Physics case of the very high energy electron–proton collider, VHEeP Allen Caldwell (MPI, Munich) Matthew Wing (UCL / DESY) • Introduction, motivation, reminder of VHEeP • Physics case of very high energy eP collisions • Total γ P cross section • Vector meson cross sections • Very low x physics and saturation British Museum • Quark substructure • Sensitivity to leptoquarks • Summary and outlook DIS 2016 Workshop — 12 April 2016, DESY Hamburg
Introduction • Much has been learnt in fixed-target DIS and HERA experiments on proton structure, diffraction, jet physics, etc.. • A high energy eP collider complements the pp programme from the LHC and a potential future e + e − linear collider. • The LHeC is a proposed eP collider with significantly higher energy and luminosity than HERA with a programme on Higgs, searches, QCD, etc.. • We want to ask, what about a very high energy eP collider ? • Plasma wakefield acceleration is a promising technology to get to higher energies over shorter distances. • Considering (e.g.) 7 TeV protons and 3 TeV electrons giving √ s ~ 9 TeV. • Driver will be the physics case: what physics can be done for such a collider ? • There is no doubt that this is a new kinematic range. • Will be able to perform standard tests of QCD. • Will be at very low x ; e.g. can we learn about saturation ? • The cross section rises rapidly to low x ; lots of data, when does the rise stop ? 2
Plasma wakefield accelerator (AWAKE scheme) Long proton beam • Long beam modulated into micro- bunches which constructively reinforce to give large wakefields. • Self-modulation instability allows current beams to be used , as in AWAKE experiment at CERN. • With high accelerating gradients, can have - Shorter colliders for same energy - Higher energy • Using the LHC beam can accelerate electrons up to 6 TeV over a reasonable distance. • We choose E e = 3 TeV as a baseline for a new collider with E P = 7 TeV ⇒ √ s = 9 TeV . - Centre of mass energy × 30 higher than HERA. A. Caldwell & K. Lotov, Phys. Plasmas 18 (2011) 103101
Plasma wakefield accelerator • Emphasis on using current infrastructure, i.e. LHC beam with minimum modifications. e • Overall layout works in powerpoint. eP • Need high gradient magnets to bend protons into the LHC ring. P P • One proton beam used for electron acceleration to then collider with other proton beam. LHC • High energies achievable and can vary electron beam energy. • What about luminosity ? • Assume • ~3000 bunches every 30 mins , gives f ~ 2 Hz . • N p ~ 4 × 10 11 , N e ~ 1 × 10 11 • σ ~ 4 µm For few × 10 7 s , have 1 pb − 1 / year of Physics case for very high energy, but running. moderate ( 10 − 100 pb − 1 ) luminosities. 4 Other schemes to increase this value ?
Physics at VHEeP • Cross sections at very low x and observation/evidence for saturation. Completely different kind of proton structure. • Measure total γ P cross section at high energies and also at many different energies; relation to cosmic-ray physics. • Vector meson production and its relation to the above. • Beyond the Standard Model physics; contact interactions, e.g. radius of quark and electron; search for leptoquarks. • Proton and photon structure, in particular e.g. F L given change in beam energy, and eA scattering. Also related to saturation and low x . • Tests of QCD, measurements of strong coupling, etc.. I.e. all usual QCD measurements can and should be done too in a new kinematic regime. • Other ideas ? 5
Total γ P cross section Total cross section, σ γ p (mb) Data VHEeP reach 1 ln 2 (W 2 ) Regge fits: DL 1992 DL 2004 -1 10 2 3 4 1 10 10 10 10 Photon-proton centre-of-mass energy, W (GeV) • Assumed same uncertainties as ZEUS measurement which used 49 nb − 1 . • Can measure at different energies with the same detector. • Can provide strong constraints on models and physics. • Related to understanding of cosmic-ray interactions. 6 • Great example of where you really gain with energy.
