顶夸克极化和TeV能区新物理

曹庆宏理论物理研究所

Phys. Rev. Lett. 108 (2012) 072002Phys. Rev. Lett. 109 (2012) 152004

报告基于以下工作：

Phys. Rev. Lett. 106 (2011) 201801 合作者： Ed Berger, Chuan-Ren Chen, Chong Sheng Li, Jiang-Hao Yu, Hao Zhang

粒子物理的标准模型已知基本粒子谱

e

⌫e ⌫µ ⌫⌧

µ ⌧

u

d

c

s

t

b

�

Z

W

gh

轻子

夸克

电磁

强

弱

希格斯粒子

SU(3) x SU(2) x U(1)规范对称性

⊗

自旋1/2 自旋1

自旋0

标准模型的两大疑难电弱对称性破缺起源 和 味对称性破缺起源（W 和 Z 质量） （费米子质量）

1019102 103101100 101510�3

e⌫e⌫µ⌫⌧

µ ⌧

ud s b

Z

Wht

普朗克能标

跷跷板能标

大统一能标

顶夸克或许是我们和新物理间的唯一联系

TeV新物理

(GeV)质子质量

费米能标

c

10�9

GeV = 109eV

顶夸克寿命非常短

顶夸克: 标准模型中唯一裸夸克

顶夸克的自旋信息完好地保存在顶夸克衰变产物中

5⇥ 10�27 s

强子化

tW

b

带电轻子倾向于沿着顶夸克自旋方向出射

Tevatron的顶夸克前后不对称性在标准模型中仅在量子辐射修正水平上出现

VOLUME 81, NUMBER 1 P HY S I CA L REV I EW LE T T ER S 6 JULY 1998

Charge Asymmetry in Hadroproduction of Heavy Quarks

J. H. Kühn and G. RodrigoInstitut für Theoretische Teilchenphysik, Universität Karlsruhe, D-76128 Karlsruhe, Germany

(Received 12 February 1998; revised manuscript received 17 April 1998)A sizable difference in the differential production cross section of top and antitop quarks, respectively,

is predicted for hadronically produced heavy quarks. It is of order as

and arises from the interferencebetween charge odd and even amplitudes, respectively. For the Fermilab Tevatron it amounts to upto 15% for the differential distribution in suitable chosen kinematical regions. The resulting integratedforward-backward asymmetry of 4% 5% could be measured in the next round of experiments. Atthe CERN Large Hadron Collider the asymmetry can be studied by selecting appropriately chosenkinematical regions. [S0031-9007(98)06481-3]

PACS numbers: 12.38.Qk, 12.38.Bx, 13.87.Ce, 14.65.Ha

Top quark production at hadron colliders has becomeone of the central issues of theoretical [1] and experimen-tal [2] research. The investigation and understanding ofthe production mechanism is crucial for the determina-tion of the top quark couplings, its mass, and the searchfor new physics involving the top system. A lot of efforthas been invested in the prediction of the total cross sec-tion and, more recently, of inclusive transverse momen-tum distributions [1].In this Letter we will point to a different aspect of the

hadronic production process, which can be studied witha fairly modest sample of quarks. Top quarks producedthrough light quark-antiquark annihilation will exhibita sizable charge asymmetry—an excess of top versusantitop quarks in specific kinematic regions—inducedthrough the interference of the final state with initial-state radiation [Figs. 1(a) and 1(b)] and the interferenceof the box with the lowest-order diagram [Figs. 1(c)and 1(d)]. The asymmetry is thus of order a

s

relativeto the dominant production process. In suitable chosenkinematical regions it reaches up to 15%, the integratedforward-backward asymmetry amounts to 4%–5%. Topquarks are tagged through their decay t ! b W

