Prospect for measuring the CP phase in the $h\tau\tau$ coupling at the LHC

0.54 MB·English

by  Andrew Askew

Prospect for measuring the CP phase in the hττ coupling at the LHC
Andrew Askew,1 Prerit Jaiswal,2,1 Takemichi Okui,1 Harrison B. Prosper,1 and Nobuo Sato3,1
1Department of Physics, Florida State University, Tallahassee, FL 32306, USA
2Department of Physics, Syracuse University, Syracuse, NY 13244, USA
3Jefferson Lab, Newport News, Virginia 23606, USA
The search for a new source of CP violation is one of the most important endeavors in particle
physics. A particularly interesting way to perform this search is to probe the CP phase in the hττ
coupling, as the phase is currently completely unconstrained by all existing data. Recently, a novel
variableΘwasproposedformeasuringtheCPphaseinthehττ couplingthroughtheτ± →π±π0ν
decaymode. WeexaminetwocrucialquestionsthattherealLHCdetectorsmustface,namely,the
issueofneutrinoreconstructionandtheeffectsoffinitedetectorresolution. Fortheformer,wefind
strong evidence that the collinear approximation is the best for the Θ variable. For the latter, we
findthattheangularresolutionisactuallynotanissueeventhoughthereconstructionofΘrequires
5
resolving the highly collimated π±’s and π0’s from the τ decays. Instead, we find that it is the
1
missing transverse energy resolution that significantly limits the LHC reach for measuring the CP
0
phase via Θ. With the current missing energy resolution, we find that with ∼ 1000fb−1 the CP
2
phase hypotheses ∆ = 0◦ (the standard model value) and ∆ = 90◦ can be distinguished, at most,
y at the 95% confidence level.
a
M
I. INTRODUCTION phase,∆,maybemeasuredfromtheΘdistributiontoan

4 accuracy of 11◦ at the 14-TeV LHC with 3000fb−1
TheStandardModel(SM)ofparticlephysicshasbeen of data, or t∼he ∆ = 0◦ and ∆ = 90◦ cases m∼ay be dis-
h] extremely successful in explaining all microscopic phe- tinguished at 5σ level with 1000fb−1. However, these
∼
p nomena observed down to distances of order 1TeV−1. conclusions are for an ideal detector. In this paper, we
- ∼ examine the impact of realistic detector effects on the
p However, the model has two notable under-explored cor-
measurement of ∆ via Θ.
e ners: the neutrino and Higgs sectors. Having discovered
h theHiggsbosonthenextmajorgoaloftheLargeHadron There are various ways that detector effects can affect
[ Collider(LHC)istoscrutinizethepropertiesoftheHiggs those estimates. Most importantly, the reconstruction of

3 bosonandsearchfordeviationsfromtheSMpredictions. the Θ variable requires resolving the charged and neu-
v A particularly interesting question is whether CP is a tral pions in the τ± ρ±ν π±π0ν decay mode, but
6 goodsymmetryoftheHiggssector. SinceallHiggsboson these τ± are highly b→oosted a→s they come from higgs de-
5 couplings are predicted to be CP even in the SM, any cays. One therefore expects the two photons from each
1 observation of a CP-odd or CP-violating component will π0 decay to hit the same tower of the electromagnetic
3
constitute unambiguous evidence of physics beyond the calorimeter (ECAL), thereby making the standard iden-
0
. SM. CP-violating Higgs interactions may be motivated tification of a π0 using photons useless. Moreover, one
1 by the fact that baryogenesis requires the existence of a expectsthesameECALtowertobehitbytheπ±,raising
0
new source of CP violation and the possibility that such the question of how much of the ECAL tower’s activity
5
1 aprimordialsourceofnewCPviolationmayleavetraces should be attributed to the π0.
