1 / 51

Expectations from LHC for Top Physics

Expectations from LHC for Top Physics. Top Mass Couplings and decays Top spin polarization Single top production. Top quark mass is a fundamental parameter of the EW theory By far has the largest mass of all known fundamental particles In SM: top- and W-mass constrain Higgs mass

hina
Download Presentation

Expectations from LHC for Top Physics

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript


  1. Expectations from LHC for Top Physics Top Mass Couplings and decays Top spin polarization Single top production

  2. Top quark mass is a fundamental parameter of the EW theory By far has the largest mass of all known fundamental particles In SM: top- and W-mass constrain Higgs mass Sensitivity through radiative corrections Scrutinize SM by precise determination top mass Top quark exists and will be produced abundantly !  window for new physics Many heavy particles decay in tt Handle on new physics by detailed properties of top And in addition… Experiment: Top quark useful to calibrate the detector (LHC) Beyond Top: Top quarks will be a major source of background for almost every search for physics beyond the SM (LHC) Motivations for Top Physics studies Marina Cobal - HCP2004

  3. pp (mainly) at s = 14 TeV Startup in April 2007 Initial/low lumi L1033 cm-2 s-1  2 minimum bias/x-ing  “Tevatron-like” environment 10 fb-1 /year Design/high lumi L=1034 cm-2 s-1 after ~ 3 years ~ 20 minimum bias/x-ing  fast ( 50 ns) radhard detect 100 fb-1 /year LHC and experiments TOTEM 27 km ring 1232 dipoles B=8.3 T ATLAS and CMS : pp, general purpose ALICE : heavy ions, p-ions LHCb : pp, B-physics Marina Cobal - HCP2004

  4. LC machine • Maybe some years after the LHC startup • ECM of operation 200-500 GeV, possible upgrade to 1 TeV • 80% Polarization of e- beam • Luminosity: 300 fb-1/year Marina Cobal - HCP2004

  5. Cross section determined to NLO precision Total NLO(tt) = 834 ± 100 pb Largest uncertainty from scale variation Compare to other production processes: Top production cross section approximately 100x Tevatron Opposite @ FNAL Top production at LHC ~90% gg~10% qq Low lumi LHC is a top factory! Marina Cobal - HCP2004

  6. ..and at LC? • The ttbar cross section is ~103 smaller than at LHC, but higher L • s ~0,85 pb at max, around 390 GeV, and falls down with energy as 1/s ~200000 tt/year at TESLA parameters Marina Cobal - HCP2004

  7. In the SM the top decays to W+b All decay channels investigated Using ‘fast parameterized’ detector response Checks with detailed simulations Di-leptons (e/) BR≈4.9%  0.4x106 ev/y No top reconstructed Clean sample Single Lepton (e/) BR=29.6%  2.5x106 ev/y One top reconstructed Clean sample Fully Hadronic BR≈45%  3.5x106 ev/y Two tops reconstructed Huge QCD background Large combinatorial bckgnd Top decay Marina Cobal - HCP2004

  8. Top mass: Where we are Marina Cobal - HCP2004

  9. Near future of Mtop Tevatron only (di-lepton events or lepton+jet ) from W decays Status of inputs (preliminary): mt=(178.0  2.7 (stat)  3.3 (syst)) GeV/c2 (latest Tevatron updated combination – RunI data) mt=(175  17 (stat)  8 (syst)) GeV/c2 (CDF di-leptons – RunII data) mt=(178+13-9(stat)  7 (syst)) GeV/c2 (CDF lepton+jets – RunII data) Matter of statistics (also for the main systematics) and optimized use of the available information. Each experiment expects 500 b-tagged tt l+jets events/fb  DMtop ~ 2-3 GeV/c2 for the Tevatron combined (2-4/fb) • mt  2.5 GeV ; mW  30 MeV  mH/mH  35% In 2009 (if upgrade is respected) from Tevatron: DMtop = 1.5 GeV !! Marina Cobal - HCP2004

