CDF実験の最新結果

筑波大学　佐藤構二6/23/2011首都大学東京

Contents

• Introduction– Tevatron Accelerator, CDF and D0 Detectors.

• Top Physics• Direct Search for Higgs Bosons

– Standard Model Higgs– MSSM Higgs Bosons

• B Physics• Exotic Physics Searches at CDF• Summary

Introduction

Tevatron Run II First collision in Run 0

was in 1985 (26 years ago!!)

collisions at =1.96 TeV (1.8 TeV in Run I).

Run II started in Summer 2001.

Collisions at world highest energy until Nov 2009.

Two multi-purpose detectors for wide range of physics studies.

Tevatron Run II — Luminosity Status

• Typical Peak Luminosity : 4 1032 cm2 s-1.• Delivers 70 - 80 pb-1/week.• Integrated Luminosity: 11.3 fb-1

– Recorded by CDF: 9.5 fb-1.• Recent CDF analyses typically use up to ~7 fb-1.• Typical data taking efficiency of CDF: ~ 85% No significant drop after 10 years of running!!

(CDF)

Tevatron Plans• 2010: strong discussion on 3 year extention of Tevatron up to FY2014.• LHC was planning to shutdown a whole year in 2012.• Tevatron was expected to compete with LHC in SM Higgs searches.

20112.4σ in MH<180 GeV

2014”>3σ Evidence”In 100<MH<180 GeV の

Summer 2010Dataset

SM Higgs Discovery Potential of Tevatron (2010 Projection)

Recommendation 1: The panel recommends that the agencies proceed with a three-year extension of the Tevatron program if the resources required to support such an extension become available in addition to the present funding for HEP. Given the strong physics case, we encourage the funding agencies to try to find the needed additional resources. (October 26, 2010, P5 report)

Tevatron Termination

Tevatron Termination

Tevatron will close at the end of FY2011 (Sep 30, 2011)

Tevatron v.s LHC

TEVATRON LHC (current) LHC (design)

Particles Collided p - pbar p - p p - p

CM Energy (TeV) 1.96 7 14

Inst. Lum (cm-2 s-1) Record 4.05 x 1032 1.2 x 1033 1 x 1034

Integ. Lum (fb-1) 11.5 1.1 --

Collider Detector at FermilabMulti-purpose detector

Tracking in 1.4 T magnetic field. Coverage |h|<~1.

Precision tracking with silicon. 7 layers of silicon detectors.

EM and Hadron Calorimeters. sE/E ~ 14%/E (EM). sE/E ~ 84%/E (HAD).

Muon chambers.

Collider Detector at Fermilab~600 physicists from

12 nations and 61 institutionsMcGill Univ.Univ. of Toronto

Argonne National Lab.Baylor Univ.Brandeis Univ.UC DavisUC Los AngelesUC San DiegoUC Santa BarbaraCarnegie Mellon Univ.Univ. of ChicagoDuke Univ.FermilabUniv. of FloridaHarvard Univ.Univ. of IllinoisThe Johns Hopkins Univ.LBNLMITMichigan State Univ.Univ. of MichiganUniv. of New MexicoNorthwestern Univ.The Ohio State Univ.Univ. of PennsylvaniaUniv. of PittsburghPurdue Univ.Univ. of RochesterRockefeller Univ.Rutgers Univ.Texas A&M Univ.Tufts Univ.Wayne State Univ.Univ. of WisconsinYale Univ.

JINR, DubnaITEP, Moscow

Univ. Karlsruhe

Univ. of Geneva

Glasgow Univ.Univ. of LiverpoolUniv. of OxfordUniv. College London

Univ. of Bologna, INFNFrascati, INFNUniv. di Padova, INFNPisa, INFNUniv. di Roma, INFNINFN-TriesteUniv. di Udine

IFAE, BarcelonaCIEMAT, MadridUniv. of Cantabria

LPNHE, Paris

KHCL

KEKOkayama Univ.Osaka City Univ.Univ. of TsukubaWaseda Univ.

