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LHC Physics Alan Barr UCL

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**This morning’s stuff… Higgs – why we expect it, how to look for it, …**

Supersymmetry – similar questions! Smorgasbord of other LHC physics

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Physics at TeV-scale Dominated by the physics of Electroweak Symmetry Breaking Answering the question: “Why do the W and Z bosons have mass?” Standard Model suggests: Higgs mechanism However Higgs boson predicted by SM not yet observed

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**Higgs mechanism - history**

1964 Demonstration that a scalar field with appropriate interactions can give mass to gauge bosons Peter Higgs (Edinburgh, previously UCL) Independently discovered by Francois Englert and Robert Brout (Brussels) Not until 1979 that Salam, Weinberg and Glashow use this in a theory of electroweak symmetry breaking For a biographic article on P. Higgs see

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**Higgs mechanism: why needed?**

Example of P. Higgs – give mass to a U(1) boson (heavy “photon” in a QED-like theory) Start with QED Lagrangian: where Which is invariant under the local U(1) gauge transformation (*) Adding a gauge boson mass term could be attempted with a term like: But this isn’t invariant under gauge transformation (*) so is not allowed Instead add a complex scalar field which couples to the gauge boson

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**Pictorial representation**

Excitations in this direction produce physical Higgs boson Quartic term self- coupling positive Excitations in this direction = gauge transformation - Global transformations unobserved - Local transformations give mass to gauge bosons Quadratic coupling term negative Degenerate minimum Vacuum (field strength≠0) If you don’t understand this, study Phys.Lett.12: ,1964 Scalar field strength = 0

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**Higgs field “eats Goldstone boson”**

φ φ Flat direction in potential usually represents zero-mass particle “Goldstone boson” But in Higgs theory this direction is coupled to the gauge boson No massless Goldstone boson Instead mass term generated for gauge boson φ' Gauge boson Example of a Feynman diagram showing a contribution to the gauge boson mass term N.B. Our example here was for a single complex scalar and for a U(1) field. In the Standard Model the Higgs is an electroweak SU(2) doublet field, with 4 degrees of freedom. 3 of these are ‘eaten’ by W±, Z0, mass terms leaving a single scalar for the physical Higgs boson. For full SU(2) treatment see e.g. Halzen & Martin section 14.9

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**Constraints on the Higgs mass**

Higgs boson mass is the remaining unpredicted parameter in Standard Model: Higgs self-couplings not predicted So Higgs mass not predicted by Electroweak theory However there are: Bounds from theory: Perterbative unitarity of boson-boson scattering Indirect bounds Loop effects on gauge boson masses Direct bounds Searches

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Perturbative limit Vector Boson scattering Without other new physics the Higgs boson must exist & have mass < 1 TeV Phys.Rev.D16:1519,1977 Halzen & Martin section 15.6

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**Indirect Higgs bounds: LEP Electroweak data**

W (and Z) mass depends on mHiggs Logarithmic loop corrections to masses Also depends on top mass Measurements Prediction as a function of mH

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**Direct bounds: Higgs searches @ LEP**

Higgsstrahlung – dominant production No discovery Direct lower bound at GeV ALEPH: Candidate vertex: Phys.Lett. B565 (2003) 61-75

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**Higgs-Hunter Situation Report**

Something very much like the Higgs must exist with: ~100 GeV < m < ~1 TeV No discovery as yet If it is a Standard Model Higgs the constraints are tighter: GeV < mSM Higgs < 199 GeV

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**The Large Hadron Collider**

27 km circumference Built in LEP tunnel Hadron Mostly protons Can also collide ions Collider ~ 7 x higher collision energy ~ 100 x increase in luminosity Compared to Tevatron Proton on Proton at √s = 14 TeV Design luminsoity ~ ~100 fb-1 / expt / year

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**General Purpose Detectors**

Similarities: Tracker Calorimeter Muon chambers ATLAS Differences: Size : CMS “compact” Magnetic-field configuration ATLAS has muon toroids Electromagnetic-Calorimeter: CMS crystals. ATLAS Liquid Argon Outer tracker technology CMS all-silicon. ATLAS straw tubes

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**Definitions * * *prove these! y φ Particle x θ Beam pipe proton proton**

η = -1 η = 0 η = +1 η = -2 η = +2 η = -3 η = +3 θ Beam pipe proton proton z Endcap “Forward” Barrel “Central” Endcap “Forward” Differences in rapidity are conserved under Lorentz boosts in the z-direction Rapidity: * Pseudorapidity: Good approximation to rapidity if E>>m * pT = (px, py) “Transverse” |pT| = √(px2, py2) *prove these!

