Understanding Single Tops using Jets
aa r X i v : . [ h e p - ph ] J un Understanding Single Tops using Jets
Tilman Plehn, Michael Rauch, and Michael Spannowsky Institut f¨ur Theoretische Physik, Universit¨at Heidelberg, Germany ITP, Universit¨at Karlsruhe, Germany
Top plus jets production at hadron collider allows us to study the couplings of the top quark.In the Standard Model, two single top processes contribute to the top-jets final state. Beyond theStandard Model, additional direct top production can occur. All three processes probe top gaugecouplings including flavor mixing. The structure of accompanying QCD jets allows us to separatethe direct top signal from the QCD backgrounds as well as to disentangle the three top plus jetsproduction mechanisms orthogonally to the usual bottom tags.
INTRODUCTION
Experimental results from flavor physics and electroweak precision measurements have long establishedthe Standard Model pattern of flavor and CP violation. The only sources of flavor and CP violationare the Yukawa couplings, and the one essentially unknown parameter is the relative coupling strengthof the heavy third-generation quark to the W boson, i.e. the CKM mixing angle V tb [1]. Its knowledgeis crucial to establish the unitarity of the CKM mixing matrix in the Standard Model. Because theSU(3) symmetry of QCD does not see electroweak charges, this coupling cannot be determined in QCD-mediated top pair production. Instead, we rely on the electroweak production process for a single topquark in association with a quark jet to measure this parameter of the Standard Model.The problem of modern particle physics is that while on the one hand we have good reasons to expectthat we will see a non-trivial ultraviolet completion of the Standard Model at the TeV scale, we donot know where in such an extended model this particular flavor structure originates from. One ofthe standard candidates for such new physics at the TeV scale with all its benefits from a dark mattercandidate and stabilized Higgs mass to a valid grand unified theory is the minimal supersymmetricStandard Model MSSM [2]. Mainly in the soft-breaking terms in the MSSM Lagrangian there aremultiple sources of flavor and CP violation which naturally predict observable effects, including flavorchanging neutral currents. Assuming only one set of supersymmetric partner states we can implementthe experimental constraints by postulating a symmetry dubbed minimal flavor violation. This impliesthat there still be no sources of flavor violation other than the Yukawa couplings, the spurions of flavorsymmetry breaking [3]. An interesting alternative might be the promotion of the gauge sector to N = 2supersymmetry, leading to Dirac fermion partners of the Standard Model gauge bosons and additionalscalar particles, all clearly visible at the LHC [4, 5].In this paper, we instead focus on the more subtle effects of an approximate minimal flavor violationsymmetry. Focussing on the quark/squark sector, minimal flavor violation forces the soft squark massesto be almost diagonal in flavor space and the scalar trilinear A terms — for example describing squark-squark-Higgs interactions — to be proportional to the Yukawa couplings. Corrections consistent withthe Standard Model flavor symmetry are induced by higher powers in the Yukawa couplings.Since we cannot derive minimal flavor violation from first principles, we need to measure if and byhow much it is broken. In the down-quark sector, squarks contribute to K -and B -physics observablesvia squark-gluino loops mediated by the strong coupling constant α s , which gives us powerful tests ofminimal flavor violation. In contrast, in the the up-quark sector such one-loop effects are proportional tothe weak coupling α or the Yukawa couplings and much harder to measure. The first-third and secondthird generation mixing between the ˜ u R and ˜ c R with ˜ t L squarks is essentially invisible for kaon, charmand B experiments [6, 7]. Integrating out the heavy supersymmetric particles, such loop contributionslead to flavor-violating quark couplings to Standard Model gauge bosons, for example a u - t - g or c - t - g vertex [8]. At the LHC processes involving valence quarks are generally more interesting, so we will focuson the u - t - g vertex, but its second generation counter part can of course be treated the same way.The search for this largely unconstrained effective coupling is linked with the measurement of V tb through the relevant LHC processes. While the effective gluon vertex leads to the direct production ofan isolated top quark, single top production is accompanied by a quark jet. However, at the LHC we knowthat the radiation of additional quark and gluon jets from the incoming quarks is ubiquitous. Therefore,the question becomes: how can we tell apart electroweak CKM effects in single top production (and itstwo production mechanisms) and strong effects from non-minimal new physics in direct top production,all including top quark decays as well as realistic QCD effects and backgrounds. DIRECT TOPS AND JETS
In spite of the fact that there are many flavor observables constraining squark mixing beyond minimalflavor violation, there are two entries in the squark mass matrices which are still largely unconstrained.Even though we actually use the diagonalized squark mass matrix, it is instructive to discuss the results interms of dimensionless mass insertions δ qAB,ij = ∆ qAB,ij / ¯ m (for the squark handedness A, B = L, R , thegeneration indices i, j = 1 ...
