The file PlotXYcontains routines to plot scale drawings in Excel from a list of XY coordinates of node points, node points for each shape, and formatting details for each shape type. The plot is scaled to fit within the selected plot range and, unlike Excel charts, is scaled equally in the X and Y directions, so circles will stay circular. Shapes may either be defined as polylines, with a series of points, or by using any of the built in Excel shapes.
Examples of the output are shown below, and data for the first three is included in the download. The final example was plotted from about 250,000 node points, using over 12,000 polyline shapes (using Excel 2007), illustrating that this tool is capable of producing drawings from very large data sets.
Concentric squares, or a square spiral?
Any comments or requests for additional features? Please let me know.
This entry was posted in Drawing, Excel, VBA and tagged Drawing, Excel, shapes, VBA. Bookmark the permalink.
First of all, thank you for these routines. I've been dealing with drawing in excel for quite some time. Mostly in structural engineering.
And now I will never have to start and make boundary's (x- x+ y- y+) scaling factors and drawing ranges, keeping the correct coordinates. Now is it just: start and select.
Basicly I've found that us engineers see the world in nodes en lines.
The idea of lines are actually easy, two points and you're done. The node is actualy different. It is infinitaly small, so we can't see it. So we make a circle fill it up, (thus defining 2dimensions).
However there are different kinds of nodes. The mass for instance is big. A keypoint is smaller. and a node is smaller.
Here the problem in the routine starts.
Lets say I want a mass node on coordinate x,y, with height (h) and width of 10. And defining it a circle (shape 9 if i remenbered it correctly). The routine starts at coordinate x,y and makes the circle. Thus placing the center at the coordinate at x+h/2 y+h/2. With a small value of h this isn't a problem. You'll won't see that. but with large values you will. And one closely spaced on the outer border will run out of the drawing area, and find problems with deletion!
To make a workaround. You'll have to make new node coordinates based on the type of shape you want. and taking into account the size of the shape. And thus increasing the number of totale node coordinates. And increasing error posibilities.
This plea is to create an new shape definition. Called a node with a single size. Incoorporate the workaround. I would also recommend creating a buffer area around the innerborder to prevend deletion difficulties.
Rick – thanks for the comments.
Good point about the offset you get with shapes. Rather than create a new node shape type it seems to me that it would be better to modify the code so that the centre coordinates can be entered for circles, and the code calculates the top left coordinate.
Arcs are also a bit of a problem because they are handled differently in XL 2007 to previous versions. (more details here .. https://newtonexcelbach.wordpress.com/2008/07/26/drawing-in-excel-5-shape-list/), so some code to detect the Excel version and adjust the arc shape accordinly would be useful.
Time permitting, I'll try and get a new version posted with these changes in a week or two.
Finally on the buffer, the routine for checking the scale at the moment just checks the limits of the nodes, without making any allowance for the size of the shapes. The easiest workaround is to specify an invisible line from one corner to the opposite one, ensuring that the limits of this line are outside the limits of all the shapes. Alternatively you could go into the VBA code and either increase the value of the constant cMargin, or reduce the value of UScale.
Can anyone show me a quick tuturiol of even how to "draw" on excel? That would be great! Currently, my task in school is requiring me to draw a shape of an I-Beam.
Hi Alvin – In 2007/2010 go to the Insert Tab, click on the Shapes Icon, and have a play with the shapes there. You could just draw three rectangles but also try the "Freeform" shape and then try editing the corners with the "edit shape" icon. With the freeform shape you click in each corner of your shape, then double click to indicate the last point. If you double click close enough to the first point it will draw a closed shape.
One trick useful for your exercise is to hold down the shift key as you draw each line segment. This will force the line to be either horizontal, vertical or at 45 degrees.
say that I've really enjoyed surfing around your blog posts. In any case I'll be subscribing in your rss feed and I hope you write once more very soon!
Great job! I haven't entered into detail yet but I think it will be very helpful spreadsheet for me.
Tony – I don't see anything wrong with that site. Using IE you can just click the back button to get out, but even if that doesn't work in some browsers surely you can just close the window?
Could you be more specific about their claims that are wrong?
I have no connection with the site, and I would be happy to delete the link if there was good reason, but at the moment it seems to be a useful Excel related site for scientists and engineers.
Tony – WordPress only allow three levels of reply, so this is a reply to your message today!
You can e-mail me at dougaj4 at gmail.
Hello – thanks for all the help with drawing in Excel.
I'm trying to put together a finite element mesh preprocessor (for buried culvert analysis using CANDE). I'd like to do it in Excel because I am likely not the only one who will be using it.
Ricky – all I can suggest is looking at the code from the open source FEA programs, and seeing if there is anything you can use, but I haven't found any that I could recommend.
I'll probably do something on this myself some time in the future, but I can't put a date on it.
I'll keep a lookout for that.
First of all thanks for the file. It's awesome.
I'm trying to construct an image with it but only have the coordinates.
Is there a way i can find the nodes for myself?
For that I used Strand7 (a finite element program) that has a good graphical editor, so I could connect the nodes by trial and error, and then get a listing of the connected node numbers. If you don't have access to a similar program the best I can suggest is to use the spreadsheet to create a text box with the node number at each node location, and use that to work out which nodes need to be connected.
I doubt I'll have any time to work on this spreadsheet in the near future, but one of the advantages of working with a spreadsheet is it's pretty easy to generate coordinates for an offset line on the worksheet, then you can use the VBA plotting routines to plot that line.
I can't check on a Mac myself. If any Mac users can confirm if it works for them, that would be good.


