* is the photon energy, which is
determined by the J/ψ mass and rapidity,

(3) $ k= 1/2 M_{J/\Psi} e^{-y} .$

Figure 4 shows the cross section measured by the ALICE muon spectrometer at four different $W_{\gamma p}$. Two calculations are available from the JMRT model: the first one referred to as LO is based on a power law description of the process, while the second model is labeled as NLO, and includes contributions which mimic effects expected from the dominant NLO corrections. Because both JMRT models have been fitted to the same data, the resulting energy dependences are very similar. ALICE data support their extracted gluon distribution up to $x \sim 2\cdot 10^{-5}$. The STARLIGHT parameterization is based on a power law fit using only fixed-target and HERA data, giving δ = 0.65±0.02.

Figure 4 shows predictions from the b-Sat eikonalized model which uses the Color Glass Condensate approach to incorporate saturation, constrained to HERA data alone. Comparisons to STARLIGHT and the b-Sat (1-pomeron) models are also shown.

The results from the models mentioned above are within one sigma of our measurement. The b-Sat (1-pomeron) prediction also agrees with the ALICE low-energy data points, but it is about 4σ above ALICE measurement at the highest energy. ALICE data are successfully fitted to a power law giving δ =0.68 ± 0.06 (stat+syst) in good agreement with the results found at HERA. This result shows that there is no change of the cross section behaviour, within the errors, between the HERA and the LHC energies.

J/ψ and ψ (2s) production in ultra-peripheral collisions was studied by LHCb in pp collisions
at $\sqrt{s}= 7$ TeV. Identical hadron interactions do not allow to distinguish which one of
the two hadrons emitted the photon and therefore an ambiguity on the rapidity is present:
as a consequence each event has two possible $W_{\gamma p}$ solutions. In this case extracting the
γ +p → J/ψ +p cross section from the measured p+p → J/ψ +p+p measured cross section is not
trivial. The analysis required 2 tracks in an otherwise empty detector. Invariant-mass distribution
showed clear J/ψ and ψ (2s) peaks. After correcting for acceptance and efficiency, the 0.93 pb^{−1}
integrated luminosity gave a cross section in the pseudorapidity interval 2.0 < η <4.5,
σ(p+p → J/ψ +p+p) = 291 ± 7 (stat) ± 19 (syst) pb and σ (p+p → ψ (2s) +p+p)=6.5 ± 0.9 (stat) ±
0.4 (syst) pb. The extraction of the γ+p → V+p (V = J/ψ, ψ, (2s) or ϒ) cross section was obtained by
using a power law to connect the two cross sections:

(4) $ \frac{\mathrm{d} \sigma ( p+p \rightarrow V+p+p ) }{\mathrm{d} y} = S^{2} ( W_{+} ) ( k_{+} \frac{\mathrm{d} n}{\mathrm{d}k_{+}} ) \sigma^{\mathrm{th}}_{+} ( \gamma p ) + S^{2} ( W_{-} ) ( k_{-} \frac{\mathrm{d} n}{\mathrm{d}k_{-}} ) \sigma^{\mathrm{th}}_{-} ( \gamma p ) $

where *S* is the gap survival probability, *k* is the photon energy, *k* d*n*/d*k* is the photon flux and
σ^{th} ± (γp) are the cross sections of the process γ+p → J/ψ+p corresponding to the two different
$W_{\gamma p}$ solutions. *S* is the probability that no other processes in
the event may affect the existence of the gap in the particle
distribution. In fact, besides the quark-antiquark pair, the
other spectator partons might participate in the interaction,
and destroy the rapidity gap (s) in the final state, for instance
by exchanging gluons with the partons of the other hadron.
This quantity has not been measured experimentally at the
LHC. One has therefore to rely on Monte Carlo simulation.
According to the eikonal model, it depends on the vector
meson mass, rapidity and center-of-mass energy. As far as
ψ (2s)(J/ψ) is concerned, at $\sqrt{s} =7 $ TeV, $S^{2} ( W^{+} )$ ranges from
~0.81 (~0.87) at y ~2 and ~0.47 (~0.68) at $y \sim 4.5$.