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**Making particles in hadron colliders**

proton proton Hadron-Hadron collisions complicated See lectures by Mark Lancaster (“Hadron Collider Physics”) QCD Lots of background events with jets QCD Lots of hadronic “rubbish” in signal events Hard scatters are largely from q-qbar or glue-glue Proton structure is important – See lectures by Robert Thorne But they provide the highest energies available Often these are the discovery machines

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**LHCb Asymmetric detector for B-meson physics**

For more information see Lazzeroni talk at:

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**LHCb Physics VCKM must be unitary: V.V† = V †.V = 1**

Quark flavour e-states are not the same as mass e-states: mixing: VCKM must be unitary: V.V† = V †.V = 1 Multiply out rows & columns: Do this!

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LHCb Physics Measurements of decay rates and kinematics tell us about squark mixings Over-constraining triangles gives sensitivity to new physics through loop effects

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ALICE Designed to examine collisions of heavy ions (e.g. lead-lead or gold-gold) Theorised to produce a new state of matter – a quark-gluon plasma Quarks no longer confined inside colourless baryons Signals for QGP: Jet quenching Quarkonim (e.g. J/ψ) suppression (“melt bound states”) QGP Jet No Jet c _ J/ψ c

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**Couplings of the SM Higgs**

Couplings proportional to mass What does this mean for the Higgs-hunter?

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**Producing a Higgs Higgs couplings mass**

u-ubar H has very small cross-section Dominant production via vertices coupling Higgs to heavy quarks or W/Z bosons

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**Production cross-sections**

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**Decay of the SM Higgs Width becomes large as WW mode opens**

Branching ratios change rapidly as new channels become kinematically accessible

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Needle in a haystack… QCD jet production at high energy Higgs production Need to use signatures with small backgrounds: Leptons High-mass resonances Heavy quarks to avoid being overwhelmed

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**Example 1 : H ZZ Only works when mHiggs >~ 2.MZ**

When the Z decays to leptons there are small backgrounds q _ H Z e+ e-

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**H ZZ CMS H ZZ e+e- e+e-**

Electrons have track (green ) & energy deposit (pink)

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H ZZ e+e- e+e- q _ H Z e+ e- mH=150 background mH=130 mH=170 Find events consistent with above topology (four electrons) Add together the four electron 4-vectors Find the mass of the resultant 4-vector ( mass of the Higgs) Plot shows simulated distributions of [invariant mass of four electrons] for 3 different values of mHiggs (We wouldn’t see all of these together!)

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**Example (2): H γγ No direct coupling of H to photon**

However allowed at loop level Branching ratio: ~ (at low mHiggs) Important at low mass Actually a very clean way of looking for Higgs Small backgrounds Production and decay of Higgs through ‘forbidden’ direct couplings

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γ γ H γγ CMS simulation. Physics TDR, 2006

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H γγ Higgs signal scaled up by factor 10! Invariant mass of the pair of photons Simulation by CMS for different Higgs masses for early LHC data (1 fb-1)

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**H γγ … backgrounds γ π0 “Irreducible” 2 real photons “Born” “Box”**

e.g. fake photons γ q Need v. good calorimeter segmentation to separate these γ q _ γ π0 gluon

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**Recent find – vector boson fusion**

Tagging Jet Smaller production cross-section Weak couplings But low backgrounds Tagging Jet No QCD COLOUR exchange between q and qbar So no QCD irradiation into central part of detector

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Significance Significance is a measure of the answer to the question “What is the probability that a background fluctuation would produce what I am seeing” H->ZZ 5- means “probability that background fluctuation does this is less than 2.85·10-7 ” 5- is usually taken as benchmark for “discovery”

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**After discovery of Higgs?**

Measure Higgs mass The remaining unconstrained parameter of the Standard Model Measure Higgs couplings to fermions and vector bosons All predicted by Standard Model Check Higgs mechanism Couplings very important since there may be more than one Higgs boson Theories beyond the Standard Model (such as Supersymmetry) predict multiple Higgs bosons. In such models the couplings would be modified Do direct searches for further Higgs bosons!