Academia Sinica

USA Canada

Russia

Germany

Switzerland

UK

Italy

Spain

France

Korea

Japan

Taiwan

D0 Detector

• Silicon detector covering up to |h|<3 rapidity

• Compact scintillating fiber tracker• 2.0 Tesla axial B field• Hermetic U/liquid Ar calorimeter• Extended muon coverage

Multi-purpose detector

Top Physics

Top Physics at Tevatron• Top quark was observed at

TEVATRON in 1995.• Top is still the least studied

observed particle.• Any deviation from SM might

suggest new physics!!• Top mass is unexpectedly heavy

~35mb.– Special role in EWSB? p

p tb

W-

q

q’

t b

W+

l+

n

X

Production cross-section

Resonance production

Production kinematics

ttbar Spin correlation

Top Mass W helicity

|Vtb|

Branching Ratios

Rare/non SM Decays

Anomalous Couplings

CP violation

Top lifetime

Top Charge

Top Width

_ _

_

_

BR (%) Bkgd.

Di-lep. 5 Low

L+jets 30 Moderate

All had. 44 High

+X 21 -ID hard

ttbar decay modes:

Top Pair Cross Section (L+jets)

~85% ~15%

• Top quark is mostly produced in pairs at Tevatron.

Event selection:• 1 lepton Pt>20, |h|<2.0• MET>25• ≥3 jets with Pt>20 , |h|<2.0 • ≥ 1 jet b-tagged

stt = 7.14 ± 0.34 (stat.) ± 0.58 (syst.) ± 0.14 (theory) pb (4.3 fb-1)

stt = 7.04 ± 0.34 (stat.) ± 0.55 (syst.) ± 0.43 (lumi.) pb

The dominant luminosity systematic can be canceled out by measuring ratio stt /sZ.

s(NLO) = 7.4 +0.5-0.7 pb

Top Pair Cross Section Summary• Cross section is sensitive to both

production and decay anomaly.• The difference between different decay

modes might indicate new physics.• CDF measures xs with various decay

modes/methods, and the results are consistent with SM.

Forward Backward Assymmetry• CDF Analysis in L+jets channel.• Related to qqbar initial state - specially

interesting at Tevatron.• Interference terms between LO and NLO

diagrams ~5% asymmetry.

tt

q

q

g

g

b

b

W+

W-

l+

n

q’

q

q: lepton chargeyh: rapidity of hadronic top

AFB = 15.8± 7.5 % AFB

SM = 5.8 ± 0.9 % consistent

5.3 fb-1, Summer 2010

Mttbar Dependence of AFB in L+jets at CDF

Mttbar Distribution:

High MassRegion

Low MassRegion

Low Mass Region

Mttbar = 450 GeV

High Mass Region

5.3 fb-1, Winter 2011 update

AFB = 47.5± 11.4 % AFB

SM = 8.8 ± 1.3 % ~3.3 σ deviation

AFB = -11.6± 15.3 % AFB

SM = 4.0 ± 0.6 % consistent

AFB Measurement in L+jets at D0• D0 analysis in L+jets.• Asymmetry defined as:

Dy = ytop – yanti-top

AFB = 8± 4(stat) ±2(syst) %AFB

SM = 1 +2-1 %

Thought not as significant, same trend as CDF!!

4.3 fb-1, Summer 2010

AFB Measurement in Dilepton at CDF

Lepton Dy distribution Full Reconstruction Dy distribution

AobsFB= 43 ±15 (stat) ±5 (syst) %

ASMFB = 6 ±1 % 2.3s deviation

5.1 fb-1, Winter 2011

Mttbar Dependence of AFB in Dilepton at CDF

Mttbar Distribution:

High MassRegionLow Mass

Region

Low Mass Region

Mttbar = 450 GeV

High Mass Region

5.1 fb-1, Winter 2011

AFB = 21.2±9.6 (stat only) % AFB

SM = -4.0 ± 5.5 %

AFB = -10.4±6.6 (stat only) % AFB

SM = 0.3 ± 3.1 %

Single Top Production• Top quark is sometimes singly produced Tevatron.

0.884±0.11 pb (NLO)

1.98±0.25 pb (NLO)

• 1 lepton, MET, 2 or 3 jets• S/B separation by Matrix Element (ME)

Signal ME bkgd ME

st+s-chan = 2.5 +0.7-0.6 pb (3.2 fb-1)

4.3 s effect

t-channel

Vtb

Vtb*

s-channel

Vtb

Vtb*

5.0 s observation!!

t-channel

Vtb

Vtb*

Single Top Combined Result

st+s-chan = 2.3 +0.6-0.5 pb

st-chan = 0.8±0.4 pbss-chan = 1.8+0.7

-0.5 pb

|Vtb| = 0.91 ± 0.11 (exp.) ± 0.07 (theory)

s-channel

Vtb

Vtb*

0.884±0.11 pb (NLO) 1.98±0.25 pb (NLO)

(2010)

|Vtb| > 0.71 at 95% C.L.

