The decays of on-shell and off-shell polarized gauge bosons into massive quark pairs at NLO QCD
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he Decays of OnShell and OffShell Polarized Gauge Bosons into Massive Quark Pairs at NLO QCD1, 2 S. Grootea, J. G. Körnerb, and P. Tuvikea a
Füüsika Instituut, Tartu Ülikool, Tartu, Estonia PRISMA Cluster of Excellence, Institut für Physik, JohannesGutenbergUniversität, Mainz, Germany
b
Abstract—We discuss the polar angle decay distribution in the decay of onshell and offshell polarized (W, Z) gauge bosons into massive quark pairs. In particular for the offshell decays in H → (W, Z) + (W*, Z*)(→q1 q 2 ) it is important to keep the masses of the charm and bottom quarks at their finite values 2
since the scale of the problem is not set by m W, Z but by the offshellness of the gauge boson which varies in the range (m1 + m2)2 ≤ q2 ≤ (mH – mW,Z)2. DOI: 10.1134/S1063779614010419 21
1. INTRODUCTION The polarization of W and Z bosons produced in electroweak processes is in general highly nontrivial. One therefore has a rich phenomenology of polariza tion effects in (W, Z) production and decay which will be explored in present and future high energy experi ments. The polarization of the W and Z bosons can be probed by decay correlations involving the momenta of the final state leptons or quarks in the decays of the polarized (W, Z) bosons. Bottom and charm quark mass effects are moderate for onshell decays but are important for offshell decays in particular in the vicinity of the threshold where the offshell value q2 becomes comparable to the quark masses. 2. ANGULAR DECAY DISTRIBUTION In the W rest frame the angular decay distribution of a polarized onshell spin1 W boson into a pair of fermions is given by 1 1 W ( θ ) ∝ 3 ρ mm d mm' ( θ )d mm' ( θ )H m'm' 2 m, m' = 0, ±
∑
2 3 = cos θ ( ρ ++ – 2ρ 00 + ρ –– ) ( H ++ – 2H 00 + H –– ) 8
3 + cos θ ( ρ ++ – ρ –– ) ( H ++ – H –– ) 4 + 3 ( ( ρ ++ + 2ρ 00 + ρ –– ) 8 × ( H ++ + 2H 00 + H –– ) – 4ρ 00 H 00 ).
The ρmm are the process dependent (unnormalized) density matrix elements of the spin1 gauge boson and the Hmm are the (unnormalized) universal polarized decay functions needed to analyze the polarization of the gauge boson. The polar angle θ is the angle between the z direction defined by the production pro cess and a z' direction specified by the decay process. When the z' axis is defined by the antiquark in the decay W + → c b the (unnormalized) O(αs) analyzing polarized decay functions Hmm are given by α 2 2 2 H ++ = 8N c q 1 + s ( 1 + ( π + 16 )m 2 / q ) + … , 6π α 2 2 2 H 00 = 8N c q 0 + s ( 4 – 2π m 2 / q ) + … , 6π
(2)
α 2 2 2 H –– = 8N c q 1 + s ( 1 + ( π – 16 )m 2 / q ) + … , 6π (cf. [1]) where we have expanded the result up to 2
O(m2/ q ). Surprisingly the mass corrections to the NLO terms are linear in the antiquark mass and carry 3
(1)
1 Invited talk given by J.G. Körner at the 20th International Sym
posium on Spin Physics, September 17–22, 2012, Dubna Rus sia. To be published in the Proceedings. 2 The article is published in the original.
rather large coefficients. From (1) one can define a normalized decay distri
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