  10. Problem for the top: what is the mass of a colored object? The top pole mass is not IR safe (affected by large long-distance contributions), cannot be determined to better than O(LQCD) Measurement of mt: At Tevatron/LHC: kinematic reconstruction, fit to invariant mass dist. at the LHC: accuracy  1-2 GeV (limited by FSR) At the LC, mainly from threshold behavior Measurement comparison data – Monte Carlo: involves transition from actually measured quantity to suitably defined (short-distance) top mass ‘Threshold mass’ at the LC: accuracy  20 MeV [M. Martinez, R. Miquel ’03] Transition to MS mass: dm  100 MeV [A. Hoang et al. ’00] What is the Top Mass? Marina Cobal - HCP2004

  11. Br(ttbbjjl)=30%for electron + muon Golden channel Clean trigger from isolated lepton The reconstruction starts with the W mass: different ways to pair the right jets to form the W jet energies calibrated using mW Important to tag the b-jets: enormously reduces background (physics and combinatorial) clean up the reconstruction Lepton side Hadron side LHC: MTop from lepton+jet Typical selection efficiency: ~5-10%: • Isolated lepton PT>20 GeV • ETmiss>20 GeV • 4 jets with ET>40 GeV • >1 b-jet (b40%, uds10-3, c10-2) Background: <2% W/Z+jets, WW/ZZ/WZ Marina Cobal - HCP2004

  12. Hadronic side W from jet pair with closest invariant mass to MW Require |MW-Mjj|<20 GeV Assign a b-jet to the W to reconstruct Mtop Kinematic fit Using remaining l+b-jet, the leptonic part is reconstructed |mlb -<mjjb>| < 35 GeV Kinematic fit to the tt hypothesis, using MW constraints j2 j1 b-jet t LHC: Lepton + jet, reconstruct top • Selection efficiency 5-10% Marina Cobal - HCP2004

  13. Method works: Linear with input Mtop Largely independent on Top PT Biggest uncertainties: Jet energy calibration FSR: ‘out of cone’ give large variations in mass B-fragmentation Verified with detailed detector simulation and realistic calibration LHC: MTop systematics Challenge: determine the mass of the top around 1 GeV accuracy in one year of LHC Marina Cobal - HCP2004

  14. Mtop LHC: Alternative mass determination • Select high PT back-to-back top events: • Hemisphere separation (bckgnd reduction, much less combinatorial) • Higher probability for jet overlapping • Use the events where both W’s decay leptonically (Br~5%) • Much cleaner environment • Less information available from two ’s • Use events where both W’s decay hadronically (Br~45%) • Difficult ‘jet’ environment • Select PT>200 GeV Various methods all have different systematics Marina Cobal - HCP2004

  15. Use exclusive b-decays with high mass products (J/) Higher correlation with Mtop Clean reconstruction (background free) BR(ttqqb+J/)  5 10-5  ~ 30%  103 ev./100 fb-1(need high lumi) Top mass from J/ MlJ/ Different systematics (almost no sensitivity to FSR) Uncertainty on the b-quark fragmentation function becomes the dominant error M(J/+l) M(J/+l) Pttop Marina Cobal - HCP2004

  16. Mtop at LC • Scan of the threshold for e+e-ttbar • Very precise measurements (< 20 MeV) • To perform this analysis with small systematic errors need to study: beam spread beamstrahlung initial state radiation • Simultaneous measurements of 3 physical observables: • stt • Pt of top • Forward-Backward asimmetry of top AtFB • Multiparameter fit up to 4 parameters • Mt (1S) • as(MZ) • Gt • gtH • Theoretical uncertainties to relate the 1S to the MS mass is ~ 100 MeV s(pb) Marina Cobal - HCP2004

  17. Georg Weiglin, LCWS04 Paris Marina Cobal - HCP2004

  18. Many theoretical models include the existence of resonances decaying to top-topbar SM Higgs(but BR smaller with respect to the WW and ZZ decays) MSSM Higgs(H/A, if mH,mA>2mt, BR(H/A→tt)≈1 for tanβ≈1) Technicolor Models, strong ElectroWeak Symmetry Breaking, Topcolor, “colorons” production, […] xBR required for a discovery σxBR [fb] 30 fb-1 830 fb 300 fb-1 mtt [GeV/c2] 1 TeV LHC: Search for resonances • Study of a resonance Χ once known σΧ, ΓΧ and BR(Χ→tt) at LHC • Reconstruction efficiency for semileptonic channel: • 20% mtt=400 GeV • 15% mtt=2 TeV 1.6 TeV resonance Mtt Marina Cobal - HCP2004

