B 0 d ( t ) → π + π − and B 0 s ( t ) → K + K − Decays : A Tool to Measure New - Physics Parameters

If physics beyond the standard model is present in B decays, experimental measurements suggest that it principally affects those processes with significant b̄ → s̄ penguin amplitudes. It was recently shown that such new-physics (NP) effects can be parametrized in terms of a single NP amplitude Aq and phase Φq, for q = u, d, s, c. In this paper, we show that the study of the decays B s (t) → KK and B d(t) → ππ allows one to measure the NP parameters Au and Φu. We examine the implications for this method of the latest experimental results on these decays. If NP is found in B s (t) → KK, it can be partially identified through measurements of B s(t) → KK̄. [email protected] [email protected] [email protected] To date, theoretical analyses of CP violation in the B system have generally concentrated on two subjects. First, many different methods have been proposed for extracting the CP-violating angles α, β and γ of the unitarity triangle [1] within the standard model (SM) [2]. Second, there have been numerous studies of newphysics (NP) signals through measurements of CP violation in B decays. We now have many ways of detecting the presence of NP. However, there has been relatively little work on the third and final ingredient, which is to find ways of measuring the NP parameters. If this can be done it might be possible to identify the new physics, before the production of new particles at high-energy colliders. A first step in this direction was taken in Ref. [3], in which it was shown that one can reduce the number of NP parameters to a manageable level, and measure them. The knowledge of these parameters then allows one to partially identify the new physics. The argument goes as follows. At present, we have a number of experimental hints of new physics. First, within the SM, the CP asymmetry in B d(t) → J/ψKS (sin 2β) is equal to that measured in other decays dominated by the quark-level transition b̄ → s̄ss̄. However, Belle finds a discrepancy of 2.2σ between the CP asymmetry in B d(t) → φKS and that in B d(t) → J/ψKS [4]. In addition, the BaBar measurement of the CP asymmetry in B d(t) → η′KS differs from that in B d(t) → J/ψKS by 3.0σ [5]. Second, ratios of various B → πK branching ratios, which are equal in the SM [6], are found to differ from one another by 1.6σ [7]. Furthermore, Belle finds a 2.4σ discrepancy with the SM in B → πK direct asymmetries: ACP (Kπ) 6= ACP (Kπ), a result confirmed by BaBar [4]. Third, BaBar has measured a nonzero triple-product asymmetry in B → φK at 1.7σ [8]. However, this effect is expected to vanish in the SM [9]. While none of these signals is conclusive, all involve B decays which receive large contributions from b̄ → s̄ penguin amplitudes. In light of this, it is reasonable to assume that the new physics contributes significantly only to those decays with sizeable b̄ → s̄ penguin amplitudes, but does not affect decays involving b̄ → d̄ penguins. Consider now a B → f decay with a b̄ → s̄ penguin. The NP operators are assumed to be roughly the same size as the SM b̄ → s̄ penguin operators, so that the new effects are important. There are many potential NP operators. At the quark level, these take the form Oij,q NP ∼ s̄Γib q̄Γjq (q = u, d, s, c), where the Γi,j represent Lorentz structures, and colour indices are suppressed. The NP contributes to B → f through the matrix elements 〈f | Oij,q NP |B〉. Each of the matrix elements can have different weak phases and in principle each can also have a different strong phase. However, it was argued in Ref. [3] that all NP strong phases are negligible, which leads to a great simplification: one can combine all NP matrix elements into a single NP amplitude, with a single weak phase: ∑ 〈f | O NP |B〉 = Aeq , (1) where q = u, d, s, c. (In general, the Aq and Φq will be process-dependent. The NP 1 phase Φq will be the same for all b̄ → s̄qq̄ decays only if all NP operators for the same quark-level process have the same weak phase.) In Ref. [10], a number of methods for measuring the Aq and Φq were examined. Here we analyze another method. It consists of using B d → ππ and B s → KK decays. These two decays, which are related by flavour SU(3), have been used in the past to both obtain information about SM parameters [11, 12] and to detect the presence of new physics [13, 14]. In all cases, one has to address the size of SU(3)-breaking effects [15]. In the present paper, we show that measurements of these two decays actually allow one to measure the NP parameters Au and Φu. Consider the decay B s → KK within the SM. It is governed by the quarklevel process b̄ → s̄uū, and in terms of diagrams [16], the amplitude receives several contributions: A(B s → KK) = −T ′ − P ′ − E ′ − PA − 2 3 P ′C EW . (2) In the above, the amplitude is written in terms of a colour-favored tree amplitude T , a gluonic penguin amplitude P , an exchange amplitude E , a penguin annihilation amplitude PA, and a colour-suppressed electroweak penguin amplitude P ′C EW . (The primes on the amplitudes indicate a b̄ → s̄ transition.) These various contributions can be grouped into two types. There are charged-current contributions, proportional to V ∗ ubVus, and the penguin-type contributions V ∗ ubVusP ′ u+V ∗ cbVcsP ′ c +V ∗ tbVtsP ′ t . (Here the charged-current term includes T ′ and E , while the penguin term includes P , PA and P ′C EW .) The unitarity of the Cabibbo-Kobayashi-Maskawa (CKM) matrix can be used to eliminate V ∗ tbVts, so that the penguin-type contributions become V ∗ ubVus(P ′ u − P ′ t ) + V ∗ cbVcs(P ′ c − P ′ t ). The amplitude for B s → KK can then be written as A(B s → KK) = V ∗ ubVus(A′u CC + A pen) + V ∗ cbVcsA′ct pen