arXiv:1001.0022v2  [hep-ph]  17 Mar 2010Preprint typeset in JHEP style - HYPER VERSION MADPH–09-1552
µτProduction at Hadron Colliders
Tao Han∗, Ian Lewis†
Department of Physics, University of Wisconsin, Madison, W I 53706, U.S.A.
Marc Sher‡
Particle Theory Group, College of William and Mary, William sburg, Virginia 23187
Abstract: Motivated by large νµ−ντflavor mixing, we consider µτproduction at hadron
colliders via dimension-6 effective operators, which can be a ttributed to new physics in the
flavor sector at a higher scale Λ. Current bounds on many of the se operators from low energy
experiments are very weak or nonexistent, and they may lead t o cleanµ+τ−andµ−τ+signals
at hadron colliders. At the Tevatron with 8 fb−1, one can exceed current bounds for most
operators, with most 2 σsensitivities being in the 6 −24 TeV range. We find that at the LHC
with 1 fb−1(100 fb−1) integrated luminosity, one can reach a2 σsensitivity for Λ ∼3−10 TeV
(Λ∼6−21 TeV), depending on the Lorentz structure of the operator. For some operators,
an improvement of several orders of magnitude in sensitivit y can be obtained with only a few
tens of pb−1at the LHC.
Keywords: Lepton flavor physics; Hadron collider phenomenology..
∗than@hep.wisc.edu
†ilewis@wisc.edu
‡mtsher@wm.eduContents
1. Introduction 1
2.µτProduction at Hadron Colliders 3
3. Signal Identification and Backgrounds 4
3.1τDecay to Electrons 5
3.1.1 Signal Reconstruction 5
3.1.2 Backgrounds and their Suppression 6
3.2τDecay to Hadrons 9
3.3 Sensitivity Reach at the Tevatron 10
3.4 Sensitivity Reach at the LHC 10
4. Discussions and Conclusions 13
A. New Physics Bounds 14
B. Partial Wave Unitarity Bounds 14
1. Introduction
The most important discovery in particle physics in the past decade has only deepened the
mystery of “flavor” of quarks and leptons. The fact that the mi xing angles in the leptonic
sector are large [1, 2] stands in sharp contrast with the obse rved small mixing angles in the
quarksector. Inparticular, mixingbetweenthesecondandt hirdgeneration neutrinosappears
to be maximal. Of course, this large mixing could occur from d iagonalizing the neutrino mass
matrix, the charged lepton mass matrix, or both. At present, the source of this large mixing
is a mystery.
In view of this, it is tempting to explore other interactions which change lepton flavor
between the second and third generations. Several years ago , two of us (TH, MS), along with
Black and He (BHHS) [3], performed a comprehensive analysis of constraints on these inter-
actions based on low energy meson physics. BHHS chose an effect ive field theory approach,
in which all dimension-6 operators of the form
(¯µΓτ)(¯qαΓqβ), (1.1)
– 1 –were studied, where Γ contains possible Dirac γ-matrices. With six flavors of quarks, there
were 12 possible combinations of qaandqb(assuming Hermiticity), six diagonal and six off-
diagonal, and four choices S,P,V,A of the gamma matrices were considered. All of these
operators were considered, and most were bounded by conside ringτ,K,Bandtdecays.
In particular, BHHS considered operators of the form
∆L= ∆L(6)
τµ=/summationdisplay
j,α,βCj
αβ
Λ2(µΓjτ)/parenleftBig
qαΓjqβ/parenrightBig
+ H.c., (1.2)
where Γ j∈(1, γ5, γσ, γσγ5) denotes relevant Dirac matrices, specifying scalar, pseu doscalar,
vector and axial vector couplings, respectively. They did n ot consider tensor operators since
the hadronic matrix elements were not known and the bounds we re expected to be weak in
any event. They chose a value of
Cj
αβ= 4πO(1) (default) , (1.3)
which corresponds to an underlying theory with a strong gaug e coupling of αS=O(1).
Arguments can be made for multiplying or dividing this by 4 π, for naive dimensional analysis
or for weakly coupled theories, respectively. A discussion is found in BHHS; we simply choose
the above definition of Λ and other choices can be made by simpl e rescaling.
Besides the four fermion operators in Eq. (1.2), there may be other induced operators
involving the SM gauge bosons, such as the electroweak trans ition operator
∆L=κv
Λ2¯µσµντFµν, (1.4)
wherevis the vacuum expectation value of the Standard Model Higgs fi eld andFµνis the
electroweak field tensor. However, when these operators are compared to the underlying
new strong dynamics of the four fermion interaction in Eq. (1 .2), it is found that they are
suppressed by O(MW/Λ), where MWis the mass of the electroweak gauge boson. For new
physics scales of order 1 TeV or greater, this is at least an or der of magnitude suppression.
Thus, we ignore these operators.