Models including saturation reproduce within the error the J/ψ and ψ (2s) cross section measured by LHCb as a function of the rapidity. Comparing the ALICE and LHCb results shows that the cross sections measured by LHCb at different $W_{\gamma p}$ agree within the error with the ALICE fit quoted above.

At a first look the interpretation of these results might
appear a bit confused: experimentally the LHC data show
no deviation from the HERA behavior, where the power law
growth of the cross section was explained as an increase
of the gluon density at smaller Bjorken-*x*, *i.e.* no smoking
gun for gluon saturation. On the other hand, few models
including gluon saturation reproduce the experimental data.
Implementing the gluon saturation in model predictions is
not a unique procedure: according to few authors, the gluon
saturation could be a slow process, whose effect grows very
smoothly as a function of *1/x*: LHC energies could not be high
enough to see remarkable effects with respect to lower-energy data. Indeed HERA data can be reproduced by few
models, that are based on gluon saturation as IP-Sat
or on the Colour Glass Condensate, as b-CGC.

**4 Photon-photon collisions**

Two-photon production of $e^{+}e^{–}$ pairs has a topology similar to that of exclusive vector mesons production followed by decay into a pair of di-leptons (fig. 1, right). This process is of interest since the coupling between the photon and the emitting nucleus is enhanced by a factor $Z$ (the nuclear charge), allowing to probe Quantum Electrodynamics in the regime of strong fields. The coupling $Z \sqrt{\alpha _{em}}$ is large, so higher-order terms may become important. It is therefore interesting to compare the experimental results with a Monte Carlo code, as STARLIGHT, implementing just the QE D at leading order for this process.

ALICE measured the cross section for di-electron
invariant mass for a rapidity in the interval |y|< 0.9 in a
wide range, outside the ρ and the J/ψ peaks. The data with
2.2 < *M*_{inv} < 2.6 GeV/ c^{2} (3.7< *M*_{inv} <10 GeV/c^{2}) gave a cross
section σ=154 ± 11 (stat) ${}^{+17}_{-11}$ (syst) μb (σ = 91±10 (stat) ${}^{+0.7}_{-0.01}$ (syst)
μb), to be compared with σ =128 μb and σ =77 μb predicted
by STARLIGHT. At lower invariant mass, the measured
cross section for the selection 0.6 < *M*_{inv} < 2.0 GeV/c^{2} and
|η_{1,2}| < 0.9 (1,2 are the pseudo-rapidities of the two tracks) is
σ =9.8± 0.6 (stat)${}^{+0.9}_{-1.2}$ (syst) mb. The STARLIGHT prediction for
the same selection is σ = 9.7 mb.

The measured values of the cross sections in the first two
invariant-mass intervals are 20% above, but compatible
within 1.0 and 1.5 σ with the STARLIGHT prediction, if the
statistical and systematic errors are added in quadrature.
At lower invariant mass (0.5 < *M*_{inv} < 2.0 GeV/*c*^{2}) the
agreement is quite good. ATLAS measured the di-muon
events in ultra-peripheral collisions with 10 < *M*_{inv} < 100.0
GeV/c^{2}. The analysis (fig. 5) is based on a single-muon
trigger with veto of additional activity in the detector. The
Level-1 required at least one track in the muon spectrometer
and less than 50 GeV of transverse energy in the calorimeters.
The High Level trigger (HLT) level rejected events with more
than one hit in the forward scintillators and required an inner
detector track with transverse momentum $p_{T}$ above 400 MeV.
This gives σ (Pb + Pb → Pb + Pb +μ^{+} + μ^{–} ) = 32.2 ± 0.3
(stat) ${}^{+4.0}_{-3.4}$ (syst) μb. The STARLIGHT predicted cross section
is 31.64 ± 0.04 (stat) μb, well within the experimental
uncertainties.

In summary predictions are in good agreement with the
measured cross-sections across a wide invariant-mass range
exceeding two orders of magnitude (from 0.6 GeV/*c*^{2} to
100 GeV/*c*^{2} ), suggesting that the nuclear electromagnetic
fields are reasonably described by the nuclear form factor
and photon fluxes used in the calculation. The above results
provide constraints on calculations that include terms of
higher orders in $\alpha_{em}$, predicting a cross section up to 30%
lower.