3, and the weak isospin q = u, d ). The ∆ qAB,ij are the relevant off-diagonalentries and ¯ m = m AA,ii m BB,jj the corresponding mean diagonal entry in the squark mass matrix.Because we are not interested in the strongly constrained down-type mixings δ d and we focus onleft-right mixing only, we denote δ ij ≡ δ uLR,ij (1)The unconstrained left-right mixing terms are the off-diagonal δ between ˜ u R and ˜ t L and the diagonal δ [7, 9]. The left-right swapped δ instead mixes ˜ u L and ˜ t R . It is constrained by b → d transitions [10]and ∆ m d in ¯ B d − B d mixing [11]. The reason why the bounds on δ are strong and those on δ hardlyexist is the chargino-top loop: if the chargino is a mix of the wino and the Higgsino, the latter willhave a large Yukawa coupling to the external bottom. The ˜ u instead couples to the wino content of thechargino, which forces is to be left handed ˜ u L . This δ constraint can only be relaxed by heavy squarks.Assuming minimal flavor violation the generation-diagonal entry ∆ is of the general form m t ( A t − µ/ tan β ) and does not need to be small. As a matter of fact, it can lead to a large splitting of the twostop masses and ameliorates the little hierarchy problem, so we do not expect it to be small either. Itis currently only constrained via the lower limit on the light Higgs mass and can be measured either instop mixing or in the minimal supersymmetric Higgs sector [12].The generation mixing entry δ mixes ˜ u R and ˜ t L and at one-loop induces the flavor-changing chromo-magnetic operator [13] m ˜ g g s π ¯ t L,α σ µν u R,β T aαβ G µνa + h.c. (2)via a squark-gluino loop. As shown on the left Fig. 1 this operator implies direct top production athadron colliders pp → t → bW + ℓ , with a leptonic W decay to avoid an undetectable purely hadronic final bl + ν l ˜ g t R t L ˜ t R ˜ t L u bl + ν l + ˜ t L ˜ u L ˜ u L g ˜ t R t R t L ˜ u R ug FIG. 1: Sample Feynman diagrams for SUSY-induced direct top production. The crosses indicate left-right massinsertions which can mix first and third generation up squarks. state. The corresponding partonic cross section is typically suppressed by the heavy gluino mass in theloop and therefore proportional to σ ( ug → t ) ∝ | δ | | δ | m g (3)The second diagram in Fig.1 contributes proportional to | δ | , which is negligible after fulfilling all flavorconstraints. Due to the absolute values squared they are invariant under complex phases of the squarkmixing parameters. This process to our knowledge is the only way to measure the otherwise unaccessible δ in the era of LHC and super- B factories.Usually, the MSSM parameter space beyond minimal flavor violation is huge, and physical processestypically involve many possible contributions which are free to cancel each other. In contrast, directtop production is a strongly interacting process and depends only on the masses m ˜ g and m ˜ t and thesquark mixing parameters δ ∼ A t , δ and δ . For small values of tan β we have to include µ/ tan β inthe expression for δ . For our numerical study we use the SPS2 [14] inspired reference point with theGUT-scale masses m = 1450 GeV, m / = 300 GeV and A = 0. The Higgs sector is characterized bytan β = 10 and µ >
0. The relevant weak-scale masses for our process aretan β = 9 . µ = 386 GeV M ˜ χ = 125 GeV M ˜ g = 350 GeV m ˜ U L, = m ˜ U L, = 1538 GeV m ˜ U L, = 1279 GeV m ˜ U R, = m ˜ U R, = 1534 GeV m ˜ U R, = 956 GeV (4)This gives us a light (mostly) stop mass of 955 GeV and a light Higgs mass of 117 GeV. The lightestneutralino is a viable dark matter candidate. For the calculation of the direct top production rate at thispoint we use FeynArts, FormCalc [15], LoopTools [16], and HadCalc [17]. We include all supersymmetricQCD and electroweak contributions.There are four major backgrounds for direct top production ug → bW + with a charge identifiedlepton from the W decay and a tagged bottom jet with a tagging probability of 50% and a mis-taggingprobability of 1% ug → bW + irreducible and CKM suppressed ug → dW + fake bottom tag¯ dg → ¯ cW + fake bottom tag u ¯ d → b ¯ bW + gluon splitting to two bottoms (5)Of the three W plus one jet backgrounds the irreducible combination is suppressed with respect to themis-tagging background by roughly two orders of magnitude. Similarly, the more likely mis-tag of acharm requires a ¯ dg initial state and should