NLO corrections to the pair production of supersymmetric particles

The analysis of recent experimental data received from LHC (CMS) restricts the range of MSSM parameters. Using computer programs SOFTSUSY, SDECAY the mass spectrum and partial width of superpatners are calculated. With the help of computer program PROSPINO the calculations of the next-to-leading ord...

Ausführliche Beschreibung

Gespeichert in:

Bibliographische Detailangaben
Datum:	2014
Hauptverfasser:	Obikhod, T.V., Verbytskyy, A.A.
Format:	Artikel
Sprache:	English
Veröffentlicht:	Національний науковий центр «Харківський фізико-технічний інститут» НАН України 2014
Schriftenreihe:	Вопросы атомной науки и техники
Schlagworte:	Ядерная физика и элементарные частицы
Online Zugang:	http://dspace.nbuv.gov.ua/handle/123456789/80367
Tags:	Tag hinzufügen Keine Tags, Fügen Sie den ersten Tag hinzu!
Назва журналу:	Digital Library of Periodicals of National Academy of Sciences of Ukraine
Zitieren:	NLO corrections to the pair production of supersymmetric particles / T. V. Obikhod, A.A. Verbytskyy // Вопросы атомной науки и техники. — 2014. — № 5. — С. 7-11. — Бібліогр.: 10 назв. — англ.

Institution

Digital Library of Periodicals of National Academy of Sciences of Ukraine

id	irk-123456789-80367
record_format	dspace
spelling	irk-123456789-803672015-04-18T03:01:25Z NLO corrections to the pair production of supersymmetric particles Obikhod, T.V. Verbytskyy, A.A. Ядерная физика и элементарные частицы The analysis of recent experimental data received from LHC (CMS) restricts the range of MSSM parameters. Using computer programs SOFTSUSY, SDECAY the mass spectrum and partial width of superpatners are calculated. With the help of computer program PROSPINO the calculations of the next-to-leading order (NLO) corrections to the production cross sections of superpartners are made. With the help of computer program PYTHIA the NLO corrections on differential distributions of pT and η for squarks and gluino are represented. Анализ последних экспериментальных данных, полученных из БАК (КМС), ограничил пространство МССМ параметров. С помощью компьютерных программ SOFTSUSY, SDECAY посчитаны спектры масс и ширины распадов суперчастиц. Проведены расчеты next-to-leading order (NLO) поправок к поперечному сечению образования суперчастиц с помощью компьютерной программы PROSPINO. Представлены NLO поправки к дифференциальному сечению распределения по pT и η для скварков и глюино. Аналiз останнiх експериментальних даних отриманих на ВАК (КМС) звузив простiр МССМ параметрiв. За допомогою комп'ютерних програм SOFTSUSY, SDECAY розраховано спектри мас i ширини розпадiв суперчастинок. Проведено розрахунки next-to-leading order (NLO) поправок до поперечного перерiзу утворення суперчастiнок за допомогою комп'ютерної програми PROSPINO. Представлено NLO поправки до диференцiйного перерiзу розподiлу по pT i η для скваркiв i глюiно. 2014 Article NLO corrections to the pair production of supersymmetric particles / T. V. Obikhod, A.A. Verbytskyy // Вопросы атомной науки и техники. — 2014. — № 5. — С. 7-11. — Бібліогр.: 10 назв. — англ. 1562-6016 PACS: 11.25.-w, 12.60.Jv, 02.10.Ws http://dspace.nbuv.gov.ua/handle/123456789/80367 en Вопросы атомной науки и техники Національний науковий центр «Харківський фізико-технічний інститут» НАН України
institution	Digital Library of Periodicals of National Academy of Sciences of Ukraine
collection	DSpace DC
language	English
topic	Ядерная физика и элементарные частицы Ядерная физика и элементарные частицы
spellingShingle	Ядерная физика и элементарные частицы Ядерная физика и элементарные частицы Obikhod, T.V. Verbytskyy, A.A. NLO corrections to the pair production of supersymmetric particles Вопросы атомной науки и техники
description	The analysis of recent experimental data received from LHC (CMS) restricts the range of MSSM parameters. Using computer programs SOFTSUSY, SDECAY the mass spectrum and partial width of superpatners are calculated. With the help of computer program PROSPINO the calculations of the next-to-leading order (NLO) corrections to the production cross sections of superpartners are made. With the help of computer program PYTHIA the NLO corrections on differential distributions of pT and η for squarks and gluino are represented.
