Advanced Topics in Particle Physics

Probing the High Energy Frontier at the LHC

Ulrich Husemann, Klaus Reygers, Ulrich Uwer Heidelberg University Winter Semester 2009/2010

Short Recap

Hints for beyond standard model (BSM) physics Experiment: neutrino mass, dark matter, … Theory: hierarchy problem, gravity, … Supersymmetry: symmetry between fermions & bosons SUSY = broken symmetry, SUSY breaking e.g. via mSUGRA Minimal model (CMSSM): reduction from 105 to 5 free SUSY parameters: tan β, m0, m1/2, A, sign(μ) In many models: lightest SUSY particle (LSP) = candidate for dark matter Typical SUSY signature: cascade decays → generic signatures at the LHC: MET + jets, MET + leptons

Probing the High Energy Frontier at the LHC, Heidelberg U, Winter Semester 09/10, Lecture 9 2 LHC: Latest News

Busy weekend: Stable beam, protons in 4x4 bunches (Sunday morning, 7:00) A few hours of collisions at injection energies (450+450 GeV) ATLAS/CMS switched on silicon pixel detectors for the first time with beam

Probing the High Energy Frontier at the LHC, Heidelberg U, Winter Semester 09/10, Lecture 9 3

Extra Dimensions Literature

Reviews, Lectures, Books Kribs: TASI 2004 Lectures on the Phenomenology of Extra Dimensions, hep-ph/0605325 PDG chapter on extra dimensions Hooper, Profumo: Dark Matter and Collider Phenomenology of Universal Extra Dimensions, Phys. Rept. 453 (2007) 29 Ewerz: Extra Dimensions (lecture notes) Sundrum: Warped Dimensions and the LHC, DESY Physics Seminar, Zeuthen, October 14, 2009 Randall: Warped Passages, Harper Perennial (2006)

Probing the High Energy Frontier at the LHC, Heidelberg U, Winter Semester 09/10, Lecture 9 4 Extra Dimensions Literature

Original Kaluza-Klein papers Kaluza: Zum Unitätsproblem der Physik, Sitzungsber. Preuss. Akad. Wiss. Berlin (Math. Phys) 1921, 966 Klein: Quantentheorie und fünfdimensionale Relativitätstheorie, Z. Phys. 37 (1926) 895 Extra dimensions models (together >7000 citations) Large extra dimensions: Arkani-Hamed, Dimopoulos, Dvali, Phys. Lett. B429 (1998) 263 Warped extra dimensions: Randall, Sundrum, Phys. Rev. Lett. 83 (1999) 3370 Universal extra dimensions: Appelquist, Cheng, Dobrescu, Phys. Rev. D64 (2001) 035002

Probing the High Energy Frontier at the LHC, Heidelberg U, Winter Semester 09/10, Lecture 9 5

Chapter 11

Physics beyond the Standard Model II: Extra Dimensions BSM Physics

SM cannot be the ultimate theory, open questions e.g. What is dark matter mode of? Hierarchy problem: why is the electroweak scale so much smaller than the Planck scale (or the GUT scale)? Idea: Planck scale only “appears” much larger than electroweak scale in 4D, in >4 dimensions: weak scale = “natural scale” Initial ideas: Nordström (1914), Kaluza & Klein (1919–1926) → unification of general relativity and U(1) requires 5 dimensions Realistic superstring theories: only consistent in 10D, extra dimensions (ED) have size ! Planck length Since 1998: extra dimensions models becoming popular → bottom-up approaches inspired by string theory Probing the High Energy Frontier at the LHC, Heidelberg U, Winter Semester 09/10, Lecture 9 7

Kaluza-Klein Model

Typical 5D scenario (scalar field for now): 4D Minkowski spacetime + 5th dimension compactified (i.e. rolled up) on a circle with radius L

L R5 R4×S1 5D coordinates: x A (x 0, x 1, x 2, x 3, y) (x, y) ≡ 1≡ 1 5D Lagrangian for scalar fields: = ∂ φ∂Aφ m2φ2 L 2 A − 2 Compactification: periodic boundary conditions for 5D fields + ∞ i ky/L φ(x, y)=φ(x, y +2πL) → expansion: φ(x, y)= φn(x) e− k= ￿−∞ Probing the High Energy Frontier at the LHC, Heidelberg U, Winter Semester 09/10, Lecture 9 8 Kaluza-Klein Model

How does 5D Lagrangian look in 4D? 2π Integrate out 5th dimension in action S = d4x dy L using ϕ = √2πL φ ￿ ￿0

∞ 2 4 1 µ 1 2 2 µ 2 k S = d x ∂µϕ0 ∂ ϕ0 m ϕ0 + ∂µϕk ∂ ϕk∗ m + 2 ϕk ϕk∗ ￿2 − 2 − L ￿ ￿ ￿k=0 ￿ ￿ ￿ ￿ “zero mode”: “KK tower”: infinitely many complex real scalar field scalar fields with effective mass 2 2 2 2 independent of y meff = m + k /L Important phenomenological consequence: Compactified 5th dimension leads to effective theory in 4D: “KK-tower” of infinitely many new massive particles Particles approximately equidistant in mass, mass splitting depends on size L of 5th dimension

Probing the High Energy Frontier at the LHC, Heidelberg U, Winter Semester 09/10, Lecture 9 9

Bulk and Branes

Many ED models: only gravity propagates in multi-dimensional Gravity bulk (=“total” space) SM particles and interactions confined to 3D branes Branes = lower-dimensional manifolds in n-dimensional space (generalization of a 2D Gravity membrane in 3-space) Branes = dynamical objects in string theory, e.g. open strings attach to “D-branes” with Dirichlet boundary conditions

Probing the High Energy Frontier at the LHC, Heidelberg U, Winter Semester 09/10, Lecture 9 10 Most Popular ED Models

Assumption from string theory: natural size of extra –35 dimensions = Planck length LPl = 1/ΛPl ! 1.6×10 m Late 1990ies: what if extra dimensions are large?

Model Spacetime Fields

Arkani-Hamed, Large extra dimensions: size SM: confined to 3-brane Dimopoulos, Dvali up to millimeter scale Gravity: 3-brane and bulk (ADD, 1998) Warped extra dimension: SM: confined to 3-brane Randall, Sundrum curvature of extra dimension (later versions: also in bulk) (RS, 1999) makes LPl look small Gravity: 3-brane and bulk

Appelquist, Cheng, Universal extra dimensions SM & gravity: propagate Dobrescu, 2001 (UED) through full bulk

Probing the High Energy Frontier at the LHC, Heidelberg U, Winter Semester 09/10, Lecture 9 11

ADD Model

Renaissance of ED models (Arkani-Hamed,

yi yj extra compactified Dimopoulos, Dvali, 1998): dimensions TeV scale = fundamental scale SM “lives” on 4D brane, gravity “diluted” via propagation through bulk 4-d spacetime ADD setup:

[Kribs, hep-ph/0605325] Figure 1. Sketch of the large extra dimension ADD model worldview. n extra dimensions, compactified on torus The idea that the quantum gravity scale could be lowered whiletheSM remain on a brane was motivated by earlier results in string theory. In (4+n)D spacetime is flat particular, it was realized in string theory that the quantumgravityscale could be lowered from the Planck scale to the GUT scale [12]. Others also pursued extra dimensions opening up between the TeV scale to the GUT Probing the High Energy Frontier at the LHC, Heidelberg U, Winter Semester 09/10, Lecture 9 12 scale [13]. In this section, however, I will concentrate solely on the ADD model and discuss several of its important phenomenologicalimplications. First, let’s be explicit about the assumptions. The ADD modelconsists of

n extra dimensions, each compactified with radius r (taken to be • the same size for each dimension) on a torus with volume Vn = (2πr)n. All SM fields (matter, Higgs, gauge fields) localized to a 3-brane • (“SM brane”) in the bulk (“gravity only”) spacetime. Bulk and boundary spacetime is flat, i.e., the bulk and boundary • cosmological constants vanish. The SM 3-brane is “stiff”; the fluctuations of the brane surface • itself in the higher dimensional spacetime can be ignored (or, more technically, the brane fluctuations have masses of order the cutoff

4 Gravity in 4+n Dimensions

Gravitational force in 4+n dimensions Gauss’ law in 4D: surface ∼r2 → force ∼1/r2 (r: distance) 5D: gravitational force ∼1/r3 → force becomes stronger at short distances w.r.t. 1/r2 on surface: Field Lines residual effect L F∼1/r2L

Surface in bulk: F∼1/r3

Solution to the hierarchy problem: gravitons propagate in >3 spatial dimensions, we only observe weak “effective gravity” in 4D → how large can extra dimension(s) be?

