Đối xứng và phá vỡ đối xứng trong vật lý hạt cơ bản

Muc dich va noi dung nghien cuti: Nghien cihi cac he qua vat ly cua cac mo hinh ly thuyet ma rong mSu chuan dugc xay dung tren ca sa cac nhom doi xiing, Dua ra cac ket luan can thiet c

DAI HOC QUOC GIA HA NOI

TRl/CfNG DAI HOC KHOA HOC TV NHIEN

DE TAI:

BOI X l ^ G VA PHA V d DOi XCHVG TRO]\G VAT LY HAT CO BAPV

MA SO: QT.07.13

CHU TRI DE TAI : PGS.TS Ha Huy Bang

PGS.TS Dang Van Soa

Cu nhan Nguyen Thi Thu Hucfng

A ! HOC Q U O C GIA HA NOI

i r<'UNG l A r / T H O N G TIN TH'J ViEN

Dl / 1K)

HA NOI - 2008

BAG CAO TOM TAT TINH HINH

VA KET QUA THUC HIEN DE TAI NAM 2008

• •

1 Ten de tai: Dot xirng vdphd vddoi xirng trong vat ly hat caban

Ma so: QT.07.13

2 Chu tri de tai: PGS.TS Ha Huy Bang

3 Cac can bo tham gia: GS.TS Hoang Ngoc Long, PGS.TS Dang Van

Soa, Cu nhan Nguydn Thi Thu Huong

4 Muc dich va noi dung nghien cuti:

Nghien cihi cac he qua vat ly cua cac mo hinh ly thuyet ma rong mSu chuan dugc xay dung tren ca sa cac nhom doi xiing,

Dua ra cac ket luan can thiet cho thuc nghiem nhSm phat hien cac hat m6i duac tien doan tu ly thuyet

5 Tinh hinh thuc hien de tai:

Xay dung ly thuyet cac tuang tac la noi dung chinh cua vat ly cac hat ca ban MSu chuan cua cac tuang tac dien tur yeu ra d5i danh dau mot budc ngoat trong vat ly va da rat thanh cong ve phuang dien thuc nghiem Tuy nhien no van khong tra lai duac mot so van d^ ly thuyet quan trong va do do can duac

ma rong Cac mau chuan ma rong gan day duac xay dung tren ca sa sieu doi xung hoa mau chuan dang duac cac nha vat ly quan tam nghien cuu vi c6 nhieu uu diem dang chu y Di theo hu6ng nghien cuu nay chung toi da dat duac cac ket qua chinh sau day:

- Tinh duac hieu chinh mot vung vao cac qua tiinh sinh axion va axino tCr cac qua trinh huy e'^e" Su hieu chinh la kha rong, do do sir hieu chinh la quan trong

- Xem xet dai so Heisenberg - Weyl va thong ke para-Bose khi tham so q tra thanh toan tu g Xay dung nen cac trang thai coherent va suy ra ket qua hay la chiing c6 dang tuang tu vai truong hap thong ke q - para - Bose

Bdnh gid chung:

- De tai thuc hien dung tien do va dat chat lugng cao Cac ket qua cua de

tai da dugfc cong bo a 2 bai bao dang tren tap chi Communications in Physics,

1 bai gui dang a Tap chi Physical Review D Cu the la:

1) Ha Huy Bang, Nguyen Thi Thu Huong, ''One loop corrections to axion production in e'^e' annihilation", Communications in Physics, vol 17, N3 (2007), 137

2) Ha Huy Bang, Phan Thi Bich Loi, "Remarks on the g - deformed operators and their properties", Communications in Physics, vol 17, N3 (2007), 145

3) Nguyen Thi Thu Huong, E R Siegel, et al, "Dark natter on the

smallest scales", trong tuyen tap bao cao Hoi nghj ve Vu tru hoc, a Les

Houches, France

De tai ddgop phan ddo tao:

03 Tien si: Dao Thi Le Thuy, Nguy6n Thi Thu Huang, Tran Minh Hieu

01 Thac si: Trieu Quynh Trang

06 Cu nhan: Nguyen Quang Huy, Thanh Thu Hang, Nguydn Thu Hucmg, Phan Thi Bich Lai, Can Kim Ngan, Nguyen Cong Kien

6 Tinh hinh six dung kinh phi cua de tai:

- Duac duyet va cap:

