Measuring Masses and Spins of New Particles at Colliders! K.C. Kong

Transcription

1 Measuring Masses and Spins of New Particles at Colliders! K.C. Kong Fermilab High Energy Physics Seminar Michigan State University January 23, 2007

2 Hints for New Physics Beyond the Standard Model Dark Matter: 23% of the unknown in the universe Best evidence for new physics beyond the Standard Model: if the dark matter is the thermal relic of a WIMP, its mass should be of the weak scale ( ) 1 2 ( ) 2 MW IMP Ω W IMP 10 2 α 1 T ev Requires a stable (electrically) neutral weakly interacting particle at O(1) TeV To be stable, it should be the lightest particle charged under a new symmetry Electroweak precision measurements There is no evidence of deviations of the EW observables from the SM predictions New physics contributions to the EW observables should be suppressed Possible if new particles are charged under a new symmetry under which SM is neutral Their contributions will be loop-suppressed and the lightest particle is stable Collider implications: Pair production of new particles Cascade decays down to the lightest particle give rise to missing energy plus jets/leptons

3 Confusion scenario What is new physics if we see jets/leptons + /E T at the colliders? The standard answer: Supersymmetry with R-parity for a long time, this was the only candidate From the above discussion, we see that any new physics satisfying hints we have may show up at the LHC with similar signals Michael Peskin s name for different kinds of new heavy particles whose decay chains result in the same final state (copied from Joe s slide, Is Particle Physics Ready for the LHC? ) How can we discriminate SUSY from confusion scenarios? How do we know new physics is SUSY? Measuring spins and masses is important!

4 Outline New physics beyond the SM is expected to be discovered at the LHC but will we know what it is? Example: Universal Extra Dimensions (5D) Relic Density of KK Dark Matter and Direct Detection Limit Collider Phenomenology of UEDs: Spin Determination Mass Measurements: bump, edges in cascade decay, m T, m T 2 Spin and Mass measurement at LC Summary

5 Universal Extra Dimensions (Appelquist, Cheng, Dobrescu, hep-ph/ ) Each SM particle has an infinite number of KK partners The number of KK states = ΛR (Λ is a cut-off) n 2 R 2 + m2 KK particle has the same spin as SM particle with a mass, SM particles became massive through electroweak symmetry breaking KK gauge bosons get masses by eating 5th components of gauge fields (Nambu- Goldstone bosons) and EWSB shifts those masses All vertices at tree level satisfy KK number conservation m ± n ± k = 0 or m ± n ± k ± l = 0 KK number conservation is broken down to KK-parity, ( 1) n, at the loop level The lightest KK partner at level 1 (LKP) is stable DM? KK particles at level 1 are pair-produced KK particles at level 2 can be singly produced Additional allowed decays: 2 00, 3 10, No tree-level contributions to precision EW observables New vertices are the same as SM interactions Couplings between SM and KK particles are the same as SM couplings Couplings among KK particles have different normalization factors There are two Dirac (KK) partners at each level n for one Dirac fermion in SM

6 Mass Spectrum : Tree level and radiative corrections (Cheng, Matchev, Schmaltz, hep-ph/ , hep-ph/ ) Tree level mass m n = ( n R) 2 + m2, e 1 is stable Radiative corrections are important! All but LKP decay promptly missing energy signals

7 Relic Density Code Kong and Matchev (UF, 2005) Fortran Includes all level 1 KK particles has a general KK mass spectra (all KK masses are, in principle, different) can deal with different types of KK dark matter (γ 1, Z 1, ν 1 ) improved numerical precision use correct non-relativistic velocity expansion ( σv = a + b v 2 ) use temperature dependent degrees of freedom (g = g (T F )) Servant and Tait (Annecy/ANL, 2002) First code (γ 1 or ν 1 dark matter) has cross sections in Mathematica, assuming same KK masses use approximate non-relativistic velocity expansion use approximate degrees of freedom (g = 92.25) Kribs and Burnell (Oregon/Princeton, 2005) has cross sections in Maple, assuming same KK masses (γ 1 dark matter) do not use non-relativistic velocity expansion deal with coannihilations with all level 1 KK Kakizaki, Matsumoto and Senami (Bonn/KEK/Tokyo, 2006) interested in resonance effects (γ 1 dark matter)