: in the couplings of the Higgs boson. Anotherobviousissueisthereconstructionoftheneu-
v
Recently, a novel variable Θ for measuring the CP trinos. In Ref. [1], the so-called collinear approxima-
i
X phase in the h-τ-τ coupling was proposed in Ref. [1]. tion[8]isadopted,wheretheneutrinofromeachτ decay
r ThedistributionofΘwasshowntohavethesimpleform is taken to be exactly collinear with its parent τ. As
a c acos(Θ 2∆), where ∆ is the phase of the h-τ-τ shown in Ref. [1], the collinear approximation results in
Y−ukawa cou−pling, with ∆ = 0◦ and 90◦ corresponding a 60–70% reduction of the amplitude of the cos(Θ 2∆)
−
to the CP-even and -odd limits, respectively, while a curve. So, one might expect that here lies a significant
and c are independent of ∆ and Θ. What distinguishes opportunity for improvement. In this paper, however,
the h-τ-τ Yukawa coupling from other couplings is that we present a theoretical calculation that strongly sug-
its phase (i.e. the CP angle ∆) is currently completely gests that it is extremely difficult, if not impossible, to
unconstrained by data [2], even though its magnitude outperform the collinear approximation for the purpose
(i.e. the rate of τ+-τ− production) is roughly consistent of Θ reconstruction.
with the SM prediction [3, 4]. Field theoretically, as dis- Adopting the collinear approximation, we then focus
cussed in Ref. [1], an (1) ∆ in the h-τ-τ coupling can on the aforementioned issues of pion identifications in
O
easily coexist with other Higgs boson couplings whose the presence of realistic detector effects, and propose a
CPphasesareknowntobesmall,suchash-t-t¯andh-b-¯b realistic algorithm to identify “τ candidates” specifically
(∆ (cid:46) 0.01 and ∆ (cid:46) 0.1, respectively [2]), and h-Z-Z suited for constructing Θ. Surprisingly, we find that the
t b
(forwhich∆ =90◦isdisfavored[5–7]). InRef.[1]using amplitude of the cos(Θ 2∆) curve of the signal is vir-
Z
−
parton-level analyses it is estimated that the h-τ-τ CP tually unchanged by the finite angular resolution of the
2
LHC detectors. Instead, we find that the measurement v 174GeV, but keep the CP phase ∆ as a free param-
of ∆ through the Θ distribution is significantly ham- et(cid:39)er to be measured. The SM prediction is ∆=0.1
pered by the contamination by the Z ττ background. We are interested in the decay chain
→
Thisdegradationarisesduetoresolutioneffectsinrecon-
h τ+τ−
structingtheττ¯invariantmassasaconsequenceoflarge
→
uncertainties in the measurement of the missing trans- ρ+ν¯ρ−ν (2)
→
verse energy. Fortunately, this is an area where future
π+π0ν¯π−π0ν.
improvement can be hoped for, unlike the angular reso- →
lution. We leave the important question of pileup effects As calculated in Ref. [1], the squared matrix element for
for future work. this decay has the form
While we focus on the measurement of ∆ through the
Θvariable,similarbutdifferentacoplanarityangleshave h→ππν¯ππν 2 c acos(Θ 2∆), (3)
|M | ∝ − −
been studied both for e+e− colliders [9–14] as well as for
where a and c are both positive and depend neither on
the LHC [15–20]. For the τ± π±π0ν decay mode,
→ Θ nor ∆. The angular variable Θ is defined through
which is the most dominant decay mode of the τ, the
acoplanarity angles used in those studies are not as ef- cosΘ (k p )(k p ) (p p )(k k ),
1 τ2 2 τ1 τ1 τ2 1 2
fective as the Θ variable at e+e− colliders in which the sinΘ∝(cid:15) · kµpν ·kρpσ−, · · (4)
neutrino momenta can be reconstructed up to a two-fold ∝ µνρσ 1 τ1 2 τ2
ambiguity [1]. An advantage of the LHC studies men- with a common proportionality factor. The subscripts
tioned above is that they can be applied to all 1-prong τ 1 and 2 refer to the τ+ and τ− branches of the decay,
decays including leptonic decays. However, realistic de- respectively (e.g., pµ = pµ and pµ = pµ ). The 4-
τ1 τ+ τ2 τ−
tectoreffectsarenotconsideredinthosestudies. Ref.[21] momenta kµ (i=1, 2) are defined by
i
performsarealisticstudyfortheLHCbutassuminguni-
kµ y qµ+rpµ, (5)
versalCPviolationforallSMfermions, unlikeourstudy i ≡ i i νi
in which we assume ∆ is non-zero only for the τ. Fi-
with
nally, the use of the τ impact parameter associated with
a displaced τ vertex was studied in Ref. [22] in the e+e− qµ pµ pµ , (6)
i ≡ π±i− π0i
context. Our Θ variable does not depend on the mea-
and
surement of the τ impact parameter.
