Luminosity measurements at the Large Hadron electron Collider (and FCC-eh) K. Piotrzkowski and M. Przybycień AGH University of Science and Technology – Kraków The beam-size effect (BSE) was discovered at the VEPP-2 collider and later observed at HERA but remained ever since an elusive and poorly studied phenomenon, despite its impact on the electron and positron beam lifetimes at LEP and KEKB, for example. At the LHeC and FCC-eh, due to very small beam-sizes, this effect will be much stronger than at HERA and its understanding is essential for a precise determination of the luminosity at these electron-hadron colliders, using bremsstrahlung. Rate = L s ? Ee E′ e Eγ Q2 Ep E′ p e + p →e’ + g + p’ unique signatures it is kinematically allowed that qg = qe’ = qp’ = 0 hence there is no transfer of transverse momentum, which results in (for LAB variables): |q|min = me2 mp Eg /(4 Ep Ee E’e), where Q2 = -q2 ≈-q2min + qT2 For example, at the LHeC, for Ee = 50 GeV, Ep = 7000 GeV and Eg = 1 GeV, one gets the minimal longitudinal momentum transfer, in the proton rest-frame, Dpz = |qmin|/c = 0.00001 eV/c. The corresponding (kinetic) energy transfer = (Dp)2/2M ≈6.10-20 eV! From the uncertainty principle Dpz corresponds to the longitudinal distance ≈ℏ/Dpz of 21 mm whereas in the transverse plane the impact parameters is often even larger, as qT is often smaller than |q|min: d4s/dEg dqedqg df ∝Q-4 Higher beam energies/lower photon energy ⇒more extreme it becomes! Beam-Size Effect – effective bremsstrahlung suppression at high energies due to small lateral beam-sizes of both colliding beams: Event rate = Luminosity × cross section where colliding particles are represented by PLANE waves – and this assumption breaks down if the lateral beam sizes are comparable to typical impact parameters of a process. Using Van der Meer scans: Longitudinal view Transverse view We proposed a novel powerful test of the BSE by measuring the bremsstrahlung spectrum while displacing transversally a hadron beam. This will be at the same time a unique direct study/demonstration of long-range nature of bremsstrahlung process – for such lateral beam displacements we predict a strong effective increase of its cross-section! BSE calculations were made following Kotkin, Serbo & Schiller, Int. J. Mod. Phys. A 7, 4707 (1992) ⇐ 3 - 10 2 - 10 1 - 10 1 y 0 0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4 /dy) BH s /dy) / (d corr s (d EIC 1 EIC 2 = 10 GeV e E 18 GeV = 275 GeV p E 275 GeV m µ = 93 x s m µ 50 m µ = 7.8 y s m µ 5 HERA = 30 GeV e E = 820 GeV p E m µ = 290 x s m µ = 77 p y s m µ = 65 e y s LHeC = 50 GeV e E = 7000 GeV p E m µ = 5 x s m µ = 5 y s At the LHeC and FCC-eh the bremsstrahlung spectrum will be strongly suppressed over the entire range of photon energies! Both the beam sizes as well as beam alignment will have to be very well controlled. https://journals.aps.org/prd/abstract/10.1103/PhysRevD.103.L051901 LHeC IR layout’22 luminometer ➝ ⤳ 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 y 0 0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4 0.45 /dy) BH s /dy) / (d corr s (d FCC-eh = 60 GeV e E = 50 TeV p E m µ = 2 x s m µ = 2 y s LHeC = 50 GeV e E = 7 TeV p E m µ = 5 x s m µ = 5 y s From paper in preparation y = Eg/Ee