8 Improved result (Kong, Matchev, hep-ph/ ) Improvements in our calculation: Include all coannihilations: many processes (51 51 initial states) Keep KK masses different in the cross sections: Use temperature dependent g Use relativistic correction in the b-term a: γ 1 γ 1 annihilation only (from hep-ph/ ) b: repeats the same analysis but uses temperature dependent g and relativistic correction c: relaxes the assumption of KK mass degeneracy MUED: full calculation in MUED including all coannihilations with the proper choice of masses Preferred mass range: GeV for < Ω CDM h 2 < 0.129

9 Dark matter in nonminimal UED The change in the cosmologically preferred value for R 1 as a result of varying the different KK masses away from their nominal MUED values (along each line, Ωh 2 = 0.1) (Kong, Matchev, hep-ph/ ) In nonminimal UED, Cosmologically allowed LKP mass range can be larger If = m 1 m γ 1 is small, m mγ LKP is large, UED escapes collider searches 1 But, good news for dark matter searches

10 CDMS (Spin independent): B 1 and Z 1 LKP (Baudis, Kong, Matchev, Preliminary) SuperCDMS (projected) A (25 kg), B (150 kg), C (1 ton) q1 = m q 1 mγ 1 mγ 1 Z 1 LKP in nonminimal UED: Q1 = m Q 1 m Z1 m Z1 g1 = = 0.1

11 Typical event in SUSY and UED B 1 g g q R q L q q q q l g 1 g 1 q 1 Q 1 q q q q l χ 0 2 l l Z 1 l 1 l Both have similar diagrams same signatures! At first sight, it is not clear which model we are considering The decay chain is complicated A lot of jets correct jet identification is difficult ISR/FSR add more confusion UED discovery reach at the Tevatron and LHC: (Cheng, Matchev, Schmaltz, hep-ph/ ) Reach at the LHC: R TeV with 100 fb 1 in 4l + /E T channel UED search by CMS group (full detector simulation) B 1

12 How to discriminate: Level 1 just looks like MSSM with LSP dark matter: (Cheng, Matchev, Schmaltz, hep-ph/ ) Can we discriminate SUSY from UED? * N = 1 SUSY SUSY UED How many new particles 1 KK tower Spin of new particles differ by 1 2 same spins Couplings of new particles same as SM same as SM Masses SUSY breaking boundary terms Discrete symmetry R-parity KK-parity = ( 1) n Dark matter LSP ( ) LKP (γ 1) Generic signature /E T /E T ** Couplings among some KK particles may have factors of 2, 3, *** with dark matter candidates Finding KK tower: Datta, Kong, Matchev, hep-ph/ Spin measurements: Barr, hep-ph/ Smillie, Webber hep-ph/ Datta, Kong, Matchev, hep-ph/ Cross section: Datta, Kane, Toharia, hep-ph/

13 Implementation of UED in Event Generators Datta, Kong and Matchev (UF, 2004) Full implementation of level 1 and level 2 in CompHEP/CalcHEP (spin information) Provided for implementation in PYTHIA Two different mass spectrum possible: A general mass spectrum in Nonminimal UED All masses/widths calculated automatically in Minimal UED Used for dark matter study/collider studies Used for ATLAS and CMS (4l + /E T, nj + ml + /E T ) Alexandre Alves, Oscar Eboli, Tilman Plehn (2006) Level 1 QCD and decays only in MADGRAPH (spin information!) Wang and Yavin (Harvard, 2006) Level 1 QCD and decays only in HERWIG (full spin information) Smillie and Webber (Cambridge, 2005) Level 1 QCD and decays only in HERWIG (full spin information) Peskin (Stanford, in progress) Level 1 QCD and decays only in PANDORA (full spin information) El Kacimi, Goujdami and Przysiezniak (2005) Level 1 QCD and decays only in PYTHIA (spin information is lost) Matrix elements from CompHEP/CalcHEP