1 and canthus be distinguished experimentally from antitop quarksthrough the sign of the lepton in the semileptonic modeand eventually also through the b tag. A sample of 100to 200 tagged top quarks should, in fact, be sufficient fora first indication of the effect.Top production at the Fermilab Tevatron is dominated

by quark-antiquark annihilation, hence the charge asym-metry will be reflected not only in the partonic rest framebut also in the center of mass system of proton and an-tiproton. The situation is more intricate for proton-protoncollisions at the CERN Large Hadron Collider (LHC),where no preferred direction is at hand in the laboratoryframe. Nevertheless, it is also in this case possible topick kinematical configurations which allow the study ofthe charge asymmetry.The charge asymmetry has also been investigated in

[3] for a top mass of 45 GeV. There, however, only

the contribution from real gluon emission was consideredrequiring the introduction of a physical cutoff on thegluon energy and rapidity to avoid infrared and collinearsingularities. Experimentally, however, only inclusivetop-antitop production has been studied to date, and theseparation of an additional soft gluon will in general bedifficult. In this Letter, we will therefore include virtualcorrections and consider inclusive distributions only. Wewill see below that the sign of the asymmetry for inclusiveproduction is opposite to the one given for the t

¯

tg processin [3]. The charge asymmetry of heavy flavor productionin quark-antiquark annihilation to bottom quarks was alsodiscussed in [4–6] where its contribution to the forward-backward asymmetry in proton-antiproton collisions wasshown to be very small. In addition, there is also a slightdifference between the distribution of top and antitopquarks in the reaction gq ! t

¯

tq. At the Tevatron itscontribution is below 10

24. (This effect should not beconfused with the large asymmetry in the top quarks’angular or rapidity distribution in this reaction which is atrivial consequence of the asymmetric partonic initial stateand vanishes after summing over the incoming partonbeams.)

(c) (d)

(b)(a)

q

q

Q

Q

FIG. 1. Origin of the QCD charge asymmetry in hadroproduc-tion of heavy quarks: interference of final-state (a) with initial-state (b) gluon bremsstrahlung plus interference of the box (c)with the Born diagram (d).

0031-9007y98y81(1)y49(4)$15.00 © 1998 The American Physical Society 49

t

t

P (q) P (q)

tttt

tt

ttpp

yyyyNyNyNyNA

yNyNyNyN

A

−=Δ=<Δ+>Δ

<Δ−>Δ=

=>+>

>−>=

)9(078.0)0()0()0()0(

)6(051.0)0()0()0()0(

前方后方

2011年国际热点

Tevatron的顶夸克前后不对称性CDF (8.7fb-1):

AinclusiveFB = 0.162± 0.041± 0.022

ANLO+EWFB = 0.066

CDF: 1101.0034

19

VII. DIFFERENTIAL CROSS-SECTION AND PARTON LEVEL RESULTS

Applying our correction procedure to the data yields the di↵erential cross-section shown in Figure 19 comparedto the standard model powheg prediction. We find an inclusive asymmetry of 0.162 ± 0.041 ± 0.022. The |�y|dependence of this distribution is shown in Figure 20, with the di↵erential asymmetry values being summarized inTable XVI. Performing a linear fit to the parton level results, we find a slope ↵�y

= (30.6± 8.6)⇥ 10�2, comparedto an expected slope of 10.3⇥ 10�2. In performing this fit in the data, we utilize the full covariance matrix for thecorrected AFB values when minimizing �2 in order to account for the correlations between bins in the parton leveldistribution. The systematic uncertainties on AFB in each bin are added to the diagonals of the covariance matrix.

yΔParton Level 0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 2

FBA

0

0.2

0.4

0.6

-1CDF Run II Preliminary L = 8.7 fb

l+Jets Data

tNLO (QCD+EW) t

yΔParton Level 0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 2

FBA

0

0.2

0.4

0.6

-1CDF Run II Preliminary L = 8.7 fb

l+Jets Data-210× 8.6)± = (30.6 yΔα

(Correlated Uncertainties)tNLO (QCD+EW) t

-210× = 10.3yΔα

FIG. 20: Parton level AFB as a function of |�y| (left) and the same distribution with a best-fit line superimposed (right).