The paper is organized as follows. In Section II, we 2q p m2 4m2
review the Θ variable and rewrite it in a simple form by yi ≡ m2i+· mτi2 , r ≡ mρ2−+m2π ≈0.14. (7)
τ ρ τ ρ
expanding it in terms of a small parameter λ that char-
acterizes the degree of collinearity of the decay products
ofthetaus,withλ 0intheexactlycollinearlimit. We B. The boosted τ± limit
→
use this expansion to argue that the collinear approxi-
mation appears the best we can do for the purpose of
The fact that the taus from Higgs boson decay are
reconstructing Θ. Section III describes the parton level
highlyboostedcanbeexploitedtoobtainanevensimpler
simulation of the signal and background processes. Sec-
expressionforΘ. Wedefinetwolightlike4-vectorsnµand
tion IV describes the detector simulation and selection 1
nµ whosespatialcomponents,(cid:126)n and(cid:126)n ,areunitvectors
of the parametrized detector quantities corresponding to 2 1 2
taken along the 3-momenta of the ρ± from the τ decays:
theHiggsbosondecayproducts. SectionVevaluatesthe
results of the simulation and sensitivity as a function of n (1,nˆ ), n (1,nˆ ). (8)
1 ρ1 2 ρ2
integrated luminosity, and we conclude in Section VI. ≡ ≡
We also define
n¯ (1, nˆ ), n¯ (1, nˆ ). (9)
1 ρ1 2 ρ2
II. THEORY ≡ − ≡ −
Then, an arbitrary 4-momentum aµ can be expanded in
terms of n and n¯ as
A. The CP phase ∆ and the variable Θ 1 1
nµ n¯µ
aµ =(a n¯ ) 1 +(a n ) 1 +a⊥µ
Following Ref. [1], we define the CP phase ∆ by · 1 2 · 1 2
(10)
nµ n¯µ
τ-Yukawa = yτ hτ¯(cos∆+iγ5sin∆)τ, (1) ≡a+ 21 +a− 21 +a⊥µ,
L −√2
where the scalar field h and Dirac spinor τ describe the
Higgsbosonandτ lepton,respectively. Inordertomain-
1 For a fully SU(2)×U(1) gauge-invariant form of the interac-
tain the SM decay rate for h ττ, we fix the h-τ-τ
tion (1) as well as an example of renormalizable realizations of
Yukawa coupling, yτ, to its SM→value yτSM = mτ/v with it,seeRef.[1].
3
where a⊥ by definition satisfies a⊥ n = a⊥ n¯ = 0. withacommonproportionalityfactor. The4-vectorsqµ,
Alternatively,aµ canbeexpandedin·as1imilarm·an1nerin nµ andnµ aredefinedin(6)and(8),respectively. Inthie
1 2
terms of n and n¯ . To avoid notational clutter, we do restofthepaper,weusetheexpressions(15)tocompute
2 2
not make explicit whether a± and a⊥ are defined in the Θ unless noted otherwise.
n -n¯ basisorthen -n¯ basis,butitshouldbeclearthat One might think we should be able to do better than
1 1 2 2
the momenta of all particles originating from the τ+ will the collinear approximation by using statistical correla-
beexpandedinthen -n¯ basis, whilethosefromτ− will tions of the neutrino momenta with other, visible, mo-
1 1
be in n -n¯ . menta in the process. However, the delicate cancellation
2 2
Next,weintroduceasmallexpansionparameterλ 1 shown in (12) implies that the correlations must get the
toquantifythedegreeofcollinearitybetweentheτ±(cid:28)and neutrinomomentacorrectlyatthelevelof (λ2) 10−4
the respective ρ±. First, by construction, “collinear” in order to outperform the collinear approOximatio∼n. Al-
means that pµ is dominated by the + component, p+, though we could not prove that this is impossible, it cer-
while the remaining components p⊥ and p− are small. tainly suggests that it is extremely difficult.