format	Article
author	Obikhod, T.V. Verbytskyy, A.A.
author_facet	Obikhod, T.V. Verbytskyy, A.A.
author_sort	Obikhod, T.V.
title	NLO corrections to the pair production of supersymmetric particles
title_short	NLO corrections to the pair production of supersymmetric particles
title_full	NLO corrections to the pair production of supersymmetric particles
title_fullStr	NLO corrections to the pair production of supersymmetric particles
title_full_unstemmed	NLO corrections to the pair production of supersymmetric particles
title_sort	nlo corrections to the pair production of supersymmetric particles
publisher	Національний науковий центр «Харківський фізико-технічний інститут» НАН України
publishDate	2014
topic_facet	Ядерная физика и элементарные частицы
url	http://dspace.nbuv.gov.ua/handle/123456789/80367
citation_txt	NLO corrections to the pair production of supersymmetric particles / T. V. Obikhod, A.A. Verbytskyy // Вопросы атомной науки и техники. — 2014. — № 5. — С. 7-11. — Бібліогр.: 10 назв. — англ.
series	Вопросы атомной науки и техники
work_keys_str_mv	AT obikhodtv nlocorrectionstothepairproductionofsupersymmetricparticles AT verbytskyyaa nlocorrectionstothepairproductionofsupersymmetricparticles
first_indexed	2025-07-06T04:20:12Z
last_indexed	2025-07-06T04:20:12Z
_version_	1836869865303965696
fulltext	NLO CORRECTIONS TO THE PAIR PRODUCTION OF SUPERSYMMETRIC PARTICLES T.V.Obikhod ∗, A.A.Verbytskyy Institute for Nuclear Research, NAS of Ukraine, 03680, Kiev, Ukraine (Received March 3, 2014) The analysis of recent experimental data received from LHC (CMS) restricts the range of MSSM parameters. Using computer programs SOFTSUSY, SDECAY the mass spectrum and partial width of superpatners are calculated. With the help of computer program PROSPINO the calculations of the next-to-leading order (NLO) corrections to the production cross sections of superpartners are made. With the help of computer program PYTHIA the NLO corrections on differential distributions of pT and η for squarks and gluino are represented. PACS: 11.25.-w, 12.60.Jv, 02.10.Ws 1. INTRODUCTION Supersymmetry played a most important role in the development of theoretical physics and strongly in- fluenced on experimental particle physics. Supersymmetry first appeared in the context of string theory as the symmetry of two-dimensional world sheet theory [1]. Later it was realized that it could be relevant to elementary particle physics through the four-dimensional quantum field theory. Why particle physicist consider supersymmetric theories? There are several famous reasons: • the vanishing or extreme smallness of the cosmological constant; • the hierarchy problem; • dark matter candidate; • gauge-coupling unification. The simplest action that can be written down for fermions, scalar fields and non-propagating complex auxiliary field consists of kinetic energy terms [2]: Lfree = −∂µϕ∗i∂µϕi + iψ+iσµ∂µψi + F ∗iFi , S = ∫ d4xLfree . The renormalizable interactions for these fields, that are invariant under supersymmetric transformations are the following Lint = ( −1 2 W ijψiψj +W iFi ) + c.c. , where W i,j ,W i are polynomials in the scalar fields ϕi, ϕ ∗i with degrees 1 and 2 respectively. It