- Da chi cho cac khoan sau:

+ Thue lao dong trong nude

+ Thue dich tai lieu

+ Cong tac phi va hoi nghj

+ Thanh toan tien dien, nu6c

+ Quan ly phi ca sa

+ H6 tra dao tao va NCKH

20.000.000 dong

12.000.000 dong 1.800.000 dong 2.000.000 dong 800.000 dong 800.000 dong 600.000 dong

Khoa Vat ly

PGS.TS Nguyen The Binh

Chu tri de tai

VIETNAM NATIONAL UNIVERSITY

<<••::•• VIETNAM NATIONAL UNIVERSITY

REPORT ON THE SITUATION AND THE RESULTS OF THE PROJECT

1 Title of the project: Summetry and breaking summetry in particle physics

Code: QT.07.13

2 Director of project: Asso Prof Dr Ha Huy Bang

3 Participants: Prof Dr Hoang Ngoc Long, Dr Nguyen Anh Ky,

Asso Prof Dr Dang Van Soa, B.Sc Nguyen Thi Thu Huong,

4 Aim and content of researchers:

Studying physical consequences of beyond standard model based on extended symmetric groups Deriving conclusions for experiences to find new particles that predicted from theories

5 Scheme for the project:

Constructing the theory of interactions is main aim of particle physics The standard model of the electroweak interations has been considered an extremely successful theory from the phenomenological point of view However, this model contains a large number of unanswered questions and its generalization is necessary The recent proposed models based on supersymmetric standard model have the nice features and have been obtained many attentions

In this direction, we have obtained the main results as follows:

We calculate the one-loop corrections to the production of axion and axino in eV annihilation We find that the corrections are rather large, which can reach about - 50% In this process it has turned out that these corrections are important

We consider g, a, a"*" operators, we show that the number operator N obeys the ralations like the case of undeformed N Next, we consider the g - deformed para-Bose statistics and construct its coherent states Interestingly, they are similar to the ones of the case of q-deformed para-Bose statistics

6 The using of the fund:

- Total fund is allowed and obtained:

THE DIRECTOR OF THE PROJECT

Asso Prof Dr Ha Huy Bang

VIETNAM NATIONAL UNIVERSITY

REPORT ON THE SITUATION AND THE RESULTS OF THE PROJECT

1 Title of the project: Summetry and breaking summetry in particle physics

Code: QT.07.13

2 Director of project: Asso Prof Dr Ha Huy Bang

3 Participants: Prof Dr Hoang Ngoc Long, Dr Nguyen Anh Ky,

Asso Prof Dr Dang Van Soa, B.Sc Nguyen Thi Thu Huong,

4 Aim and content of researchers:

Studying physical consequences of beyond standard model based on extended symmetric groups Deriving conclusions for experiences to find new particles that predicted from theories

5 Scheme for the project:

Constructing the theory of interactions is main aim of particle physics The standard model of the electroweak interations has been considered an extremely successful theory from the phenomenological point of view However, this model contains a large number of unanswered questions and its generalization is necessary The recent proposed models based on supersymmetric standard model have the nice features and have been obtained many attentions

In this direction, we have obtained the main results as follows:

We calculate the one-loop corrections to the production of axion and axino in e'^e" annihilation We find that the corrections are rather large, which can reach about - 50% In this process it has tumed out that these corrections are important

We consider g, a, a"^ operators, we show that the number operator N obeys the ralations like the case of undeformed N Next, we consider the g - deformed para-Bose statistics and construct its coherent states Interestingly, they are similar to the ones of the case of q-deformed para-Bose statistics

P H A N C H I N H BAO C A O

1 MUC LUC

Bao cao torn tat (phan tieng Viet)

Bao cao tom tat (phan tieng Anh)