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**If no Higgs found? Arguably more exciting than finding Higgs**

Look at WW scattering process Look for whatever is “fixing” the cross-section E.g. exotic resonances

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What is supersymmetry? Examples of Supersymmetric partner-states Nature permits only particular types of symmetry: Space & time Lorentz transforms Rotations and translations Gauge symmetry Such as Standard Model force symmetries SU(3)c x SU(2)L x U(1) Supersymmetry Anti-commuting (Fermionic) generators Changes Fermions into Bosons and vice-versa Consequences? Supersymmetric theory has a Boson for every Fermion and vice-versa Doubles the particle content Partners to Standard Model particles not yet observed

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**Supersymmetric partners**

(S)Particles Standard Model Supersymmetric partners quarks (L&R) leptons (L&R) neutrinos (L&?) squarks (L&R) sleptons (L&R) sneutrinos (L&?) Spin-1/2 Spin-0 After Mixing Z0 W± gluon B W0 Bino Wino0 Wino± gluino Spin-1 4 x neutralino Spin-1/2 gluino h0 H0 A0 H± ~ H0 H± ~ 2 x chargino Spin-0 (Higgsinos) Extended higgs sector 2 cplx doublets 8-3 = 5 Higgs bosons!

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**Why Supersymmetry? Higgs mass Enter Supersymmetry (SUSY)**

Quantum corrections to mH Would make “natural” mass near cut-off (Unification or Planck scale) But we know mH <~ 1 TeV mH = mH bare + DmH Severe fine tuning required between two very big numbers Enter Supersymmetry (SUSY) Scalar partner of quarks also provide quantum corrections Factor of -1 from Feynman rules Same coupling, λ Quadratic corrections cancel mH now natrually at electroweak scale top Δm2(h) Λ2cutoff higgs λ Quantum correction to mHiggs stop higgs λ Cancelling correction to mHiggs

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**Further advantages Lightest SUSY particle is:**

Weakly interacting Stable Massive Good dark matter candidate Predicts gauge unification Extra particles modify running of couplings Step towards “higher things” Big Bang relic abundance calculations are in good agreement with WMAP microwave background observations in regions of SUSY parameter space 1/α 1/α +SUSY miss Hit! SM Log10 (μ / GeV) Log10 (μ / GeV)

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**R-parity Multiplicative discrete quantum number RP = (-1)2s+3B+L**

S=spin, B=baryon number, L=lepton number Standard Model particles have RP = +1 SUSY Model particles have RP = -1 If RP is conserved then SUSY particles must be pair-produced If RP is conserved then the Lightest Supersymmetric Particle (LSP) is stable Example of a Feynman diagram for proton decay which is allowed if the RP-violating couplings (λ) are not zero

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**How is SUSY broken? Direct breaking in visible sector not possible**

Weak coupling (mediation) Direct breaking in visible sector not possible Would require squarks/sleptons with mass < mSM Not observed! Must be strongly broken “elsewhere” and then mediated Soft breaking terms enter in visible sector (>100 parameters) Strongly broken sector Soft SUSY- breaking terms enter lagrangian in visible sector Various models offer different mediation e.g. Gauge “GMSB” Gravity “mSUGRA” (supergravity) Anomaly “AMSB”

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**Sparticle Interactions**

Interactions & couplings same as SM partners 2 SUSY legs for RP conservation Largely partner of W0 boson Largely partner of W0 boson Q: Does the gluino couple to: the quark? the slepton? the photino?

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**“typical” susy spectrum (mSUGRA)**

General features Mass/GeV Complicated cascade decays Many intermediates Typical signal Jets Squarks and Gluinos Leptons Sleptons and weak gauginos Missing energy Undetected Lightest Susy Particle Production dominated by squarks and gluinos “typical” susy spectrum (mSUGRA)

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**The “real thing” (a simulation of…)**

Invisible particles Two high-energy jets of particles Visible decay products “Missing” momentum From two invisible particles these are the invisible Dark Matter guys Proton beams perpendicular to screen

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**Standard Model backgrounds: measure from LHC DATA**

μ μ n With SUSY Measure in Z -> μμ Use in Z -> νν R: Z -> nn B: Estimated Example: background to “4 jets + missing energy” Measure background in control region Extrapolate to signal region Look for excess in signal region Missing PT / GeV

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**Constraining SUSY masses**

Mass constraints Invariant masses in pairs Missing energy Kinematic edges Frequently- studied decay chain Observable: Depends on: Limits depend on angles between sparticle decays