Therefore, by definition, we assign the λ scaling law
p⊥ λp+ tothe component. Thisimpliesthatnumer-
ical∼ly we have λ⊥ mτ/mh 10−2. Then, in the ultra- III. PARTON-LEVEL SIMULATION
relativistic limit,∼we have 0∼ p p = p+p−+p⊥ p⊥
p+p−+ (λ2p+p+), so we se(cid:39)e tha·t p− λ2p+. To· sum∼-
O ∼ In this section, we outline our generation of the par-
marize, we characterize the collinearity of p as
ton level samples used in the detector simulation. We
(p+,p−,p⊥) (1,λ2,λ)p+. (11) generated tree level event samples with a combination of
∼ MadGraph5[23]andMCFMasexplainedbelowfortheback-
ground (Z +j) and the signal (h+j) with p = 70
Tmin
GeV for the jet. The associated jet facilitates trigger-
C. The reconstruction of neutrinos
ing and provides sufficient τ+τ− transverse momentum
for the collinear approximation to hold. Other associ-
Since neutrinos are invisible at the LHC, we must de-
atedproductionmodescouldbeused,notablyh+Z and
vise a method to assign momenta to the neutrinos from
h+W, but they have lower cross sections than h+j,
the τ± decays. However, the choice of method is a deli-
though potentially better signal to noise that could be
cate issue for the reconstruction of the Θ variable. Per-
exploitedinafurtherstudy. Multijeteventsareapoten-
forming the λ expansion in the expressions (4), we see
tialbackground;however,thisbackgroundisfoundtobe
thatall (λ0)and (λ1)termsexactlycancel, soweare
O O small once tau selection criteria are imposed. Therefore,
left with
considerationofZ+j aloneissufficientforourpurposes.
(k p )(k p ) (p p )(k k ) (λ2), The jet-p cut was imposed at the generator level in
1 τ2 2 τ1 τ1 τ2 1 2 T
· · − · · ∼O (12)
(cid:15) kµpν kρpσ (λ2). anticipation of the high-pT jet requirement we impose in
µνρσ 1 τ1 2 τ2 ∼O ouranalysistoensurethattheeventwillpassthetrigger
Therefore, for the purpose of reconstructing Θ, values as well as to avoid kinematic configurations where the
must be carefully assigned to the invisible neutrino mo- τ+τ− is produced back-to-back in the transverse plane
menta so as not to disturb these delicate cancellations. and the collinear approximation for the neutrino mo-
In particular, the λ scaling law (11) must be respected. menta fails.
Asimplemethodwiththispropertyisprovidedbythe ThemodelfilesweregeneratedusingFeynRulespack-
collinear approximation [8], where we set age [24] by modifying the SM template provided by
FeynRules to include the CP violating coupling in the
p⊥µ =p− =0, p⊥µ =p− =0, (13) h-τ-τ vertexaswellastheeffectiveverticesforthedecay
τi τi νi νi
of τ ρ+ν and ρ π+π0 given by
for each i. In other words, the collinear approximation → →
applies the λ 0 limit to the τ and ν momenta. Then, = ρ∗ν¯γµP τ ρµ(cid:0)π0∂ π∗ π∗∂ π0(cid:1)+c.c.,
to (λ2), the→expressions (4) become Leff − µ L − µ − µ
(16)
O
cosΘ (k⊥ n )(k⊥ n ) (n n )(k⊥ k⊥),
sinΘ∝(cid:15) 1 · k2⊥µn2νk·⊥1ρn−σ, 1· 2 1 · 2 (14) whahnedreedPcLh≡ira(l1it−y.γ5W)/e2imispthleempernotjetchteioHniogpgserbaotsoornonptroodleufct--
∝ µνρσ 1 1 2 2
tionfromgg fusionusingtheeffectivefieldtheory(EFT)
again with a common proportionality factor. Finally,
(in which the top quark is integrated out) available from
noticingthatthedefinitionsofkiµin(5)giveki⊥µ =yiqi⊥µ the FeynRules repository. In principle, such an effec-
inthecollinearapproximation,wearriveatthefollowing tive vertex is applicable only when the energy scale of
very simple expressions that determine Θ: the process lies well below the mass of the top quark.