is possi- ble to write W ij = δ2 δϕiδϕj W , where W = Liϕi + 1 2 M ijϕiϕj + 1 6 yijkϕiϕjϕk is the superpotential. Here Li are parameters, which affect the scalar potential part of the Lagrangian,M ij is a symmetric mass matrix for the fermion fields, and yijk is a Yukawa coupling of a scalar ϕk and two fermions ψiψj that must be totally symmetric under interchange of i, j, k. The Minimal Supersymmetric Standard Model (MSSM) superpotential has the form WMSSM = uyuQHu − dydQHd − eyeLHd + µHuHd. The fields Hu, Hd, Q, L, u, d, e are chiral superfields corresponding to the chiral supermultiplets. yu, yd, ye are Yukawa coupling parameters yu ≈ 0 0 0 0 0 0 0 0 yt  , yd ≈ 0 0 0 0 0 0 0 0 yb  , ye ≈ 0 0 0 0 0 0 0 0 yτ  . The µ term is the supersymmetric version of the Higgs boson mass. The models of spontaneous sym- metry breaking should be soft (of positive mass di- mension) in order to be able to naturally maintain a hierarchy between the electroweak scale and the Planck (or any other very large) mass scale. In the Lagrangian of a general theory the possible soft supersymmetry-breaking terms are ∗Corresponding author E-mail address: obikhod@kinr.kiev.ua ISSN 1562-6016. PROBLEMS OF ATOMIC SCIENCE AND TECHNOLOGY, 2014, N5 (93). Series: Nuclear Physics Investigations (63), p.7-11. 7 Lsoft = = − ( 1 2 Maλ a λ a + 1 6 a ijk ϕiϕjϕk + + 1 2 b ij ϕiϕj + t i ϕi ) + c.c. − (m 2 ) i jϕ j∗ ϕi, (1) where Ma are gaugino masses, (m2)ij and bij are scalar squared-mass terms, aijk and ti are couplings - scalar and ”tadpole”. The advantage of the MSSM is the unification of gauge couplings. The 1-loop RG equations for the gauge couplings g1, g2, g3 are βga ≡ d dt ga = 1 16π2 bag 3 a, (b1, b2, b3) = { (41/10,−19/6,−7) Standard Model (33/5, 1,−3) MSSM where t = ln(Q/Q0), with Q the Renorm group (RG) scale. The quantities α = g2a/4π run linearly with RG scale at one-loop order: d dt α−1 a = − ba 2π (a = 1, 2, 3) and can unify at a scale MU ∼ 2×1016 GeV. As this uni- fication is not perfect, however, this small difference can be corrected due to the application of the RG analysis for MSSM model. The form of the renormalization group equations with the parameters appearing in the superpo- tential is the following βyijk ≡ d dt yijk = γi ny njk + γj ny ink + γk ny ijn, βMij ≡ d dt M ij = γi nM nj + γj nM in, (2) βLi ≡ d dt Li = γi nL n, where the γi j are anomalous dimension matrices associ- ated with the superfields. At 1-loop order γi j = 1 16π2 [ 1 2 yimny∗ jmn − 2g2aCa(i)δ i j ] , where Ca(i) are the quadratic Casimir group theory in- variants for the superfield Φi , defined in terms of the Lie algebra generators T a by (T aT a)ji = Ca(i)δ j i with gauge couplings ga. For the MSSM supermultiplets C3(i) = { 4/3 for Φi = Q,u, d, 0 for Φi = L, e,Hu, Hd, C2(i) = { 3/4 for Φi = Q,L,Hu, Hd, 0 for Φi = u, d, e, C1(i) = { 3Y 2 i /5 for each Φi with weak hypercharge Yi. The one-loop renormalization of gauge couplings has the form βga = d dt ga = 1 16π2 g3a [∑ i Ia(i)− 3Ca(G) ] , where Ca(G) is the quadratic Casimir invariant of the group, Ia(i) is the Dynkin index of the chiral supermulti- plet ϕi . Putting RG equations for γi j at the 1-loop order into (2), we can receive the