PhSn chinh bao cao

Mucluc

Ma dau

Noi dung chinh

Ket luan

Tai lieu tham khao

Cac bai bao khoa hoc

Phieu dang ky

2 M 6 DAU

Cho den nay ngu6i ta biet rang, giua cac hat co ban ton tai 4 loai tucmg tac: tirang tac manh, tuang tac yeu, tuang tac dien tur va tuang tac hap dan xay dung ly thuyet cac tuang tac la noidung chinh cua vat ly c6 hat ca barj Y tuofng cua Einstein v6 van de ihong nha't tat ca cac tuang tac vat ly c6 trong tu nhiSn dong thdi cung la u6c ma chung cua tat ca cac nha vat ly hien nay Ly thuyet Maxwell m6 ta cac hien tuang di6n va ttr mot each thong nha't trong khuon kh6 cua tuang tac di6n tir M6t bu6c ngoat dang ke khi Glashow, Weinberg va Salam dua ra duac mo hinh thong nha't tuang tac y6'u va tuang tac dien tCr tren ca sd nhom gauge SU^ (2)®Uy (1) Viec phat hien cac boson gauge vecta truy6n tuang tac yeu V/", Z^phii hap vol tien doan cua ly thuyet

da khang dinh cho tinh dung dan cua mo hinh, Cac tuang tac manh cung dugc

mo ta rat thanh cong trong khuon kho cua sac dong hoc lugng tu (QCD) dua tren nhom gauge SU^ (3) Mot each tu nhien, mSu chuan (SM - Standard Model) da ra ddi tren ca sa nhom gauge SU,(3)®SU,(2)®Uy(i) nham thong nhat ttrang tac manh va tuang tac dien tuf - yeu Mau chuan da chung to la mot

ly thuyet tot khi ma hau het cac du doan cua no da dugc thuc nghiem khang dinh a vung nang lugng < 200 GeV

Mac du vay, no vSn con iihieu han che, tru6c het la lien quan den qua trinh xay ra a vung nang lirgng cao han va han nua la chua giai quyet dugc mot so van de ly thuyet cua ban than mo hinh nhu: cac hat dugc dua ra bang tay vao cac da tuyen cua nhom gauge, c6 mot so 16n cac tham so nhu cac hang

so tirang tac va khoi lugng Nhirng han che nay dan den su can thiet phai nghien ciiu cac mfiu chuan ma rong

Cac ly thuyet thong nhat vl dai (GUTs) ve nguyen tac phai dugc dac irung bang hang so tuang tac duy nhat Ly thuyet nay da cai Ihien dugc tinh hinh noi tren va c6 the giai thich sir bat doi xiing vat cliat - phan vat chat hien nay trong vu tru nha cac lu'c tirang tac vi pham so baryon B No da chi ra each giai thich do pho bien cua He trong vu tru Ngoai ra, cac ly thuyet thong nhat

16n kh6ng mau thuSn (tham chi con phu hgp) v6i gia thiet cac hat natrino c6 kh6i lugng nho vao ca vai chuc eV, di6u nay c6 the dong gop vao viec giai quye't van d^ kh6i lugng an (vat cha't toi)

Ly thuy6't thong nha't vi dai (GUTs) thuc ra cung con nhieu van d6, trong

do n6i c6m nha't theo hu6ng thong nha't cac tuang tac la no chua da dong gi den tuang tac hap din De giai quyet van de nay, ngu5i ta da sir dung them m6t ytucfng m6i, do la y tuang ve si6u doi xiing, dugc de xuat vao nhung oam

70 Sieu doi xiing la doi xu:ng duy nha't da biet c6 the lien h6 cac hat v6i spin khac nhau la boson va fermion No chiing to la quan trong trong nhieu linh vuc phat trien cua vat ly ly thuyet 6 giai doan hien nay, vi du nhu trong ly thuyet day Ngoai ra con c6 nhiSu nguyen nhan ve mat hien tugng luan lam

cho si6u doi xirng tra nen hap dan Thu: nhStt la, no hua hen giai quyet van di

hierachy con ton tai trong mSu chuan: hang so tuang tac dien tu la qua nho so vdi hang so planck Tliii hai la, trong ly thuyet sieu doi xung, hat Higgs c6 the xua't hien mot each tu nhien nhu hat v6 hudng ca ban va nhe Phan ky bac hai lien quan den khoi lugng ciia no tu dong bi loai bo bai phan ky nhu vay nay siiih tCr cac fermion Hon nua, trong su ma rong sieu doi xiing cua mau chuan, tuang tac Yukawa gop phan tao nen ca che pha va doi xiing dien tu yeu