However, using the MCFM program [25], we have verified
cosΘ (q⊥ n )(q⊥ n ) (n n )(q⊥ q⊥),
∝ 1 · 2 2 · 1 − 1· 2 1 · 2 (15) that the Higgs boson pT distribution from the EFT in
sinΘ (cid:15) q⊥µnνq⊥ρnσ, the region of interest (70 < p < 200 GeV) agrees at
∝ µνρσ 1 1 2 2 T
4
the percent level with the full 1-loop QCD calculation. amined as potential τ-candidates. The lead track within
Finally, note that all the coupling constants in Eq. (16) ∆R < 0.2 of the jet axis is selected, and the sum of
aresettounity. Togetthephysicalcrosssection,weuse the transverse momenta of the remaining tracks, within
the cross sections from MCFM re-weighted by τ ρ+ν ∆R < 0.4, is required to be less than 7GeV in order to
andρ π+π0 branchingfractions. TheCTEQ→6l1PDF exclude jets that are unlikely to be taus. These selection
→
set was used throughout. requirementsemulatethemoresophisticatedselectionof
Parton showering and hadronization effects are in- taus in the LHC experiments, and are treated as equiva-
cluded by processing the Madgraph5 samples using the lent to the Delphes efficiency of 65%.
Pythia8 program [26]. In principle, higher order correc- We make further selections on the individual elements
tionscanbeimplementedbyincludingeventswithhigher withinthetaucandidateinordertoensurethatthedecay
jet multiplicity from tree level matrix elements and per- productshavebeenmeasuredwithsufficientprecisionfor
formingthecorrespondingjetmergingwithPythia’spar- the calculation of Θ. The lead track is required to have
ton showering. However, we have verified that the inclu- p > 5GeV, or this candidate is rejected. We then pro-
T
sionofthesecorrectionsdonotaffecttheHiggsbosonp ceed to examine calorimeter towers within ∆R < 0.2 of
T
distribution and they differ at most by a few percent in the jet axis. We select the tower with the largest trans-
the region of interest. verse energy in the electromagnetic portion of the tower.
Thetowerinquestionmustalsohaveanelectromagnetic
fraction (EMF) of 0.9, that is, at least 90% of its total
IV. DETECTOR SIMULATION energywithintheECAL.IfthistowerhaspT >5GeV,is
within∆R<0.2oftheselectedtrack,andthesumofthe
selected tower transverse energy and the track momen-
In order to incorporate detector effects into the mea-
tum is greater than 20GeV, then this jet becomes a τ-
surement of the Θ angle, we use the Snowmass detector
candidate suitable for Θ reconstruction, and the charged
model [27], implemented in Delphes 3 [28]. In Delphes,
pionisassumedtobetheselectedtrackwiththeneutral
energy from particles deposited within the calorimeter
pion the selected tower.
is partitioned between the electromagnetic and hadronic
Finally, the electromagnetic portion of the actual AT-
sections according to a fixed ratio. This ratio is unity
LAS and CMS detectors have finer granularity than a
for the fraction of energy from a charged pion deposited
single tower, which is not properly accounted for by the
in the hadronic calorimeter, which fails to account for
Snowmass detector. To approximate a position resolu-
energy depositions from hadronic showers that begin be-
tion of one detector element of the LHC detectors, we
fore the hadronic calorimeter. We account for this ef-
introduce the resolution for the position in η-φ of the
fect,includingpotentialsystematiceffectsduetooverlap
neutral pion as a Gaussian smearing with standard de-
between the energy deposition of the neutral pion and
viation 0.025/√12. A resolution no better than a tower
the charged pion, by distributing the energy of charged
(as in the default Snowmass detector) was found to de-
pions in both calorimeter sections according to a proba-
grade significantly the sensitivity to the modulation in
bility distribution that models the one given in Ref. [29]
the Θ distribution. Finally, events are required to have
for 30GeV pions. 85% percent of the time the parti-
at least two τ-candidates with opposite charges. Should
cle is presumed to deposit energy via ionization only,
therebemorethantwoτ-candidates,thehighestp pair
and the energy is entirely deposited within the hadronic T
with opposite charge is selected.
