Fun physics at the LHC

Transcription

1 Fun physics at the LHC Edinburgh Cambridge /2008

2 Outline Effective Standard Model Underlying parameters Annoying TeV-scale MSSM: Large extra dimensions Effective KK theory completion Fixed-point completion

3 Effective Standard Model ata vs renormalizable Standard Model dark matter? [only solid evidence for new physics, weak scale?] (g 2) µ? [loop effects around weak scale?] flavor physics? [new operators above 0 4 GeV?] neutrino masses? [see-saw at 0 GeV?] gauge coupling unification? [something happening above 0 6 GeV?] gravity? [mostly negligible below 0 9 GeV] obviously effective theory, cutoff negotiable Problem with fundamental Higgs mass driven to cutoff: δm 2 H /m2 H g2 (2m 2 W + m2 Z + m2 H 4m2 t ) Λ2 easy solution: tune counter term whole idea of fundamental gauge theories betrayed, evil or new physics at TeV scale: supersymmetry extra dimensions little Higgs, Higgsless, composite Higgs... typically cancellation by new states or discussing away high scale beautiful concepts, challenged at TeV scale whatever is there - LHC s job to sort it out H t H W

4 Effective Standard Model in the LHC era Expectations from the LHC find light Higgs? [Uli Baur s rule: there is always new physics at higher scales ] find new physics stabilizing Higgs mass? see dark matter candidate? Particle theory and new physics model independent analyses likely not helpful testing testable hypotheses [theory: e.g. Higgs sector and underlying theory?] discrete hypotheses: spins,... continuous hypotheses: masses,... link to other observations [M+Tevatron: Hooper, TP, Valinotto] reconstruction of Lagrangian [theory+experiment]

5 Effective Standard Model in the LHC era Expectations from the LHC find light Higgs? [Uli Baur s rule: there is always new physics at higher scales ] find new physics stabilizing Higgs mass? see dark matter candidate? Particle theory and new physics model independent analyses likely not helpful testing testable hypotheses [theory: e.g. Higgs sector and underlying theory?] discrete hypotheses: spins,... continuous hypotheses: masses,... link to other observations [M+Tevatron: Hooper, TP, Valinotto] reconstruction of Lagrangian [theory+experiment] Special about LHC [except bigger than Tevatron] beyond inclusive searches [that was Tevatron] lots of strongly interacting particles cascade decays to M candidate general theme: try to survive QC aim at underlying theory ν ν χ o + 2 χ σ tot [pb]: pp g g, q q, t t, χ 2 o χ +, ν ν, χ o g, χ + q χ + q t t χ o g g g S = 2 TeV q q NLO LO m [GeV]

6 Effective Standard Model in the LHC era Expectations from the LHC find light Higgs? [Uli Baur s rule: there is always new physics at higher scales ] find new physics stabilizing Higgs mass? see dark matter candidate? Particle theory and new physics model independent analyses likely not helpful testing testable hypotheses [theory: e.g. Higgs sector and underlying theory?] discrete hypotheses: spins,... continuous hypotheses: masses,... link to other observations [M+Tevatron: Hooper, TP, Valinotto] reconstruction of Lagrangian [theory+experiment] Special about LHC [except bigger than Tevatron] beyond inclusive searches [that was Tevatron] lots of strongly interacting particles cascade decays to M candidate general theme: try to survive QC aim at underlying theory χ o + 2 χ σ tot [pb]: pp g g, q q, t t, χ o 2χ +, ν ν, χ g, χ q 2o 2o t t ν ν χ 2o q χ 2o g q q g g S = 4 TeV NLO LO m [GeV]

7 Masses from cascades Cascade decays [Atlas-TR, you Cambridge people] b b µ µ if new particles strongly interacting and LSP weakly interacting like Tevatron: jets + missing energy tough: (σbr) /(σbr) 2 [model dependence, QC uncertainty] easier: cascade kinematics [ events] long chain g b b χ 0 2 b b µ + µ b b χ 0 thresholds & edges m 2 χ 0 < m 2 0 m 2 l m 2 l m2 χ µµ < 2 0 m l m l new physics mass spectrum from cascade kinematics g b ~ χ o 2 µ ~ o χ