Probing the High Energy Frontier at the LHC, Heidelberg U, Winter Semester 09/10, Lecture 9 13

Size of the 5th Dimension [R. Sundrum, DESY Physics Seminar, 10/14/09] Sundrum,[R. Seminar, DESY Physics

Probing the High Energy Frontier at the LHC, Heidelberg U, Winter Semester 09/10, Lecture 9 14 Planck Mass in (4+n)D

Compactification on torus in 4+n dimensions R4+n = R4×S1×…(n times)…×S1 Volume of n-dimensional torus: (2πL)n Planck mass in (4+n)D: M2 [4D] M2+n[(4 + n)D] Pl D ∼ (2πL)n Assume Planck scale in (4+n) dimensions = 1 TeV n = 1 (5D): L ! 2.3 × 1028 GeV–1 = 1014 m → excluded!

PHYSICAL REVIEW LETTERS week ending n = 2 (6D): L ! 3.1PRL ×98, 0211011011 (2007) GeV–1 = 1.5 mm → getting 12 JANUARY 2007 interesting! Tests of the Gravitational Inverse-Square Law below the Dark-Energy Length Scale D. J. Kapner,* T. S. Cook, E. G. Adelberger, J. H. Gundlach, B. R. Heckel, C. D. Hoyle, and H. E. Swanson Center for Experimental Nuclear Physics and Astrophysics, Box 354290, University of Washington, Seattle, Washington 98195-4290, USA Experimentally: gravity on short(Received 16distance October 2006; published 8scales January 2007) (sub-mm) We conducted three torsion-balance experiments to test the gravitational inverse-square law at separations between 9.53 mm and 55 m,probingdistanceslessthanthedark-energylengthscaled not well tested before4 2000 ˆ @c=d 85 m. We find with 95% confidence that the inverse-square law holds ( 1) down to a length scale  56 m and that an extra dimension must have a size R 44 m.j j  p ˆ  Probing the High Energy Frontier at the DOI:LHC,10.1103/PhysRevLett.98.021101 Heidelberg U, Winter Semester 09/10,PACS numbers: Lecture 04.80.Cc, 95.36.+x 9 15

Recent cosmological observations [1–3] have shown azimuthal symmetry. The attractor had a similar 21-fold that 70% of all of the mass and energy of the Universe is azimuthal symmetry and consisted of a 0.997-mm-thick amysterious‘‘darkenergy’’withadensityd molybdenum disk with 42 3.178-mm-diameter holes 3:8 keV=cm3 and a repulsive gravitational effect. This mounted atop a thicker tantalum disk containing dark-energy density corresponds to a distance  21 6.352-mm-diameter holes. The gravitational interaction d ˆ 4 between the missing masses of the detector and attractor @c=d 85 m that may represent a fundamental length scale of gravity [4,5]. Although quantum- holes applied a torque on the detector that oscillated p mechanical vacuum energy should have a repulsive gravi- 21 times for each revolution of the attractor, giving torques 60 tational effect, the observed d is between 10 and at 21!, 42!, 63!, etc., that we measured by monitoring 10120 times smaller than the vacuum energy density com- the pendulum twist with an autocollimator system. The puted according to the standard laws of quantum mechan- holes in the lower attractor ring were displaced azimuthally ics. Sundrum [6] has suggested that this huge discrepancy by 360=42 degrees and were designed to nearly cancel the (the ‘‘cosmological constant problem’’) could be resolved 21! torque if the inverse-square law holds. On the other if the graviton were a ‘‘fat’’ object with a size comparable hand, an interaction that violated the inverse-square law, to d that would prevent it from ‘‘seeing’’ the short- which we parametrize as a single Yukawa Limits distanceon physics that dominatesED the vacuum Radius energy. His scenario implies that the gravitational force would weaken for objects separated by distances s & d. Dvali, Gabadaze, and Senjanovic´ [7] argue that a similar weak- ening of gravity could occur if there are extra time dimen- sions. In their scenario, the standard model particles are Most stringent limitslocalized inon ‘‘our’’ time,ED while radius: the gravitons propagate in the extra time dimension(s) as well. Other scenarios predict Eöt-Wash group (Uthe oppositeWashington) behavior: The extra space dimensions of M theory would cause the gravitational force to get stronger for s & R, where R is the size of the largest

compactified dimension [8]. These considerations, plus Torsion pendulum othersafter involving newR. forces von from theEötvös exchange of proposed scalar or vector particles [9], motivated the tests of the gravitational inverse-square law we report in this Letter. Our tests were made with a substantially upgraded ver- Disk with 21x2 holession of therotates ‘‘missing mass’’ with torsion-balance instrument used in our previous inverse-square-law tests [10,11]. constant angular velocityThe instrument used in this work [12], shown in Fig. 1, consisted of a torsion-pendulum detector suspended by a thin 80-cm-long tungsten fiber above an attractor that was rotated with a uniform angular velocity ! by a geared- “Missing” gravitation of holes introduces FIG. 1. Scale drawing of our detector and attractor. The 3 small down stepper motor. The detector’s 42 test bodies were spheres near the top of the detector were used for a continuous 4.767-mm-diameter cylindrical holes machined into a gravitational calibration of the torque scale. Four rectangular oscillations on torque0.997-mm-thick of molybdenum pendulum detector ring. The hole cen- plane mirrors below the spheres are part of the twist-monitoring ters were arrayed in two circles, each of which had 21-fold system. The detector’s electrical shield is not shown.

Measurement tests0031-9007 Newtonian=07=98(2)=021101(4) 1/r 021101-1  2007 The American Physical Society potential on short distances, ansatz: Yukawa potential Gm m V (r)= 1 2 [1+α exp( r/λ)] − r − Current best limit: λ " 44 μm for single extra dimension Probing the High Energy Frontier at the LHC, Heidelberg U, Winter Semester 09/10, Lecture 9 16 PHYSICAL REVIEW LETTERS week ending PRL 98, 021101 (2007) 12 JANUARY 2007

ciently high that m 21 deformations were insignificant. No corrections for backgroundsˆ were necessary. A combined Newtonian fit to the data from all 3 experi- ments gave 2 407 for  421 degrees of freedom. The best fit with anˆ additional Yukawaˆ interaction improved the 2 by 3.5 for 0:0037,  2 mm. The combined data showed no evidenceˆÿ for a ˆ2 effect at any . Our resulting constraints on violations of the inverse-square law, shown in Fig. 6,improveonpreviousworkbyafactor