calorimeter. For the remaining 15% of events, the frac-
tion of the particle energy deposited in the electromag-
netic calorimeter is drawn from a Gaussian distribution
of mean 0.4 and width 0.3 (selecting only physical val- V. RESULTS
ues). The rest of the energy is assigned to the hadronic
calorimeter. The Gaussian models the probability with We now come to the critical question of whether
whichthepioninteractsearly,inwhichcaseasignificant the signal modulation survives detector effects. In or-
fraction of its energy will be deposited in the ECAL. der to answer that question, consider the analysis cut-
Tau identification in Delphes is abstracted to an ef- flow shown in Table I. The signal acceptance – the ra-
ficiency, which is insufficient for our purposes. There- tio of the second number to the first in column two
fore, we develop an algorithm to identify taus explicitly of Table I – is 0.430, while that of the background is
that assigns the charged pion and the neutral pion to a 0.254. The products of the efficiencies of all the re-
track and a calorimeter tower, respectively. We select maining cuts including the 65% τ reconstruction effi-
jets reconstructed with the anti-k algorithm [30] with ciency are 0.652 143979/1078279=0.0564 and 0.652
T
× ×
a distance parameter of 0.5, which are reconstructed in 134628/1069747=0.0531forthesignalandbackground,
Delphes using FastJet [31]. At least three jets are re- respectively. Therefore, overall, the signal and back-
quired in each event with p > 30GeV within η < 2.5 ground efficiencies are 0.430 0.0564=2.42 10−2 and
T
(the tracking limit of the detector), of which |th|e lead 0.254 0.0531=1.35 10−2×, respectively. ×
× ×
jet must have p >100GeV (well above the parton level To see the effects of finite detector resolution on our
T
requirementof70GeV).Alljetswithp >30GeVareex- ability to reconstruct the signal Θ distribution (3), we
T
5
Selection criterion Z+j→ττ+j h+j→ττ+j
None 9618732 4698651 U.0.055
A.
At least three jets 0.05
p >30GeV, lead jet
T
0.045
p >100GeV 2445860 2019316
T
Two τ-candidates 0.04
only ∆R and 1069747 1078279
0.035
isolation requirements
τ-track pT >5GeV 903429 941368 0.03
Monte Carlo Truth
Tower E >5GeV 804566 856299
T
Tower EMF >0.9 156140 160312 0.025 Delphes Simulation
Sum pT >20GeV 143508 149591 0.02-3 -2 -1 0 1 2 3
Opposite Charge 134628 143979 Q
TABLE I: Cut-flows for Z→ ττ and h → ττ. The generator FIG. 1: Comparison of parton level Θ distribution (Monte
andreconstructionlevelcutsonthejetarepT >70GeV,and Carlo Truth) with the distribution after the Delphes simula-
100GeV, respectively. See text for more details. tion and event reconstruction for h→ττ.
parameters MC Truth Delphes Sim.
c 0.0397±0.0001 0.0397±0.0002 U.0.055
A.
a 0.0089±0.0001 0.0085±0.0002 0.05
γ 1.03±0.01 1.03±0.02
0.045
δ −0.003±0.003 0.01±0.01
α≡a/c 0.225±0.002 0.214±0.004 0.04
TABLEII: FitstothesignalΘdistributionbeforeandafter 0.035
theinclusionofdetectoreffectsusingthefunctionalformc−
acos(γΘ−2δ). 0.03
Monte Carlo Truth
0.025
Delphes Simulation
present in Fig. 1 the reconstructed Θ distribution from
0.02
thesignalsamplesgeneratedwith∆=0beforeandafter -3 -2 -1 0 1 2 3
Q
the inclusion of detector effects, labelled as Monte Carlo
Truth and Delphes Simulation, respectively. We perform
FIG. 2: Comparison of parton level Θ distribution (Monte
fits to these distributions using the functional form c
Carlo Truth) with the distribution after the Delphes simula-
−
acos(γΘ 2δ) with free parameters a, c, γ, and δ in
tion and event reconstruction for Z →ττ.
