arXiv:0706.3356v2 [nucl-ex] 25 Jun 2007
The Physics of Ultraperipheral Collisions at the
LHC
Editors and Conveners: K. Hencken
7,8
, M. Strikman
18
,
R. Vogt
11,19,20
, P. Yepes
22
Contributors: A. J. Baltz
1
, G. Baur
2
, D. d’Enterria
3
,
L. Frankfurt
4
, F. Gelis
5
, V. Guzey
6
, K. Hencken
7,8
,
Yu. Kharlov
9
, M. Klasen
10
, S. R. Klein
11
, V. Nikulin
12
,
J. Nystrand
13
, I. A. Pshenichnov
14,15
, S. Sadovsky
9
,
E. Scapparone
16
, J. Seger
17
, M. Strikman
18
, M. Tverskoy
12
,
R. Vogt
11,19,20
, S. N. White
1
, U. A. Wiedemann
21
, P. Yepes
22
,
M. Zhalov
12
1
Physics Department, Brookhaven National Laboratory, Upton, NY, USA
2
Institut fuer Kernphysik, For schungszentrum Juelich, Juelich, Ger many
3
Experimental Physics Division, CERN, Geneva, Switzerland
4
Nuclear Physics Department, Tel Aviv University, Tel Aviv, Israel
5
CEA/DSM/SPhT, Saclay, France
6
Institut f ¨ur Theoretische Physik II, Ruhr-Universit¨at Bochum, Bochum, Germany
7
Unive rsity of Basel, Basel, Switzerland
8
ABB Corporate Research, Baden-Daettwil, Switzerland
9
Institute for High Energy Physics, Pr otvino, Russia
10
Laboratoire de Physique Subatomique et de Cosmologie, Universit´e Joseph
Fourier/CNRS-IN2P3, Grenoble, France
11
Nuclear Science Division, Lawrence Berkeley National Laboratory, Berkeley, USA
12
Petersburg Nuclear Physics Institute, Gatchina, Russia
13
Department of Physics and Technology, University of Bergen, Bergen, Norway
14
Frankfurt Institute for Advanced Studies, Frankfurt am Main, Germany
15
Institute for Nuclear Resear ch, Russian Academy of Sciences, Moscow, Russia
16
INFN, Sezione di Bologna, Bologna, Italy
17
Physics Department, Creighton University, Omaha, NE, USA
18
Physics Department, Pennsylvania State Unive rsity, State Co llege, PA, USA
19
Physics Department, Unive rsity of California at Davis, Davis, CA, USA
20
Lawrence Livermore National Laboratory, Livermore, CA, USA
21
Theory Division, CERN, Geneva, Switzerland
22
Physics and Astronomy Department, Rice University, Houston, TX, USA
Abstract. We discuss the physics of large impact parameter interactions at the
LHC: ultraperipheral collisions (UPCs). The dominant pro ces ses in UPCs are photon-
nucleon (nucleus) interactions. The current LHC detector config urations can explore
small x hard phenomena with nuclei a nd nucleons at photon-nucleon center-of-mass
energies above 1 TeV, extending the x rang e of HERA by a factor of ten. In particular,
it will be possible to probe diffractive and inclusive parton densities in nuclei using
several processes. The interaction of small dipoles with protons and nuclei can be
investigated in elastic and quasi-elastic J/ψ and Υ production as well as in high t ρ
0
production accompanied by a rapidity gap. Several of these phenomena provide clean
signatures of the onset of the new high gluon density QCD regime. The LHC is in
the kinematic range where nonlinear effects are several times larger tha n at HERA.
Two-photon processes in UPCs are also studied. In addition, while UPCs play a role
in limiting the maximum beam luminos ity, they can also be used a luminosity monitor
by measur ing mutual electromag netic dissociation of the beam nuclei. We also review
similar studies at HERA and RHIC as well as describe the potential use of the LHC
detectors for UPC measurements.
