The LHC Inverse Problem :

1. The LHC Inverse Problem: Some Thoughts SreerupRaychaudhuri Tata Institute of Fundamental Research Mumbai

2. Plan of the Talk • Definition of the problem • Attempts at a general solution • Arkani-Hamed et al, JHEP 0608:070 (2006) • Berger et al, arXiv:0711.1374 (2007) • Critique of general methods • Criteria for model discrimination • Some specific instances • Higgs boson signals • missing energy signals • pairs • Summary

3. Definition of the problem • At the LHC, we expect to have proton-proton collisions at 10 TeV and then at 14 TeV. • Final states will have all possible products, including those predicted in the Standard Model and in those predicted in models beyond the Standard Model. • A deviation from the Standard Model prediction would indicate the existence of new physics… • If such a deviation is indeed seen, how do we identify the nature of the new physics causing it? • Can we develop a systematic method?

4. Deviations from the Standard Model • Excess or deficit cross-section for some sub-process • Unexpected resonances in invariant mass of some final states, e.g. dileptons, dijets, diphotons, … • Deviant distribution in some variable, e.g. pT , η , # of jets, … • A combination of particles not predicted in the SM, e.g. m+ t - with invariant mass peaking at Z mass • Appearance of a stable/metastable state not identifiable as a lepton, photon, or jet • Explicit non-conservation of some quantum number, e.g. charge, lepton number, baryon number, … • Something completely unexpected…

5. Wealth of possibilities • Excess in dijets but not in dileptons or diphotons • generally indicative of deviant parton distributions at really low x – but can also be an exotic object, e.g. a heavy coloured boson… • Resonant state decaying to di-photons • classic Higgs boson signal – but can also be, for example a massive Kaluza-Klein resonance of the graviton in an RS- type model… • A harder missing pT spectrum in pairs • normally indicative of radiation of a Z’ boson which decays to neutrinos – but can be many things, e.g. radiation of an ADD graviton, or an invisibly decaying Higgs boson

6. Many pitfalls for the unwary 1984 UA1 data at CERN seemed to indicate a top quark of mass 40 GeV… UA2 and later UA1 failed to find more events of this kind. Eventually the top quark was found at 174 GeV.

7. 1985 Crystal Ball data at the SLAC seemed to indicate a Higgs boson of mass 8.3 GeV… Further data did not see any more events with this kind of peak, which was dismissed as a fluctuation … we are still looking for the Higgs boson!

8. 1995 The CDF Collaboration at the Tevatron reported an excess in high pT dijet events, seeming to indicate a contact interaction… Turned out to be due to incorrect gluon PDF’s at low-x

9. 1997 HERA data at high Q2 seemed to indicate a leptoquark of mass around 200 GeV… More running of HERA failed to find more deviations of this nature… was dismissed as a fluctuation…

10. 2003 Many experiments , including the CLAS experiment at CEBAF, reported the ‘discovery’ of a pentaquark of mass around 1540 MeV… Later CLAS themselves reported higher statistics data with no peak… the pentaquark seems to have quite disappeared by now…

11. If it is so hard to separate out genuine new physics effects from the SM background, does it make sense to talk of separating out different models if new physics is found? We can take the ‘hard-headed’ view that we’ll worry about the nature of the new physics when it is found… Or we can start developing techniques to do this right now, so that we are prepared for the new physics discovery when (if?) it comes…

12. If we see NP, can we tell what it is? • Great question • Supersymmetry and the LHC inverse problem (hep-ph/0512190) • Great fun (Olympics...) • But give me a break  • Let's 1st find a NP signal, and celebrate • Emphasis shifts to "Given that you see X, if the NP is Y, you should see Z" • suggestions with Z experimentally impossible not very useful  • but do not underestimate your experimental colleagues! • a well developed feel for experimental issues could make a difference Views of a CMS experimentalist…

13. Views of a string phenomenologist…

14. The “we’ll cross the bridge when we come to it” approach is wrong – unless one is more-or-less sure that there will be no new physics signal… It is like advertising a job, and only after someone has joined work, we start thinking of what that person will work on… Because of its intrinsic difficulty, and this kind of conservative attitude, very few systematic studies of the Inverse Problem have been undertaken…

15. Attempts at a General Solution • . Can we develop a universal tool, which will not only • zero in on a new physics signal, but also tell us what • kind of new physics it is? Simple. Create a database of simulations of all possible Standard Model signals, and of all signals for new physics models which have been proposed till now. When the data become available, use the computer to compare it with the database, and it will zero in on the right one. Easier said than done…

16. Attempt of Arkani-Hamed, Kane, Thaler and Wang (AKTW) • JHEP (2006) Identify all possible parameters in all possible (available!) theory models. Plot one along each axis of a multi-dimensional space. Call this the Theory Space. Each point in Theory Space corresponds to a particular model (including the SM) with a particular set of parameters.