Mot he qua rat quan trong trong ly thuyet lugng tu, do la b6 chinh vong Viec tinh bo chinh vong da dan den su phii hgp rat tot giua ly thuyet va thirc nghiem trong viec tinh momen tCr di thuo'ng va dich chuyen Lamb Mac du hang so tirang tac trong QED la be — ma da c6 sir phii hgp tuyet v5i nhu vay Tiep theo, trong QCD va cac ly thuyet thong nhat, viec tinh den bo chinh vong Ccin thiet Tuy nhien ky thuat tinh toan se tra nen phiic tap han nhieu so vo'i truong hgp QED

Vi pham doi xung CP xuat hien mot each tu nhien trong the he thu.ba ci!]a nifiu chuan va ton tc7i a pha cua ma tran CKM Cac ket qua nghien cuii gan day cho tha'y anh huang ciia vi pham doi xung CP cung nhu viec tinh den bo

^W HOC QUOC GtA HA NOI

i rpuNG TAM T H O N G T I N T H U V I | N

1 T)T / f'^O'^

chinh vong cua cac qua trinh vat ly trong cac mau thuin sieu doi xiing la khong nho va c6 y nghia v6 cung quan trong vdi thuc nghiem

Trong cac mau thuSn sieu doi xutig, fermion luon cap vdd boson nen so hat da tang len Cac tien bo v^ mat thuc nghi6m doi v6i viec do chinh xac cac hang so tuang tac cho phep ta timg bu6c kiem tra lai cac mo hinh thong nhat

da CO Han mu5i nam sau giai quyet cac ly thuyS't thong nhat sieu doi xumg, cac s6 lieu tiir LEP da khang dinh rang cac mo hinh sieu doi xutig cho ket qua

ra't tot tai diim dan (single point) Tuy nhien cho tofi nay, thuc nghiem chua

phat hien dugc hat nao trong cac ban dong hanh sieu doi ximg cua cac hat da

biet Do nghien cuu do, mot trong nhung wSin de c6 tinh th5i su cua vat ly hat

ca ban hien nay la nghien curu cac qua trinh vat ly trong do c6 su tham gia cua cac hat dugc doan nhan trong cac mau chuan sieu doi xutig de hy vong tim dugc chiing tir thuc nghiem Nhimg qua trinh vat ly dugc thuc hien quan tam hang dau phai ke den la cac qua trinh va cham e^e", va cham |i^|i' va cac qua trinh phan ra cua cac hat m6i

Nam 1977 van d6 strong CP dugc giai quyet bang ca che Peccei Quinn (PQ) Theo ca che nay thanh phan vi pham strong - CP 0 (0 < 10'^) dugc thay bang mot trucmg gia v6 hu6ng goi la trucmg axion va no la mot gia boson - Goldstone Axion la mot hat nhe c6 khoi lugng quan sat trong khoang lO'^eV den lO'^eV Dac tinh cua axion la tuang tac yeu v6i vat chat, nhung no

-CO mot vai tro quan trong trong vat cha't toi (dark matter) Axion c6 the xuat hien trong nhi^u mo hinh khac nhau ma dang ke nhat la xuat hien nhu pha mdi cua trucmg Higgs trong ly thuyet dien - yeu, hoac xua't hien nhu mot thanh ph^n ciia sieu trucmg chiral trong ly thuyet sieu doi xiing (SUSY = supersymmetry) nang lugng thap

Trong mo hinh SUSY v6i N = 1, axion con c6 ban dong hanh sieu doi xumg la axion Di^u dang chii y nha't cua axion la hat sieu doi xiing nhe nhat (LSP), khoi lugng ciia no phu thuoc vao mlu, nhung gia tri dang tin cay han

ca la trong vai keV Cung nhu axion, axino tuang tac rat yeu vdi cac hat thong thucmg va dong vai tro quan trong trong vat chat toi Cac nghien ciiu v6 axino

cho thay, cung vdi axion no dong gop khoang 80% ± 20% cua mat do nang lugng t6i han

I Trong nhutig nam g^n day viec nghien ciiu ve axino trong vu tru tra nen

j kha soi noi va da thu dugc m6t so ket qua quan trong Tuy nhien, viec nghien

ciiu ve axino phai dugc tiep tuc va chiing toi cho rang axino c6 kha nang dugc phat hien trong dieu kien phong thi nghiem