text:
Ahead 2000 - Mississippi Department of Transportation
mdot.ms.gov
Mississippi Moving A.H.E.A.D.
(ADVOCATING HIGHWAYS FOR ECONOMIC ADVANCEMENT AND DEVELOPMENT)
1987 Four-Lane
Highway Program
Brief History ...................................................................................................................................................... 3
Executive Summary ...................................................................................................................................... 4
1987 Four-Lane Highway Program Map (including Phase IV) ........................................... 7
Receipts and Disbursements ........................................................................................................ 8
Cash Flow Projections for Fiscal Years 2001-2018...................................................... 10
Zack Stewart
Northern District
Highway Segments Open to Traffic................................................................................................. 12
Map - Status of Construction.............................................................................................................. 14
List of Construction Projects............................................................................................................... 15
Brief Summary of Phases I, II and III ................................................................................................. 20
Projects to be Let FY 2001 .................................................................................................................. 21
Map - Status of Right of Way .............................................................................................................. 22
Right of Way Activity Under Way .................................................................................................... 23
Right of Way Not Acquired ................................................................................................................. 23
Dick Hall, chairman
Wayne Brown
Southern District
Mississippi Moving A.H.E.A.D. is a report published by the Public Affairs Division of the Mississippi
Department of Transportation (MDOT). Correspondence should be directed to MDOT, Attn. Public
Affairs Division, P.O. Box 1850, Jackson, MS 39215-1850. Mississippi Moving A.H.E.A.D. is available to
the general public upon request by writing to the address given above, or by calling (601) 359-7017.
M i s s i s s i p p i M o v i n g · A h e a d
In 1987, the Mississippi Legislature passed a long-range highway program,
which was one of the most comprehensive in the country. The
program was estimated to cost $1.6 billion and expected to build 1,077
miles of four-lane highways over a 14-year period.
The highways were to be built in phases based primarily on vehicle
count and road capacity. Three phases were established with each having
a mileage goal and an estimated cost.
Highway user revenues were dedicated to build the system. The
Mississippi Department of Transportation was given the authority to temporarily
borrow $200 million if funding resources dictated.
Major sources of funding designated to pay for the program included
a motor fuel tax, a $5 car tag fee, a highway contractor's tax, federal aid,
and proceeds from the transportation bond retirement fund.
During the 1994 Regular Legislative Session, lawmakers extended the
original funding repealer in order to provide for improvements to an additional
619-mile Phase IV, which was also added to the original program
at that time. The addition of Phase IV will ensure that the transportation
system more adequately meets Mississippi's long-range needs.
Subsequent legislation has added approximately 104 miles to Phase
IV. The 1987 Program is presently predicted to be a $5.2 billion program
which will four-lane or make other improvements to approximately 1,811
miles of state highways.
W. Hugh Long
Pictured below are lawmakers and highway officials who were instrumental in securing passage of
the 1987 Four-Lane Highway Program. They are (from left to right): Charlie Williams, H. L.
Merideth, Billy McCoy, John David Pennebaker, Anse Dees, Bill Minor, John William Powell, Sam
W. Waggoner, Zack Stewart, Robert Joiner, John R. Tabb, Ollie Mohamed, and Robert Montgomery;
(seated): Morris Lewis, Buddie Newman, and Brad Dye.
James H. Kopf
Fiscal Year 2000
That every Mississippian would be linked to a fourlane
highway within 30 miles or 30 minutes was the
goal of the Mississippi Department of Transportation
(MDOT) at the inception of the 1987 Four-Lane Highway
Program ('87 Program) and it remains our goal today.
This state-of-the-art four-lane highway construction
program didn't just happen. In 1987, state lawmakers
put into place a means to fund this effort and through
a shared vision among legislative leaders and grassroots
advocates, the '87 Program (or A.H.E.A.D.* Program
as it is sometimes known) was born.
The MDOT staff is committed to seeing this fourphase
program completed in a timely, cost-efficient manner
as funds become available. The good news is 13 years
into the program Mississippians are already realizing
benefits through improved safety and a stronger economy.
As of June 30, 2000, 622 miles of new four-lane highway
are in use by the public. An additional 319.4 miles
are under contract, which leaves 146.6 miles of Phases
II and III to be let to contract as funds are received.
The dedicated revenue stream for the '87 Program
remains strong. A complete history of MDOT's receipts
and disbursements for this program and its funding source
can be found on pages 8 and 9 of this booklet. For
fiscal year 2000, MDOT recorded $216.2 million in receipts
and $303.7 million in disbursements. The additional $87.5
million in disbursements was met utilizing bond revenue
and a cash balance from earlier in the program.
When the '87 Program was passed into law by the
Mississippi Legislature, it was funded with a dedicated
revenue stream on a "pay as you go" philosophy. This
revenue stream was to construct 1,088 miles of fourlane
highway in three phases by the year 2001. Since
that time, rising costs, environmental issues, the addition
of extra lane miles for bypasses, and the addition
of Phase IV (723 miles), have pushed the price
tag for the program higher than the original estimate.
Instead of the $1.6 billion price tag first estimated in
1987, the total program – including Phase IV – is now
expected to cost in the neighborhood of $5.2 billion.
The chart on the following page details the cost
history of the '87 Program from 1987 – 2000 and shows
the rising costs over the years. Approximately $2.2 billion
have already been expended on this program.
In order to keep the program moving forward and
in an attempt to meet the construction pace mandated
y the Legislature, MDOT was authorized to borrow
$200 million in bonds. These bonds were sold in fiscal
Where does that leave us today
MDOT has worked diligently to meet legislatively
mandated deadlines that were specified at the inception
of the '87 Program and in fact, did so for 109 of
the construction projects listed on the map found on
page 14 of this booklet. However, in some cases, projects
fell short of the intended time frame because revenue
was not readily available to meet all of the needs due
to numerous factors that occurred in the pre-construction
phase. These factors include: environmental issues, relocation
of utilities and lack of replacement housing.
The intent of the original drafters of the '87 Program
was for the work to be completed in phases that
overlapped each other with the bulk of the work being
conducted in Phase II. The original deadlines to have
every project of each phase let to contract were June
30, 1993, for Phase I; June 30, 1998, for Phase II; and
June 30, 1999, for Phase III. The chart below lists those
projects that were let to contract, but failed to meet
mandated deadlines. (A description of these projects
can be found on pp. 15-20, under the section entitled
"List of Construction Projects.")
Key Highway County
# 57 US 82 Webster
# 61 & 62 US 45 Monroe
# 63 US 45 Monroe/Lee
in Billions
1987 1,600.0
# 84 SR 302 DeSoto
# 93 SR 302 DeSoto/Marshall
# 112 US 49W Yazoo
# 114 US 84 Lincoln
# 115 US 45A Lowndes
# 117 US 82 Webster/Choctaw
# 122 US 61 Jefferson
# 111 US 98 Marion
# 120 SR 25 Attala/Winston
# 121 US 82 Montgomery
The chart below lists the Phase II and Phase III projects
that are scheduled to be let in fiscal year 2001 (A more
complete description can be found on page 21.)
All Phase I projects are completed or under
Highway County
US 61 Jefferson
SR 25 Oktibbeha
US 45 Wayne
US 82 Oktibbeha (2)
US 84 Lincoln
US 45 Wayne/Clarke
US 82 Webster
Leake
Preliminary engineering has begun on every segment
of highway to be improved under Phase IV of
the program. Construction of this phase is not scheduled
to begin until fiscal year 2005.
Mississippi is making a renewed commitment to its
ports, air services, rails and public transit system. But,
we can not forget the impact an adequate highway system
has made – and is still making – on our economy and
overall prosperity. Through improved safety and economic
growth, we are well on our way to realizing the
dream envisioned by lawmakers and grassroots advocates
just 13 years ago. With our continued commitment
to the 1987 Four-Lane Highway Program, we will
move Mississippi AHEAD.
* A.H.E.A.D. is an acronym for Advocating Highways for Economic
Advancement and Development.
Map 1987 Four-Lane Highway Program (including Phase IV)
1987 Four-Lane Highway Program Financial Report
Receipts and Disbursements
FY 1988 FY 1989 FY 1990 FY 1991 FY 1992 FY 1993 FY 1994 FY 1995
Fuel Tax 26.4 48.0 57.7 57.4 59.9 60.5 63.9 65.0
Lubricating Oil Tax 0.9 1.1 1.1 1.0 1.3 1.1 1.1 1.2
Contractor's Tax 0.4 2.1 2.1 2.7 3.1 2.9 3.7 1.6
Tag Fees 7.3 9.7 9.7 9.5 9.8 10.3 10.2 11.3
Debt Service Funds 3.2 4.2 4.2 9.9 15.0 20.9 25.5 42.0
Federal Funds 16.4 34.6 33.6 34.8 28.0 64.8 67.7 55.7
State Matching Funds 9.0 7.3 8.5 6.2 6.3 5.2 5.2 6.8
Other Income 0.1
Bond Proceeds
Total Receipts 63.6 107.0 116.9 121.5 123.4 165.7 177.3 183.7
Highway Expenditures 32.9 79.9 95.7 115.5 132.0 147.8 147.4 156.7
Total Disbursements 32.9 79.9 95.7 115.5 132.0 147.8 147.4 156.7
Excess Receipts Over
(Under) Disbursements 30.7 27.1 21.2 6.0 (8.6) 17.9 29.9 27.0
Projected vs. Actual Receipts
Fiscal Years 1988-2000
Cost Estimate History
Fuel Tax/Oil Tax 751.2 812.1
Contractor's Tax 42.0 42.0
Tag Fees 132.5 137.1
Debt Service Funds 344.6 334.9
Federal Funds 559.5 588.6
State Matching Funds 85.7 88.5
Other 11.3
Bond Proceeds 200.0 203.9
Total Receipts 2,115.5 2,218.4
Note: The Mississippi Legislature added Phase IV
during 1994.
FY 1996 FY 1997 FY 1998 FY 1999 FY 2000 Totals
66.7 67.5 72.2 74.2 78.0 797.4
1.2 1.1 1.1 1.2 1.3 14.7
191.9 189.7 189.8 371.7 216.2 2218.4
203.7 230.0 235.2 256.9 276.9 2,110.6
(11.8) (40.3) (45.4) 114.8 (87.5) 81.0
Cash Flow Projection
For Fiscal Years 2001-2018*
Fiscal Year Receipts Hwy. Expend. Debt Service Excess/(Under) Beg. Cash Bal. End. Cash Bal.
FY01 191.1 210.0 26.7 (45.6) 81.0 35.4
FY03 190.1 164.6 27.0 (1.5) 13.0 11.5
FY04 190.1 142.1 26.8 21.2 11.5 32.7
FY08 190.1 161.4 25.9 2.8 84.7 87.5
FY10 190.1 197.7 (7.6) 67.6 60.0
FY14 189.1 204.5 (15.4) 45.9 30.5
FY15 169.1 202.3 (33.2) 30.5 (2.7)
FY16 159.1 190.4 (31.3) (2.7) (34.0)
FY17 149.1 118.1 31.0 (34.0) (3.0)
FY18 144.1 54.9 89.2 (3.0) 86.2
Totals 3,280.8 3,042.0 233.6 5.2 81.0 86.2
* MDOT will update this projection annually and will revise as viable factors change.
Highway Segments Open to Traffic
Highway Segments Open to Traffic as of June 30, 2000.
Route Description Phase Miles* Cost* County(ies)
i US 45 from Lauderdale/Clarke Co. Line to Corinth
US 45 between Saltillo & Corinth I 38.2 105,334,084.28 Lee; Prentiss; Alcorn
US 45 between New Wren & Shannon I 11.6 41,928,101.14 Monroe; Lee
US 45 between Columbus Air Force Base & Aberdeen I 16.7 52,629,584.95 Monroe; Lowndes
US 45 between Macon Bypass & Brooksville I 12.1 17,852,345.26 Noxubee
US 45 from south of Clarke County Line to I-59 I 12.1 50,983,096.08 Lauderdale
ii US 45A from US 82 to Shannon
US 45A south of Okolona to Shannon I 14.1 44,041,377.78 Chickasaw; Monroe; Lee
US 45A between US 82 & West Point I 7.1 19,064,790.88 Lowndes; Clay
iii US 49W from US 49 to Yazoo River
iv US 49W from Inverness to Indianola
US 49W between Inverness & Indianola I 5.4 10,652,541.43 Sunflower
v US 61 from Port Gibson to south of Vicksburg
US 61 between Port Gibson & Yokena I 14.2 32,267,551.88 Claiborne; Warren
vi US 72 from Mt. Pleasant to Burnsville
US 72 between Stricklin & Burnsville I 7.0 11,733,320.68 Alcorn; Tishomingo
US 72 between Walnut & Corinth I 20.1 61,174,741.57 Alcorn; Tippah
US 72 between Mount Pleasant & SR 5 I 20.3 52,743,577.77 Benton; Marshall
vii US 78 from Holly Springs to Tremont
US 78 between Fulton Bypass & Tremont I 9.3 32,982,267.44 Itawamba
US 78 between Holly Springs & New Albany Bypass I 23.7 80,762,748.08 Marshall; Benton; Union
viii US 82 from I-55 to Alabama State Line
US 82 between SR 12 & Alabama Line I 8.4 25,448,632.43 Lowndes
US 82 from 2 miles West of Eupora to SR 15 I 12.1 40,361,769.93 Webster
US 82 from Winona Bypass to Kilmichael I 14.0 41,337,664.33 Montgomery
ix US 84 from I-59 to Jones/Wayne Co. Line
US 84 between Laurel (I-59) & Jones/Wayne county line I 10.6 25,447,786.84 Jones
x US 98 from Columbia to Alabama State Line
US 98 from 1.5 miles East of US 49 to Ala. State Line I 60.2 109,310,456.11 Forrest; Perry; Greene; George
US 98 between Columbia & Marion/Lamar County Line I 7.5 7,640,786.25 Marion
Route Description Phase Miles Cost County(ies)
i SR 25 from SR 471 to Starkville
SR 25 between SR 471 & SR 43 II 9.9 9,514,840.41 Rankin
ii SR 63 from Jackson/George Co. Line to Lucedale
SR 63 between Jackson County Line & Lucedale Bypass II 7.4 9,068,629.00 George
iii SR 302 from I-55 Southaven to US 72 Mt. Pleasant
SR 302 from 2.2 km east of Hacks Cross Rd to SR 309** II 4.4 12,427,364.97 DeSoto; Marshall
SR 302 between Airways Boulevard & US 78 II 11.0 31,464,722.35 DeSoto
iv US 45 from Alabama State Line north to US 278
US 45 from Kemper/Noxubee County Line to Macon II 9.6 22,729,139.51 Noxubee
US 45 between Lauderdale & Noxubee County Line II 28.5 46,614,062.16 Lauderdale; Kemper
US 45 from Clarkco State Park to Lauderdale Co. Line** II 8.7 10,088,213.02 Clarke
v US 45A from West Point to 4 miles south of Okolona
US 45A from SR 8 to south of Okolona** II 6.8 16,341,657.85 Chickasaw; Monroe
US 45A from SR 25 to SR 8 II 6.7 15,679,999.30 Monroe
US 45A from West Point to SR 25 II 8.2 24,077,004.56 Clay; Monroe
vi US 45A from Brooksville to US 82
US 45A from Brooksville to Lowndes County Line** II 4.6 18,158,561.90 Noxubee
vii US 49W from Yazoo River to Inverness
US 49W between Belzoni (SR12) & Inverness II 15.0 17,607,470.91 Sunflower; Humphreys
US 49W between Silver City & SR 12 at Belzoni** II 6.3 8,992,166.31 Humphreys
viii US 61 from Louisiana State Line to Tennessee State Line
US 61 from SR 4 (south of Tunica) to Tenn. State Line II 29.1 91,792,777.37 Tunica; Desoto
US 61 between Clarksdale Bypass & US 49 II 13.2 22,379,858.79 Coahoma
US 61 between Natchez Trace & Jefferson County Line II 2.8 5,412,471.13 Adams
US 61 at the Homochitto River Bridge II 2.0 10,447,487.60 Wilkinson; Adams
US 61 between Buffalo River & Adams County Line II 7.3 20,251,897.38 Wilkinson
US 61 at the Buffalo River II 1.6 5,715,907.16 Wilkinson
ix US 72 from SR 5 to Walnut
US 72 between SR 5 & Walnut** II 16.8 51,128,635.85 Benton; Tippah
x US 78 from Tremont to Alabama State Line
US 78 between Tremont & Alabama State Line II 4.0 13,378,923.79 Itawamba
xi US 82 from Montgomery/Webster Co. Line to Starkville
xii US 84 from Leesdale to Waynesboro
US 84 from Jones/Wayne County Line to Waynesboro II 13.6 11,754,073.19 Jones; Wayne
US 84 from Covington County Line to Laurel II 14.2 29,853,027.32 Jones
US 84 between Auburn Road & I-55 II 5.5 3,956,286.24 Lincoln
US 84 between Leesdale & Roxie II 7.1 6,122,675.52 Franklin
xiii US 98 from Pike/Walthall Co. Line to west of Hattiesburg
US 98 between Marion/Lamar County Line & SR 589 II 10.6 15,925,178.23 Lamar
US 98 Bypass at Tylertown II 5.1 6,762,997.29 Walthall
US 98 Bogue Chitto River to Tylertown Bypass** II 6.6 13,901,190.31 Walthall; Pike
i SR 25 from SR 43 to Winston/Oktibbeha Co. Line
SR 25 between SR 16 & SR 35 III 9.2 17,117,596.34 Leake
SR 25 from SR 43 to SR 16** III 21.5 30,980,628.53 Leake; Scott; Rankin
As of June 30, 2000 622.0 1,463,342,669.39
* Construction costs may change due to incidental changes after a segment of highway is open to traffic. Slight differences in mileage totals are the
result of rounding figures.
** Opened to traffic during fiscal year 2000.
Map Status of Construction
List of Construction Projects
(Map with corresponding key numbers on page 14)
Key County Highway Project Description
1 Franklin US 84 From Leesdale to Roxie, 7.1 miles. Four lanes open to traffic.
2 Forrest & Perry US 98 From 1.5 miles east of US 49 to 1.0 mile east of SR 29, 15.4 miles. Four lanes
open to traffic.
3 Alcorn & Tishomingo US 72 From Stricklin to Burnsville, 7.0 miles. Four lanes open to traffic.
4 Montgomery US 82 The US 82 Winona Bypass, 3.0 miles. Four lanes open to traffic.
5 Leake State Route 25 From SR 16 to SR 35 (the Carthage Bypass), 9.2 miles. Four lanes open to traffic.
6 Lauderdale US 45 From SR 19 northward to the US 45 Bypass at I-59, 1.3 miles. Four lanes open to traffic.
7 Wilkinson & Adams US 61 Homochitto River Bridge and approaches, 2.0 miles. Four lanes open to traffic.
8 Itawamba US 78 From the interchange south of Fulton to the Alabama State Line, 12.8 miles. Four
lanes open to traffic.
9 Sunflower US 49W From the Inverness Bypass to Indianola, 7.2 miles. Four lanes open to traffic.
