Top Quark Mass from Reconstruction

Transcription

1 Top Quark Mass from Reconsrucion André H. Hoang Universiy of Vienna MPI Munich

2 Ouline Which Top Mass is Measured a he LHC? Why he quesion is relevan. Wha op mass is measured (= m Pyhia ) Wha is he relaion o any mass heoriss know? - Facorizaion Theorem in e+e- - Firs rough answer - Plans o go on. oward LHC Oulook and Conclusions

3 Top Quark is Special! Heavies known quark (relaed o SSB?) Imporan for quanum effecs affecing many observables Very unsable, decays before hadronizaion ( ) M = ± 0.9 GeV 0.5% precision! How shall we heoriss judge he error? Wha is he heoreical error? Wha mass is i?

4 Concep of a Quark Mass Quanum Field Theory: Paricles: Field-valued operaors made from creaion and annihilaion operaors Lagrangian operaors consruced using correspondence principle Classic acion: is he res mass No oher mass concep exiss a he classic level.

5 Concep of a Quark Mass Renormalizaion: UV-divergences in quanum correcions Fields, couplings, masses in classic acion are bare quaniies ha need o be renormalized o have (any) physical relevance + Mass Renormalizaion Schemes you know: Pole mass: mass = classic res mass Unphysical due o confinemen! MS mass:

6 Need for a precise Top mass Fi o elecroweak precision observables known o 2 GeV error: change in Bes convergence using he MS op scheme:

7 Need for a precise Top mass Blick in die Zukunf: Minimales Supersymmerisches Sandard Model 5 Higgs Bosonen: Heinemeyer, Kraml, Porod, Weiglein Correcions known o Bes convergence using he MS op scheme: Haber, Hempfling, Hoang

8 Top Quark Pole Mass Top decay widh Γ 0 = G F m 3 V b 2 8 2π m pole m (m ) Rho parameer Top MS mass preferred for elecroweak precision fis and mos op mass relaed predicions. Pole mass leads o arificially large perurbaive correcions.

9 Main Mehods a Tevaron Templae Mehod Dynamics Mehod

10 Main Mehods a Tevaron Templae Mehod Wha mass is measured? Dynamics Mehod The Pyhia Mass

11 Descripion of Jes Quark q q µ e e Je µ

12 Descripion of Jes Mone Carlo generaors: m Pyhia = m pole Universal insrumen o describe hadronic final saes. Hadronizaion model and α s are uned o experimenal daa. perurbaive Paron- Shower ( leading log ) Q Λ cu nonperurbaive uning parameers α s m Pyhia model parameers

13 Descripion of Jes LHC: Principle of mass measuremens: je je je Idenificaion of he op decay producs Invarian mass disribuion W b m + m non per. p - p W - b je ATLAS

14 Descripion of Jes LHC: Top Mass +? Principle of mass measuremens: je je je Idenificaion of he op decay producs p W - b p Problem is non-rivial! Measured objec does no exis a priori, bu only hrough he experimenal prescripion for he measuremen. Quanum effecs!! W - b The idea of a - by iself - well defined objec having a well defined mass is incorrec!! je Deails and uncerainies of he paron shower and he hadronizaion models in den MC s influence he measured op quark mass.

15 Descripion of Jes LHC: Principle of mass measuremens: Idenificaion of he op decay producs je je je Invarian mass disribuion W b m + m non per. p W - - b p depends on: * mass definiion * je definiion * Mone Carlo je ATLAS

16 QCD Facorizaion Top Invarian Mass Disribuion: Simpler case: je je je e + e W b - ( p T m ) W - b je We need: QCD facorizaion in he final sae

17 QCD Facorizaion Top Invarian Mass Disribuion: Definiion of he observable Fleming, Manry, Sewar, AHH Phys.Rev.D77:074010,2008 Phys.Rev.D77:114003,2008 Phys.Le.B660: ,2008 resonance region: Double differenial hemisphere mass disribuion

18 QCD Facorizaion Fleming, Manry, Sewar, Hoang Phys.Rev.D77:074010,2008 Phys.Rev.D77:114003,2008 Phys.Le.B660: ,2008 Sof-Collinear-Effecive Theory Heavy Quark Effecive Theory Unsable Paricle Effecive Theory SOFT JET JET SOFT JET JET SOFT

19 QCD Facorizaion Je funcions: perurbaive dependen on mass, widh, color charge Sof funcion: non-perurbaive analogous o he pdf s dependen on color charge, kinemaics Independen of he mass! even shapes

20 QCD Facorizaion full QCD: 3 phase space regions: n-collinear: n-collinear: sof: Gluon collinear o he op: (n-collinear) n-je gauge dependen gauge independen

21 QCD Facorizaion full QCD: 3 phase space regions: n-collinear: n-collinear: sof: Gluon sof:

22 QCD Facorizaion Fleming, Manry, Sewar, AHH Phys.Rev.D77:074010,2008 M peak = m + Γ (α s + αs ) + Q m Λ QCD Ω 1 + O m Q firs momen of he sof funcion: Ω 1 = ds(,µ)

23 QCD Facorizaion Higher Orders & Top Mass Scheme: Fleming, Manry, Sewar, AHH Phys.Rev.D77:074010,2008 Jain, Scimemi, Sewar PRD77, (2008)

24 Theory Issues for definiion of je observables iniial sae radiaion final sae radiaion underlying evens Sof funcion? color reconnecion & sof gluon ineracions beam remnan paron disribuions summing large logs relaion o Lagrangian shor disance mass Hadron even shapes Banfi, Salam, Zanderighi Can be addressed in he framework of a LC. Requires exensions of LC conceps and oher known conceps

25 MC Top Mass Use analogies beween MC se up and facorizaion heorem Final Sae Shower Facorizaion Theorem Sar: a ransverse momena of primary parons, evoluion o smaller scales. Renormalizaion group evoluion from ransverse momena of primary parons o scales in marix elemens. Shower cuoff Subracion in je funcion ha defines he mass scheme Hadronizaion models fixed from reference processes Addiional Complicaions: Iniial sae shower, underlying evens, combinaorial background, ec Sof funcion model exraced from anoher process wih he same sof funcion Le s assume ha hese aspecs are reaed correcly in he MC

26 MC Top Mass Conclusion (quick answer): consan of order uniy Deerminaion of he MSbar mass: 3-loop R-evoluion equaion AHH,Jain, Scimemi, Sewar PRL 101,151602(2008) More sysemaic sudy needed for final answer! The exercise jus carried ou does no accoun for possible concepual uncerainies!

27 Oulook & Conclusion Conclusion: Curren op mass measuremens from he Tevaron refer o he op mass parameer in Pyhia m Pyhia. m J (2 GeV) For a high energy Linear Collider we have a facorizaion heorem o do MC independen shor-disance Lagrangian op mass measuremens (je mass) The analogy beween MC generaors and facorizaion heorem indicaes ha he m Pyhia is a shor-disance mass like he je mass (and no he pole mass). m Pyhia m J (2 GeV) Plans: Measure he in erms of he Je mass using hrus and oher even shapes m Pyhia m J (2 GeV) Derivaion of evenshape-like facorizaion heorems for Tevaron/LHC Measure m Pyhia for LHC-Pyhia