be at maximum of the same order as the valence-quarkinduced ug → dW + process. Most importantly, the kinematic distributions of the three are very similar,so we expect all three to vanish as a roughly constant fraction of the leading ug → dW + background.The two-bottoms background process can become dangerous when the two bottom jet are close enoughto look like one bottom jet from gluon splitting. If we require the two bottom jets to be close (∆ R bb < . W + b ¯ b rate is of the same order as the subleading bW + production, which again means thatin the following discussion we will focus on the mis-tagged ug → d b W + background.All of the background and the signal pass the acceptance (and triggering) cuts p T b >
20 GeV p T ℓ >
15 GeV | η b | , | η ℓ | < . R bℓ > . W+JetDirect Top p T j,b [GeV] / σ d σ / d p T j , b [ f b / G e V ] . . . . . W+JetDirect Top √ ˆ s [GeV] / σ d σ / d √ ˆ s [ f b / G e V ] . . . . . FIG. 2: Normalized distributions for direct top production and the main background pp → νℓ + +jets, afteracceptance cuts. These distributions (and only these) are generated without QCD jet radiation but includingmomentum smearing to account for detector effects. There are two key distributions to separate direct top production from the continuum backgrounds,shown in Fig. 2: due to the signal kinematics, the transverse momentum of the bottom jet is stronglypeaked around p T b ∼ ( m t − m W ) / (2 m t ) ≃ . √ ˆ s should also peak around the top mass. The unmeasured longitudinalneutrino momentum we compute from the mass shell condition m lν = m W . The remaining two-foldambiguity we resolve by choosing the better top mass reconstruction [13]. These kinematic features weexploit by requiring 55 GeV < p T b <
80 GeV 165 GeV < p ˆ s rec <
185 GeV (7)As shown in Table I the statistical significance after cutting on the kinematic features of the signal isnot sufficient to extract single top production at the LHC, even though the Gaussian significance for60 fb − of data looks promising. Theory and other systematic errors require a reasonable value of atleast S/B & /
10 for such a counting experiment, which means we have to search for additional ways toextract direct top production out of the QCD background.A distinguishing feature of direct top production which has nothing to do with the decay kinematics isthat coming from a ug initial state the produced top quark will be boosted longitudinally following thedirection of the valence quark. We can follow this behavior by noticing that for the signal the lepton andin particular the bottom quark are moving into the forward direction, peaked around pseudorapidities oftwo. In contrast, the QCD background behaves like Drell-Yan W production with one parton splitting inthe initial state, where the W boson as well as the lepton are central. Interestingly enough, the radiatedmis-tagged jet above our p T threshold is also fairly central. The problem with this general kinematicfeature is that it is not strong enough to allow for an efficient cut in our analysis. This changes once weinclude further QCD jet radiation.To simulate the radiation of QCD jets beyond the leading jet we employ the MLM matching schemeas implemented in MadEvent [18, 19], which allows us to consistently add pp → t + jets samples with σ S σ Wj σ Wb S/B S/ √ B after acceptance cuts 50 fb 12944 fb 105 fb 1/260 3.4after resonance cuts 13 . . . . − of luminosity at 14 TeV. For the merged sample we only consider theleading background. W+JetDirect Top∆ η ( l , j ) / σ d σ / d ∆ η ( l , j ) . . . . . . . . . . W+JetDirect Top∆ η ( b , j ) / σ d σ / d ∆ η ( b , j ) . . . . . . . . . W+JetDirect Top∆ η ( l , b ) / σ d σ / d ∆ η ( l , b ) . . . . . . . W+JetDirect Topcos θ ( l , j ) / σ d σ / d c o s θ ( l , j ) . . . . . . . . W+JetDirect Topcos θ ( b , j ) / σ d σ / d c o s θ ( b , j ) . . . . . . . . . . W+JetDirect Topcos θ ( l , b ) / σ d σ / d c o s θ ( l , b ) . . . . . FIG. 3: Correlations of the first radiated QCD jet with the particles from the hard process for the direct topsignal and the QCD background, after applying all acceptance and the top resonance cuts. We show the (similar)behavior of the pseudorapidity difference and the full opening angle. an arbitrary number of additional jets [20]. For large transverse momenta these jets will be correctlydescribed by the hard matrix element and for small transverse momenta also correctly by the partonshower. While the main motivation for such jet merging simulations are for example W +jets samplesas backgrounds to Higgs and new physics searches, the same method allows us to simulate jet radiationaccompanying heavy states at the LHC and exploit these patterns to improve the signal extraction [5, 21].First, we ask for additional jet from QCD radiation which have to pass the staggered jet acceptancecuts p T j > , ,