10 Lowndes US 82 From SR 12 to the Alabama State Line, 7.7 miles. Four lanes open to traffic.
11 Benton & Union US 78 From Hickory Flat to the west end of the New Albany Bypass, 9.1 miles. Four lanes
12 George US 98 From the Lucedale Bypass to the Alabama State Line, 6.9 miles. Four lanes open to traffic.
13 Lee US 45 From Saltillo to SR 370, 9.7 miles. Four lanes open to traffic.
14 Wayne US 84 From the Jones County Line to 3.0 miles east of Whistler, 9.6 miles. Four lanes
15 Marshall & Benton US 78 From the Holly Springs Bypass to Hickory Flat, 14.6 miles. Four lanes open to traffic.
16 Marion US 98 From Columbia to the Lamar County Line, 8.2 miles. Four lanes open to traffic.
17 Lauderdale US 45 From 5.0 miles north of the Clarke County Line to SR 19, 6.1 miles.
Four lanes open to traffic.
18 Jones US 84 From I-59 to the Wayne County Line, 10.6 miles. Four lanes open to traffic.
19 Lauderdale & Kemper US 45 Northbound from 2.0 miles north of Lauderdale to Porterville, 11.1 miles.
(Map with corresponding key numbers on page 14) List of Construction Projects
20 Wilkinson US 61 Replace bridges at Buffalo River, 1.5 miles. Four lanes open to traffic.
21 Lincoln US 84 From Auburn Road to I-55, 5.5 miles. Four lanes open to traffic.
22 Coahoma US 61 From the Clarksdale Bypass northward, 7.0 miles. Four lanes open to traffic.
23 Alcorn US 45 From the Prentiss County Line to Corinth, 10.3 miles. Four lanes open to traffic.
24 Lowndes & Clay US 45A From US 82 north to West Point, 7.1 miles. Four lanes open to traffic.
25 DeSoto State Route 302 From Airways Blvd. to Swinnea Road, 1.1 miles. Four lanes open to traffic.
26 Prentiss US 45 From SR 370 to SR 4, 12.4 miles. Four lanes open to traffic.
27 Perry & Greene US 98 From 2.0 miles west of the Perry/Greene County Line to Little Oktibee Creek, 9.2
miles. Four lanes open to traffic.
28 Warren US 61 From the Big Black River Bridge to the beginning of four lanes at Yokena, 7.0 miles.
29 Jones US 84 From SR 28 to the beginning of four lanes west of Laurel, 1.8 miles. Four lanes
30 Wayne US 84 From 3.0 miles east of Whistler to the Waynesboro Bypass, 4.2 miles. Four lanes
31 Kemper US 45 From Porterville to Scooba, northbound, 10.1 miles. Four lanes open to traffic.
32 Greene US 98 From Little Oktibee Creek to the East Relief Bridge over the Chickasawhay River,
5.8 miles. Four lanes open to traffic.
33 Lauderdale & Clarke US 45 From 1.0 mile south of the Clarke County Line to the Meridian Bypass, 6.3 miles.
34 Prentiss US 45 From SR 4 to the Alcorn County Line, 6.1 miles. Four lanes open to traffic.
35 Greene & George US 98 From the East Relief Bridge over the Chickasawhay River to the Lucedale Bypass,
36 Coahoma US 61 From 7.0 miles north of Clarksdale to US 49 near Lula, 6.2 miles. Four lanes open
to traffic.
37 Claiborne US 61 From Port Gibson to the Big Black River, 7.8 miles. Also, replaced bridge at
Kennison Creek approximately 1.0 mile south of the Big Black River. Four lanes
38 Noxubee US 45 From the south end of the Macon Bypass to Brooksville, 12.1 miles. Four lanes
39 George US 98 The Lucedale Bypass, 9.7 miles. Four lanes open to traffic.
40 Monroe & Lee US 45A From south of SR 41 to Shannon, 8.7 miles. Four lanes open to traffic.
41 Chickasaw & Monroe US 45A From 4.0 miles south of Okolona to south of SR 41, 5.4 miles. Four lanes open to traffic.
42 Humphreys & Sunflower US 49W From SR 12 to Inverness, 15.0 miles. Four lanes open to traffic.
43 Perry US 98 From 1.0 mile east of SR 29 to 2.0 miles west of the Greene County Line, 9.9
44 Adams US 61 From 0.3 mile north of the Natchez Trace Parkway to the Jefferson County Line,
45 Montgomery US 82 From the Winona Bypass to Kilmichael, 11.0 miles. Four lanes open to traffic.
46 George SR 63 From the Jackson County Line to the Lucedale Bypass, 7.4 miles. Four lanes open to traffic.
List of Construction Projects (Map with corresponding key numbers on page 14)
47 Marshall US 72 From Mount Pleasant eastward to the Benton County Line, 12.0 miles. Four lanes
48 Alcorn US 72 From Goose Creek Bottom to Corinth, 11.1 miles. Four lanes open to traffic.
49 Alcorn US 72 From 1.0 mile east of the Tippah County Line to Goose Creek Bottom, 3.8 miles.
50 Tippah & Alcorn US 72 From Walnut to 1.0 mile east of the Alcorn County Line, 5.7 miles. Four lanes
51 Rankin State Route 25 From SR 471 to SR 43, 9.9 miles. Four lanes open to traffic.
52 Lowndes & Monroe US 45 From Columbus Air Force Base to McKinley Creek, 8.0 miles. Four lanes open to traffic.
53 Monroe US 45 From McKinley Creek to the interchange at SR 25 and SR 8 near Lackey, 6.1 miles.
54 Webster US 82 From 2.0 miles west of Eupora eastward, 5.8 miles. Four lanes open to traffic.
55 Benton US 72 From the Marshall County Line to SR 5, 8.3 miles. Four lanes open to traffic.
56 Kemper US 45 From Scooba to the Noxubee County Line, northbound, 7.3 miles. Four lanes open
57* Webster US 82 From 5.8 miles east of Eupora to one-half mile west of SR 15, 6.4 miles. Four lanes
58 Noxubee US 45 From the Kemper County Line to the Macon Bypass, 9.6 miles. Four lanes open to traffic.
59 Lamar US 98 From the Marion County Line to SR 589, 10.6 miles. Four lanes open to traffic.
60 Jones US 84 From SR 29 to SR 28 west of Laurel, 3.5 miles. Four lanes open to traffic.
61* Monroe US 45 From Lackey to near Aberdeen, 2.7 miles. Four lanes open to traffic.
62* Monroe US 45 From New Wren to Town Creek, 4.96 miles. Four lanes open to traffic.
63* Monroe & Lee US 45 From Town Creek to Shannon, 6.614 miles. Four lanes open to traffic.
64 DeSoto State Route 302 From Swinnea Road to US 78, 9.902 miles. Four lanes open to traffic.
65 Tunica US 61 From SR 4, south of Tunica, to State Aid Road 72, 5.7 miles. Four lanes open to traffic.
66 Tunica US 61 From State Aid Road 72 to 6.0 miles north of Tunica, 4.3 miles. Four lanes open to traffic.
67 Tunica & DeSoto US 61 From 6.0 miles north of Tunica to SR 3, 9.2 miles. Four lanes open to traffic.
68 Tippah US 72 From the Benton County Line to the four-lane section at Walnut, 6.0 miles. Four
69 Benton US 72 From east of the Wolfe River to the Tippah County Line, 10.0 miles. Four lanes
70 Wilkinson US 61 From north of the Buffalo River to the Adams County Line, 7.3 miles. Four lanes
71 DeSoto US 61 From SR 3 to the Tenn. State Line, 9.9 miles. Four lanes open to traffic.
72 Walthall US 98 The Tylertown Bypass, 5.1 miles. Four lanes open to traffic.
73 Jones US 84 From the Covington County Line to west of SR 29, 8.9 miles. Four lanes open to traffic.
74 Clay & Monroe US 45A From north of West Point to SR 25, 8.2 miles. Four lanes open to traffic.
75 Wilkinson US 61 From SR 563 to the Buffalo River, 6.7 miles. Four lanes open to traffic.
* Project failed to meet legislatively mandated letting date of June 30, 1993, for Phase I.
76 Pike & Walthall US 98 From the Bogue Chitto River to the west end of the Tylertown Bypass, 6.6 miles.
77 Monroe US 45A From SR 25 to SR 8, 6.7 miles. Four lanes open to traffic.
78 Monroe & Chickasaw US 45A From SR 8 to 4.0 miles south of Okolona, 6.8 miles. Four lanes open to traffic.
79 Bolivar US 61 A. From Merigold to Shelby, 11.76 miles. Grade, drain and bridge four lanes on new
location. Awarded 9/95.
B. Paving contract awarded 4/98.
80 Franklin US 84 A. From Eddiceton to Lucien, 7.4 miles. Grading complete on two lanes.
81 Franklin & Lincoln US 84 From Lucien to Auburn Road, 5.8 miles. Four lanes open to traffic.
82 Clarke US 45 From the Clarkco State Park to 1.0 mile south of the Lauderdale County Line, 8.5
83 Humphreys US 49W From Silver City to SR 12 West at Belzoni, 6.3 miles. Four lanes open to traffic.
84** DeSoto State Route 302 From US 78 to 1.5 miles east of Hacks Cross Road, 4.9 miles. Grade, drain, bridge,
and pave four lanes on new location. Paving contract awarded 6/96.
85 Coahoma & Tunica US 61 A. From US 49 near Lula to Dundee, 7.1 miles. Grade, drain, and bridge two
additional lanes. Awarded 6/96.
86 Tunica US 61 A. From Dundee to SR 4, 8.4 miles. Grade, drain, and bridge two additional lanes.
Awarded 6/96.
87 Noxubee US 45 From Brooksville to the Lowndes County Line, 4.6 miles. Four lanes open to traffic.
88 George SR 63 A. The Lucedale Bypass, 8.7 miles. Grade, drain and bridge four lanes on new
89 Clarke US 45 A. From DeSoto to Clarkco State Park, 11.5 miles. Grade, drain and bridge four
lanes on new location. Awarded 11/96.
90 Monroe US 45 A. From Aberdeen to New Wren, 12.7 miles. Grade, drain, and bridge two
additional lanes. Awarded 11/96.
91 Wayne US 45 A. The Waynesboro Bypass, 6.6 miles. Grade, drain and bridge four lanes on new
92 Oktibbeha State Route 25 A. From existing SR 25 south of Starkville to the interchange with relocated US 82
northwest of Starkville, 8.4 miles. Grade, drain and bridge four lanes on new
B. Paving contract scheduled to be let fiscal year 2001.
93** DeSoto & Marshall State Route 302 From 1.5 miles east of Hacks Cross Road to 1.0 mile west of SR 309, 4.4 miles.
94 Rankin, Scott & Leake State Route 25 From SR 43 to Ludlow, 11.4 miles. Four lanes open to traffic.
95 Wayne & Clarke US 45 A. From Hiwanee to DeSoto (Shubuta Bypass), 10.0 miles. Grade, drain and bridge
four lanes on new location and some construction of two lanes parallel to existing
lanes. Awarded 7/97.
** Project failed to meet legislatively mandated letting date of June 30, 1998, for Phase II.
96 Oktibbeha US 82 A. From 2.7 miles west of Adaton to the interchange with relocated SR 25
northwest of Starkville, 7.7 miles. Grade, drain and bridge four lanes on new location.
97 Covington/Jefferson Davis US 84 A. From the Jefferson Davis County Line to Collins, 12.5 miles. Grading completed
on two lanes.
98 Oktibbeha US 82 A. From the Choctaw County Line to 2.7 miles west of Adaton, 7.32 miles. Grade,
drain and bridge awarded 9/97.
99 Leake State Route 25 From Ludlow to SR 16, 9.6 miles. Four lanes open to traffic.
100 Marshall State Route 302 A. From 1.0 mile west of SR 309 to Mt. Pleasant, 9.939 miles. Grade, drain and
bridge four lanes on new location. Awarded 2/98.
101 Leake State Route 25 A. From SR 35 to Renfroe, 7.3 miles. Grade, drain, and bridge two lanes parallel to
existing SR 25. Awarded 3/98.
B. Grade, drain, and bridge, two lanes; pave four lanes on 7.3 miles. Awarded 4/00.
102 Wayne US 45 A. From the North Waynesboro Bypass, 2.2 miles. Grade, drain and bridge four
lanes on new location. Awarded 7/96.
B. From Winchester to US 84 (South Waynesboro Bypass) 5.9 miles. Grade, drain
and bridge four lanes on new location. Awarded 6/98. Paving contract scheduled to
be let fiscal year 2001.
103 Claiborne US 61 A. From the Jefferson County Line to 1.0 mile south of the Natchez Trace south of
Port Gibson, 3.636 miles. Grade, drain and bridge two lanes parallel to existing US
61. Awarded 4/98.
104 Oktibbeha US 82 A. From relocated SR 25 to Clayton Village (Starkville Bypass), 4.894 miles. Grade,
drain and bridge four lanes on new location. Awarded 4/98.
105 Coahoma US 61 A. From the Bolivar County Line to US 49 (bypass near Clarksdale), 9.53 miles.
Grade, drain and bridge two lanes parallel to existing US 61.
106 Yazoo US 49W From the US 49W and SR 3 interchange to Carter Road, 2.86 miles. Grade, drain,
bridge, and pave four lanes on new location. Includes the bridge over the Yazoo
River. Awarded 5/98.
107 Webster US 82 A. From the Montgomery County Line to Eupora Bypass, 6.534 miles. Grade, drain
and bridge two lanes parallel to existing US 82. Awarded 5/98.
108 Yazoo & Humphreys US 49W A. From Carter Road to Silver City, 13.0 miles. Grade, drain and bridge four lanes
on new location. Awarded 5/98. Rescinded 11/98.
B. Grade, drain, bridge and pave contract scheduled to be let fiscal year 2002.
109 Walthall US 98 A. From the east end of the Tylertown Bypass to the Marion County Line, 5.05
miles. Grading completed on two lanes.
B. Paving contract awarded 10/99.
110 Leake State Route 25 A. From Renfroe to the Attala County Line, 9.6 miles. Grade, drain, and bridge two
lanes parallel to existing SR 25. Awarded 6/98.
111*** Marion US 98 A. From the Walthall County Line to Foxworth, 9.5 miles. Grading completed on
two lanes.
*** Project failed to meet legislatively mandated letting date of June 30, 1999, for Phase III.
112** Yazoo US 49W From Yazoo City to SR 3, 1.8 miles. Grade, drain, bridge, and pave four lanes on
new location. Awarded 7/98.
113 Bolivar US 61 From Shelby to Coahoma County Line, 10.7 miles. Grade, drain, bridge, and pave
two lanes parallel to existing US 61. Awarded 9/98.
114** Lincoln US 84 A. From the Brookhaven Bypass to the Lawrence County Line, 7.3 miles. Grade,
drain and bridge two lanes parallel to existing US 84. Awarded 3/99.
115** Lowndes US 45A From Artesia Road to US 82 near Mayhew, 5.7 miles. Grade, drain, bridge, and pave
two lanes parallel to existing lanes. Awarded 1/99.
116 Wayne US 45 From the Waynesboro Bypass to Hiwanee, 6.7 miles. Grade, drain, bridge and pave
117** Webster & Choctaw US 82 From 0.5 mile west of SR 15 to Oktibbeha County Line, 1.62 miles. Grade, drain,
bridge, and pave four lanes on new location. Awarded 4/99.
118 Winston State Route 25 From SR 15 to old SR 25 north of Louisville, 6.2 miles. Grade, drain, bridge, and
pave two lanes parallel to existing lanes. Awarded 5/99.
119 Winston State Route 25 From Noxapater Creek to Louisville Relocation, 5.9 miles. Grade, drain and bridge
two lanes; pave four lanes. Awarded 3/99.
120*** Attala & Winston State Route 25 From the Leake County Line to SR 19, 2.0 miles. Grade, drain, bridge and pave four
lanes parallel to existing lanes. Awarded 10/99.
121*** Montgomery US 82 A. From Kilmichael to the Webster County Line, 9.3 miles. Grade, drain and bridge
two lanes. Awarded 10/99.
B. Paving project scheduled to be let fiscal year 2002.
122** Jefferson US 61 From the Fayette Bypass to 0.077 mile north of the Claiborne County line, 9.7
miles. Awarded 3/00.
123 Wayne US 45 A. From SR 42 at State Line to Winchester 13.1 miles. Grade, drain and bridge two
Brief Summary of Phases I, II and III
Miles Open to Four-Lane Traffic ......................................................................................................................................................................................................622.0
Miles Let to Contract (no other contract letting necessary) ................................................................................................................................ 319.4
Miles Remaining to be Let ......................................................................................................................................................................................................................146.6
TOTAL miles improved once Phases I, II and III have been completed .............................................1,088
Projects to be Let Fiscal Year 2001 (July 1, 2000 -June 30, 2001)
All highway segments of Phase I are completed or under contract.
COUNTY HIGHWAY PROJECT DESCRIPTION
Jefferson US 61 From the Adams County Line to Fayette Bypass, 8.67 miles. Grade, drain,
bridge, and pave.
Oktibbeha SR 25 From the Winston County Line to Starkville Bypass, 8.48 miles. Grade,
drain, bridge, and pave.
Wayne US 45 Waynesboro Bypass, 8.16 miles. Pave.
Oktibbeha US 82 From 2.7 miles west of Adaton to relocated SR 25, 7.66 miles. Pave.
Lincoln US 84 From Brookhaven Relocation to the Lawrence County Line, 7.29 miles.
Pave.
Wayne/Clarke US 45 From Hiwanee to the Clarke County Line, 2.43 miles, and from the Wayne
County Line to DeSoto, 7.60 miles. Pave.
Webster US 82 From the Montgomery County Line to Eupora, 6.53 miles. Pave.
Oktibbeha US 82 From relocated SR 25 to Clayton Village, 4.89 miles. Pave.
Coahoma US 61 From the Bolivar County Line to US 49, 6.71 miles. Pave.
Leake SR 25 From Renfroe to the Attala County Line, 10.59 miles. Pave.
Map Status of Right of Way
Right of Way* Activity Under Way (Map with corresponding key numbers on page 22)
1 State Route 25 From Louisville Bypass to Oktibbeha County Line; Winston County
2 US 45A From the Noxubee County Line to US 82; Lowndes County
3 State Route 25 From State Route 19 to Noxapater; Winston County
4 US 84 From the Lincoln County Line to the end of the Monticello Bypass; Lawrence County
5 US 84 From State Route 27 to Prentiss; Lawrence and Jefferson Davis Counties
6 US 84 From Prentiss to the Covington County Line; Jefferson Davis County
7 US 84 The Collins Bypass; Covington County
8 US 84 From Waynesboro to the state line; Wayne County
9 State Route 63 From Leakesville to HWY 98; Greene County, George County
*Right of Way includes all activities relating to acquisition of property required to build a highway, such as right of way engineering,
title search, appraisal, relocation assistance, utility adjustment and negotiation.
Right of Way Not Acquired
* US 61 From 1.0 mile south of the Natchez Trace Parkway to the north city limits of Port Gibson;
Claiborne County.
MISSISSIPPI DEPARTMENT OF TRANSPORTATION
JACKSON, MISSISSIPPI 39215-1850
1987 FOUR-LANE HIGHWAY PROGRAM
<strong>Mississippi</strong> Moving A.H.E.A.D. (ADVOCATING HIGHWAYS FOR ECONOMIC ADVANCEMENT AND DEVELOPMENT) 1987 Four-Lane Highway Program ANNUAL REPORT JULY <strong>2000</strong>
Page 2 and 3: Transportation Commissioners Table
Page 4 and 5: Executive Summary Fiscal Year 2000
Page 6 and 7: 6 M i s s i s s i p p i M o v i n g
Page 8 and 9: 1987 Four-Lane Highway Program Fina
Page 10 and 11: Cash Flow Projection For Fiscal Yea
Page 12 and 13: Highway Segments Open to Traffic Hi
Page 14 and 15: Map Status of Construction 14 M i s
Page 16 and 17: (Map with corresponding key numbers
Page 22 and 23: Map Status of Right of Way 22 M i s
Page 24: MISSISSIPPI DEPARTMENT OF TRANSPORT
Magazine: Ahead 2000 - Mississippi Department of Transportation