−
ordertoextractthemodulationamplitudeα a/c. The
≡
fit results are presented in Table II and show that γ 1
(cid:39)
and δ 0 as expected from the analytical result (3) and ∆=0. A standard choice for t is
(cid:39) (cid:54)
the assumption ∆=0, even after detector effects. Most
crucially,thedilutionofthemodulationamplitudeαdue L(∆)
t=2ln , (17)
to the detector effects is only about 4%, going down L(0)
∼
from 0.225 to 0.214.
where
In order to check that our τ reconstruction algorithm
does not introduce artificial modulations in the back-
N
ground Θ distribution, we present in Fig. 2 the Monte (cid:89)
L(∆)= f(Θ ∆) (18)
i
Carlo Truth and Delphes Simulation Θ distributions us- |
i=1
ing the background samples. Clearly, the background is
consistent with a flat distribution after the detector ef- is the likelihood function, while f(Θ ∆) is the Θ distri-
i
|
fectsandwemayconcludethatthelatterdonotbiasthe bution for a given value of ∆.
shape of the Θ distribution. In order to enhance the signal to background ratio
Now,weaddressthecrucialquestion: howwellcanwe (S/B), we use a boosted decision tree (BDT), trained
distinguishtheΘdistributionwith∆=0fromthatwith usingtheinvariantmassofthereconstructedτ± system,
∆=0? Given N events, each yielding a measurement of thekinematicvariables(p ,φ,η)ofthefinalstatevisible
T
(cid:54)
Θ , we construct a test statistic t designed to distinguish particles, and the missing transverse energy. Therefore,
i
between the SM hypothesis ∆ = 0 and the alternatives each event can be characterized by the measurement of
6
Θ andthevalueoftheBDTdiscriminantd ,whichyields
i i
the modified likelihood function,
0.14
∆=0
N ∆=π/4
(cid:89) 0.12
L(∆)= f(Θ ,d ∆), (19)
i i
|
i=1 0.10
d
where the probability density function of the data yiel0.08
(Θ,d) is modelled as follows, d
{ } ze
f(Θ,d∆) mali0.06
∝Bρ|BBDT(d)+SρSBDT(d)(cid:2)1−αcos(Θ−2∆)(cid:3), (20) nor0.04 p−value
where ρS (d) and ρB (d) are, respectively, the signal 0.02
BDT BDT
and background BDT distributions for the discriminant
parameter d, while B and S are, respectively, the total 0.00
15 10 5 0 5 10 15
expected background and signal counts given by − − − t
B =(cid:15) σ , S =(cid:15) σ . (21)
B B S S FIG.3: DistributionsofthetstatisticfortheSMhypothesis
L L
(∆ = 0) and a non-SM hypothesis (∆ = π/4). The “ob-
Here, σS and σB are the associated cross section times served”valueofthestatisticistakentobethemedianofthe
branchingfractions,the(cid:15)’sarethesignalandbackground t distribution of the non-SM hypothesis.
efficiencies discussed above and is the integrated lumi-
L
nosity.
In order to quantify how well one might be expected
to distinguish a ∆ = 0 hypothesis from the SM hypoth- 4.0
esis ∆ = 0, we gen(cid:54)erate three samples of Θ and d val- ∆=π/2
3.5
ues with ∆ = 0, π/4, and π/2. For each sample, we ∆=π/4
calculate the values of t as defined in Eq. (17), which ∆=π/2noBDT
3.0
yield the t distributions as illustrated in Fig. 3 for the ∆=π/4noBDT
∆ = 0 and π/4 samples. To quantify the discrimination 2.5 ∆=π/2(B 0.5B)
→
between the two hypothesis, the p-value of the SM t dis-
Z
2.0
tribution is computed using the median of the non-SM
t distribution. As proxies for systematic uncertainties in
1.5
the S and α parameters, the p-values are varied in the
10% neighborhood of their nominal values. In Fig. 4 we 1.0
present the reach as a function of the integrated lumi-
nosity for ∆ = π/4 and π/2. Because we have chosen 0.5
the “observed” value of t to be the median of the non-
0.0
SM hypothesis, the reach in this context is interpreted 500 1000 1500 2000 2500 3000
as follows: if the non-SM hypothesis is true, then there (fb 1)
−
L
is a 50% chance to reject the SM hypothesis ∆ = 0 at
theZ-sigmalevel, whereZ =Φ−1(p) √2erf−1(2p 1)
≡ − FIG. 4: The reach, quantified on the Z-sigma scale of the
with p being the p-value shown in Fig. 3.