W Mass MeasurementCDF, 200 pb-1 (2007)

D0, 1 fb-1 (2009)

Best single measurement of the time. Best single measurement!

W Mass Uncertainty Future Projection

CDF working on 2.3 fb-1 data

W Mass World Average

Top Mass Measurement in L+jets Events (CDF)

t

tq

q

g

g

b

b

W+

W-

l+

n

q’

q15% 85%

100%

100%

Controls background by a Neural Net Discriminant:

Matrix Element

Detector Response Func.

x: parton level momentay: measured momenta

PDFs

2-D likelihood Fit to data :

In-situ JES calibration

1-btag 2>b-tag

Background 261.8 ± 60.6 28.0 ± 9.6’

Top signal 767.3 ± 97.2 276.5 ± 43.0

Observed Data 1016 247

mt = 173.0 ± 0.7 (stat.) ± 0.6 (JES) ± 0.9 (syst.) GeV/c2

= 173.0 ± 1.2 (total) GeV/c2 Best single measurement, 0.7% precision!

Top Mass World Average

Top Mass Uncertainty Future Projection

Constraint to SM Higgs Mass (Jul 2010)

30Mtop = 173.3 ± 1.1 GeV/c2

MW = 80.399 ± 0.023 GeV/c

Precise W and Top Mass measurements constrains the SM Higgs Mass due to the radiative correction:

　　 mH < 158 GeV @ 95% CL　 　 (mH = 89.0 +35/-26 GeV)　mH < 185 GeV @ 95% CL including LEP2 direct search limit

Constraint to SM Higgs Mass (Jul 2010)

31

　　 mH < 158 GeV @ 95% CL　 　 (mH = 89.0 +35/-26 GeV)Mtop = 173.3 ± 1.1 GeV/c2

MW = 80.399 ± 0.023 GeV/c2

In 2003:Mtop = 178.0 4.3 GeV/c2

MW =　 80410 32 MeV/c2Mhiggs < 260 GeV/c2 (95% C.L.)

Progress due to the TEVATRON Run II Results

Precise W and Top Mass measurements constrains the SM Higgs Mass due to the radiative correction:

Direct Search for Higgs Bosons

Production Cross Sections

recently observed

SM Higgs Properties at Tevatron

bb WW• mH<135 GeV (low mass):

– gg→H→bb is difficult to see.– Look for WH/ZH with leptonic vector boson decays.

• mH>135 GeV (high mass):– Easiest to look for H→WW with one or two W

decaying to lepton.

WHlbb (low mass)• S/B separation by NN.• Four tagging categories, using 3 algorithms

(including NN tagger).• NN based b-jet energy correction

NN Outputs:

2 tag 1 tag

Observed upper limit4.5 x σ(SM)(@115 GeV)

l

l

• 3 b-tag categories with 2 algorithms.• S/B separation by NN.• Improved lepton coverage with new

loose muon category.• Dominant backgrounds:

– Z+jets, top, diboson

ZH ll+bb (low mass)

(mH=120 GeV)

NN Outputs:

Observed upper limit6.0 x σ(SM)(@115 GeV)

WH/ZHMET+bb (low mass)• Target process: ZHnnbb

– Also complementary to WHlnbb search.

• 3 b-tag categories with 2 algorithms.• S/B separation by NN.• Dominant backgrounds:

– QCD with MET miscalculation– W/Z+jets, top, diboson

(mH=115 GeV)

2 tag 1 tag

Observed upper limit2.3 x σ(SM)(@115 GeV)

H WW*l+ l- (high mass)• Opposite Sign 2 leptons.

– Lepton acceptance improved by using isolated tracks.• S/B separation by NN.

– Matrix element calculation result input to NN.• Dominant background

– DY, Diboson, top• Independently analyses OS/SS 2 leptons + 1/2 jets events to include WHWWW and VBF HWW signal inacceptance.