redpajama_set_name: RedPajamaCommonCrawl


Have you ever joined an office pool and tried to predict the gender, birthday, and birth time of a newborn? This website gives you an easy, interactive way to participate and join in the fun of the baby guessing game. And it's completely free!
WhatsInMyBelly.com allows you to set up a baby pool and invite friends and family to join in. Think of it as a combination of fantasy football and childbirth.
Can you tell we love numbers?


The government's digital transformation programme is on track to save £1.2bn over the course of this parliament alone and over £1.7bn a year after 2015. Announcing the rapidly shrinking costs just 200 working days after launching the challenge to transform 25 key government services, Cabinet Office Minister, Francis Maude invited a collection of ministers and department bigwigs to give the Sprint 14 audience a live demo of their digital transformation results.
A brave move when relying on an external venue's wifi. However, the odd wifi glitche did nothing to diminish the impressiveness of the solutions showcased: truly so easy to use that a minister could demo them in front of 400 civil servants and the odd journalist.
Greg Clark, minister of state for the cabinet office, kicked off the demoes by registering to vote - a simple and elegant process that collated and checked key information before sending details to the right local electoral registration officer - along with a flag to highlight any suspicious activity that the officer might want to look investigate further. The facility will be available by June this year, with every citizen in the country able to register online to vote by the end of 2014.
Mike Parsons, COO and digital leader at the Home Office (and digital leader) walked the audience through the process for applying for or extending a Tier 2 Priority Visa. Crucially, he explained, the focus was on creating a modular product catalogue of digital building blocks that could be reused across the department's services - or shared with other departments.
David Gauke, exchequer secretary to the treasury, was next up to demonstrate how simple it would be to tell HMRC about a change to your company car - and indeed take control of PAYE details and pay tax due online. The service is the first to use GDS Identity Assurance Service; today's demonstration validated the application via Experian. The service is due for 'private beta' launch in a few weeks' time and, according to Gauke, "is just a taster of bigger changes to come. In future you will be able to use a smartphone, laptop or tablet to manage your tax affairs."
Oliver Morley, chief executive at the DVLA, said that his agency aimed to make being on the road 'simpler, better, safer', and that the new online facility would play a key part in delivering these aims. The new Driver Record programme - part of a wider set of deliverables, including removal of car tax disc and paper counterpart in 2015 - will save around £14m compared to previous service delivery costs. Despite the simplicity, Morley explained that 13 rounds of user testing had been involved: "It looks incredibly simple, but has taken a lot of work to get here."
Jeremy Wright, minister for prisons and rehabilitation, gave the final demonstration: enabling people to plan and book prison visits to loved ones online. This, he said, would not only dramatically speed up a currently paper-laden and slow process and make life easier for citizens, but would also deliver huge savings in staff time. The facility is currently being tested in three prisons, with a wider test planned for the summer before roll out to the public.


text:
New FCC Officer No Friend of Conservative Talk Radio
Posted on Friday, August 07, 2009 by Susan Brinkmann
By Susan Brinkmann, OCDS Staff Writer The Federal Communications Commission (FCC) has named a communications attorney who once railed against conservative and Christian talk radio as its new "Chief Diversity Officer." Newsbusters.com is reporting that the FCC has named Mark Lloyd, a former Senior Fellow at the George Soros-backed Center for American Progress (CAP) as its new Chief Diversity Officer. Lloyd is the author of a June 2007 report entitled, "The Structural Imbalance of Political Talk Radio" in which he suggests ways other than the Fairness Doctrine to shut down conservative talk radio: • Restore local and national caps on the ownership of commercial radio stations. • Ensure greater local accountability over radio licensing. • Require commercial owners who fail to abide by enforceable public interest obligations to pay a fee to support public broadcasting. These last two suggestions are similar to what is known as "localism," an FCC regulatory requirement that radio stations must meet to get and keep their broadcast licenses. The ambiguous term can be used to enforce anything from airing public service announcements to shutting down political talk to which the enforcer does not subscribe. In a follow-up to another CAP report entitled "Forget the Fairness Doctrine," Lloyd instructed liberal activists to use the "localism" requirement to harass conservative stations by filing complaints with the FCC. The FCC would then levy fines against these stations or even shut them down. Therefore, there is no need for the mis-named "Fairness" Doctrine, Lloyd says, obviously endorsing the levying of costly fines and other means to force conservative talk radio off the air. © All Rights Reserved, Living His Life Abundantly®/Women of Grace® http://www.womenofgrace.com
Posted in: Breaking News
Tagged: Chief Diversity Officer • Fairness Doctrine • FCC


text:
\section{Introduction}
Rare $B$ meson decays, induced by flavor--changing neutral current (FCNC)
$b \rightarrow s(d)$ transitions, is one of the most promising research area in
particle physics. Theoretical interest to the $B$ meson decays lies in their
role as a potential precision testing ground for the standard model (SM) at
loop level. Experimentally, these decays will provide quantitative
information about the Cabibbo--Kobayashi--Maskawa (CKM) elements
$V_{td},~V_{ts}$ and $V_{tb}$. Besides these rare decay have the potential
for establishing new physics beyond SM, such as two Higgs doublet model
(2HDM), minimal supersymmetric extension of the SM (MSSM) \cite{R1}.

Firstly the most reliable quantitative test of FCNC processes in $B$ decays
is expected to be measured in inclusive channels. In particular, the decays
$B \rightarrow X_{s,d} \ell^+ \ell^-$ are important probes of the effective
Hamiltonian governing the FCNC transition $b \rightarrow s(d) \ell^+ \ell^-$. The
hope that $B \rightarrow X_s \ell^+ \ell^-$ decay will be measurable in experiments
in the near future, encourage extensive investigation of this process in
the SM, 2HDM and MSSM \cite{R2}--\cite{R15}. The matrix element of the
$b \rightarrow s \ell^+ \ell^-$ contains terms describing the virtual effects
induced by $t\bar t$,  $c\bar c$  and $u\bar u$ loops which are proportional
to $V_{tb}\,V_{ts}^*$, $V_{bc}\,V_{cs}^*$ and $V_{bu}\,V_{su}^*$,
respectively. Using unitarity of the CKM matrix and neglecting
$V_{bu}\,V_{su}^*$ in comparison to $V_{tb}\,V_{ts}^*$ and
$V_{bc}\,V_{cs}^*$, it is obvious that the matrix element for the
$b \rightarrow s \ell^+ \ell^-$ involves only one independent CKM factor
$V_{tb}\,V_{ts}^*$ so that CP--violation in this channel is strongly
suppressed in the SM.

The situation is totally different for the $b \rightarrow d \ell^+ \ell^-$ decay,
since all three CKM factors $V_{tb}\,V_{td}^*$, $V_{cb}\,V_{cd}^*$ and
$V_{ub}\,V_{ud}^*$, are all of the same order (in SM) and therefore can
induce considerable CP--violating difference  between the decay rates of the
reactions $b \rightarrow d \ell^+ \ell^-$ and $\bar b \rightarrow \bar d \ell^+ \ell^-$.

It should be noted here that in presence of a much stronger decay
$b \rightarrow s \ell^+ \ell^-$, the detection of the $b \rightarrow d \ell^+ \ell^-$
decay seems to be more problematic. For this reason, in search of
CP violation the corresponding exclusive decay channels
$B \rightarrow \pi \ell^+ \ell^-$ and $B \rightarrow \rho\, \ell^+ \ell^-$ are more
preferable.
In general, the inclusive decays are rather difficult to measure in
comparison to the exclusive ones. CP--violating effects in inclusive
$b \rightarrow d \ell^+ \ell^-$ and exclusive $B \rightarrow \pi \ell^+ \ell^-$,
$B \rightarrow \rho\, \ell^+ \ell^-$ channels were studied within the framework of
the SM in \cite{R15,R16}.

The aim of the present work is to derive quantitative predictions for the
CP violation in the exclusive $B \rightarrow \pi \ell^+ \ell^-$ and
$B \rightarrow \rho\, \ell^+ \ell^-$ decays, in context of the general two Higgs doublet
model, in which a new source for CP violation is present (see below). 2HDM
model is one of the simplest extension of the SM, which contains
two complex Higgs doublets, while the SM contains only one. In general,
in 2HDM the flavor changing neutral currents (FCNC) that appear at tree
level, are avoided by imposing an {\it ad hoc} discrete symmetry \cite{R18}.
One possible approach to avoid these unwanted FCNC at tree level is to
couple all fermions to only one of the above--mentioned Higgs doublets
(model I). The other possibility is the coupling of the up and down quarks
to the first and second Higgs doublets, with the vacuum expectation values
$v_2$ and $v_1$, respectively (model II). Model II is more attractive since
its Higgs sector coincides with the ones in the supersymmetric model.
In this model there exist five physical Higgs fields: neutral
scalars $H^0$, $h^0$, neutral pseudoscalar $A$ and charged Higgs bosons
$H^\pm$. The interaction vertex of fermions with Higgs fields depends on
$tan \beta=v_2/v_1$, which is the free parameter of the model. The new
experimental results of CLEO and ALEPH Collaborations \cite{R19,R20}
on the branching ratio
$b \rightarrow s \gamma$ decay impose strict restrictions on the charged Higgs
boson mass and $tan \beta$. Recently, the lower bound on these parameters
were determined from the analysis of the $b \rightarrow s \gamma$ decay, including
NLO QCD corrections \cite{R21,R22}. Other indirect bound on the ratio
$m_{H^\pm}/tan \beta$ come from $B \rightarrow D \tau \bar \nu_\tau$ decay, where
$m_{H^\pm} \ge 2.2 tan \beta~GeV$ \cite{R23}, and from
the $\tau$ lepton decays $m_{H^\pm} \ge 1.5 \, tan \beta ~GeV$
\cite{R24}. The consequence of an
analysis without discrete symmetry has been investigated in a more general
model in 2HDM, namely, model III \cite{R25,R26}. In this model FCNC appears
naturally at tree level. However, the FCNC's involving the first two
generations are highly suppressed, as is observed in the low energy
experiments, and those involving the the third generation is not as severely
suppressed as the first two generations, which are restricted by the
existing experimental results.