of up to 100. In particular, at 95% confidence, we find that any gravitational-strength ( 1) Yukawa interaction must have  56 m. Thej j resultsˆ in Fig. 6 yield a model-independent upper limit on the size of a compact extra dimension. A single extra dimension with R & smin would give a signal corresponding to a Yukawa interaction with 8=3 and  R [9], leading to a 95%-confidence upper boundˆ of R ˆ44 m. For the two large extra- dimension scenario discussed in Ref. [8], we require a 2 lower limit on unification mass M 3:2 TeV=c2, FIG. 5 (color online). Experiment III torques. Notation is the where M is defined in Ref. [11]. Constraints  from the same as in Fig. 4, except that diamonds (triangles) show the 21!  torque from the upper (lower) attractor plate alone. The solid and data in Figs. 3–5 on other possible forms of inverse- dashed curves in the lower panel show the residuals expected square-law violation will be submitted as a separate from 1,  80 m and 105,  10 m Yukawa publication. interactions,ˆ respectively.ˆ Both areˆ excludedˆ by our results. We thank Anton Andreev, Paul Chesler, Robert Jaffe, Steven Lamoreaux, and Laurence Yaffe for illuminating deflect so as to trace the hole pattern of the attractor. Private remarks on the finite-temperature Casimir force. This work communications [17] have shown that our beryllium- was supported by NSF Grant No. PHY0355012 and by the copper membrane was thick enough to reduce direct DOE Office of Science. Casimir forces between the attractor and detector to a negligible level. The observed 1.6 kHz frequency of the lowest ‘‘drumhead’’ mode of the membrane was suffi- *Present address: Kavli Institute for Cosmological Physics, Limits on ED Radius University of Chicago, Chicago, IL 60637, USA. [1] A. G. Riess et al., Astron. J. 116, 1009 (1998). [2] S. Perlmutter et al., Astrophys. J. 517, 565 (1999). [3] C. L. Bennet et al., Astrophys. J. Suppl. Ser. 148,1 (2003). [4] S. R. Beane, Gen. Relativ. Gravit. 29, 945 (1997). [5] G. Dvali, G. Gabadadze, M. Kolanovic´, and F. Nitti, Phys. Rev. D 65, 024031 (2001). [6] R. Sundrum, Phys. Rev. D 69, 044014 (2004). [7] G. Dvali, G. Gabadadze, and G. Senjanovic´, hep-ph/ 9910207. [8] N. Arkani-Hamed, S. Dimopoulis, and G. R. Dvali, Phys. Lett. B 436, 257 (1998). [9] E. G. Adelberger, B. R. Heckel, and A. E. Nelson, Annu. Rev. Nucl. Part. Sci. 53, 77 (2003). [10] C. D. Hoyle et al., Phys. Rev. Lett. 86, 1418 (2001). [11] C. D. Hoyle et al., Phys. Rev. D 70, 042004 (2004). [12] D. J. Kapner, Ph.D. thesis, University of Washington, 2005 (unpublished). [D. Kapner et al., Phys. Rev. Lett. 98 (2007) 021101][13] R. Spero et al., Phys. Rev. Lett. 44, 1645 (1980); J. K. FIG. 6 (color online). Constraints on Yukawa violations of the Probing the High Energy Frontier at the LHC, Heidelberg U, Winter Semester 09/10, Lecture 9 17 Hoskins et al., Phys. Rev. D 32, 3084 (1985). gravitational 1=r2 law. The shaded region is excluded at the 95% [14] J. C. Long et al., Nature (London) 421, 922 (2003). confidence level. Heavy lines labeled Eo¨t-Wash 2006, Eo¨t-Wash [15] J. Chiaverini et al., Phys. Rev. Lett. 90, 151101 (2003). 2004, Irvine, Colorado, and Stanford show experimental con- [16] S. J. Smullin et al., Phys. Rev. D 72, 122001 (2005). straints from this work and Refs. [11,13–16], respectively. [17] Robert Jaffe, Paul Chesler, Anton Andreev, and Laurence Lighter lines show various theoretical expectations summarized Yaffe (private communications). in Ref. [9].

ADD Phenomenology 021101-4

f(p1)

Feynman rules for interaction i Gµν [Wµν + Wνµ] of tower of KK gravitons with −4MPl

f(p2) (a) SM matter: Virtual Graviton → Fermions/Photons High density of KK states in Aα(p1) tower → approximately i Gµν [Wµναβ + Wνµαβ ] continuum of KK states −MPl Aβ(p2) (b) Continuum cross section: similar to electroweak cross sections f Gµν Gravitoni eQ [γµηνα + γν ηµα] Generic property: density of KK + −Photon2MPl

in tower decreases with f (c) Aα increasing n → smaller signals a G for more dimensions gα(p1) µν

Gravitong3 abc f K(p1,p2,p3)µναβγ N.B.: KK graviton = spin-2 particle +M PlJet b c gβ(p2) (d) gγ(p3)

Probing the High Energy Frontier at the LHC, Heidelberg U, Winter Semester 09/10, Lecture 9 18 Figure 5. Some of the Feynman rules connecting gravitons to SMfields,from (f) (γ) Ref. [21]. Here Wµν =(p1 + p2)µγν and the other kinematical functions Wµναβ and K(p1,p2,p3)µναβγ can be found in [21]. Rules (b) and (c) are present for all SM groups; rule (d) occurs for non-Abelian groups (gluons shown).

in an n-dimensional spatial volume having Kaluza-Klein index between k | |

17 week ending PRL 101, 181602 (2008) PHYSICAL REVIEW LETTERS 31 OCTOBER 2008

TABLE II. Number of observed events and expected SM back- TABLE III. Percentage of signal events passing the candidate grounds in the jet ET candidate sample. sample selection criteria () and observed 95% C.L. lower limits þ 6 obs on the effective Planck scale in the ADD model (MD ) in Background Events GeV=c2 as a function of the number of extra dimensions in Z ## 388 30 the model (n) for both individual and the combined analysis. W ! (# 187 Æ 14  E jet E Combined W ! "# 117 Æ 9 T T n  þ 6 Mobs  þ 6 Mobs Mobs W ! e# 58 Æ 4 D D D Z ! ‘‘ 8 Æ 1 2 7.2 1080 9.9 1310 1400 Multijet! 23 Æ 20 3 7.2 1000 11.1 1080 1150  jet 17 Æ 5 4 7.6 970 12.6 980 1040 Noncollisionþ 10 Æ 10 5 7.3 930 12.1 910 980 Total predicted 808 Æ 62 6 7.2 900 12.3 880 940 Data observed 809Æ f(p1) search for new physics using three sets of kinematic cuts, i simply an update to the previously published analysis. The the most sensitive of which is used here.G Toµν compute the[Wµν + Wνµ] −4MPl SM background estimates and the number of observed expected 95% C.L. cross section upper limits we combine events are shown in Table II, and a comparison of the the predicted ADDf(p2) signal and(a) background estimates with expected and observed leading jet ET distributions is systematic uncertainties on the acceptance using a shown in Fig. 2. Bayesian method with a flat prior [16]. The acceptance is Based on the observed agreement with the SM expecta- found to be almostAα(p1) independent (within 2%) of the mass tion in both the  E and jet E candidate samples, M . The total systematic uncertainties on the number of þ 6 T þ 6 T D i we proceed to set lower limits on M for the LED model. expected signal events are 5.7% and 12.4%Gµ forν the  E[Wµναβ + Wνµαβ ] D −MPl T The limits are obtained solely from the total number of and jet E candidate samples, respectively. The largestþ 6 þ 6 T observed events in each of the samples (no kinematic shape systematic uncertaintiesAβ(p2) arise(b) from modeling of initial or information is incorporated). In order to estimate our sen- final state radiation convoluted with jet veto requirements, sitivity to the ADD model we simulateADD expected signals Signatures in choice of renormalization and factorization scales, model- f G both final states using the PYTHIA [14] event generator in ing of parton distribution functions, modelingµν of the jet conjunction with a GEANT [15] based detector simulation. energy scale (jet ET sample only), and the luminosityi Key signature I for ADD- þ 6 eQ [γµηνα + γν ηµα] For each extra dimension scenario we simulate event measurement. −2MPl samples for MD ranging between 0.7 and 2 TeV. In the Since the underlying graviton production mechanism is like large ED at hadron (c) A case of the  ET analysis, the final kinematic selection equivalent for bothf final states, the combinationα of the requirements forþ colliders:6 the candidate sample are determined by independent limits obtained from the two candidate optimizing the expected cross section limit without looking samples is based on the predicted relative contributions a gα(p1) Gµν at the data. The jet High-energyET analysis was donemonojet as a generic + METof the four graviton production processes. Systematic un- þ 6 certainties on the signal acceptances are treated asg 100%3 abc f K(p1,p2,p3)µναβγ High-energy photon + METcorrelated, while uncertainties on background estimates,MPl 300 obtained in most cases from data, are considered to be -1 b c CDF II ( 1.1 fb ) gβ(p2) (d) gγ(p3)

250 PRL 101 (2008) 181602] [CDF, LEP/Tevatron limits: 1.6 Data CDF II Jet/γ + ET 200 -1 n=2: MDSM > Prediction 1.6 TeV Figure 5. Some of the FeynmanCDF II rulesγ + ET connecting (2.0 fb ) gravitons to SMfields,from 1.4 -1 SM + LED (n=2,M =1TeV) (f) CDF II Jet + E (1.1 fb ) (γ) D Ref. [21]. Here Wµν =(p1 + p2)µγν and theT other kinematical functions Wµναβ and 150 K(p ,p ,p ) can be foundLEP in [21].Combined Rules (b) and (c) are present for all SM groups; n=6: MD > 0.9 TeV 1.2 1 2 3 µναβγ rule (d) occurs for non-Abelianjet/ groupsγ (gluons+ MET shown). 100 Events / 10 GeV More stringent limits from 1

50 Lower Limit (TeV) D in an n-dimensional spatial volume having Kaluza-Klein index between k virtual graviton exchange M 0.8 | | 0 17 100 150 200 250 300 350 400 0.6 Leading Jet ET (GeV) 23456 Number of Extra Dimensions FIG. 2 (colorProbing online). the Predicted High Energy and observed Frontier leading at the jet LHC,ET Heidelberg U, Winter Semester 09/10, Lecture 9 19 distributions for the jet E candidate sample. The expected FIG. 3 (color online). 95% C.L. lower limits on M in the þ 6 T D LED signal contribution for the case of n 2 and MD ADD model as a function of the number of extra dimensions in 1:0 TeV is also shown. ¼ ¼ the model.

