# Supersymmetric radiative corrections at large tan {beta} Page: 4 of 10

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Here at = yt/47r and I(a, b, c) is a loop integral,

I(a, b, c) = [a2b2 log(a2/b2) + b2c2 log(b2/c2)

+c2a2 log(c2/a2)]/(

[(a2 - b2)(b2 - c2)(a2 - c2)], (17)

which is positive for any a, b, c and goes like

1/max(a2, b2, c2).

Solving Eq. 15 for yb [6], we find9mb 1

Yb ='2Mw cos 1 + Ab(18)

where we have not expanded the denominator to

one loop order. It was proven in Ref. [14] that

Eq. 18 includes a resummation of terms of order

(at tan #/Msusy)" to all orders of perturbation

theory. In particular, Ab in Eq. 18 gets no tan #

enhanced corrections at higher orders of the form

(ap tan /Msusy). The remaining higher or-

der corrections to Ab are not tan a enhanced and

are thus insignificant compared to the one loop

piece (Eq. 16). The proof in Ref. [14] that Eq. 18

receives no higher order tan # enhanced contri-

butions relies on the facts (1) that tan # enters

the calculation at higher orders only multiplied

by mb, e.g., from the mb tan # term in the bot-

tom squark mass matrix; and (2) that no factors

of 1/mb can arise from the loop diagrams to can-

cel the mb factor multiplying tan o, because the

Yukawa coupling operator is dimension four.

Expanding Eq. 18 to one loop order, we have

9m6

Yb- = 9mb A) (19)

v/2Mw cos b)

An expression of this form arises in on-shell di-

agrammatic one-loop calculations, in which Ab

enters through the b quark mass counterterm.

Although Eqs. 18 and 19 are equivalent at one

loop, they differ at higher orders: Eq. 19 does

not contain a resummation of terms of order

(at tan #/Msusy)" to all orders of perturbation

theory.6 In our EFT analyses in the remainder of

this paper we will use Eq. 18 in order to take ad-

vantage of the resummation of higher order terms.

The remainder of this paper is organized as fol-

lows. We examine the effect of the SUSY Yukawa

6A proof as in Ref. [14] does not hold for Eq. 19, in which

the b mass operator is renormalized, because the b mass

operator is not dimension four. See Ref. [14] for details.corrections on the process h0 -+ bb in Sec. 2 and

on the H+fb coupling in Sec. 3. In Sec. 4 we

describe how flavor-changing neutral Higgs inter-

actions arise in the EFT from the SUSY Yukawa

corrections, and in Sec. 5 we summarize recent

results for specific flavor changing processes. In

Sec. 6 we discuss the renormalization of the CKM

matrix. In Sec. 7 we briefly discuss resummation

of the SUSY Yukawa corrections to flavor chang-

ing processes. Finally in Sec. 8 we give a summary

and outlook.

2. SUSY CORRECTIONS TO h0 -+ bb

Accurate knowledge of the h0 -+ bb branching

ratio is important for determining the reach of

the upcoming Higgs searches at the Tevatron and

LHC [15]. Also, once a light Higgs boson is dis-

covered, precision measurements of its branching

ratios (e.g., at a future e+e- linear collider) can

be used to distinguish a SM Higgs boson from a

MSSM Higgs boson in some regions of parameter

space [16]. The SUSY Yukawa corrections can

have a significant effect on these branching ra-

tios [6,15-17]. For example, the ratio BR(h' -+

bb)/BR(h -+ T+T-) is sensitive to the SUSY

Yukawa corrections to h -+ bb.7 At tree level, the

ratio BR(ho -+ bb)/BR(h -+ T+T-) is the same

in the SM and the MSSM (oc m /m?). Further,

in the MSSM the h0bb and hoT+T- couplings have

the same dependence on the CP-even Higgs mix-

ing angle a, so that BR(ho -+ bb)/BR(h -4

T+T-) is also insensitive to the radiative correc-

tions to a. Thus in the context of the MSSM, a

deviation of BR(ho -+ bb)/BR(h -+ T+T-) from

its SM value provides a direct window onto the

SUSY Yukawa corrections [6,15-17].

2.1. EFT calculation

We begin by computing the SUSY corrections

to h- 4 bb in the EFT approach; that is, we as-

sume Msusy > MA and neglect the external mo-

menta.8 Using Eqs. 4 and 18, the hobb coupling

7The hOr+T- coupling also receives tan fi enhanced SUSY

Yukawa corrections, but they are proportional to elec-

troweak gauge couplings and are expected to be much

smaller than the corrections to the hObb coupling.

8We will consider the effects of the external momenta and

lower Msusy in the next section.

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Logan, H.E. Supersymmetric radiative corrections at large tan {beta}, article, February 20, 2001; Batavia, Illinois. (digital.library.unt.edu/ark:/67531/metadc721228/m1/4/: accessed December 17, 2018), University of North Texas Libraries, Digital Library, digital.library.unt.edu; crediting UNT Libraries Government Documents Department.