CDF Run II Preliminary L = 8.7 fb�1

Parton Level Data NLO (QCD+EW) tt|�y| AFB (± stat. ± syst.) AFB

Inclusive 0.162 ± 0.041 ± 0.022 0.066< 0.5 0.037 ± 0.035 ± 0.020 0.023

0.5� 1.0 0.163 ± 0.058 ± 0.036 0.0721.0� 1.5 0.384 ± 0.084 ± 0.041 0.119� 1.5 0.547 ± 0.140 ± 0.085 0.185< 1.0 0.088 ± 0.042 ± 0.022 0.043� 1.0 0.433 ± 0.097 ± 0.050 0.139

Data NLO (QCD+EW) ttSlope ↵�y of Best-Fit Line (30.6 ± 8.6)⇥ 10�2 10.3⇥ 10�2

TABLE XVI: Measured and predicted parton level asymmetries as a function of |�y|.

We also can determine the parton level mass dependence of AFB by correcting the �y and Mtt

distributionssimultaneously. Doing so yields the M

tt

distributions for forward and backward events shown in Figure 21. Thesedistributions can then be combined to determine the di↵erential AFB as a function of M

tt

shown in Figure 22and summarized in Table XVII. The best fit line to the parton level data has a slope ↵

Mtt= (15.6 ± 5.0)⇥ 10�4,

compared to the powheg prediction of 3.3⇥ 10�4.

A. Comparison to Previous Results

In the 5.3 fb�1 version of this analysis, parton level di↵erential asymmetries were considered in two bins of |�y|(above and below 1.0) and two bins of M

tt

(above and below 450 GeV/c2). In Table XVIII, we provide the parton

20

)2 (GeV/ctt

Parton Level M350 400 450 500 550 600 650 700 750

(pb)

y)Δ)d

(tt

d(M

σ2 d

0

0.5

1

1.5

2

2.5 y > 0Δl+Jets Data,

y < 0Δl+Jets Data,

-1CDF Run II Preliminary L = 8.7 fb

FIG. 21: Parton level Mtt distributions for events with positive and negative �y.

)2 (GeV/cttParton Level M350 400 450 500 550 600 650 700 750

FBA

0

0.1

0.2

0.3

0.4

0.5

0.6

-1CDF Run II Preliminary L = 8.7 fb

l+Jets Data

tNLO (QCD+EW) t

)2 (GeV/cttParton Level M350 400 450 500 550 600 650 700 750

FBA

0

0.1

0.2

0.3

0.4

0.5

0.6

-1CDF Run II Preliminary L = 8.7 fb

l+Jets Data-410× 5.0)± = (15.6

ttMα(Correlated Uncertainties)

tNLO (QCD+EW) t-410× = 3.3

ttMα

FIG. 22: Parton level AFB as a function of Mtt (left) and the same distribution with a best-fit line superimposed (right).

level results from this analysis with the same divisions into two bins in order to directly compare to the previousanalysis. The change in central values across the two bins has been reduced somewhat compared to the previousanalysis, but the trend of growth of the asymmetry with mass and |�y| remains.

VIII. CONCLUSIONS

We have studied the forward-backward asymmetry AFB in top quark pair production in the full CDF dataset.In the full dataset, we observe a raw asymmetry of 0.066 ± 0.020, and an approximately linear dependence onboth |�y| and M

tt

. After subtracting o↵ the predicted background contribution, we determine the significance ofthe rapidity and mass dependence by comparing the best fit slopes in the data to the standard model powheg

prediction, finding a p-value of 0.00892 for AFB as a function of |�y| and a p-value of 0.00646 for AFB as a functionof M

tt

. Finally, we correct our results to the parton level to find the di↵erential cross-section in �y and allow

标准模型预言值

带电轻子的前后不对称性 A`FB

P (q) P (q)

`+

~pt

t

`+

前方后方

标准模型理论预言:

A`FB = 0.021± 0.001

AtFB = 0.051± 0.001

A`FB

AtFB

�����SM

⇠ 1

2

D0: AtFB = 0.196± 0.065

A`FB = 0.152± 0.040

A`FB

AtFB

�����D0

⇠ 3

4

CDF:(8.7fb-1)

