Top Quark Polarization and the Search for New Physics
aa r X i v : . [ h e p - ph ] J a n TOP QUARK POLARIZATION AND THE SEARCH FOR NEW PHYSICS a Edmond L. Berger
High Energy Physics Division, Argonne National Laboratory, Argonne, IL 60439, USA
Forward-backward asymmetries A tF B and A ℓF B are observed in the top quark t rapidity dis-tribution and in the rapidity distribution of charged leptons ℓ from top quark decay at theTevatron proton-antiproton collider, and a charge asymmetry A C is seen in proton-protoncollisions at the Large Hadron Collider (LHC). In this presentation, I summarize research mycollaborators and I have done on the interpretation and implications of the Tevatron asym-metries and provide expectations for A C at the LHC. The two asymmetries A tF B and A ℓF B are connected through the ( V − A ) spin correlation between the charged lepton and the topquark with different polarization states. The ratio of the two asymmetries provides indepen-dent insight into the physics interpretation of the top quark asymmetry. A new physics modelwhich produces more right-handed than left-handed top quarks appears to be indicated bythe present Tevatron data, but an improvement in precision is desirable. The large mass of the top quark, of order the electroweak scale, suggests that the top quarkmay be sensitive to electroweak symmetry breaking and to physics beyond-the-standard model.Experimentally, the observation of a larger than expected forward-backward asymmetry A tF B in the rapidity of top quarks produced at the Fermilab Tevatron collider 1 , A tF B = N (∆ y > − N (∆ y < N (∆ y >
0) + N (∆ y < , (1)where ∆ y = y t − y ¯ t is the difference between the rapidities of the top quark and the anti-topquark, and N (∆ y >
0) ( N (∆ y < y > y < z . In the standard model (SM), the asymmetry isinduced by perturbative quantum chromodynamics (QCD) processes beyond the leading order.The enhanced asymmetry is one of few manifestations of a deviation from predictions of theSM. Many models of new physics (NP) have been proposed to explain the data. A lengthlylist of references and a discussion of constraints on these models may be found in Berger etal. et al.
4. Some of the NP models postulate the existence of new states withright-handed couplings of the top quark.The large mass of the top quark is important in another respect. Its short lifetime meansthat the top quark decays as a “bare” quark. Its polarization information is retained in the weakdecay t → bℓν , passed to its decay products. The lepton ℓ angular distribution in the top quarkrest frame is maximally correlated with the top quark spin orientation, providing the opportunity a Argonne preprint ANL-HEP-CP-12-87. Invited paper presented at Beyond the Standard Model of ParticlePhysics, Quy Nhon, Vietnam, July 15 – 21, 2012. To appear in the Proceedings. o test non-standard features of NP models such as right-handed couplings. Another method tomeasure the polarization is based on the lepton momentum distribution 5 and is valuable for usewith complex final states in which the top quark rest frame is hard to determine. Of particularinterest to us have been the implications of models of new physics for the polarization of thetop quark, and methods that can be used to measure the polarization 5. In the SM, strongproduction of t ¯ t pairs in quantum chromodynamics (QCD) yields an equal number of positiveand negative helicity top quarks, hereafter referred to as t R and t L . Electroweak production insingle top quark production, for example, yields primarily t L . Therefore, a demonstration thata significant fraction of top quarks are produced with positive helicity would herald new physics.In addition to A tF B of the top quark, the D0 group reports a positive forward-backwardasymmetry of charged leptons from top quark decays. The measurement is done in two ways 2 , . − . The value A ℓF B =(15 . ± . ℓ +jets final states 2. The second method uses the dilepton finalstates from t ¯ t production, where the W bosons from the t and ¯ t decays both decay leptonically,and the result obtained is A ℓ FB = (5 . ± . ± . A ℓ FB = 11 . ± . . ± . . ± . ,