UPC photon-photon collisions offer the possibility to search
for physics beyond the standard model. CMS has studied
interactions where two photons annihilate upon p-p collision
to produce of W^{+}W^{–} pairs, implying four particles at the same
vertex in a Feynman diagram. Using a luminosity 5.05 fb^{–1}
collected in pp interactions at $\sqrt{s} =7$ TeV, two signal events
were observed, consistent with standard model expectations:
the result sets competitive limits on the anomalous quartic
gamma-W couplings. More stringent limits (or maybe
evidence for new physics) will be provided by the new CMSTOTEM
CT-PPS detector.

Photons produced by the huge electromagnetic field
of relativistic ions circulating in the LHC pipe can interact
each through the process γγ → γγ (light-by-light scattering).
The last LHC Pb-Pb run delivered enough luminosity to study
this rare channel. This scattering is mediated by a loop (fig. 6)
of SM particles (q, l, W). As proposed by D'Enterria and Silveira, exotic particles
could also give a contribution to the total cross section.
Finding an excess of γγ → γγ events therefore would be a
hint of new physics. Possible backgrounds can arise from
misidentified electrons from the QE D process γγ → e^{+}e^{-},
as well as from the central exclusive production of two
photons from the fusion of two gluons (gg → γγ). The ATLAS
experiment has conducted a preliminary search for light-bylight-scattering in 480 μb^{–1} of Pb-Pb data collected at $\sqrt{s_{NN}} =5.02$ TeV during the 2015 heavy-ion run. While almost
four billion strongly interacting events were provided by the
LHC, only 13 di-photon candidates were observed.

After background subtraction and analysis corrections, the cross section γγ → γγ process for photon transverse energy $E_{T} > 3$ GeV, photon pseudo-rapidity |η| < 2:4, di-photon invariant mass larger than 6 GeV, di-photon transverse energy lower than 2 GeV and di-photon acoplanarity below 0.01, was measured to be 70 ± 20 (stat) ± 17 (syst) nb, in agreement with the SM prediction of 49 ± 10 nb.

**5 Conclusions**

The UPC physics will benefit from the LHC luminosity
increase in the next years: the ϒ vector meson cross
section measurement will allow to study the nuclear gluon
shadowing at larger $Q^{2}$, where the pQCD-inspired theoretical
model provides higher precision cross section predictions. In
addition high statistics measurement of the J /ψ production
will allow to study the UPC J/ψ cross section as a function
of |t|: gluon saturation signature is expected to manifest
with the presence of a pronounced dip (or multiple dips) at
relatively large $ |t| $ (1–3 GeV^{2}).

As discussed above, the γ+p → J/ψ +p cross section is still growing with the photon-proton centre-of-mass energy at the LHC. Nevertheless we expect that the rise of the gluon PDF at low x should be tamed to avoid cross section divergence, by mechanisms as gluon recombination. Is the nuclear gluon shadowing observed in ultra-peripheral Pb-Pb interactions a manifestation of gluon saturation in the nucleus?

The LHC experiments showed clearly that the gluon field
in the nucleus at low Bjorken-*x* and at Q^{2} ~ 2.2 GeV/c^{2} is not
a simple superposition of that of the single nucleons. On the
other hand, a precise quantification of the effect and an
explanation of its origin is not available yet.

A new machine is now under consideration in USA: the Electron Ion Collider (EI C) is a facility with a versatile range of kinematics, beam polarization, high luminosity and beam energy designed to improve our understanding of QCD phenomena. The broad physics program spans from spin physics with polarized proton beams to 3D tomography of the gluons and sea quark in the nucleus, and includes a comprehensive electron–heavy-ion interaction program to explore gluon saturation and test the Colour Gluon Condensate model.

EIC would be a powerful tool to address a systematic study
of the nuclear gluon shadowing signals observed at the LHC,
taking advantage of an expected luminosity 10^{33–34} cm^{–2} s^{–1}
and a centre-of-mass energy $\sqrt{s_{NN}}$ = 30-140 GeV. While in
photo-production events the $Q^{2}$ is set by the mass of the
produced vector meson, this new machine will allow to
tune the $x$, $Q^{2}$ working point, covering a wide region to
understand the nuclear gluon shadowing and its mechanism
down to $x \sim 10^{–5}$.