Vector meson cross sections σ ( γ p → Vp) (nb) Strong rise with energy related to gluon W 0.16 density at low x . 10 5 σ tot Can measure all particles within the same experiment. W 0.22 10 4 Comparison with fixed-target, HERA and ρ LHCb data—large lever in energy. W 0.22 ω At VHEeP energies, σ (J/ ψ ) > σ ( φ ) ! 10 3 W 0.80 Onset of saturation ? φ 10 2 W 1.1 J/ ψ γ ∗ J/ ψ c ¯ 10 ψ (2S) W 1.2 c k T k T Υ (1S) H1 1 ZEUS x ′ x VHEeP, √ s fixed target + new H1, LHCb data -1 10 p p 7 2 3 4 Martin et al., Phys. Lett. 1 10 10 10 10 Photon-proton centre-of-mass energy, W (GeV) B 662 (2008) 252
σ γ P at large coherence lengths Look at behaviour of σ γ P in the proton rest frame in terms of Q 2 and coherence length, l. Electron is a source of photons which is a source of partons. γ e proton Coherence length is distance over e which quark − antiquark pair can survive. Low x means long-lived photon fluctuations (not proton structure) If cross sections become same as a function of Q 2 , the photon states have had enough time to evolve into a universal size. Look at what HERA data has shown and what the potential of VHEeP is. See A. Caldwell, “The evolution of the virtual photon-proton cross section with coherence length”, WG5, 12/Apr, 9:00, arXiv:1601.04472. 8
σ γ P maths Using published HERA data, calculate F 2 from e.g. double-differential cross section: Then calculate σ γ P from F 2 : Plot σ γ P versus the coherence length, l : ≈ 9
σ γ P versus l results example Photon-Proton Cross Section 0.0063 • Consider HERA inclusive data and transform to σ γ P versus coherence length, l. 0.0052 • Example data for Q 2 = 35 GeV 2 . • σ γ P fit as ( σ 0 ⋅ l λ ) for individual Q 2 values (green). 0.0041 ✓ ◆ q • σ γ p = A exp B · log(1 /x ) · log( Q 2 /L 2 ) (red). • Very good fit of data using simple 0.003 parametrisations. • True for all Q 2 values considered. 0.0019 2 10 10
σ γ P versus l results Photon-Proton Cross Section Cross sections for all Q 2 are rising; 3.5 < Q 2 < 90 GeV 2 again luminosity not an issue, will have -1 10 huge number of events. LHeC Depending on the form, fits cross; physics does not make sense. Different forms deviate significantly from each other. -2 10 VHEeP has reach to investigate this region and different behaviour of the cross sections. VHEeP Can measure lower Q 2 , i.e. lower x and higher l. -3 10 At VHEeP Q 2 ~ 1 GeV 2 is l ~ 2 × 10 7 fm . 3 5 7 8 10 10 10 10 VHEeP will explore a region of QCD where we have no idea what is happening. 11
BSM: Quark substructure ZEUS SM a) 1.05 + -1 σ HERA NC e p 0.5 fb / σ - -1 HERA NC e p 0.4 fb Deviations of the theory from the data for 1 ZRqPDF total unc. inclusive cross sections could hint 0.95 3 4 10 10 towards quark substructure. 1 Extraction of quark radius has been done 3 4 10 10 2 2 Q (GeV ) SM b) Quark Radius 1.05 σ / 95% CL Limits σ 2 -16 2 1 R = (0.43 10 cm) ⋅ q 2 -16 2 R = -(0.47 ⋅ 10 cm) q 0.95 3 4 10 10 Generate some “data” for VHEeP and 1 look at sensitivity. 3 4 10 10 2 2 Q (GeV ) ZEUS Coll., DESY-16-035, accepted by Phys. Lett. B Assuming the electron is point-like, HERA limit is R q < 4 × 10 − 19 m Assuming the electron is point-like, VHEeP limit is R q ≾ 10 − 20 m 12
Leptoquark production Electron − proton colliders are the ideal machine to look for leptoquarks. e ± , ν e e ± s -channel resonance production LQ λ λ possible up to √ s . q q P ZEUS λ 1 L S 1/2 -1 10 -1 ± ZEUS e p (498 pb ) ± H1 e p Sensitivity depends mostly on √ s ATLAS pair prod. and VHEeP = 30 × HERA -2 10 L3 indirect limit 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 13 M (TeV) LQ ZEUS Coll., Phys. Rev. D 86 (2012) 012005
Leptoquark production at the LHC LQ q g q Can also be produced g LQ in pp singly or pair q ` ¯ production LQ q LQ1LQ1 production 1 e q) q ¯ ` ATLAS → 0.9 (LQ1 -1 s = 8 TeV, 20.3 fb Reach of LHC currently about 1 TeV , to 0.8 β 2-electrons + 2-jets increase to 2 − 3 TeV . 0.7 All limits at 95% CL Coupling dependent. 0.6 0.5 jj ν 0.4 eejj+e expected limit 0.3 observed limit 0.2 expected 1 ± σ expected 2 ± σ 0.1 -1 s = 7 TeV, 1.03 fb 0 300 400 500 600 700 800 900 1000 1100 1200 14 m [GeV] ATLAS Coll., Eur. Phys. J. C 76 (2016) 1 LQ1
Leptoquark production at VHEeP 10 3 Assumed L ~ 100 pb − 1 Required Q 2 > 10,000 GeV 2 and y > 0.1 10 2 Generated “data” and Standard Model “prediction” using ARIADNE (no LQs). 10 10 1 -3 -2 -1 10 10 10 1 1 Sensitivity up to kinematic limit, 9 TeV. -1 As expected, well beyond HERA limits 10 and significantly beyond LHC limits and potential. -2 10 2 4 6 8 15
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