In this work we assume that all tree level FCNC couplings are negligible.
It should be noted however that, even with this assumption, the couplings of
fermions to Higgs bosons may have a complex phase $e^{i\theta}$.
In other words, in this model there exists a new source of CP violation that
is absent in the SM, model I and model II.
The effects of such an extra phase in the $b \rightarrow s \gamma$ decay were discussed
in \cite{R27,R28}. The constraints on the phase angle $\theta$ in the product
$\lambda_{tt} \lambda_{bb}$ of Higgs--fermion coupling (see below)
imposed by the neutron electric dipole moment,
$B^0 - \bar B^0$ mixing. $\rho \,_0$ parameter and $R_b$ is discussed in
\cite{R28}.

The paper is
organized as follows: In Section 2 we present the necessary theoretical
framework. The branching ratios, CP--violating effects in the partial
widths and forward--backward asymmetry for the above--mentioned
exclusive decay channels are studied in section 3. Section 4 is devoted to
the numerical analysis and concluding remarks.

\section{Theoretical framework}

Before presenting the necessary theoretical background, let us go through
the main essential points of the general Higgs doublet model (model III).
In this model, both Higgs
doublets can couple to up and down quarks. Without loss of generality we can
work in a basis such that the first doublet generates all the fermion and
gauge boson masses, whose vacuum expectation values are
\begin{eqnarray}
\left< \phi_1 \right> = \left( \begin{array}{c}
0 \\ \\
\displaystyle{\frac{v}{\sqrt{2}}}
\end{array} \right)~~~~~,~ \left< \phi_2 \right>~. \nonumber
\end{eqnarray}
In this basis the first doublet $\phi_1$ is the same as in the SM, and all
new Higgs bosons result from the second doublet $\phi_2$, which can be
written in the following form
\begin{eqnarray}
\phi_1 = \frac{1}{\sqrt{2}} \left( \begin{array}{c}
\sqrt{2}\, G^+ \\ \\
v + \chi_1^0 + i G^0
\end{array} \right)~~~~~,
~ \phi_2  = \frac{1}{\sqrt{2}} \left( \begin{array}{c}
\sqrt{2}\, H^+ \\ \\
\chi_2^0 + i A^0
\end{array} \right)~, \nonumber
\end{eqnarray}
where $G^+$ and $G^0$ are the Goldstone bosons. The neutral $\chi_1^0$ and
$\chi_2^0$ are not the physical mass eigenstate, but their linear
combinations give the neutral $H^0$ and $h^0$ Higgs bosons:
\begin{eqnarray}
\chi_1^0 = H^0 cos \alpha - h^0 sin \alpha~, \nonumber \\
\chi_2^0 = H^0 sin \alpha + h^0 cos \alpha~. \nonumber
\end{eqnarray}
The general Yukawa Lagrangian can be written as
\begin{eqnarray}
{\cal L}_Y = \eta_{ij}^U \bar Q_{iL} \tilde \phi_1 U_{jR} +
\eta_{ij}^{\cal D} \bar Q_{iL} \phi_1 {\cal D}_{jR}
+ \xi_{ij}^U \bar Q_{iL} \tilde \phi_2  U_{jR} +
\xi_{ij}^{\cal D} \bar Q_{iL} \phi_2  {\cal D}_{jR} + h.c.~,
\end{eqnarray}
where $i$, $j$ are the generation indices, $\tilde \phi= i \sigma_2 \phi$,
$\eta_{ij}^{U,{\cal D}}$ and $\xi_{ij}^{\cal U,D}$, in general, are the
non--diagonal coupling matrices, $L=(1-\gamma_5)/2$ and $R=(1+\gamma_5)/2$ are
the left-- and right--handed projection operators. In Eq. (1) all states
are weak states, that can be transformed to the mass eigenstates by
rotation. After performing this rotation on the Yukawa Lagrangian, we get
\begin{eqnarray}
{\cal L}_Y = - H^+ \bar U \left[ V_{CKM} \hat \xi^{\cal D} R -
\hat \xi^{U^+} V_{CKM} L \right] {\cal D}~,
\end{eqnarray}
where $U({\cal D})$ represents the mass eigenstates of $u,~c,~t~(d,~s,~b)$
quarks. In the present analysis, we will use a simple ansatz for
$\hat \xi^{U^+,{\cal D}}$ \cite{R25},
\begin{eqnarray}
\hat \xi^{U^+,{\cal D}} = \lambda_{ij}
\frac{g \sqrt{m_i m_j}}{\sqrt{2} m_W}~.
\end{eqnarray}
Also it assumed that $\lambda_{ij}$ is complex, i.e.,
$\lambda_{ij} = \left| \lambda_{ij} \right| e^{i\theta}$, and for simplicity we
choose $\xi^{U,{\cal D}}$ to be diagonal to suppress all tree level FCNC
couplings, and as a result $\lambda_{ij}$ are also diagonal but remain
complex. Note that the results for model I and model II can be obtained from
model III by the following substitutions:
\begin{eqnarray}
&&\lambda_{tt} = cot \beta ~~~~~~~ \lambda_{bb} = - \, cot \beta ~~\mbox{\rm
for model I}~, \nonumber \\
&&\lambda_{tt} = cot \beta ~~~~~~~ \lambda_{bb} = + \, tan  \beta ~~\mbox{\rm
for model II}~,
\end{eqnarray}
and $\theta = 0$.

After this brief introduction about the general Higgs doublet model,
let us return our attention to the $b \rightarrow d \ell^+ \ell^-$
decay. The powerful framework into which the
perturbative QCD corrections to the physical decay amplitude incorporated
in a systematic way, is the effective Hamiltonian method.
In this approach, the heavy degrees of freedom in the present case,
i.e., $t$ quark, $W^\pm,~H^\pm,~h^0,~H^0$ are integrated out.
The procedure is to match the
full theory with the effective theory at high scale $\mu = m_W$, and then
calculate the Wilson coefficients at lower $\mu \sim {\cal O}(m_b)$ using the
renormalization group equations. In our calculations we choose the higher
scale as $\mu = m_W$, since the charged Higgs boson is heavy enough
($m_{H^\pm} \ge 210 ~GeV$ see \cite{R21}) to neglect the evolution from
$m_{H^\pm}$ to $m_W$.

In the version of the 2HDM we consider in this work, the charged Higgs boson
exchange diagrams do not
produce new operators and the operator basis is the same as the one used
for the $b \rightarrow d \ell^+ \ell^-$ decay in the SM.
For this reason in the model under consideration,
the charged Higgs boson contributions to leading order change only the value
of the Wilson coefficients at $m_W$ scale, i.e.,
\begin{eqnarray}
C_7^{2HDM}(m_W) &=& C_7^{SM}(m_W) + C_7^{H^\pm}(m_W) \nonumber \\
C_9^{2HDM}(m_W) &=& C_9^{SM}(m_W) + C_9^{H^\pm}(m_W) \nonumber \\
C_{10}^{2HDM}(m_W) &=& C_{10}^{SM}(m_W) + C_{10}^{H^\pm}(m_W)~. \nonumber
\end{eqnarray}
The coefficients $C_i^{2HDM} (m_W)$ to the leading order are given by
\begin{eqnarray}
C_7^{2HDM}(m_W) &=&
x \, \frac{(7-5 x - 8 x^2)}{24 (x-1)^3} +
\frac{x^2 (3 x - 2)}{4 (x-1)^4} \, \ell n x \nonumber \\
&+& \left| \lambda_{tt} \right|^2 \Bigg( \frac{y(7-5 y - 8 y^2)}
{72 (y-1)^3} + \frac{y^2 ( 3 y - 2)}{12 (y-1)^4} \, \ell n y \Bigg) \nonumber \\
&+& \lambda_{tt} \lambda_{bb} \Bigg( \frac{y(3-5 y)}{12 (y-1)^2} +
\frac{y (3 y - 2)}{6 (y-1)^3} \, \ell n y \Bigg)~, \\ \nonumber \\ \nonumber \\
C_9^{2HDM}(m_W) &=& - \frac{1}{sin^2 \theta_W} \, B(m_W) +
\frac{1 - 4 sin^2 \theta_W}{sin^2 \theta_W} \, C(m_W) \nonumber \\
&+& \frac{-19 x^3 + 25 x^2}{36 (x-1)^3} +
\frac{-3 x^4 + 30 x^3 - 54 x^2 + 32 x -8}{18 (x-1)^4} \, \ell n x
+ \frac{4}{9} \nonumber \\
&+& \left| \lambda_{tt} \right|^2 \Bigg[
\frac{1 - 4 sin^2 \theta_W}{sin^2 \theta_W} \, \frac{x y}{8} \Bigg(
\frac{1}{y-1} - \frac{1}{(y-1)^2} \, \ell n y \Bigg)\nonumber \\
&-& y \Bigg( \frac{47 y^2 - 79 y + 38}{108 (y-1)^3}
-\frac{3 y^3 - 6 y^3 + 4}{18 (y-1)^4} \, \ell n y \Bigg) \Bigg]~,
\\ \nonumber \\ \nonumber \\
C_{10}^{2HDM}(m_W) &=& \frac{1}{sin^2 \theta_W} \Big( B(m_W) -
C(m_W) \Big) \nonumber \\
&+& \left| \lambda_{tt} \right|^2 \frac{1}{sin^2 \theta_W} \,\frac{x y}{8}
\Bigg( - \frac{1}{y-1} + \frac{1}{(y-1)^2} \, \ell n y \Bigg)~,
\end{eqnarray}
where
\begin{eqnarray}
B(x) &=& - \frac{x}{4 (x-1)} + \frac{x}{4 (x-1)^2} \, \ell n x ~, \nonumber \\
C(x) &=& - \frac{x}{4} \Bigg( \frac{x-6}{3 (x-1)} +
\frac{3 x +2 }{2 (x-1)^2} \ell n x \Bigg)~,\nonumber \\
x &=& \frac{m_t^2}{m_W^2} ~, \nonumber \\
y &=& \frac{m_{H^\pm}^2}{m_W^2}~.
\end{eqnarray}
and $sin^2\theta_W = 0.23$ is the Weinberg angle.
It follows from Eqs. (5--7)
that among all the Wilson coefficients, only $C_7$ involves the new phase
angle $\theta$.
We have neglected the
neutral Higgs boson exchange diagram contributions, since Higgs boson--fermion
interaction is proportional to the lepton mass.

The effective Hamiltonian for the $b \rightarrow d \ell^+ \ell^-$ decay is
[29--32]
\begin{eqnarray}
{\cal H} = -4 \frac{G_F}{2\sqrt 2} V_{tb} V^*_{td}
\left\{\sum_{i=0}^{10} C_i(\mu) O_i(\mu) +
\lambda_u \sum_{i=1}^{2} C_i(\mu) \left[ O_i(\mu) - O_i^u(\mu)
\right] \right\}~, \nonumber
\end{eqnarray}
where
$$ \lambda_u = \displaystyle{\frac{V_{ub} V^*_{ud}}{V_{tb} V^*_{td}}}~,$$ and $C_i$ are
the Wilson coefficients.
The explicit form of all operators $O_i$ can be found in [29--32].