Observed upper limit :1.08 x σ(SM)(@165 GeV)

Updating for Winter 2011…

Summary of SM Higgs Searches at CDF

SM HiggsCDF and D0 Combined Limits

CDF Combined: D0 Combined:

SM HiggsTevatron Combined Limit

95% CL exclusion : 158 < mH <175 GeV mH<110 GeV (LEP2: mH<114.4 GeV)

SM Higgs Search –competition with ATLAS experiments, March 2011

Tevatron and LHC Summer 2011 Projection

Tevatron Summer 2011~ 8fb-1 / exp.

Tevatron:Exclusion of Mh<180 GeV

ATLAS:Exclusion of 130<Mh<450GeV

Results will be shown in ~1 month!!

Search for MSSM Higgs • Extended Higgs sector in SUSY models

– f = (H0, A0, h0) and H±

• Higgs coupling enhancement at large tan :b– Large increase (×~tan2b) in production cross sections

compared to SM: ggf, gbbf• for MA>100 GeV.

– Br(f )~9%tt– fbb~90%

Useful search modes at Tevatron:• f ττ• f + b ττ + b• f + b bb + b

MSSM ftt• Both experiments analyzed τe τhad, τμ τhad,

τeτμ channels (Opposite Sign)CDF 1.8 fb-1 (2007)

τe τhad+τμ τhad+τeτμ

D0 2.2 fb-1 (2008)

MSSM f tt Tevatron Combination

Combined, 2010

MSSM fbbbb at CDF• Analyze events with 3 b-tagged jets.• Utilizes trigger-level b-tagging.• Fully data-driven multi-jets backgrounds.• Define a flavor separator based on Mvtx for improved

background understanding.

~ 2s deviation from background at ~140 GeV

Di-jet mass, m12 of the leading 2 jets: 2.2 fb-1

MSSM fbbbb at D0• Analyze events with 3 b-tagged jets.• Subdivide candidates into 3- and 4-jets samples.• S/B separation by Likelihood Discriminant.

Likelihood Discriminant:

Di-jet mass:

Upper Limit on Cross Section:

Working on fbbbb TEVATRON combination this summer!!

MSSM fbttb at D0• A new search channel!!• Search in bτμτhad channel.

– Event selection: Isolated m, τhad, MET and a b-tagged jet.• Improve S/B separation using NN-based discriminant.• Dominant Bkg: Z+jets, ttbar, multi-jets.

Reconstructed Higgs Mass (GeV) NN-based Discriminant Upper Limit on Cross Section

Mjj in W+2jets events

Event Selection - Mjj in W+2jets events• 1 e/m: Pt>20 GeV, | |h <1.0• MET>25 GeV to ensure there was a neutrino• 2 jets: Et>30 GeV, |h|<2.4

– (cone size R=0.4 at CDF, R=0.5 at D0)

• Mt(e/m, MET)>30 GeV• Ptjj>40 GeV

• Dhjj<2.5• Df(MET, j1)>0.4

• Thresholds (especially the jet Pt cut) were set high in order to focus on the high dijet invariant mass range.

Mjj Distribution at CDF (4.3 fb-1)

Phys.Rev.Lett.106:171801 (2011)“Invariant Mass Distribution of Jet Pairs Produced in Association with a W boson in ppbar Collisions at sqrt(s) = 1.96 TeV”

• 3.2s deviation from SM.• Corresponds to 4 pb.

March, 2011

Mjj Distribution at CDF (7.3 fb-1)

• 4.8 s deviation from SM.Preliminary update in June 2011.

D0 follow up (4.3 fb-1)

DR(j,j) Distributions

D0 fluctuates the fraction of gg/qg/qq ingredients of the W+2jets MC sample (ALPGEN), while CDF simply trusts the fraction given by ALPGEN.

B Physics

B Production at Tevatron

• Large production rates ~10mb– Ο(100) B bosons every minutes!!– e+e-(4S)B experiments ~1.1nb– Not just BL

• CDF employs displaced-track trigger (SVT), and can collect all-hadronic finial states.

sOscillation (2006)

)cos1(2

1)(prob 00 tmeBB s

tss

Frequency ms~|Vts |2

measurement gave a Strong constraint on the CKM matrix (orange band).

𝐵𝑠→𝜇𝜇

FCNC decay is heavily suppressed in the Standard Model.