A`FB

AtFB

�����>450

⇠ 3

5A`

FB

AtFB

�����inc

⇠ 3

4

A`FB = 0.066± 0.025

AtFB = 0.085± 0.025

P (q) P (q)

`+

~pt

t

`+

前方后方

AtFB A`

FB和 的关联

源于顶夸克极化和带电轻子的自旋关联效应Phys. Rev. Lett. 108 (2012) 072002

AtFB A`

FB和 的关联

=

8>>>>>><

>>>>>>:

1

2

+

1

2

�1 + ��2

coth

2 yt�1/2 +

�t coth2 yt

4��2�1 + ��2

coth

2 yt�3/2 , (yt > 0)

1

2

� 1

2

�1 + ��2

coth

2 yt�1/2 � �t coth

2 yt

4��2�1 + ��2

coth

2 yt�3/2 , (yt < 0)

R�tF (�, yt)

精简的解析表达式

A`FB ⇡ ⇢tLA

tLFB ⇥

�2RtL

C � 1�+⇢tRA

tRFB ⇥

�2RtR

C � 1�

AtFB ⇡

⇥⇢tL AtL

FB + ⇢tR AtRFB

⇤

| {z }0

| {z }1

标准模型：⇢tL = ⇢tR = 12

AtLFB = AtR

FB

A`FB

AtFB

�����SM

⇠ 1

2

顶夸克AFB的新物理解释

标准模型胶子

味守恒的新轴矢胶子

味改变的新玻色子

味改变中性流Z-prime已被CMS实验排除

200 400 600 800 1000mZ’ (GeV)

0

1

2

3

4

5

6

7

8

f R (b)

5000 events

1000 events

5m3m

100 events

3

We used the external model interface in the MADGRAPH [28] event generator to calculate atthe leading order (LO) the tt + ttj cross section as a function of fR and MZ0. In this calculationwe used the CTEQ6L [29] parton distribution functions (PDFs), fixed the top quark mass Mtopto be 172.5 GeV, and set the renormalization and factorization scales to be µ = Mtop.

MADGRAPH was also used to generate pp!tt and pp!ttj events according to the diagrams ofFig. 2. These events were then processed by PYTHIA [30] for parton showering, followed by theCMS parametrized event simulation, and the same chain of reconstruction and analysis pro-grams used for collision data. The event selection efficiency, including all relevant branchingratios, is (0.95 ± 0.13)%, independent of Z0 mass. Note that the branching ratio for tt! `nb`nb(` = e, µ) is 4.54% [31], but our selection is also sensitive to leptons from tau decays. The frac-tional systematic uncertainty on the event selection efficiencies was calculated as in Ref. [1],and its components are summarized in Table 1.

Table 1: Fractional systematic uncertainties on the pp ! tt(j) signal selection. ISR/FSR denote initialand final state radiation.

Source ee µµ eµ allLepton selection 11.8% 10.6% 10.8% 10.7%Energy scale 8% 8% 8% 8%ISR/FSR and PDF 3% 3% 3% 3%Total without luminosity 14.6% 13.6% 13.8 13.7%Integrated luminosity 4% 4% 4% 4%Total 15% 14% 14% 14%

(GeV)Z'm200 400 600 800 1000 1200 1400 1600 1800 2000

Rf

00.5

11.5

22.5

33.5

44.5

5

, Berger et al.FB consistent with Aσ1

, Berger et al.FB consistent with Aσ2

Combined Observed Limit tt + ttj

= 7 TeVs, -1 = 35 pbintCMS L

Figure 3: The exclusion region at 95% CL as a function of Z0 mass for various choices of theright-handed coupling fR in the Lagrangian of Eq. (1). We also show the region of parameterspace consistent with the Tevatron measurements of AFB and s(tt) as inferred in Ref. [9].

We compute the upper limits using a Bayesian method [31]. We assume a flat prior for thesignal strength and a log-normal distribution for the nuisance parameters. The 95% CL upperlimit on the number of signal events is 5.7 using a 14% uncertainty on the signal efficiency(Table 1). The expected upper limit is 4.4+1.4

�1.3 events. The limit on the cross section is s(pp !