14 Spin measurement spin measurement is difficult LSP/LKP is neutral missing energy There are two LSPs/LKPs cannot find CM frame Decay chains are complicated cannot uniquely identify subchains Look for something easy : look for 2 SFOS leptons, χ 0 2 l ± l l ± l or Z 1 ll 1 L l+ l γ 1 Dominant source of χ 0 2 /Z 1: squark/kk-quark decay q q χ 0 2 q l ± l ql ± l or Q 1 qz 1 ll 1 L l+ l γ 1 : SUSY: UED: q Q 1 Z1 χ 0 2 q l l ± (near) l (far) l 1 γ 1 Study this chain: Observable objects are q and l ± Can do: M l + l, M ql and M ql + where M 2 ab = (p a p b ) 2 Which jet? Which lepton? Charge of jets (q and q)? M l + l, Asymmetry = A + = Masses don t discriminate ( ) ( ) dσ dσ dm ql + dm ( ) ( ql (Barr,Phys.Lett.B596: ,2004) dσ dσ dm ql ++ dm )ql

15 Dilepton distribution Look for spin correlations in M l + l Choose a study point in one model and fake mass spectrum in the other model SUSY: UED: q Q 1 Z1 χ 0 2 q l l ± (near) l (far) l 1 γ 1 (Kong, Matchev Preliminary and Smillie, Webber hep-ph/ ) Why are they the same?

16 Dilepton distribution How do we fake the M l + l distribution? (Smillie, Webber hep-ph/ ) (Kong, Matchev Preliminary) Phase Space : dn d ˆm = 2 ˆm SUSY : dn d ˆm = 2 ˆm UED : dn d ˆm = 4(y+4z) (1+2z)(2+y) r = (2 y)(1 2z) y+4z ( ˆm + r ˆm 3 ) where ˆm = m ll m max ll, y = ( ) 2 m l m and z = χ 0 2 ( m ) χ m l r 0.4 in msugra

17 Spin measurement : Barr method SUSY: UED: q Q 1 Z1 χ 0 2 q l l ± (near) l (far) l 1 γ 1 dp/dm^ 4 3 (Barr,Phys.Lett.B596: ,2004) 4m^ 3 Invariant mass distribution of q and l (near) dp P S d ˆm = 2 ˆm from phase space dp 1 d ˆm = 4 ˆm3 for l + q or l q in SUSY dp 2 d ˆm = 4 ˆm(1 ˆm2 ) for l q or l + q in SUSY m^ 4m^ (1-m^ 2) m^ ˆm = ( mnear lq m near ) lq max Complications: Which jet? Which lepton? We don t distinguish q and q Asymmetry: A + = ( ) ( ) dσ dσ dm ql + dm ( ) ( ) ql dσ dσ dm ql ++ dm ql

18 Barr method SUSY: UED: q Q 1 Z1 χ 0 2 q l l ± (near) l (far) l 1 γ 1 Look at correlation between q and l (Barr, hep-ph/ ) Complications: Which (quark) jet is the right one? (Webber, hep-ph/ cheated, picked the right one) One never knows for sure. There can be clever cuts to increase the probability that we picked right one (work in progress) Which lepton? : near and far cannot be distinguished must add both contributions. Improvement on selection (work in progress) Don t know q or q But more q than q at the LHC in t-channel production Can distinguish charge of leptons: look at ql + and ql separately and compare

19 Barr method q P 1 P 2 P 1 P q q q 2 q q q q χ 0 2 l χ 0 2 l + χ 0 2 l χ 0 2 l + fq l L l + ll l l R l + lr l q P 2 P 1 P 2 P q 1 q q q q q q χ 0 2 l χ 0 2 l + χ 0 2 l χ 0 2 l + f q l L l + l L l lr l + l R l f q + f q = 1

20 Barr method (Datta, Kong, Matchev, hep-ph/ and Smillie, Webber, hep-ph/ ) Choose a study point : UED500 and SPS1a (L = 10fb 1 ) Each M ql distribution contains 4 contributions ( ) ( dσ dp2 = f q + dp ) 1 dm ql + dm n dm f ( ) ( dσ dp1 = f q + dp ) 2 dm ql dm n dm f ( dp1 + f q + dp ) 2 dm n dm f ( dp2 + f q + dp ) 1 dm n dm f Asymmetry: A + = ( dσ dm ( dσ dm ) ql + ( ) dσ dm ) ql + + ( ) dσ dm ql ql f q + f q = 1 If f q = f q = 0.5, A + = 0 (for example, in the focus point region)