17. Identify the set of all observables at the LHC, including distributions, where every bin is considered an observable. Plot one along each axis of a multi-dimensional space. Call this the Signature Space of LHC. Ideally, when data become available from the LHC, we shall be able to identify a single point in the Signature Space. In fact, because of errors, we will have a progressively shrinking ball in the Signature Space, rather than a point.

18. Use a simulation software to map each point in the Theory Space to a point in the Signature Space. Store this huge set of maps on the computer. AKTW chose a 15-parameter MSSM, and simulations using Spythia→ PGS with 1808 dimensional signature space… 43026 points in Theory Space were considered …

19. When data become available, just ask the computer to check which point(s) in Theory Space map on to the experimental ball in Signature Space. Those are the viable models, parameters and all – Eureka! Map is not one-one – existence of degeneracies… AKTW found 283 degenerate pairs (flippers, sliders, squeezers)…

20. 15-parameters of AKTW A

21. Extension to ILC by Berger, Gainer, Hewett, Rizzo & Lillie (BGHRL) 2007 Their

24. AKTW : no of cases studied = 43 026 no of degenerate pairs = 283 BGHRL: unphysical cases (bug) = 41 actually studied = 242 degeneracy lifted = 63 irreducible = 179 Statistically speaking, the technique(s) does pretty well in 98.9% of the cases for LHC alone In 99.6% of the cases for LHC + ILC …but there remains an irreducible set of degenerate models

25. Further Analysis by Altunkaynak, Holmes and Nelson 2008

26. Conclusion: dark matter relic density analysis and detection experiments experiments can improve upon the ILC in removing degeneracies

27. Critique of General Methods AGAINST FOR

28. AGAINST FOR • Courageous attempt • to take the bull by the horns…. • Uses only available calculations and software • Seems to work in 99% cases • Degeneracies lifted by • more statistics • other variables • other experiments Non-intuitive and too blindly computer-centric Only MSSM-15 has been considered so far Nature may be perverse and land LHC right on a degeneracy Maybe there’s a cleverer use for these… What if the identification turns out to be wrong?

30. The Novum Organon 1620 Q. What is the cause of heat? List all the situations where heat is found. List all the situations that are similar to those of the first list except that heat is lacking. List situations where heat can vary. Sir Francis Bacon The form nature, or cause, of heat must be that which is common to all instances in the first table, is lacking from all instances of the second table and varies by degree in instances of the third table.

31. Instances Agreeing in the Nature of Heat • The rays of the sun, especially in summer and at noon. • 2. The rays of the sun reflected and condensed, as between mountains, or on walls, and most of all in burning glasses and mirrors. • 3. Fiery meteors. • 4. Burning thunderbolts. • 5. Eruptions of flame from the cavities of mountains. • 6. All flame. • 7. Ignited solids. • 8. Natural warm baths. • 9. Liquids boiling or heated. • 10. Hot vapors and fumes, and the air itself, which conceives the most powerful and glowing heat if confined, as in reverbatory furnaces. • 11. Certain seasons that are fine and cloudless by the constitution of the air itself, without regard to the time of year. • 12. Air confined and underground in some caverns, especially in winter. • 13. All villous substances, as wool, skins of animals, and down of birds, have heat. • 14. All bodies, whether solid or liquid, whether dense or rare (as the air itself is), held for a time • near the fire. • 15. Sparks struck from flint and steel by strong percussion. • 16. All bodies rubbed violently, as stone, wood, cloth, etc., insomuch that poles and axles of wheels sometimes catch fire; and the way they kindled fire in the West Indies was by attrition. • 17. Green and moist vegetables confined and bruised together, as roses packed in baskets; insomuch that hay, if damp, when stacked, often catches fire. • 18. Quicklime sprinkled with water. • 19. Iron, when first dissolved by strong waters in glass, and that without being put near the fire. And in like manner tin, etc., but not with equal intensity. • 20. Animals, especially and at all times internally; though in insects the heat is not perceptible to the touch by reason of the smallness of their size. • 21. Horse dung and like excrements of animals, when fresh. • 22. Strong oil of sulphur and of vitriol has the effect of heat in burning linen. • 23. Oil of marjoram and similar oils have the effect of heat in burning the bones of the teeth. • 24. Strong and well rectified spirit of wine has the effect of heat, insomuch that the white of an egg being put into it hardens and whitens almost as if it were boiled, and bread thrown in becomes dry and crusted like toast. • 25. Aromatic and hot herbs, as dracunculus, nasturtium vetus, etc., although not warm to the hand (either whole or in powder), yet to the tongue and palate, being a little masticated, they feel hot and burning. • 26. Strong vinegar, and all acids, on all parts of the body where there is no epidermis, as the eye, tongue, or on any part when wounded and laid bare of the skin, produce a pain but little differing from that which is created by heat. • 27. Even keen and intense cold produces a kind of sensation of burning: "NecBoreæpenetrabilefrigusadurit." 1 • 28. Other instances. These tables constitute the purely Inductive Method of discovery

32. Like Bacon’s tables, the AKTW method leaves very little room for human intuition… Science has always progressed by short-cuts … hypothesis – prediction – verification … in a focussed context… using: …educated guesswork… ...serendipity…. …trial and error…. Can we approach the LHC Inverse Problem in this old-fashioned way?