2
1. Introduction
Contributed by: K. Hencken, M. Strikman, R. Vogt and P. Yepes
In 1924 Enrico Fermi, 23 at the time, proposed the equivalent photon method [1]
which treated the moving electromagnetic fields of a charg ed particle as a flux of virtual
photons. A decade later, Weizs¨acker and Williams applied the method [2] to relativistic
ions. Ultraperipheral collisions, UPCs, are those reactions in which two ions interact via
their cloud of virtual photons. The intensity of the electromagnetic field, and therefore
the number of photons in the cloud surrounding the nucleus, is proportional to Z
2
. Thus
these types of interactions are highly favo r ed when heavy ions collide. Figure 1 shows
a schematic view of an ultraperipher al heavy-ion collision. The pancake shape of the
nuclei is due to Lorentz contraction.
b>R +R
Z
Z
A B
Figure 1. Schematic diagram of an ultraperipheral c ollision of two ions. The impact
parameter, b, is larger than the sum of the two radii, R
A
+R
B
. Reprinted from Ref. [3]
with permission from Elsevie r.
Ultraperipheral photon-photon collisions are interactions where the radiated
photons interact with each other. In addition, photonuclear collisions, where one
radiated photon interacts with a constituent of the other nucleus, are also p ossible.
The two processes are illustrated in Fig . 2 (a) and (b). In these diagrams the nucleus
that emits the photon remains intact after the collision. However, it is possible to have
an ultraperipheral interaction in which one or both nuclei break up. The breakup may
occur through the exchange of an additional photon, as illustrated in Fig. 2(c).
In calculations of ultraperipheral AB collisions, t he impact parameter is usually
required to be larger than the sum of the two nuclear radii, b > R
A
+ R
B
. Strictly
speaking, an ultraperipheral electromagnetic interaction could occur simultaneously
with a hadro nic collision. However, since it is not possible to separate the hadronic and
electromagnetic components in such collisions, the hadronic components are excluded
by the impact parameter cut.
1
B
A
γ
B
A
X
(a)
B
A
γ
A
X
(b)
B
A
γ
A’
X
(c)
γ
Figure 2. A schematic view of (a) an electromagnetic interaction where photons
emitted by the ions interact with each other, (b) a photon-nuclear reaction in which a
photon emitted by an ion interacts with the other nucleus, (c) photonuclear reaction
with nuclear breakup due to photon exchange.
Photons emitted by ions a re coherently radiated by the whole nucleus, imp osing
a limit on the minimum photon wavelength of greater than the nuclear radius. In
the transverse plane, where there is no Lorentz contraction, the uncertainty principle
sets an upper limit on the transverse momentum of the photon emitted by ion A of
p
T
<
∼
¯hc/R
A
≈ 28 (330) MeV/c for Pb (p) beams. In the longitudinal direction, the
maximum possible momentum is multiplied by a Lorentz factor, γ
L
, due to the Lorentz
contraction of the ions in t hat direction: k
<
∼
¯hcγ
L
/R
A
. Therefore the maximum γγ
collision energy in a symmetric AA collision is 2¯hcγ
L
/R
A
, about 6 GeV at the Relativistic
Heavy Ion Collider (R HIC) and 200 GeV at the Large Hadron Collider (LHC).
The cross section for two-photon processes is [4]
σ
X
=
Z
dk
1
dk
2
dL
γγ
dk
1
dk
2
σ
γγ
X
(k
1
, k
2
) , (1)
where σ
γγ
X
(k
1
, k
2
) is the two-photon production cross section o f final state X and
dL
γγ
/dk
1
dk
2
is the two-photon luminosity,
dL
γγ
dk
1
dk
2
=
Z
b>R
A
Z
r>R
A
d
2
bd
2
r
d
3
N
γ
dk
1
d
2
b
d
3
N
γ
dk
2
d
2
r
, (2)
where d
3
N
γ
/dkd
2
r is the photon flux from a charge Z nucleus at a distance r. The
two-photon cross section can a lso be written in terms of the two-photon center-of-mass
energy, W
γγ
=
√
s
γγ
=
√
4k
1
k
2
by introducing the delta function δ(s
γγ
− 4k
1
k
2
) to
integrate over k
1
and changing the integration variable from k
2
to W
γγ
so that
σ
X
=
Z
dL
γγ
dW
γγ
W
γγ
σ
γγ
X
(W
γγ
) . (3)
(Note that we use W and
√
s for the center-of-mass energy interchangeably throughout
the text.