8 2 Fun with the LHC Masses from cascades Cascade decays [Atlas-TR, you Cambridge people] if new particles strongly interacting and LSP weakly interacting like Tevatron: jets + missing energy g b b ~ χ o 2 b µ µ µ ~ o χ tough: (σbr) /(σbr) 2 [model dependence, QC uncertainty] easier: cascade kinematics [ events] long chain g b b χ 0 2 b b µ + µ b b χ 0 thresholds & edges m 2 χ 0 < m 2 0 m 2 l m 2 l m 2 χ µµ < 2 0 m l m l new physics mass spectrum from cascade kinematics Gluino decay [Gjelsten, Miller, Osland, Raklev...] all decay jets b quarks [otherwise dead by QC] m 0 χ m~ l R m 0 χ2 no problem: off-shell [Catpiss] m~ - m q L 0 χ no problem: jet radiation? gluino mass to % - m χ 0 l R m~ - m χ 0 m χ 0 b ~ - m m g ~ m~ - m b 0 χ m~ - m g m~ b 0 χ m~ q L m~ g Sparticle masses and mass differences [GeV]

9 Masses from cascades Cascade decays [Atlas-TR, you Cambridge people] if new particles strongly interacting and LSP weakly interacting like Tevatron: jets + missing energy g b b ~ χ o 2 b µ µ µ ~ o χ tough: (σbr) /(σbr) 2 [model dependence, QC uncertainty] easier: cascade kinematics [ events] long chain g b b χ 0 2 b b µ + µ b b χ 0 thresholds & edges m 2 χ 0 < m 2 0 m 2 l m 2 l m 2 χ µµ < 2 0 m l m l new physics mass spectrum from cascade kinematics Likely bad ideas [Tait & TP; Alwall, Maltoni, de Visscher] decay jets vs QC radiation collinear initial state radiation [p T,j < M hard ] proper description: CKKW/MLM [in MadEvent] N jet dependent on hard scale study: two heavy states QC basics useful at LHC /σ tot dσ/dn jet (pp tt /GG+jets) jet radiation p T > 30 GeV N jet tt GG 600 GeV GG 300 GeV

10 Masses from cascades Cascade decays [Atlas-TR, you Cambridge people] if new particles strongly interacting and LSP weakly interacting like Tevatron: jets + missing energy g b b ~ χ o 2 b µ µ µ ~ o χ tough: (σbr) /(σbr) 2 [model dependence, QC uncertainty] easier: cascade kinematics [ events] long chain g b b χ 0 2 b b µ + µ b b χ 0 thresholds & edges m 2 χ 0 < m 2 0 m 2 l m 2 l m 2 χ µµ < 2 0 m l m l new physics mass spectrum from cascade kinematics Likely bad ideas [Tait & TP; Alwall, Maltoni, de Visscher] decay jets vs QC radiation collinear initial state radiation [p T,j < M hard ] proper description: CKKW/MLM [in MadEvent] N jet dependent on hard scale study: two heavy states QC basics useful at LHC /σ tot dσ/dn jet (pp tt /GG+jets) jet radiation p T > 50 GeV tt GG 600 GeV GG 300 GeV N jet

11 Masses from cascades Cascade decays [Atlas-TR, you Cambridge people] if new particles strongly interacting and LSP weakly interacting like Tevatron: jets + missing energy g b b ~ χ o 2 b µ µ µ ~ o χ tough: (σbr) /(σbr) 2 [model dependence, QC uncertainty] easier: cascade kinematics [ events] long chain g b b χ 0 2 b b µ + µ b b χ 0 thresholds & edges m 2 χ 0 < m 2 0 m 2 l m 2 l m 2 χ µµ < 2 0 m l m l new physics mass spectrum from cascade kinematics Likely bad ideas [Tait & TP; Alwall, Maltoni, de Visscher] decay jets vs QC radiation collinear initial state radiation [p T,j < M hard ] proper description: CKKW/MLM [in MadEvent] N jet dependent on hard scale study: two heavy states QC basics useful at LHC /σ tot dσ/dn jet (pp tt /GG+jets) jet radiation p T > 00 GeV tt GG 600 GeV GG 300 GeV N jet

12 Underlying parameters From kinematics to weak scale parameters parameters: weak-scale Lagrangian [Fittino; : Lafaye, TP, Rauch, Zerwas] measurements: better edges than masses, branching fractions, rates,... [NLO, of course] flavor, dark matter, electroweak constraints,... errors: general correlation, statistics & systematics & theory [flat theory errors!] problem in grid: huge phase space, no local maximum? problem in fit: domain walls, no global maximum? problem in interpretation: bad observables, secondary maxima? Probability maps of new physics [Baltz,...; Roszkowski,...; Allanach,...; ] want to evaluate probability of model being true p(m d) can compute fully exclusive likelihood map p(d m) over m [tough] additional LHC challenge: remove poor directions [e.g. endpoints vs rates] Bayesian: p(m d) p(d m) p(m) with theorists bias p(m) [cosmology, BSM] frequentist: best fitting point max m p(d m) [flavor] LHC era: () compute high-dimensional map p(d m) (2) find and rank local best-fitting points (3) predict additional observables