  19. Couplings and decays • Does the top quark behaves as expected in the SM? • Yukawa coupling to Higgs from ttbarH events • Electric charge • Top spin polarization • CP violation • At the LHC Yukawa coupling can be measured to < 20% from t-tbar H production • @ the LC, the precision of the measurement of the top Yukawa coupling will be better than ~ 10 % if mH ≤ 190 GeV/c2 • For a light Higgs (mH~120 GeV/c2): Precision ~ 5-6 % Marina Cobal - HCP2004

  20. LHC: Couplings and decays • According to the SM: • Br(t Wb)  99.9%, Br(t  Ws)  0.1%, Br(t  Wd)  0.01% (difficult to measure) • Can probe t W[non-b] by measuring ratio of double b-tag to single b-tag • Statistics more than sufficient to be sensitive to SM expectation for Br(t  W + s/d) • need excellent understanding of b-tagging efficiency/purity Marina Cobal - HCP2004

  21. Search for anomalous Wtb couplings • The Wtb vertex can be probed and measured using either top pair production or single top production • Total tt rate depends weakly from Wtb vertex structure • C and P asymmetries, top polarization, spin correlations can provide interesting info • The single top production rate is instead directly proportional to the square of the Wtb coupling • LHC could rivale the reach of a high L (500 fb-1) 500 GeV LC Marina Cobal - HCP2004

  22. LHC: FCNC Rare decays • In the SM the FCNC decays are highly suppressed (Br<10-13-10-10) • Any observation would be sign of new physics • FCNC can be detected through top decay or single top production • Sensitivity according to CMS studies (of top decays) : • t  Zq(CDF Br<0.137, ALEPH Br<17%, OPAL Br<13.7%) • Reconstruct t  Zq  (l+l-)j • Sensitivity to Br(t  Zq) = 1,6 X 10-4 (100 fb-1) • t  q(CDF Br<0.032) • Sensitivity to Br(t  q) = 2,5 X 10-5 (100 fb-1) • t  gq • Difficult identification because of the huge QCD bakground • One looks for “like-sign” top production (ie. tt) • Sensitivity to Br(t  gq) = 1,6 X 10-3 (100 fb-1) Marina Cobal - HCP2004

  23. FCNC • In general, the LHC will improve by a factor of at least 10 the Tevatron sensitivity to top-quark FCNC couplings • LC has smaller statistics but also smaller background • For anomalous interactions with a gluon the LHC has an evident advantage Marina Cobal - HCP2004

  24. LHC: tWbZ rare decay • Studied at LHC: Interesting: BR depends strongly on Mtop • Since Mtop~MW+Mb+MZ • With present error mt  5 GeV, BR varies over a factor  3 • B-jet too soft to be efficiently identified   “semi-inclusive” study for a WZ near threshold, with Z  l+l-and W ->jj • Requiring 3 leptons reduces the Z+jets background • Sensitivity to Br(t  WbZ)  10-3 for 1 year at low lumi. • Even at high L can’t reach SM predictions ( 10-7 -10-6) G. Mahlon hep-ph/9810485 G(tWbZ)/G(tWb) M(top) (GeV) Marina Cobal - HCP2004

  25. Radiative top production Radiative top decay LHC: Top Charge determination • Can we establish Qtop=2/3? • Currently cannot exclude exotic possibility Qtop=-4/3 • Assign the ‘wrong’ W to the b-quark in top decays • tW-b with Qtop=-4/3 instead of tW+b with Qtop=2/3 ? • Technique: • Hard  radiation from top quarks • Radiative top production, pptt cross section proportional to Q2top • Radiative top decay, tWb • On-mass approach for decaying top: two processes treated independently • Matrix elements havebeen calculated and fed intoPythia MC Marina Cobal - HCP2004

  26. LHC: Top Charge determination • Yield of radiative photons allows to distinguish top charge • Determine charge of b-jet andcombine with lepton • Use di-lepton sample • Investigate ‘wrong’ combination b-jet charge and lepton charge • Effective separation b and b-bar possible in first year LHC • Study systematics in progress 10 fb-1 One year low lumi events pT() Marina Cobal - HCP2004