21 Asymmetry Asymmetry with UED500 mass spectrum (L = 10fb 1 ) (Datta, Kong, Matchev, hep-ph/ ) Asymmetry with SPS1a mass spectrum (L = 10fb 1 ) (Kong, Matchev Preliminary) Z 1 ll 1 L l+ l γ 1 Chirality Z 1 ll 1 R l+ l γ 1 χ 0 2 l l L l + l χ 0 2 l l R l + l

22 SPS1a msugra point (Kong, Matchev Preliminary) x = ( m χ 0 2 m q ) 2, y = ( ) 2 m l m, z = χ 0 2 ( m χ 0 1 m l How to fake SPS1a asymmetry five parameters in asymmetry : f q, x, y, z, m q three kinematic endpoints : m qll, m ql and m ll m qll = m q (1 x)(1 yz) m ql = m q (1 x)(1 z) m ll = m q x(1 y)(1 z) two parameters left : f q, x minimize χ 2 in the (x, f q ) parameter space minimum χ 2 when UED and SUSY masses are the same and f q 1 10% jet energy resolution + statistical error χ 2 better but not enough to fake SPS1a in UED effect of wrong jets asymmetry smaller? Flavor subtraction? (work in progress) ) 2, f q = N q, f q = N q, f q +f q = 1 Nq+N q Nq+N q

23 How do we measure masses?: bump hunting! (Datta, Kong, Matchev, hep-ph/ ) Bump hunting!: ex. two resonances in UEDs Level 2 resonances can be seen at the LHC: up to R 1 1 TeV for 100 fb 1, M 2 ab = (p a + p b ) 2 covers dark matter region of MUED Mass resolution: δm = 0.01M V2 for e + e δm = M V ( M 2 V 2 1T ev ) for µ + µ Narrow peaks are smeared due to the mass resolution Two resonances can be better resolved in e + e channel Is this a proof of UED? Not quite : resonances could still be interpreted as Z s Smoking guns : Their close degeneracy M V2 2M V1 Mass measurement of W ± 2 KK mode However in nonminimal UED models, degenerate spectrum is not required just like SUSY with a bunch of Z s need spins to discriminate

24 How do we measure masses?: cascade decays! Cascade decays! (Bachacou, Ian Hinchliffe, Paige, hep-ph/ ) q L χ 2 0 q L l R - l R + (near) χ 1 0 l R - (far) M max ll = M max qll = ( )( ) M 2 χ 0 M 2 lr M 2 lr M 2 χ M 2 lr ( )( ) M 2 q M 2 χ L 0 M 2 χ 2 0 M 2 χ M 2 χ 0 2 Events/0.5 GeV/100 fb / 197 P P P Events/20 GeV/100 fb / 25 P P E-03 P P P M ll (GeV) M llq (GeV)

25 How do we measure masses?: cascade decays! Cascade decays! (Bachacou, Ian Hinchliffe, Paige, hep-ph/ ) q L χ 2 0 q L l R - l R + (near) - l R 0 χ 1 (far) M max ql = M min llq ( )( ) M 2 q M 2 χ L 0 M 2 χ 2 0 M 2 lr 2 M 2 χ 0 2 with M ll > M max ll / / 12 P P P / 11 P P P Events/20 GeV/100 fb Events/20 GeV/100 fb M lq (GeV) M llq (GeV)

26 How do we measure masses?: cascade decays! Cascade decays! (Bachacou, Ian Hinchliffe, Paige, hep-ph/ ) (M min llq )2 = 1 4M2 2M e 2 [ M 2 1 M M 2 1 M 2 2 M 2 e M 4 2 M 2 e M 2 2 M 4 e M 2 1 M 2 2 M 2 q M 2 1 M 2 e M 2 q + 3M 2 2 M 2 e M 2 q M 4 e M 2 q + (M 2 2 M 2 q ) ] (M1 4 + M e 4)(M M e 2)2 + 2M1 2M e 2(M 2 4 6M 2 2M e 2 + M e 4) with M ll > M max ll / 2 M 1 = M χ 0 1, M 2 = M χ 0 2, M e = M lr and M q = M ql