13 Correlations and errors Toy model: MSUGRA map from LHC [LHC endpoints with free y t ] model unrealistic but useful testing ground [will do anything for citations] weighted Markov chains: several times faster output #: fully exclusive likelihood map output #2: ranked list of local maxima strong correlation e.g. of A 0 and y t [including all errors ] correlations and secondary maxima significant [ ] m t χ 2 m m /2 tan β A 0 µ m t e A 0

14 Correlations and errors Toy model: MSUGRA map from LHC [LHC endpoints with free y t ] model unrealistic but useful testing ground [will do anything for citations] weighted Markov chains: several times faster output #: fully exclusive likelihood map output #2: ranked list of local maxima strong correlation e.g. of A 0 and y t [including all errors ] correlations and secondary maxima significant [ ] A word on errors central values secondary locally statistical errors Gaussian systematic errors Gaussian, correlated theory errors flat RFit scheme [CKMFitter] χ 2 = 2 log L = χ T d C χ d 8 >< 0 d i d i < σ (theo) i χ d,i = d i d i σ (theo) i >: σ (exp) d i d i > σ (theo), i i C i,i = C i,j = C j,i = 0.99 σ(l) i σ (l) σ (j) σ (j) j i j σ (exp) i σ (exp) j

15 Correlations and errors Toy model: MSUGRA map from LHC [LHC endpoints with free y t ] model unrealistic but useful testing ground [will do anything for citations] weighted Markov chains: several times faster output #: fully exclusive likelihood map output #2: ranked list of local maxima strong correlation e.g. of A 0 and y t [including all errors ] correlations and secondary maxima significant [ ] A word on errors central values secondary locally statistical errors Gaussian systematic errors Gaussian, correlated theory errors flat theory error sizeable SPSa theo exp zero expnocorr zero theo exp zero theo exp gauss theo exp flat masses endpoints m m / tan β A m t errors mean: endpoints instead of masses

16 TeV-scale MSSM: MSSM map from LHC shifting from 6 to 9 parameter space [killing grids, Minuit, laptop style fits...] Markov chain globally + hill climber locally outputs # and #2 still the same [weighted Markov chain plus hill climber] three neutralinos observed [left: Bayesian right: likelihood] e+08 e+06 µ M

17 TeV-scale MSSM: MSSM map from LHC shifting from 6 to 9 parameter space [killing grids, Minuit, laptop style fits...] Markov chain globally + hill climber locally outputs # and #2 still the same [weighted Markov chain plus hill climber] three neutralinos observed [left: Bayesian right: likelihood] 6e e /χ 2 4e-07 3e-07 /χ e e M M quality of fit not always useful µ < 0 µ > 0 M M µ tan β M M µl M µr A t ( ) A t (+) m A m t means probably much more work to do...

18 Beyond the LHC Why theorists involved? want to learn statistics [usually get that badly wrong] theory errors not negligible [rates for focus point scenarios] link with other observations model dependent

19 Beyond the LHC Why theorists involved? want to learn statistics [usually get that badly wrong] theory errors not negligible [rates for focus point scenarios] link with other observations model dependent MSSM parameters beyond LHC remember: unknown sign(µ), believe based tan β from m h LHC rates: tan β from heavy Higgs tough [Kinnunen, Lehti, Moortgat, Nikitenko, Spira] µ e+08 e M

20 Beyond the LHC Why theorists involved? want to learn statistics [usually get that badly wrong] theory errors not negligible [rates for focus point scenarios] link with other observations model dependent MSSM parameters beyond LHC remember: unknown sign(µ), believe based tan β from m h LHC rates: tan β from heavy Higgs tough [Kinnunen, Lehti, Moortgat, Nikitenko, Spira] () use current precision on (g 2) µ tan β [ + Alexander, Kreiss] strongly correlated and promising LHC LHC (g 2) SPSa tan β 0.0± ± M 02.± ± M ± ± M ± ± M µl 93.2± ± M µr 35.0± ± M q3l 48.4± ± M br 50.7± ± M ql 524.6± ± M qr 507.3± ± m A 406.3±O(0 3 ) 4.±O(0 2 ) µ 350.5± ±