SM prediction:

SUSY scenarios boost the branching ratio by up to 100 times.

(3.7 fb-1)

Vertex displacement Candidate track isolation

S/B separation by Neural Net with 7 variables Dimuon mass in signal rich regions

BR( Bd → μμ ) < 7.6x10-9 @95% CL

BR( Bs → μμ ) < 4.3x10-8 @95% CL BR( Bs → μμ ) < 5.1x10-8 @95% CL (D0 6.1 fb-1)

World best limit

Prospect

We are HERE!!

CDF is updating the analysis this summer with 8 fb-1 of data!

Expected to give strong constraint on mSUGRA parameters.

CP Violation in

Bd unitarity triangle Bs unitarity triangle

Decay rate ~ +2

New physics?

CP Violation in (2)

CP Violation in (3)

CP Violation in (4) candidates:

Unbinned likelihood fit to data:

CP Violation in (5)• Previous result from July 2009 was:

2.1s deviation from SM

CP Violation in (6)

May 2010

Consistent with SM.~1s deviation.

Rare Decay

• Could be enhanced by Flavor Changing Neutral Current

New particle could appear in the loop ()

, Branching Ratio Measurements

BaBar Belle CDF (4.4 fb-1)

)

)

--- ---

𝐵→𝐾 ±𝜇𝜇 𝐵→𝐾 ∗(→𝜋±𝐾∓)𝜇𝜇 𝐵→𝜙𝜇𝜇

∼9𝜎 ∼10𝜎 ∼6𝜎

×𝟏𝟎−𝟔World best measurement

Observation

Forward-Backward Asymmetry

• Measure the F-B asymmetry as a function of

F-B Asymmetry Result

• Consistent with SM so far.

, Nov 2009

𝐽 /𝜓

Υ

F-B Asymmetry Result (2)

• Each experiment is consistent with SM within uncertainty.

• Is there a common trend off the SM prediction?• CDF is updating the result with 7 fb-1 data.

Babar: PRD79,031102(2009)Belle: PRL103,171801(2009)

CDF 4.4 fb-1

Exotic Physics Searches

Search for Diphoton Resonance (5.4 fb-

1)• Select events with 2g’s with Et>15 GeV.• Main background: SM 2g and jets faking photons.

Result consistent with SM.Excess around 200 GeV: 13% probability.

Limit on Randall-Sundrum Graviton Production Cross Section:

Dielectron Resonance Search in 2009 (2.3 fb-1)

• A 2.5s excess around Mee=240 GeV mass region!!

Dielectron Resonance Search in 2011 (5.7 fb-

1)• 1 electron with Et>20 GeV, |h|<1.1.• Opposite sign second electron with

Et>20 GeV, |h|<2.8.

Previous excess ~240 GeV is reduced to a 1.7s effect.

Limit on Randall-Sundrum Graviton Production Cross Section:

R-S Graviton Mass Limit (ee+ ggcombined):

Dimuon Resonance Search (4.6 fb-1) • Two opposite sign muons with

Pt>30 GeV, |h|<1.1.

Invariant mass of dimuon

Limits on Z’

W’ Search (5.3 fb-1) • 1 electron with Et>25 GeV, |h|<1.1.• MET>25 GeV.

Mt Distribution:Observed Cross Section Limit:

MW’ > 1.1 TeV (95% C.L.)

g+jets+MET Topology• Model independent search.• 1 electron w/ Et>30 GeV, |h|<1.1.• Jets w/ Et>15 GeV, |h|<3.0.• MET>20 GeV.

• Scanned kinematic plots in 1 and 2 jet bins for abnormaly.

Consistent with SM.MET: Eg: M(j1, )g : Ht:

Multijets Resonance• Model independent search for ppbarQQ3j+3j.• 6 jets with Et>15 GeV, |h|<2.5.• QCD background parameterized with 5 jet events.

• Separate 3-jet combinations that are potentially correlated using diagonal cut.

• Optimize cut for each point.• Set limit for RPV gluino scenario:

Mass below 144 GeV/c2 excluded.

Search for b’• Assume br(b’tW)=100%.• Search for : • 1 e/m with Pt>20 GeV, |h|<1.1.• MET>20 GeV.

Jet Multiplicity:Cross section Limit:

Mb’ > 372 GeV/c2 (95% C.L.)