27 How do we measure masses?: m T m T! M 2 W m 2 T (e, ν) ( p et + p νt ) 2 ( p et + p νt ) 2

28 What if there are two missing particles?: m T 2 (Barr, Lester, Stephens, hep-ph/ , m(t2): The Truth behind the glamour ) (Lester, Summers, hep-ph/ ) m 2 l = m E l T = p T E χ0 1 T = ( p T [ E l T E χ0 1 T cosh ( η ) ] p l T p χ0 1 T ) 2 + m 2 ] η = 1 2 log [ E + pz E p z (tanh η = p z E, sinh η = p z m 2 ( T p l T, p χ0 1 T, m ) E T and cosh η = E E T ) m m T m l ( ) E l T E χ0 1 T p l T p χ 1 T We don t measure p χ0 1 T Most of new physics have at least two missing particles in the final state

29 What if there are two missing particles?: m T 2 (Barr, Lester, Stephens, hep-ph/ , m(t2): The Truth behind the glamour ) (Lester, Summers, hep-ph/ ) l + p 1 q 1 /E T = q 1 + q 2 = ( p 1 + p 2 ) l p 2 q 2 l l + If q 1 and q 2 are obtainable, m 2 l max { m 2 T ( ) ( )} p1, q 1, m 2 T p2, q 2 But /E T = q 1 + q 2 the best we can say is that m 2 l m 2 T 2 [ ] min max {m 2 T ( p 1, q 1 ), m 2 T ( p 2, q 2 )} /q 1 +/q 2 =/E T

30 What if there are two missing particles?: m T 2 (Barr, Lester, Stephens, hep-ph/ , m(t2): The Truth behind the glamour ) (Lester, Summers, hep-ph/ ) m 2 l m 2 T 2 [ ] min max {m 2 T ( p 1, q 1 ), m 2 T ( p 2, q 2 )} /q 1 +/q 2 =/E T m 2 Rely on momentum scan can be reduced to one dimensional parameter scan can not get analytic differential distribution Have to assume m χ 0 1 correlation between m l and m χ 0 1

31 The Cambridge m T 2 Variable Demystified q 1y (Kong, Matchev, Preliminary) q 1y q 2 < q 1 q 1x q 1x q 1 good: uniform scan bad: non-uniform scan bad: how far should we scan? good: compact scan 0 q 1x, q 1y # p 1 q 2 q 1, 0 θ 2 2π q 1 + q 2 = /E T

32 The Cambridge m T 2 Variable Demystified (Kong, Matchev, Preliminary)

33 The Cambridge m T 2 Variable Demystified (Kong, Matchev, Preliminary) p 1 p2 m 2 T 2 [ ] min max {m 2 T ( p 1, q 1 ), m 2 T ( p 2, q 2 )} /q 1 +/q 2 =/E T P vis P miss Constraint: m 2 T ( p 1, q 1 ) = m 2 T ( p 2, q 2 ) q 1 q 2 q m2 q m2 = p 1 p 2 > 0 massless case (m = 0): WW production, m χ 0 1 << m l 2a p 1 p 2 = q 2 q 1 2c /E T e = c a c a q 2 a q 1 c Solution: q 1 = p 2 and q 2 = p 1 Warning: q 1 and q 2 are NOT neutrino momenta

34 The Cambridge m T 2 Variable Demystified (Kong, Matchev, Preliminary) massive case (m 0) num = 16 e ( 1 + ( 1 + e 2) µ 2)3 2 ( e + cos(φ) ) ( 1 + e cos(φ) ) sin(φ) ( 1 + ( 1 + e 2) µ 2) ( 2 ( 1 + e 2 + e 4) ( 1 + e ) ( 1 + e ) ( 2 + e 4) µ 2 4 e ( 1 + e 2 + ( 1 + e 2) µ 2) cos(φ) + e 2 ( 2 + ( 2 3 e 2 + e 4) µ 2) cos(2 φ) ) sin(φ) 2 den = 8 ( e 2 + e 4) 4 ( 2 + e 2) ( 2 5 e e 4) µ 2 + ( 8 16 e 2 12 e e 6 3 e 8) µ 4 8 e ( 4 ( 1 + µ 2)2 + 2 e 2 ( 2 3 µ 2 + µ 4) + e 4 ( µ 2 + µ 4)) cos(φ) + 4 e 2 ( ( 6 + e 2 + e 4) µ 2 + ( e 2 2 e 4 + e 6) µ 4) cos(2 φ) + e 3 µ 2 ( 8 ( 2 + e 2 + ( 2 + e 2) µ 2) cos(3 φ) + e ( 4 ( 2 + e 2)2 µ 2) cos(4 φ) ) 4 sin 2 θ = num den