181602-6

ADD Signatures

f(p1) Key signature II: virtual i Gµν [Wµν + Wνµ] graviton exchange in −4MPl f(p2) (a) Drell-Yan dileptons Diphotons (γγ) Aα(p1) i Gµν [Wµναβ + Wνµαβ ] LEP & Tevatron ADD limits: −MPl Aβ(p2) (b) week ending PRL 102, 051601 (2009) PHYSICAL[DØ, PRL 102 (2009) 051601] REVIEW LETTERS 6 FEBRUARY 2009 n=2: MD > 2.1 TeV 3 ‡ D0 PRL 86, 1156 (2001) Visitor from Rutgers University, Piscataway, NJ, USA. f Gµν n=7: MD > 1.3 TeV expected limit xVisitor from II. Physikalisches Institut, Georg-August- 2.5 ee/γγ observed limit i University, Go¨ttingen, Germany. eQ [γµηνα + γν ηµα] −2MPl kVisitor from Centro de Investigacion en Computacion- –1 2 LHC discovery with 1 fb at DØ, 1.05 fb-1 IPN, Mexico City, Mexico.

[TeV] (c) s f Aα 14 TeV (numbers: CMS): M {Visitor from ECFM, Universidad Autonoma de Sinaloa, 1.5 Culiaca´n, Mexico. a **Visitor from Helsinki Institute of Physics, Helsinki, n=3: MD = 5.8 TeV gα(p1) Gµν 1 Finland. †† g3 abc Visitor from Universita¨t Bern, Bern, Switzerland. 234567 f K(p ,p ,p ) 1 2 3‡‡µναβγ n=6: MD = 4.0 TeV Number of Extra Dimensions (n ) MPl ¨ d Visitor from Universitat Zu¨rich, Zu¨rich, Switzerland. b c xxDeceased. Probing the High Energy Frontier at the LHC, Heidelberg U, Winterg ( pSemester2) 09/10,(d) Lecturegγ (9p3) 20 FIG. 3 (color online).β Observed and expected limits on the [1] N. Arkani-Hamed, S. Dimopoulos, and G. Dvali, Phys. effective Planck scale, Ms, in the di-EM channel along with Lett. B 429, 263 (1998); I. Antoniadis, N. Arkani-Hamed, previously published limits in di-EM channel. S. Dimopoulos, and G. Dvali, Phys. Lett. B 436, 257 Figure 5. Some of the Feynman rules connecting gravitons to SMfields,from(1998); N. Arkani-Hamed, S. Dimopoulos, and G. Dvali, (f) (γ) Ref. [21]. Here Wµν =(p1 + p2)µγν and the other kinematical functions WPhys.µναβ and Rev. D 59, 086004 (1999); N. Arkani-Hamed, S. and expectedK limits(p1,p2,p on3)µMναβγs, forcan be different found in [21]. formalisms Rules (b) and and (c) are for present for all SMDimopoulos, groups; and J. March-Russell, Phys. Rev. D 63, rule (d) occurs for non-Abelian groups (gluons shown). six different nd are summarized in Table III. The observed 064020 (2001). and expected limits on Ms for a given number of extra [2] J. L. Hewett, Phys. Rev. Lett. 82, 4765 (1999); K. Cheung, dimensions are found to be similar. The present limits are a Phys. Lett. B 460, 383 (1999); K. Cheung and significant improvementin an n-dimensional over spatial the volume published having limit Kaluza-Klein [6]. index betG.ween Landsberg,k Phys. Rev. D 62, 076003 (2000); | | Figure 3 summarizes the observed and expected limits on K. Cheung, Phys. Rev. D 61, 015005 (1999); O. J. P. 17 Eboli et al., Phys. Rev. D 61, 094007 (2000). Ms along with the previously published limits on Ms in the di-EM channel. [3] G. Giudice, R. Rattazzi, and J. Wells, Nucl. Phys. B544,3 In summary, we have performed a dedicated search for (1999), and revised version arXiv:hep-ph/9811291. [4] T. Han, J. Lykken, and R. Zhang, Phys. Rev. D 59, 105006 large extra spatial dimensions by looking for effects of (1999), and revised version arXiv:hep-ph/9811350. virtual Kaluza-Klein graviton in the dielectron and dipho- [5] V.M. Abazov et al. (D0 Collaboration), Nucl. Instrum. 1 ton channels using 1:05 fbÀ of data collected by D0 Methods Phys. Res., Sect. A 565, 463 (2006). detector. We see no evidence of excess over the standard [6] B. Abbott et al. (D0 Collaboration), Phys. Rev. Lett. 86, model prediction and set limits at 95% C.L. on the effective 1156 (2001). Planck scale at 2.09(1.29) TeV for 2(7) extra dimensions. [7] D. Gerdes et al., Phys. Rev. D 73, 112008 (2006). These are presently the most restrictive limits on the ef- [8] V.M. Abazov et al. (D0 Collaboration), Phys. Rev. Lett. fective Planck scale from searches for large extra 95, 161602 (2005). dimensions. [9] V.M. Abazov et al. (D0 Collaboration), Phys. Rev. Lett. We thank the staffs at Fermilab and collaborating insti- 101, 011601 (2008); T. Aaltonen et al. (CDF Collabo- tutions, and acknowledge support from the DOE and NSF ration), Phys. Rev. Lett. 101, 181602 (2008). [10] V.M. Abazov et al. (D0 Collaboration), Phys. Rev. D 76, (USA); CEA and CNRS/IN2P3 (France); FASI, Rosatom 012003 (2007). and RFBR (Russia); CNPq, FAPERJ, FAPESP and [11] T. Sjo¨strand, S. Mrenna, and P. Skands, J. High Energy FUNDUNESP (Brazil); DAE and DST (India); Phys. 05 (2006) 026; we used version 6.323. Colciencias (Colombia); CONACyT (Mexico); KRF and [12] J. Pumplin et al., J. High Energy Phys. 07 (2002) 012; D. KOSEF (Korea); CONICET and UBACyT (Argentina); Stump et al., J. High Energy Phys. 10 (2003) 046. FOM (The Netherlands); STFC (United Kingdom); [13] R. Brun and F. Carminati, CERN Program Library Long MSMT and GACR (Czech Republic); CRC Program, Writeup W5013, 1993 (unpublished). CFI, NSERC and WestGrid Project (Canada); BMBF and [14] P. Mathews, V. Ravindran, K. Sridhar, and W. L. van DFG (Germany); SFI (Ireland); The Swedish Research Neerven, Nucl. Phys. B713, 333 (2005); R. Hamberg, Council (Sweden); CAS and CNSF (China); and the W. L. van Neerven, and T. Matsuura, Nucl. Phys. B359, Alexander von Humboldt Foundation (Germany). 343 (1991); B644, 403(E) (2002). [15] K. Cheung and G. Landsberg, Phys. Rev. D 62, 076003 (2000). [16] T. Junk, Nucl. Instrum. Methods Phys. Res., Sect. A 434, 435 (1999); A. Read, CERN Report No. 2000-005 (2000); *Visitor from Augustana College, Sioux Falls, SD, USA. W. Fisher, FERMILAB-TM-2386-E (2007). †Visitor from The University of Liverpool, Liverpool, United Kingdom.