BHHS found that operators involving the three lightest quar ks were strongly bounded,
with bounds ranging from 3 to 13 TeV on the related value of Λ. T hese bounds can be found
in Appendix A. Not surprisingly, operators involving the to p quark were either unbounded or
very weakly bounded, with only the tuoperator for vector and axial vector couplings being
bounded by Λ <650 GeV (the bound arises through a loop in B→µτdecay). Operators
involving the b-quark and a light quark also have bounds on Λ which were gener ally in
the several TeV range. However, there were some surprises. T he scalar and pseudoscalar
operators involving cuandccwere completely unbounded, and the bboperator was essentially
unbounded for all S,P,V,A operators. And, as noted above, noneof the tensor operators
were considered at all, for all quark combinations.
In this note, we point out that the operators in Eq. (1.1) (wit hout involving top quarks)
will contribute to µ−τproduction at hadron colliders. Given that many of the possi ble
– 2 –operators, as noted above, are completely unbounded or weak ly bounded from the current
low energy data, study of pp→µτat the LHC or pp→µτat the Tevatron will probe
unexplored territory.
There have been some previous discussions of µ−τproduction at hadron colliders. Han
and Marfatia [4] looked at the lepton-violating decay h→µτat hadron colliders, and a very
detailed analysis of signals and backgrounds was carried ou t by Assamagan et al. [5] after-
wards. Other work looking at Higgs decays focused on mirror f ermions [6], supersymmetric
models [7], seesaw neutrino models [8], and Randall-Sundru m models [9]. In addition to
Higgs decays, others have considered lepton-flavor violati on in the decays of supersymmetric
particles [10] and in horizontal gauge boson models [11]. Th ese analyses, however, were done
in the context of very specific models (often relying on the as sumption that the µandτare
emitted in the decay of a single particle). Here, we will use a much more general effective
field theory approach.
This paper is organized as follows. In the next section, we di scuss the cross sections
forµτproduction via the various operators. A detailed analysis o f the signal identification
and background subtraction is in Section 3, and Section 4 con tains some discussions and our
conclusions. Appendix A reiterates the bounds from BHHS for comparison, and Appendix B
outlines the calculation of partial-wave unitarity bounds .
2.µτProduction at Hadron Colliders
Dueto the absenceof appreciable µτproductionin theSM, their production can beestimated
via the effective operators in Eq. (1.1). On dimensional groun ds, the cross section for ¯ qiqj→
µτgrows with center of mass energy, i.e.,
σ(¯qiqj→µτ)∝s
Λ4, (2.1)
where√sis the center of mass energy for the partonic system. This gro wth of cross section
with energy will eventually violate unitarity bounds. Expa nding the scattering amplitudes in
partial waves, we find the unitarity bounds to be (see Appendi x B)
s≤/braceleftBigg
2Λ2for scalar ,pseudoscalar ,and tensor;
3Λ2vector and axial vector case .(2.2)
The total cross sections for µτproduction at the hadronic level after convoluting with
the parton distribution functions (pdfs) are
σScalar=π
3S
Λ4/integraldisplayτmax
τ0dτ(q⊗q)(τ)/parenleftbigg
1−τ0
τ/parenrightbigg2
τ (2.3)
σVector=4π
9S
Λ4/integraldisplayτmax
τ0dτ(q⊗q)(τ)/parenleftbigg
1−τ0
τ/parenrightbigg2/parenleftbigg
1+τ0
2τ/parenrightbigg
τ (2.4)
σTensor=8π
9S
Λ4/integraldisplayτmax
τ0dτ(q⊗q)(τ)/parenleftbigg
1−τ0
τ/parenrightbigg2/parenleftbigg
1+2τ0
τ/parenrightbigg
τ, (2.5)
– 3 –whereτ=s/S,τ0=m2
τ/S,mτis the tau mass, and√
Sis the center of mass energy in the
lab frame. The pseudoscalar cross section is of the same form as the scalar cross section, and
the axial vector cross section is of the same form as the vecto r cross section. Our perturbative
calculation will become invalid at the unitarity bound, hen ce there is a maximum on the τ
integration. It is given by τmax= 2Λ2/Sfor the scalar, pseudoscalar, and tensor cases, and
τmax= 3Λ2/Sfor the vector and axial-vector cases. Also, q(x) is the quark distribution
function with flavor sum suppressed, and ⊗denotes the convolution defined as
(g1⊗g2)(y) =/integraldisplay1
0dx1/integraldisplay1
0dx2g1(x1)g2(x2)δ(x1x2−y). (2.6)
The CTEQ6L parton distribution function set is used for all o f the results [12].
Results for the cross sections for the scalar, pseudoscalar , vector, axial vector, and tensor
structures at the Tevatron, LHC at 10 TeV and 14 TeV are given i n Table 1. Thecross section
for the pseudoscalar (axial vector) current is the same as fo r the scalar (vector) current. For
all cases, Λ is set equal to 2 TeV and the unitarity bounds are t aken into consideration. At
this rather high scale, the production rates are dominated b y the valence quark contributions.