The two-photon luminosity in Eq. (2) can be multiplied by the io n-ion luminosity,
L
AA
, yielding an effective two-photon luminosity, dL
eff
γγ
/dW
γγ
, which can be directly
compared to two-photon luminosities at other facilities such as e
+
e
−
or pp colliders [5].
2
Figure 3 shows the two-photo n effective luminosities for various ion species and protons
as a f unction of W
γγ
for the LHC (left) and for RHIC (right) [3]. Note the difference
in energy scales between the LHC and RHIC. The ion collider luminosities are also
compared to the γγ luminosity at LEP II. The LHC will have significant energy and
luminosity r each beyond LEP II and could be a bridge to γγ collisions at a future linear
e
+
e
−
collider. Indeed, the LHC two-photon luminosities for light ion beams are higher
than available elsewhere for energies up to W
γγ
≈ 500 GeV/c
2
.
10
23
10
24
10
25
10
26
10
27
10
28
10
29
10
30
10
31
100 200 300 400
Pb+Pb
Ar+Ar
p p
e
+
e
–
W
γγ
[GeV/c
2
]
L
AA
dL
γγ
/dW
γγ
[cm
–2
s
–1
GeV
–1
]
10
24
10
25
10
26
10
27
10
28
10
29
10
30
10
31
5 10 15
Au+Au
Cu+Cu
p p
e
+
e
–
W
γγ
[GeV/c
2
]
L
AA
dL
γγ
/dW
γγ
[cm
–2
s
–1
GeV
–1
]
Figure 3. Effective γγ luminosity at LHC (left) and RHIC (right) for different ion
sp e c ie s and protons a s well as at LEP II. In pp and e
+
e
−
collisions, L
AA
corresponds
to the pp or e
+
e
−
luminosity. Reprinted from Ref. [3] with permission from Elsevier.
The photoproduction cross section can also be factorized into the product of the
photonuclear cross section and the photon flux, dN
γ
/dk,
σ
X
=
Z
dk
dN
γ
dk
σ
γ
X
(k) , (4)
where σ
γ
X
(k) is the photonuclear cross section.
The photon flux used to calculate the two- photo n luminosity in Eq. (2) and the
photoproduction cross section in Eq. (4) is given by t he Weizs¨acker-Williams method
[8]. The flux is evaluated in impact parameter space, as is appropriate for heavy-ion
interactions [9, 10]. The flux at distance r away from a charge Z nucleus is
d
3
N
γ
dkd
2
r
=
Z
2
αw
2
π
2
kr
2
"
K
2
1
(w) +
1
γ
2
L
K
2
0
(w)
#
(5)
where w = kr/γ
L
and K
0
(w) and K
1
(w) are modified Bessel functions. The photon flux
decreases exponentially above a cutoff energy determined by the size of the nucleus. In
the laboratory frame, the cutoff is k
max
≈ γ
L
¯hc/R
A
. In the rest frame of the target
nucleus, the cutoff is boosted to E
max
= (2γ
2
L
− 1)¯hc/R
A
, about 500 GeV at RHIC and
1 PeV (1000 TeV) at the LHC. The photon flux for heavy ions at RHIC and the LHC
3
![Figure 51. The same as Fig. 50 at −t = 5 GeV2 [93].](/figures/figure-51-the-same-as-fig-50-at-t-5-gev2-93-1mrsgfqi.webp)
![Figure 26. The J/ψ t distribution in pPb UPCs. Reprinted from Ref. [118] with permission from Elsevier.](/figures/figure-26-the-j-ps-t-distribution-in-ppb-upcs-reprinted-from-23f4p422.webp)