051601-7 ADD Signatures week ending PRL 103, 191803 (2009) PHYSICAL REVIEW LETTERS 6 NOVEMBER 2009

−1 0.1 DØ 0.7 fb based on NLOJET++ [21,22]. All theory calculations use Generic signature of new Standard Model 0.05 MSTW2008NLO PDFs [16] and the corresponding value Quark Compositeness of M 0:120. The PDF uncertainties are provided physics: deviation from QCD 0.25 < Mjj/TeV < 0.3 Λ = 2.2 TeV (η=+1) s Z 0 by theð 20Þ¼ MSTW2008NLO 90% C.L. eigenvectors. predictions of jet production 0.1 ADD LED (GRW) Ms = 1.4 TeV Renormalization and factorization scales  are varied

-1 [DØ, PRL 103 (2009) 191803] 0.05 TeV ED simultaneously around the central value of 0 pT in 0.3 < M /TeV < 0.4 ¼ h i Example: dijet correlation jj Mc = 1.3 TeV the range 0:5  2 where p is the average 0 0   0 h Ti y1 0.1 dijet pT. The quadratic sum of scale and PDF uncertainties * is displayed as a band around the central SM value in θ dijet 0.05 χ Fig. 1. The scale (PDF) uncertainties are always below /d 0.4 < Mjj/TeV < 0.5 0.5 < Mjj/TeV < 0.6 σ 0 5% (2%) so the band is nearly a line. The theory, including dijet CMS lab frame y2 d 0.1 the perturbative results and the nonperturbative correc- dijet σ tions, is in good agreement with the data over the whole

1/ 0.05 2 θ 0.6 < M /TeV < 0.7 0.7 < M /TeV < 0.8 M range with a (defined later) of 127.2 for 120 data y1 y2 1 + cos ∗ jj jj jj χdijet e| − | = 0 points in ten normalized distributions. Based on the agree- ≡ 1 cos θ∗ 0.1 − ment of the dijet measurement with the SM, we proceed to 0.05 1 set limits on quark compositeness, ADD LED, and TeVÀ → χ 0.8 < M /TeV < 0.9 0.9 < M /TeV < 1.0 dijet ! constant in QCD jj jj ED models. * 0 (θ decay angle in dijet CMS) 0.1 Hypothetically, quarks could be made of other particles, as assumed in the quark compositeness model in Refs. [1– 0.05 3]. We investigate the model in which all quarks are Interesting at the LHC: dijets 1.0 < Mjj/TeV < 1.1 Mjj/TeV > 1.1 0 considered to be composite. The parameters in this model available with very early data 5 10 15 5 10 15 are the energy scale à and the sign of the interference term χ = exp(|y -y |) dijet 1 2  between the standard model and the new physics terms. Probing the High Energy Frontier at the LHC, Heidelberg U, Winter Semester 09/10, Lecture 9 21 FIG. 1 (color online). Normalized differential cross sections in The ADD LED model [4,5] assumes that extra spatial dijet compared to standard model predictions and to the pre- dimensions exist in which gravity is allowed to propagate. dictions of various new physics models. The error bars display Jet cross sections receive additional contributions from the quadratic sum of statistical and systematic uncertainties. The virtual exchange of Kaluza-Klein excitations of the gravi- standard model theory band includes uncertainties from scale ton. There are two different formalisms (GRW [23] and variations and PDF uncertainties (see text for details). HLZ [24]). The model parameter is the effective Planck scale, MS, and the HLZ formalism also includes the sub- leading dependence on the number n of extra dimen- 1 In order to take into account correlations between sys- sions. The TeVÀ ED model [6–8] assumes that extra 1 tematic uncertainties, the experimental systematic uncer- dimensions exist at the TeVÀ scale. SM production cross tainties are separated into independent sources, for each of sections are modified due to virtual Kaluza-Klein excita- Miniature Blackwhich the effects Holes are fully correlated between all data tions of the SM gauge bosons. In this model, gluons can points. In total, we have identified 76 independent sources, travel through the extra dimensions, which changes the of which 48 are related to the jet energy calibration and 15 dijet cross section. The parameter in this model is the Dimopoulos, Landsberg [Phys.to Rev. the jet pLett.T resolution 87 (2001) uncertainty. 161602] These are: the dominant compactification scale, MC. sources of uncertainty. Smaller contributions are from the The new physics contributions have only been calcu- Objects with mass well abovejet Planck resolution scale and fromcan the form systematic black shifts in y. All lated to leading order (LO), while the QCD predictions are holes (BH) → if TeV-scale gravityother sourcesexists: are sizable negligible. AllBH sources production and their effects known to NLO. In this analysis, to obtain the best estimate are documented in Ref. [19]. For Mjj < 1 TeV (Mjj > for new physics processes, we multiply the new physics LO cross section (LHC production1 rate: TeV), systematicaround uncertainties 1 BH per are second 1%–5% (3%–11%);) calculations bin-by-bin by the SM k-factors (k ¼ they are in all cases less than the statistical uncertainties. NLO=LO). The k-factors are in the range 1.25–1.5, in- Semiclassical approach: geometricThe resultscross are section available in Ref. [19] and displayed in creasing with Mjj and decreasing with dijet. Their effects / n (n Fig.3)/12. The normalized dijet distributions1 (n+1) are presented in on single bins of the normalized dijet distributions within 2 2 π − n +3 √s ten Mjj regions, starting from Mjj > 0:25 TeV, and in- the different Mjj regions is below 12%. The new physics σBH πRS with RS = Γ n+2 ∼ n +2cluding one region2 forMMDjj > 1:1 TeV. The data are com- cross sections are computed using the matrix elements ￿ pared to￿ predictions￿ from a perturbative￿ QCD calculation from Refs. [2,3,5,8]. The theoretical variations (scale var- (MD Planck mass in 4+n dimensions,at next-to-leading RS Schwarzschild order (NLO) with nonperturbativeradius) cor- iations and PDF uncertainties) are consistently propagated rections applied. The nonperturbative corrections are de- into both the SM and the new physics contributions. termined using PYTHIA. They are defined as the product of Predictions for the different models are compared to the LHC: situation may be more thecomplicated corrections due to hadronization and to the underlying dijet data and to the SM results in Fig. 1. It is observed that event. The NLO results are computed using FASTNLO [20] all models predict increased contributions as dijet 1 #s ! MD → semiclassical approach for #s >> MD invalid ! Dijet final states may be more promising signature of TeV- 191803-5 scale gravity [Meade, Randall, JHEP05 (2008) 003]

Probing the High Energy Frontier at the LHC, Heidelberg U, Winter Semester 09/10, Lecture 9 22 Black Hole Signatures Event Horizon BH decay: BH loses energy by Hawking radiation: pair production close to event horizon → one particle tunnels through horizon Black Hole

BH lifetime for MD = 1 TeV: (n+3)/(n+1) MBH 26 τ 10− s ∼ 2(n+2)/(n+1) ≈ MD “Democratic” thermal decay (obeying all conservation laws): equal fractions of all SM particles

Spectacular signature: spherical high- [atlas.ch] multiplicity events (“hard to be missed”)

Probing the High Energy Frontier at the LHC, Heidelberg U, Winter Semester 09/10, Lecture 9 23

EXOTICS –DISCOVERY REACH FOR BLACK HOLE PRODUCTION Black Holes at the LHC

7 -1 -1 10 ATLAS n=2, m>5TeV ATLAS BH n=2 6 n=4 10 QCD Z+jets LHC studies3 based on n=7 5 10 10 W+jets n=2, m>8TeV ttbar semiclassical approach: 104 103 102 102 HighEvents / 200 GeV fb multiplicity: can be Events / 200 GeV fb 10 [CERN-OPEN-2008-020] recorded10 with many triggers 1 EXOTICS –DISCOVERY REACH FOR BLACK HOLE PRODUCTION 10-1 -2 Event1 selection: scalar sum of 10 0 1000 2000 3000 4000 5000 6000 7000 8000 0 1000 2000 3000 4000 5000 6000 7000 8000 Sum |P | [GeV] Sum |P | [GeV] transverse momenta $|pT|, T T

number of high-pT objects 4 ATLAS ] n=2

-1 10 n=4 n=7 103 Luminosity required Figure 10: ∑ pT distributions for (left) black hole samples and (right) backgrounds (QCD dijet, tt¯ and Mass reconstruction:| | 2 σ vector boson plus jets), along with one signal sample2 10 for reference.for They5 discovery are normalised to an integrated 2 1 MluminosityBH = of 1p fbi−+(. E/T, E/T ,x , E/T ,y , 0) 10 1 fb–1 ￿￿ ￿ 1 Integrated Luminosity [fb

-1 -1 -1 ATLAS BH n=2 10 ATLAS BH n=2 Expectation (ATLAS): BH QCD 3 QCD -2 10 3 Z+jets 10 Z+jets 10 W+jets W+jets discovery for MBH < 5 TeV ttbarwith 10-3 ttbar 102 2 –1 –1: 10 -4 “few pb ”, 1 fb MBH < 8 TeV 10 5 5.5 6 6.5 7 7.5 8 8.5 9 9.5 BH Mass Threshold [TeV] 10 Events / 200 GeV fb 10 Events / 200 GeV fb

Figure 17: Discovery potential using ∑ pT and lepton selections: required luminosity as a function of Probing the High Energy Frontier at the LHC, Heidelberg U, Winter Semester| | 09/10, Lecture 9 24 1 black hole mass threshold.1 Error bars reflect statistical uncertainties only.