20 GeV | η j | < . p T b >
55 GeV as listed in eq.(7). This feature as well as ouraim to be not too dependent on the details of the jet merging simulation motivates us to even for thelight-flavor jets only consider maximum pseudorapidities of 2.5. In this aspect, a more dedicated analysisof the bottom tag could significantly improve the signal efficiency and hence the Gaussian significance.While 20 GeV for the third jet sounds very small, this analysis is also meant to show the impact theanalysis of the QCD jet activity can have on new-physics searches, so we decide to keep it as low aspossible. Depending on the structure of the measured underlying event this threshold might have to beincreased eventually.The improvement of the direct top analysis just through requiring the existence of two jets we show inTable. I. The higher apparent probability to radiate one additional jet from the signal process is relatedto a larger number of soft jets for the continuum background, as we will see in Fig. 4. This is due to thecontinuum structure of the background diagrams without a hardly radiating resonant top quark and thefact that the mis-tagged bottom is actually a massless jet and more likely to split collinearly.Just based on our argument above and on color factors, in the signal case the radiation off the incominggluon will dominate the radiation pattern. This means that the top quark and the leading QCD jet flyinto opposite directions. We can see this behavior in the pseudorapidity distributions as well as in theopening angle distributions in Fig. 3: the first radiated jet for the signal is indeed widely separated fromthe lepton as well as the bottom jet, i.e. from the top quark. In contrast, the continuum QCD background
W+JetDirect TopNumber of Jets / σ d σ / d N J e t s . . . . . . . . W+JetDirect Top∆ η ( l , j ) / σ d σ / d ∆ η ( l , j ) . . . . . . . . . W+JetDirect Top∆ η ( j , j ) / σ d σ / d ∆ η ( j , j ) . . . . . . . . . FIG. 4: Correlations of the second radiated QCD jet, corresponding to Fig. 3. radiates jets over a wide pseudorapidity range, bounded only by the maximum pseudorapidity of 2.5.Because the lepton is central, this means that the pseudorapidity difference between the lepton andthe first jet has to drop off fast once we go to pseudorapidities of order two. The same is true for thepseudorapidity difference of the first two radiated jets, once of which is falsely tagged as a bottom jet:if both of them are reasonably central their pseudorapidity difference is rarely going to exceed values of2.5.These well distinguishable jet distributions we can now cut on, to separate signal and background.Symmetrically, we constrain the two pseudorapidity differences to be∆ η b ,j > η ℓ,j > S/B to a manageable level. Refining these jet cuts we canfurther improve
S/B , but an the expense of the number of signal events left in the analysis.Just out of curiosity we can check what happens once we include a second QCD jet ( i.e. altogetherthree jets) in our analysis. Obviously, this is not suitable for the full analysis, but it could give interestinginformation for those signal nd background events in which we see such an additional jet. The distributionof the number of jets we show in the first panel of Fig. 4. In the jet distributions the general pattern ofthe first QCD jet is still present — largely because it is based on the boosted nature of the top quarkin the hard signal process. In Fig. 4 we see a similar correlation between the second QCD jet and thelepton as we see for the first jet. The pseudorapidity difference between the two QCD jets is also morestrongly peaked in the generally central continuum background. A t [GeV] (cid:0) u L R , I n t e g r a t e d L u m i n o s i t y [ / f b ] FIG. 5: Necessary integrated luminosity for 95% CL signal, assuming gaussian statistics with S/ √ B . The whitearea in the upper right corner is already excluded by experimental squark searches. We adopt a squark massbound of m ˜ q > . Based on Table I we can compute the 95% confidence level coverage of direct top production in the δ − δ plane. In Fig. 5 we see that with a mild dependence on A t ∼ δ q m t,L m t,R / h H u i the LHCwill be able to rule out non-minimal flavor violation through the mass matrix entry above δ & . SINGLE TOPS AND JETS