The evolution of the Wilson coefficients from the higher scale
$\mu = m_W$ down to the low energy scale $\mu = m_b$ is described by the
renormalization group equation
\begin{eqnarray}
\mu \frac{d}{d\mu}C_i^{eff(\mu)} =
C_i^{eff}(\mu) \gamma_\mu^{eff}(\mu)~, \nonumber
\end{eqnarray}
where $\gamma$ is the anomalous dimension matrix.
The coefficient $C_7^{eff}(\mu)$ at the scale ${\cal O}(m_b)$
in NLO is calculated in \cite{R21,R22}:
\begin{eqnarray}
C_7^{eff}(m_b) = C_7^0(m_b) + \frac{\alpha_s(m_b)}{4 \pi}
C_7^{1,eff}(m_b)~,\nonumber
\end{eqnarray}
where $C_7^0(m_b)$ is the leading order (LO) term and $C_7^{1,eff}(m_b)$
describes the NLO terms, whose explicit forms can be found in
\cite{R21}. In our case,
the expressions for these coefficients can be obtained from the results of
\cite{R21} by making the following replacements:
\begin{eqnarray}
\left| Y \right|^2  \rightarrow \left| \lambda_{tt} \right|^2 ~~~~~ \mbox{\rm and} ~~~~~
X Y^*  \rightarrow \left| \lambda_{tt} \lambda_{bb} \right| e^{i\theta}~. \nonumber
\end{eqnarray}
In the SM, the QCD corrected Wilson coefficient $C_9(m_b)$, which
enters to the decay amplitude up to the next leading order has been
calculated in [29--32]. The Wilson coefficient $C_{10}$ does not
receive any new corrections at all, i.e., $C_{10}(m_b) \equiv
C_{10}^{2HDM}(m_W)$.  As we have already noted, in the version of the 2HDM we
consider in this work, there does not appear any new operator other than
those that exist in the SM, therefore it is enough to make the
replacement $C_9^{SM}(m_W) \rightarrow C_{9}^{2HDM}(m_W)$ in [29--32], in order
to calculate $C_{9}^{2HDM}$ at $m_b$ scale. Hence, including the NLO
QCD corrections, $C_9(m_b)$ can be written as:
\begin{eqnarray}
\lefteqn{
C_9(\mu) = C_9^{2HDM}(\mu)
\left[1 + \frac{\alpha_s(\mu)}{\pi} \omega (\hat s) \right]} \nonumber \\
&&+ \, g(\hat m_c,\hat s) \Big[ 3 C_1(\mu) + C_2(\mu) + 3 C_3(\mu) + C_4(\mu)
+ 3 C_5(\mu) + C_6(\mu) \Big] \nonumber \\
&&+ \,\lambda_u \Big[g(\hat m_c,\hat s) - g(0,\hat s)\Big]
\Big( 3 C_1(\mu) + C_2(\mu) \Big) -
\frac{1}{2} g(0,\hat s) \left( C_3(\mu) + 3 C_4(\mu) \right) \nonumber \\
&&-\,  \frac{1}{2} g \left( 1, \hat s\right)
\left( 4 C_3 + 4 C_4 + 3 C_5 + C_6 \right)
- \frac{1}{2} g \left( 0, \hat s\right) \left( C_3 + 3 C_4 \right) \nonumber \\
&&+\, \frac{2}{9} \left( 3 C_3 + C_4 + 3 C_5 + C_6 \right)~,
\end{eqnarray}
where $m_c = m_c/m_b~, ~\hat s = p^2/m_b^2$, and
\begin{eqnarray}
\lefteqn{
\omega \left( \hat s \right) = - \frac{2}{9} \pi^2 -
\frac{4}{3} Li_2  \left( \hat s \right) - \frac{2}{3} \ell n \left( \hat s\right)
\,\ell n \left( 1 -\hat s \right)} \nonumber \\
&&- \,\frac{5 + 4 \hat s}{3 \left( 1 + 2 \hat s \right)} \ell n \left( 1 -\hat s \right)
-\frac{2 \hat s \left( 1 + \hat s \right) \left( 1 - 2 \hat s \right)}
{3 \left( 1 - \hat s \right)^2 \left( 1 + 2 \hat s \right)} \, \ell n \left( \hat s\right)
+ \frac{5 + 9 \hat s - 6 {\hat s}^2}
{3 \left( 1 - \hat s \right) \left( 1 + 2 \hat s \right)}~
\end{eqnarray}
represents the ${\cal O}\left( \alpha_s \right)$ correction from the one gluon
exchange in the matrix element of $O_9$, while the function
$g \left( \hat m_c, \hat s \right)$ arises from one loop contributions of the
four--quark operators $O_1$--$O_6$, whose form is
\begin{eqnarray}
\lefteqn{
g \left( \hat m_c, \hat s \right) = - \frac{8}{9} \ell n \left( \hat m_i\right)
+ \frac{8}{27} + \frac{4}{9} y_i - \frac{2}{9} \left( 2 + y_i \right)} \nonumber \\
&& +\, \sqrt{\left| 1-y_i \right|} \Bigg\{ \Theta \left( 1 - y_i \right)
\Bigg( \ell n \frac{1+\sqrt{\left| 1-y_i \right|}}{1-\sqrt{\left| 1-y_i \right|}}
- i \, \pi \Bigg)
+ \Theta \left( y_i -1 \right) 2 arctan \frac{1}{\sqrt{y_i - 1}} \Bigg\}~,
\end{eqnarray}
where $y_i = 4 {\hat m_i}^2/{\hat p}^2$.

The Wilson coefficients $C_9$ receives also long distance contributions,
which have their origin in the real $u\bar u$, $d\bar d$ and $c\bar c$
intermediate states, i.e., $\rho$, $\omega$ and $J/\psi$, $\psi^\prime$,
$\cdots$. In the case of the $J/\psi$ family this usually
accomplished by introducing a Breit--Wigner distribution for the resonance
through the replacement ([4--7,33])
\begin{eqnarray}
g \left( \hat m_c, \hat s \right) \rightarrow g \left( \hat m_c, \hat s \right) -
\frac{3\pi}{\alpha^2_{em}}
\, \kappa \sum_{V_i=J/\psi_i,\psi^\prime,\cdots}
\frac{m_{V_i} \Gamma(V_i \rightarrow \ell^+ \ell^-)}
{(p^2 - m_{V_i}^2) + i m_{V_i} \Gamma_{V_i}}~,
\end{eqnarray}
where the phenomenological parameter $\kappa =2.3$ is chosen in order to
reproduce correctly the experimental value of the branching ratio
(see for example \cite{R16})
\begin{eqnarray}
{\cal B}(B \rightarrow J/\psi X \rightarrow X \ell^+ \ell^-)={\cal B}(B \rightarrow J/\psi X)
\,{\cal B}(J/\psi \rightarrow X \ell^+ \ell^-)~. \nonumber
\end{eqnarray}
In order to avoid the double counting,
in this work,  as an alternative to the functions
$g \left( \hat m_u, \hat s \right)$ and $g \left( \hat m_c, \hat s \right)$ that
describe the effects of $u \bar u$ and $c \bar c$ loops, we have used a
different procedure, in which these functions are expressed through the
normalized vacuum polarization $\Pi^\gamma_{had}(\hat s)$ that is related to
the experimentally measurable quantity
\begin{eqnarray}
R_{had}(\hat s) = \frac{\sigma_{tot} (e^+ e^- \rightarrow hadrons)}
{\sigma(e^+ e^- \rightarrow \mu^+ \mu^-)}~,
\end{eqnarray}
via the dispersion relation ( see \cite{R16,R17} for more detail).
In this way it is possible to include the
$\rho,~\omega,~J/\psi,~\psi^\prime,~\cdots$ resonances into the differential
cross section in an approximate way, consistent with the idea of global
duality. In this approach the $\omega$ and $J/\psi$ family resonances are
well described through the Breit--Wigner form and $\rho$ resonance is
introduced by
\begin{eqnarray}
R_{res}^\rho = \frac{1}{4} \left( 1 - 4 \frac{\hat m_\pi^2}{\hat s} \right)^{3/2}
\left| F_\pi (\hat s) \right|^2~,
\end{eqnarray}
where $F_\pi (\hat s)$ is the pion form factor that is represented by a
modified Gounaris--Sakurai formula (see \cite{R34,R35}).

The effective short--distance Hamiltonian for $b \rightarrow d\ell^+ \ell^-$
decay [29--32] leads to the QCD corrected matrix element (when the $d$
quark mass is neglected)
\begin{eqnarray}
{\cal M} &=& \frac{G_F \alpha}{2\sqrt 2 \pi} V_{td} V^*_{tb} \Bigg\{
C_9^{eff} \bar d \gamma_\mu (1- \gamma_5) b \, \bar \ell \gamma^\mu \ell +
C_{10} \bar d \gamma_\mu (1- \gamma_5) b \, \bar \ell
\gamma^\mu \gamma_5 \ell \nonumber \\
&-& 2 C_7\frac{m_b}{p^2}\bar d i \sigma_{\mu \nu}p^\nu (1+\gamma_5)  b  \,
\bar \ell \gamma^\mu \ell~,
\end{eqnarray}
where $p^2$  is the invariant dilepton mass. In Eq. (12) all Wilson
coefficients are evaluated at the $\mu = m_b$ scale.