21 Beyond the LHC Why theorists involved? want to learn statistics [usually get that badly wrong] theory errors not negligible [rates for focus point scenarios] link with other observations model dependent MSSM parameters beyond LHC remember: unknown sign(µ), believe based tan β from m h LHC rates: tan β from heavy Higgs tough [Kinnunen, Lehti, Moortgat, Nikitenko, Spira] () use current precision on (g 2) µ tan β [ + Alexander, Kreiss] strongly correlated and promising (2) use BR(B s µµ) with stop chargino sector [Hisano, Kawagoe, Nojiri] 7% error on f Bs by 205 crucial [ella Morte, el ebbio; + Jäger, Spannowsky] perturbative effects secondary no theory error BR/BR = 5% true best error best error tan β M A M M M µ M t,r

22 Beyond the LHC Why theorists involved? want to learn statistics [usually get that badly wrong] theory errors not negligible [rates for focus point scenarios] link with other observations model dependent MSSM parameters beyond LHC remember: unknown sign(µ), believe based tan β from m h LHC rates: tan β from heavy Higgs tough [Kinnunen, Lehti, Moortgat, Nikitenko, Spira] () use current precision on (g 2) µ tan β [ + Alexander, Kreiss] strongly correlated and promising (2) use BR(B s µµ) with stop chargino sector [Hisano, Kawagoe, Nojiri] 7% error on f Bs by 205 crucial [ella Morte, el ebbio; + Jäger, Spannowsky] perturbative effects secondary Renormalization group bottom up SUSY breaking, unification, GUT? [ + Kneur] /M i M M 2 M 3 scale-invariant sum rules? [Cohen, Schmalz] solidly inference from weak scale log(q)

23 Large extra dimensions Remember the hierarchy problem fundamental scalars bad with high scale present weakness of gravity means large Planck scale G N = /(6πM Planck ) 2 solution: another reason why we see huge non-fundamental M Planck Large extra dimensions (A) [Antoniadis, Arkani-Hamed, imopoulos, vali] Einstein Hilbert action for low fundamental Planck scale S = Z q d 4 x g M 2 2 R Z q d 4+n x 2 = Z q 2 (2πr)n d 4 x 2 Z g M 2+n R g M 2+n q d 4 x g M 2 Planck R R express M Planck in terms of fundamental M M Planck = M (2πrM ) n/2 Numbers to make it work free parameter rm constraints from gravity tests above O(mm) signatures of strong gravity in extra dimension? M = TeV n r 0 2 m m m m

24 Effective KK theory Toy model: only gravitons in extra dimensions expand the metric [graviton field h] ds 2 = g (4+n) MN dx M dx N = η MN + M n/2+ h MN! dx M dx N matter in Einstein s equation [no cosmological constant] R AB 2 + n g ABR = «Tµν (x) δ (n) (y) 0 M 2+n 0 0 Fourier transformation of extra dimensions [KK excitations for periodic boundary conditions] h AB (x; y) = X m = X m j = h (m) AB p (x) m j y j (2πr) n ei r universal interactions of KK gravitons [h AB Gµν, QC massless] ( + m 2 k ) G(k) µν = " «# µ ν T λ λ T µν + + η M Planck ˆm 2 µν = T µν 3 M Planck tiny KK mass splitting [M = TeV] 8 δm «2/n r = 2πM M < = M Planck : continuum of weakly interacting gravitons at the LHC ev (n = 2) 0. MeV (n = 4) 0.05 GeV (n = 6)

25 Effektive KK theory at the LHC Effective KK theory [Giudice, Rattazzi, Wells; Han, Lykken, Zhang;...] real radiation of continuous KK tower [dm/d k = /r; (dσ) /M 2 Planck ] Z (dσ) Z dm (dσ) S n m n r n = dm (dσ) S n m n (2πM ) n «2 MPlanck higher-dimensional operator from virtual graviton exchange [s channel in Y] A = M 2 Planck /M 2 interactions for KK tower s m 2 KK S δ 2 Λ n 2 M n+2 M like any effective theory valid for E < M Real emission pp G KK +jets [Giudice, Rattazzi, Wells; Vacavant, Hichliffe...] recoil against hard jet [E j M ] background: radiation of Z ν ν M = 0 for E parton > Λ cutoff M = 0 automatically for m KK > E parton effective cutoff: steep gluon density little UV sensitivity for Λ cutoff explicit cutoff not crucial