3 NOI DUNG CHINH

Di tai nghien ciiu thuoc phuang hudrng "Ly thuyet thong nhat cac tuang

tac cua hat sa ca'p" tren ca s6 sieu d6'i xiing hoa miu chuan Cac nghien ciiu theo hudng nay cua de tai cho phep tiep can cac phuang phap toan hoc mdi phat trien manh trong thdi ky g^n day va dugc ap dung trong vat ly ca ban: phuang phap khir phan ky, phuang phap giai tich so

De tai nghien ciiu su sinh axion va axino tir cac va cham e'^e" Tiep theo, chiing t6i cung xem xet va'n de chat toi 6 khoang each nho va thao luan kha nang tao chat toi a khoang each nho Ngoai ra, chiing toi cung kham pha ra cac ling cir vien da dang cho cha't toi va xac dinh cac tinh cha't tuang ling

De tai cung xem xet cac toan tu bien dang N, a, a*^ vdi cac dieu kien mdi

va ca'u triic nen cac trang thai coherent cho toan tir huy Cac toan tir nay se cd nhieu dug dung trong nhieu va'n de cua vat ly

4 K £ T LUAN

Cac ket qua cua de tai cd ich trong viec tim kiem cac hat mdi va lam sang

to ban cha't cua chat toi trong vu tru Va'n de can dugc trien khai tiep tuc trong thdi gian tdi

TAI LIEU THAM KHAO

1 Bartl A et al.,"Geneial Flavor Blind MSSM and CP Violation",

hep-ph/0103324

2 Bartl A et al., "T- Slepton and T- Sneutrino in the MSSM with Complex

Parameters", hep-ph/0207186

3 Bartl A., Hesselbach S., Hidaka K and Prod W., "Top Squaik and Bottom

Squark in the MSSM with Complex Parameters", hep - ph/0311338

4 Bartl A et al., "Impact of CP phases on the search for top and bottom

squark", hep - ph/0409347

5 Be'langer G Boudjema F and Sridhar K., "SUSY Higgs at the LHC:

large stop mixing effects and associated profduction", hep - ph/9904348

6 Be'langer G et al., "Z radiation off stop at a linear collider", hep

-ph/99(LAPTH - 704/99)

7 Be'langer G et al., "Associated stop Higgs Production at the Linear

Collider and Extraction of the stop Parameters", hep -ph/9811334

8 Branco G C (1997), "Flavour Physics", 1996 European School of High

-Energy Physucs, Cern - Geneva, phuang phap 143-162

9 BranGoG.C.etal (1999), CP Violation, Clarendon, Oxford

10 Buras A J et al., " K^ - ify v _and K,^ K* -.7c° Decay in the

General MSSM", hep - ph/0408142

11 Choi S Y et al., "Loop Correction to the Neutral Higgs Bosson Sector of

the MSSM with Explicit CP Violation" hep - ph/0002287

12 Choi S Y et al., " Chargino Pair Production at e^ e" colliders with

Polaried Beams" hep - ph/0001175

13 Christova E and Fabbrichesi M (1993), "T Violation Induced by

Supersymmetry in tt" and V / ' W Phys Lclt., B315,phuong phap 338-348

Liiiiiuiiications in Physics, Vol 17, No 3 (2007), pp 137-144

ids.:yj

ONE-LOOP C O R R E C T I O N S TO AXION P R O D U C T I O N IN e+e Hiru m - ANNIHILATION

1, I'Ai •:' 'I HA HUY BANG AND NGUYEN THI THU HUONG

Laboratory for High Energy Physics and Cosmology, Department of Physics, Vietnam National University,

334 Nguyen Trai, Hanoi, Vietnam

A b s t r a c t We calculate the one-loop corrections to the production of axion in e'^e~ annihilation

We find that the corrections are rather large, which can reach about -50% In this process it has tumed out that these corrections are important

L I N T R O D U C T I O N

Axion hypothesis has remained to be one of the big open questions in particle physics for almost 30 years Conceived initially to resolve the problem of strong CP violation in QCD, the axion has gradually become also one of the candidates for cold dark matter in the universe

Recently, the PVLAS collaboration has observed anomaly in behavior of the linearly polarized laser beams propagating through a strong magnetic field in vacuum- the observed miniscule rotation of the polarization plane (dichroism) can be interpreted a^ due to the axion production in the Primakoff process (i.e via photon - photon fusion) [1]