6, an excess at the level of 2.2 standard deviations. The fact that A ℓF B and A tF B are larger than the SM predictions indicates that the charged lepton strongly prefers to movein the same direction as the top quark from which it originates. Data on the ratio of the twoasymmetries tend to favor models in which more t R than t L are produced 3, but confirmationwith greater statistical and systematic precision is desirable.In Sec. 2 the asymmetries measured at the Tevatron are defined and our fits in the frameworkof Z ′ , W ′ , and axigluon new physics models are discussed. The LHC proton-proton collideroffers no preferred direction for the measurement a rapidity asymmetry. Nevertheless, chargeasymmetries A tC for top quarks and A ℓC for leptons can be defined and computed. Using datafrom the Tevatron, we may obtain expectations for these charge asymmetries, and we comparethese expectations with LHC data in Sec. 3. Despite limited statistics, the LHC data on thecharge asymmetry are also consistent with a deviation from the SM, although perhaps not asgreat a deviation as expected from an extrapolation of the Tevatron observations.The relationship of A tF B and A ℓF B is addressed in Sec. 4. The essential starting point isthe V − A structure of the matrix element for the decay t → W + b → bℓ + ν . We pay particularattention to the positive/negative helicity state of the top quark because the final momentumand angular distributions of leptons in the laboratory frame depend significantly on the topquark’s polarization state. We derive the relationship of the lepton asymmetry A ℓF B and the topquark asymmetry A tF B separately for the left- and right-handed polarization states of the topquark. Different models of new physics produce top quarks with different proportions of left-and right-handed polarization. For example, W ′ models produce predominantly right-handedtop quarks, whereas the axigluon model generates unpolarized top quarks. We use an axigluonmodel and a W ′ model in Sec. 4 to illustrate their different expectations for the ratio of thelepton and top quark asymmetries. In Berger et al.
3, we present fits for three models: flavor-changing Z ′ exchange, flavor-changing W ′ exchange, and axigluon models. The minimal version of the Z ′ model implies a large ratefor same-sign top quark pair production at the LHC, not supported by data 9 , ,
11. The W ′ model is constrained by data on the t ¯ t plus jets final state at the LHC 13 , ,
12. The absence ofpronounced deviations from the SM expectation in the measured m t ¯ t invariant mass distributionindicates to us that the axigluon should be heavy and/or broad. Another possibility would beo place it below m t ¯ t threshold 15.We fit data at the Tevatron to determine the parameters of the three new physics models.under consideration. We scan the parameter space of the models requiring that the predictions fitthe total cross section as well as CDF data on A tF B for both m t ¯ t <
450 GeV and m t ¯ t ≥
450 GeVwithin 2 σ accuracy. (GeV) W’ m
200 400 600 800 1000 1200 W ’ f W’ (GeV) G’ m G ’ f G’ =0.3 G’ /m G’ Γ Figure 1: The parameter space of two new physics models determined from fits to the Tevatron t ¯ t total crosssection and A tF B measured by the CDF collaboration in the intervals m t ¯ t <
450 GeV and m t ¯ t ≥
450 GeV. Theyellow region fits the data within 1 σ and the green region fits within 2 σ : flavor-changing W ′ model, and axigluonmodel. The dashed line in the W ′ case shows the bound on the coupling f W ′ obtained from an analysis of theCMS data on top-pair-plus-one-jet events at the LHC. The blue shaded region in the axigluon case is inferredfrom the limits set by ATLAS on axigluons from the search for enhancements in the dijet mass distribution. Figure 1 shows the results of our fits for two of the models. The fit for the Z ′ model maybe found in Berger et al.