The cross sections at the LHC are larger than those at the Teva tron by roughly an order of
magnitude, reaching about 100 pb.
For some cases the bounds from BHHS are greater than 2 TeV, hen ce the cross section
needs to be scaled to determine a realistic cross section at h adron colliders. The partonic
cross sections scale at Λ−4, but at the hadronic level a complication arises since the un itarity
bounds introduce a dependence on the new physics scale in the integration over pdfs. If
the unitarity bounds are ignored ( τmax= 1), one finds that with Λ = 2 TeV neglecting the
unitarity bounds has at most a 10% effect on the cross sections a t the LHC for both 10 TeV
and 14 TeV and no effect at the Tevatron since the unitarity boun ds are greater than the lab
frame energy. Hence, if Λ is increased from 2 TeV, at the LHC it is a good approximation to
assume the cross section scales as Λ−4and at the Tevatron the cross section scales exactly as
Λ−4. For example, the lower bound on Λ for the vector u¯ucoupling from BHHS is 12 TeV, so
the maximum cross section at the 14 TeV LHC from this operator would be approximately
160×(2/12)4pb = 120 fb. On the other hand, there is no bound whatsoever for the vector
u¯ccoupling, and thus a cross section limit of 110 pb would yield a new limit of 2 TeV on the
scale of this operator. This would constitute an improvemen t of many orders of magnitude.
3. Signal Identification and Backgrounds
Upon production at hadron colliders, τ’s will promptly decay and are detected via their decay
products. About 35% of the time the τdecays to two neutrinos and an electron or muon, the
other 65% of the time the τdecays to a few hadrons plus a neutrino. We will consider the τ
decay to an electron as well as hadronic decays in this work. T he decay to a muon will result
in aµ+µ−final state that has a large Drell-Yan background. We will stu dy the signal reach
at the Tevatron and at the 14 TeV LHC.
– 4 –Table 1: Cross sections for all the scalar, pseudoscalar, vector, axial ve ctor, and tensor structures at
the Tevatron at 2 TeV, the LHC at 10 TeV, and the LHC at 14 TeV. Th e pseudoscalar (axial vector)
cross section is the same as the scalar (vector) cross section. All cross sections were evaluated with
the new physics scale Λ = 2 TeV and the unitarity bounds are taken int o consideration.
Tevatron 2 TeV ( p¯p)LHC 10 TeV ( pp) LHC 14 TeV ( pp)
σ(pb)1,γ5γµ,γµγ5σµν1,γ5γµ,γµγ5σµν1,γ5γµ,γµγ5σµν
u¯u8.4 11 22 63 85 170 120 160 310
d¯d2.5 3.3 6.7 38 51 100 72 98 190
s¯s0.18 0.24 0.49 5.5 7.4 15 11 15 30
d¯s1.3 1.7 3.4 34 45 91 66 89 180
d¯b0.50 0.67 1.3 17 22 45 34 46 90
s¯b0.13 0.17 0.34 5.0 6.7 13 11 14 28
u¯c1.5 2.0 3.9 41 55 110 80 110 210
c¯c0.070 0.094 0.19 2.6 3.5 7.0 5.5 7.3 15
b¯b0.021 0.028 0.056 1.1 1.5 2.9 2.4 3.2 6.4
3.1τDecay to Electrons
3.1.1 Signal Reconstruction
Theτdecays to an electron plus two neutrinos about 18% of the time . We thus search for a
final state of an electron and muon
e+µ. (3.1)
The electromagnetic calorimeter resolution is simulated b y smearing the electron energies
according to a Gaussian distribution with a resolution para meterized by
σ(E)
E=a/radicalbig
E/GeV⊕b, (3.2)
where the constants are a= 10% and b= 0% at the Tevatron [13], a= 5% and b= 0.55% at
the LHC [14], and ⊕indicates addition in quadrature. For simplicity, we have u sed the same
form of smearing for the muons.
The decay of the τleaves us with some missing energy and we need to consider how to
effectively reconstructthe τmomentum. Forourprocessallthemissingtransversemoment um
is coming from the τ, hence
pτ
T=pe
T+pmiss
T. (3.3)
At hadron colliders, we have no information on the longitudi nal component of the missing
momentum on an event-by-event basis. However, the τwill be highly boosted and its decay
– 5 –products will be collimated. Hence, the missing momentum sh ould be aligned with the
electron momentum and the ratio pe
z/pmiss
zshould be the same as the ratio of the magnitudes
of the transverse momenta, pe
T/pmiss
T. Therefore, the longitudinal component of the τcan be
reconstructed as [4]
pτ
z=pe
z/parenleftbigg
1+pmiss
T
pe
T/parenrightbigg
. (3.4)
Once the three-momentum is reconstructed, we can solve for t heτenergy,E2
τ=p2
τ+m2
τ.