-1 -1 10 0 1000 2000 3000 4000 5000 6000 7000 8000 900010000 10 0 1000 2000 3000 4000 5000 6000 7000 8000 900010000 Reconstructed BH Mass [GeV] Reconstructed BH Mass [GeV] 102 -1 n=2 fb ATLAS 10 n=4 n=7 Figure 11: Black hole mass distribution with a requirement1 ∑ pT >2.5 TeV (left), and black hole mass | | distribution with an additional requirement on the lepton-pT of pT > 50 GeV (right). The signal sample -1 with n = 2 and m > 5 TeV and backgrounds are shown.10

-2

Integrated Luminosity 10

Dataset Before selection ∑ pT > 2.5 TeV-3 After requiring a lepton acceptance | | 10 (fb) (fb) (fb) -4 = , > . . 3 . . 10 3 5 5.5 . 6 6.5. 7 3 7.5 8 8.5. 9 n 2 m 5 TeV 40 7 0 1 10 39 2 0 3 10 18 6 0 2 10 0 M46 TeV ± × ± × ± × BH cut n = 4,m > 5 TeV 24.3 0.1 103 22.6 0.2 103 6668 83 0.27 ± × ± × ± n = 7,m > 5 TeV 22.3 0.1 103 20.1 0.2 103 3574 60 0.17 ± × Figure± 18: Discovery× potential for black holes± using four-object and lepton requirements. The required n = 2,m > 8 TeV 338.2 1luminosity 338.1 is shown2.5 as a function of the 212 requirement16 on the reconstructed 0.63 black hole mass. The error ± 3 bars correspond+±12. to2 experimental systematic uncertainties.+±2.43 (See text for constraints.)6 tt¯ 833 100 10 23.6 6.7 8.2 2.43 9.8 10− ± × 6 −+1773 −+3.25 × 7 QCD dijets 12.8 3.7 10 5899 1771 5.37 2.02 4.3 10− ± × 6 −+9.0 +−8.7520 × 6 W￿ν + 2 jets 1.9 0.04 10 12.3 1.8 4.67 01822.93 2.4 10− ≥ ± × 3 +−2.02 +−0.95 × 5 Z￿￿ + 3 jets 51.8 1 10 2.75 2.01 2.57 0.64128 5.0 10− ≥ ± × − − × Table 6: Acceptance for each signal and background dataset in fb after requiring ∑ pT >2.5 TeV, and a | | lepton with pT > 50 GeV.

15 1817 123 Warped Extra Dimensions [R. Sundrum, DESY Physics Seminar, 10/14/09] Sundrum,[R. Seminar, DESY Physics

24

Probing the High Energy Frontier at the LHC, Heidelberg U, Winter Semester 09/10, Lecture 9 25

Warped Extra Dimensions

Initial Randall-Sundrum model (1999): 5D universe bounded by two branes: SM located on IR brane (TeV brane), gravity is strong on UV brane (Planck brane) 5th dimension highly curved (compare ADD: flat space-time) → Anti-de-Sitter (AdS) space: constant negative curvature k

2 k y µ ν 2 2 µ ν Metric:%%ds %= e %− %| | %ηµν %dx %dx % %d %y % (4D flat:%%ds = %ηµ %ν dx %d x ) warp − factor

RS model: solution to hierarchy problem

All fundamental mass parameters are O(MPl) at the UV brane, –k|y| k y scaled by e , e.g. for Higgs v.e.v. 0 φ 0 M e− | | ￿ | | ￿≈ Pl Need k|y| ! 35 to get Higgs v.e.v. to few 100 GeV → only little fine-tuning, “not too unnatural”

Probing the High Energy Frontier at the LHC, Heidelberg U, Winter Semester 09/10, Lecture 9 26 RS Phenomology26 JH,MS Nucl. Part. Sci. 52 (2002) 397] Sci. Part. Nucl. [Hewett, Spiropulu, Ann. Rev. Rev. Ann. Spiropulu, [Hewett, ee→μμ cross section Warp factor: masses & mass for KK tower of differences of Kaluza-Klein RS gravitons excitations around 1 TeV: resonances, e.g. in dilepton spectrum RS model has been developed

Figure 4: The cross section for e+e− µ+µ− including the exchange of a KK tower of gravitons in further: → the Randall-Sundrum model with m1 =500GeV.Thecurvescorrespondtok/M Pl =intherange 0.01 0.05. − Wave functions of SM particles propagate in the bulk

m1 Reach (TeV) Explanation of different particle − Tevatron Run II 2 fb 1 1.1 LHC 100 fb−1 6.3 masses: overlap with Higgs wave LEP II 3.1 LC √s =0.5TeV500fb−1 13.0 function LC √s =1.0TeV500fb−1 23.0 LC √s =1.5TeV500fb−1 31.0

Table 4: 95% CL search reach for the mass m1 of the first KK gauge boson excitation (46). Gauge unification works, too [R. Sundrum, DESY Seminar] Probing the High Energy Frontier at the LHC, Heidelberg U, Winter Semester 09/10, Lecture 9 27

RS and Top Physics

SM particles in bulk: Large overlap (= strong coupling) of KK graviton (spin-2) and d p/0GV) GeV (pb/20 /dM

heavy fermions σ d Expect distinct width depends on resonances in top pair curvature k = &κ mass spectrum Signatures: bump in mass spectrum, highly [Frederix, Maltoni, hep-ph/0712.2355] boosted top quarks g t¯ q t¯ Also possible: KK gluon (spin-1) exchange g KK graviton t q¯ KK gluon t

Probing the High Energy Frontier at the LHC, Heidelberg U, Winter Semester 09/10, Lecture 9 28 Universal Extra Dimensions

Appelquist, Cheng, Dobrescu (2001): All SM fields live in 4+n dimensions, EDs compact & flat Many interesting theoretical properties: proton decay protected, motivation for 3 quark/lepton generations, … Experimentally: KK resonances of photon and gluons not observed → size of EDs must be L < 1/(few 100 GeV) UED: attractive phenomenology UED models look a lot like SUSY including dark matter candidate (“bosonic SUSY”: KK partners have same spin) New conserved quantum number KK parity: k-th KK mode k has PKK = (–1) → lightest KK mode (k=1) is stable, k-odd KK modes only produced in pairs (less restricted by EW data)

Probing the High Energy Frontier at the LHC, Heidelberg U, Winter Semester 09/10, Lecture 9 29

