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Study of the Rare Hyperon Decays in the Standard Model and New Physics*

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Study of the Rare Hyperon Decays in the Standard Model and New Physics* Chinese Physics C Vol. 43, No. 9 (2019) 093104 Study of the s ! dνν¯ rare hyperon decays in the Standard Model and new physics* 1) 2) Xiao-Hui Hu(胡晓会) Zhen-Xing Zhao(赵振兴) INPAC, Shanghai Key Laboratory for Particle Physics and Cosmology, MOE Key Laboratory for Particle Physics, Astrophysics and Cosmology, School of Physics and Astronomy, Shanghai Jiao-Tong University, Shanghai 200240, China Abstract: FCNC processes offer important tools to test the Standard Model (SM) and to search for possible new physics. In this work, we investigate the s ! dνν¯ rare hyperon decays in SM and beyond. We find that in SM the branching ratios for these rare hyperon decays range from 10−14 to 10−11 . When all the errors in the form factors are included, we find that the final branching ratios for most decay modes have an uncertainty of about 5% to 10%. After taking into account the contribution from new physics, the generalized SUSY extension of SM and the minimal 331 model, the decay widths for these channels can be enhanced by a factor of 2 ∼ 7. Keywords: branching ratios, rare hyperon decays, form factors, light-front approach, new physics PACS: 12.39.-x, 12.60.-i DOI: 10.1088/1674-1137/43/9/093104 1 Introduction flight technique, and the corresponding observed upper limit is [8] : B + ! π+νν < × −10; : The flavor changing neutral current (FCNC) trans- (K ¯)exp 14 10 at 95% CL (3) itions provide a critical test of the Cabibbo-Kobayashi- Similarly, the E391a collaboration reported the 90% C.L. Maskawa (CKM) mechanism in the Standard Model upper bound [9] (SM), and allow to search for possible new physics. In − B(K ! π0νν¯) 6 2:6 × 10 8: (4) SM, the FCNC transition s ! dνν¯ proceeds through the Z- L exp penguin and electroweak box diagrams, and thus the de- The KOTO experiment, an upgrade of the E391a ex- 0 cay probabilities are strongly suppressed. In this case, a periment, aims at a first observation of the KL ! π νν¯ de- precise study allows to perform very stringent tests of SM cay at J-PARC around 2020 [3, 10]. Given the goal of a and ensures large sensitivity to potential new degrees of 10% precision by NA62, the authors of Ref. [11] intend freedom. to carry out lattice QCD calculations to determine the A large number of studies have been performed of the long-distance contributions to the K+ ! π+νν¯ amplitude. + + 0 + + 0 K ! π νν¯ and KL ! π νν¯ processes, and reviews of Analogous to K ! π νν¯ and KL ! π νν¯ , the rare these two decay modes can be found in [1–6]. On the the- hyperon decays Bi ! B f νν¯ also proceed via s ! dνν¯ at oretical side, using the most recent input parameters, the the quark level, and thus offer important tools to test SM SM predictions for the two branching ratios are [7] and to search for possible new physics. Compared to the + + + + −11 widely considered K ! π νν¯ and K ! π0νν¯ , there are B(K ! π νν¯)SM = (8:4 1:0) × 10 ; (1) L few studies devoted to rare hyperon decays B ! B νν¯ . B ! π0νν = : : × −11: i f (KL ¯)SM (3 4 0 6) 10 (2) This work aims to perform a preliminary theoretical re- The dominant uncertainty comes from the CKM matrix search of the rare hyperon decays both in and beyond elements and the charm contribution. On the experiment- SM. al side, the NA62 experiment at the CERN SPS has re- A study of the hyperon decays at the BESIII experi- ported the first search for K+ ! π+νν¯ using the decay-in- ment is proposed using the hyperon parents of the J= de- Received 18 January 2019, Revised 4 May 2019, Published online 7 August 2019 * Supported in part by National Natural Science Foundation of China (11575110, 11735010, 11911530088), Natural Science Foundation of Shanghai (15DZ2272100) and Key Laboratory for Particle Physics, Astrophysics and Cosmology, Ministry of Education 1) E-mail: [email protected] 2) E-mail: [email protected] Content from this work may be used under the terms of the Creative Commons Attribution 3.0 licence. Any further distribution of this work must main- tain attribution to the