Figure 1 illustrates the effectiveness of this method at the Te vatron. Figure 1(a) (Figure 1(b))
shows the transverse momentum (longitudinal momentum) dis tribution for the theoretically
generated (solid) and kinematically reconstructed (dashe d)τmomenta. As can be seen, the
τmomentum is reconstructed effectively.
We first apply some basic cuts on the transverse momentum and t he pseudo rapidity
to simulate the detector acceptance and triggering, as well as to isolate the signal from the
background,
pµ
T>20 GeV,|ηµ|<2.5,
pe
T>20 GeV,|ηe|<2.5. (3.5)
Since the signal does not contain any jets, we also require a j et veto such that there are no
jets with pT>50 GeV and |η|<2.5.
There are several distinctive kinematic features of our sig nal. The decay products of the
τwill be highly collimated, and the electron transverse mome ntum will be traveling in the
same direction as the missing transverse momentum. Also, in the transverse plane the muon
and tau should be back to back. Since the electron will mostly be in the direction of the τ,
it will also be nearly back to back with the muon. Finally, the τandµhave equal transverse
momenta; hence, the decay products of the τhave less transverse momentum than the µ. We
can measure this discrepancy using the momentum imbalance
∆pT=pµ
T−pe
T. (3.6)
For the signal, this observable should be positive. Based on the kinematics of our signal, we
apply the further cuts [5]
δφ(pµ
T,pe
T)>2.75 rad, δφ(pmiss
T,pe
T)<0.6 rad, (3.7)
∆pT>0.
3.1.2 Backgrounds and their Suppression
Theleadingbackgrounds are W+W−pair production, Z0/γ⋆→τ+τ−, andt¯tpair production
[5]. The total rates for these backgrounds at the Tevatron an d the LHC are given in Table 2
with consecutive cuts. We consider both of the final states wi thµ+andµ−.
– 6 –0 100 200 300
pτ
T (GeV)10-410-310-210-1dσ/dpT (pb/GeV)Generated
Reconstructed
(a)-300 -200 -100 0 100 200 300
pτ
z (GeV)10-310-210-1dσ/dpz (pb/GeV)Generated
Reconstructed
(b)
Figure 1: Distributions of the theoretically generated (solid line) and kinematic ally reconstructed
(dashed line) τmomentum at the Tevatron at 2 TeV with a u¯cinitial state, scalar coupling, and new
physics scale of 1 TeV. Fig. (a) is the τtransverse momentum distribution, and Fig. (b) is the τ
longitidunal momentum distribution.
Table 2: Leading backgrounds to the τ’s electronic decay before and after consecutive kinematic and
invariant mass cuts for (a) the Tevatron at 2 TeV and (b) the LHC a t 14 TeV.
Backgrounds (pb) No Cuts Cuts Eq. (3.5) + Eq. (3.7) + Eq. (3.8)
(a) Tevatron 2 TeV
W+W−→µ±νµτ∓ντ0.032 0.0046 0.0012 2.6×10−4
W+W−→µ±νµe∓νe0.18 0.13 0.0060 9.8×10−4
Z0/γ⋆→τ+τ−→µ±νµτ∓610 0.21 0.091 1.4×10−4
t¯t→µ±νµbτ∓ντ¯b 0.020 6.5×10−47.4×10−54.4×10−5
t¯t→µ±νµbe∓νe¯b 0.11 0.0099 7.3×10−42.7×10−4
(b) LHC 14 TeV
W+W−→µ±νµτ∓ντ0.34 0.030 0.0088 0.0031
W+W−→µ±νµe∓νe 1.9 0.99 0.051 0.014
Z0/γ⋆→τ+τ−→µ±νµτ∓2300 1.1 0.49 0.0014
t¯t→µ±νµbτ∓ντ¯b 1.9 0.070 0.010 0.0077
t¯t→µ±νµbe∓νe¯b 11 1.5 0.10 0.050
The partonic cross section of our signal increases with ener gy while the cross sections
of the backgrounds will decrease with energy. Hence, the inv ariant mass distribution of our
signal does not fall off as quickly as the backgrounds.
