A theoretical study of new observables to measure the top quark mass at hadron colliders

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A theoretical study of new

observables to measure the top quark mass at hadron colliders

DESY, Zeuthen, Berlin S. Alioli, S. Moch

IFIC, CSIC-Universitat de València J. Fuster, A. Irles, M. Vos

Humboldt Universität, Berlin P. Uwer

XXXIII Reunion Bienal de la Real Sociedad Española de Física

20

^th

September, 2011

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Introduction (I)

It is being one of the main actors in the LHC's first years picture.

It is important to measure its properties:

• Spin, charge, isospin.

• Couplings (at, vt, Vtd, Vts, Vtb, gttH)

• Mass and decay width (Γ)

The top quark was discovered by CDF and D0 at Tevatron in 1995,

observing its decay channels (one b-jet and a reconstructed W)

mtop = 173.3±1.1 GeV Plays a special role in the electroweak sector due to its large mass

Pole mass (mt)

• It is defined as the pole of the renormalized quark propagator.

• Can only be defined order by order in perturbation theory.

?

Intrinsic non perturbative ambiguity

Running mass (mt(µ))

• Corresponds to the renormalized mass in the MS scheme

[

¹ ⁽ ⁾ ⁽ ⁾ ^...

]

)

( + ₁+ ² ₂ +

= m c c

m_t_pole _t µ α_s µ α_s µ

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Introduction (II)

Top quark mass measurements

Exploring another ways to obtain a top quark mass measurement:

Gluon and photon emission from quarks depend on the quark mass. In the past this property has been studied for three-jet final state in e+e- collisions.

At LEP and SLD, an observable (R₃) based on the probability of reconstruct three-jet events (bb+jet)

have been used to measure the b-quark mass. Explicit quark mass dependency m_top^pole=166.7_−4.5^5.2GeV

Aprox NLO

m_top^pole=166.4_−7.3^7.8 GeV

Aprox NLO _m_top^pole_=173.2_±0.9_GeV

W. Bernreuther et al, Phys. Rev. Lett. 79 (1997) 189, G. Rodrigo et al Phys Rev Lett, 79 (1997) 193, M.S. Bilenky et al. Phys. Rev. D60 (1999) 114006 Kinematic measurements Measurement from the cross section

arXiv:1104.2887

ATL-CONF-29011-054

arXiv:1107.5255

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Top quark mass (GeV)

Cross section (pb) with pT(jet)>50 GeV and |ŋ|<2.5

LO NLO

160

48,177(2) 60,08(7)

165

41,739(2) 52,19(6)

170

36,275(4)

⁺²⁰_-12

(scale)

⁺_-

1(pdf) 45,44(5)

⁺¹_-6

(scale)

⁺_-

1(pdf)

175

31,620(3) 39,66(4)

180

27,641(1) 34,69(4)

tt+1-Jet at NLO for LHC at 7 TeV

Based on S. Dittmaier, P. Uwer, Weinzierl Eur. Phys. J. C. (2009) 625-646

tt+1-Jet calculations have been performed at NLO for hadronic collisions at both Tevatron and LHC. Updated results of this calculation for the LHC present operating conditions at 7 TeV are shown in the following table:

These values have been obtained using CTEQ6.6 and MSTW2008nlo90cl (to evaluate the PDF dependences). The

“jet” has been reconstructed using the FastJet Package (Phys. Lett. B 641 (2006) 57) and the anti-Kt algorithm (JHEP 0804 (2008) 63) with R=0.4.

We set the renormalisation scale equal to the factorisation scale. To estimate the impact of higher order corrections the scale is varied between µ=m_top/2 and µ=2m_top.

Theoretical Introduction (I)

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Theoretical Introduction (II)

**tt+1-Jet* cross section (pb) calculated with POWHEG**

POWHEG tt NLO tt+1-Jet (at LO) 36,3(1)

tt+1-Jet (LHE**, after POWHEG emission) 50,42(6)

+Pythia8 shower tt+1-Jet* 40,21(6)

POWHEG tt+1-Jet NLO tt+1-Jet (NLO) 45,5(1)

tt+1-Jet (LHE**, after POWHEG emission) 48,8(2)

+Pythia8 shower tt+1-Jet 45,1(1)

m_top=170. GeV CTEQ6.6 PDF and μ=m_top

* Jet reconstructed with the anti-Kt algorithm, R=0.4.