26 Effektive KK theory at the LHC Effective KK theory [Giudice, Rattazzi, Wells; Han, Lykken, Zhang;...] real radiation of continuous KK tower [dm/d k = /r; (dσ) /M 2 Planck ] Z (dσ) Z dm (dσ) S n m n r n = dm (dσ) S n m n (2πM ) n «2 MPlanck higher-dimensional operator from virtual graviton exchange [s channel in Y] A = M 2 Planck /M 2 interactions for KK tower s m 2 KK S δ 2 Λ n 2 M n+2 M like any effective theory valid for E < M Real emission pp G KK +jets [Giudice, Rattazzi, Wells; Vacavant, Hichliffe...] recoil against hard jet [E j M ] background: radiation of Z ν ν M = 0 for E parton > Λ cutoff M = 0 automatically for m KK > E parton effective cutoff: steep gluon density little UV sensitivity for Λ cutoff explicit cutoff not crucial M [TeV] σ: pp j+e T,miss 00 fb - 0 fb - δ= δ=2 δ=3 δ=4,5, Λ[TeV]

27 Virtual gravitons at LHC of virtual gravitons [Giudice & Strumia; Giudice, Strumia, TP; Kachelries & Plümacher,...] virtual graviton in s channel pp µ + µ [q q and gg initial states] reconstructed m µµ for photon, Z, graviton loop-induced 6 operator [axial vector axial vector] O = π n 2 6 Γ 2 (n/2) M 2 «2n+2 Λcutoff M tree-induced 8 operator [leading constant in s/λ cutoff ] 8 4π S = S n M 2+n Z dm mn s + m 2 = >< >: M 4 (effective scale) eff «S n n 2 Λcutoff M 4 (NA) 2 M «S n n 2 Λcutoff M 4 (cutoff Θ) n 2 M 5σ: pp l + l (8) M eff [TeV] fb - 0 fb Λ eff [TeV]

28 Virtual gravitons at LHC of virtual gravitons [Giudice & Strumia; Giudice, Strumia, TP; Kachelries & Plümacher,...] virtual graviton in s channel pp µ + µ [q q and gg initial states] reconstructed m µµ for photon, Z, graviton loop-induced 6 operator [axial vector axial vector] O = π n 2 6 Γ 2 (n/2) M 2 «2n+2 Λcutoff M tree-induced 8 operator [leading constant in s/λ cutoff ] 8 4π S = S n M 2+n Z dm mn s + m 2 = two-dimensional integration over (m, s) cutoff requiring m M additional cutoff for s M >< >: rates scaling M max Λ (n 2)/(n+2) cutoff breakdown of effective theory M 4 (effective scale) eff «S n n 2 Λcutoff M 4 (NA) 2 M «S n n 2 Λcutoff M 4 (cutoff Θ) n 2 M M [TeV] σ: pp l + l (8) 00 fb - 0 fb - δ=6 δ=4 δ=3 δ=2 δ= Λ[TeV]

29 completion as UV completion [e.g. Cullen, Perelstein, Peskin; Antoniadis, Benakli, Laugier...] In particular, the only known framework that allows for a self-consistent description of quantum gravity is string theory Regge excitations of Standard Model [Burikham, Figy, Han] compute different helicity contributions, like r u u A(e + L e R γ Lγ R ) = 2e 2 t s + t «r u s = 2e 2 t r u u = 2e 2 t s S(s, t) + t «S(s, u) S(t, u) s with Veneziano form factor S(s, t) = Γ( α s) Γ( α t) Γ( α (s + t)) = π2 6 st M 4 + O M 6 S S = Γ( s/m2 S ) Γ( t/m2 S ) Γ( (s + t)/m 2 S ) dominant over KK because M eff M S closed-string gravitons suppressed effective operator below string scale string resonances: n M S

30 Renormalization flow of gravity Renormalization flow of gravity [Reuter; Litim; Wetterich;...] Einstein Hilbert action with running Z G(µ) and Λ(µ) Γ k = /(6πG k ) d 4+n x g [ R(g) + ] dimensionless coupling g(µ) = G(µ) µ 2+n = G 0 Z (µ) µ2+n G attractive finite UV fixed point [anomalous dimension: η = µ µ log Z G g] µ µ g (µ) = (2 + n + η(g )) g (µ) = 0 for g 0 η(g ) = 2 n gravity asymptotically free in UV G(µ) g µ (2+n) coupling weak enough for finite LHC predictions?