expressions of the running superpotential parameters βyt ≡ d dt yt = yt 16π2 [ 6y ∗ t yt + y ∗ b yb − 16 3 g 2 3 − 3g 2 2 − 13 15 g 2 1 ] , βyb ≡ d dt yb = yb 16π2 [ 6y ∗ b yb + y ∗ t yt + y ∗ τyτ − 16 3 g 2 3 − 3g 2 2 − 7 15 g 2 1 ] , βyτ ≡ d dt yτ = yτ 16π2 [ 4y ∗ τyτ + 3y ∗ b yb − 3g 2 2 − 9 5 g 2 1 ] , βµ ≡ d dt µ = µ 16π2 [ 3y ∗ t yt + 3y ∗ b yb + y ∗ τyτ − 3g 2 2 − 3 5 g 2 1 ] . The 1-loop renormalization group equations for the gaug- ino mass parameters in the MSSM are determined by βMa ≡ d dt Ma = 1 8π2 bag 2 aMa (ba = 33/5, 1,−3) for a = 1, 2, 3. Near the scale Q = MU = 2 × 1016 GeV gaugino masses unify with the value m1/2 M1 g21 = M2 g22 = M3 g23 = m1/2 g2U . Our goal is to learn GUT theory at the GUT scale and seeing which models are consistent with the experimental data. At hadron colliders, sparticles can be produced in pairs from parton collisions of QCD strength: gg → g̃g̃, gq → g̃q̃i, qq → g̃g̃, qq → q̃iq̃j . The total hadronic cross-sections are obtained by inte- grating the parton cross-sections over the parton distri- butions fi in the proton/antiproton: σ(ij → q̃, g̃) = ∫ dx1dx2fi(x1)fj(x2)σ B (ij → q̃, g̃; s = x1x2S), where the total centre-of-mass energy of the collider is de- noted by √ s. Lowest-order (LO) partonic cross-sections are the following [3]: σ B (qiqj → q̃q̃) = πα̂2 s s [ βq̃ ( − 4 9 − 4m4 − 9(m2 g̃ s + m4 −) ) + + ( − 4 9 − 8m2 − 9s ) L1 ] + +δij πα̂2 s s [ 8m2 g̃ 27(s + 2m2 −) L1 ] , σ B (qq → g̃g̃) = πα2 s s βg̃ ( 8 9 + 16m2 g̃ 9s ) + + παsα̂s s [ βg̃ ( − 4 3 − 8m2 − 3s ) + + ( 8m2 g̃ 3s + 8m4 − 3s2 ) L2 ] + + πα̂2 s s [ βg̃ ( 32 27 + 32m4 − 27(m2 q̃ s + m4 −) ) + + ( − 64m2 − 27s − 8m2 g̃ 27(s − 2m2 −) ) L2 ] , 8 σ B (gg → g̃g̃) = πα2 s s [ βg̃ ( −3 − 51m2 g̃ 4s ) + + ( − 9 4 − 9m2 g̃ s + 9m4 g̃ s2 ) log ( 1 − βg̃ 1 + βg̃ )] , σ B (qg → q̃g̃) = παsα̂s s [ κ s ( − 7 9 − 32m2 − 9s ) + + ( − 8m2 − 9s + 2m2 q̃m 2 − s2 + 8m4 − 9s2 ) L3 + + ( −1 − 2m2 − s + 2m2 q̃m 2 − s2 ) L4 ] with L1 = log ( s+ 2m2 − − sβq̃ s+ 2m2 − + sβq̃ ) , L2 = log ( s− 2m2 − − sβg̃ s− 2m2 − + sβg̃ ) , L3 = log ( s−m2 − − κ s−m2 − + κ ) , L4 = log ( s+m2 − − κ s+m2 − + κ ) , βq̃ = √ 1− 4m2 q̃ s , βg̃ = √ 1− 4m2 g̃ s , m2 − = m2 g̃ −m2 q̃, κ = √ (s−m2 g̃ −m2 q̃) 2 − 4m2 g̃m 2 q̃ , αs = g2s 4π , α̂s = ĝ2s 4π . The momenta of the two partons in the initial states are denoted by k1 and k2, s = (k1 + k2) 2 - kinematical invari- ant, gs - Yukawa couplings. Squarks and gluinos can be produced at the LHC, if their masses are in the accessible range. The LO cross sections and NLO corrections in SUSY-QCD can be calculated with the computer program PROSPINO [4]. The next-to-leading order (NLO) strong supersymmet- ric Quantum chromodynamics (SUSY-QCD) corrections increase the cross-sections for the various production pro- cesses with respect to the leading-order (LO) predictions and reduce the dependence on the renormalization and factorization scale significantly [5, 6]. According to the experimental data [7] with the ob- served and exclusion limits in the (m0,m1/2) plane for tanβ = 10 and A0 = 0, calculated with SUSY in final states with missing transverse energy and 0,1,2,or ≥ 3 b-quark jets in 7 TeV pp collisions we can consider two sets of input parameters