3. There is a large region of parameter space in which the W ′ modelcan fit the Tevatron data within 1 σ and 2 σ . However, the region above the blue dashed curveis not allowed since too many t ¯ t + j events would be produced. In the axigluon case, to achievegood agreement with data at the 1 σ level, the mass of axigluon is required to be in the range ofabout 900 GeV to 1900 GeV. For other axigluon masses, the model can only fit data at the 2 σ level. Also shown are some bounds on axigluon masses and couplings obtained from a searchfor resonances in the dijet invariant mass distribution 16 , The LHC proton-proton collider is symmetric in rapidity, and it is ambiguous to define a forwardor backward region. However, the u and d parton densities carry, on average, a larger fractionof the momentum of the proton than the u and d antiquark densities. With the knowledgethat there is a forward-backward asymmetry in the perturbative production process for ¯ qq → t ¯ t production, we expect that the top quark at the LHC will be boosted in the direction of theincident quark. As a result, top quarks should accumulate in the region of large rapidity andanti-top quarks will be preferentially in the central region. An asymmetry A C may be definedat the LHC as A C = N ( | y t | > | y ¯ t | ) − N ( | y t | < | y ¯ t | ) N ( | y t | > | y ¯ t | ) + N ( | y t | < | y ¯ t | ) . (2)Measurements of A C at the LHC have been published by the CMS and ATLAS collaborationsbased on data sets with 4 . − of integrated luminosity 17 ,
18. The ATLAS central value is anrder of magnitude larger than the CMS value, but they agree within the large uncertainties inboth experiments, and they are consistent with the SM prediction.At the Tevatron, t ¯ t production is driven by the quark-antiquark initial state parton den-sities, whereas at the LHC, it is dominated by the gluon-gluon initial state which provides noasymmetry. The overall asymmetry A C is therefore expected to be diluted substantially at theLHC. An approximate estimate for the LHC asymmetry may be obtained by an extrapolationfrom the Tevatron result: A C ≈ σ ( q ¯ q → t ¯ t ) σ ( gg → t ¯ t ) + σ ( q ¯ q → t ¯ t ) × A tF B ( q ¯ q → t ¯ t ) × ˜ ǫ. (3)The first term represents the fraction of the top-quark pair production cross section inducedby the q ¯ q initial state which is about 17 % in the SM at the LHC at 7 TeV. The second termis the asymmetry induced by the q ¯ q initial state. Given that about 88% of the t ¯ t productioncross section in the SM comes from the q ¯ q initial state at the Tevatron, A tF B ( q ¯ q → t ¯ t ) can beextracted from the top quark forward-backward asymmetry observed at the Tevatron; we use A tF B ( q ¯ q → t ¯ t ) ≈ A tF B / A tF B is the measured top quark asymmetry. The last term˜ ǫ in Eq. (3) represents the probability of correct identification of the forward direction, namelyhow frequently the forward direction represents the direction of the initial state quark. Thisprobability is evaluated in Berger et al. A C ≃ . × A tF B / × ≃ . A tF B , where A tF B is the value measured at the Tevatron. With A tF B ∼ A tC ≃ .
02, in reasonable agreement withthe central value of the ATLAS measurement but in excess of the central value of the CMSmeasurement. Setting aside for the moment the still large uncertainties of the LHC data, theagreement of the ATLAS measurement with our extrapolation lends credence to the suggestionthat new physics contributions are playing a role in the asymmetry measured at the Tevatron.On the other hand, there is evident tension between the Tevatron asymmetry and the centralvalue of the CMS measurement. (GeV) W’ m
500 1000 t C A bound σ ATLAS 1 bound σ ATLAS 1ATLAS central value W’ (GeV) G’ m t C A bound σ ATLAS 1 bound σ ATLAS 1ATLAS central value G’ Figure 2: The predicted top quark charge asymmetry, A tC , at the LHC at 7 TeV from the W ′ (left) and axigluon(right) models, compared with the ATLAS results. The yellow and green regions are for the couplings that fit theTevatron t ¯ t total cross section and A tF B within 1 σ and 2 σ , respectively. The central value measured by ATLAS ismarked with the red horizontal line, and the two black dashed lines show the 1 σ uncertainty of the measurement.The blue dashed line on the W ′ figure shows the bound obtained from the analysis of top-pair-plus-one-jet events.The region above this dashed line is disfavored. The extrapolation from the Tevatron is admittedly rough as it ignores possibly subtle energy-ependent effects and cancellations between SM and new physics contributions. Turning next tothe explicit new physics models discussed in the previous section, we use the allowed parametersfor the flavor-changing W ′ and axigluon models shown in Fig. 1 and calculate A C at the LHC.The results are shown in Fig. 2, along with a comparison to the ATLAS data. To obtain theATLAS predictions we use A C = 0 .
006 for the SM prediction, as done by ATLAS. For the CMScomparison, we use the SM value A C = 0 . et al. A C predicted in the W ′ model are larger than the ATLAS central value,but they are within the 1 σ uncertainty band. For the axigluon model, all of the predictions of A C agree with the ATLAS result within the 1 σ level. In the axigluon model A C does not simplyincrease with the axigluon coupling to SM particles. For m G ′ = 1500 GeV, A C reaches itsmaximum at about 4 . f G ′ = 2 .
7. Therefore, the upper boundary of the yellowregion (couplings that fit Tevatron data within 1 σ ) overlaps the green region (couplings that fitTevatron data within 2 σ ) for some m G ′ . The G ′ model predicts smaller values of A C than the W ′ model because there is a change of the sign of the s- channel propagator. When the invariantmass of the t ¯ t system is larger than the mass of the axigluon, the contribution to A C from theinterference term is negative. When comparing with the CMS data, we find in Berger et al. A C are outside of the 1 σ band. Unless the central value increasesin updated measurements, the CMS data disagree with the simplest new physics models basedon W ′ or axigluon contributions. A tF B and A ℓF B The top quark is the only quark that decays quickly, before hadronization takes place, and itspolarization determines the kinematic distribution of its final state decay particles. Therefore,it should be possible to understand the relationship of A tF B and A ℓF B based on the kinematics ofthe charged lepton in the decay of a top quark with different polarization states.The charged lepton in top quark decay is a powerful analyzer of the polarization of thetop quark 19. Owing to the V − A structure of the charged current in the SM, the angulardistribution of a charged lepton ℓ + from top quark decay ( t → W + ( → ℓ + ν ) b ) in the top quarkrest frame is 1Γ d Γ d cos θ hel = 1 + λ t cos θ hel , (4)where λ t denotes the top quark helicity, and θ hel is the angle of ℓ + with respect to the directionof motion of the top quark in the overall center-of-mass system of the t ¯ t production process. Weuse the helicity basis in our calculations; λ t = + denotes a right-handed top quark ( t R ), and λ t = − a left-handed top quark ( t L ). Once the top quark is boosted along its spin direction,the angular distribution of the charged lepton relative to the direction of motion of the topquark deviates from (1 ± cos θ ), and it becomes sensitive to the energy of the top quark E t (orequivalently its velocity β ). We derive d ΓΓ d cos θ tℓ = 1 − β cos θ tℓ + λ t (cos θ tℓ − β )2 γ (1 − β cos θ tℓ ) , (5)where β = q − m t /E t , γ = E t /m t , and θ tℓ is the angle between the charged lepton and thedirection of motion of its parent top quark.To obtain the forward-backward asymmetry in the laboratory frame, we must rotate theangular distribution in Eq. 5 from the top quark direction of motion to the laboratory coordinateaxes. We use a function R ℓ, λ t F ( β, y t ) to represent the probability that a lepton with positivecharge lands in the forward region when it originates from a top quark with velocity β , rapidity t , and polarization λ t . Formally, R ℓ, λ t F ( β, y t ) = N ℓF N ℓF + N ℓB . (6)where N ℓF ( N ℓB ) denotes the number of leptons ℓ in the forward (backward) region in the labo-ratory. Moreover, A ℓ, λ t F B ( β, y t ) = 2 R ℓ, λ t F ( β, y t ) − . (7)It is noteworthy that an explicit analytic expression can be obtained in closed form for R ℓ, λ t F ( β, y t )in the laboratory frame. The derivation is somewhat lengthy, and it is presented in the Appendixof Berger et al. R ℓ, λ t F ( β, y t ) in Eq. 6 and A ℓ, λ t F ( β, y t ) in Eq. 7 are functions of the top quarkmomentum. To obtain the numbers of leptons in the forward and backward regions, we mustconvolve R ℓ, λ t F ( β, y t ) with the top quark momentum spectrum, i.e. N ℓF N ℓF + N ℓB = 1 σ X λ =+ , − Z R λF ( β, y t ) d σ | λ t = λ dβdy t dβ ∧ dy t , (8) N ℓB N ℓF + N ℓB = 1 σ X λ =+ , − Z h − R λF ( β, y t ) i d σ | λ t = λ dβdy t dβ ∧ dy t , (9) A ℓF B = 1 σ X λ =+ , − Z h R λF ( β, y t ) − i d σ | λ t = λ dβdy t dβ ∧ dy t (10)where d σ | λ t = λ dβdy t labels the differential t ¯ t production cross section for a top quark with specifickinematics ( β , y t , λ t ), and σ stands for the t ¯ t total production cross section.The observed positive top-quark asymmetry A tF B indicates that more top quarks are pro-duced in the forward region than in the backward region of rapidity. Both t R and t L can generatea positive lepton asymmetry A ℓF B from a positive A tF B . However, a t L would need a large boostalong the proton beam line (i.e. in the large forward rapidity region) to overcome the fact thatmost of the charged leptons from its decay move against it in its rest frame. A right-handed topquark t R can yield a positive A ℓF B even for top quarks near the t ¯ t threshold region. Therefore,the large positive top quark and lepton asymmetries A tF B and A ℓF B observed by the D0 collab-oration indicate that the top quark polarization and the kinematics of the top quarks, y t and E t , may be playing a non-trivial role.The correlation between the charged lepton asymmetry and the top quark asymmetry issignificantly different for different polarization states of the top quark, and it may thereforeshed light on the nature of the physics that causes the forward-backward asymmetries at theTevatron. We choose the W ′ and axigluon models as two reference models to examine thecorrelation at the Tevatron and the LHC.The axigluon and W ′ models admit good fits to A tF B at the Tevatron, but they providedistinct predictions for the polarization and kinematics of the final state top quark. The W ′ model produces dominantly t R while the axigluon model generates an equal number of t R and t L with more energetic top quarks since the quarks come from the decay of a heavy axigluon.In Fig. 3, we show the results of our calculation of the charged lepton asymmetry at the LHCusing the parameters determined in our 1 σ fits to the t ¯ t total cross section and the most recentCDF data on A tF B . Figure 3 shows charged lepton asymmetry for the LHC together with thetop quark charge asymmetry A tC . The results for the Tevatron are shown in Berger et al. A tC ∼ .