31 Renormalization flow of gravity Renormalization flow of gravity [Reuter; Litim; Wetterich;...] Einstein Hilbert action with running Z G(µ) and Λ(µ) Γ k = /(6πG k ) d 4+n x g [ R(g) + ] dimensionless coupling g(µ) = G(µ) µ 2+n = G 0 Z (µ) µ2+n G attractive finite UV fixed point [anomalous dimension: η = µ µ log Z G g] µ µ g (µ) = (2 + n + η(g )) g (µ) = 0 for g 0 η(g ) = 2 n gravity asymptotically free in UV G(µ) g µ (2+n) coupling weak enough for finite LHC predictions? UV safe gravity [Weinberg (979)] gravity really non fundamental becauseg /M 2+n? t Hooft s perturbative renormalizability: finite number of counter terms Wilson s renormalizability: no unphysical UV divergences consistent theory beyond perturbation theory [no ghosts: Weinberg & Gomez] fixed point seen for p g R 8 and including matter [no proof; not perturbative series] great idea for gravity great for LHC

32 Fixed-point form factor Naive form factor [Hewett & Rizzo] dress s-channel coupling M 2+n M 2+n F (s) = M 2+n avoids matching of s integration (unitarity) M 2+n F (s) M 2+n improvement of s integration/matching still cutoff in KK-mass integration + tm s «2+n! 2+n! s tm s (2+n)/2

33 Fixed-point form factor Naive form factor [Hewett & Rizzo] dress s-channel coupling M 2+n M 2+n F (s) = M 2+n avoids matching of s integration (unitarity) M 2+n F (s) M 2+n improvement of s integration/matching still cutoff in KK-mass integration + tm s «2+n! 2+n! s tm s (2+n)/2 also applicable to graviton emission [less impressive effect]

34 Fixed-point completion Modified graviton propagator [Reuter; Fischer & Litim] effective action: Γ k = /(6πG k ) R d 4+n x g [ R(g) + ] IR no running; M regime strong effects; UV fixed point iterative approach: start with anomalous dimension of graviton 8 >< s, m < k s + m P(s, m) = 2 trans M >: n+2 s, m > k (s + m 2 ) n/2+2 trans IR and UV contributions to 8 operator [leading in s/m, matched to /s 2 ] S (FP) = S «n k n 2 trans n M 4 = ( + (n 2)) S(Θ) M n 2 needed and not needed: () transition scale k trans M [anomalous dimension modeled] (2) no artificial Λ cutoff for m integration (3) matching/cutoff for s integration UV fixed point indeed solution to our problems

35 Fixed-point completion test with artificial Λ cutoff setting M KK = 0 perfect decoupling, as expected [similar to real emission] mild effects for k trans = M ± 0% [more details to be studied] reach largely independent of n max M [TeV] 5σ: pp l + l (8) fb - 2 δ=5 δ= Λ[TeV] max M [TeV] 5σ: pp l + l (8) fb - 2 δ=6 δ= Λ[TeV]

36 Fixed-point completion test with artificial Λ cutoff setting M KK = 0 perfect decoupling, as expected [similar to real emission] mild effects for k trans = M ± 0% [more details to be studied] reach largely independent of n Shape of graviton kernel shift to larger m ll [shown n = 3] small m ll : factor S (n ) large m ll : factor S 2 (n ) 2 UV contribution predicted and not negligible 0.6 /σ dσ/de parton (pp l + l ) 0.4 dσ/de parton (pp l + l ) M =5 TeV 0.4 M =8TeV FP cutoff 0.2 δ=3,6 σ Theta scaled (δ-) cutoff FP-cut FP M =5 TeV E parton [TeV] E parton [TeV]

37 Fixed-point completion test with artificial Λ cutoff setting M KK = 0 perfect decoupling, as expected [similar to real emission] mild effects for k trans = M ± 0% [more details to be studied] reach largely independent of n Shape of graviton kernel shift to larger m ll [shown n = 3] small m ll : factor S (n ) large m ll : factor S 2 (n ) 2 UV contribution predicted and not negligible predicted LHC rates S (FP) : UV regime in addition to S (Θ) S IR σ[ fb] n = 3 n = 6 M 2 TeV 5 TeV 8 TeV 2 TeV 5 TeV 8 TeV S (NA) S (Θ) S (FP) proof of concept quantitatively very promising

38 Outlook Understanding the TeV scale () look for solid new physics signals (2) measure weak scale Lagrangian (3) determine fundamental physics construct new physics hypotheses compute reliable predictions avoid getting killed by QC enjoy toying around with UV gravity LHC more than a discovery machine!

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