for SUSY at the LHC in Table 1 Table 1. The input parameters for two mSUGRA scenarios m0, GeV m1/2, GeV A0, GeV tanβ sgn(µ) I 800 650 0 10 +1 II 1300 425 0 10 +1 For calculation the mass spectra was used SOFT- SUSY program [8]. The masses are listed in Table 2. Table 2. The masses of superparticles (GeV) mũL mũR m d̃L m d̃R mg̃ m χ̃0 1 I 1546 1504 1548 1500 1498 272 II 1552 1538 1554 1536 1053 176 With the help of computer program SDECAY [9] we can calculate branching ratios (BR) for superparti- cles. In Table 3 we will show the decays of the pro- duced squarks with the shortest ’cascade’, q̃ → qχ̃0 1 Table 3. The branching ratios for the decay q̃ → qχ̃0 1 for the two scenarios ũL → uχ̃0 1 ũR → uχ̃0 1 d̃L → dχ̃0 1 d̃R → dχ̃0 1 I 0.012 0.997 0.015 0.997 II 0.003 0.095 0.005 0.026 It can be seen that BR is larger for the first scenario I and BR for q̃L is quite small. Using the parameter set of Table 1 it is possible to calculate production cross sections of superpartners by application of the computer program PROSPINO. These cross sections at the center- of-mass energy √ s = 14 TeV are shown in Table 4. Table 4. LO and NLO cross sections (pb) and K-factors for superpartners channel σ Prospino LO σ Prospino NLO KProspino I squark-squark 0.397E-01 0.469E-01 1.1788 squark-gluino 0.434E-01 0.678E-01 1.5616 gluino-gluino 0.462E-02 0.127E-01 2.7549 II squark-squark 0.406E-01 0.511E-01 1.2601 squark-gluino 0.163 0.264 1.6130 gluino-gluino 0.988E-01 0.230 2.3269 The computations of NLO cross sections for SUSY par- ticles at hadron collider are made with some simpli- fications. The NLO corrections are always summed over the subchannels assumming a common mass for all squarks. The K-factor, i.e. the ratio between the NLO and LO cross section K = σNLO σLO is deter- mined for the total cross section, with all subchan- nels summed up. With the help of computer pro- gram PYTHIA [10] we can represent NLO corrections on differential distributions. Fig.1 displays this distri- bution, normalized with the appropriate cross section. Fig.1. Normalized pq̃T distribution for the first scenario with the center-of-mass energy of 14 TeV For both scenarios we also calculated the NLO results and received several distributions of inclusive quantities: the transverse momentum pT , the pseudorapidity η for both squarks and gluino (Figs. 2 - 9). Fig.2. pT distribution with NLO corrections for squarks (first scenario) 9 Fig.3. pT distribution with NLO corrections for gluino (first scenario) Fig.4. η distribution with NLO corrections for squarks (first scenario) Fig.5. η distribution with NLO corrections for gluino (first scenario) Fig.6. pT distribution with NLO corrections for squarks (second scenario) Fig.7. pT distribution with NLO corrections for gluino (second scenario) Fig.8. η distribution with NLO corrections for squarks (second scenario) Fig.9. η distribution with NLO corrections for gluino (second scenario) 6. CONCLUSIONS Supersymmetry is probably the best motivated scenario today for physics beyond the SM and has been the object of intense searches at high-energy collider. We have used different analysis methods for clarification of the experi- mental strategies in