Figure 2(a) shows the invariant mass distributions of backg rounds and our signal at the
Tevatron with initial states c¯candu¯cwith various couplings and a new physics scale of
1 TeV after applying the cuts in Eqs. (3.5) and (3.7). The cros s section for the pseudoscalar
– 7 –0 200 400 600800 1000
Mµτ (GeV)10-510-410-310-2dσ/dMµτ (pb/GeV)eµνν
τ+τ−
Tensor
Vector
Scalaru c-bar
c c-barTevatron
(a)0 200 400 600800 1000
Mµτ (GeV)10-510-410-310-2dσ/dMµτ (pb/GeV)eµνν
τ+τ−1 TeV
2 TeV
3 TeVTevatron
(b)
Figure 2: The invariant mass distributions of the reconstructed τ−µsystem at the Tevatron at 2
TeV. Fig. (a) shows the distributions of the leading backgrounds (d otted and dot-dot-dash) and of
our signal for the u¯candc¯cinitial states with coupling of various Lorentz structures and a new physics
scale of 1 TeV. Fig. (b) shows the distributions of the leading backgr ounds (dotted and dashed) and
of our signal (solid) for the u¯cinitial state with scalar coupling and various new physics scales. The
cuts in Eqs. (3.5) and (3.7) have been applied.
(axial-vector) couplings are the same as those for the scala r (vector) couplings. The decline
in the signal rates is due to a suppression of the pdfs at large x. Although the signal rates
steeply decline with invariant mass the background falls off faster. The u¯csignal is still clearly
above background due to a valence quark in the initial state, but thec¯csignal distribution is
much closer to the background distribution due to the steep f all with invariant mass and a
lack of an initial state valence quark. Figure 2(b) shows the invariant mass distributions of
backgroundsandoursignalattheTevatronwithinitial stat eu¯candscalarcouplingforvarious
new physics scales. The 3 TeV new physics scale invariant mas s distribution is approaching
the background distribution. A higher cutoff on the invarian t mass will be needed to separate
the weak signal from the backgrounds. Based on Fig. 2, we prop ose a selection cut on
Mµτ>250 GeV . (3.8)
Table 2 shows the effects of the invariant mass cut on the backgr ounds in the last column.
Similar analyses can be carried out for the LHC. Figure 3(a) s hows the invariant mass
distribution for our signal with the u¯candc¯cinitial states and various Lorentz structures, as
well as the backgroundsafter thecuts in Eqs. (3.5) and(3.7) . Thenewphysics scale was set to
1 TeV and the unitarity bound is imposed. Figure 3(b) shows th e invariant mass distribution
of theu¯cinitial state with various new physics scales. The cutoff on t he invariant mass
corresponds to the unitarity bound, the scale at which the pe rturbative calculation becomes
untrustworthy. In the lack of the knowledge for the new physi cs to show up at the scale Λ,
we simply impose a sharp cutoff at the unitarity bound. As comp ared with the Tevatron,
the LHC signal rates fall off much less quickly with invariant mass since the Tevatron’s lower
– 8 –0 500 1000 1500
Mµτ (GeV)10-410-310-210-1dσ/dMµτ (pb/GeV)Tensor
Vector
Scalar
bbeµνντ+τ−u c-bar
c c-barLHC
(a)0 1 2 3 4
Mµτ (TeV)10-510-410-310-210-1dσ/dMµτ (pb/GeV)bbeµνν
τ+τ−1 TeV
2 TeV
3 TeV
4 TeV
5 TeVLHC
(b)
Figure 3: The invariant mass distributions of the reconstructed τ−µsystem at the LHC at 14 TeV.
Fig. (a) shows the distributions of the leading backgrounds (dotte d and dot-dot-dash) and of our
signal for the u¯candc¯cinitial states with coupling of various Lorentz structures and a new physics
scale of 1 TeV. Fig. (b) shows the distributions of the leading backgr ounds (dotted and dashed) and
of our signal (solid) for the u¯cinitial state with scalar coupling and various new physics scales. The
cut offs in the distributions at high invariant mass are due to the unita rity bounds. The cuts in Eqs.
(3.5) and (3.7) have been applied.
energy leads to a suppression from the pdfs at large x. As can be seen, as the new physics
scale increases the cross section decreases and the backgro und becomes more problematic at
lower invariant mass. Also, as the new physics scale increas es the unitarity bound becomes
less strict. Hence, although the backgrounds at the LHC are c onsiderably larger than at the
Tevatron, for large new physics scales the LHC has an enhance ment in the signal cross section
from the large invariant mass region.
3.2τDecay to Hadrons
Although with significantly larger backgrounds, the signal fromτhadronic decays can be
very distinctive as well. We limit the hadronic τdecays to 1-prong decays to pions, i.e.,
τ±→π±ντ,τ±→π±π0ντ, andτ±→π±2π0ντ. Theτ’s have 1-prong decays to these final
states about 50% of the time. We thus search for a final state of aτjet and a muon
jτ+µ. (3.9)
To simulate detector resolution effects, the energy is smeare d according to Eq. (3.2) with
a= 80% and b= 0% for the jet at the Tevatron [13] and a= 100% and b= 5% at the LHC
[14]. As in the electronic decay, the τis highly boosted and its decay products are collimated.
Hence, all the missing energy in the event should be aligned w ith theτ. The signal is then
reconstructed as described in Eqs. (3.3) and (3.4) with the e lectron momentum replaced by
the momentum of the τ-jet.