At the LHC, more signal processes contribute to the one-top-plus-jets final state [23]. The two irre-ducible cousins of direct top production with jet radiation are the single top production channels shownin Fig. 6: one of them proceeds via a time-like t -channel W boson [24, 25] and the other through aspace-like s -channel W boson [26]. The associated tW production [27] we do not consider in this analysisbecause its final state is significantly different and neither related to QCD not irreducible from direct topproduction. Encouraged by the signal vs background direct top analysis in the last section we can ask ifmore generally the structure of QCD jet radiation [22] will allow us to distinguish these three single topand direct top production mechanisms and tell apart the responsible coupling in or beyond the StandardModel [28].Usually, the three direct/single top production channels are distinguished using bottom tags, whereaside from the top decay products the t -channel process involves a forward bottom jet while the s -channelprocess is accompanied by a central bottom jet and direct to production does not involve additionalbottom jets at all [29]. Already for the single top channels alone, identifying the different QCD featuresfirst and cross checking for bottom flavor later might allow us to improve the V tb measurement in andbeyond the Standard Model. Studying the forward b jet in the t -channel process without tagging it fromthe beginning also improves our sensitivity to flavor changing q - t - W couplings enhanced by the valencequark parton densities [28].We simulate direct top production as well as the two single top production processes including twoadditional hard QCD jets. Additional QCD jets can arise from the parton shower and are describedover their entire phase space by MLM jet merging implemented in MadEvent [18, 19] [32]. All t ¯ t eventsappearing as part of the merged sample we subtract. Because at this stage we are not suggesting adedicated analysis we first assume we know which of the jets are bottom jets and which are light-flavorjets. For all of them we require the staggered acceptance cuts p T j > , , , , · · · GeV | η j | < . p T ℓ >
15 GeV | η ℓ | < . R jℓ > . p T spectrum of the accompanyingjets in the three processes: in the t -channel process there will be one hard central jet balancing the top t ¯ q ′ l ¯ ν l bb t bt l ¯ ν l l ¯ q ′ ¯ b ¯ ν l qbq guWWW WW FIG. 6: Sample Feynman diagrams for the three single/direct top production mechanisms at hadron colliders.For direct top production we represent the effective ugt vertex with a solid circle.
Direct TopS channelT channel∆ η ( l, j ) / σ d σ / d ∆ η ( l , j ) . . . . . Direct TopS channelT channelcos θ ∗ ( l, j ) / σ d σ / d c o s θ ∗ ( l , j ) . . . . . Direct TopS channelT channelcos θ ∗ ( l, a ) / σ d σ / d c o s θ ∗ ( l , a ) . . . . . . . . . . Direct TopS channelT channel∆ η ( l, j ) / σ d σ / d ∆ η ( l , j ) . . . . . . . . . Direct TopS channelT channelcos θ ∗ ( l, j ) / σ d σ / d c o s θ ∗ ( l , j ) . . . . . . . Direct TopS channelT channelcos θ ∗ ( l, a ) / σ d σ / d c o s θ ∗ ( l , a ) . . . . . . . Direct TopS channelT channel∆ η ( l, j ) / σ d σ / d ∆ η ( l , j ) . . . . . . . . . . Direct TopS channelT channelcos θ ∗ ( l, j ) / σ d σ / d c o s θ ∗ ( l , j ) . . . . . Direct TopS channelT channelcos θ ∗ ( l, a ) / σ d σ / d c o s θ ∗ ( l , a ) . . . . . . . Direct TopS channelT channelcos θ ∗ ( l, a ) / σ d σ / d c o s θ ∗ ( l , a ) . . . . . . . . FIG. 7: QCD jet–lepton correlations for single and direct top production. We show the pseudorapidity differenceas well as the cos θ ∗ dependence as discussed in the text. The label a represents all-flavor jets which might bebottom jets ( b ) or light-flavor jets ( j ). quark and a second forward b jet from the gluon splitting. Tagging this forward bottom jet might ormight not be useful, dependent for example on the optimization of the signal vs background analysiswith respect to S/B or S/ √ B [30]. This forward bottom jet will be collinearly divergent, regularized bythe bottom mass, i.e. down to transverse momenta of p T <