searches for SUSY at the LHC. For the interpretation of the experimental data precise theo- retical predictions are of great importance. The present paper contributes to this effort by providing NLO cor- rections to the pair production of squarks and gluinos of the first two generations in a Monte Carlo programs. Current and future LHC data for searching physics be- yond the Standard Model requires theoretical prediction for observables, including distributions and cross sections with kinematical cuts. The results presented in this paper provide a diffrential description of supersymmetric parti- cle production and decay, and should form the theoretical basis for experiments at the LHC in future. 10 References 1. A.Bilal. Introduction to Supersymmetry // arXiv:hep-th/0101055v1. 2. S.P.Martin. A Supersymmetry Primer // arXiv:hep- ph/9709356. 3. G.L.Kane, J.P. Leveille. Experimental constraints on gluino masses and supersymmetric theories // Phys. Lett. 1982, v. B112, p. 227-332. 4. W.Beenakker, R.Hopker, M. Spira. PROSPINO: A Program for the production of supersymmetric par- ticles in next-to-leading order QCD // arXiv:hep- ph/9611232. 5. W.Beenakker, R.Hopker, M. Spira, P.M. Zerwas. Squark Production at the Fermilab Tevatron // Phys. Rev. Lett. 1995, v. 74, p. 2905-2908. 6. W.Beenakker, R.Hopker, M. Spira, P.M. Zerwas. Squark and Gluino Production at Hadron Colliders // arXiv:hep-ph/9610490. 7. The CMS Collaboration. Search for supersymmetry in final states with missing transverse energy and 0, 1, 2, or ≥ 3 b-quark jets in 7 TeV pp collisions using the variable αT // arXiv: 1210.8115 [hep-ex]. 8. B.C.Allanach. SOFTSUSY2.0: a program for cal- culating supersymmetric spectra // Comput. Phys. Commun. 2002, v. 143, p. 305-331. 9. M.Muhlleitner, A.Djouadi, Y.Mambrini. SDECAY: a fortran code for the decays of the supersymmetric particles in the MSSM // Comput. Phys. Commun. 2005, v. 168, p. 46-70. 10. T. Sjostrand, S.Mrenna, P. Skands. PYTHIA 6.4 Physics and Manual // JHEP 2006, v. 05, p. 1-26. NLO ÊÎÐÐÅÊÖÈÈ Ê ÎÁÐÀÇÎÂÀÍÈÞ ÏÀÐÛ ÑÓÏÅÐÑÈÌÌÅÒÐÈ×ÍÛÕ ×ÀÑÒÈÖ Ò.Â.Îáèõîä, À.À.Âåðáèöêèé Àíàëèç ïîñëåäíèõ ýêñïåðèìåíòàëüíûõ äàííûõ, ïîëó÷åííûõ èç ÁÀÊ (ÊÌÑ), îãðàíè÷èë ïðîñòðàíñòâî ÌÑÑÌ ïàðàìåòðîâ. Ñ ïîìîùüþ êîìïüþòåðíûõ ïðîãðàìì SOFTSUSY, SDECAY ïîñ÷èòàíû ñïåêòðû ìàññ è øèðèíû ðàñïàäîâ ñóïåð÷àñòèö. Ïðîâåäåíû ðàñ÷åòû next-to-leading order (NLO) ïîïðàâîê ê ïîïåðå÷íîìó ñå÷åíèþ îáðàçîâàíèÿ ñóïåð÷àñòèö ñ ïîìîùüþ êîìïüþòåðíîé ïðîãðàììû PROSPINO. Ïðåäñòàâëåíû NLO ïîïðàâêè ê äèôôåðåíöèàëüíîìó ñå÷åíèþ ðàñïðåäåëåíèÿ ïî pT è η äëÿ ñêâàðêîâ è ãëþèíî. NLO ÊÎÐÐÅÊÖI� ÄÎ ÓÒÂÎÐÅÍÍß ÏÀÐÛ ÑÓÏÅÐÑÈÌÅÒÐÈ×ÍÈÕ ×ÀÑÒÈÍÎÊ Ò.Â.Îáiõîä, À.Î.Âåðáèöüêèé Àíàëiç îñòàííiõ åêñïåðèìåíòàëüíèõ äàíèõ îòðèìàíèõ íà ÂÀÊ (ÊÌÑ) çâóçèâ ïðîñòið ÌÑÑÌ ïàðàìåò- ðiâ. Çà äîïîìîãîþ êîìï'þòåðíèõ ïðîãðàì SOFTSUSY, SDECAY ðîçðàõîâàíî ñïåêòðè ìàñ i øèðèíè ðîçïàäiâ ñóïåð÷àñòèíîê. Ïðîâåäåíî ðîçðàõóíêè next-to-leading order (NLO) ïîïðàâîê äî ïîïåðå÷íî- ãî ïåðåðiçó óòâîðåííÿ ñóïåð÷àñòiíîê çà äîïîìîãîþ êîìï'þòåðíî¨ ïðîãðàìè PROSPINO. Ïðåäñòàâëåíî NLO ïîïðàâêè äî äèôåðåíöiéíîãî ïåðåðiçó ðîçïîäiëó ïî pT i η äëÿ ñêâàðêiâ i ãëþiíî. 11

NLO corrections to the pair production of supersymmetric particles

Institution

Ähnliche Einträge