\section{The exclusive $B \rightarrow \pi \ell^+ \ell^-$ and
$B \rightarrow \rho\, \ell^+ \ell^-$ decays}
In this section, we proceed to calculate the
branching ratio and CP violating asymmetry in the
$B \rightarrow \pi \ell^+ \ell^-$ and $B \rightarrow \rho\, \ell^+ \ell^-$ decays. It
follows from the matrix element of the $b \rightarrow d \ell^+ \ell^-$ that
in order to be able to calculate the matrix element of the exclusive decay
$B \rightarrow M \ell^+ \ell^-$, the matrix elements
$\langle M \vert \bar d \gamma_\mu (1 + \gamma_5 ) b \vert B \rangle$ and
$\langle M \vert \bar d i\, \sigma_{\mu\nu}p_\nu (1 + \gamma_5 ) b \vert B \rangle$
($M=\pi$ or $\rho$)
have to be calculated. These matrix elements can be parametrized in the
following way:
\begin{eqnarray}
\left< \pi \left( p_\pi \right) \left| \bar d \gamma_\mu (1 - \gamma_5 ) b
\right| B \left( p_B \right) \right> &=&
f^+(p^2) \left( p_B + p_\pi \right)_\mu + f^-(p^2) p_\mu~, \\
\left< \pi \left( p_\pi \right) \left| \bar d i\, \sigma_{\mu\nu}p_\nu (1 + \gamma_5 ) b
\right| B \left( p_B \right) \right> &=&
\left[\left( p_B + p_\pi \right)_\mu p^2 - p_\mu \left( m_B^2 - m_\pi^2 \right) \right]
\frac{f_T(p^2)}{m_B+m_\pi}~, \\
\left< \rho (p_\rho, \varepsilon) \left| \bar d \gamma_\mu( 1- \gamma_5) b \right|
B(p_B) \right> &=&
- \epsilon_{\mu \nu \lambda \sigma} \varepsilon^{*\nu} p_\rho^\lambda p_B^\sigma
\frac{2 V(p^2)}{m_B + m_{\rho}} \nonumber \\
&-& i \varepsilon_\mu^* ( m_B + m_\rho) A_1(p^2)
+ i (p_B + p_\rho)_\mu (\varepsilon^* p) \frac{A_2(p^2)}{m_B + m_\rho}\nonumber \\
&+& i p_\mu (\varepsilon^* p) \frac{2 m_\rho}{p^2} \left[ A_3(p^2) - A_0 (p^2)
\right] ~, \\
\left< \rho (p, \varepsilon) \left| \bar d i \sigma_{\mu \nu} p^\nu (1+ \gamma_5) b
\right| B(p_B) \right> &=&
4 \epsilon_{\mu \nu \lambda \sigma} \varepsilon^{* \nu} p^\lambda
p^\sigma T_1 (p^2) \nonumber \\
&+&  2 i \left[ \varepsilon_\mu^* (m_B^2 - m_\rho^2) - (p_B + p_\rho)_\mu (\varepsilon^* p)
\right] T_2 (p^2) \nonumber \\
&+&  2 i (\varepsilon^* p) \left[ p_\mu - (p_B+p_\rho)_\mu \frac{p^2}{m_B^2 -
m_\rho^2} \right] T_3 (p^2)~.
\end{eqnarray}
In all of the matrix elements above,
$p = p_B-p_M$ ($M = \pi$ or $\rho$) and $\varepsilon^*$ is the
four--polarization vector of the $\rho$ meson.
Using Eqs. (15--19) we obtain for the matrix elements of the
$B \rightarrow \pi \ell^+ \ell^-$ and $B \rightarrow \rho\, \ell^+ \ell^-$ decays:
\begin{eqnarray}
{\cal M}^{B \rightarrow \pi} &=& \frac{G \alpha}{2 \sqrt{2} \pi}\,
V_{tb} V_{td}^* \Bigg\{ \left( 2 A p_{\pi\mu} + B p_\mu \right)
\bar \ell \gamma_\mu \ell
+\left( 2 C p_{\pi\mu} + D p_\mu \right)\bar \ell \gamma_\mu \gamma_5 \ell
\Bigg\}~, \\ \nonumber \\ \nonumber \\
{\cal M}^{B \rightarrow \rho} &=& \frac{G \alpha}{2 \sqrt{2} \pi} V_{tb} V_{td}^*
\Bigg\{ \bar \ell \gamma_\mu \ell
\left[ 2 A_1 \epsilon_{\mu \nu \lambda \sigma}
\varepsilon^{* \nu} p_\rho^\lambda p_B^\sigma +
i B_1 \varepsilon^*_\mu - i B_2 ( \varepsilon^* p) ( p_B + p_\rho)_\mu
- i B_3 (\varepsilon^* p) p_\mu \right] \nonumber \\
&+& \bar \ell \gamma^\mu \gamma_5 \ell
\left[ 2 C_1 \epsilon_{\mu \nu \lambda \sigma}
\epsilon^{* \nu} p_\rho^\lambda p_B^\sigma +
i D_1 \epsilon^*_\mu - i D_2 (\varepsilon^* p) ( p_B + p_\rho)_\mu -
i D_3 (\varepsilon^* p) p_\mu \right] \Bigg\}~,
\end{eqnarray}
where
\begin{eqnarray}
A &=& C_9^{eff} f^+ - C_7 \frac{2 m_b f_T(p^2)}{m_B + m_\pi}~, \nonumber \\
B &=& C_9^{eff} \left( f^+ + f^- \right) + C_7 \left( \frac{2 m_b f_T}{p^2} \right)
\left( \frac{m_B^2 - m_\pi^2 - p^2}{m_B+m_\pi}\right)~,\nonumber \\
C &=& C_{10} f^+ ~, \nonumber \\
D &=& C_{10} \left( f^+ + f^- \right) ~, \nonumber \\
A_1 &=& C_9^{eff} \frac{V}{m_B + m_\rho} + 4 C_7 \frac{m_b}{p^2} T_1~, \nonumber \\
B_1 &=& C_9^{eff} (m_B + m_\rho) A_1 + 4 C_7 \frac{m_b}{p^2} (m_B^2 -
m_\rho^2) T_2~,  \nonumber \\ \nonumber \\
B_2 &=& C_9^{eff} \frac{A_2}{m_B + m_\rho} + 4 C_7 \frac{m_b}{p^2} \left( T_2
+
 \frac{p^2}{m_B^2 - m_\rho^2} T_3 \right)~,  \nonumber \\ \nonumber \\
B_3 &=& -C_9^{eff}\frac{ 2 m_\rho}{  p^2}(A_3 - A_0) + 4 C_7
\frac{m_b}{p^2}T_3~,  \\ \nonumber \\
C_1 &=& C_{10} \frac{V}{m_B + m_\rho}~,  \nonumber \\ \nonumber \\
D_1 &=& C_{10} (m_B + m_\rho) A_1~,  \nonumber \\ \nonumber \\
D_2 &=& C_{10} \frac{A_2}{m_B + m_\rho}~,  \nonumber \\ \nonumber \\
D_3 &=& C_{10} \frac{2 m_\rho}{p^2} (A_3 - A_0)~. \nonumber
\end{eqnarray}
Using Eqs. (20) and (21) and performing summation over final lepton
and $\rho$ meson polarization (in the $B \rightarrow \rho\, \ell^+ \ell^-$ case),
we obtained the following results for the double differential decay rates
(the masses of the leptons, in our case electron or muon, are neglected):
\begin{eqnarray}
\lefteqn{
\frac{d \Gamma^{B \rightarrow \pi}}{dp^2 dz} = \frac{G^2 \alpha^2 }{2^{11} \pi^5} \,
\frac{ \left| V_{tb} V_{ts}^* \right|^2 \sqrt \lambda}{m_B}
\,\lambda m_B^4 (1-z^2) \Bigg[ \left( \left| A \right|^2 +
\left| C \right|^2 \right) \Bigg]~,} \\ \nonumber \\ \nonumber \\
\lefteqn{
\frac{d \Gamma^{B \rightarrow \rho}}{d p^2 dz} = \frac{G^2 \alpha^2
\left| V_{tb} V_{td}^* \right|^2\sqrt{\lambda}}{2^{12}
\pi^5 m_B} \Bigg\{ 2 \lambda m_B^4 \Bigg[ m_B^2 s ( 1+ z^2) \left(
\left| A_1 \right| ^2 +\left| C_1 \right| ^2 \right) \Bigg] } \nonumber \\
&&+ \frac{1}{2 r} \Bigg[ m_B^2 \left( \lambda (1- z^2) + 8 r s \right)
\left( \left| B_1 \right|^2 + \left| D_1 \right|^2 \right)
- 2 \lambda m_B^4
(1-r-s)(1-z^2)  \nonumber \\ && \times \Big( Re\left(  B_1 B_2^*  \right) + Re \left( D_1 D_2^*  \right)
\Big)\Bigg]
+ \lambda^2 m_B^6 (1- z^2) \, \frac{1}{2 r}\, \left( \left| B_2
\right| ^2 + \left| D_2 \right| ^2 \right) \nonumber \\
&&+ 8 m_B^4 s z \sqrt{\lambda} \Big( Re\left(  B_1 C_1^* \right) + Re\left( A_1 D_1^*\right) \Big)
 \Bigg\}~,
\end{eqnarray}
where $z=cos \theta$\,, $\theta$ is the angle between the three--momentum of the
$\ell^+$ lepton and that of the $B$ meson in the center of mass frame of the
lepton pair,
$\lambda(1,r_M,s) = 1+r_M^2+s^2 -2 r_M - 2 s - 2 r_M s$, $r_M =
\frac{\displaystyle{m_M^2}}{\displaystyle{m_B^2}}$, and
$s=\frac{\displaystyle{p^2}}{\displaystyle{m_B^2}}$ ($M=\pi$ or $\rho$).
The CP violating asymmetry between $B \rightarrow M \ell^+ \ell^-$
and $\bar B \rightarrow \bar M \ell^+ \ell^-$ decays is defined as
\begin{eqnarray}
A_{CP} (p^2) = \frac{\displaystyle{\frac{d \Gamma}{dp^2} -
\frac{d \bar \Gamma}{dp^2}}}{\displaystyle{\frac{d \Gamma}{dp^2}+
\frac{d \bar \Gamma}{dp^2}}}~.
\end{eqnarray}
where
\begin{eqnarray}
\frac{d \Gamma}{dp^2} = \frac{d \Gamma \left( \bar B \rightarrow M \ell^+ \ell^- \right)}
{dp^2}~~~~~~~~~~\mbox{\rm and}~~~~~~~~~~
\frac{d \bar \Gamma}{dp^2} = \frac{d \Gamma \left(  B \rightarrow \bar M \ell^+ \ell^-
\right)} {dp^2}~. \nonumber
\end{eqnarray}
The differential decay widths $B \rightarrow \pi \ell^+ \ell^-$ and
$B \rightarrow \rho\, \ell^+ \ell^-$ can easily be obtained from Eqs. (23) and
(24) by integrating over $z$. Finally we get the following results
for CP violating asymmetry for the $B \rightarrow \pi \ell^+ \ell^-$ and
$B \rightarrow \rho\, \ell^+ \ell^-$ decays
\begin{eqnarray}
A_{CP}^{B \rightarrow \pi}(p^2) &\simeq& - \frac{2}{\left( \left| A \right|^2
+ \left| C \right|^2 \right)}
\Bigg\{ \left| f_+ \right|^2 \left( \mbox{\rm Im} \lambda_u \right)
\left( \mbox{\rm Im}\xi_1^* \xi_2 \right) \\
&+& f_+ f_T \, \frac{2 m_b}{m_B + m_\pi}
\Big[ \left( \mbox{\rm Im} \xi_1 \right) \eta_2 -
\left( \mbox{\rm Im} \lambda_u \right) \left( \mbox{\rm Im} \xi_2 \right) \eta_1
+ \left( \mbox{\rm Re} \lambda_u \right) \left(  \mbox{\rm Im} \xi_2 \right) \eta_2
\Big]\Bigg\}~, \nonumber \\ \nonumber \\ \nonumber \\
A_{CP}^{B \rightarrow \rho}(p^2) &\simeq& {\displaystyle \frac{1}{\Sigma^\rho}} \, \Bigg\{ - 2
\left( \mbox{\rm Im} \lambda_u \right) \left( \mbox{\rm Im}\xi_1^* \xi_2 \right)
\Bigg[ \frac{16}{3} \lambda m_B^6 s \left| \frac{V}{m_B+m_\rho} \right|^2
+ \frac{2 \lambda^2 m_B^6}{3 r}
\left| \frac{A_2}{m_B+m_\rho} \right|^2 \nonumber \\
&+& \frac{1}{2 r} m_B^2 \left( \frac{4}{3} \lambda  + 16 r s \right)
\left( m_B + m_\rho \right) \left| A_1 \right|^2  -
\frac{4}{3} \lambda m_B^4 \frac{(1-r-s)}{r} A_1 A_2 \Bigg] \nonumber \\
&+& \Bigg[ 2 \left( \mbox{\rm Im} \xi_1 \right) \eta_2 -
2 \left( \mbox{\rm Im} \lambda_u \right) \left( \mbox{\rm Im} \xi_2 \right) \eta_1
+ 2 \left( \mbox{\rm Re} \lambda_u \right) \left(  \mbox{\rm Im} \xi_2 \right) \eta_2 \Bigg]
\nonumber \\
&\times&\Bigg[ \frac{64 \lambda m_B^6 m_b s}{3 p^2} \, \frac{T_1 V}{m_B + m_\rho} +
\frac{8 \lambda^2 m_B^6 m_b}{3 r p^2}  \, \frac{A_2}{m_B + m_\rho}
\left( T_2 + \frac{p^2}{(m_B^2 - m_\rho^2)} \, T_3 \right) \nonumber \\
&+& \frac{2 m_B^2 m_b}{r p^2} \left( \frac{4}{3} \lambda + 16 r s \right)
A_1 T_2 ( m_B + m_\rho ) (m_B^2 - m_\rho^2) \nonumber \\
&-& \frac{2}{3} \lambda m_B^4 (1-r-s) \Bigg(
( m_B + m_\rho ) \frac{4 m_b}{p^2}\,
A_1 \Big( T_2 + \frac{p^2}{(m_B^2 - m_\rho^2)} \, T_3 \Big) \nonumber \\
&+& \frac{4 m_b ( m_B - m_\rho )}{p^2} \,A_2 T_2 \Bigg) \Bigg] \Bigg\}~,
\end{eqnarray}
where
\begin{eqnarray}
\Sigma^\rho &=& \frac{16}{3} \lambda m_B^6 s
\left( \left| A \right|^2+ \left| C \right|^2 \right) +
\frac{2}{3r} \lambda^2 m_B^6  \left( \left| B_2 \right|^2+ \left| D_2 \right|^2 \right) \nonumber \\
&+& \frac{1}{2 r} \Bigg[ m_B^2 \left( \frac{4}{3} \lambda + 16 r s \right)
\left( \left| B_1 \right|^2+ \left| D_1 \right|^2 \right) \nonumber \\
&-& \frac{8}{3} \lambda m_B^4 (1-r-s) \Big( \left( \mbox{\rm Re} B_1 B_2 \right)
 + \left( \mbox{\rm Re} D_1 D_2 \right) \Big) \Bigg]~.
\end{eqnarray}
In deriving these expressions, we have used the following parametrization
\begin{eqnarray}
C_9^{eff} &\equiv& \xi_1 + \lambda_u \xi_2~, \nonumber \\
C_7^{eff} &\equiv& \eta_1 + i \,\eta_2~,
\end{eqnarray}
and assumed that all form factors are positive (see below). Interference of
$C_9^{eff}$ and $C_7^{eff}$ terms gives new contribution to the CP
violating asymmetry.
The results for the CP asymmetry in model II can be
obtained from
Eqs. (26) and (27) by substituting Eq. (3) (i.e., $\eta_2 = 0$).

At the end of this section we present forward--backward asymmetry $A_{FB}$,
which involve different combination of the Wilson coefficients. The analysis
of $A_{FB}$ is very useful in extracting precise information about the sign
of the Wilson
coefficients and the new physics. The forward--backward asymmetry is defined
as
\begin{eqnarray}
A_{FB} (p^2) = \frac{\displaystyle{\int_0^1 dz \frac{d \Gamma}{dp^2 dz} -
\int_{-1}^0 dz
\frac{d \Gamma}{dp^2 dz}}}{\displaystyle{\int_0^1 dz \frac{d \Gamma}{dp^2
dz}+
\int_{-1}^0dz\frac{d \Gamma}{dp^2 dz}}}~.
\end{eqnarray}
The forward--backward asymmetry for the $B \rightarrow \pi \ell^+ \ell^-$ decay is
zero, both in SM and 2HDM, in the limit $m_\ell \rightarrow 0$. We can explain
this fact briefly as follows. The hadronic current for $B \rightarrow \pi \ell^+
\ell^-$ decay is a pure vector and the lepton current is also
conserved when $m_\ell \rightarrow 0$. The charge asymmetry (or $A_{FB}$) is
non--zero if there exist $C$--vilolating terms but such terms are clearly
absent in the $B \rightarrow \pi \ell^+ \ell^-$. Using Eq. (24), the
forward--backward asymmetry for the $B \rightarrow \rho\, \ell^+ \ell^-$ takes the
following form:
\begin{eqnarray}
A_{FB}^\rho = \frac{8 m_B^4 s \sqrt{\lambda}
\Big[ \left( \mbox{\rm Re} B_1 C_1^* \right) + \left( \mbox{\rm Re} A_1 D_1^* \right) \Big]}
{\Sigma^\rho} ~.
\end{eqnarray}

Finally, we examine the CP--violating difference between $A_{FB}$ and
$\bar A_{FB}$, i.e.,
\begin{eqnarray}
\delta A_{FB} = A_{FB} - \bar A_{FB} \nonumber~,
\end{eqnarray}
with $\bar A_{FB}$ being the forward--backward asymmetry in the
anti particle channel, which can be obtained by the replacement
\begin{eqnarray}
C_9^{eff}(\lambda_u) \rightarrow \bar C_9^{eff}(\lambda_u \rightarrow \lambda_u^*)~, \nonumber
\end{eqnarray}
whose explicit can easily be obtained from Eq. (31), with the above
mentioned replacement of $C_9^{eff}$.

\section{Numerical analysis}
Before presentation of our quantitative calculations and graphics,
we would like to note that we have considered two different versions, namely
model II and model III of the 2HDM, in our analysis. For the free parameters
$\lambda_{bb}$ and $\lambda_{tt}$ of model III, we have used the
restrictions coming from $B \rightarrow X_s \gamma$ decay, $B^0$--$\bar B^0$
mixing, $\rho$ parameter and neutron electric--dipole moment \cite{R28},
that yields $\left| \lambda_{bb} \right| = 50$, $\left| \lambda_{tt}\right| \le 0.03$.