35 The Cambridge m T 2 Variable Demystified (Kong, Matchev, Preliminary) Applications: Mass correlation even if there are two missing particles: W and slepton pair production Can be used for background rejection N = σ BR L ɛ = fixed σ > σ 0 (BR = 1) m < m 0

36 Kolmogorov-Smirnov Test Is there another mass measurement? KS test? (Kong, Matchev, Preliminary) Difficulties: Not enough statistics Cuts distort shapes of the distributions

37 SUSY vs UED at LC in µ + µ + /E T channel e µ e µ e + Z Z 2 γ B 2 µ D 1 µ S 1 µ + µ + S 1 D 1 B 1 B 1 µ + e + Z γ µ L µr µ L µ R µ + Angular distribution ( dσ d cos θ )UED 1 + E2 µ M 2 1 µ 1 Eµ 2 +M 2 cos 2 θ 1 µ cos 2 θ ( dσ ) d cos θ SUSY 1 cos2 θ µ energy distribution Threshold scan Photon energy distribution

38 The Angular Distribution (LC) (Battaglia, Datta, De Roeck, Kong, Matchev,hep-ph/ ) Entries / 0.1 ab cos θ µ ( ) dσ d cos θ 1 + UED cos2 θ ( ) dσ d cos θ 1 cos2 θ SUSY

39 The µ Energy Distribution (LC) (Battaglia, Datta, De Roeck, Kong, Matchev,hep-ph/ ) Entries / 0.1 ab ) E max/min = 1 2 M µ (1 M2 N M µ 2 γ(1 ± β) M µ : mass of smuon or KK muon M N : LSP or LKP mass γ = 1 with β = 1 M 2 1 β 2 µ /Ebeam 2 (µ boost) p µ (GeV)

40 Threshold scans (LC) (Battaglia, Datta, De Roeck, Kong, Matchev,hep-ph/ ) Mass determination Cross section at threshold in UED β in MSSM β 3 (β = ) 1 M2 E beam 2

41 The Photon Energy Distribution (LC) (Battaglia, Datta, De Roeck, Kong, Matchev,hep-ph/ ) e µ D 1 e γ µ D 1 Z Z 2 Z Z 2 γ B 2 γ B 2 e + γ µ + D 1 e + µ + D 1 Events/500 fb Smuon production is mediated by γ and Z On-shell Z 2 µ 1 µ 1 is allowed by phase space Radiative return due to Z 2 pole at E γ = s M 2 Z 2 2 s E photon (GeV)

42 The Angular Distribution at the LHC p µ p µ p Z Z 2 γ B 2 µ D 1 µ S 1 µ + µ + S 1 D 1 B 1 B 1 µ + p Z γ µ L µr µ L µ R µ + (Datta, Kong, Matchev, Preliminary) If we simply do the same trick as in linear collider, it doesn t work There is no fixed CM frame

43 Exact Beamstrahlung Function Required Analytic solutions are limited for small Υ only Good agreement with simulation data This is true for LC Can t use same solution for large Υ Need new approximation No analytic solution for large Υ in the case of high energy e + e colliders such as CLIC Solve rate equation numerically instead or Use simulation data Caution : Implementation in event generators Most event generators have one of these two parametrizations Either numerically worse or has normalization problem How to fix the event generator Use old parametrizations and fake parameters Use numerical solution/simulation data and import in the event generator A lot of soft photons at high energy e + e colliders distort physical distributions, e.g. E µ

44 Summary LHC is finally coming New physics beyond the SM is expected to be discovered but will we know what it is? Many candidates for new physics have similar signatures at the LHC (SUSY, UEDs, T-parity...). Crucial to know spin information of new particles. Important to know mass spectrum. Need to develop new methods: m T 2... Issues at LC: beamstrahlung...