10 GeV its p T spectrum will diverge. TheQCD jet balancing the top peaks at transverse momenta around 40 −
50 GeV, almost as high as thebottom jet from the top decay (with its Jacobian peak around 65 GeV). This we can understand whenwe consider this process as one-sided weak boson fusion.In the s channel the flavor structure of the Standard Model enforces a second bottom jet from theoff-shell W decay. This jet plays a similar balancing role as the light-flavor jet in the t -channel process.We now we see two competing hard bottom jets of comparable p T , both peaking around 40 −
80 GeV.Direct top production in contrast does not predict any additional hard jets in the detector. Becauseit involves a flavor changing production vertex there should be no additional bottom jets, and the light-
Direct TopS channelT channelNumber of Jets / σ d σ / d N J e t s . . . . . . . . Direct TopS channelT channelcos θ ∗ ( l, b ) / σ d σ / d c o s θ ∗ ( l , b ) . . . . . . . . S channelT channelcos θ ∗ ( l, b ) / σ d σ / d c o s θ ∗ ( l , b ) . . . . . . . . . . . Direct TopS channelT channelcos θ ∗ ( b , j ) / σ d σ / d c o s θ ∗ ( b , j ) . . . . . . . . . Direct TopS channelT channelcos θ ∗ ( b , j ) / σ d σ / d c o s θ ∗ ( b , j ) . . . . . . . . . . FIG. 8: Correlations of the up to two bottom jets with the lepton from the top decay, corresponding to Fig. 7.We also show the correlation of the leading bottom jet with the first two light-flavor jets. flavor jets will follow the typical initial state radiation pattern.To describe the angular correlations of the final state [31] including QCD jets in more detail we considerthe observable cos θ ∗ ( P , P ). It parameterizes the angle between ~p in the rest frame of P + P and( ~p + ~p ) in the lab frame. It is not symmetric in its arguments; if the two particles are back to backand | ~p | > | ~p | it approaches cos θ ∗ = 1, whereas for | ~p | < | ~p | it becomes −
1. In between it vanishes inthe case where ~p in the center of mass frame is orthogonal to the lab frame movement of this center ofmass.This behavior we confirm in the first row of Fig. 7. For t -channel single top production the hardestlight-flavor jet balances the top, so the lepton is most likely back to back with the hardest jet. Becauseit balances the heavy top, the leading jet is harder than the lepton and the cos θ ∗ ℓj distribution peaksat −
1. For the s channel the decay lepton will be central, as will be the first QCD jet. Except for theazimuthal angle we expect no back-to-back configuration, which gives us cos θ ∗ values flat around zero.In direct top production the first jet is radiated at high rapidity. Because of the color factor it mostlikely comes from the gluon, which means it will be collinear as well as soft. The top is boosted againstthe incoming gluon and with it the decay lepton. This means that the lepton and the first QCD jet areback to back, and the hard decay lepton will be more energetic than the soft collinear jet. The cos θ ∗ distribution will then peak around +1.Considering further jets in t -channel single top production the lower energy of subsequent jet radiationwashes out the cos θ ∗ behavior. This is due to the role of the energy hierarchy with respect to the leptonin this observable. Once we arrive at jet number three all we see is a general parton shower jet radiation,slightly forward but uncorrelated with the top decay products. For the direct top channel the patternof the second jet resembles the first, because the radiation off the incoming gluon will still dominate.Similarly, additional jets accompanying s -channel top production will become slightly more forward andhence more likely to move towards larger | cos θ ∗ | values, but without an exploitable structure.Following our original motivation, what is most interesting are angular correlation of light-flavor andbottom jets without assuming a b tag. In the right column of Fig 7 we see that for t -channel single topproduction the hardest all-flavor jet indeed balances the top quark, i.e. it is not bottom flavored. Thesecond hardest jet then comes from the top decay, which we can check by comparing it features with the0 T channelcos θ ∗ ( l, a ) c o s θ ∗ ( l , a ) . . . . − . − . − . − . − S channelcos θ ∗ ( l, a ) c o s θ ∗ ( l , a ) . . . . − . − . − . − . − Direct Topcos θ ∗ ( l, a ) c o s θ ∗ ( l , a ) . . . . − . − . − . − . − T channelcos θ ∗ ( l, a ) c o s θ ∗ ( l , a ) . . . . − . − . − . − . − S channelcos θ ∗ ( l, a ) c o s θ ∗ ( l , a ) . . . . − . − . − . − . − Direct Topcos θ ∗ ( l, a ) c o s θ ∗ ( l , a ) . . . . − . − . − . − . − FIG. 9: Sample angular correlations between the cos θ ∗ ℓa for all-flavor jets. From left to right we show t -channelsingle top production, s -channel single top production, and direct top production. bottom correlations shown in Fig. 8. The third and forth jets both arise from parton splitting and havenot distinct correlations with the top decay products — being bottom flavored or not. Checking their p T distribution we can confirm that they simultaneously drop off fast at values above 40 GeV.For s -channel single top production both leading all-flavor jets have little to do with the cos θ ∗ ℓj distribution, which means they are the two bottom jets from the hard process. Again, we confirm thisbehavior in Fig. 8. In this figure we also see that essentially all bottom jets prefer values cos θ ∗ ℓb → − W decay step which softens the W decay productas compared to the bottom jet.For direct top production the hardest jet is usually the bottom decay jet. In addition we expect nomore bottom jets, so the distributions of j n match those of a n +1 . Because the argument of the colorfactor preferring radiation off the incoming gluon combined with the boosted center of mass frame holdsin general, subsequent jets show a similar preference for cos θ ∗ → t channel process we already know that the two leading jets, one light-flavor and one thebottom decay jet, both reside at small values of cos θ ∗ ℓa . The third and fourth jet, again one bottomand one light-flavor, do not have a strong preference for large values of | cos θ ∗ ℓa | , but in contrast to theleading two jets they show a correlation with each other, based on the general radiation pattern.In the s -channel process the two leading jets are the two bottom jets. They are correlated and prefersmall values of cos θ ∗ ℓa j , dependent mostly on the lepton energy. For the next two jets the correlations isconsiderably weaker, and from Fig. 7 we already know not to expect much in formation in their cos θ ∗ ℓa distributions.Direct top production produces a hard bottom jet with a slight preference towards cos θ ∗ → −
1. Asidefrom that, the universal jet radiation structure shows a diagonal correlation with the slightly favoredregion cos θ ∗ →
1, becoming much more prominent for the two subleading jets.1
OUTLOOK
In this paper we have shown how we can exploit the QCD jet activity to extract direct top produc-tion from the QCD background and to tell apart t -channel single top production, s -channel single topproduction, and direct top production.Direct top production is the only way to observe or constrain the supersymmetric flavor-violatingsquark mass entry δ uLR, in the near future. It is mediated by the flavor changing neutral current u - t - g interaction and has to be extracted from W +jets backgrounds with a light-flavor jet mis-tagged asa bottom. While kinematic cuts based on the top resonance structure of the matrix element are notsufficient to produce a promising signal-to-background ratio S/B , we find that additional cuts on the jetcorrelation from QCD radiation improve this ratio enough to allow for a meaningful LHC analysis.The same kind of QCD jet correlations with the top decay lepton allow us to distinguish (normalized)samples of t -channel single top production, s -channel single top production, and direct top production.All three channels are irreducible if we consider searches for one top quark plus jets. Our distinction ispurely based on angular correlations and serves as an orthogonal test to possible bottom tags. In singletop searches applying explicit bottom tags only later in the analysis allows us to make use of the partondensity enhancement when looking for flavor-changing top couplings. Both methods combined should beable to unambiguously determine the third generation flavor structure of the Standard Model, includingthe CKM mixing element V tb as well as new-physics effects. Acknowledgments
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