Phys. Rev. Lett. 106 (2011) 201801 CMS实验组 JHEP 1108 (2011) 005

三类新物理模型

源于顶夸克极化和带电轻子的自旋关联效应

Phys. Rev. Lett. 108 (2012) 072002

(%)tFBA

10 12 14 16 18 20 22 24 26 28 30 (%

)l FBA

0

2

4

6

8

10

12

14

16

18

20

(200GeV,400GeV)

(400GeV,600GeV)

(600GeV,800GeV)

(800GeV,1000GeV)

(b)

(%)tFBA

10 12 14 16 18 20 22 24 26 28 30

(%)

l FBA

0

2

4

6

8

10

12

14

16

18

20

(800GeV,1000GeV)

(1000GeV,1200GeV)

(1200GeV,1400GeV)

(1400GeV,1600GeV)

(1600GeV,2500GeV)

(a) G0 W 0

AtFB A`

FB和 的关联

A`FB ' 3

4⇥At

FBA`FB ' 1

2⇥At

FB

无极化的顶夸克 右手极化的顶夸克

顶夸克对和暗物质联合产生

P P

实验困境： 末态中含有三个 无法观测的粒子

DM: 暗物质t

b `+

⌫

DM

?

t

b

jj

DM

?

带电轻子的能量和空间角分布在顶夸克静止系中

�t = +

�t = �右手顶夸克左手顶夸克

`+

t~st ~pt

✓

( )

helecos-1 -0.5 0 0.5 1

hel

e/dcos

Kd-1

K

00.10.20.30.40.50.60.70.80.91

RtLt

(a) tL tR

当顶夸克运动时，带电轻子的能量和空间角纠缠起来。

d�

dxd cos ✓

=

↵

2Wmt

32⇡AB

x(1� x)Arctan

Ax

B � x

�1 + st cos ✓

2

x ⌘ E`/Et能量（ ） 极化角

带电轻子的能量敏感依赖于顶夸克极化性质

d�(st)

dx

=↵

2Wmt

64⇡AB

Z zmax

zmin

x�

2[1� x�

2(1� z�)]

⇥✓1 + st

z � �

1� z�

◆Arctan

Ax�

2(1� z�)

B � x�

2(1� z�)

�dz

A =�W

mWB =

m2W

m2t

⇡ 0.216

� =Et

mt� =

p1� 1/�2

zmin = max[(1� 1/�

2x)/�,�1]

z

max

= min[(1�B/�

2

x)/�, 1] 0 0.5 1 1.5 2xl

0

1

2

3

1/K

dK/x

l

Et = 250 GeV (tL)Et = 250 GeV (tR)Et = 500 GeV (tL)Et = 500 GeV (tR)Et = 1000 GeV (tL)Et = 1000 GeV (tR)

x = 2E`/Et

Phys. Rev. Lett. 109 (2012) 152004

此方法被人们忽视了近20年

分布可以区分 和R0 tL tR

cx’0 0.5 1 1.5 2

R’

0

0.2

0.4

0.6

0.8

1

in lab after cutsl: x’Lt

in lab after cutsl: x’Rt

R and tL

(b) tLt

Rt

14 TeV100fb-1

pp ! t˜t ! tt�0 ˜�0 ! bbjj`+ 6ET

pp ! TT ! ttAHAH ! bbjj`+ 6ET

最小超对称模型：

T-宇称守恒的小希格斯模型：

顶夸克对和暗物质联合产生

t

P P

b `+

⌫

t

b

jj

DM

DM

?

?

✓不依赖于未知的暗物质质量和自旋

✓不依赖于未知的新物理粒子质量和自旋

✓不依赖于对撞机能量

探测新物理粒子，暗物质和顶夸克的相互作用手征性

顶夸克和TeV能区新物理展望

Gluino

Exoticcoloredstates

4th Gen

Vector-likeQuark

Z’ W’

顶夸克

FCNC

G’

ChargedHiggs

AFB

Extra gauge bosons

New heavyquarks

CP

Heavy quark production via pQCD

谢谢！