The values of the main input parameteres, which appear in the expressions
for the branching ratios, $A_{FB}$ and $A_{CP}$ are:
$m_b = 4.8~GeV,~m_c = 1.4~GeV,~m_\tau = 1.78~GeV,~m_B = 5.28~GeV,
m_\pi = 0.14~GeV$. For $B$ meson lifetime we take
$\tau(B) = 1.56 \time 10^{-12}~s$ \cite{R36}.
The values of the Wilson coefficients are,
$C_1 = - 0.249$, $C_2 = 1.108$, $C_3 = 1.112 \times 10^{-2}$,
$C_4 = -2.569 \times 10^{-2}$, $C_5 = 7.4 \times 10^{-3}$,
$C_6 = - 3.144 \times 10^{-2}$.
Throughout the course of the numerical analysis, we have used the
Wolfenstein parametrization of the CKM matrix elements, i.e.,
\begin{eqnarray}
\lambda_u =\frac{V_{ub}V_{ud}^*}{V_{tb} V_{td}^*} =
\frac{\rho(1-\rho) -\eta^2 + i\, \eta}{(1-\rho)^2 + \eta^2}
+ {\cal O}(\lambda^2)~, \nonumber
\end{eqnarray}
for which we have used the following three different sets of parameters,
\begin{eqnarray}
(\rho,\eta) = \left\{ \begin{array}{l}
~~~(0.3;0.34) \\ \\
~~~(-0.07;0.34)\\ \\
~~~(-0.3;0.34)~.
\end{array} \right. \nonumber
\end{eqnarray}
Of course the explicit expressions for the form factors are needed in the
present numerical analysis. In the current literature these form factors
have been calculated in the
framework of the three point QCD sum rule \cite{R37}, relativistic quark
model \cite{R38}, and light
cone QCD sum rules [39--41]. In further numerical analysis we have used
the light cone QCD sum rule predictions on the form factors. It should be
noted that the light cone QCD sum rule predictions on the form factors are
reliable in the region $m_b^2 - p^2 \sim {\cal O}$(few $GeV^2$). In order to
extend to the full physical region we have used best fitted expressions by
extrapolating the numerical results with the condition that these approximate
formulas reproduce the light cone QCD sum rule predictions to a good
accuracy, in the above--mentioned region. The form of form factors which satisfy
this condition can be written in terms of three parameters as \cite{R39,R40}
\begin{eqnarray}
F(p^2) = \frac{\displaystyle {F(0)}}{\displaystyle{1-a_F\,\frac{p^2}{m_B^2} + b_F \left
    ( \frac{p^2}{m_B^2} \right)^2}}~, \nonumber
\end{eqnarray}
where the values of parameters $F(0)$, $a_F$ and $b_F$ for the relevant
decays, $B \rightarrow \pi$ and $B \rightarrow \rho$,
are listed in Table 1 (this Table is taken from \cite{R39,R40}

Firstly we consider model II for numerical calculations.
In Figs. (1) and (2) we present the dependence of the differential decay
widths of the $B \rightarrow \pi e^+ e^-$ and $B \rightarrow \rho\, e^+ e^-$ on $p^2$ for
$(\rho,\eta) = (0.3;0.34)$ at $m_{H^\pm} = 250~GeV$ and $tan\beta=1$, with and
without long distance contributions, correspondingly.
In Figs. (3) and (4) we plot the variation of the CP--violating asymmetry
$A_{CP}$ with respect to $p^2$, with the following set of parameters:
$(\rho,\eta) = (0.3;0.34)$ and $tan\beta=1$. In both figures, the solid
line corresponds to the SM case, dash--dotted and dotted lines represent
the CP--violating asymmetry at two different values of the mass of
charged Higgs boson $m_{H^\pm} = 250~GeV$ and $500~GeV$, respectively. The
total branching ratios for the $B \rightarrow \pi e^+ e^-$ and $(B \rightarrow \rho\, e^+ e^-)$
decays at three different sets of Wolfenstein parameters and at $m_{H^\pm} =
250 ~GeV$ are presented in Table 2.
From Figs. 1--4 we see that, in model II the dependences of the branching
ratio and $A_{CP}$
asymmetry on $p^2$ are very similar to those predicted by the SM, but their
magnitudes different in these models. These results are expected, since in
model II, the charged Higgs contributions change only the values of the
Wilson coefficients $C_7$, $C_9$ and $C_{10}$. In this version of the 2HDM
charged Higgs contributions give rise to constructive interference to the SM
result. Therefore the branching ratio increases and CP asymmetry decreases.

We presented in Table 2, the numerical values of the average values of the CP
violating asymmetry $\langle A_{CP} \rangle$, in the
region $1~GeV^2 < p^2 < \left( m_{J/\psi} - 0.02~GeV \right)^2$, using the same values
of the Wolfenstein parameters used in Figs. 3 and 4.

The dependence of the forward--backward asymmetry on $p^2$
$A_{FB}(B \rightarrow \rho\, e^+ e^-)$ is plotted in Fig. (5)
for SM and model II, with the same set of parameters as in Fig. (1).
It is observed that the value of $p^2$ at which $A_{FB}$ becomes zero is
shifted in model II. Therefore, in future experiments,
the determination of the value of $p^2$ at which
$A_{FB}$ is zero can give unambiguous information about the presence of
new physics.
In Fig. (6) we plot the resulting difference in the forward--backward
asymmetry for the values of Wolfenstein parameters
$(\rho,\eta) = (-0.07;0.2)$, with and without the long distance effects.
From these figures we observe that, $\delta F_{AB}$ for the
$B \rightarrow \rho\, e^+ e^-$ decay is positive in the non resonant region for all
values of $p^2$, both in SM and model II.

Note that, the results we have presented for forward--backward
asymmetry and its difference are performed for $(\rho,\eta) = (-0.07;0.2)$.
However, for sake
of completeness, we have gone through the same analysis
for two different sets of the Wolfenstein parameters, namely,
$(\rho,\eta) = (-0.3;0.34)$ and $(\rho,\eta) = (-0.07;0.34)$, as well as
several different choices of $\tan\beta$. The numerical
results and the relevant graphical presentations have demonstrated that, no
remarkable differences have been observed among these different choices.
In Figs. (7) and (8) we present the dependence of the CP asymmetry
$A_{CP}$, integrated over $p^2$, for the $B \rightarrow \pi e^+ e^-$ and
$B \rightarrow \rho\, e^+ e^-$ decays on the phase angle $\theta$ at
$m_{H^\pm} = 250~GeV$, $\left| \lambda_{bb}\right| = 50$ and
$\left| \lambda_{tt}\right| = 0.03$,
without the long distance effects in model III. From both figures, especially from
$B \rightarrow \rho\, e^+ e^-$ case,  we observe that, the average CP asymmetry
differs essentially from the one predicted by model II. In the region
$\pi/2 < \theta < 3 \pi/2$, the change in $\left< A_{CP} \right>$ is more
than 2.5 times than that predicted by model II. This fact can be explained
as, the charged Higgs and SM contributions interference destructively in the
above--mentioned region of $\theta$. It should be stressed that, depending
on the value of the phase angle $\theta$, the charged Higgs contributions
can interfere with the SM results, either constructively or destructively.
This case is absolutely different in model II, where the above--mentioned
contributions interfere only constructively. The values of the branching
ratios $B \rightarrow \pi \ell^+ \ell^-$ and $B \rightarrow \rho \, \ell^+ \ell^-$ decays
at different values of the phase angle $\theta$ in model III are presented
in Table 4.

In conclusion, the exclusive $B \rightarrow \pi \ell^+ \ell^-$ and
$B \rightarrow \rho \, \ell^+ \ell^-$ decays are analyzed in the 2HDM and it is
found that, the CP violating asymmetry in model III differs essentially from
the ones predicted by model II.
\newpage

redpajama_set_name: RedPajamaArXiv


I am going to confess that I was somewhat biased in favour of the 2017 Subaru Impreza, before even driving it – five years ago, I bought a 2004 Impreza RS with almost 200,000 kilometres on the clock. It was from a friend who had bought it from another friend, who had bought it new. This hand-me-down Impreza now belongs to my girlfriend, and it will probably turn over 300,000 kilometres before the end of this summer. The car is still tight, rattle-free, rust-free and it handles exceptionally well, though the engine is somewhat noisy when cold.
In the five years we've owned the car, we've never had a problem with it. Neither did either of its previous owners. However, another reason why I'm biased towards the Impreza is that with a starting price of $19,995, it's the least expensive way to get into a new all-wheel-drive car. That said, does the new Impreza meet my expectations?
Since our second-generation model left the factory in 2004, the Impreza has gone through three major upgrades, the latest arriving with the 2017 model tested here. This fifth-generation Touring is Subaru's most popular Impreza trim, and with the optional CVT ($1,300), it lists for $23,195.
Under the hood is an all-new 2.0-litre boxer four with direct injection, boosting output by only four horsepower to 152 from the previous 2.0-litre, while claiming a tiny improvement in fuel consumption – now at 8.3L/100 kilometres city and 6.4 highway with the CVT. In the dead of winter we only managed an average of 10.4L/100 kilometres, with about two thirds of the driving done in the city.
The Impreza has grown considerably over the years, and one thing I'm not too keen about is that it has grown yet again, gaining 2.5 centimetres of wheelbase, four centimetres in overall length, and the body is 3.7 centimetres wider. While most will probably welcome this change, I live in a congested city where parking is always at a premium, and these porkier dimensions don't help.
Of course, this adds more interior space. The Impreza is both roomy and accommodating, with the rear passengers benefitting the most with almost 13 centimetres of extra legroom. And while I've always forgiven Subaru for skimping on interior lavishness in the interest of offering an affordable all-wheel-drive car, the new interior is well ahead of the outgoing version in terms of fit and finish; materials are richer, there's more stitching and when on the road, the cabin is very quiet.
Another thing I appreciate is the simplicity of the dash layout. The instruments are uncluttered and easy to read, featuring two large analogue gauges and a central display screen. There are manual controls for the sound and climate control systems, with a 6.5-inch touchscreen providing additional system controls. The Touring has a second, configurable screen located high in the centre of the dash that provides mostly vehicle information, such as fuel consumption and engine status. But that info could have easily been included in the main screen, and it proved more gadgety than useful. Apple CarPlay and Android Auto are standard in all trim levels, and figuring out how to connect my iPhone via Bluetooth took just over a minute.
Behind the wheel is where the Impreza really shines. Aside from a quiet cabin, the car feels much more taut than the previous version. The body is 70 per cent stiffer according to its maker, and this has really improved ride quality and handling on what was already a fine car. The Impreza exhibits very little body roll through turns and the suspension subdues even large potholes to muted thumps, without upsetting the chassis. The ride is surprisingly upscale for a car in this price range.
I'm really not a fan of CVTs in general, but the automatic in the Impreza didn't offend. It provides a surprisingly direct link to the engine, especially at lower speeds where the car accelerates with gusto. The transmission is programmed to mimic gear changes through seven ratios, and it does so quite convincingly. If you prefer, you can use steering wheel-mounted paddle shifters to manually change ratios (not gears) but I found this feature redundant, having only used it once to see how it worked — and it was lazy. I'd opt for a clutch pedal and save more than a grand, but if you prefer automatics, you'll like this CVT and you'll use about 1.5 litres less fuel per 100 kilometres.
The most useful features included in the Touring model above the base model are the heated seats; most of the other extras are either aesthetic, or features that improve comfort and convenience, like automatic climate control and automatic headlights, and even things I could easily do without – like 'welcome lighting' and chrome interior door handles. I'm not sure I'd want to dish out almost $2,000 more than the base model just to warm my buns in winter, so heated seats should be standard. The Sport-Tech trim, with its firmer suspension, torque-vectoring AWD system and sporty bodywork, among other things, might have interested me were it available with a manual gearbox. But aside from the CVT, at $28,595, the Sport-Tech is just $1,400 shy of the 268-horsepower WRX, which will be updated next year.
The 2017 Impreza met most of my expectations, exceeding them in a few areas like handling and ride quality, while coming up a bit short in others — mostly regarding its appearance. The Impreza has always had distinctive, easily recognizable styling. The new one, with its smoothed-out silhouette, is much more generic and less exciting. That's not a deal breaker for me, because overall, the Impreza represents great value, proven reliability and with standard AWD, it's ready for the worst that winter can throw at it.
My girlfriend and I will likely replace our aging Impreza with this latest generation eventually, but unfortunately for Subaru, we're going to drive our current one into the ground. Which looks like it might take a while.


Happy with this product at the price point. It does the job.
Light and fresh scent. Not too over powering which I like.
Lovely fresh scent, light and citrusy, and doesn't leave the skin feeling dried out like some bath products do.


Dr. Lee is a practicing cardiothoracic surgery with a specific interest in heart and lung transplantation and the surgical treatment of end-stage heart failure. His laboratory research interests including the application of tissue-engineered constructs to understand mechanisms of muscle atrophy and heart failure, and to use these tissues to deliver therapeutic proteins.
In 2016, Dr. Lee was awarded a research grant from the National Aeronautical and Space Administration (NASA) for his study entitled "Microgravity sensing in tissue engineered muscle." This project is in response of a call from NASA to U.S. institutions of higher education to develop an undergraduate-led project team that will fly a science and/or technology payload relevant to NASA's strategic goals and objectives on a suborbital reusable launch vehicle. Dr. Lee's project was considered by the NASA reviewers as "…comprehensive with an excellent approach to mentoring, education and outreach. There is a high scientific value to NASA clearly linked to strategic goals." Dr. Lee was also awarded the prestigious 2016 American College of Surgeons Faculty Research Fellowship.