03 to show the central values of the asymmetriesmeasured by ATLAS, and two black dashed lines show the extent of the quoted experimental 1 σ C A l C A W’ tC A l C A G’ Figure 3: The correlation between A tC and A ℓC at the LHC for the W ′ (left) and axigluon models (right). Thevertical (horizontal) red line and the two black dashed lines show the central value of A tC ( A ℓC ) and the 1 σ uncertainty bands measured by ATLAS at the LHC. The green (red) dots are obtained from the parameters thatfit the Tevatron t ¯ t cross section and A tF B within 1 σ (2 σ ). uncertainty bands. The horizontal red line shows the central value of A ℓC measured by ATLAS,and the horizontal black dashed lines show the 1 σ uncertainty values.The predicted charged lepton asymmetries stretch out over a range of values depending onthe values of the axigluon or W ′ masses used in the fits to the Tevatron data. At the LHC, thereare parameters in both models (obtained from the Tevatron fits) that can reproduce the valuesof A tC and A ℓC measured by ATLAS, shown by the fact that the intersection of the vertical andhorizontal red lines passes through the scattering of dots. On the other hand, there is a widerange of dots in the W ′ model that are above the central values of A tC and A ℓC , and out of the1 σ uncertainty band. In the axigluon model, all the values of A tC and A ℓC are consistent withATLAS measurements within the 1 σ bands. The LHC and Tevatron data together could reducethe allowed parameter spaces of the two models.The size of the top quark asymmetry, in excess of SM expectations, is one indication thatnew physics may be playing a role. The charged lepton asymmetry provides a second andindependent indication of the presence of new physics since it points to the possibility that moreright- than left-handed top quarks are being produced. It is important to confirm the chargedlepton asymmetry. This goal could be realized with an analysis of the full data set in D0. Itwould be valuable also to have a measurement of the charged lepton asymmetry from the CDFcollaboration. Acknowledgments
The work reported here was done in collaboration with Qing-Hong Cao, Chuan-Ren Chen, andHao Zhang. The High Energy Physics Division at Argonne is supported by the U.S. DOE underGrant No. DE-AC02-06CH11357.I am pleased to commend Marc Besancon for his very professional and self-effacing organi-zation of the excellent scientific program of this conference on Beyond the Standard Model ofParticle Physics in Quy Nhon, Vietnam in July 2012. I am glad to have had this opportunityto make his acquaintance.This conference was the most recent in of the “Rencontres du Vietnam” series established byJean Tran Thanh Van. Van has contributed much over the years to fostering international scien-ific collaboration, and to facilitating interactions among experimenters and theorists, throughhis establishment of the ongoing “Rencontres de Moriond” series begun in 1966 and the “Rencon-tres de Blois” series started in 1989. During this visit to Vietnam, conference participants hadthe opportunity to learn first-hand of the ambitious International Center for InterdisciplinaryScience and Education that he is creating in Quy Nhon, Vietnam and to visit the sea-sideconstruction site. Once operational, the intent is that the Center will host high-level national,regional, and international meetings in basic and applied science, medicine, the humanities, andsocial sciences.
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