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Ultra-p eripheral nuclear collisions. What we can study here
I.F. Ginzburg Sob olev Institute of Mathematics, Novosibirsk, 630090 Russia

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What are?
Standard definition: Ultra-p eripheral collisions of heavy nuclei (UPC) are interactions that o ccur at impact parameters b large enough that no hadronic interactions can o ccur. In simple terms, b > 2RA, where RA is the nuclear radius. Only electromagnetic interactions are p ossible, they can b e purely electromagnetic ("two­photon") or photo­nuclear ( A) (G. Baur et al., Hot topics in Ultra­ p eripheral ion collisions. Pro c. Workshop on Electromagnetic Prob es of Fundamental Physics, (Eriche, Sicily) World Sc. (2003) 235­242; hep-ex/0201034). In terms of observable (in principle) pro cesses Ultra-p eripheral interactions of heavy nuclei A1A2 A1A2X are those in which parental nuclei don't destroyed. The interaction of pro duced system with parental nuclei can b e either in electromagnetic or strong.
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In pp p pX the amplitude e2 =
4 (one factor e in the p vertex, the second ­ from the X ). If the energy of is and its transverse momentum q is small, this amplitude is enhanced by factor 1/q 2 with 2 2 2 q 2 = qm + q, qm = ( / )2 ( is Lorenz­factor of incident proton) This cross section can overcome strong cross section of pp ppX at /q 2 > max{1/m2 , 1/2} where is the scale of form-factor ( m for proton). The total cross section of such em pro cess is suppressed in comparison with 2 strong pro cess as (L)2 where L = log(2/qm).

UPC:

The contribution of each exchanged photon is enhanced coherently by factor Z in amplitude or Z 2 in cross section. The strong interacting cross section in the same coherent region is also enhanced by factor A4/3 for each nuclei. To prevent nuclear destruction (keep coherence), the momentum transferred by nuclei should b e small enough,
2 |q 2| 2 = 1/RA, 30 MeV .

tot U P C AA the first problem is signature of UPC.
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Signature of UPC
· Kinematical condition: The exchanged photon energy and transverse momentum are low:

q 2 < 2

q | p z | < < =

30 Â 60 M eV , 3 Â 6 GeV for RHIC Au-Au, 90 Â 180 GeV for LHC Pb-Pb.

These limits are practically identical for each mechanism of system X pro duction ­ electromagnetic and strong. · Absence of other pro duced par-

ticles and decay pro ducts of A, at least large rapidity gaps. · Quantum numb ers of pro duced system X

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Typ es of UPC
· In double UPC (2-UPC) kinematical condition hold for b oth nuclei can b e checked for the pro duced system. · In single UPC (1-UPC) kinematical condition holds for only one nuclei and other nuclei can b e destroyed, second condition can b e realized in weak form (rapidity gap).

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1-UPC
The signature is given only by quantum numb ers of pro duced system + rapidity gaps. The pro cesses are diffractive AA A A X A where X is vector meson. These exp eriments deal in fact with photopro duction on nuclei in the exp eriments with high flux of photon Z 2 d 2 2 dn = L, L = max{ ln - 1 , 0}. 2 Vector b osons cannot b e pro duced in the Pomeron-Pomeron collision in the central region. The spread of vector mesons in p is given by diffraction laws. This effect was observed by ALICE at RHIC as the pro duction of mesons in the central region in the events with large rapidity gap. One can exp ect new results here for the production mesons and J / mesons. Perhaps, at LHC one can b e see also pro duction.
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Problem for future study:
The measurement of the phase of A A amplitude to find phase of "nuclear" Pomeron in comparison with "proton Pomeron" which can b e studied at HERA. At nuclear A collisions, the interaction of separate "elementary" Pomerons joining to physical diffractive amplitude ("soft Pomeron") can b e distributed over protons and neutrons, changing overall phase for the forward scattering amplitude as compare p case Rig htar row The comparative study of these phenomena at protons and nuclei can help in the understanding of soft Pomeron. (Metho d ­ the study of charge asymmetry of pions due to interference of considered "soft Pomeron" pro duction and Primakoff pro duction AA A A ).

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2-UPC. Signature
To see 2-UPC events unambiguously at the collider with mean numb er of nuclear collisions p er bunch crossing col < 1, 3 conditions should b e checked: · Total transverse momentum ; · Longitudinal momentum - < pz < ; · Total energy 2 ; · No other particles in detector This typ e final state are separable

if all particles of system X are observed.

If some of this conditions is violated, at least one nucleus can b e broken and the decay pro ducts are directed to b eam pip e or avoid detector for some other reason. The same is valid for the events with rapidity gap(s). Coherence disapp ears, strong interactions with p ossible nuclear breaking b ecome dominant. The pro duction of e+e-, µ+µ-, P s, + - (at LHC), ... without hadrons will b e clear signal of 2-UPC with separate interesting physics.
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At RHIC col < 1, and the UPC are observable with s 6 Â 12 GeV. The clear signal of 2-UPC mechanism with double electromagnetic pro duction would b e observation of f2 with relatively small energy in c.m.s. Note that the double Pomeron exchange in pp collisions give no f2 p eak in the centre of rapidity scale. I cannot imagine other interesting problems for 2-UPC here.

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At LHC col > 1 Observation of UPC (even only with rapidity gap) lo oks very difficult. Nevertheless, I discuss this very opp ortunity. Here s 180 Â 360 GeV.

In New Physics effects total transverse momentum of pro duced system cannot b e fixed with necessary accuracy of ab out 30-60 MeV ­ either due
to low efficiency of complete observation of ALL decay pro ducts or since at least one of final particles cannot b e observed ­ , ,... ~

2-UPC mechanisms for pro duction of new states cannot b e separated from nuclear and (often) from other backgrounds.

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Example: Higgs b oson pro duction Mh 120 GeV, decay studied h b¯. b 2-UPC electromagnetic pro cess (Z1)2(Z2)2L2 h , (L 1 - 2) 3 Mh Strong 2-UPC pro cess (with accuracy to factors given by gluon structure functions) 2 h 4/3 (m2 )2 (M 2)2 (A1A2) s s p h 2 3 Mh QC D Strong incoherent pro cess, k unlimited 2/3 (m2 )2 (M 2)2 h (A1A2) s s p h M3 h Background g g b¯ for Mb¯ = Mh ± M b b M > (A1A2)2/3s(m2)4 3 p Mh 1) The separation of 2-UPC mechanism for Higgs b oson pro duction from other mechanisms lo oks hardly probable. 2) The g g b¯ background makes 2-UPC b pro duction of Higgs with b¯ decay unobservb able like for gluon fusion at Tevatron. For the h channel the 2-UPC cross section is very small for observation while purely electromagnetic background (double bremsstrahlung) is huge.
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In 2-UPC collisions at LHC one can study the exclusive V1V2 pro cesses (Vi ­ vector mesons) in diffractive kinematics up to s 200 GeV.

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