34. Arkani-Hamed and Kane (open letter to the HEP community) have split the LHC Inverse Problem into three categories: • LHC-1A - What is the new physics? • LHC-1B - What is the spectrum and effective Lagrangian of the new physics at the weak scale? • LHC-1C - How can we begin to study what the underlying theory is, perhaps at a high scale and/or in extra dimensions? …in increasing order of urgency

35. Criteria for model discrimination • Mass spectrum • Absolute values of the masses • Mass differences, leading to thresholds • Spin structure of new physics (resonances, new interactions) • Angular and pT distributions • Asymmetries, e.g. centre-edge • Conservation/non-conservation of quantum numbers • Exotic final states • Asymmetries, e.g. forward-backward (problem at LHC) • Correlation of different effects • Excess cross-sections • Spin effects • Thresholds • Displaced vertices/Stable tracks …one (or a few) at a time…

36. Mass spectrum • Absolute values of the masses • Mass differences, leading to thresholds Threshold in lepton energy is a diagnostic of chargino-LSP mass difference Choi et al 2006 Repeated resonances in ratio of zeroes of Bessel J1 indicate RS gravitons Rizzo 2000

37. Spin structure of new physics (resonances, new interactions) • Angular and pT distributions • Asymmetries, e.g. centre-edge Angular distributions of two-body decay products follow Legendre polynomials of same order as the spin of a resonance Rai et al 2004 ‘center-edge asymmetry’ is a useful tool to pick up the spin of an intermediate state Osland et al, arXiv : 0805.2734

38. Conservation/non-conservation of quantum numbers • Exotic final states • Asymmetries, e.g. forward-backward (problem at LHC) AFB is the usual diagnostic of parity violation The CDF 1994 event : much ado about nothing… D0 home page

39. Correlation of different effects • Excess cross-sections • Spin effects • Thresholds • Displaced vertices/Stable tracks Rai et al 2003 Two-dimensional Theory Space  Signature Space map helps distinguish UED from SUSY Two-dimensional Signature Space map helps distinguish RS model from ADD model Bhattacherjee et al 2008

40. Belyaev et al, arXiv: 0806.2838

41. Some Specific Instances • Higgs boson signals • missing energy signals • pairs

42. Higgs boson signals Cleanest signature is as a resonance in di-photons or in ZZ → 4 leptons

43. SM or extended Higgs Sector ? • estimate of sensitivity from rate measurements in VBF channels (30 fb-1) • compare expected measurement of R in MSSM with prediction from SM BR(h WW) BR(h tt) R = D=|RMSSM-RSM|/sexp ATLAS (prel.) ATLAS (prel.) • potential for discrimination • seems promising • needs further study incl. sys. errors • only statistical errors • assume Mh exactly known MSSM Higgs Bosons with ATLAS

44. Most studied problem… Mass and width measurement Spin and CP properties Couplings to gauge bosons Self couplings A SM Higgs boson must be: a scalar with mass in the correct range and expected decay width and branching ratios

45. Missing Energy Signals • Missing energy arises from • neutrinos • stable (quasi-stable) particles with only weak interactions • exotica: ADD gravitons, unparticles, … WIMPS also good candidates for cold dark matter • Three popular models: • SUSY with R-parity conservation (stable LSP) • UED with KK-parity conservation (stable LP) • little Higgs with T-parity conservation (stable LTP)

46. … almost identical collider signals… Multileptons and/or jets, plus missing energy,…. • Distinguishing them is a real challenge… • Thresholds • Spin measurements

47. Belyaev et al

48. Top-anti top pairs LHC will act as a top factory SM Top-pair signal is : 1. Two b jets + dilepton + MET 2. upto 6 jets, no MET Lots of new physics possibilities: SUSY : stop pair production (RPC) , LQD couplings (RPV) UED : t1 pair production, : Z2 resonance decaying to top-antitop LHT : tTpair production ADD : exchanged + radiated gravitons RS : graviton resonance decaying to top-antitop Z’ : resonance decaying to top-antitop W’ : pair production, decay to top and anti-top radiated unparticles ….

49. Semileptonic decays of the tops (isolated leptons) cannot distinguish between MET in W-decay and MET from new physics… or can it..? Hadronic decays of the tops (jets peaking at top mass) will automatically pick out genuine missing energy candidates… i.e. SUSY, UED, LHT, ADD, W’, unparticles… • Thresholds • Spin measurements

50. Summary