author(s) and the title of the work, journal citation and DOI. Article funded by SCOAP3 and published under licence by Chinese Physical Society and the Institute of High Energy Physics of the Chinese Academy of Sciences and the Institute of Modern Physics of the Chinese Academy of Sciences and IOP Pub- lishing Ltd 093104-1 Chinese Physics C Vol. 43, No. 9 (2019) 093104 = (1 2) 0 cay. The electron-positron collider BEPCII provides a where CNL and BNL correspond to the Z -penguin and clean experimental environment. About 106-108 hyperons, the box-type contribution, respectively, given as [16] = " ! Λ, Σ, Ξ and Ω, are produced in the J and (2S ) decays 24 x(mc) 48 24 696 4π C = K 25 K+ + K− − K with the proposed data samples at the BESIII experiment. NL 32 c 7 11 77 33 α (µ) Based on these samples, the sensitivity of the measure- ! ! s µ2 15212 −1 ment of the branching ratios of hyperon decays is in the + (1 − K ) + 1 − ln (16K+ − 8K−) − − c 2 range of 10 5-10 8. The author of Ref. [12] proposed that 1875 mc rare decays and decays with invisible final states may be 1176244 2302 3529184 − K+ − K− + K33 probed. 13125 6875 48125 !# The paper is organized as follows. In Sec. 2, our com- 56248 81448 4563698 + K K+ − K− + K ; puting framework is presented. Sec. 3 is devoted to per- 4375 6875 144375 33 " ! forming the numerical calculations. The branching ratios 24 (1=2) x(mc) 4π 15212 − B = K 25 3(1 − K ) + (1 − K 1) of several rare hyperon decays are calculated in SM. The NL 4 c 2 α (µ) 1875 c new physics contribution, the Minimal Supersymmetric s # µ2 r lnr 305 15212 15581 Standard Model (MSSM) and the minimal 331 model, are − ln − − + K + KK ; 2 − 2 2 considered. We also discuss possible uncertainties from mc 1 r 12 625 7500 the form factors. The last section contains a short sum- (9) = 2= 2 µ µ = O mary. where r ml mc( ), (mc) and αs(MW ) αs(µ) K = ; Kc = ; 2 Theoretical framework αs(µ) αs(mc) 6 − 12 − 1 K+ = K 25 ; K− = K 25 ; K33 = K2 = K 25 : (10) The next-to-leading order (NLO) effective Hamiltoni- In the following, we consider the transitions between ! νν an for s d ¯ reads [13]: the baryon octet (Ξ, Σ, Σ and N) and the transitions from α X − − GF ∗ l the baryon decuplet to the octet Ω ! Ξ . H ff = p [V V X e π 2 θ cs cd NL 2 2 sin W l=e,µ,τ The transition matrix elements of the vector and axi- + ∗ ν ν + : :; al-vector currents between the baryon octets can be para- VtsVtd X(xt)](¯sd)V−A(¯l l)V−A h c (5) 2 metrized in terms of six form factors f1;2;3(q ) and l 2 where X(xt) and XNL are relevant for the top and the g1;2;3(q ): charm contribution, respectively. Their explicit expres- 0 0 0 hB (P ;S )jd¯γµ(1 − γ )sjB (P;S )i = = 2= 2 8 z " 5 8 z # sions can be found in Ref. [13]. Here, xt mt mW. To ν 0 0 2 q 2 qµ 2 leading order in αs, the function X(xt) relevant for the top u¯(P ;S ) γµ f (q ) + iσµν f (q ) + f (q ) u(P;S ) z 1 M 2 M 3 z contribution reads [14, 15] " # ν α q qµ s − 0; 0 γ 2 + σ 2 + 2 γ ; ; X(x) =X0(x) + X1(x); u¯(P S z) µg1(q ) i µν g2(q ) g3(q ) 5u(P S z) " 4π # M M x 2 + x 3x − 6 (11) X (x) = − + ln x ; 0 0 8 1 − x (1 − x)2 where q = P − P , and M denotes the mass of the parent ! 0 23x + 5x2 − 4x3 x − 11x2 + x3 + x4 baryon octet B8. The form factors for the B8 B8 trans- X1(x) = − + ln x ition, f (q2) and g (q2) , can be expressed by the following 3(1 − x)2 (1 − x)3 i i formulas [17]: + 2 + 3 − 4 8x 4x x x 2 + ln x f =aF q2 + bD q2 ; 2(1 − x)3 m m( ) m( ) 2 2 3 gm =aFm+3(q ) + bDm+3(q ); (m = 1;2;3); (12) 4x − x @X0(x) − L2(1 − x) + 8x ln xµ; (6) 2 2 (1 − x)2 @x where Fi(q ) and Di(q ) , with i = 1;2;··· ;6, are different functions of q2 for each of the six form factors. Some re- where xµ = µ2=M2 with µ = O(m ) and W Z t x marks are necessary [17]: − = lnt : ● The constants a and b in Eq. (12) are the SU(3) L2(1 x) dt − (7) 1 1 t Clebsch-Gordan coefficients that appear when an octet l operator is sandwiched between octet states. The function XNL corresponds to X(xt) in the charm sec- 2 = tor. It results from the renormalization group (RG) calcu- ● For q 0, the form factor f1(0) is equal to the elec- lation in next-to-leading-order logarithmic approxima- tric charge of the baryon, therefore F1(0) = 1 and D1(0) = 0.
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