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**Mass determination Try various masses in equations Measure edges**

C.G. Lester Narrow bands in ΔM Wider in mass scale Improve using cross- section information Variety of edges/variables These measurements can tell us about SUSY breaking

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**Other things to do with SUSY**

Measure the sparticle spins “prove” that it is really supersymmetric partners we are seeing Measuring the couplings & mixings Use to “predict” Dark Matter relic density Find the extra Higgs bosons Recall that SUSY predicts 5 Higgs bosons Now we want to find H0, h0, A0, H± Also measure their couplings, CP, …

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**Standard Model Physics**

The ATLAS and CMS experiments also potentially can measure: Top mass W mass Rare B-meson decay rates Jet physics To much higher precision that is currently achievable Large number of e.g. top quarks produced Small statistical errors Systematic errors (such as jet energy scale determination) limiting Mass of hadronic top

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**Other things to look for…**

Leptoquarks Motivated by Grand Unified Theories Carry lepton and baryon number E.g. LQ bμ New heavy quarks Predicted by some non-SM Higgs theories New heavy gauge bosons Indications of new symmetry groups Extra dimensions Large variety of models on the market!

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**Extra dimensions models**

Motivated by need for ED in string theory and m-theory Logical a possibility for a LHC discovery Different models… Which particles are localised where (bulk/brane) Form of space-time metric (flat/warped) Geometry and size of extra dimensions …make different predictions Kalazua-Klein resonances of SM particles Graviton states Stringy resonances Effects of strong gravity (micro Black Holes) Energy loss into extra dimensions More information:

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General sources Higgs at the LHC: talk by Zeppenfeld Physics at the LHC: Higgs talk by Harlander: ATLAS physics Technical Design Report (TDR) (1999) CMS physics Technical Design Report (TDR) (2006) Supersymmetry:

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**Constraints on mHiggs No perturbative unitarity Unstable vacuum**

Scale at which new physics enters

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**Producing a Higgs @ LHC Higgs couplings mass**

top H g top H g W/Z H q _ Higgs couplings mass Direct e.g. u-ubar H very small cross-section Dominant production via vertices coupling Higgs to heavy quarks or W/Z bosons W/Z H q _

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**Higgs’ mechanism Add a complex scalar field**

In fact he adds 2 real scalar fields, (fermion part of L now ignored) This is gauge invariant when the scalars have covariant derivatives: N.B. scalar field must couple to gauge field like this for the Higgs mechanism to work Now if the potential, V, has a degenerate minimum at φ≠0 we get interesting consequences…

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**mSUGRA – “super gravity”**

A.K.A. cMSSM Gravity mediated SUSY breaking Flavour-blind (no FCNCs) Strong expt. limits Unification at high scales Reduce SUSY parameter space Common scalar mass M0 squarks, sleptons Common fermionic mass M½ Gauginos Common trilinear couplings A0 Susy equivalent of Yukawas 1016 GeV Unification of couplings Iterate using Renormalisation Group Equations EW scale Correct MZ, MW, … Programs include e.g. ISASUSY, SOFTSUSY

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**Other suggestions for SUSY breaking**

Gauge mediation Gauge (SM) fields in extra dimensions mediate SUSY breaking Automatic diagonal couplings no EWSB No direct gravitino mass until Mpl Lightest SUSY particle is gravitino Next-to-lightest can be long-lived (e.g. stau or neutralino) Anomaly mediation Sequestered sector (via extra dimension) Loop diagram in scalar part of graviton mediates SUSY breaking Dominates in absence of direct couplings Leads to SUSY breaking RGE β-functions Neutral Wino LSP Charged Wino near-degenerate with LSP lifetime Interesting track signatures Not exhaustive!

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**Producing exotics? If exotics can be produced singly they can decay**

Time standard exotic Time standard exotic If exotics can be produced singly they can decay No good for Dark Matter candidate If they can only be pair-produced they are stable Only disappear on collision (rare) No RP Time standard exotics Time standard exotics With RP Require an even number of exotic legs to/from blobs (Conserved multiplicative quantum number) If we want a good dark matter candidate

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**How do they then behave? Production part Complete “event” Decay part**

Time Complete “event” standard 2 exotics Time Time standard heavy exotic lighter exotic Decay part Events build from blobs with 2 “exotic legs” A pair of cascade decays results Complicated end result = exotic = standard

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