  27. e+/+ + top LHC: Top spin correlations • In SM with Mtop175 GeV, (t)  1.4 GeV » QCD • Top decays before hadronization, and so can study the decay of ‘bare quark’ • Substantial ttbar spin correlations predicted in pair production • Can study polarization effects through helicity analysis of daughters • Study with di-lepton events • Correlation between helicity angles + and -for e+/+ and e-/- <CosΘ+ · CosΘ-> <CosΘ+ · CosΘ-> No helicity correlation With helicity correlation Marina Cobal - HCP2004

  28. Able to observe spin correlations in parameter C 30 fb-1 of data: ± 0,035 statistical error ± 0,028 systematic error 10 statistical significance for a non-zero value with 10 fb-1 Top spin correlations 30 fb-1 <CosΘ+ · CosΘ-> • For the LC case one can find a top spin quantization axis in which there • will be very strong spin correlations . Detailed studies, both at the ttbar • threshold and in the continuum region remain to be done. Marina Cobal - HCP2004

  29. Direct determination of the tWb vertex (=Vtb) Discriminants: - Jet multiplicity (higher for Wt) More than one b-jet (increase W* signal over W- gluon fusion) 2-jets mass distribution (mjj ~ mW for the Wt signal only) Three production mechanisms at LHC: Main Background [xBR(W→ℓ), ℓ=e,μ]: tt σ=833 pb [ 246 pb] Wbbσ=300 pb [ 66.7 pb] Wjjσ=18·103 pb [4·103 pb] LHC: Single top production 1) Determination of Vtb 2) Independent mass measurement 3) Opportunity to measure top spin pol. 4) May probe FCNC +16.6 Wg fusion: 245±27 pb S.Willenbrock et al., Phys.Rev.D56, 5919 Wt: 62.2 pb A.Belyaev, E.Boos, Phys.Rev.D63, 034012 W* 10.2±0.7 pb M.Smith et al., Phys.Rev.D54, 6696 -3. 7 Wg [54.2 pb] Wt [17.8 pb] W* [2.2 pb] Marina Cobal - HCP2004

  30. LHC: Single top results • Detector performance critical to observe signal • Fake lepton rate • b and fake rate id  • Reconstruction and vetoing of low energy jets • Identification of forward jets • Each of the processes have different systematic errors for Vtb and are sensitive to different new physics • heavy W’  increase in the s-channel W* • FCNC gu  t  increase in the W-gluon fusion channel • Signal unambiguous, after 30 fb-1: • Complementary methods to extract Vtb • With 30 fb-1 of data, Vtb can be determined to %-level or better(experimentally) Marina Cobal - HCP2004

  31. e+ e-  e+bt, ebt Single top at LC • Cross section calculated to LO at e+e-, gg and ge collision modes, including various beam polarizations • Recently calculated NLO corrections in the ge case, well under control • Production in ge collisions is of special interest • Rate is smaller than the top pair rate in e+e- only by a factor of 1/8 at 500-800 GeV energies. • It becomes the dominant LC process for top production at a multi-TeV LC • Direct Vtb measurement: • Same precision as LHC in the e+e- option. • Can arrive to 1% for a polarized ge collider. • Improved accuracy in |Vtb| could be input for LHC • Measure b-quark distribution function in proton (or be used as consistency check for new interactions) Marina Cobal - HCP2004

  32. Few final thoughts… • e+-e- collisions at 0.5-1 TeV • Kinematics: • can use momentum conservation • Better defined initial state • Background smaller than LHC • Not sure yet IF, WHEN, WHERE it will be built • LHC pp collision at 14 TeV • Kinematics: • can use PT conservation • Composite nature of protons  Underlying events, not fixed • Strongly interacting particle •  Large QCD background • Under construction Marina Cobal - HCP2004

  33. Interplay between LHC and LC • Not much interaction between the LHC and LC communities up to short time ago • In 2002 a LHC/LC study group was formed first in Europe and then soon it took a worldwide character • Working Group contains 116 members from among Theorists, CMS, ATLAS, Members of all the LC study Groups + Tevatron contact persons. • Document in preparation: www.ippp.dur.ac.uk/~georg/lhclc Electroweak and QCD precision physics E. Boos, A deRoeck, S. Heinemeyer, W.J. Stirling. Marina Cobal - HCP2004