normal distribution, versus the integrated luminosity. The
ItisclearfromFig.4thattheoptimisticconclusionob-
uppermost plot shows the effect of reducing the background
tainedforanidealdetectordoesnotsurvivethesmearing by a factor of two, while keeping every else fixed.
effectsofarealisticdetectorandourreconstructionalgo-
rithms. At best, at 1500 fb−1, there is a 50:50 chance
∼
ofrejectingthe∆=0hypothesisat95%confidencelevel.
Itisimportanttonotewherethepoorperformancestems
detectors is too low to achieve a sufficient reduction of
from. As mentioned earlier, the reduction of the modu-
the total background count B.
lation amplitude α of the signal due to the angular res-
olution is negligible. Rather, we find that the discrim- Toillustratetheeffectsofimprovedmissingtransverse
ination power of the BDT dominantly comes from the energyresolution,weshowintheuppermostplotinFig.4
invariant mass of the reconstructed τ+-τ− system, and theeffectofincreasingS/B byafactoroftwobydecreas-
consequently the S/B ratio is sensitive to the mass reso- ing B by a factor two, while keeping everything else the
lution, which in turn is sensitive to the resolution of the same. Increasing the S/B by increasing S by a factor
missing transverse energy (MET). Therefore, our anal- two (while keeping α unchanged) has a similar but more
ysis shows that the current MET resolution of the LHC pronounced effect.
7
VI. CONCLUSIONS from the τ decays, we have found that the finite angular
resolution of the LHC detectors reduces the modulation
We have examined a recent proposal [1] for measur- amplitude of the signal Θ distribution by only 4%,
∼
ing a potentially non-zero CP phase ∆ in Higgs to τ+τ− compared to that of an ideal detector. Instead, we have
decays using an angular variable Θ that can be recon- found that the experimental ability to distinguish the
structed from the decay chains τ± ρ±ν π±π0ν. A hypotheses ∆ = 0 from ∆ = 0 is strongly limited by
non-zero phase of the h-τ-τ Yukaw→a coupli→ng would be the missing transverse energy(cid:54) resolution. The finite en-
unambiguous evidence of physics beyond the SM. Con- ergy resolution significantly degrades the use of the ττ
trary to previous expectations [1], with 1000fb−1 we invariant mass distribution as the principal discriminant
find that the standard model CP phase,∼∆=0◦, can be between the h ττ signal and the Z ττ background.
→ →
distinguished from the ∆ = 90◦ hypothesis at no more In contrast, the reconstruction of Θ itself is nearly unaf-
than 95% confidence level. fected by the finite energy resolution, as the Θ variable
We have addressed two obvious effects that are ex- is basically determined by the angular topology of the
pected to degrade our ability to measure ∆ from the Θ Higgs boson decay products. Fortunately, the resolution
distribution. First, we examined the issue of neutrino ofmissingtransverseenergyisanareainwhichimprove-
momentum reconstruction, for which the original pro- mentscanbehopedfor,e.g.,byusingmultivariatemeth-
posal[1]employedthecollinearapproximation. Wehave ods [32].
presented a theoretical argument that strongly suggests
that this cannot be improved further.
Second, we have closely studied how finite resolutions Acknowledgment
ofarealisticdetectoraffectsourabilitytodistinguishbe-
tweentheSMsignalanditsdeviationsinducedbyanon- This work was supported in part by the US Depart-
zeroCPviolatingphase∆, usingtheSnowmassdetector ment of Energy under grant DE-FG02-13ER41942. The
model implemented in the Delphes detector simulation work of N. S. was partially supported by the US De-
program. Contrarytothenaiveexpectationthatafinite partment of Energy contract No. DE-AC05-06OR23177,
angular resolution should hamper the reconstruction of under which Jefferson Science Associates, LLC operates
Θ as it requires resolving the charged and neutral pions Jefferson Lab.
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