Another, very complementary technique of detecting photon - axion interactions, is based on the so-called photon regeneration, or light shining through walls concept [2].It requires a strong source of axions and an isolated detector next to a zone of strong magnetic field - as argued below, such a photon regeneration experiment could be performed at HERA with modest effort and at low cost, and would provide an important verification of the PVLAS axion interpretation

In [3], we have considered photon-axion conversions in statics magnetic fields and in

a periodic field with frequency equal to the axion mass by the Feynman diagram methods The differential cross-sections are presented and numerical evaluations are given It is shown that there is a resonant conversion for the considered process Some estimates for experimental conditions are given from our results

It is well-known that the e"*"e~ colliders have been playing complementary roles to the hadron colliders in high energy experiments In general, e^e~ colliders have reasonable signal rates in a clean environment with a definite center-of-mass energy, enabling us

to perform precision measurements of particle masses, lifetimes, and various differential cross-sections, while hadron colliders provide opportunities to quickly survey high energy frontier In [4] the cross-section for the production or axion in e'^e" collisions at tree level were calculated

In the supersymmetric extension of the axion model, the axion supermultiplet $

can be written by $ = 5 -h ia -h y/29d -\- 9'^F^, where a denotes an axion, s a saxion and

d an axino

UINh>LUOP CORRECTIONS TO AXION PRODUCTION 139

The self-energy correction is as follows

138 HA HUY BANG AND NGL^EN THI THU HUONG

Very recently, the tree-level results of the cross-section for the production of saxion

in e'^e~ annihilation have been discussed [5] However, the one-loop corrections to the

results of [4, 5] have not been calculated so far

In this paper, we will calculate the one-loop corrections to the cross-section of the

process e'^e" —*• a-y We point out that one-loop corrections to tree-level cross-section are

rather large and remarkable They can reach about —50%

The paper is organized a^ follows In the Sec 2 w^e present the tree-level results

Next, we will give the analytical results for the one-loop correction in Sec 3 We make a

numerical analysis with drawing some conclusions for our calculations in Sec 4 A short

conclusion is given in Sec 5 For completeness, we will list in t h e Appendix the scalar

one-, two-, three- point functions which appear in our results

11 N O T A T I O N S A N D T R E E - L E V E L R E S U L T S

The production of axion and photon in e'^e~ collisions proceeds through s-channel

photon exchange The interaction of a ajcion with two photons is described by the

La-grangian [6]

La-y-y = gy—y-F^iyF , (1)

where 0a is the axion field, rria its mass, F^^^ = ^t^^paF^, and the axion decay constant

defined in terms of the £Lxion mass rria by [6, 7]

fa = fnTriT, ^ymumd[7na{my, + md)]~^

The coupling constant in (1) is model-dependent In the Dine-Fishler-Srednicki-Zhitnitskii

(DFSZ) model [8]: g^{DFSZ) ^ 0.36 and in the Kim-Shifman-Vainshtein-Zakharov model

[9]: g - 7 ( / ^ 5 K Z ) - - 0 9 7

Fig 1 Tree level diagram for the process e"'"e" —• 07

At high-energy limit, the lowest order cross-section is given by

where ^ = ^ ^ IQ-'^^GeV-'^

III O N E - L O O P C O R R E C T I O N S

I I I l S e l f - e n e r g y c o r r e c t i o n s

Since external self-energies do not contribute on the complete one-shell

renormaliza-tion scheme, the only relevant self-energy in.serrenormaliza-tions are those corresponding to the internal

photon hnes At the one-loop level also a mixing appears between photon and Z

ONE-LOOP CORRECTIONS TO AXION PRODUCTION 139

The self-energy correction is as follows

140 HA HUY BANG AND NGUYEN THI THU HUONG

ONE-LOOP CORRECTIONS TO AXION PRODUCTION 141

Bs Yl IZZ^.i^^ooiKm^^m^.) - - e - 4k'^Bi{k,m^^,m^^) otS' V 2

(16)

(17)

Let US now discuss the vertex corrections due t o sneutrinos exchange, neutralinos

ex-changes, neutrinos and j^X exchanges T h e corresponding Feynman diagrams are shown