  34. ATLAS cavern CMS yoke LHC is a reality now: Huge construction activities going on!! Marina Cobal - HCP2004

  35. What is left before the LHC starts? • Cover topics still open: cross section, couplings, exotic, resonances, • Define a strategy for validation of the MC input models (e.g: UE modeling and subtraction, jet fragmentation properties, jet energy profiles, b-fragmentation functions..) see M. Mangano talk at IFAE 2004 • Explore the effects of changing detector parameters in evaluating the top mass. • Perform commissioning studies with top events • Contribute to simulation validation • … Marina Cobal - HCP2004

  36. Determination MTop in initial phase Use ‘Golden plated’ lepton+jet Selection: Isolated lepton with PT>20 GeV Exactly 4 jets (R=0.4) with PT>40 GeV Reconstruction: Select 3 jets with maximal resulting PT Signal can be improved by kinematic constrained fit Assuming MW1=MW2 and MT1=MT2 LHC: Commissioning the detectors • Calibrating detector in comissioning phase • Assume pessimistic scenario: • -) No b-tagging • -) No jet calibration • -) But: Good lepton identification No background included Marina Cobal - HCP2004

  37. Signal plus background at initial phase of LHC Most important background for top: W+4 jets Leptonic decay of W, with 4 extra ‘light’ jets Alpgen, Monte Carlohas ‘hard’ matrix element for 4 extra jets(not available in Pythia/Herwig) LHC: Commissioning the detectors ALPGEN: W+4 extra light jets Jet: PT>10, ||<2.5, R>0.4 No lepton cuts Effective : ~2400 pb L = 150 pb-1 (2/3 days low lumi) With extreme simple selection and reconstruction the top-peak should be visible at LHC measure top mass (to 5-7 GeV) give feedback on detector performance Marina Cobal - HCP2004

  38. Conclusions • Precise determination of Mtop is crucial for EW physics: • Precision tests, constraints on Higgs sector, sensitivity to new physics • Challenge to get Mtop ~ 1 GeV with LHC, and ~ 100 MeV with LC • Confirmation that top-quark is SM particle and search for deviation from SM • Measure Vtb, charge, CP, spin, decays • Many precision measurements from LC • Use top quark for the LHC detectors commissioning • Interplay between LC and LHC could be as useful as it was for LEP+SLC+Tevatron Marina Cobal - HCP2004

  39. BACKUP SLIDES

  40. LEP+SLD: VCKM (4) UA2+Tevatron: s(1) NuTeV: predictions GF (1) SM APV: mfermions (9) (down to 0.1% level) mbosons (2) eeqq l.e.: What we know.. mH No observable directly related to mH. However the dependence can appear through radiative corrections. tree level quantities changed , r = f [ln(mH/mW), mt2] The uncertainties on mt, mW are the dominating ones in the electroweak fit By making precision measurements (already interesting per se): • one can get information on the missing parameter mH • one can test the validity of the Standard Model Marina Cobal - HCP2004

  41. LC Timeline • . Graphically summarized by Jae Yu Marina Cobal - HCP2004

  42. LC Machines • BASELINE MACHINE • ECM of operation 200-500 GeV • Luminosity and reliability for 500 fb-1 in 4 years • Energy scan capability with <10% downtime • Beam energy precision and stability below about 0.1% • Electron polarization of > 80% • Two IRs with detectors • ECM down to 90Gev for calibration • UPGRADES • ECM about 1 TeV • Allow for ~1 ab-1 in about 3-4 years http://www.fnal.gov/directorate/ icfa/LC_parameters.pdf Marina Cobal - HCP2004

  43. Rare SM top decays • Direct measurement of Vts, Vtdvia decays tsW, tdW • Decay tbWZ is near threshold (mt~MW+ MZ+mb)  BRcut(t bWZ)  610-7 (cut on m(ee) is 0.8 MW) • Decay tcWW suppressed by GIM factorBR(t cWW) ~ 110-13 • If Higgs boson is light: tbWH • FCNC decays: tcg, tc, tcZ(BR: 510-11 , 510-13 , 1.310-13 ) • Semi-exclusive t-decays tbM (final state 1 hadron recoiling against a jet: BR(t b)  410-8, BR(t bDs)  210-7) Marina Cobal - HCP2004