– 9 –The hadronic decay of the τalso has the backgrounds W+W−pair production, Z0/γ⋆→
τ+τ−, andt¯tpair production plus an additional background of W+jet, where the jet is
misidentified as a τ-jet. At the Tevatron, we assume a τ-jet tagging efficiency of 67% and
that a light jet is mistagged as a τ-jet 1.1% of the time [15] and at the LHC we assume a τ-jet
tagging efficiency of 40% and a light jet misidentification rat e of 1% [14]. Even with a low
rate of misidentification, the W+jet background is large. To suppress this background, we
note that for hadronic decays most of the τtransverse momentum will be carried by the jet.
Hence the τ-jet should be traveling in the same direction as the reconst ructedτmomentum.
Motivated by this observation, we apply the same cuts as Eqs. (3.5), (3.7), and (3.8) with the
electron momentum replaced by the τ-jet momentum and the additional cuts
pτ−jet
T
pτ
T>0.6 ∆ R(pτ−jet
T,pτ
T)<0.2 rad. (3.10)
3.3 Sensitivity Reach at the Tevatron
One can determine the sensitivity of the Tevatron to the new p hysics scale with 8 fb−1of
data. Table 3 shows the sensitivity of the Tevatron for (a) el ectronic and (b) hadronic τ
decays. The tables list the maximum new physics scale sensit ivity at 2 σand 5σlevel at the
Tevatron. The reaches for scalar (vector) and pseudoscalar (axial-vector) are the same at the
Tevatron, although the previous bounds from BHHS for the sca lar (vector) and pseudoscalar
(axial-vector) couplings may not be the same. The bounds fro m BHHS can be found in
Appendix A. If only one of the bounds for scalar (vector) or ps eudoscalar (axial-vector)
coupling from BHHS is greater than the Tevatron reach one sta r is placed next to the new
physics scale, if both bounds are greater than the Tevatron r each two stars are placed next
to the new physics scale. Due to the larger backgrounds from W+jet, the Tevatron is much
less sensitive to the τhadronic decays than the τelectronic decays.
There were no bounds from BHHS for the tensor couplings, so th e Tevatron will be
able to exlude some of the parameter space. Since the tensor c ross sections are generally at
least twice as large as the scalar cross sections, the Tevatr on is more sensitive to the tensor
couplings than it is to scalar couplings. Also, in general, t he Tevatron is more sensitive to
processes with initial state valence quarks than those with out initial state quarks. With 8
fb−1of data most of the bounds can be increased, some quite string ently.
Somewhat similar leptonic final states have been searched fo r in a model-independent
way at the Tevatron [16], although these included substanti al missing energy and possible
jets. We encourage the Tevatron experimenters to carry out t he analyses as suggested in this
article.
3.4 Sensitivity Reach at the LHC
The LHC is also sensitive to flavor changing operators. For th e signal and background anal-
ysis, we used the same kinematical cuts as we used at the Tevat ron, see Eqs. (3.5), (3.7),
and (3.8). Table 4 shows the sensitivity of the LHC to all poss ible initial states and the
– 10 –Table 3: Maximum new physics scales the Tevatron is sensitive to with 8 fb−1of data at the 2 σ
and 5σlevels. The sensitivities are presented for both (a) electronic and ( b) hadronic τdecays with
various initial states. One star indicates that the Tevatron reach is less than only one of the scalar
(vector) or pseudoscalar (axial-vector) bounds from BHHS, and two stars indicates that the Tevatron
reach is less than both bounds from BHHS. BHHS does not contain bo unds on the tensor coupling.