UED Phenomenology

UED particle spectrum: 2 Early LHC data: signature- based analysis very similar preserve the 5th dimensional momentum (KK number). The corresponding coupling constants among KK modes to SUSY searches are simply equal to the SM couplings (up to normaliza- tion factors such as √2). The Feynman rules for the KK modes can easily be derived (e.g., see Ref. [8, 9]). ATLAS: discovery with In contrast, the coefficients of the boundary terms are –1 not fixed by Standard Model couplings and correspond 200'pb up to ED size of to new free parameters. In fact, they are renormalized by the bulk interactions and hence are scale dependent L'!'1/(700 GeV) [10, 11]. One might worry that this implies that all pre- dictive power is lost. However, since the wave functions 6 ATLAS Preliminary of Standard Model fields and KK modes are spread out 10 TeV over the extra dimension and the new couplings only UED model exist on the boundaries, their effects are volume sup- 5 pressed. We can get an estimate for the size of these Significance volume suppressed corrections with naive dimensional 4 analysis by assuming strong coupling at the cut-off.The FIG. 1: One-loop corrected mass spectrum of the first KK −1 result is that the mass shifts to KK modes from bound- level in MUEDs for R =500GeV, ΛR =20and mh =120 3 ary terms are numerically equal to corrections from loops GeV. 2 2 2 2 3jet+0lep δmn/mn g /16π . 2 We will∼ assume that the boundary terms are symmetric [Cheng, Matchev, Schmaltz, 2jet+1lep under the exchange of the two orbifold fixed points, which PRD 66 (2002) 056006] 1 2jet+2lep OS preserves the KK parity discussed below. Most relevant to the phenomenology are localized kinetic terms for the SM fields, such as 300 400 500 600 700 800 900 1000 1/R [GeV] δ(x5)+δ(x5 πR) 2 − G4(Fµν ) + F4Ψi/DΨ + F5Ψγ5∂5Ψ , [ATLAS-PHYS-PUB-2009-084] Λ Probing the High Energy Frontier at the LHC, Heidelberg U, Winter Semester 09/10, Lecture 9 ! (2)" Figure 11: Significance σ as a function of 1/R for the Universal Extra Dimensions30 scenario, taking into account channels with 0, 1 and 2 leptons. where the dimensionless coefficients G4 and Fi are arbi- trary and not universal for the different Standard Model fields. These terms are important phenomenologically for several reasons: (i)theysplitthenear-degeneracyofKK modes at each level, (ii)theybreakKKnumberconserva- tion down to a KK parity under which modes with odd KK numbers are charged, (iii)theyintroducepossible new flavor violation. FIG. 2: Radiative corrections (in %) to the spectrum of the −1 Since collider signatures depend strongly on the values first KK level for R =500GeV, versus ΛR. of the boundary couplings it is necessary to be definite and specify them. A reasonable ansatz is to take flavor- universal boundary terms. Non-universalities would give dictive and has only three free parameters: rise to FCNCs as in supersymmetry with flavor violating scalar masses. This still leaves a large number of free pa- R, Λ,mh , (3) rameters. For definiteness, and also because we find the { } resulting phenomenology especially interesting, we make where mh is the mass of the Standard Model Higgs boson. the assumption that all boundary terms are negligible at The low energy KK spectrum of MUEDs depends on 20 some scale Λ >R−1.Thisdefinesourmodel. the boundary terms at low scales which are determined Note that this is completely analogous to the case of from the high energy parameters through the renormal- the Minimal Supersymmetric Standard Model (MSSM) ization group. Since the corrections are small we use the where one has to choose a set of soft supersymmetry one-loop leading log approximations. In addition to the breaking couplings at some high scale, before studying boundary terms we also take into account the non-local the phenomenology. Different ansaetze for the parame- radiative corrections to KK masses. All these were com- ters can be justified by different theoretical prejudices but puted at one-loop in [10]. ultimately one should use experimental data to constrain AtypicalspectrumforthefirstlevelKKmodesis them. In a sense, our choice of boundary couplings may shown in Fig. 1. Fig. 2 shows the dependence of the split- be viewed as analogous to the simplest minimal super- tings between first level KK modes on the cutoff scale Λ. gravity boundary condition – universal scalar and gaug- Typically, the corrections for KK modes with strong in- ino masses. Thus the model of MUEDs is extremely pre- teractions are > 10% while those for states with only There’s much more…

Popular BSM models I didn’t have time to speak about Generic additional gauge group, e.g. additional U(1) → heavy Z’ resonance decaying to l+l– 4th generation quarks: heavy t’ and b’ → 4D CKM matrix: enhanced flavor sector EW symmetry breaking via new strong force at the TeV scale (e.g. Technicolor): W/Z masses from new Goldstone bosons Little Higgs models: Higgs as pseudo-Goldstone boson of new symmetry at about 10 TeV → new gauge bosons and a heavy T quark (mixed with the SM top quark) Leptoquarks (LQ): gauge bosons of a larger group with baryon and lepton number ( 0 → decay LQ → ql Unparticles: stuff that cannot be described as particles

Probing the High Energy Frontier at the LHC, Heidelberg U, Winter Semester 09/10, Lecture 9 31

Chapter 12

High-pT Physics at the LHC: Summary and Outlook Attempting to summarize…

LHC start marks new era of particle physics Pushing up the high-energy frontier Unprecedented CMS energies, highly sophisticated particle detectors designed to discover Higgs and/or BSM physics Shed light on EW symmetry breaking mechanism (Higgs?) If there is BSM physics at the TeV scale, the LHC will very likely discover it What’s next? Looking forward to 5–10 years of (initial) LHC data-taking Physics results will have major impact on next steps in particle physics: LHC upgrade → e+e– collider → ???

Probing the High Energy Frontier at the LHC, Heidelberg U, Winter Semester 09/10, Lecture 9 33

From LHC to sLHC

Super-LHC (sLHC): 5-10× more instantaneous luminosity Current planning: Phase I 2014/5 → Phase II 2019/20 Accelerator upgrade: new CERN pre-accelerator chain, better beam focusing in interaction regions Detector upgrades: replacement of inner detectors (problems: radiation damage, high occupancy), triggers with improved selectivity (e.g. track triggers), … sLHC physics case: No single most important channel, but higher luminosity is needed in general if BSM physics is at 3 TeV rather than 1 TeV Incremental improvements on Higgs & BSM particle properties, better sensitivity in searches for new high-mass particles

Probing the High Energy Frontier at the LHC, Heidelberg U, Winter Semester 09/10, Lecture 9 34 sLHC Physics Case

2010* 2019/20* *estimate in late 2009 Probing the High Energy Frontier at the LHC, Heidelberg U, Winter Semester 09/10, Lecture 9 35

Linear e+e– Collider Philip Bechtle et al.: Constraining SUSY models with Fittinousingmeasurementsbefore,withandbeyondtheLHC 37

Derived Mass Spectrum of SUSY Particles LE+LHC300 MSSM18 Hadron colliders (= discovery 1000 Table 24: Result of the fit of the mSUGRA model to the 900 1$ Environment existing measurements and to the expected results from int −1 2 Environment LHC with =300fb and ILC. machines) usually complemented 800 $ L 700 Best Fit Value by lepton colliders (= precision 600 Parameter Nominalvalue Fit Uncertainty ± 500 LHC Only tan β 10 9.999 0.050 M1/2 (GeV) 250 249.999 ± 0.076 machines) 400 M0 (GeV) 100 100.003 ± 0.064 300 A0 (GeV) −100 −100.0 ± 2.4 Avoid large synchrotron radiation 200