  44. Signal Signal ttH ttH tt tt topHq • Various approaches studied • Previously: ttbarHq Wb(b-bbar)j(lb) for m(H) = 115 GeV • Sensitivity to Br(t  Hq) = 4.5 X 10-3(100 fb-1) • New results for: • t tbarHq WbWW*q Wb(l lj) (lb) • ≥ 3 isolated lepton with pT(lep) > 30 GeV • pTmiss > 45 GeV • ≥ 2 jets with pT(j) > 30 GeV, incl. ≥ 1 jet con b-tag • Kinematical cuts making use of angular correlations • Sensitive to Br(t  Hq) = 2.4 X 10-3 for m(H) = 160 GeV (100 fb-1) Marina Cobal - HCP2004

  45. Non-SM Decays of Top • 4thfermion family Constraints on Vtqrelaxed: • Supersymmetry (MSSM) • Observed bosons and fermions would have superpartners  2-body decays into squarks and gauginos (t  H+ b ) • Big impact on 1 loop FCNC • two Higgs doublets • H LEP limit 77.4 GeV (LEP WG 2000) • Decay t  H+ b can compete with t  W+ b • 5 states (h0,H0,A0,H+,H-) survive after giving W & Z masses • H couples to heaviest fermions  detection through breakdown of e / m / t universality in tt production Marina Cobal - HCP2004

  46. Continuous jet algorithm Reduce dependence on MC Reduce jet scale uncertainty Repeat analysis for many cone sizes R Sum all determined top mass:robust estimator top-mass Determining Mtop from (tt)? huge statistics, totally different systematics But: Theory uncertainty on the pdfs kills the idea 10% th. uncertainty  mt  4 GeV Constraining the pdf would be very precious… (up to a few % might not be a dream !!!) Alternative methods • Luminosity uncertainty then plays the game (5%?) Luminosity uncertainty then plays the game (5%?) Marina Cobal - HCP2004

  47. Use the events where both W’s decay leptonically (Br~5%) Much cleaner environment Less information available due to two neutrino’s Sophisticated procedure for fitting the whole event, i.e. all kinematical info taken into account (cf D0/CDF) Compute mean probability as function of top mass hypothesis Maximal probability corresponds to top mass Top mass from di-leptons 80000 events (tt) = 20 % S/B = 10 • Selection: • 2 isolated opposite sign leptons • Pt>35 and Pt>25 GeV • 2 b-tagged jets • ETmiss>40 GeV Mean probability Marina Cobal - HCP2004 mass

  48. Use events where both W’s decay hadronically (Br~45%) Difficult ‘jet’ environment (QCD, Pt>100) ~ 1.73 mb (signal) ~ 370 pb Perform kinematic fit on whole event b-jet to W assignment for combination that minimize top mass difference Increase S/B: Require pT(tops)>200 GeV Top mass from hadronic decay • Selection • 6 jets (R=0.4), Pt>40 GeV • 2 b-tagged jets • Note: Event shape variables like HT, A, S, C, etc not effective at LHC (contrast to Tevatron) 3300 events selected: (tt) = 0.63 % (QCD)= 2·10-5 % S/B = 18 Marina Cobal - HCP2004

  49. j2 j1 b-jet Mtop t High Pt sample • The high pT selected sample deserves independent analysis: • Hemisphere separation (bckgnd reduction, much less combinatorial) • Higher probability for jet overlapping • Use all clusters in a large cone R=[0.8-1.2] around the reconstructed top- direction • Less prone to QCD, FSR, calibration • UE can be subtracted Mtop Statistics seems OK and syst. under control R Marina Cobal - HCP2004

  50. Calibration demands: Ultimately jet energy scale calibrated within 1% Uncertainty on b-jet scale dominates Mtop: light jet scale constrained by mW At startup jet-energy scale known to lesser precision ±10% MTop MTop Scale light-jet energy Scale b-jet energy Jet scale calibration Uncertainty on light jet scale:Hadronic 1%  Mt < 0.7 GeV 10%  Mt = 3 GeV Uncertainty On b-jet scale:Hadronic 1%  Mt = 0.7 GeV 5%  Mt = 3.5 GeV 10%  Mt = 7.0 GeV Marina Cobal - HCP2004

More Related