A pT jet>50 GeV and a |ŋ|<2.5 have been required for the jet.

** LHE : Les Houches Accord Format

tt+1-Jet with POWHEG

P. Nason, JHEP 0411 (2004) 040; S. Frixione, P. Nason and C. Oleari, JHEP 0711 (2007) 070; S. Alioli, P. Nason, C. Oleari and E. Re, JHEP 1006 (2010) 043

POWHEG is a general method to merge full NLO calculations with SMC (Standard Monte Carlo Event Generators i.e. Pythia, Herwig, etc) for hadronic collisions avoiding double-counting.

For this work POWHEG has been used with Pythia8.150 as SMC for proton-proton collisions at 7 TeV. A parton shower from gluon and quark emission has been generated but top quarks have been kept stable.

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The variable ρ_s is defined as:

ρ

_s

= 2 ⋅ m

₀

 ^s

tt +1-Jet

with m₀=170 GeV and √s_tt+1-Jet being the invariant mass of the multi-jet system.

The following distributions are then defined:

Representing the differential tt+1-Jet cros section as a function of ρ_s and

as the differential tt+1-Jet cross section normalized,

Definition of the Observable (I)

d N₃

d_s m_top,=d _t__t_1−_Jet

d _s m_top,

d n₃

d _sm_top,= 1

_t__t_1−_Jet

d N₃

d_s m_top ,

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Comparison between dn₃/ρ_s(m_top,µ) calculated at LO and at NLO for a m_top=170 GeV and using the CTEQ6.6 PDF set.

The dN

3/dρ

s(m

top,µ) (left) and the dn

3/dρ

s(m

top,µ) (right) distributions for m_top=170 GeV. The calculations for the two different PDF sets are shown as well as the scale dependence.

Definition of the Observable (II)

The theoretical dependences (PDF and scale dependence)

of the observable are well know at NLO

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Scale, PDF and mass dependence

dn₃/dρ_s(m_top,µ) distribution at NLO for different masses (m_top=160, 170 and 180 GeV). Due to the normalization to σ_tt+1-Jet close to the 0.55<ρ_s<0.62 region all curves cross implying a decrease of the sensitivy in this region.

Crossing region

The impact to the top mass value (for m_top=170 GeV) of the scale (magenta solid line). The equivalent impact of the difference between the two PDFs considered in this exercise is also shown (blue dashed line).

The crossing region is excluded.

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LO&NLO and POWHEG&NLO comparisons

 m=1 GeV

LO & NLO COMPARISON

Mass fit to NLO calculations. The NLO dn₃/dρ_s(m_top, µ) distribution is used as reference and the equivalent LO curve is computed to reproduce the same dn₃/dρ_s(m_top,µ) value.

Equivalent radiation at LO with respect to NLO is obtained with smaller masses.

POWHEG & NLO COMPARISON

Mass fit to NLO calculations. The NLO dn₃/dρ_s(m_top,µ) distribution is used as reference and the equivalent curves for POWHEG tt at NLO and tt+1Jet at NLO are computed to reproduce the same dn₃/dρ_s(m_top,µ) value.

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CONCLUSIONS & PROSPECTS

● A new distribution: dn₃/dρ_s(m_top,µ) has been presented and its theoretical properties have been studied.

● Theoretical predictions have been obtained at NLO accuracy. The distributions have been shown to be sensitive to the top quark mass with well understood theoretical behaviour with respect to the renormalization scale and PDF choices.

● The uncertainty of the extracted top-quark mass on the renormalization scale and the PDFs is observed to be below 1 GeV for a certain region of the ρ_s variable and within the usual scale and PDF variations.

● Good behaviour of these observables is also observed when comparing LO and NLO computations and different POWHEG scenarios.

● Future work:

● pT cut optimization in the jet reconstruction (>50 GeV at present).

● Study the impact of more realistic/experimental situations when reconstructing jets using stable final state particles.

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A theoretical study of new observables to measure the top quark mass at hadron colliders