Derived Particle Mass [GeV] 100 losses:38 need Philip Bechtle linear et al.: Constraining accelerators SUSY models with Fittino using0 measurements before, with and beyond the LHC 0 0 0 + 0 0 0 0 + + ~ ~ # # ~ ~ ~ ~ ~ ~ ~ h A H H ! ! ! ! ! ! " " 1 2 3 4 1 2 lR lL 1 2 qR qL b1 b2 t1 t2 g masses and couplings. In addition to just increasing the experimental precision, the ILC is also expected to de- Physics4.4.2 MSSM18case: precision Derived Mass Spectrum of SUSY Particles LE+LHC+ILC MSSM18 Fig. 38: SUSY mass spectrum consistent with the ex- liver a wealth of measurements of absolute branching frac- tions and cross-sections, many cross-section times branch- measurementsAs discussed in Section of 4.3.2Higgs,,thefitoftheMSSMparam- top, BSM isting600 low-energy measurements1$ Environment from Table 1 and the int ing fraction measurements, and many model-independent eters at the SUSY breaking scale allows a bottom-up test expected LHC measurements2$ Environment from Table 2 at = 300 fb−1 for the MSSM18 model. The uncertaintyL ranges measurements of quantum numbers and CP-properties. physicsof SUSY (cf. breaking LEP and precision is independent oftests any assumptions of 500 Best Fit Value about physics at the GUT scale. Section 4.3.2 showed that represent model dependent uncertainties of the sparticle This expected wealth of data, especially in a SUSY sce- the SM)for the MSSM18 model, the parameter uncertainties from masses400 and not direct mass measurements. nario with a rich phenomenology below a mass scale of fits to existing data and expected LHC data are larger by 500 GeV, as predicted by the present measurements in at least one order of magnitude with respect to the fits of 300 Section 4.1,willstronglyenhancetheknowledgefromthe Requiredthe mSUGRA energy scenario. range unknown, The obtained MSSM18LHC + fit resultILC can again be trans- LHC due to the expected complementarity of ILC and Table 25 shows a comparison of the parameter uncer- lated200 into a corresponding sparticle mass spectrum. This LHC results [13]. dependstainties on of the nature fits of the MSSM18and modelmasses using LEof data spectrum is presented in Figure 38.Againthemassesin In this section, first the expected precision on the pa- −1 BSM inphysics combination discovered with int =300fb atof data the at the LHC thisDerived Particle Mass [GeV] Figure100 are model dependent predictions and do not rameters of the mSUGRA model is studied, followed by a (LE+LHC300) and theL latter plus the expected ILC re- represent direct mass measurements. Compared to the detailed comparison of the results of the MSSM18 fit us- 0 0 0 + 0 0 0 0 + + ~ ~ # # ~ ~ ~ ~ ~ ~ ~ correspondingh A H resultH ! ! for! ! the! ! morel l constrained" " q q b b mSUGRAt t g LHC →sults decisions (LE+LHC300+ILC). around The results 2012 of Markov Chain 1 2 3 4 1 2 R L 1 2 R L 1 2 1 2 ing only LE and LHC data with those obtained using LE, Monte Carlo scans and Toy Fits are in good agreement, model (Figure 35), some of the sparticle masses have sig- LHC and ILC data. Finally, the increase in precision is therefore just the Markov Chain result is shown. For most Fig.nificantly[Bechtle 39: Derived larger uncertaintieset mass al., distributions arXiv:09072589] in the MSSM18. of the SUSY This particles is par- used to predict the cosmic cold dark matter relic density 2 2 parameters, the uncertainties decrease by approximately usingticularly existing pronounced measurements, for the heavy expected Higgs results boson from masses, LHC ΩCDMh from collider data, from fits excluding ΩCDMh Probing the High Energy Frontier at the LHC, Heidelberg U, Winter Semester−1 09/10, Lecture 9 one order of magnitude. Interestingly, the increase in pre- withwhichint are=300fb – as statedand above expected – not results directly from accessible36 ILC. at itself from the list of observables. cision is not only limited to those parameters which are the LHCL for the considered SUSY benchmark point. linked directly to observables at tree level. For example Although not studied explicitly for the MSSM18, one it is expected that the uncertainties of the gaugino mass may expect that chain ambiguities may have a larger im- pact for this model than in the mSUGRA case. Since parameters M1 and M2 are significantly decreased at ILC 4.4.1 mSUGRA 0 ± MSSM18450 has more independently adjustable parameters, due to the increased precision on theχ ˜1/2 andχ ˜1 masses LE+LHC+ILC mSUGRA: % = 0.99995 ± 0.00098 and the additional information from precise measurements different400 decay chain LE+LHC+ILC interpretations MSSM18: % can = 1.00009 be more ± 0.00208 easily of cross-sections times branching fractions for different po- matched with the model LE+LHC due MSSM18: to the % = increased 0.97286 ± 0.07131 flexibility. WMAP % h2 ± 1$ DM Using the same available and expected measurements as larisations. Also, the precision of the heavy Higgs sector 350 2 Planck % h ± 1$ int −1 DM in the fit using =300fb of LHC luminosity in Sec- parameter mA is expected to increase dramatically, since ± 4.4 Low-Energy300 Observables, LHC and Expectations tion 4.3.1,plustheexpectedILCmeasurementsdiscussedL the heavy Higgs bosons A, H and H are not expected 120 to be discovered at the LHC in this scenario, but to be for ILC in Section 2.3,thefitofthemSUGRAmodeltothedata 250 100 precisely measured at the ILC [13]. In contrast to those of the SPS1a scenario is shown in Table 24.Thecompari- The results of80 the previous sections show that the expected son with the results without ILC in Table 22 shows the in- measurements, no additional experimental information is Toy fits 200 obtained on the gluino mass or the heavier squark masses data of the LHC60 allow to obtain rather precise constraints crease in precision by a factor of 5 to 10. However, the pure on the mSUGRA parameters once sufficient luminosity is increase in precision for the fit of a high scale scenario is at ILC. In any case, with the exception of Mq˜R ,allpa- 150 40 accumulated. However, for the MSSM18 scenario, the con- not the only improvement using ILC. First, possible devi- rameter uncertainties improve dramatically. The reason 20 for this behaviour is the strong decrease of correlations. straints100 severely diminish due to the increased theoretical ations of the SUSY breaking implemented in Nature from 0 For example, the ˜b masses are determined by M and freedom. The0.992 parameter 0.994 0.996 0.998 1 uncertainties 1.002 1.004 1.006 1.008 typically increase agivenGUT-scaleSUSYbreakingscenario,involvingas- 1/2 q˜L by a factor50 of 10 or more. Therefore an extrapolation of sumptions on unification, are much more visible using also M˜ ,butalsobytheoff-diagonal elements mbXb with bR the SUSY parameters from the electro-weak scale to the ILC data. Second, the high accuracy and especially the Xb = Ab µ tan β.Duetothestrongincreaseinthede- 0 termination− of µ and tan β from the measurements in the GUT scale0 is a 0.2fflicted with 0.4 large 0.6 uncertainties, 0.8 1if only 1.2 low- larger variety (covering couplings, mixings, masses, widths energy, flavour physics, electro-weak precision, cosmolog- and quantum numbers) and stronger model independence Higgs sector (where also Ab plays a role in loop effects) % h2(predicted)/% h2(measured) and the gaugino sector, also the precision of the param- ical and LHCDM observables are used.DM of the measurements allow to fit more general models of The expected measurements at the International Lin- New Physics. This makes it possible to study the SUSY eter M˜ is strongly improved, although no direct mea- bR ear Collider, however, could dramatically increase2 the breaking mechanism using a bottom-up instead of a top- surement in the sbottom sector is made at the ILC in Fig. 40: Ratio of the predicted value of Ωpredh to the experimental precision of2 the measurements of sparticle down approach. this scenario. This example highlights the importance of nominal value of ΩSPS1ah in the SPS1a scenario for a va- 2 precision measurements for the detailed unravelling of the riety of Toy Fits without using ΩCDMh as an observable. SUSY spectrum, and it is an example of the complemen- tarity of LHC and ILC. The resulting derived spectrum of sparticle masses is ILC using the Toy Fit technique. The resulting predicted 2 shown in Figure 39.Itrepresentsaverystrongimprove- values of ΩCDMh are shown in Figure 40 and compared ment over the results without ILC in Figure 38.TheHiggs with the present and expected experimental precision of 2 sector exhibits the strongest improvement due to the di- ΩCDMh from the WMAP [57]andPlanck[103]data.The 2 rect observation of heavy Higgs states. Apart from the prediction of ΩCDMh from collider data without ILC in squark mass mq˜L ,solelygovernedbytheparameterMq˜R , the MSSM18 model shows a long non-Gaussian tail down 2 the uncertainties of all other derived masses increase dra- to ΩCDMh =0.TheGaussiancoreofthedistributionis matically. one order of magnitude wider than the expected precision As a final test of the agreement between cosmology and from the Planck satellite. Therefore witout ILC, the relic collider data, and as a showcase for the predictive power density constraints inferable from particle physics within of precision collider measurements, additional fits with- the MSSM18 model do not match the precision of cosmo- 2 out ΩCDMh are performed with and without the use of logical measurements. ILC and CLIC Artist’s view of ILC Tunnel ILC (International Linear Collider) Most advanced plans: superconducting RF cavities with >30 MV/m acceleration 32 km e+e– collider at 0.5-1.0 TeV CMS energy CLIC (Compact Linear Collider) Drive-beam acceleration up to 100 MV/m 48 km e+e– collider at 3'TeV CMS energy [http://clic-study.web.cern.ch/CLIC-Study/] Probing the High Energy Frontier at the LHC, Heidelberg U, Winter Semester 09/10, Lecture 9 37

LHC Flavor Physics

LHC physics program is not just high-pT physics Flavor physics (mainly LHCb) Heavy ion physics (mainly ALICE) Next three lectures: flavor physics at the LHC Lecturer: Ulrich Uwer, PI Probing the high energy frontier in rare B meson decay Stay on board! – Thanks! –

Probing the High Energy Frontier at the LHC, Heidelberg U, Winter Semester 09/10, Lecture 9 38