(a)τ→e
ΛNP(TeV) 2σsensitivity 5σdiscovery
Coupling 1,γ5γµ,γµγ5σµν1,γ5γµ,γµγ5σµν
u¯u20 21 24 14 15 17
d¯d17 18 21 12 13 15
s¯s9.9 10 12 7.2* 7.7** 8.7
d¯s15 16 18 10 11* 13
d¯b13 14 16 9.8 10* 11
s¯b9.5 10 11 6.9 7.3 8.3
u¯c17 18 20 12 13 14
c¯c7.9 8.3 9.5 5.7 6.0 6.9
b¯b6.4 6.8 7.7 4.6 4.9 5.6
(b)τ→h±
ΛNP(TeV) 2σsensitivity 5σdiscovery
Coupling 1,γ5γµ,γµγ5σµν1,γ5γµ,γµγ5σµν
u¯u8.6** 9.2** 10 6.5** 6.9** 8.1
d¯d5.7** 6.1** 7.1 4.3** 4.6** 5.4
s¯s1.8* 1.9** 2.3 1.4** 1.4** 1.7
d¯s3.7 4.0* 4.6 2.8* 3.0** 3.5
d¯b2.7* 2.9* 3.4 2.0** 2.2 2.5
s¯b1.5** 1.6** 1.9 1.1** 1.2** 1.4
u¯c3.9 4.1 4.8 2.9 3.1 3.6
c¯c1.1 1.2 1.4 0.89 0.95** 1.1
b¯b0.91 0.97 1.1 0.68 0.73 0.86
couplings under consideration with 100 fb−1of data. The table contains the maximum new
physics scales the LHC is sensitive to at the 2 σand 5σlevels. As with the Tevatron, the
LHC reach for scalar (vector) couplings is the same as that fo r pseudoscalar (axial-vector)
couplings, although the bounds from BHHS may be different. If o nly one of the bounds for
scalar (vector) or pseudoscalar (axial-vector) coupling f rom BHHS is greater than the LHC
reach one star is placed next to the new physics scale, if both bounds are greater than the
LHC reach two stars are placed next to the new physics scale. D espite the larger backrounds
for the hadronic τdecays, at the LHC the reaches for the hadronic and electroni cτdecays are
– 11 –Table 4: Maximum new physics scales the LHC is sensitive to at 14 TeV with 100 fb−1of data at the
2σand 5σlevels. The sensitivities are presented for both (a) electronic and ( b) hadronic τdecays with
various initial states. One star indicates that the LHC reach is less t han only one of the scalar (vector)
or pseudoscalar (axial-vector) bounds from BHHS, and two stars indicates that the LHC reach is less
than both bounds from BHHS. BHHS does not contain bounds on the tensor coupling.
(a)τ→e
ΛNP(TeV) 2σsensitivity 5σdiscovery
Coupling 1,γ5γµ,γµγ5σµν1,γ5γµ,γµγ5σµν
u¯u18 19 21 14 15 17
d¯d16 17 19 12 13 15
s¯s9.0* 9.6* 11 7.1* 7.6** 8.6
d¯s13 14 16 10 11* 13
d¯b12 13 14 9.7 10 11
s¯b8.7 9.2 10 6.8 7.3 8.2
u¯c15 16 18 12 13 14
c¯c7.2 7.6 8.6 5.7 6.0 6.8
b¯b5.8 6.2 7.0 4.6 4.9 5.5
(b)τ→h±
ΛNP(TeV) 2σsensitivity 5σdiscovery
u¯u15 16 18 12 13 14
d¯d13 14 16 10* 11* 13
s¯s7.9* 8.4** 9.7 6.2* 6.7** 7.7
d¯s11 12* 14 9.3 9.9* 11
d¯b10 11 13 8.4* 8.9 10
s¯b7.6 8.1 9.3 6.0 6.4 7.4
u¯c13 14 16 10 11 12
c¯c6.3 6.7 7.8 5.0 5.3 6.2
b¯b5.1 5.5 6.3 4.1 4.3 5.0
much more similar than at the Tevatron since the LHC cross sec tion receives an enhancement
from the large invariant mass region. For electronic (hadro nic)τdecays the LHC with 100
fb−1of data is less (more) sensitive than the Tevatron with 8 fb−1of data.
Figure 4 shows the integrated luminosities needed for 2 σand 5σobservation at the LHC
with various initial states and τdecay to electrons as a function of the new physics scale.
For some initial states and Lorentz structures BHHS had a bou nd on the new physics scale
larger than 1 TeV. In those cases the distribution does not be gin until the BHHS bound on
the new physics scale. The sensitivity for the pseudoscalar (axial-vector) is the same as the
scalar (vector) state, although the bounds from BHHS are diffe rent. Note that extraordinary
– 12 –1 2 3 4 5 6 78 9 10
ΛNP (TeV)10-310-210-1100101102103L (fb-1)Scalar
Vector
Tensor
2σu c-bar Initial State
5σLHC 14 TeV
(a)1 2 3 4 5 6 78 9 10
ΛNP (TeV)10-310-210-1100101102103L (fb-1)
Scalar
Vector
Tensor
2σc c-bar Initial State
5σLHC 14 TeV
(b)
1 2 3 4 5 6 78 9 10
ΛNP (TeV)10-310-210-1100101102103L (fb-1)Scalar
Vector
Tensor
2σd b-bar Initial State
5σLHC 14 TeV
(c)1 2 3 4 5 6 78 9 10
ΛNP (TeV)10-310-210-1100101102103L (fb-1)
Scalar
Vector
Tensor
2σs b-bar Initial State
5σLHC 14 TeV
(d)
Figure 4: The luminosity at the 14 TeV LHC needed for 2 σand 5σobservation as a function of the
new physics scales with couplings of various Lorentz structures an d electronic τdecay. The sensitivity
for theu¯cinitial state is shown in (a), for the c¯cinitial state in (b), for the d¯binitial state in (c), and
for thes¯binitial state in (d). The lower bounds on the new physics scale were ta ken from BHHS.
improvementintheboundscouldbefound(oradiscoverymade )withrelatively lowintegrated
luminosity. Consider, for example, the u¯cinitial state. There is currently no bound at all;
in principle, Λ could be tens of GeV. The figure shows that a tot al integrated luminosity of
an inverse picobarn would give a 5 σsensitivity for a Λ of 1 TeV. An integrated luminosity of
an inverse femtobarn would give substantial improvements f or all of the operators shown in
Fig. 4.