Mb’ =350 GeV

Search for t’• t’t’WqWq(ln)q(qq)ql+4jets.• 1 e/m with Pt>25 GeV, |h|<1.1.• MET>20 GeV.• 4 jets with Et>20 GeV, |h|<2.0.

Limit on Cross Section:

Reconstructed t’ mass:

Mt’ > 335 GeV (95% C.L.)

Mt’ = 400 GeV

Summary (1)• Tevatron is running smoothly.

– Integrated delivered luminosity: 10.4 fb-1

– Will be terminated at the end of September, 2011.• Dijet invariant mass anomaly in W+2jets events

– D0 didn’t see the same excess.– Careful investigation ongoing.

• Top Physics– Mass measurement at 0.6% precision.

• mH < 158 GeV @ 95% CL.– Interesting deviation from SM in ttbar forward-backward

asymmetry:• >2s deviation from SM in L+jets and dilepton analyses at

CDF.• >3s deviation in high Mttbar region in L+jets.• This analysis is unique to ppbar initial state. Cannot

reproduce in LHC.

• Higgs Search– SM Higgs Mass Region 158<Mh<175 GeV excluded (95% C.L.)– Main channels have very elaborate analyses.– Fierce competition expected with LHC experiments during

Summer 2011.• Exotic Physics Searches

– A wide variety of interesting search analyses.– So far, consistent with SM.

• B Physics– We have very interesting B physics program ongoing.

• CDF and D0 keep working hard to produce interesting physics results!!

Summary (2)

Backup

http://www-cdfonline.fnal.gov/ops/opshelp/stores/grand_summary/lumi.eps

AFB in L+jets by Lepton Type

Prediction

AFB by Fine Mass Bins

• Prediction:

• Data

AFB by Fine Jet Bins

AFB in Dilepton By Lepton Type at CDF

W Mass Syst. Uncertainty

MTM3 Top Mass Measurement

log Lsig(mt, JES) = Σi[log Li(mt, JES) - fbg(qi) log Lavg(mt, JES | background)]

SM combined channels

MSSM f tt Tevatron Combination

MSSM fbbbb at CDF

Tevatronの今後

2011年末MH<200 GeVの全質量領域で 2.4σ

発見に必要なルミノシティの予想値：

2014年末100<MH<180 GeVの質量領域で”>3σ Evidence”

Tevatronは 2014年までの実験延長を模索している（ＬＨＣとの兼ね合い）。

7 TeVでのＡＴＬＡＳの棄却能力

• 3 探索モードのみの合成：– H→WW→lνlν– H→ZZ→4l– H→γγ

• 1ｆｂ -1（ 2011 年末に相当）のデータ量で、 135-188 GeVのヒッグス質量を棄却することができる。

2011年の状況

×1.3

リミットが√ Lumでスケールするならば、2011年の Tevatronは、√ (10fb-1/5.9fb-1)～1.3だけリミットを下げる。⇒　上の赤線を跨ぐところが 2011年の質量棄却領域になる。⇒　 142－ 184 GeVの領域を棄却できる。

ＡＴＬＡＳは、 2011年に 135-188 GeVのヒッグス質量を棄却できる。それまでに検出器の校正・理解は十分できるか？解析手法はスムーズに確立できるか？ＣＭＳとの足し合わせはすぐにできるか？

BsBsOscillation Motivation

from Dmd

from Dmd/DmsLower limit on Dms

md~|Vtd |2 (BdBd Oscillation)

constrains a side of unitarity triangle.

By taking ratio md / ms we can rule out theoretical uncertainties and tighten the constraint on unitarity triangle.

Orange band in the plot: the upper limit on |Vtd| is set by the lower limit of ms.

)cos1(2

1)(prob 00 tmeBB s

tss

Frequency ms~|Vts |2

BsBsOscillation Result (355 pb-1)• Oscillation not yet observed.• Frequency scan of the oscillation:

– Fit for A for each ms.– A=1 for true ms.

• Results will be updated very soon!– With double data (765 pb-1).– Newly developed same-side kaon

flavor tagging will improve eD2 by a factor of ~3!!

– Overall eD2=1.6% in current analyses.

ms > 8.6 ps-1 (95% CL limit)

Frequency scan, semileptonic andhadronic channels combined :

CP in

3.2 +/- 1.4%