4. Discussions and Conclusions
In a previous article, motivated by discovery of large νµ−ντmixing in charged current
interactions, bounds on the analogous mixing in neutral cur rent interactions were explored.
A general formalism for dimension-6 fermionic effective oper ators involving τ−µmixing with
– 13 –typical Lorentz structure ( µΓτ)(qαΓqβ) was presented, and the low-energy constraints on
the new physics scale associated with each operator were der ived, mostly from experimental
bounds on rare decays of τ, hadrons or heavy quarks. Tensor operators were not conside red,
and some of the operators, such as cuµτ, were completely unbounded.
Inthis article, weconsider µτproductionat hadroncolliders viatheseoperators. Tables 3
and4 list thenewphysics scales that are accessible at the Te vatron and theLHC, respectively.
Duetomuchsmallerbackgrounds, boththeLHCandTevatronar emoresensitivetoelectronic
τdecays than hadronic τdecays. For hadronic τdecays, the LHC receives an enhancement
from the large invariant mass region and is more sensitive th an the Tevatron. Since the
backgrounds to electronic τdecays at the Tevatron are much smaller than those at the LHC,
the Tevatron is more sensitive than the LHC to electronic τdecays. We found that at the
Tevatron with 8 fb−1, one can exceed current bounds for most operators, with most 2σ
sensitivities being in the 6 −24 TeV range. We find that at the LHC with 1 fb−1(100 fb−1)
integrated luminosity, one can reach a 2 σsensitivity for Λ ∼3−10 TeV (Λ ∼6−21 TeV),
depending on the Lorentz structure of the operator.
Acknowledgments
We would like to thank Vernon Barger and Xerxes Tata for discu ssions. MS would like to
thank the Wisconsin Phenomenology Institute, in particula r Linda Dolan, for hospitality
during his visit. The work of TH and IL was supported by the US D OE under contract
No. DE-FG02-95ER40896, and that of MS was supported in part b y the National Science
Foundation PHY-0755262.
A. New Physics Bounds
The bounds from BHHS in units of TeV are presented in Table 5. T he *s indicate there are
no bounds on the new physics scale. Also, there are no bounds f rom BHHS for the tensor
coupling.
B. Partial Wave Unitarity Bounds
Since the cross section from our higher-dimensional operat ors increases as s, it is necessary
to determine the unitarity bound for q¯q→µτ. The partial wave expansion for a+b→1+2
can be written as
M(s,t) = 16π∞/summationdisplay
J=M(2J+1)aJ(s)dJ
µµ′(cosθ)
where
aJ(s) =1
32π/integraldisplay1
−1M(s,t)dJ
µµ′(cosθ)dcosθ,
µ=sa−sb,µ′=s1−s2andJ≤max(|µ|,|µ′|). The condition for unitarity is |ℜ(aJ)| ≤1/2.
– 14 –Coupling type 1 γ5 γµ γµγ5
u¯u 2.6 12 12 11
d¯d 2.6 12 12 11
s¯s 1.5 9.9 14 9.5
d¯s 2.3 3.7 13 3.6
d¯b 2.2 9.3 2.2 8.2
s¯b 2.6 2.8 2.6 2.5
u¯c * * 0.55 0.55
c¯c * * 1.1 1.1
b¯b * * 0.18 *
Table 5: Bounds on the new physics scales from BHHS in units of TeV for variou s operators and the
scalar, pseudoscalar, vector, and axial-vector couplings. The *s indicate there were no bounds.
It is straightforward to calculate the coefficients for the S, V,T operators. For example,
for the scalar operator
M=4π
Λ2¯vλ1(p1)uλ2(p2)¯uλ3(p3)vλ4(p4)
one can just plug in the explicit expressions:
uλ(p)≡/parenleftBigg/radicalbig
E−λ|p|χλ(ˆp)/radicalbig
E+λ|p|χλ(ˆp)/parenrightBigg
vλ(p)≡/parenleftBigg
−/radicalbig
E+λ|p|χ−λ(ˆp)/radicalbig
E−λ|p|χ−λ(ˆp)/parenrightBigg
whereχ+(ˆz) =/parenleftbig1
0/parenrightbig
,χ−(ˆz) =/parenleftbig0
1/parenrightbig
. In the massless limit, this simply gives a0=s/(4Λ2) and
so the unitarity bound gives s≤2Λ2. For the vector case, a0= 0 and a1=s/(6Λ2) giving
the unitarity bound s≤3Λ2. The tensor case gets contributions from both a0anda1, and
the stronger bound then applies.
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